Allen's Astrophysical Quantities Fourth Edition Allen's Astrophysical Quantities Fourth Edition Arthur N. Cox Editor AIP eR~ 'Springer ArthurN. Cox Theoretical Division Los Alamos National Laboratory MS B288 P.O. Box 1663 Los Alamos, NM 87545 USA anc@ lanl.gov Cover illustration: An international team of astronomers, led by Dr. Wendy Freedman of the Observatories of the Carnegie Institution of Washington, Robert Kennicutt of the University of Arizona, and Jeremy Mould of the Australian National University observed this spiral galaxy NGC 4414 on 13 different occasions over the course of two months. (AURA/STScJJNASA) In 1995, the majestic spiral galaxy NGC 4414 was imaged by the Hubble Space Telescope as part of the HST Key Project on the Extragalactic Distance Scale. Images were obtained with Hubble's Wide Field Planetary Camera 2 (WFPC2) through three different color filters. Based on their discovery and careful brightness measurements of variable stars in NGC 4414, the Key Project astronomers were able to make an accurate determination of the distance to the galaxy. The resulting distance to NGC 4414, 19.1 megaparsecs or about 60 million light-years, along with similarly determined distances to other nearby galaxies, contributes to astronomers' overall knowledge of the rate of expansion of the universe. The Hubble constant (Ho) is the ratio of how fast galaxies are moving away from us to their distance from us. This astronomical value is used to determine distances, sizes, and the intrinsic luminosities for many objects in our universe, and the age of the universe itself. Library of Congress Cataloging-in-Publication Data Cox,Arthur Allen 's astrophysical quantities/editor, Arthur Cox. p. cm. Includes bibliographical references. Additional material to this book can be downloaded from http://extras.springer.com. 1. Astrophysical-Tables. QB461.A7685. 1999 523.01'021-dc21 1. Cox, Arthur N. 98-53154 ISBN 978-1-4612-7037-9 ISBN 978-1-4612-1186-0 (eBook) DOI 10.1007/978-1-4612-1186-0 Printed on acid-free paper. © 2002 Springer Science+Business MediaNew York Originally published by Springer-Verlag New York, lnc., AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. 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Production managed by Frank MC(Juckin; manufacluring supervised by Jeffrey Taub and L.uke Jensen. Photocomposed copy prepared from lhe edilor's TeX files. 987654321 Preface This handbook is the result of compilations and writing of ninety authors who have worked over a period of nine years to revise the famous Allen's Astrophysical Quantities. The need for such a revision had been known since shortly after the last edition edited by C.W. Allen in 1972. Even though his 1973 edition remained in print through the late 1980s, Allen himself called for help in revising the book in that third edition Preface. His death unfortunately prevented any revision, and only a few attempts known to me were made by interested astronomers. By 1990, with the third edition completely outdated, Arlo Landolt convinced the American Institute of Physics that they should undertake extensive revisions of the Allen book. How my name came up, in late 1990, I do not know, but once friends discovered I had been solicited by the AlP, they all encouraged me to find the various astrophysics experts to prepare this new edition, published jointly by the AlP and Springer-Verlag. The task of finding suitable authors and anonymous referees for the chapters was made easier by the help of Peter Boyce at the American Astronomical Society and its publications board. Chairpersons Caty Pilachowski, Hugh Van Horn, Jim Liebert, and Bob Hanisch suggested and helped recruit many contributors. Numerous AAS officials, especially Roger Bell, helped me and the authors interface with AlP and Springer. The basic structure of the earlier Allen editions has been followed, but many changes were necessary. For example, radio astronomy was represented by Allen with a page-long table of sources and a few supplementary ones plus some data about solar radio emission. Today a complete chapter is necessary, and even that does not seem to be as much as the author and I would have liked to include. Other advances in astrophysics have required us to include new chapters for infrared, ultraviolet, X-ray, and gamma-ray and neutrino astronomy. The explosion in observations of our solar system has resulted in a great expansion in information about these nearby bodies, as well as for our Sun itself. Later in the development of this book we found that we needed to add a chapter about stellar evolution because the level of understanding essentially the entire lives of stars had matured enormously. Most dramatically, modem large telescopes have revealed huge quantities of data about galaxies, galaxy clusters, and their exotic emissions. Three separate chapters cover different aspects of this material. A much expanded Cosmology chapter was needed to include our current understanding of the structure of the Universe. Finally, we have added many supplemental tables including an attempt to list the world's largest optical telescopes, with the help of Kari Parker, that surely will be out of date soon. While writing the chapters, many authors found that they needed some specialists to supply and even write sections that were beyond their current knowledge. These section authors are not given in the table of contents, but only at the start of the sections where they contributed. Thanks are due to these scientists who have supplied important information that we found relevant, often rather late in the book development. Their submissions could easily merit a mention in the table of contents, but the complicated process of assembling this greatly revised handbook and keeping its structure in control has resulted in this special format. Readers must realize that a project that involves ninety otherwise very busy astrophysicists is bound to be uneven. Some authors were able to get their material to me as early as mid-1992, while others were not even solicited by me for last-minute data until mid-1998. Our plan to include updates to a uniform date for all chapters could not be carried out because of its complexity, but some data as recent as the summer of 1999 are included. Readers are invited to contact individual authors directly for details. Our hope is that we have adequately pointed the way to the extensive literature for each subject. v vi I PREFACE Some astrophysicists have already decided to adopt our carefully compiled data as standard for their own special lists. This is reasonable, since this new Allen edition has been prepared by the world's experts in the various areas of astrophysics. One thing we have learned is that definitive data depend on interpretations for those last little details, and the best source for the most current and accurate data is always the experts. We hope our authors are these. The contents of this new edition of Allen will be available in electronic form with many tables and graphs "live" for interactive searching, correlating, interpolating, and so forth. The electronic version will be available by subscription and kept up-to-date on the publisher's web site (www.springer-ny.com) and will also be available as a CD-ROM for use on a Windows PC. At the minimum, these electronic data will greatly assist in future editions. Every publishing undertaking ends with regrets that some things could not be included. Thus all should realize that our book is a good reference book, but it still misses, for example, the newly published definitive NIST physical constants, the recent discovery of a satellite around the asteroid (45) Eugenia, the growing list of brown dwarf candidates, a new and unexpected class of intrinsic variable (Gamma Doradus) stars, and the latest gamma burst explosions now optically detected from the far reaches of our Universe. The organization of these new astrophysical quantities into an additional concise revised-again edition awaits future generations of authors, I hope as skilled and dedicated as ours. Los Alamos, New Mexico October 1999 Arthur N. Cox [email protected] Contents Preface v Contributors xv Introduction 1 1.1 1.2 1.3 Arthur N. Cox Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astronomical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astronomical and Astrophysical Journals ... . . . . . . . . . . . . . . . . . . . . . . . . 2.1 2.2 2.3 2.4 2.5 2.6 Arthur N. Cox Mathematical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Astronomical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astronomical Constants Involving Time . . . . . . . . . . . . . . . . . . . . . . . . . . ., Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , Electric and Magnetic Unit Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 1 1 2 2 General Constants and Units 2 Atoms and Molecules 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 Werner Diippen Online Databases and Other Sources Elements, Atomic Mass, and Solar-System Abundance . . . . . . . . . . . . . . . . . . Excitation, Ionization, and Partition Functions . . . . . . . . . . . . . . . . . . . . . . . Ionization Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron Affinities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atomic Cross Sections for Electronic Collisions . . . . . . . . . . . . . . . . . . . . . . Atomic Radii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particles of Modem Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasmas 27 . . . . . . . . Spectra 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Charles Cowley, Wolfgang L Wiese, Jeffrey Fuhr, and Ludmila A. Kuznetsova Online Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology for Atomic States, Levels, Terms, etc. . . . . . . . . . . . . . . . . . . . . Electronic Configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectrum Line Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative Strengths Within Multiplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wavelengths and Wave Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atomic Oscillator Strengths for Allowed Lines . . . . . . . . . . . . . . . . . . . . . . . Nuclear Spin and Hyperfine Structure: Low-Level Hyperfine Transitions . . . . . . . Forbidden Line Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 7 7 8 12 13 17 22 . . . . . . . . . 27 28 31 35 35 35 43 44 45 47 53 53 54 57 60 65 68 69 78 79 viii / CONTENTS 4.10 4.11 4.12 4.13 Spectra of Diatomic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection Rules: Dipole Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation 5 J.J. Keady and D.P. Kilcrease 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 Radio Astronomy Robert M. HjeUming 6 95 95 100 102 106 109 11 0 114 114 115 117 117 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Atmospheric Window and Sky Brightness . . . . . . . . . . . . . . . . . . . . . . . . . .. Radio Wave Propagation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Radio Telescopes and Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio Emission and Absorption Processes. . . . . . . . . . . . . . . . . . . . . . . . . .. Radio Astronomy References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 121 121 123 125 128 131 140 Infrared Astronomy A. T. Tokunaga Useful Equations; Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.1 7.2 Atmospheric Transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Background Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.3 7.4 Detectors and Signal-to-Noise Ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Photometry ().. < 30 JLm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.5 7.6 Photometry ().. > 30 JLm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Infrared Line List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 7.8 Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.9 Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.10 Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.11 Extragalactic Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 143 143 144 146 148 149 154 155 158 161 163 164 6.1 6.2 6.3 6.4 6.5 6.6 7 Radiation Quantities and Interrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Refractive Index and Average Polarizability . . . . . . . . . . . . . . . . . . . . . . . . .. Absorption and Scattering by Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Photoionization and Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Attenuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Absorption of Material of Stellar Interiors . . . . . . . . . . . . . . . . . . . . . . . . . .. Absorption of Material of the Solar Photosphere . . . . . . . . . . . . . . . . . . . . . .. Solar Photoionization Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Free-Free Absorption and Emission ...... . . . . . . . . . . . . . . . . . . . . . . .. Reflection from Metallic Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Visual Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83 85 87 89 8 8.1 8.2 8.3 8.4 8.5 Ultraviolet Astronomy Terry J. Teays Ultraviolet Wavelengths. . . . . . . . . . . . . . . . Ultraviolet Astronomy Satellite Missions .... . Significant Atlases and Catalogs. . . . . . . . . . . Interstellar Extinction in the Ultraviolet . . . . . . Commonly Observed Ultraviolet Emission Lines. 169 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. 169 170 172 174 175 CONTENTS / ix 8.6 8.7 Ultraviolet Spectral Classification . . . . . . . . . . . . . . . . . . . . . . . . Ultraviolet Spectrophotometric Standards . . . . . . . . . . . . . . . . . . . 178 180 9.1 9.2 9.3 9.4 9.5 9.6 9.7 X-Ray Astronomy Frederick D. Seward Useful Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic X-Ray Transitions . . . . . . . . . . . . . . . . . . . . . . .. . ..... Emission Mechanisms and Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transmission of X-Rays Through the Interstellar Medium . . . . . . . . . . . . . . . . . Cosmic X-Ray Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diffuse Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Astronomy Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 183 184 184 194 198 203 205 9 10 V-Ray and Neutrino Astronomy R.E. Lingenfelter and R.E. Rothschild 10.1 Continuum Emission Processes . . . . . . . . . . . . . . . . . 10.2 Line Emission Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Scattering and Absorption Processes . . . . . . . . . . . . . . . . . . . 10.4 Astrophysical v-Ray Observations . . . . . . . . . . . . . . . . . . . . 10.5 Neutrinos in Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Current Neutrino Observatories . . . . . . . . . . . . . . . . . . . . . . 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 11.13 11.14 11.15 11.16 11.17 11.18 11.19 11.20 11.21 11.22 11.23 11.24 11.25 207 . . . . . . . Earth Gerald Schubert and Richard L. Walterscheid Oblate Ellipsoidal Reference Figure . . . . . . . Mass and Moments of Inertia . . . . . . . . . . . Gravitational Potential and Relation to Products of Inertia . . . . . . . . . . . . Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotation (Spin) and Revolution About the Sun . . . . . . . . . . . . . . . . . . . Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid Body Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geological Time Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glaciations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plate Tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Earth Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Earth Interior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Earth Atmosphere, Dry Air at Standard Temperature and Pressure (STP) Composition of the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . Water Vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Homogeneous Atmosphere, Scale Heights and Gradients . . . . . . . . . Regions of Earth's Atmosphere and Distribution with Height . . . . . . . Atmospheric Refraction and Air Path. . . . . . . . . . . . . . . . . . . . . . Atmospheric Scattering and Continuum Absorption . . . . . . . . . . . . . Absorption by Atmospheric Gases at Visible and Infrared Wavelengths . Thermal Emission by the Atmosphere . . . . . . . . . . . . . . . . . . . . . Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Night Sky and Aurora . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 208 213 216 235 237 239 240 240 241 243 244 245 245 246 246 248 251 252 252 255 257 258 259 259 260 262 265 268 270 271 279 I x CONTENTS 11.26 Geomagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11.27 Meteorites and Craters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 282 285 Planets and Satellites David J. Tholen, Victor G. Tejfel, and Arthur N. Cox 12.1 Planetary System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12.2 Orbits and Physical Characteristics of Planets. . . . . . . . . . . . . . . . . . . . . . . .. 12.3 Photometry of Planets and Asteroids. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12.4 Physical Conditions on Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Names, Designations, and Discoveries of Satellites . . . . . . . . . . . . . . . . . . . . . 12.6 Satellite Orbits and Physical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12.7 Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.8 Planetary Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 293 293 294 298 300 302 303 308 311 Solar System Small Bodies Richard P. Binzel, Martha S. Hanner, and Duncan I. Steel 13.1 Asteroids or Minor Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13.2 Comets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Zodiacal Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13.4 Infrared Zodiacal Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13.5 Meteoroids and Intetplanetary Dust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14 315 315 321 328 331 333 SUD 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13 14.14 14.15 15 William C. Livingston 339 Basic Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 340 Interior Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . .. 341 Solar Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Photospheric-Chromospheric Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 348 Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Spectral Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 353 Limb Darkening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 355 C o r o n a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Solar Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Granulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 364 Surface Magnetism and its Tracers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 364 Sunspots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 367 Sunspot Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 Flares and Coronal Mass Ejections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 373 Solar Radio Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Normal Stars John S. Drilling and Arlo U. Landolt 15.1 Stellar Quantities and Interrelations. 15.2 Spectral Classification. . . . . . . . . 15.3 Photometric Systems . . . . . . . . . 15.4 Stellar Atmospheres. . . . . . . . . . 15.5 Stellar Structure . . . . . . . . . . . . 381 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. 381 383 385 393 395 CONTENTS 16 / xi Stars with Special Characteristics J. Donald Fernie 397 Variable Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Cepheid and Cepheid-Like Variables. . . . . . . . . . . . . . . . . . . . .. . . . . . . .. Variable White Dwarf Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Long-Period Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotating Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. T Tauri Stars ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Flare Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolf-Rayet and Luminous Blue Variable Stars . . . . . . . . . . . . . . . . . . . . . . .. Be Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Characteristics of Carbon-Rich Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Barium, CH, and Subgiant CH Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Hydrogen-Deficient Carbon Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Blue Stragglers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Peculiar A and Magnetic Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Galactic Black Hole Candidate X-Ray Binaries. . . . . . . . . . . . . . . . . . . . . . .. Double Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 398 399 400 406 406 407 408 409 410 413 415 416 417 418 419 420 422 424 Cataclysmic and Symbiotic Variables W.M. Sparks. S.G. Starrfield. E.M. Sion. S.N. Shore. G. Chanmugam. and R.F. Webbink 17.1 Types of Cataclysmic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17.2 Types of Symbiotic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 429 429 447 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 16.12 16.13 16.14 16.15 16.16 16.17 16.18 17 18 Supernovae J. Craig Wheeler and Stefano Benetti 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 18.10 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 Spectral Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Older Population, Type Ia Supernovae. . . . . . . . . . . . . . . . . . . . . . . . . . . .. Young Population Supernovae. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Characteristic Spectral Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Radio Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Polarization............................................. Supernova Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Old Supernovae, Historical Supernovae, and Supernova Remnants . . . . . . . . . . .. Radioactive Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 451 451 452 454 460 463 466 466 467 468 468 Star Populations and the Solar Neighborhood Gerard F. Gilmore and Michael Zeilik 471 The Nearby Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 471 The Brightest Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Stellar Populations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 478 Star Counts at High Latitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 480 Vertical Stellar Density Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 481 Main Sequence Field Stellar Luminosity Function. . . . . . . . . . . . . . . . . . . . .. 485 White Dwarf Luminosity Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 485 xii / CONTENTS 19.8 19.9 19.10 19.11 20 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 20.10 20.11 20.12 20.13 20.14 20.15 20.16 20.17 20.18 20.19 20.20 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 21.10 22 Luminosity Class Distribution for Nearby Field Stars . . . . . . . . . . . . . . . . . . " Mass Density in the Solar Neighborhood . . . . . . . . . . . . . . . . . . . . . . . . . . . Stellar Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solar Motion and Kinematics of Nearby Stars . . . . . . . . . . . . . . . . . . . . . . . . 486 487 488 493 Theoretical Stellar Evolution Arthur N. Cox, Stephen A. Becker, and W. Dean Pesnell Basic Equations of Stellar Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stellar Nuclear Energy Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Stellar Opacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Electron Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Element Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Mixing in Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Pre-Main-Sequence Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Main-Sequence Population I Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main-Sequence Population II Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Stellar Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Stellar Evolution Tracks: Massive and Intermediate-Mass Stars . . . . . . . . . . . . .. Evolution to Red Giant Branch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal Branch Evolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Red Giant Mass-Loss Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Asymptotic Giant Branch Evolution ..... . . . . . . . . . . . . . . . . . . . . . . . .. White Dwarfs and Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binary Star Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Theory Versus Observation in the HR Diagram . . . . . . . . . . . . . . . . . . . . . . " 499 500 502 503 505 506 506 506 507 508 509 509 509 511 514 514 515 518 518 519 520 Circumstellar and Interstellar Material John S. Mathis Overview of the Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Galactic Interstellar Extinction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Abundances in Interstellar Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Line Emissions from the ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. H2 and Molecular Clouds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Neutral Gas; Clouds; Depletions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hn Regions, Ionized Gas, and the Galactic Halo. . . . . . . . . . . . . . . . . . . . . .. Planetary Nebulae (PNe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmic Rays (Excluding Photons and Neutrinos) . . . . . . . . . . . . . . . . . . . . . . 523 523 527 529 530 532 534 536 538 540 541 Star Clusters Hugh C. Harris and William E. Harris 545 22.1 Open Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 545 22.2 Globular Clusters in the Milky Way. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 554 22.3 Globular Clusters in Other Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 / xiii Milky Way and Galaxies Virginia Trimble 23.1 Milky Way Galaxy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23.2 Normal Galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 569 569 576 CONTENTS 23 24 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9 24.10 24.11 25 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 25.10 25.11 25.12 25.13 25.14 25.15 26 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 26.10 Quasars and Active Galactic Nuclei Belinda J. Wilkes Introduction............................................. The TYPes of Active Galactic Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catalogs and Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commonly Measured Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absorption Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectral Energy Distributions (SEDs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luminosity Functions and the Space Distribution of Quasars. . . . . . . . . . . . . . . . BL Lacs, HPQs, and OVVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low-Luminosity Active Galactic Nuclei (LLAGN) . . . . . . . . . . . . . . . . . . . . . AGN Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clusters and Groups of Galaxies Neta A. Bahcall Typical Properties of Clusters and Groups of Galaxies . . . . . . . . . . . . . . . . . . . Cluster Catalogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catalog of Nearby Rich Clusters of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . Cluster Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cluster Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cD Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luminosity Function of Galaxies in Clusters . . . . . . . . . . . . . . . . . . . . . . . . Mass Function of Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Emission from Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Sunyaev-Zeldovich Effect in Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . Clusters and Large-Scale Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Groups of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quasar-:-Cluster Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clusters as Gravitational Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recent Results . . . . . . . . . . . . . . 613 614 615 617 620 625 627 627 628 630 632 633 637 639 640 640 Cosmology Douglas Scott, Joseph Silk, Edward W. Kolb, and Michael S. Turner Friedmann-Robertson-Walker Metric and Distance Measures . . . . . . . . . . . . . . The Age of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conversion Factors for the Early Universe . . . . . . . . . . . . . . . . . . . . . . . . . . Other Useful Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmological Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Friedmann-Lemaitre Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Epochs of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Age Limits .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmological Tests: Ho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmological Tests: qO . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . 585 585 586 591 593 595 601 602 605 607 608 608 643 . . . . . . . . . . 644 646 647 648 649 650 650 652 653 653 XIV I 26.11 26.12 26.13 26.14 26.15 26.16 26.17 26.18 26.19 26.20 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 CONTENTS Other Cosmological Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 654 Primordial Nucleosynthesis and Neutrinos. . . . . . . . . . . . . . . . . . . . . . . . . .. 654 Power Spectrum of Density Fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . .. 655 Structure Formation Scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 656 Cosmic Microwave Background Anisotropies. . . . . . . . . . . . . . . . . . . . . . . .. 658 Large-Scale Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 659 Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660 Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 661 Intergalactic Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 662 Extragalactic Diffuse Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 663 Incidental Tables Alan D. Fiala, William F. van Altena, Stephen T. Ridgway, and Roger W. Sinnott The Julian Date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Standard Epochs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Reduction for Precession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Solar Coordinates and Related Quantities . . . . . . . . . . . . . . . . . . . . . . . . . .. Constellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Messier Objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Optical and Infrared Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. The World's Largest Optical Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . .. 667 668 669 670 672 674 677 687 689 Index 701 667 Contributors This list of the contributors gives the institution where the author did the bulk of the writing of the chapter or section for this handbook. For those authors who participated only in a topic section, that subject is briefly indicated. Chapter 1 Arthur N. Cox Los Alamos National Laboratory David P. Kilcrease Los Alamos National Laboratory Sarah Stevens-Rayburn Space Telescope Science Institute Astrophysical Journals Chapter 6 Robert M. Hjellming National Radio Astronomy Observatory Chapter 2 Arthur N. Cox Los Alamos National Laboratory Chapter 7 Alan T. Tokunaga University of Hawaii Alan D. Fiala United States Naval Observatory Astronomical Constants, General and Time Chapter 8 Terry J. Teays Goddard Space Fight Center Chapter 3 Werner Dappen University of Southern California Chapter 9 Fredrick D. Seward Smithsonian Astrophysical Observatory Chapter 4 Charles R. Cowley University of Michigan Chapter 10 Richard E. Lingenfelter University of California-San Diego Wolfgang L. Wiese National Institute of Standards and Technology Jeffrey Fuhr National Institute of Standards and Technology Richard E. Rothschild University of California-San Diego Ludmila A. Kuznetsova Moscow State University Thomas J. Bowles Los Alamos National Laboratory Neutrino Observatories Chapter 5 John J. Keady Los Alamos National Laboratory Wick C. Haxton University of Washington Neutrino Observations xv xvi / CONTRIBUTORS Chapter 11 Gerald Schubert University of California-Los Angeles Pierre Demarque Yale University Solar Model Richard L. Walterscheid The Aerospace Corporation David B. Guenther St. Mary's University Solar Model David Crisp Jet Propulsion Laboratory/California Institute of Technology Earth Atmosphere Scattering, Absorption, Emission Chapter 12 David J. Tholen University of Hawaii Victor G. Tejfel Fessenkov Astrophysical Institute Arthur N. Cox Los Alamos National Laboratory Glenn S. Orton Jet Propulsion Laboratory/California Institute of Technology Physical Conditions on Planets DanPascu United States Naval Observatory Names, Designations, and Discoveries of Satellites, Satellite Orbits and Physical Elements Frank Hill National Solar Observatory Solar Oscillations Eugene Avrett Harvard-Smithsonian Center for Astrophysics Photospheric Model Oran R. White High Altitude Observatory Solar Spectral Lines Heinz Neckel Hamburger Sternwarte Solar Spectral Energy Distribution A. Keith Pierce National Solar Observatory Solar Limb Darkening Serge Koutchmy Institut d' Astrophysique Solar Corona Robert F. Howard National Solar Observatory Solar Rotation Chapter 13 Richard P. Binzel Massachusetts Institute of Technology Richard Muller Observatoire Pic du Midi Granulation Martha S. Hanner Jet Propulsion Laboratory/California Institute of Technology Peter V. Foukal Cambridge Research and Instrumentation, Inc. Surface Magnetism and Tracers Duncan I. Steel University of Salford, UK Sami Solanki Institute of Astronomy, ETH-Zentrum Surface Magnetism and Tracers, Sunspots Chapter 14 William C. Livingston National Solar Observatory Jack B. Zirker National Solar Observatory Surface Magnetism and Tracers CONTRIBUTORS / xvii Karen L. Harvey Solar Physics Research Corporation Sunspot Statistics Peter S. Conti University of Colorado Wolf-Rayet and Luminous Blue Variable Stars Peter Wilson University of Sydney Sunspot Statistics Arne Slettebak Ohio State University Be Stars Stephen W. Kahler United States Air Force Research Laboratory Flares, CMEs Myron Smith Computer Science Corporation Be Stars Timothy Bastian National Radio Astronomy Observatory Solar Radio Emission Cecilia S. Bambaum University of California-Berkeley Characteristics of Carbon-rich Stars Chapter 15 John S. Drilling Louisiana State University Arlo U. Landolt Louisiana State University Normal Stars James W. Liebert University of Arizona White Dwarf Spectral Classification Edward M. Sion Villanova University White Dwarf Spectral Classification Chapter 16 J. Donald Fernie David Dunlap Observatory Douglas S. Hall Vanderbilt University Variable Stars, Rotating Variables, Flare Stars Paul A. Bradley Los Alamos National Laboratory Variable White Dwarf Tables Gibor S. Basri University of California-Berkeley T Tauri Stars Kenneth R. Brownsberger University of Colorado Wolf-Rayet and Luminous Blue Variable Stars William Dean Pesnell Nomad Research, Inc. Barium, CH, and Subgiant CH Stars Warrick Lawson Australian Defence Force Academy Hydrogen Deficient Carbon Stars Peter J. T. Leonard Goddard Space Flight Center Blue Stragglers KaiyouChen Los Alamos National Laboratory Pulsars John Middleditch Los Alamos National Laboratory Pulsars Jonathan E. Grindlay Harvard College Observatory Galactic Black Hole Candidate X-Ray Binaries Chapter 17 Warren M. Sparks Los Alamos National Laboratory Sumner G. Starrfield Arizona State University Edward M. Sion Villanova University Steven N. Shore Indiana University South Bend xviii / CONTRIBUTORS Ganesh Chanmugam Louisiana State University Ronald F. Webbink University of lllinois Chapter 18 J. Craig Wheeler University of Texas William E. Harris McMaster University Chapter 23 Virginia Trimble University of California-Irvine and University of Maryland Stefano Benetti European Southern Observatory Chapter 24 Belinda J. Wilkes Smithsonian Astrophysical Observatory Chapter 19 Gerard F. Gilmore Cambridge University Chapter 2S Neta A. Bahcall Princeton University Michael Zeilik University of New Mexico Chapter 20 Arthur N. Cox Los Alamos National Laboratory Stephen A. Becker Los Alamos National Laboratory Chapter 26 Douglas Scott University of British Columbia Joseph Silk University of California-Berkeley Edward W. Kolb Fermi National Accelerator Laboratory William Dean Pesnell Nomad Research, Inc. Barium, CH, and Subgiant CH Stars Michael S. Turner The University of Chicago Chapter 21 John S. Mathis University of Wisconsin Chapter 27 Alan D. Fiala United States Naval Observatory Donald P. Cox University of Wisconsin Cosmic Rays Excluding Photons and Neutrinos William F. van Altena Yale University Jonathan F. Ormes Goddard Space Flight Center Cosmic Rays Excluding Photons and Neutrinos Chapter 22 Hugh C. Harris United States Naval Observatory Stephen T. Ridgway National Optical Astronomy Observatory Roger W. Sinnott Sky and Telescope Karl Parker Sky and Telescope Largest Optical Telescopes Chapter 1 Introduction Arthur N. Cox 1.1 Background. . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Astronomical Symbols . . . . . . . . . . . . . . . . . . 2 1.3 Astronomical and Astrophysical Journals . . . . . . . 2 1.1 BACKGROUND This handbook is a revision of the third edition of Allen's Astrophysical Quantities [1], published in 1973, with further printings in 1976, 1981, and 1983. An attempt has been made to follow the original format, but the great advances in astronomical and astrophysical subfields have made this very difficult. More modern styles have been adopted, and many more subjects have been included. However, the original concept to present a rather concise, but still extensive, listing of astrophysical quantities has been retained. It is expected that scientists can use this book for quick information and also for key references to more detailed data sources. One concept was that this handbook be a companion to A Physicist's Desk Reference, the second edition of Physics Vade Mecum, edited by Herbert L. Anderson. That book also has a long author list, and its currently planned revision will undoubtedly include even more. To allow for space to present information for newly developed astronomical and astrophysical subfields, some more classical material has been deleted. Reference to the older Allen editions might be necessary. The current fields are so extensive that we needed 90 authors. They are indicated either as chapter authors or authors of individual sections. All were asked to present their information using the electronic editing language M1EX 2e , so that the submissions to the publisher could be almost camera ready. Not all authors could completely comply with this policy, and the editor, with help from the publisher, occasionally needed to reformat the material. With so many involved, including the copyeditors, it is easy to see why it is important to keep the presentation style as consistent as possible. One hope is that the electronic files now available for this book can be revised in the coming years, and an updated version can be published more easily. With the extensive use of the World Wide Web 1 2/1 INTRODUCTION by so many scientists, it is conceivable that individual chapters can be updated after some years and made available there. At least future revisions should be easier to produce based on the very great efforts over most of eight years by all the authors. The editor requested authors to update their information to about the end of 1997 or later. Obviously this has not been completely successful. For questions and corrections, readers should consult individual authors, mostly since no one single individual can know more than a fraction of the knowledge of the entire area of astronomy and astrophysics. Just a small part of the Allen introduction chapter has been retained here. 1.2 ASTRONOMICAL SYMBOLS The standard symbols for astronomical objects and zodiacal areas are given in Table 1.1. Table 1.1. Sun, Moon, planetary, zodiacal, and orbit symbols [1, 2]. Symbol * , ~ 0 4{' y €9 :!:= / """ n Name Star Mercury Mars Saturn 2 Neptune 2 Aries (0°) Cancer (90°) Libra (180°) Sagittarius (240°) Aquarius 2 (300°) Ascending Node Autumnal Equinox Symbol Name Symbol 0 Sun Venus Jupiter Uranus Pluto «: 9 4 0 I? 8 ~ ~ -t5 ~ U l' Taurus (30°) Leo (120°) Libra 2 (180°) Capricornus (270°) Aquarius 3 (300°) 6 h W t) :n: I1lJ In ~ }{ Name Moon Earth Saturn Neptune Pluto 2 Gemini (60°) Virgo (150°) Scorpio (210°) Aquarius (300°) Pisces (330°) Descending Node Vernal Equinox References 1. Rahtz, S. & Rose, K. ftp to sunsite.unc.edu in directory publpackageslfeX/cmastro 2. Schmitt, P. 1992, ftp to sunsite.unc.edu in directory pub/packageslfeX/astro 1.3 ASTRONOMICAL AND ASTROPHYSICAL JOURNALS by Sarah Stevens-Rayburn The names of 51 journals thought to be of interest to readers with an astronomy and astrophysics background is given together with their first publication dates and the current publisher. Many of these journals are now available electronically on the World Wide Web. Note that the older European journals, Annales d'Astrophysique, Bulletin o/the Astronomical Institutes o/the Netherlands, Bulletin Astronomique, Journal des Observateurs, Zeitschrift jUr Astrophysik, and a few other smaller ones have been discontinued and have been replaced by Astronomy and Astrophysics. 1.3 ASTRONOMICAL AND ASTROPHYSICAL JOURNALS Acta Astronomica 1925 Acta Astronomica Sinica = Tien wen hsueh pao Acta Astrophysica Sinica = Tien t i wu Ii hsueh pao Acta Cosmologica Annual Review of Astronomy and Astrophysics (ARA&A) Annual Review of Earth and Planetary Sciences The Astronomical Journal (AJ) 1953 / 3 1973 1963 Warsaw: Copernicus Foundation for Polish Astronomy Beijing, China: Science Press Beijing: K' 0 hsueh ch'u pan she Beijing, China: Science Press Beijing: K'o hsueh ch'u pan she Krakow: Uniwersytet Jagiellonski Palo Alto, Calif.: Annual Reviews, Inc. 1973 Palo Alto, Calif.: Annual Reviews. Inc. 1894 Chicago: University of Chicago Press for the American Astronomical Society Berlin: Wiley-VCH Berlin: Springer. on behalf of the Board of Directors Berlin: Springer on behalf of the Board of Directors Les Ulis, France: EDP Sciences on behalf of the Board of Directors Bristol: Institute of Physics Publishing Ltd. for the Royal Astronomical Society 1981 Astronomische Nachrichten Astronomy and Astrophysics (A&A) 1823 1869 The Astronomy and Astrophysics Review (A&A Rev) Astronomy & Astrophysics Supplement series (A&AS) Astronomy & Geophysics The Journal of the Royal Astronomical Society (continues QJRAS, 1960-1996) Astronomy Letters (continues Soviet Astronomy Letters, 1975-1992) 1989 Astronomy Reports (continues Soviet Astronomy, 1974-1992, which continues Soviet Astronomy AJ, 1957-1973) The Astrophysical Journal (ApJ) 1993 The Astrophysical Journal Supplement series (ApJS) Astrophysical Letters & Communications (Astrophys. Lett) (continues Astrophysical Letters, 1967-1987) Astrophysics 1954 Astrophysics and Space Science (Ap&SS) Astrophysics Reports: Publications of the Beijing Astronomical Observatory (continues Publications of the Beijing Astronomical Observatory, 1987-1994) Astrophysics Reports: Publications of the Beijing Astronomical Observatory (Supplement series) Baltic Astronomy: An International Journal 1968 1994 Boletin / Asociacion Argentina de Astronomia 1958 1970 1997 1993 1895 1987 1965 Moscow: Maik NaukalInterperiodica Publishing, distributed by the AlP (translation of Pisma v astronomicheskii zhurnal) Moscow: Maik NaukalInterperiodica Publishing, distributed by the AlP (translation of Astronomicheskii zhurnal) Chicago: University of Chicago Press for the American Astronomical Society Chicago: University of Chicago Press for the American Astronomical Society New York: Gordon and Breach New York: Consultants Bureau (translation of Astrofizika) Dordrecht: Kluwer Academic Beijing, China: Beijing Astronomical Observatory, Chinese Academy of Sciences 1997 Beijing, China: Beijing Astronomical Observatory, Chinese Academy of Sciences 1992 Vilnius: Institute of Theoretical Physics and Astronomy La Plata: La Asociacion 4/1 INTRODUCTION Bulletin of the Astronomical Society of India Celestial Mechanics and Dynamical Astronomy (continues Celestial Mechanics, 1973 1989 Hyderabad: Astronomical Society of India Dordrecht: Kluwer Academic Chinese Astronomy and Astrophysics (continues Chinese Astronomy, 1977-1980) Earth, Moon, and Planets (continues The Moon and Planets, 1978-1983, which continues The Moon, 1969-1977) Experimental Astronomy Icarus International Journal of Modem Physics, D Gravitation, Astrophysics, Cosmology The Irish Astronomical Journal Journal for the History ofAstronomy Journal ofAstrophysics and Astronomy Journal of Geophysical Research. A, Space Physics (J. Geophys. Res. A) (continues in part Journal of Geophysical Research, - 1981 Kidlington, Oxford; Elsevier Science 1984 Dordrecht: Kluwer Academic 1989 1962 1992 Dordrecht: Kluwer Academic Orlando: Academic Press Singapore: World Scientific 1950 1970 1980 1949 Sheffield: IAJ Editorial Board Cambridge: Science History Publications Bangalore: Indian Academy of Sciences Washington, DC: American Geophysical Union 1991 Washington, Union 1907 1872 Toronto: Royal Astronomical Society of Canada Firenze: Societa Astronomica Italiana 1940 Observatory, S.A.: The Society 1931 Edinburgh: Blackwell Science for the Royal Astronomical Society 1869 1877 London: Macmillan Magazines Ltd. Chilton, Didcot, Oxon: Editors of The Observatory Kidlington, Oxford: Elsevier Science Ltd. 1969-1988) 1949) Journal of Geophysical Research. E, Planets (J. Geophys. Res. E) (continues in part Journal of Geophysical Research, -1990) The Journal of the Royal Astronomical Society of Canada (JRASC) Memorie della Societa Astronomica Italiana (Mem. Soc. Astron. Italiana) Monthly Notes of the Astronomical Society of Southern Africa Monthly Notices of the Royal Astronomical Society (MNRAS) (continues Monthly Notices of the Astronomical Society of London, 1927-1931) Nature The Observatory Planetary and Space Science (Planet. Space Sci.) Publications / Astronomical Society of Australia (continues Proceedings of the Astronomical Society of Australia, 1967-1994) Publications of the Astronomical Society of Japan (PASJ) Publications of the Astronomical Society of the Pacific (PASP) Revista Mexicana de Astronomia y Astrofisica 1959 Science 1883 DC: American Geophysical 1995 Australia: Published for the Astronomical Society of Australia by CSIRO, Australia 1949 Tokyo: Astronomical Society of Japan 1889 Chicago: University of Chicago Press for the Astronomical Society of the Pacific Mexico D.E: Instituto de Astronomia, Universidad Nacional Autonoma de Mexico Washington: American Association for the Advancement of Science 1974 1.3 ASTRONOMICAL AND ASTROPHYSICAL JOURNALS Solar Physics (Sol. Phys.) Southern Stars 1967 1934 Space Science Reviews (Space Sci. Rev) Zvaigznota debess 1962 1958 / 5 Dordrecht: Kluwer Academic Wellington. N.Z.: Royal Astronomical Society of New Zealand Dordrecht: Kluwer Academic Riga: Zinatne REFERENCES 1. Allen, C.W. 1973, Astrophysical Quantities (Ath1one Press, London) Chapter 2 General Constants and Units Arthur N. Cox 2.1 2.1 Mathematical Constants 7 2.2 Physical Constants 8 2.3 General Astronomical Constants 12 2.4 Astronomical Constants Involving Time 13 2.5 Units . . . 2.6 Electric and Magnetic Unit Relations. .. 17 MATHEMATICAL CONSTANTS [1-3] Constant Number 7r 27r 47r 7r 2 3.1415926536 6.283 185 3072 12.5663706144 9.8696044011 1.7724538509 2.7182818285 vrr eore mod = M = loge I/M=lnlO 2 ..ti v'3 00 0.434294481 9 2.302585 093 0 2.0000000000 1.4142135624 1.732050 807 6 3.1622776602 7 Log 0.497149872 7 0.7981798684 1.099209864 0 0.9942997454 0.2485749363 0.434294481 9 0.6377843113 - 1 0.3622156887 0.301 0299957 0.1505149978 0.238 5606274 0.500 000 000 0 22 8/2 GENERAL CONSTANTS AND UNITS Constant In rr e1r Euler constant y 1 radian Number 1.144 729 885 8 23.1406926328 0.577 215 6649 rad = 57?295 779 513 1 = 3437~74677078 = 206 264~'806 25 1° =0~0174532925 I' = O!"lldOOO 290 888 2 1/1 = O!"lldOOO 004 848 1 Log 0.058 703 021 2 1.364 376 3538 0.7613381088- 1 1.7581226324 3.5362738828 5.3144251332 0.241877 3676 - 2 0.463 726 1172 - 4 0.6855748668 - 6 Square degrees on a sphere = 129600/rr = 41252.96125. Square degrees in a steradian = 32400/rr 2 = 3282.806 35. . d'IStn'b' tior GaUSSlan utlon 1~ exp uv2rr (x2 ) -2 2u . Probable error/Standard error = r/u = 0.6744897502. Probable error/Average error = r/rJ = 0.8453475394. u/rJ = 1.253314137. p = (r/u)/..ti = 0.4769362762. 2.2 PHYSICAL CONSTANTS [4,5] These fundamental physical constants, mostly in SI units from [5], are the latest available. A revision by Cohen and Taylor is expected by the end of 1998. For many values, the standard error of the last digits follows in parentheses. In the formulations the electron charge e is in esu and e in emu = e/c. Fundamental constants Speed of light (exact) Gravitation constant Standard acceleration of gravity (exact) Planck constant Planck mass Planck length Planck time Elementary charge Mass of electron c c2 G gn = 2.99792458 X 108 ms- 1 = 8.98755179 x 10 16 m2 s-2 = 6.67259(85) X 10- 11 m3 kg- 1 s-2 = 9.80665 ms- 1 2rrli = h = 6.6260755(40) X 10-34 Js Ii = 1.054572 66(63) x 10-34 J S (Iic/G)I/2 = 2.17671(14) x 10-8 kg (IiG/c 3 )1/2 = 1.61605(10) x 10-35 m (IiG/c 5 )1/2 = 5.39056(34) x 10-44 s e = 4.803206 8(15) x 10- 19 C e = 1.60217733(49) x 10-20 emu e 2 = 23.070796 x 10-20 in esu e4 = 5.3226161 x 10-38 in esu me = 9.1093897(54) x 10-31 kg = 5.48579903(13) X 10-4 u 2.2 PHYSICAL CONSTANTS Mass of unit atomic weight ( 12C = 12 scale) Boltzmann constant e Gas constant 2C scale) Joule equivalent (chemical, exact) [4] Avogadro constant Loschmidt constant Volume of gram-molecule at STP (T = 273.15 K, P = 101 325 Pa) Standard atmosphere pressure (exact) Ice point Triple point (H20) Faraday Atomic constants Rydberg constant for IH Rydberg constant for infinite nuclear mass 2rr2mee4/ch3 Fine structure constant 2rre 2/ hc Radius for first Bohr orbit (infinite nuclear mass) h 2/4rr 2m ee 2 Time for (2rr) -1 revolutions in first Bohr orbit m!/2a 3/ 2e- 1 = h 3/8rr 3m ee 4 Frequency of first Bohr orbit Area of first Bohr orbit Electron speed in first Bohr orbit Atomic unit of energy (Hartree = 2 Rydbergs) e 2 /ao = 2chRoo Energy of Rydberg (often adopted as atomic unit) Atomic unit of angular momentum h /2rr Classical electron radius e 2 / moc 2 SchrOdinger constant for fixed nucleus SchrOdinger constant for 1H atom / 9 u = 1.6605402(10) x 10-27 kg k = 1.380658(12) x 10-23 JK- 1 = 8.617385(73) x 10-5 eVK- 1 10-8 ergl/2 K-l/2 R = 8.314510(70) JK- 1 mol- 1 = 1.987216 calK-l mol- 1 = 82.05783(70) cm3 atmK- 1 mol- 1 = 4.184 J cal- 1 NA = 6.0221367(36) x 1023 mol- 1 no = 2.686763(23) x 1025 m- 3 NA/no = Vo = 22.41410(19) x 10-3 m3 mol- 1 Po = 1013 250 dyn cm- 2 = 760mmHg 0° C = 273.150 K = 273.160K NM/C = 96485.309(29) C mol- 1 k 1/ 2 = 1.175014 x RH = 10967758.306(13) m- 1 1/ RH = 911.7633450 A Roo = 10973731.534(13) m- 1 1/ Roo = 911.2670534 A cRoo = 3.289841950 x 1015 s-1 a = 7.29735308(33) x 10-3 l/a = 137.0359895(61) a 2 = 5.325 13620 x 10-5 ao = 0.529177249(24) x 10- 10 m 1"0 = 2.4188844 x 10- 17 s = 6.5796837 x 1015 s-1 rra5 = 8.79735670 x 10-21 m2 2.1876914 x 106 ms- 1 4.3597482(26) x 10- 18 J 27.2113961(81) eV 2.1798741(13) x 10- 18 J = 13.605698 1(40) eV Ii = 1.05457266(63) x 10-34 kgm2s- 1 1= 2.81794092(38) x 10- 15 m 8rr2meh-2 = 1.63819748 x 1027 erg- 1 cm- 2 = 1.63730578 x 1027 erg-l cm- 2 ao1"OI = = = ryd = 10 / 2 GENERAL CONSTANTS AND UNITS Hyperfine structure splitting of I H VH ground state Doublet separation in IH atom (1/16)RHa 2 [1 + a/7f + (5/8 - 5.946/7f 2 )a 2 ] Reduced mass of electron in IH atom me(mp/mH) Mass of IH atom Mass of proton Mass of neutron Mass of deuteron Mass energy of unit atomic mass Rest mass energy of electron Mass ratio proton/electron Specific electron charge Quantum of magnetic flux Quantum of circulation Compton wavelength Band spectrum constant (moment of inertia/wave number) Atomic specific heat constant C2/C = h/k Electron magnetic moment Proton magnetic moment Gyromagnetic ratio of proton corrected for diamagnetism of H20 Magnetic moment of 1 nuclear magneton /Le /Lp Yp he/47fmpc Atomic unit of magnetic moment 2/LB/a Magnetic moment per mole of 1 Bohr magneton per molecule Zeeman displacement 3/47fme c (e in emu) in frequency = 0.365 866231 cm- I = 1.096839 36x 1010 s-I = 9.1044313 x = = = 4.799216 X /LB = he/47fmec 1420.405751768 x 106 s-I 10-31 kg 1.6735344 x 10-27 kg 1.007825050(12) u = 1.6726231(10) x 10-27 kg = 1.007276470(12) u = 1.6749286(10) x 10-27 kg = 1.008664 904(14) u = 3.3435860(20) x 10-27 kg = 2.013 553 214(24) u uc2 = 1.4924191 x 10- 10 J = 931.4942(28) MeV mec2 = 8.1871111 x 10- 14 J = 0.51099906(15) MeV = 1836.152701(37) e/me = 1.75881962 x 107 emu g-I e/me = 5.2728086 x 10 17 esu g-I hie = 1.37951077 x 10- 17 erg s esu- I hc / e = 4.135 669 2 x 10-7 gauss cm2 h/me = 7.2738962 erg s g-I h/mec = 2.42631058(22) x 10- 12 m h/27fmec = 3.86159323(35) x 10- 13 m h/87f 2c = 27.992774 x 10-40 g cm Magnetic moment of 1 Bohr magneton 1/2 5/2 -I I /LB='i.ame ao t'o = /Ln IO- II sK = 9.2740154(31) x 10-21 I erg gauss= 1.001159652193(1O)/LB = 1.521032202(15) x 1O-3/LB = 2.67522128(81) x 104 rad S-I gauss- I = 5.0507866(17) x 10- 24 erg gauss- I = 2.5417478 x 10- 18 erg gauss- l = 5584.9388 erg gauss- I mol- l = 4.6686437(14) x 10-5 cm- I gauss- l = 1.39962418(42) x 106 s-l gauss- l 2.2 PHYSICAL CONSTANTS The electron-volt and photons [5] Wavelength associated with 1 eV Wave number associated with 1 e V Frequency associated with 1 eV Energy of 1 eV Photon energy associated with unit wavenumber Photon energy associated with wavelength A Speed of 1 e V electron (2 x 108 (e/mec»1/2 Speed2 Wavelength of electron of energy V in e V h(2me E O)-1/2V- I / 2 Temperature associated with 1 eV Eo/k Temperature associated with 1 eV in common logs = (Eo/ k) log e Temperature associated with 1 kilo-kayser in common logs = 1<P(hc/ k) loge Energy of 1 e V per molecule Radiation constants Radiation density constant 87l' 5k4 /15c 3 h 3 Stefan-Boltzmann constant = ac/4 First radiation constant (emittance) = 27l' hc 2 First radiation constant (radiation density) Second radiation constant = hc/ k Wien displacement law constant c2/4.965 11423 Some general constants [1,5] Density of mercury (00 C, 760 mmHg) Ratio, grating to Siegbahn scale of X-ray wavelengths [5] Lattice spacing of Si (in vacuum, 22.50 C) Molar volume of Si Maximum density of water Cesium resonance frequency (defining the SI second) [6] = So = = V() = Eo = = hc = AO / 11 12398.4282 x 10- 10 m 8065.53851 cm- I 8.065 538 51 kilo-kayser 2.41798836(72) x 1014 s-I 1.602177 33(49) x 10- 19 J 0.0734986176 ryd 1.9864480 x 10-23 J = 1.9864480 x 1O-8 /A erg (A in A) = 5.93096892 x = 3.517 639 23 = lOS m s-I x lOll m 2 s-2 263 x 10-8 ) cm V- I / 2 (12.264 = 11604.45 K = 5039.75 K = 624.8493 K = 23060.0542 cal mol- I a = 7.56591(25) x 10- 15 ergcm-3 K-4 u = 5.67051(19) x 10-5 erg cm-2 K- 4 s-I CJ = 3.7417749(22) x 10-5 erg cm2 s-I 87l' hc = 4.9924870 x 10- 15 erg cm C2 = 1.438769(12) cm K = 0.2897755 = 13.395080 g cm- 3 Ag/ As = 1.002077 89(70) [As (Cu Kal) = 1.537400 kXu] = 0.543 101 96(11) x 10-9 m = 12.058 817 9(89) cm3 mol- I = 0.999972 g cm-3 = 9192631770 Hz 12 / 2 2.3 GENERAL CONSTANTS AND UNITS GENERAL ASTRONOMICAL CONSTANTS by Alan D. Fiala Astronomical unit of distance Parsec (= 206264.806 AU) Light (Julian) year Light time for 1 AU [6] Solar mass Solar radius Solar radiation Earth mass Earth mean density Earth equatorial radius [6] = mean Sun-Earth distance = semimajor axis of Earth orbit [2, 6]. AU = 1.495978706 6 x lOll m. pc = 3.085 677 6 x 10 16 m. = 3.261 5638 light (Julian) year. = 9.460730472 x 1015 m. = 499.004 783 70 s = 0.00577551833 d. M0 = 1.9891 x 1030 kg. 'R0 = 6.95508 ± 0.00026 x 108 m. £0 =3.845(8) x 1033 ergs-I. Me = 5.9742 x 1024 kg. Pe = 5.515 g cm- 3. = 6378.136 km. Galactic pole (J2000.0) GY3 = 192?85948123 83 Direction of galactic center (J2000.0) Solar motion toward galactic center [7] toward direction of galactic rotation vertically up in north direction Galactic rotation [8] Sun's equatorial horizontal parallax [6] Moon's equatorial horizontal parallax at mean distance Constant of nutation [6] Constant of aberration [6] 21l' x 206265 x AU = +27?12825120 + 27°7'41 ~'704 81 = -28?93617242 GYI = 266.40499625 17h45m37~ 1991 -28°56' 1O~'221 U = 10.00 ± 0.36 km s-1 V = 5.23 ± 0.62 kms- i w= 7.17±0.38kms- 1 Ro = 7.66 ± 0.32 kpc Vcirc = 237 ± 12 kms- 1 = 8~'794144(3) = 4.263521 x 10-5 rad = 3422~'608 12h51m26~2755 = = 9~'2025 20~'495 52 ct(1 - e2 )1/2 t = sidereal year, e = Earth orbital eccentricity Gaussian gravitational constant k in n 2 a 3 = k 2 (1 + m), where m = mass of planet in solar units, n = mean daily in AU motion, and a = semimajor axis (a defining constant) k/86400 = 21l' /(sidereal year in sec) Heliocentric gravitational constant = AU3(k')2 Semimajor axis of Earth orbit in tenns of AU k = 0.01720209895 rad = 3548~'187 607 = 0?985 607 668 6 k' = 1.990 983675 x 10-7 rad, for use with seconds of time = 1.32712440 x 1026 cm2 S-i = 1.00000105726665 AU 2.4 ASTRONOMICAL CONSTANTS INVOLVING TIME Mass ratios [6,9] Me/Mrt. M0/ M e M 0 /(M e +Mrt.} Obliquity of ecliptic (fixed ecliptic of J2000.0) / 13 = 81.30059 = 332946.05 = 328900 56(2} E = 23°26'21~'4119 2.4 ASTRONOMICAL CONSTANTS INVOLVING TIME [6] by Alan D. Fiala The basic unit of time is the Systeme International (SI) second which is defined to be the duration of 9 192631 770 cycles of one of the hyperfine transitions of the ground state of l33Cs. Based on this defined unit, International Atomic Time (TAl) is formed from statistical analysis of individual frequency standards and time scales based on atomic clocks in many countries. It was introduced in January 1972, and is a coordinate time scale. Universal Time (UT) is the measure of time used for all civil time keeping, and conforms closely to the mean diurnal motion of the Sun. It is directly related to sidereal time by means of an adopted numerical formula. It does not refer to the motion of the Earth and is not precisely related to the hour angle of the Sun. UTO is the uncorrected observed rotational time scale derived from observation of sidereal time at a particular station. When this time scale is corrected for the shift in longitudes caused by polar motion, it is designated UTI. This still contains the variable rotation of the Earth and is generally implied when the symbol .oUT" is used without qualification. Coordinated Universal Time (UTC) is the time scale distributed by radio signals, satellites, communication media, as the basis for civil time keeping around the world. UTC is maintained within 0.9 second of UTI by the introduction of leap seconds. UTC differs from TAl by an integer number of seconds, which difference changes when leap seconds are introduced. Dynamical time represents the independent variable of the equations of motion of the bodies in the Solar System. It depends on the theory of relativity being used, as does the transformation between barycentric and geocentric time scales. In the transformation, the constants can be chosen so that the timescales have only periodic variations with respect to each other. The dynamical time scale for apparent geocentric ephemerides was chosen to be unique and independent of the theories; the barycentric timescales are theory dependent. Terrestrial Dynamical Time (TDT), or Terrestrial Time (TT), is the idealized time on the geoid of the Earth and is approximated as being equal to TAl + 32.184 seconds. Terrestrial Time is a continuation of Ephemeris TIme (ET), beginning 1977 Jan. 1.0 TAl. The relationship between UT and TT changes according to the variations in the rotation of the Earth. Barycentric Dynamical Time (TDB) is the relativistically transformed time for referring equations of motion to the barycenter of the Solar System. It is defined to contain only periodic variations with respect to TDT. The time scales Geocentric Coordinate TIme (TCG) and Barycentric Coordinate Time (TCB) are the time-like arguments appropriate for coordinate systems defined with respect to the geocenter of the Earth and the barycenter of the Solar System, respectively, including all relativistic transformations from terrestrial time. Up to 1984, the tropical year was used as the basis of time for reference systems and the Besselian year was used as the epoch for such reference frames, thus designated, for example, as B 1950.0. Since 1984, the Julian Century has been used as the time unit for reference frames and the standard epoch is then designated as, for example, J2000.0. 14 / 2 GENERAL CONSTANTS AND UNITS Sidereal time is defined by the hour angle of the equinox. The relationship between Greenwich Mean Sidereal Time (GMST) and UTt is specified by an adopted equation, which is often considered to be the definition of UTI. At 0 hours UTI: GMST = 24110.54841 + 8640184~812866Tu + 0~093104T; - 6.2 x 1O-6 T,; seconds of time, where Tu = du /36525, du is the number of days of Universal Time elapsed since JD 2451545.0 UTt (2000 January 1, 12 hrs UTI), taking on values ±0.5, ±1.5, etc. The ratio of mean sidereal time to UTI is r' = 1.002737909350795 + 5.900 6 x 1O- 11 T - 5.9 x 10- 15 T2, where T is the number of Julian centuries elapsed since JD 2451 545.0. The ratio of UTI to mean sidereal time is l/r' = 0.997269566329084 - 5.8684 x 1O- 11 T + 5.9 x 1O- 15 T 2• The relationships between time scales in seconds of time are: TT = TDT = ET = TAl + 32.184, .6.T = ET - UT = TDT - UT = TT - UT, .6.AT = TAl - UTC, DUT", .6.UT = UTI - UTC, TDB=TDT+P, TCG - TT = 6.9692904 x lO- lO (J D - 2443144.5) x 86400, TCB - TCG = 1.480813 x 10-8 (1 D - 2443144.5) x 86400 + Ve· (x - Xe)c- 2 + P, TCB - TDB = 1.550506 x 1O- 8 (J D - 2443144.5) x 86400, P = 0.0016568 sin(35 999.37T + 357.5) + 0.0000224 sin(32 964.5T + 246) + 0.000013 8 sin (7 1 998.7T + 355) + 0.000004 8 sin(3 034.9T + 25) + 0.000004 7 sin(34 777.3T + 230), where T is the elapsed time from J2ooo.0 measured in Julian centuries and the coefficients are rounded at their last digits [6, 10, 11]. Arguments are in degrees. Here Xe and Ve denote the barycentric position and velocity of the Earth's center of mass, the difference (x - Xe) is the vector distance of the observer from this center of mass, and c is the speed of light. 2.4.1 Reduction of Time Scales The variations in the Earth's rotation rate have resulted in differences between time based on it and that based on planetary orbits. The differences between the ephemeris and the (generally slower) universal time are given in Tables 2.1 and 2.2 for the last 130 years. For dates back to 1620, see the Astronomical Almanacs [12]. Even earlier to the year 1500 B.C., one can find a table in the Canon of Lunar Eclipses [13]. Before 1884, .6.T = ET - UT, after 1984, .6.T = TDT - UT, and after 1989, the differences are for exactly 1 Jan. 0" UTC. 2.4 ASTRONOMICAL CONSTANTS INVOLVING TIME Table 2.1. Reduction of time scales from 1870 to 1974. Year t:..T Year t:..T Year t:..T Year t:..T Year t:..T 1870 1875 1880 1885 1890 +1.61 -3.24 -5.40 -5.79 -5.87 1895 1900 1905 1910 1915 -6.47 -2.72 +3.86 +10.46 +17.20 1920 1925 1930 1935 1940 +21.16 +23.62 +24.02 +23.93 +24.33 1945 1950 1955 1960 1965 +26.77 +29.15 +31.07 +33.15 +35.73 1970 1971 1972 1973 1974 +40.18 +41.17 +42.23 +43.37 +44.49 Table 2.2. UTe leap seconds since 1971 and staning at the given date. Year t:..T Year t:..T Year t:..T Year t:..T 1972, Jan. 1 1972, July 1 1973, Jan. I 1974, Jan. 1 1975, Jan. I 1976, Jan. I 10 11 12 13 14 15 1977, Jan. 1 1978,Jan.l 1979, Jan. 1 1980, Jan. 1 1981, July 1 1982, July 1 16 17 18 19 20 21 1983, July 1 1985, July I 1988, Jan. 1 1990, Jan. 1 1991, Jan. 1 22 23 24 1992, July 1 1993, July 1 1994, July 1 1996, Jan. 1 1997, July 1 27 28 29 30 31 25 26 Day 1 day = 24 hours = 1440 minutes = 86400 SI seconds Period of rotation of Earth (referred to fixed stars) In mean sidereal time In mean solar time 1 day of mean sidereal time 1 day of mean solar time Rate of rotation Year 1 Julian year = 365.25 days = 86164.09054 SI seconds. = 23h56m04~090 549. = 0.99726956633 of mean solar time. = 1.002737909 35 of mean sidereal time. = 15~/041 067178 66910 s-I. = 7.29211510 x 10-5 rads- I . = 8766 hours = 525960 minutes = 31557600 SI seconds Tropical (equinox to equinox) Sidereal (fixed star to fixed star) Anomalistic (perihelion to perihelion) Eclipse (Moon's node to Moon's node) Gaussian (Kepler's law for a = 1) Julian (based on Julian calendar) Gregorian (based on Gregorian calendar) d d h m s 365.242 1897 365.25636 365.25964 346.62005 365.25690 365.25 365.2425 365 365 365 346 365 365 365 05 06 06 14 06 06 05 48 09 13 52 09 45.19 10 53 52 56 49 12 / 15 16 / 2 GENERAL CONSTANTS AND UNITS Calendar Julian Dates (see Chapter 27 also) 1900 January 0.5 = JD 2415020.0, 1925 January 0.5 = JD 2424151.0, 1950 January 0.5 = JD 2433 282.0, 2000 January 0.5 = JD 2451 544.0, 2050 January 0.5 = JD 2469 807.0, 2100 January 0.5 = JD 2488 069.0. Length of the month Synodic (new Moon to new Moon) Tropical (equinox to equinox) Sidereal (fixed star to fixed star) Anomalistic (perigee to perigee) Draconic (node to node) Orbit of the Moon about the Earth Sidereal mean motion of Moon Mean distance of Moon from Earth d d h m s 29.53059 27.32158 27.32166 27.55455 27.21222 29 27 27 27 27 12 07 07 13 05 44 43 43 18 05 03 05 12 33 36 2.661699489 x 10-6 rads- l 3.844 x 10 * 5 kIn 60.27 Earth radii 0.002570 AU 57' 02~'608 Equatorial horizontal parallax at mean distance 3422~'608 Mean distance of center of Earth from Earth-Moon barycenter 4.671 x 103 kIn Mean eccentricity 0.05490 Mean inclination to ecliptic 5?145396 Mean inclination to lunar equator 60 41' Limits of geocentric declination ±29° Saros = 223lunations = 19 passages of Sun through node = 6585l days 6798 days Period of revolution of node Period of revolution of perigee 3232 days Mean orbital speed 1023 ms- l =0.000591 AU day-l Mean centripetal acceleration 0.00272 m s-2 = 0.0003 g. Precession Annual rates of precession (T in centuries from J2000.0) general precession in longitude lunisolar precession in longitude planetary precession geodesic precession (relativistic nonperiodic Coriolis effect) 50~'290966 50~'387 784 -O~'OI8 862 3 1~'92T. + O~'0222226T, + O~'OO4 926 3T, - O~'047 612 8T, 2.5 UNITS I 17 2.5 UNITS The seven SI base units are: meter (m), kilogram (kg), second (s), ampere (A), Kelvin (K), mole (mol), and candela (cd) [14]. All other units are derived from these. Units used with SI are: the time units of minute (min), hour (h), and day (d); the plane angle units of radian (rad), degree e), minute ('), and (arc)second ("); the solid angle unit, steradian (sr); the volume unit liter; (L); the mass unit metric ton (t); and the land area hectare (ha). Other experimentally determined units used with SI are: the special energy unit (eV), and the atomic mass unit (u). Units used in astronomy and astrophysics are often not standard but unique to the special subfield. This procedure is followed for many chapters in this book. They are frequently defined at the beginning of each chapter. Table 2.3 gives the SI unit prefixes. Table 2.3. The SI prefixes. Factor 1024 1021 1018 1015 1012 109 106 103 102 101 Prefix yotta zetta exa peta tera giga mega kilo hecto deka Symbol Factor Prefix Symbol Y 10- 1 10-2 10-3 10-6 10-9 10- 12 10- 15 10- 18 10-21 10- 24 deci centi milli micro nano pico femto atto zepto yocto d c m Z E P T G M k b da /.t n p f a z y Unconventional (nonstandard) units sometimes used in astronomy and astrophysics are listed below. Length Angstrom unit Micron Foot Inch Mile Nautical mile [2] Area Square foot Acre Bam A = 10- 8 cm = 10- 10 m J.L = J.Lm = 10-4 cm = 10-6 m ft = 30.4800 cm = 12 in in = 2.540 000 cm = 1.609 344 km = 5280 ft 1.853 km 6080 ft = tt2 = = 929.03 cm = 4046.85 m 2 =43560 ft2 = 10-24 cm2 18 I 2 GENERAL CONSTANTS AND UNITS Volume Cubic foot Fluidounce Mass Kilogram (SI unit) Pound avoirdupois Pound troy and apothecary Grain (all systems) Carat Slug Ton = tonne Metric ton Energy louIe (SI unit) Calorie [4] (exact) Kilowatt-hour British thermal unit Therm Foot-pound Kiloton of TNT Power Watt (SI unit) British horse-power Force de cheval Force Newton (SI unit) Poundal Pound weight Slug Gram weight Acceleration Standard gravity Gravity (equator) Gravity (pole) Speed Mile per hour Knot ft3 = 28316.8 cm3 = = = = = 6.229 British gallons 7.481 US gallons 480 minims (British and US) 28.413 cm3 (British) 29.574 cm3 (US) kg = lO00g British lb = 453.59237 g = 7000 grains US lb = 453.59243 g = 7000 grains = 373.242 g = 5760 grains = 0.064 7989 g =0.2000g = 14.594 kg = 2240lb = 1.016047 x 106 g = 106 g 1 = 107 erg cal = 4.1841 = 4.184 x 107 erg = 3600 x 103 1 = 8.6042 x lOS cal BTU = 1055 1 = 252.0 cal = 100000 BTU = 1.35582 x 107 erg = 4.184 x 1019 erg - = 107 ergls = 1 s-1 = 745.7W = 735.5W N= = = = = lOS dyn 1.3825 x lQ4 dyn 4.4482 x lOS dyn 14.594 kg 980.665 dyn 1 gal = 1 em s-2 g = 978.031 em s-2 = 32.09 ft s-2 g = 983.217 em s-2 32.26 ft s-2 = = 44.704 cms- 1 = 1.4667 fts- 1 = 51.47 cms- 1 2.5 UNITS / Pressure Pascal (SI unit) Barye (occasionally called Bar) Bar Millibar Atmosphere (standard) Millimeter of mercury (= 1 Torr) Inch of mercury Pound per square inch Density Kilogram/cubic meter (SI unit) Density of water (4° C) Density of mercury (0° C) Solar mass/cubic parsec STP gas density where /.LO is molecular weight Temperature Degree scales (Kelvin K, Celsius (centigrade) C, Fahrenheit F) Temperature comparisons Triple point of natural water Viscosity (dynamic) Poise SI unit Viscosity (kinematic) Stokes SIunit Frequency Hertz Kayser (a wave number unit) Rydberg frequency Frequency in first Bohr orbit Frequency of free electron in magnetic field 'H. (gauss) Plasma frequency associated with electron density Ne in cm-3 ) = 10 dyn cm- 2 = /.Lb = 1.000 dyn cm-2 10 /.Lb bar = = = mb = = atm = 1.000 x 106 dyn cm- 2 0.986923 atm 1.0197 x 103 g-weight cm-2 10-3 bar = 103 /.Lb 103 dyn cm-2 1.013 250 x 106 dyn cm- 2 = 760 mmHg = 1013.25 mb mmHg = 1333.22 dyn cm-2 = 0.0013158 atm = 3.38638 x 104 dyn cm- 2 = 0.033421 atm = 6.8947 x 104 dyn cm- 2 = 0.068046 atm = = = = = 1.000 X 10-3 g cm-3 0.999972 g cm- 3 13.5951 g cm- 3 6.770 x 10-23 g cm-3 4.4616 x 1O-5 /.LO g cm- 3 K = deg C = 1.8 deg F 0° C = 273.150 K = 32° F 100° C = 373.150 K = 212° F = 273.160 K = 0.010° C P = 1 g cm- 1 s-l = 0.1 Pas Nsm- 2 = 10gcm- 1 s-l = 1 cm2 s-l m2 s-l = 10000 cm2 s-l Hz = cm- 1 = c Roo = 2c Roo = = cycle s-l cHz~ 3 x 10 10 Hz 3.28984 x 1015 Hz 6.5797 X 1015 Hz 2.7993 x 106 'H. Hz ,,1 1/2 = 8.979 x hr Ne Hz 19 20 / 2 GENERAL CONSTANTS AND UNITS Angular velocity (= 21l' frequency) Unit of angular velocity 1" of arc per tropical year I" of arc per day Angular velocity of Earth on its axis Mean angular velocity of Earth in its orbit = 1 rad s-I = = 1.5363147 = 5.6112695 = 7.2921152 = 1.9909867 Momentum Linear momentum, SI unit = lOS g cm s-I = 1 kg m s-I = 2.73093 x 10- 17 gcm s-I mc Angular momentum SI unit Electron momentum in first Bohr orbit Quantum unit Homogeneous sphere angular momentum (R radius, M mass, w = angular velocity) Angular momentum of solar system = = Luminous intensity Luminous intensity is defined as the luminous emission per sterad Candela (SI unit) Star, mv = 0, outside Earth atmosphere = 107 g cm2 s-I = 1 kg m2 s-I = 1.993 x 10- 19 g crn s-I Ii = 1.0546 x 10-27 erg s = (2/5)R 2 Mw = 3.148 x = flux from 1 cd into 1 sr = flux from (1/601l') crn2 of black body at 2044 K = 1.470 x 10-3 W Lumen of maximum visibility radiation at 5550 A therefore 1 W at 5550 A Jansky = 680 lumens = 10-23 ergs cm-2 s-1 Hz- 1 = 10-26 W m- 2 Hz- I Luminous energy Talbot (SI unit) Lambert IOS0 g cm-2 S-I cd = (1/60) luminous intensity of 1 projected cm2 black body at the temperature of melting platinum (2044 K) = 2.45 x 1029 cd Luminous flux Lumen (both SI and CGS unit) Surface brightness Stilb 21l' Hz x 1O- 13 rads- 1 x 10- 11 rad s-I x 10-5 rad s-1 x 10-7 rad s-I = 1 lumerg (CGS unit) = 1 lumen second sb = 1 cd cm- 2 = 1l' lambert = 1 lumen cm- 2 SCi = (1/1l') cd cm-2 = 1000 millilambert == 1 lumen cm- 2 for a perfectly diffusing surface 2.5 UNITS / 21 Apostilb Nit (SI unit) Candle per square inch Foot-lambert = 0 star per square degree outside atmosphere 1mv = 0 star per square degree inside clear unit airmass 1mv Luminous emittance (of a suiface) Lumen per square meter (SI unit) Illuminance (light received per unit suiface) Phot (CGS unit) Lux (SI unit) Foot-candle Star, mv = 0, outside Earth atmosphere = 1 lumen m- 2 for a perfectly\ diffusing surface = 10-4 lambert = 10-4 sb = cd m- 2 = 0.487 lambert = 0.155 stilb = 1.076 x 10-3 lambert = 343 x 10-4 stilb = 0.84 x 10-6 stilb = 0.84 x 10-2 nit = 2.63 x 10-6 lambert = 0.69 x 10-6 stilb = 10-4 lumen cm- 2 = Ix = = = = = 1 lumen cm- 2 1 lumen m- 2 = 10-4 phot 1 m-candle 10.76 lux = 1.076 x 10-3 phot 1 lumen ft- 2 2.54 x 10- 10 phot Electrical units The general inter-relations between electric and magnetic units are given in Sec. 2.6 Electrical charge Coulomb (SI unit) Electron charge Electrical potential Volt (SI unit) Potential of electron at first Bohr orbit distance Ionization potential from first Bohr orbit Electric field Volt per meter (SI unit) Nuclear field at first Bohr orbit Resistance Ohm (SI unit) Electric current Ampere (SI unit) Current in first Bohr orbit C = 2.997925 x 109 esu = 0.10 emu = -6.24151 x 10 18 electrons e = -4.803 25 x 10- 10 esu e = -1.60218 x 10- 19 C V = 3.33564 x 10- 3 esu = 108 emu = 27.211 volt = 0.090767 esu = 13.606 volt = 0.045384 esu = 3.33564 x 10-5 esu = 106 emu = 5.1402 x 1011 voltm- 1 = 1.7152 x 107 esu Q= 1.11265 x 1O- 12 esu= 109 emu A = 2.997 925 x 109 esu = 0.10 emu = -6.24151 x 10 18 electrons s-1 = 1.054 x 10-3 A = 3.160 x 106 esu 22 / 2 GENERAL CONSTANTS AND UNITS Electric dipole moment Coulomb-meter (SI unit) Dipole moment of nucleus and electron in first Bohr orbit Cm Magnetic field Ampere-turn per meter (SI unit) Gauss (in free space) Gamma . umt . (me1/2 a -1/2 .0-1) A tomlc O Field at nucleus due to electron in first Bohr orbit am!/2aol/2.0-1, .0 = W01 = 2.4189 x 10- 17 s 1 ILB(mel m p ) Earth magnetic moment Radioactivity Curie [4] Roentgen 2.6 1011 esu = 10 emu x 10- 29 Cm x 10- 18 esu = 1 oersted = y = = = 79.58 amp-tumm- 1 10-5 oersted 1.715 x 107 gauss 1.252 x 105 oersted = 104 gauss = 1 weberm- 2 ILB = (l/41l") 1010 emu = 0.02654 esu = 2.541 x 10- 18 erg gauss- 1 = 0.9274 x 10-20 erg gauss- 1 ILK = 5.051 1/2 5/2 -1 zame a o .0 Nuclear magneton Rad = 0.8478 = 2.5417 = 41l" x 10-3 oersted [emu] = 3.767 x 108 esu Magnetic flux density, Magnetic induction Tesla (SI unit) Magnetic moment Weber-meter (SI unit) . umt . (me1/2 a 5/2 .0-1) A tomlc O Bohr magneton, magnetic moment of electron in first Bohr orbit = 2.9979 x = 7.98 X 10-24 erg gauss- 1 x 1025 emu = 3.700 x 1010 disintegrations s-1 = exposure to radiation producing 2.082 x 109 ion pairs in 0.001293 g of air = I esu cm- 3 = 2.58 x 10-4 C kg- 1 = 10- 2 Jkg- 1 ELECTRIC AND MAGNETIC UNIT RELATIONS Table 2.4 on pages 24 and 25 is adapted from the previous Astrophysical Quantities edition. Many of these quantities are now superseded by the SI units, but the older esu and emu units are still frequently used for special cases in astrophysics. For the SI units, the permittivity (EO) and permeability (ILO) of free space are defined to be exact as (l/41l"c 2 ) x 1011 Fm- 1 = 8.854187817 ... Fm- 1 and 41l" x 10-7 N A -2, respectively. Here F is the farad capitance unit, N is the newton force unit, and A is the ampere current unit. 2.6 ELECTRIC AND MAGNETIC UNIT RELATIONS / 23 REFERENCES 1. Astrophysical Quantities. I, §7 2. Astrophysical Quantities, 3, §1O 3. Abramowitz, M. & Stegun, I.A. 1965, Handbook of Mathematical Functions, (Dover, New York), p. 2 4. Anderson, H.L. 1989, A Physicist's Desk Reference, the second edition of Physics Vade Mecum (American Institute of Physics, New York) & Taylor, B.N. 1998, 5. Cohen, E.R., http://physics.nist.gov/cuulReferencelversioncon.html 6. Seidelmann, p.K. 1992, Explanatory Supplement to the Astronomical Almanac (University Science Books, Mill Valley, CA) 7. Dehnen, W, & Binney, J.J. 1998, MNRAS, 298, 387 8. Metzger, M.R., Caldwell, J.A., & Schechter, P.L. 1998, AJ, 115,635 9. Standish M. 1995, Report of the IAU WGAS SubGroup on Numerical Standards, in Highlights ofAstronomy edited by Appenzeller (Kluwer Academic, Dordrecht) 10. Fairhead L., Bretagnon, P. & Lestrade, J.E 1998, IAU Symposium 128 (Kluwer, Dordrecht) p. 419 II. Hirayama, Th. et al. 1987, Proc. lAG Symposia I., IUGG XIX General Assembly, Vancouver 12. Astronomical Almanacs (USNO, GPO) 13. Liu, Bao-Lin, & Fiala, A.D. 1992, Canon of Lunar Eclipses 1500 B.C.-A.D. 3000 (Willmann-Bell, Richmond) 14. Nelson, R.A. 1998, Physics today, BGll 24 / 2 GENERAL CONSTANTS AND UNITS Table 2.4. Electric and Quantity SI symbol and unit Charge Q coulombC = c x 10- 1 esu Current I ampere A = c x 10- 1 esu Potential, EMF V volt V = (l/c) x 10- 12 esu Electric field £ volt/m = (l/c) x 1O- 14esu Resistance R ohmQ = (l/c 2 ) x 109 esu Resistivity p ohmm = (l/c 2 ) x 10- 11 esu Conductance G siemens, mho = c 2 x 10-9 esu Conductivity a mho/m = c 2 x 10- 11 esu Capitance C farad F = c 2 x 10-9 em Electric flux \11 coulombC = 4rrc x 10- 1 esu Electric flux density, displacement D coulomb/m2 = 4rrc x 10-5 esu Polarization P coulomb/m2 = c x 10-5 esu coulomb/m = c x 10 1 esu Electric dipole moment in esu Permittivity, dielectric constant E farad/m = 4rrc 2 x 10- 11 esu Permittivity of free space EO (1/4rrc 2 ) x 1011 F/m = 1 esu Inductance L henry H = (l/c 2 ) x 109 esu Magnetic pole strength m weberWb = (l/4rrc) x 108 esu Magnetic flux <I> weberWb = (l/c) x 108 esu Magnetic field 1i ampere turn/m = 4rrc x 10-3 esu Magnetomotive force, magnetic potential :F ampere turn AT = 4rrc x 10- 1 esu Magnetic dipole moment M weberm = (l/4rrc) x 10 10 esu Electromagnetic moment m ampere m 2 Mag. flux density, induction B tesla T = (l/c) x 104 esu Intensity of magnetization J weber/m2 T = (l/4rrc) x 10 16 esu Magnetic energy density Permeance Bx1i joule/m3 A henry H = (l/4rrc 2 ) x 109 esu l/henry = 4rrc 2 x 10-9 esu Reluctance Permeability JL henry/m = (l/4rrc 2 ) x 107 esu Permeability of free space JLO 4rr x 10- 7 H/m = (l/c 2 ) esu 2.6 / 25 T I 001 1 000 1 ELECTRIC AND MAGNETIC UNIT RELATIONS magnetie units. Dimensions in emu, etc. ESU EMU L M T 112 112 112 112 -1 = 106 emu 312 312 112 -112 = 109 emu -1 0 = 10- 1 emu = 10- 1 emu = 108 emu esu JL emu SI K L M T 112 112 312 112 112 112 112 0 -1 112 112 -112 -112 1 -1 1 o -1 1 1 -1 2 -1 1 1 -1 1/e2 -2 -1 3 2 1 -1 1/e2 -3 -1 3 2 -1 o o o o 2 -1 1/e2 -2 -1 4 2 -2 -1 liz -1 -2 -2 -112 lie -112 lie 112 e 112 e L M 2 -3-1 1 -3-1 e2 2 1 -3 -2 e2 3 -3 -2 = 1011 = 10-9 emu = 10- 11 emu o = 10-9 emu 1 o o o o 312 112 -1 112 112 112 0 -112 lie 0 0 112 112 112 -1 112 -312 112 -312 112 312 112 112 112 0 -2 0 -2 0 0 -112 lie -112 lie -112 lie 1 0 1 1 2 1/e2 -3 -1 4 2 = 4:rr x = 4:rr 10- 1 emu 1 o x 10-5 emu = 10-5 emu = 10 emu o = 4:rr x 10- 11 emu -1 -1 -1 1 0 -1 -1 0 1 -2 -2 o 0 -1 = O/e2 ) emu = 109 em = O/4:rr) x 108 emu = 108 maxwell (Mx) = 4:rr x 10-3 oersted (Oe) = 4:rr x 10- 1 gilbert (Gb) = (1/4:rr) -1 o 2 112 112 112 312 112 112 112 112 0 112 112 112 = 104 gauss (Gs) = O/4:rr) x 104 emu = 40:rr Gs Oe = 4:rr x 10-9 GblMx = (l/4:rr) = 1 emu 0 -2 -2 -1 -112 312 -112 312 112 -112 112 112 o 0 e2 2 1 -2 -2 112 112 112 112 -1 112 e 112 e -112 lie -112 lie 2 -2 -1 2 1 -2 -1 -1 -1 -1 x 1010 emu x 109 Mx/Gb x 107 emu 1 1/e2 = 103 emu = (1/4:rr) 1 -1 1 -2 0 112 512 -112 -112 -112 -112 1 -2 0-1 0 -2 0 2 0 -2 0 2 -1 1 1-1 -1 0 112 112 112 -1 -112 lie -1 -1 1 -2 o o o -1 1 0 -1 0 1 e2 001 3 1 -2 -1 2 001 o o 1 -2 -1 1 -2 -1 1 -2 2 e2 0 -2-2 1/e2 -2 -1 e2 0 0 -1 0 o 2 2 1 -2 -2 Chapter 3 Atoms and Molecules Werner Dappen 3.1 3.1 Online Databases and Other Sources. . . . . . . . .. 27 3.2 Elements, Atomic Mass, and Solar-System Abundance 28 3.3 Excitation, Ionization, and Partition Functions . . .. 31 3.4 Ionization Potentials. . . . . . . . . . . . . . . . . . .. 35 3.5 Electron Affinities . . . . . . . . . . . . . . . . . . . .. 35 3.6 Atomic Cross Sections for Electronic Collisions . .. 35 3.7 Atomic Radii. . . . . . . . . . . . . . . . . . . . . . .. 43 3.8 Particles of Modem Physics . . . . . . . . . . . . . .. 44 3.9 Molecules. . . . . . . . . . . . . . . . . . . . . . . . .. 45 3.10 Plasmas. . . . . . . . . . . . . . . . . . . . . . . . . .. 47 ONLINE DATABASES AND OTHER SOURCES The National Institute of Standards and Technology (NIST) gives access to extensive physical and atomic data (http://physics.nist.gov). The Plasma Laboratory of the Weizmann Institute (http://plasma-gate.weizmann.ac.il) and the Southwest Research Institute (http://espsun.space.swri.edulspacephysics/www.atomic.html) provide, besides their own data. many useful links to other databases. For astrophysical applications, among the most extensive databases are those of the Harvard-Smithsonian Center for Astrophysics (http://cfa-www.harvard.edulamp/data) (giving, e.g., searchable access to the data by R.L. Kurucz and R.L. Kelly) and of the Opacity Project (http://astro.u-strasbg.fr/OP) (with monochromatic opacities, collision strengths, and other atomic data). A further source of important data is the Iron Project (http://www.am.qub.ac.uk/projects/iron). Gary Ferland's Web Page (http://www.pa.uky.edulgary/cloudy) has references to CLOUDY ("Photoionization Simulations for the Discriminating Astrophysicist"), which contains pointers to the atomic 27 28 I 3 ATOMS AND MOLECULES databases they use and maintain (e.g., http://www.pa.uky.edulverner/atom.html. "Atomic Data for Astrophysics"). The CHIANTI group (http://www.solar.nrl.navy.miUchianti) has installed a database with information suitable for extreme-UV applications. The Particle Data Group (http://pdg.lbl.com) makes available periodically its newest releases of particle properties. Other sources of information are the recent Atomic, Molecular, and Optical Physics Handbook [1], the results of the work of the Collaborative Computational Project No. 7 (United Kingdom) [2], and the Handbook of Chemistry and Physics [3]. 3.2 ELEMENTS, ATOMIC MASS, AND SOLAR-SYSTEM ABUNDANCE Atomic masses (weighted by the fractional abundances of the stable isotopes in normal terrestrial composition [4]) are scaled to 12C = 12.00. Standard values abridged to five significant digits are given (from the International Union of Pure and Applied Chemistry (IUPAC); see [5]). For some elements, atomic masses can be accurately measured to seven or more significant figures. IUPAC regularly publishes these values irrespective of interest to any user. For many users, however, it is often desirable that the published data remain valid over an extended period, which is helpful for textbooks and numerical tables derived from atomic-mass data. IUPAC has recognized this need and approved the use of the designation standard to its abridged atomic-mass table, with the hope that the quoted values may survive for at least a decade. The solar-system abundances (formerly denoted as cosmic abundances) are expressed logarithmically on a scale for which H is 12.00 dex. The intention is that they express cosmic abundance [6]. Thus, abundances are taken mainly from meteorites and the Sun's photosphere. In both cases, values by number are quoted. The agreement between meteoritic and solar data has improved remarkably since the 1970s. Discrepancies have mostly gone away as the solar values-thanks especially to improved transition probabilities and other atomic data-have become more accurate [6]. The two principal exceptions are'the solar photospheric Li and Be abundances that are smaller than the meteoritic ones by 2.15 and 0.27 dex, respectively. The reason is that these elements are destroyed by nuclear reactions at the bottom of the solar convection zone. For most other elements the agreement is better than ±0.04 dex (for this, and exceptions, see [6]). In the case of iron, a previous controversy has been solved: the solar and meteoritic values agree now [7]. For details on isotopic abundances, see [1] and [4]. The group abundance ratios given in Table 3.1 are derived from Table 3.2. The H ratio is set to 100. Table 3.1. Group abundance ratios. Element group Number Mass Stripped electrons H He C,N,O,Ne Other 100 9.8 0.145 0.013 100 39 2.19 0.44 100 20 1.1 0.21 Total 109.96 141.63 121.3 The composition by mass [2] is as follows: fraction of H, X fraction of He, Y fraction of other atoms, Z 0.707 ±2.5% 0.274±6% 0.0189 ± 8.5% 3.2 ELEMENTS, ATOMIC MASS, AND SOLAR-SYSTEM ABUNDANCE / 29 Mean atomic mass of cosmic material Mean atomic mass per H atom Mean atomic mass for fully ionized cosmic plasma 1.30 1.41 0.62 Table 3.2. Atomic 1NJSses and solar-system abundances. Log abundance [2] Symbol [1] Atomic number Atomic mass Hydrogen Helium [3] Lithium Beryllium Boron H He Li Be B 1 2 3 4 5 1.0079 4.0026 6.941 9.0122 10.811 Carbon Nitrogen Oxygen Auorine Neon C N 0 F Ne 6 7 8 9 10 12.011 14.007 15.999 18.998 20.180 8.56" 8.05" 8.93" 4.48 8.09 8.56 8.05 8.93 4.56 8.()9<i Sodium Magnesium Aluminum Silicon Phosphorus Na Mg Al Si P 11 12 13 14 15 22.990 24.305 26.982 28.086 30.974 6.31 7.58 6.48 7.55 5.57 6.33 7.58 6.47 7.55 5.45 Sulphur Chlorine Argon Potassium Calcium S CI Ar K Ca 16 17 18 19 20 32.066 35.453 39.948 39.098 40.078 7.27 5.27 6.56d 5.13 6.34 7.21 5.5 6.56d 5.12 6.36 Scandium Titanium Vanadium Chromium Manganese Sc Ti V Cr Mn 21 22 23 24 25 44.956 47.88 50.942 51.996 54.938 3.09 4.93 4.02 5.68 5.53 3.10 4.99 4.00 5.67 5.39 Iron [2] Cobalt Nickel Copper Zinc Fe Co Ni Cu Zn 26 27 28 29 30 55.847 58.933 58.693 63.546 65.39 7.51 4.91 6.25 4.27 4.65 7.54 4.92 6.25 4.21 4.60 Gallium Germanium Arsenic Selenium Bromine Ga Ge As Se Br 31 32 33 34 35 69.723 72.61 74.922 78.96 79.904 3.13 3.63 2.37 3.35 2.63 2.88 3.41 Krypton Rubidium Strontium yttrium Zirconium Kr Rb Sr Zr 36 37 38 39 40 83.80 85.468 87.62 88.906 91.224 3.23 2.40 2.93 2.22 2.61 2.60 2.90 2.24 2.60 Niobium Molybdenum Technetium Ruthenium Rhodium Nb Mo Tc Ru Rh 41 42 43 44 45 92.906 95.94 98.906 101.07 102.91 1.40 1.96 1.42 1.92 1.82 1.09 1.84 1.12 Element Y Meteoritic 12.{)()" 10.99" 3.31 1.42 2.8 Solar 12.00 1O.wh 1.16 1.15 2.6c 30 / 3 ATOMS AND MOLECULES Table 3.2. (Continued.) Element Symbol [l] Atomic number Atomic mass Log abundance [2] Meteoritic Solar Palladium Silver Cadmium Indium Tin Pd Ag Cd In Sn 47 48 49 50 106.42 107.87 112.41 114.82 118.71 1.70 1.24 1.76 0.82 2.14 1.69 O.94c 1.86 1.66c 2.0 Antimony Tellurium Iodine Xenon Cesium Sb Te I Xe Cs 51 52 53 54 55 121.76 127.60 126.90 131.29 132.91 1.04 2.24 1.51 2.23 1.12 1.0 Barium Lanthanum Cerium Praseodymium Neodymium Ba La Ce Pr Nd 56 57 58 59 60 137.33 138.91 140.12 140.91 144.24 2.21 1.20 1.61 0.78 1.47 2.13 1.22 1.55 0.71 1.50 Promethium Samarium Europium Gadolinium Terbium Pm Sm Eu Gd Tb 61 62 63 64 65 146.92 150.36 151.96 157.25 158.93 0.97 0.54 1.07 0.33 1.00 0.51 1.12 -0.1 Dysprosium Holmium Erbium Thulium Ytterbium Dy Ho Er Tm Yb 66 67 68 69 70 162.50 164.93 167.26 168.93 170.04 1.15 0.50 0.95 0.13 0.95 1.1 0.26c 0.93 O.OOC 1.08 Lutetium Hafnium Tantalum Thngsten Rhenium Lu Hf Ta W Re 71 72 73 74 75 174.97 178.49 180.95 183.85 186.21 0.12 0.73 0.13 0.68 0.27 0.76c 0.88 Osmium Iridium Platinum Gold Mercury Os Ir Pt Au Hg 76 77 78 79 80 190.2 192.22 195.08 196.97 200.59 1.38 1.37 1.68 0.83 1.09 1.45 1.35 1.8 1.01 c Thallium Lead Bismuth Polonium Astatine Tl Ph Bi Po At 81 82 83 84 85 204.38 207.2 208.98 209.98 209.99 0.82 2.05 0.71 0.9c 1.85 Radon Francium Radium Actinium Thorium Rn Fr Ra Ac Th 86 87 88 89 90 222.02 223.02 226.03 227.03 232.04 0.08 0.12 Protactinium Uranium Neptunium Plutonium Americium Pa U Np Pu Am 91 92 93 94 95 231.04 238.03 237.05 239.05 241.06 46 -0.49 1.11 c < -0.45c 3.3 EXCITATION, IONIZATION, AND PARTITION FUNCTIONS I 31 Table 3.2. (Continued.) Element Symbol [l] Atomic number Atomic mass Curium Berkelium Californium Einsteinium Fermium Cm Bk Cf Es Fm 96 97 98 99 100 244.06 249.08 252.08 252.08 257.10 Mendelevium Nobelium Lawrencium Md No Lr 101 102 103 258.10 259.10 262.11 Log abundance [2] Meteoritic Solar Notes aBased on solar data. bBased on stellar observations and solar models [1, 3, 4]. cUncertain. dBased on other astronomical data. References 1. IUPAC 1969, Comptes Rendus XXV Conference, p. 95 2. Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197; Grevesse, N., & Noels, A. 1993, in Origin and Evolution· of the Elements, edited by N. Prantzos, E. Vangioni, & M. CasSIS (Cambridge University Press, Cambridge), p. 15 3. Christensen-Dalsgaard, J., Diippen, W., & the GONG Team 1996, Science, 272, 1286 4. Biemont, E., Baudoux, M., Kurucz, R.L., Ansbacher, W., & Pinnington, E.H. 1991, A&A, 249, 539 5. Kosovichev, A.G., Christensen-Dalsgaard, J., Diippen, W., Dziembowski, W.A., Gough, D.O., & Thompson, M.J. 1992, MNRAS, 259,536 3.3 EXCITATION, IONIZATION, AND PARTITION FUNCTIONS 3.3.1 Introduction Finding the occupation of individual levels of atoms and ions and the fractions of ions of any given chemical element in a plasma is a complex task. The difficulty arises from the interaction of the plasma with the atoms. Therefore, in principle, the problems of modified atoms and of their statistical occupation should be solved simultaneously and self-consistently. The typical task of quantumstatistical mechanics consists of the calculation of a density operator (ensemble) for the system of all particles. The partition function, i.e., the trace over the density operator, not only gives the occupation of all states, but it also leads to a thermodynamical potential. It is evident that various approximations are necessary before this procedure can be carried out. One such approximation consists of treating the motion of the heavy particles (nuclei, atoms, ions) according to classical mechanics. Once the heavy particles are separated out, quantum-mechanical electrons remain. In the treatment of electrons, we find a bifurcation into two distinct classes of approach, the "chemical picture" and the ''physical picture." While in the more conventional chemical picture, bound configurations (atoms, ions, and molecules) are introduced and treated as new and independent species, only fundamental particles (electrons and nuclei) appear in the physical picture. In the chemical picture, reactions between the various species occur. Thus the thermodynamical equilibrium must be sought among the stoichiometrically allowed set of concentration variables by means of a maximum entropy (or minimum free-energy) principle. In contrast, the physical picture 32 I 3 ATOMS AND MOLECULES has the aesthetic advantage that there is no need for a minimax principle. The question of bound states is dealt with implicitly through the Hamiltonian describing the interaction between the fundamental particles. It is obvious that these self-consistent approaches require extensive analytical and numerical work. For a recent realization of the chemical-picture approach, see, e.g., [8-10]. For the physical picture, the most detailed work so far was done as part of the OPAL opacity project [11-14]. In the OPAL project, the physical picture was not only used to model excitation and ionization processes, but for the first time also to yield the highly accurate thermodynamic quantities needed in computations of stellar models [15]. The book by Ebeling et al. [16] contains further information and references on the physical picture. The most recent addition to the set of stellar equations of state is based on the formalism of the path integral in the framework of the Feynman-Kac representation. This formalism leads to a virial expansion of the thermodynamic functions in the power of the total density of a Coulomb plasma ([17,18], and references therein). For many lower-density applications, especially stellar spectroscopy, adequate qualitative and quantitative information can be extracted from simpler considerations, in which atoms are assumed to have an unperturbed structure. In this case, excitation fractions are given by the Boltzmann factor, and the ionization degree follows from the Saba equation, which is the mass-action law for the ionization reaction. The Saba equation contains the internal partition functions for bound systems. A fundamental theoretical flaw of this approximate approach is that isolated atoms would have infinite partition functions because of their infinite number of excited states. Many heuristic recipes to truncate partition functions exist. However, only the physical picture comes to a satisfactory solution, which then can often be used to justify the intuitive concepts [19]. In many cases, neglecting all excited states, that is, assuming ground-state-only internal partition functions, is a reasonable approximation. The following simple treatment of excitation, ionization, and partition functions is, with reasonable care, still very useful for many qualitative and semiquantitative astrophysical applications. 3.3.2 Approximate Methods and Results For practical applications, a useful introduction to the statistical mechanics of plasmas is the book by Eliezer et al. [20]. The number of atoms existing in various atomic levels 0, 1,2, ... when in thermal eqUilibrium at temperature T is approximately described by the Boltzmann distribution N2/Nl = (g2/gl)exp(-Xl,2/kT), N2/ N = (g2/ U) exp( - XO,2/ kT). Numerically log(N2/ Nl) = log(g2/gt} - Xl2(5040/T) (X12 in eV), where N is the total number of atoms per cm3 , No, NI, and N2 are the numbers of atoms per cm3 in the zero and higher levels, gO, g). and g2 are the corresponding statistical weights, XI,2 is the potential difference between levels 1 and 2, and U is the partition function. The degree of ionization in conditions of thermal eqUilibrium is given by the Saba equation Ny+! U Y +!2 (27fm)3/2(kT)5/2 - N Pe = - U 3 exp(-xY,Y+l/kT). y Numerically y h 3.3 EXCITATION, IONIZATION, AND PARTITION FUNCTIONS / or NY+l ) log ( ~Ne = -XY,Y+le - 23 log 33 e + 20.9366 + log (2UY+l) --u;- , where Ny and Ny + 1 are the numbers of atoms per cm3 in the Y and Y + 1 stages of ionization (Y = 1, neutral; Y = 2nd, 1st ion; etc.), Ne is the number of electrons per cm3 , Pe is the electron pressure in dyncm- 2, XY,Y+I the ionization potential in eV from the Y to the Y + 1 stage of ionization, e = 5040 KIT, Uy and UY+I are the partition functions, and the factor 2 represents the statistical weight of an electron. The degree of ionization, when ionizations are caused by electron collisions and recombinations are radiative, can be approximately given by NY+I/Ny = SlOt, where the effect of both collisional ionizations from state of ionization Y + 1 and of recombinations of Y + 2 in the abundance of ions in Y + 1 is neglected, and the possibility of multiple-ionization events is excluded. In the formula, S is the collision ionization coefficient (such that SNeNy = rate of collisional ionization, see Sec. 3.6), and a is the recombination coefficient (such that aNeNY+l = rate of recombination, see Chap. 5). Detailed calculations of partition functions are given by Irwin [21] (atoms and molecules) and Sauval and Tatum [22] (molecules). However, for the approximate purposes of this section, the partition function may simply be regarded as the effective statistical weight of the atom or ion under existing conditions of excitation. Except in extreme conditions it is approximately equal to the weight of the lowest ground term. The ground term weight gO is therefore given and this can normally be extrapolated along the isoelectronic sequences to give the approximate partition function for any ion. The partition functions, given in Table 3.3 in the form log U for e = 1.0 and 0.5, are not intended to include the concentration of terms close to each series limit. The part of the partition function associated with these high-n terms is dependent on both T and Pe. This part is usually negligible unless the atom concerned is mainly ionized in which case the high-n terms may be counted statistically with the ion. Lowering of XY,Y+I in the Saba equation to allow for the merging of high-level spectrum lines gives [23] ~XY,Y+I = 7.0 x -7 10 1/3 2/3 Ne Y , with ~X in eV and Ne in cm- 3 , and where Y is the charge on the Y + 1 ion. Table 3.3. Partition junction [1-3]. Y=II Y =1 logU logU Element 1 2 3 4 5 6 7 8 9 III go Y=ill 8 = 1.0 8=0.5 go 8 = 1.0 8=0.5 go H He Li Be B 2 1 2 1 6 0.30 0.00 0.32 0.01 0.78 0.30 0.00 0.49 0.13 0.78 1 2 1 2 1 0.00 0.30 0.00 0.30 0.00 0.00 0.30 0.00 0.30 0.00 1 2 1 2 C 9 4 9 6 0.97 0.61 0.94 0.75 1.00 0.66 0.97 0.77 6 9 4 9 0.78 0.95 0.60 0.92 0.78 0.97 0.61 0.94 1 6 9 4 IlM IlM F. Il 7'1 Il 7<; 0 N 0 F 1\1" 34 / 3 ATOMS AND MOLECULES Table 3.3. (Continued.) Y =1 Y=II 10gU Element go Y=ill 10gU 0=1.0 0=0.5 gO 0=1.0 0=0.5 go 11 12 13 14 15 Na Mg Al Si P 2 1 6 9 4 0.31 0.01 0.77 0.98 0.65 0.60 0.15 0.81 1.04 0.79 1 2 1 6 9 0.00 0.31 0.00 0.76 0.91 0.00 0.31 0.01 0.77 0.94 6 1 2 1 6 16 17 18 19 20 S Cl AI K Ca 9 6 1 2 1 0.91 0.72 0.00 0.34 0.07 0.94 0.75 0.00 0.60 0.55 4 9 6 1 2 0.62 0.89 0.69 0.00 0.34 0.72 0.92 0.71 0.00 0.54 9 4 9 6 1 21 22 23 24 25 Sc Ti V Cr Mn 10 21 28 7 6 1.08 1.48 1.62 1.02 0.81 1.49 1.88 2.03 1.51 1.16 15 28 25 6 7 1.36 1.75 1.64 0.86 0.89 1.52 1.92 1.89 1.22 1.13 10 21 28 25 6 26 27 28 29 30 Fe Co Ni Cu Zn 25 28 21 2 1.43 1.52 1.47 0.36 0.00 1.74 1.76 1.60 0.58 0.03 30 21 10 1 2 1.63 1.46 1.02 0.01 0.30 1.80 1.66 1.28 0.18 0.30 25 28 21 10 1 31 32 34 36 37 38 39 Ga Ge Se Kr Rb Sr Y 6 9 9 1 2 1 10 0.73 0.91 0.83 0.00 0.36 0.10 1.08 0.77 1.01 0.89 0.00 0.7 0.70 1.50 1 6 4 6 1 2 1 + 15 0.00 0.64 0.00 0.70 0.62 0.00 0.34 1.18 0.66 0.00 0.53 1.41 2 1 9 9 6 1 10 40 48 50 56 57 70 82 'h: Cd Sn Ba La Yb Pb 21 1 9 1 10 1 9 1.53 0.00 0.73 0.36 1.41 0.02 0.26 1.99 0.02 0.88 0.92 1.85 0.21 0.54 28 2 6 2 21 2 6 1.66 0.30 0.52 0.62 1.47 0.30 0.32 1.91 0.30 0.61 0.85 1.71 0.31 0.40 21 1 1 1 10 References I. Astrophysical Quantities, I, §15; 2, § 15 2. Cayrel, R., & Jugaku, J. 1963, Ann. d'Astrophys., 26, 495 3. Bolton, C.T. 1970, ApJ, 161, 1187 The degree of ionization in the material of stellar atmospheres is given in Table 3.4, relating gas pressure Pg• electron pressure Pe , and temperature T. The data are averaged from [24] (rather high heavy-element abundance) and [25] (rather low heavy-element abundance). 3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS / 35 Table 3A. log Pg. E> and T 10gPe E> T (K) -2 -1 0 1 2 3 4 5 3.4 0.1 50400 0.2 25200 0.4 12600 0.6 8400 0.8 6300 1.0 5040 1.2 4200 1.4 3600 -1.9 -0.8 +0.27 1.27 2.27 3.28 4.28 5.59 -1.8 -0.74 +0.29 1.30 2.30 3.30 4.31 5.30 -1.70 -0.70 +0.31 1.33 2.34 3.35 4.43 5.87 -1.67 -0.66 +0.35 1.47 2.98 4.87 6.84 8.66 -1.54 -0.01 +1.90 3.87 5.65 7.0 8.7 10.4 +0.78 2.57 3.9 5.2 6.7 8.3 10.0 11.8 +2.0 3.1 4.5 6.0 7.7 9.4 11.2 13.2 +2.4 3.9 5.3 6.7 8.5 10.4 12.4 14.4 IONIZATION POTENTIALS Table 3.5 gives the energy in eV required to ionize each element to the next stage of ionization. I (Y = 1) denotes the neutral atom, II the first ion, etc. Dividing lines between shells and subshells are added to assist interpolation. Part of the data is based on an especially accurate compilation for selected ions [6-20], made available by the National Institute of Standards and Technology (NIST. see Sec. 3.1 for online access). If the data are given in wave numbers, the currently recommended conversion factor to energy is 1 eV = 8065.541 cm- 1 [26]. 3.5 ELECTRON AFFINITIES Electron affinity is the energy difference between the lowest state of the atom (or molecule or ion) and the lowest state of the corresponding negative ion (see Table 3.6). It is positive for those atoms or molecules that form stable negative ions. Regarding the astrophysically important H-, it was thought earlier that a second stable state exists [27]. Later, however, it was proven rigorously that there is only one stable state [28, 29]. 3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS Definitions of symbols are presented below: Q v 2 7rao Ne,Na,Nj L=vQ NeL NeNaL Pc Atomic cross section [= Q(v)]. Precollision electron velocity. Atomic unit cross section = 8.797 X 10- 17 cm2 • Electron, atom, ion densities (per cm3 ). Collision rate for each atom per unit N e. Collision rate per atom (or ion). Collision rate per cm3 . Collisions encountered by an electron per cm at 0° C and 1 mm Hg. pressure, then Q = 2.828 X 10- 17 Pc = 0.32157ra5Pc. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 11 2 3 4 5 6 7 8 9 10 I Zn Cr Mn Fe Co Ni Cu V n Ca Sc Ar K Cl P S F Ne Na Mg Al Si 0 Be B C N Li H He Atom 13.59844 24.58741 5.39172 9.32263 8.29803 11.26030 14.53414 13.61806 17.42282 21.56454 5.13908 7.64624 5.98577 8.15169 10.48669 10.36001 12.96764 15.75962 4.34066 6.11316 6.56144 6.8282 6.7463 6.76664 7.43402 7.9024 7.8810 7.6398 7.72638 9.39405 54.41778 75.640 18 18.21116 25.15484 24.38332 29.6013 35.11730 34.97082 40.96328 47.2864 15.03528 18.82856 16.34585 19.7694 23.3379 23.814 27.62967 31.63 11.87172 12.79967 13.5755 14.66 16.4857 15.63999 16.1878 17.083 18.16884 20.29240 17.96440 II 122.454 153.897 37.931 47.888 47.449 54.936 62.708 63.45 71.620 80.144 28.448 33.493 30.203 34.79 39.61 40.74 45.806 50.913 24.757 27.492 29.311 30.96 33.668 30.652 33.50 35.19 36.841 39.723 m 217.713 259.366 64.492 77.472 77.413 87.140 97.12 98.91 109.265 119.99 45.142 51.444 47.222 53.465 59.81 60.91 67.27 73.489 43.267 46.71 49.16 51.2 54.8 51.3 54.9 55.2 59.4 IV 340.22 392.08 97.89 113.9O 114.24 126.21 138.40 141.27 153.83 166.77 65.03 72.59 67.8 75.02 82.66 84.50 91.65 99.30 65.28 69.46 72.4 75.0 79.5 75.5 79.9 82.6 V 489.98 552.06 138.12 157.17 157.93 172.18 186.76 190.49 205.27 220.42 88.05 97.03 91.01 99.4 108.78 111.68 119.53 128.1 90.64 95.6 99.1 103 108 103 108 VI 667.03 739.29 185.19 207.28 208.50 225.02 241.76 246.49 263.57 280.95 114.20 124.32 117.56 127.2 138.0 140.8 150.6 161.18 119.20 124.98 131 134 139 136 VII 871.41 953.91 239.10 264.25 265.96 284.66 303.54 309.60 328.75 348.28 143.46 154.88 147.24 158.1 170.4 173.4 184.7 194.5 151.06 160 164 167 175 vm Stage of ionization 1103.1 1195.8 299.9 328.1 330.1 351.1 372.1 379.6 400.1 422.5 175.8 188.5 180.0 192.1 205.8 209.3 221.8 233.6 186.2 193 199 203 IX Table 3.5. Ionization potentials (electron volts) [1-20]. 1362.2 1465.1 367.5 398.8 401.4 424.4 447.5 455.6 478.7 503.8 211.3 225.2 215.9 230.5 244.4 248.3 262.1 276.2 224.6 232 238 X 1648.7 1761.8 442.0 476.4 479.5 504.8 529.3 539.0 564.7 591.9 249.8 265.1 255.1 270.7 286.0 290.2 305 321 266 274 XI 1963 2086 523 561 564 592 618 629 657 688 292 308 298 314 331 336 352 369 311 XII 2304 2438 612 652 657 686 715 727 757 788 336 355 344 361 379 384 401 412 xm 2673 2817 707 750 756 787 818 831 863 896 384 404 392 411 430 435 454 XIV (I) tTl c::t'" (') t'" tTl 0 ~ t:I > Z (I) a: ~ 0 UJ ....... UJ 0'1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 F Ne Na Mg Al Si p S C1 Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn 0 H He Li Be B C N Atom 3070 3224 809 855 862 895 927 941 975 1011 435 457 444 464 484 490 XV 3494 3658 918 968 974 1009 1044 1060 1097 1136 489 512 499 520 542 XVI 3946 4121 1034 1087 1094 1131 1168 1185 1224 1266 547 571 557 579 xvn 4426 4611 1157 1213 1221 1260 1299 1317 1358 1402 607 633 619 xvrn 5129 1288 1346 1355 1396 1437 1456 1500 1546 671 698 4934 XIX 5470 5675 1425 1486 1496 1539 1582 1602 1648 1698 738 XX 6034 6249 1569 1634 1644 1689 1734 1756 1804 1856 XXI 6626 6851 1721 1788 1799 1846 1894 1919 1970 XXll 7246 7482 1879 1950 1962 2010 2060 2088 XXllI Stage of ionization Table 3.5. (Continued.) 7895 8141 2045 2119 2131 2182 2234 XXIV 8572 8828 2218 2295 2310 2363 XXV 9278 9544 2398 2478 2495 XXVI 10030 10280 2560 2660 xxvn 10790 11050 2730 xxvrn W ......:J w til Z - 0 .... ....til t"" t"" 0 (J n Z .... 0 ::0 n~ trl t"" tI1 0 ::0 '11 til Z 0 ....~ n CI'.l trl til til 0 (J ::0 ....3:n 0 ~ 0'1 38 I 3 ATOMS AND MOLECULES Table 3.5. (Continued.) Stage of ionization Atom 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg TI Pb Bi Po At 5.99930 7.900 9.8152 9.75238 11.81381 13.99961 4.17713 5.69484 6.217 6.63390 6.75885 7.09243 7.28 7.36050 7.45890 8.3369 7.57624 8.99367 5.78636 7.34381 8.64 9.0096 10.45126 12.12987 3.8939 5.21170 5.5770 .5387 5.464 5.5250 5.55 5.6437 5.6704 6.1500 5.8639 5.9389 6.0216 6.1078 6.18431 6.25416 5.42585 6.82507 7.89 7.98 7.88 8.7 9.1 9.0 9.22567 10.43750 6.10829 7.41666 7.289 8.41671 9.3 II m IV V VI VII vm IX X 20.514 15.935 18.633 21.19 21.8 24.360 27.285 11.0:30 12.24 13.13 14.32 16.16 15.26 16.76 18.08 19.43 21.49 16.908 18.870 14.632 16.531 18.6 19.131 21.21 23.157 10.004 11.06 10.85 10.55 10.73 10.90 11.07 11.241 12.09 11.52 11.67 11.80 11.93 12.05 12.176 13.9 14.9 16 18 17 17 17 18.563 20.5 18.756 20.428 15.032 16.69 19 20 30.71 34.224 28.351 30.820 36 36.95 40 42.89 20.52 22.99 25.04 27.13 29.54 28.47 31.06 32.93 34.83 37.48 28.03 30.503 25.3 27.96 33 32.123 35 64 45.71 50.13 42.944 47.3 52.5 52.6 57 61.8 34.34 38.3 46.4 46 50 48 53 56 59 54.4 40.734 44.2 37.41 42 46 46 49 87 93.5 62.63 68.3 59.7 64.7 71.0 71.6 77.0 81.5 50.55 61.2 55 60 65 62 68 72 116 112 127.6 81.7 88.6 78.5 84.4 90.8 93 99 102.6 68 80 92 97 90 89 94 98 103 140 144 147 155.4 103.0 111.0 9.2 106 116 117 125 126.8 170 174 179 184 192.8 126 136 122.3 129 140 142 153 212 207 212 218 224 230.9 150 162 146.2 155 161 163 187 243 250 242 250 257 263 277.1 177 191 19.177 20.198 21.624 ~ 110 115 115 120 125 130 137 100 100 100 95 100 100 105 130 140 145 145 150 155 165 170 120 120 120 115 120 120 130 135 155 160 170 180 175 185 190 200 210 145 145 145 140 145 150 155 160 180 185 195 205 210 210 220 230 240 250 160 165 165 160 170 175 180 190 23.68 25.05 20.959 23.3 22 24 26 25 27 28 30 34.2 29.83 31.937 25.56 27 29 n 72.28 56 58.75 lOS 36.72 38.95 ~ 57.45 70.7 81 82 74 80 80 85 ~ 33.3 33 35 38 40 39 41 44 46 50.7 42.32 45.3 38 41 45 48 51 54 57 55 58 61 64 68.8 56.0 61 51 61 64 68 72 75 73 77 81 84 88.3 73 78 66 57 62 62 66 !.!!L. 79 83 88 92 96 94 98 103 107 112 91 100 105 110 115 120 115 120 125 130 140 120 125 l35 140 145 140 150 155 160 145 155 160 165 175 170 175 185 3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS / 39 Table 3.S. (Continued.) Stage of ionization Atom 86 87 88 89 90 91 92 93 94 95 Rn Fr Ra Ac Th Pa U Np Pu Am 10.74850 4 5.27892 5.17 6.08 5.89 6.19405 6.2657 6.06 5.993 II ill IV V 21 22 10.147 12.1 11.5 29 33 34 20 20.0 44 43 46 49 28.8 55 59 58 62 65 VI 67 71 76 76 80 84 VII Vill IX X 97 84 89 95 94 100 104 110 115 105 110 115 115 120 165 135 140 125 130 140 140 190 195 155 165 145 155 160 References 1. Astrophysical Quantities, 1, §16; 2, §16; 3, §16 2. Lotz, W. 1966, Ionisierungsenergien von Ionen H his Ni (lost. Plasrnaphys, Miinchen) 3. Moore, C.E. 1970, Ionization Potentials, NSRDS-NBS 34, Washington 4. Finkelnberg, W., & Humbach, W. 1955, Naturwiss., 42, 35 5. Handbook of Chemistry and Physics, 77th ed. (CRC, Boca Raton, FL, 1996) 6. Martin, W.e. 1987, Phys. Rev. A, 36, 3575 (He I) 7. Martin, w.e., Kaufman, V., & Musgrove, A. 1993, J. Phys. Chem. Ref Data, 22,1179 (011) 8. Martin, w.e., & Zalubas, R. 1981, J. Phys. Chem. Ref Data, 10, 153 (Na I-XI) 9. Martin, W.C., & Zalubas, R. 1980, J. Phys. Chem. Ref Data, 9, 1 (Mg I-XII) 10. Martin, W.C., & Zalubas, R. 1979, J. Phys. Chem. Ref Data, 8,817 (AI I-XIII) 11. Martin, W.C., & Zalubas, R. 1983, J. Phys. Chem. Ref Data, 12, 323 (Si I-XIV) 12. Martin, w.e., Zalubas, R., & Musgrove, A. 1985, J. Phys. Chern. Ref Data, 14, 751 (PI-XV) 13. Martin, W.C. Zalubas, R., & Musgrove, A. 1990, J. Phys. Chem. Ref Data, 19, 821 (S I-xvI) 14. Sugar, J., & Corliss, C. 1985, J. Phys. Chem. Ref Data, 14, Supp!. No.2 (K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni) 15. Sugar, J., & Musgrove, A. 1990, J. Phys. Chem. Ref Data, 19, 527 (I-XXIX) 16. Sugar, J., & Musgrove, A. 1995, J. Phys. Chem. Ref Data, 24, 1803 (Zn I-XXX) 17. Sugar, J., & Musgrove, A. 1993, J. Phys. Chem. Ref Data, 22,1213 (Gel-XXXII) 18. Sugar, J., & Musgrove, A. 1991, J. Phys. Chem. Ref Data, 20,859 (KrI-xxxvI) 19. Sugar, J., & Musgrove, A. 1988, J. Phys. Chem. Ref Data, 17, 155 (Mo I-XLII) 20. Martin, W.C., Zalubas, R., & Hagan, L. 1978, Nat!. Stand. Ref. Data Ser. (Nat!. Bur. Stand., U.S.) 60 (Rare-Earth Elements) 21. Cohen, E.R., & Taylor, B.N. 1988, J. Phys. Chern. Ref. Data, 17,1795 Table 3.6. Electron affinities [1-2]. Atom Electron affinity (eV) Atom Electroo affinity (eV) H He Li Be B +0.754 -0.3 +0.618 -0.4 +0.277 Na Mg Al Si P +0.479 -0.4 +0.441 +1.385 +0.747 C N 0 0F Ne +1.263 -0.2 +1.461 -6.7 +3.401 -0.7 S CI Br I K Ca +2.077 +3.612 +3.48 +3.17 +0.501 +0.018 Molecule Electron affinity (eV) 02 03 OH SH C2 C3 +0.451 +2.1028 +1.82767 +2.314 +3.269 +1.981 CN NH2 NO N02 N03 CH +3.862 +0.771 +0.026 +2.273 +3.951 +1.238 References \ 1. Astrophysical Quantities, 1, § 17; 2, § 17; 3, § 17 2. Handbook of Chemistry and Physics. 77th ed. (CRC, Boca Raton, FL, 1996) 40 I 3 3.6.1 Ionization Cross Section ATOMS AND MOLECULES The classical cross section of atoms for ionization by electrons [30] is Ql = 4mraJ-1- XE (1 - !) , E where X is the ionization energy in rydbergs (Ry), E the electronic energy before collision in Ry, and n the number of optical electrons. The general approximation for cross sections of atoms for ionization by electrons (see, [30-33]) is Ql 2 1 mraJ = mrao-F(Y, E/x) = -2- q X~ X = 1.63 x 1O-14n (l/x;v)(x/E)F(Y, E/x), where Y is the charge on the ionized atom (or next ion stage) and XeV is the ionization energy in eY. The function F(Y, E/x) is given and also q = (X/E)F(Y, E/x), which is sometimes called the reduced cross section in Table 3.7. The Y = 1 and Y = 2 values are from experiment and Y = 00 from calculation. About ±1O% accuracy may be expected for hydrogenic ions. In other cases ±0.3 dex may be expected. Other empirical forms have been suggested (see, e.g., [34-36]). Table 3.7. Numericalfunctions F(Y. ~/X) and q(Y. E/X). E/X F(c1assical) F(l. E/X) F(2. ~/X) F(OO.E/X) = 4(1 - q(c1assical) q(l. ~/X) q(2. E/X) q(oo. E/X) = 4(X/E)(l- X/E) X/E) 1.0 1.2 1.5 2.0 3 5 10 0.00 0.0 0.00 0.00 0.67 0.31 0.53 0.74 1.33 0.78 1.17 1.54 2.00 1.60 2.02 2.56 2.67 2.9 3.3 3.8 3.20 4.6 4.7 5.0 3.60 6.4 6.4 6.4 0.00 0.00 0.00 0.00 0.56 0.26 0.44 0.62 0.89 0.52 0.78 1.03 1.00 0.80 1.01 1.28 0.89 0.97 1.09 1.28 0.64 0.92 0.94 1.00 0.36 0.64 0.64 0.64 The maximum ionization cross section for the classical case is Qmax = mraJx-2 atE = 2X· The value of Qmax is approximately the same in actual cases but the maximum occurs near E The rate of ionization by electrons (see [30-32]) is Ll = VQ1. The neutral atom approximation (with kT < ionization energy) gives Ll = 1.1 x 1O-8nTl/2xc11O-5040Xev/T cm3 s-l. The coronal ion approximation (with kT < ionization energy) gives Ll = 2.1 x 1O-8nTl/2Xe11O-5040xev/T cm3 s-l. = 4X. 3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS 1 41 3.6.2 Excitation Cross Section (permitted Transitions) An approximation for Qex, the excitation cross section of an atom (see [30,37]), is given. The approximation applies fairly well when I::!.n 2: 1 (notation of Chap. 5). For I::!.n = 0 the approximation tends to be small: Qex = 8n 2 f -nao-b .J3 EW = 1740na5)..2(WIE)fb = 1.28 x 10- 15 (fIE W)b cm2 , where f is the oscillator strength, W is the excitation energy in Ry (= 0.09121).. with ).. in JLm), and E is the electron energy before collision, also in Ry. See Table 3.8. Table 3.8. Numerical/actors b and bW IE. 1.0 1.2 1.5 2.0 3 5 10 30 100 b, neutral atoms b, ions 0.00 0.20 0.03 0.20 0.06 0.20 0.11 0.20 0.21 0.24 0.33 0.33 0.56 0.56 0.98 0.98 1.33 1.33 b WI E, neutral atoms bW/E, ions 0.00 0.20 0.03 0.17 0.04 0.13 0.06 0.10 0.07 0.08 0.07 0.07 0.06 0.06 0.03 0.03 0.01 0.01 E/W The maximum excitation cross section is as follows: • The neutral atom approximation gives • The ion approximation gives The rate of excitation (see [34,35,37]) is L = vQe=x170 x · 10-4 f Tl/2WeV 1O-5040Wev/ T P(WlkT) ' where WeV and Ware the excitation energy in eV and in ergs (with 11600Wev 1kT = WI kT) and P(W1kT) is tabulated from [37] (see Table 3.9). Table 3.9. Numerical/actors pew I kT) and WI kT. P(WlkT) WlkT < 0.01 0.01 0.02 0.05 Neutral atoms Ions 0.29E] (WlkT)a 1.16 0.96 0.70 1.16 0.98 0.74 42 / 3 ATOMS AND MOLECULES Table 3.9. (Continued.) P(W/kT) W/kT 0.1 0.2 0.5 I 2 5 10 >10 Neutral atoms Ions 0.49 0.33 0.11 0.10 0.063 0.035 0.023 0.55 0.40 0.26 0.22 0.21 0.20 0.20 O.066/(W/ kT) 1/2 0.20 Note a E 1( ) is the first exponential integral. The tabulated P(W j kT) are too small when the total quantum number of Chap. 5 is unchanged. The approximations quoted should be replaced by quantum calculations when available (see [30,38-40]). A Coulomb approximation for ions [41] gives b = geff(2L + l)jgl (L in Chap. 5). The tabulations of geff, the effective Gaunt factor, range from 0.5 to 0.9. 3.6.3 Deexcitation Cross Sections Deexcitation cross sections Q21 are related to excitation cross sections Q12 (2 being the upper level) through where E"2 = E"l + W, and g2 and gl are statistical weights. The deexcitation rate L21 and excitation rate LI2 are related by 3.6.4 Excitation Cross Sections (Forbidden Transitions) The collision strength Q for each line is defined by (see [33,42]) Qf = rrQjglk~ = rra5QjglE" h2 Q = - - 2 - - 2 =4.21Qjglv 2 , 4rrm glv where kv j2rr is the wave number of the incident electron (then k~ in atomic units = E" in Ry), v is the electron velocity, gl is the statistical weight of the initial (lower) level, and Qf is the forbidden line cross section for atoms in this level. Then QI2(excitation) = Q21 (deexcitation). 3.6.5 Collision Strengths: Extensive Databases Crude recipes to estimate the order of magnitude of collision strengths (for allowed and forbidden transitions) can be found in older references [43]. In recent years, however, a wealth of accurate 3.7 ATOMIC RADII / 43 collision strengths have been obtained for a very large number of transitions. They are based on extensive UV and IR emission-line observations and on theoretical calculations. Data are available, e.g., from the Opacity Project, the Iron Project, and the Harvard-Smithsonian Center for Astrophysics (see Sec. 3.1 for information about online access of these sources). 3.6.6 Total Atomic Cross Section (Elastic and Inelastic) An approximation for the total cross section is (see [31, 32, 44]) Q ~ 1801l"a6J../E1/2 (J.. in /.Lm, E in Ry), where J.. is the wavelength of the strongest low-level lines. 3.6.7 Ionic Collision Cross Section Cross section for collision deflection of at least a right angle (see [45]) QJ = 1l"(Y - 1)2(e2/mv2)2 = IT(Y - 1)2(e2 /2EhcR)2 = 1l"a6(Y - 1)2/E2 (E in Ry), where Y - 1 is the ionic charge. The effective ionic collision cross section is usually concerned with the more distant collision involving deflections much less than a right angle. These increase the effective Q by a factor depending logarithmically on the most distant collisions that enter the integration and also on the circumstances. The factor is usually between 10 and 50 (see Sec. 3.10). We may write a general approximation: Q(effective) ~ 201l"a6(Y - 1)2 /E2. 3.7 ATOMIC RADII Atomic radii are defined through the closeness of approach of atoms in the formation of molecules and crystals. The radius r so derived is approximately that of maximum radial density in the charge distribution of neutral atoms (see Table 3.10). For ions the appropriate radius measures to the point where the radial density falls to 10% of its maximum value. The atomic mass divided by the atomic volume (4/3)1l"r 3 gives the density of the more compact solids. 2r is approximately the gas-kinetic diameter of monoatomic molecules. Table 3.10. Atomic radii [1-5]. Atom r (A) Ion [3] r (A) Atom r (A) H He Li Be B 0.7 1.2 1.58 1.06 0.83 H- 1.8 S Cl Ar K Ca 1.05 1.02 1.6 2.37 1.97 Li+ Be2+ B3+ 0.68 0.39 0.28 Ion [3] r (A) Atom r (A) Ion [3] r (A) S2- Cl- 1.70 1.67 1.82 1.52 1.14 1.2 1.82 2.54 2.3 1.44 Br- K+ Ca2+ Br Kr Rb Sr Ag Rb+ sr2+ Ag+ 1.66 1.32 1.29 44 / 3 ATOMS AND MOLECULES Table 3.10. (Continued.) Atom rCA) Ion [3) rCA) Atom rCA) Ion [3) rCA) Atom rCA) Ion [3) rCA) C N 0 F Ne 0.77 0.70 0.66 0.62 1.3 C4+ N 30 2F- 0.22 1.92 1.26 1.19 Sc Ti Y Cr Mn 1.64 1.46 1.39 1.28 1.26 Sc3+ Ti4+ y4+ 0.89 0.75 0.61 1.09 0.76 2.06 0.81 1.6 1.62 1.4 2.00 2.73 Cd2+ Sn4+ 1- Mn2+ Cd Sn I Xe Cs Cs+ 1.81 1.27 1.25 1.29 1.28 1.39 Fe2+ Co2+ Ni2+ Cu+ Zn2+ 2.24 1.38 1.44 1.57 Ba2+ 1.49 Au+ Hg2+ 1.51 1.16 1.91 1.62 1.43 1.09 1.08 Na Mg Al Si P Na+ Mg2+ A13+ Si4+ p3- 1.16 0.86 0.67 0.47 2.3 Fe Co Ni Cu Zn 0.75 0.79 0.83 0.91 0.77 Ba Pt Au Hg References 1. Astrophysical Quantities, I, §19; 2, §19; 3, §19 2. Teatum, E., Gschneidner, K., & Waber, J. 1960, Los Alamos Scientific Laboratory, Report No. LA-2345 3. Shannon, R.D. 1976, Acta Cryst., A32, 751 4. Allen, EH., Kennard, 0., Watson, D.G., Brammer, L., Orpen, A.G., & Taylor, R. 1987,1. Chern. Soc. Perkin /l, SI 5. Alcock, N.W. 1990, Bonding and Structure: Structural Principles in Inorganic and Organic Chemistry, (Ellis Horwood, New York) 3.8 PARTICLES OF MODERN PHYSICS A representative selection of particles is given in Table 3.11. Hadrons include mesons, nucleons, and baryons. Possible proton decay is not included. I denotes the isotopic spin, J the spin, and P the parity. The lifetime is that in free space. In the column labeled "Decay" are given the main decay products. The mean life r for Wand Z bosons is given as the linewidth f (rf ~ h). Table 3.11. Selected particles o/modem physics [1-3]. Name Symbol Charge Mass (amu) JP Mean life (s) 1I 1 r=2.IGeV r = 2.5 GeV Decay Bosons Gauge bosons Photon W y W Z Z 0, I 0 +1,-1 0 0.000 86.24 97.90 +1, -1 0 +1, -I 0.14984 0.14490 0.53015 000- 2.603 x 10- 8 0.83 x 10- 16 1.237 x 10- 8 JLv I Ih s 0 0.53438 Ih 0- 0.892 x 10- 10 ,,+,,- ,,,0,,0 L 0 0.53438 Ih 0- 5.38 x 10-8 "eo," JLV, 3,,0 Mesons ,,-mesons (pion) n+,Jr,,0 K meson (kayon) K(j,KKO KO 00 eV,etc. e+e-, etc. yy /Lv, ",,0 Fermions Leptons e Neutrino JL Neutrino T Neutrino Electron, Positron JL meson (muon) T meson (tauon) Ve vI' VT e JL T 0 0 0 -1,+1 -1,+1 -1,+1 < 5 x 10- 8 < 5 x 10-4 <0.2 0.0005486 0.1134 1.915 Ih Ih Ih Ih Ih Ih 00 00 00 00 2.197 x 10-6 (3.4 ± 0.5) x 10- 13 evv evii 3.9 MOLECULES / 45 1Bble 3.11. (Continued.) Name Symbol Charge p n +I, -1 A Nonstrange baryons Proton Neutron Mass (amu) Mean life (s) 1.007275 1.008664 lil lil Ih+ Ih+ 0.932 x 103 0 +1,-1 0 -1,+1 1.1976 1.2768 1.2802 1.2854 0 Ih+ Ih+ Ih+ Ih+ 2.632 x 10- 10 0.800 x 10- 10 < 10- 19 1.482 x 10- 10 p",-, n,..O, etc. p,..O, fill" + , etc. Ay, etc. fill" - , etc. 0 Strangeness-} baryons A };+ };+ };O };O };- };- Strangeness-2 baryons Decay 00 pe - v SO SO 8- 8- 0 -1,+1 1.411 6 1.4185 lil lil Ih+ Ih+ 2.90 x 10- 10 1.641 x 10- 10 A"'O, etc. A,..-. etc. n- -1,+1 1.795 0 3h+ 0.819 x 10- 10 AK-, etc. -1,+1 2.450 0 Ih+ 2.3 x 10- 13 AK-,etc. Strangeness-3 baryons !Or Nonstrange charmed baryons Ac Ac Composite particles IH 2H 0 a Hydrogen (251/2) Deuterium (251/2) Deuteron a particle 0 0 +I +2 1.00782 2.01410 2.0\355 4.00140 00 00 00 00 References 1. Astrophysical Quantities, 1, §20; 2, §20; 3, §20 2. Barnett, R.M. et al. 1996, Rev. Mod. Phys.• 68, 611 3. Barnett. R.M. et al. 1996. Phys. Rev.. D54. 1 3.9 MOLECULES Some definitions follow: NA, NB, NAB mAB ro Do gO We, WeXe IP UA,UB QAB I Number of atoms A, B, and molecules AB per cm3 . Reduced mass = mAmB/(mA + mB)' Internuclear distance (lowest state). Dissociation energy (lowest state). Electronic statistical weight (lowest state), or Multiplicity, = 2S + 1 for 1: states, = 2(2S + 1) for other states. = 1 for heteronuclear molecules, = 2 for homonuclear molecules. Vibrational quantum number. Rotational constants [46,47]. Energy change = heB = h 2/87r 2 1= h 2/87r 2mABr;. Vibrational constants. Ionizational potential. Atomic partition functions (Sec. 3.3). Molecular partition function, = QrotQvibQeI. each term dimensionless. Moment of inertia, = m ABr;. 46 / 3 ATOMS AND MOLECULES Molecular diameters (diatomic) are ~ 3ro ~ 3.4A. Molecular dissociation is represented by Numerically, log(NANB/NAB) = 20.2735 + ~ log mAB + ~ log T - 5040D/T + log(UAUB/QAB) with min amu, Din eV, N in cm- 3 , Qrot = kT/uhcBv = (T/1.439 K)uBv , Bv = Be - OIe(V + i), Qvib = "" ~ exp (1.439 T K [We V Qel = Lgel exp ( el - WeXe(V 2) + v)] , 1.439 K ) T Tel, with Bv , We, Tel (= electronic excitation energy) in em-I. The main ground-level constants are given in Tables 3.12 and 3.13, but upper level constants [46, 47] are required for dissociation calculations. Table 3.12. Diatomic molecules [l-3].Q Molecule gO u H2 H2+ He2 DH DO C2 CH CH+ CO CO+ 1 4 1 1 2 1 4 1 1 2 2 2 2 1 2 1 1 1 1 CN 2 1 2 3 4 3 4 4 3 2 1 2 2 1 1 2 2 1 1 1 N2 N+ 2 NH NO 02 02+ OH OH+ MgH AlH AIO SiH 1 2 4 I Be ae (em-I) We (em-I) WeXe (em-I) TO (A) IP (em-I) 60:85 30.2 3.06 1.68 4401 2321 15.426 12.02 1.78 1.82 14.46 14.18 1.93 1.977 0.412 0.017 0.018 0.53 0.49 0.018 0.019 2367 1886 1855 2859 2740 2170 2214 121 66.2 22.22 49.4 11.8 13.3 63.0 1.131 13.29 15.16 0.741 1.052 3.42 8.28 6.296 3.465 4.085 11.092 8.338 0.504 0.504 2.002 0.923 6.452 6.003 0.930 0.930 6.856 6.859 1.232 1.205 1.243 1.120 9.77 7.0 12.15 10.64 1.128 1.115 14.01 26.8 7.76 9.759 8.713 3.47 6.497 5.116 6.663 4.392 5.09 1.34 6.462 7.002 7.001 0.940 7.467 7.997 7.997 0.948 0.948 0.967 1.90 1.998 1.932 16.699 1.672 1.445 1.691 18.91 16.79 5.826 0.017 0.017 0.019 0.649 0.017 0.016 0.020 0.724 0.749 0.185 2068 2359 2207 3282 1904 1580 1905 3738 3113 1495 13.09 14.32 16.10 78.35 14.08 11.98 16.26 84.88 78.52 31.89 1.172 1.098 1.116 1.036 1.151 1.208 1.116 0.970 1.029 1.730 14.17 15.58 27.1 13.63 9.26 12.07 24.2 12.90 3.06 5.27 3.06 0.972 10.042 0.973 6.391 0.641 7.500 0.186 0.006 0.219 1683 979 2042 29.09 6.97 1.648 1.618 1.520 Do (eV) 4.4781 2.6507 ob mAB (amu) (eV) 9.53 8.04 3.10 PLASMAS / 47 Table 3.12. (Continued.) go SiO SiN SO CaR CaO ScO TiO 2 3 2 1 2 6 VO crO FeO YO zrO LaO a I 4 2 6 2 IP mAB (amu) Be (em-I) 8.26 4.5 5.359 1.70 4.8 6.96 6.87 10.177 9.332 10.661 0.983 11.423 11.797 11.994 0.727 0.731 0.721 4.276 0.445 0.513 0.535 0.005 0.006 0.006 0.097 0.003 0.003 0.003 1242 1151 1149 1298 732 965 1009 5.97 6.47 5.63 19.10 4.81 4.20 4.50 1.510 1.572 1.481 2.003 1.822 11.43 1.620 6.4 6.4 4.4 4.20 7.29 7.85 8.23 12.173 12.229 12.438 13.556 13.579 14.343 0.548 0.541 0.513 0.388 0.423 0.353 0.004 0.005 0.004 0.002 0.002 0.001 lOll 4.86 6.75 8.71 2.93 4.90 2.22 1.589 1.615 8.2 1.790 1.712 1.825 4.95 DO Molecule (eV) Q!e (em-I) We (em-I) WeXe (em-I) 898 965 861 970 812 rO (eV) 10.29 5.86 Notes a See Sec. 4.11 for further molecular data and references. bThe lowest electronic state supports no bound state. However, the ground-state energy (as a function of nuclear separation) has a potential well. Its depth is De = 0.0009 eV. References 1. Astrophysical Quantities, 1, §21; 2, §22; 3, §21 2. Herzberg, G. 1950, Spectra of Diatomic Molecules (Van Nostrand, New York) 3. Huber, K.P., & Herzberg, G. 1979, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules (Van Nostrand, New York) Table 3.13. Selected polyatomic molecules [1-2]. Molecule IP (eV) (eV) (A) H2O N2 0 CO2 NH3 Cf4 HCN 12.61 12.89 13.77 10.15 13.0 13.91 5.11 1.68 5.45 4.3 4.4 5.6 3.5 4.0 3.8 3.0 3.5 D Diameter References 1. Astrophysical Quantities, 1, §21; 2, §22; 3, §21 2. Herzberg, G. 1966, Electronic Spectra of Polyatomic Molecules (Van Nostrand, New York) 3.10 PLASMAS Some definitions follow: Ne , Ni, Np , N Zj L T,B,p A Electron, ion, proton, total heavy-particle densities. Charge on i ion (denoted Yj - 1 in other sections). Characteristic size (e.g., diameter) of plasma. Temperature, magnetic field, density. Mass in amu. 48 / 3 ATOMS AND MOLECULES The Debye length, electron screening, the distance from an ion over which Ne can differ appreciably from Li NiZi is with T in K and Ne in cm- 3 . The plasma oscillation frequency is Vpl = (Ne2/rrme)I/2 = 8.978 x 103 N~/2s-2 (in cgs). The gyrofrequency for electrons is Vgy = (e/2rrmec)B = 2.7994 x 106 B s-l, and for ions is Vgy = (Ze/2rrmic)B = 1.535 x lo3Zi B/A s-l, with B in G. The gyroradius for electrons is a e = mev1. c/ eB = 5.69 x 1O-8v1.B cm :::::2.21 x 1O-2 T 1/ 2 jBcm, and for ions is al = miV1.cjZieB = 1.036 x 1O-4v1.AjZiB cm ::::: 0.945Tl/2Al/2jZiB cm, where v1. is the velocity normal to B. The most probable thermal velocity for electrons is v and for atoms and ions is v = (2kT jme)I/2 = 5.506 x loST1/2 cm/s, = (2kT jm)I/2 = 1.290 x 104(T j A)I/2 cm/s. For rms velocities increase v by the factor.../'J12 = 1.225. The velocity of sound is comparable with thermal velocity. The Alfven speed (magnetohydrodynamic or hydromagnetic wave) is VA = Bj(4rrp)I/2 = 0.282Bjp l/2. 3.10 PLASMAS / 49 The phase velocity is cO + 4npc 2I B2)1/2. The electron drift velocity in crossed magnetic and electric fields is 108 E.LI B cm/s, with E.L in V/cm and B in G. The electron drift velocity in magnetic and gravitational fields is megcleB = 5.686 x 1O-8g 1B cm/s, with g in cm/s2 and B in G. The collision radius p for right-angle deflection of electrons by an ion is PO = Zje2Imev;::::: = 8.3 x ~Zle2lkT 1O-4 ZtlT cm. The corresponding collision cross section is The cross section for all electron collisions with an ion is with In A = In(dlc) = ld p- 1 dp and where c is the minimum of p in circumstances and d is the maximum of p in circumstances. c is the largest of Ci or = 8.3 X C2 = 1.06 10-4 Z11 T cm from the right-angle definition 1O-6 T -l/2 cm X from electron size. d is the smallest of dl = N- 1/ 3 cm d2 = D d3 = 1.8 x 105 T 1/2 Iv or or from ion spacing = 6.9T 1/ 2N- 1/ 2 (the Debye length) for collisions giving free-free absorption of frequency v radiation. The most general approximation for A is In A = 9.00 + 3.45 log T - 1.15 log N e . The collision cross section for neutral atoms and molecules is ::::: 10- 15 cm2 . The collision frequency for electrons is Nl vex(cross section) = 2.5(ln A)NeT- 3 / 2 Zj s-l. The collision frequency for ions with ions is 8 x 1O-2 (ln A)NeA -1/2T- 3/ 2 s-l. The mean free path of electrons among charged particles is 4.7 x IOST 2 NIl NI2 cm. The mean free path of electrons among neutral particles is 10 15 N- 1 cm. Zf 50 / 3 ATOMS AND MOLECULES The electrical resistivity [48] is T/ = 8 x lO l2 (1n A)T-3/ 2 = 9 x 1O-9 (1n A)T-3/ 2 (emu) (esu) , applying when the energy gains during free path < kT. The thermal conductivity [48-50] is 1.0 x 1O-6 T5/2 ergcm- l s-l K- l . The life of a magnetic field in a plasma is 'f = 47CL 2/T/ = 1.5 x (T/inemu) 1O- 12 L 2 (ln A)-IT 3 / 2 s. For approximate parameters for some plasmas, see Table 3.14. Table 3.14. Approximate parameters for some plasmas. a Values are logarithmic. Interstellar. f Definition Quantity Unit log log log log log cm cm- 3 cm- 3 K G L Ne N T B Ion.b Intpl.c 0Cor.d o Rev.e HIg Huh 7.0 5.5 11.0 3.0 -1.0 13.0 0.5 0.5 5.0 -5.0 10.0 8.0 8.0 6.0 0.0 7.0 12.5 16.5 3.7 0.0 19.5 -3.0 0.0 2.0 -5.0 19.5 0.0 0.0 4.0 -5.0 s-1 6.8 4.2 8.0 10.2 2.5 4.0 cm -0.6 3.0 -0.3 -3.6 3.2 2.7 6.4 0.7 6.4 3.2 1.4 -1.8 1.4 -1.8 Debye length i log Ne 0.7 + i log T - i log Ne Gyro freq. Electron Ion 6.4+ log B 3.2 + log B s-1 s-1 5.4 2.2 1.4 -1.8 Collision freq. Electron 1.7 + log Ne - ~ log T s-1 2.2 -5.9 3.2 8.7 -1.8 -4.3 0.2 + log Ne - ~ log T s-1 1.2 -7.4 -0.8 7.2 -5.8 -5.8 6.3 + ~ log T esu 10.8 13.8 15.3 11.9 9.3 12.3 -14.6+ ~log T emu -10.1 -7.1 -5.6 -9.0 -11.6 -8.6 5.7 + 210g T -log Ne 15.0-10g N cm cm 6.2 4.0 15.2 14.5 9.7 7.0 0.6 -1.5 12.7 15.0 13.7 15.0 cm cm 0.8 2.5 5.8 7.5 1.3 3.0 0.1 1.8 4.3 6.0 5.3 7.0 cmls 7.5 6.1 7.3 5.1 7.8 6.3 cmls 5.7 6.7 7.2 6.0 5.2 6.2 5.4 -2.1 19.4 11.9 15.9 8.4 6.5 -1.0 29.9 22.4 31.9 24.4 Plasma freq. Ion Electrical conductivity Mean free path Ion Neutron Gyroradius Electron Proton 4.0+ Sound v i i 11.3 - i log N + log B 4.2+ i log T B decay -13.1 +2 log L+ ~log T Alfv~n v -1.7 + log T -log B 0.0 + log T - log B s yr Notes aFor spectral emission from high-temperature plasmas, see Chap. 14. 3.10 PLASMAS I 51 blon. denotes ionosphere. cIntpl. denotes interplanetary space. d 0 Cor. denotes solar corona. e 0 Rev. denotes solar reversing layer. f Interstellar denotes interstellar space. 8H I denotes the H I region. hH II denotes the H II region. ACKNOWLEDGMENT The author was supported in part by Grant No. AST-9315112 of the National Science Foundation. REFERENCES 1. Drake, G., editor, 1996, Atomic. Molecular, and Optical Physics Handbook (AlP, New York) 2. Jeffery, C.S. 1996, QJRAS. 37, 39, and references therein 3. Lide, D.R., editor-in-chief 1996, Handbook of Chemistry and Physics. 77th ed. (CRC. Boca Raton, FL) 4. DeLaeter, J.R., Heumann, K.G., & Rosman, K.J.R. 1991, Pure Appl. Chem., 63. 991, reprinted in J. Phys. Chem. Ref. Data. 20, No.6, 1327 5. DeLaeter, J.R., & Heumann, K.G. 1991, Pure Appl. Chem., 63, 975, reprinted in J. Phys. Chem. Ref. Data, 20, No.6, 1313 6. Anders, E., & Grevesse, N. 1989. Geochim. Cosmochim. Acta 53.197; Grevesse, N .• & Noels, A. 1993. in Origin and Evolution of the Elements, edited by N. Prantzos, E. Vangioni, and M . Casse (Cambridge University Press, Cambridge), p. 15 . 7. Biemont, E., Baudoux, M., Kurucz, R.L., Ansbacher, W., & Pinnington, E.H. 1991, A&A, 249, 539 8. Hummer. D.G., & Mihalas, D. 1988, ApJ, 331. 794 9. Mihalas, D., Dii.ppen W., & Hummer, D.G. 1988, ApJ, 331,815 10. Dippen. W., Anderson, L.S., & Mihalas, D. 1987, Api, 319. 195 11. Rogers. F.J. 1981. Phys. Rev. A, 24. 1531 12. Rogers. F.J. 1986, ApJ, 310, 723 13. Iglesias, C.A., & Rogers, F.J. 1991.ApJ. 371, L73 14. Rogers, FJ., & Iglesias, C.A. 1992.ApJS.401, 361 15. Rogers, F.J., Swenson, FJ.• & C.A. Iglesias 1996. ApJ, 456,902 16. Ebeling, W., Forster, A., Fortov, V.E., Gryaznov, V.K., & Polishchuk, A.Ya. 1991, Thermodynamic Properties of Hot Dense Plasmas (Teubner, Stuttgart) 17. Alastuey, A., & Perez, A. 1992, Europhys. Len., 20,19 18. Alastuey, A .• & Perez, A. 1996, Phys. Rev. E 53.5714 19. Iglesias. C.A., & Rogers. FJ. 1992, in Astrophysical Opacities. edited by C. Mendoza and C. Zeippen (Revista Mexicana de Astronomfa y Astrofisica. Mexico City), Vol. 23, p. 161 20. Eliezer, S., Ghatak, A., & Hora, H. 1986, An Introduction to Equations of Stale: Theory and Applications (Cambridge University Press, Cambridge) 21. Irwin, A.W. 1981,ApJS, 45. 621 22. Sauval. A.J., & Tatum, J.B. 1984. ApJS, 56,193 23. Lochte-Holtgreven, W. 1958, Rep. Prog. Phys., 21, 312 24. Rosa, A. 1948. Z. Ap.• 25, 1 25. Aller. L.H. 1961, Stellar Atmospheres, edited by J. Greenstein (University of Chicago Press. Chicago.), p.232 26. Cohen, E.R., & Taylor, B.N. 1988. J. Phys. Chem. Ref. Data,17,1795 27. Hyleraas, E. 1950. ApJ, 111, 209 28. Thirring, W. 1979. Lehrbuch der mathematischen Physik, VoL 3: Quantenmechanik von Atomen und Molektilen (Springer, Berlin), p. 207 29. Hill, R.N. 1977, J. Math. Phys., 18, 2316 30. Bely. 0., & Van Regemorter, H. 1970, ARA&A, 8, 329 31. Astrophysical Quantities, 1, §l8 32. Astrophysical Quantities. 2, §18 33. Seaton, MJ. 1962, Atomic and Molecular Processes, edited by D. R. Bates (Academic Press, New York), p.375 34. Lotz, W. 1967, ApJS, 14,207 35. Sampson. D.H. 1969, ApJ, 155, 575 36. Bely, 0., & Faucher, P. 1972, A&A. 18,487 37. Van Regemorter, H. 1962,ApJ, 136.906 38. Moiseiwitsch, B.L., & Smith, S.L. 1968, Rev. Mod. Phys, 40, 238 39. Seaton, M.J. 1970, Trans. IAU, XIVA, 128 and references therein 40. Kieffer, L.J. 1969, JILA Rep. 7 41. Blaha, M. 1969. ApJ, 157,473 42. Hebb, M.H.• & Menzel, D.H. 1940. ApI, 92, 408 43. Astrophysical Quantities, 3. §18, and references therein 44. Bederson, B., & Kieffer, L.J. 1971, Rev. Mod. Phys., 43, 601 45. Spitzer, L. 1956, Physics of Fully Ionized Gases (lnterscience, New York) 46. Herzberg, G. 1950, Spectra ofDiatomic Molecules (Van Nostrand, New York) 47. Tatum, J.B. 1966, Pub. Dom. Ap. Obs., 13,1 48. Spitzer, L. 1962, Physics of Fully Ionized Gases (Interscience, New York) 49. Astrophysical Quantities, 1; 2; 3, §22 50. Delcroix. A., & Lemaire, A. 1969, ApI, 156, 787 Chapter 4 Spectra Charles Cowley, Wolfgang L. Wiese, Jeffrey Fuhr, and Ludmila A. Kuznetsova 4.1 4.1 Online Database . . . . . . . . . . . . . . . .. ... 53 4.2 Tenninology for Atomic States, Levels, Tenus, etc. 54 4.3 Electronic Configurations 57 4.4 Spectrum Line Intensities 60 4.5 Relative Strengths Within Multiplets . . . . . . . . .. 65 4.6 Wavelengths and Wave Numbers . . 68 4.7 Atomic Oscillator Strengths for Allowed Lines. . . 69 4.8 Nuclear Spin and Hyperfine Structure: Low-Level Hyperfine Transitions . . . . . . . . . . .. 78 4.9 Forbidden Line Transition Probabilities . . . . . . . 79 4.10 Spectra of Diatomic Molecules . . .. .. 83 4.11 Energy Levels . . . . . . . . . . . . . . . . . . . . . . 85 4.12 Transitions. . . . . . . . . . . . . . . . . . . . . . . 87 4.13 Selection Rules: Dipole Radiation 89 . . .... .......... ONLINE DATABASE Extensive data and references are available online through the Internet [1]. A comprehensive, critically evaluated database, whose address is given below, is maintained by the National Institute of Standards and Technology (NIST). Files of special relevance to atomic spectroscopy are the Atomic Spectroscopic 53 54 / 4 SPECTRA Database by J.R. Fuhr, W.C. Martin, A. Musgrove, J. Sugar, and W.L. Wiese, Bibliographic Database on Atomic Transition Probabilities by J .R. Fuhr and H.R. Felrice, and Program of the NIST Atomic Data Centers by W.L. Wiese and W.C. Martin. The unifonn resource locator, or URL, is currently http://physics.nist.govlPhysRefData/contents.html. File names and locations are subject to change. The above files might be found by first "opening" http://physics.nist.gov/ and following the appropriate links, or simply by doing a network search for the keywords "NIST atomic data." 4.2 TERMINOLOGY FOR ATOMIC STATES, LEVELS, TERMS, ETC. The angular momenta of atoms are vector quantities describing the orbital angular momenta (I, L), the spin (s, S), and the sum of the two (j, J). Lowercase letters are used for individual electrons, and uppercase letters refer to corresponding sums (e.g., L = L I). The magnitudes of these vectors are specified by quantum numbers usually written with lightface italic symbols. For example, III = ,.j1(1 + 1)11. Spectroscopists often interchange the meaning of the vector quantities and the associated quantum numbers, and say, for example, that L is the sum of the I's, although the relation is only valid for the vector quantities. This loose usage is convenient and is followed here. Spectroscopic levels are typically described by quantum numbers based on LS (Russell-Saunders) coupling. For other coupling schemes, see [2) and [3). Often, levels are expressed as mixtures of LS terms, where the leading component is the single LS tenn that best describes the level. Orbital angular momentum (or azimuthal quantum number), L = vector sum of orbital angular momenta I of individual electrons. The unit is h/27r == Ii, and the designations are L (or I) 0 1 2345678 9 Designation (L) Designation (I) S s P P DFGHIKL d f g h k I M N 0 m n 0 10 11 12 Q q 13 R r 14 15 T t u u Spin angular momentum, S = vector sum of s for individual electrons. The multiplicity of terms = 2S + 1. The effects of the atomic nucleus on atomic structure, including nuclear spin I, are treated in a separate section below. Total angular momentum quantum number, J = vector sum L+S (in LS coupling). In j j coupling, j = vector sum I + s for each electron, and J = L j. The total angular momentum J is said to be a "good quantum number," independent of the coupling scheme. Electron shells are described by the principal quantum number n as follows: n 123 4 5 6 7 Shell designation K N 0 P Q L M Only the magnitude of an angular momentum (e.g., ILl) and one of its components (e.g., L z ) are observables. The z component is chosen arbitrarily. Quantum numbers corresponding to these z components are designated, for example, by m" ML, or M J = M. If the atom is in a magnetic field, it is convenient to choose the z direction along the field, so the m's have been called magnetic quantum numbers. 4.2 TERMINOLOGY FOR ATOMIC STATES, LEVELS, TERMS, ETC. / 55 Maximum values of various quantum numbers are limited as follows: I ~ n - 1; s = 1; 1 ~ S + L; S~1na; ML ~ L; Ms ~ S; M~ 1; L~II+12+···+lna' where there are na electrons in open shells. Interpretation of a typical symbol for an atomic level, e.g., 2 p 3 Principal quantum number of outer electrons = 2; i.e., L shell. Three outer electrons with I = 1. Multiplicity = 2, whence S = Orbital momentum L = 2. 1 = 11, whence statistical weight g = 21 + 1 = 4. The level is odd (omitted when level is even). 1. Possible 1 values for given L and S: Singlets Doublets Triplets Quartets Quintets Sextets Septets The magnetic quantum numbers are usually not indicated unless the level is split by a magnetic field. In the absence of such a perturbation, the energies of all levels with a given 1 are the same, and are therefore (21 + 1)-fold degenerate. Classical atomic spectroscopists have used the following hierarchial scheme to describe energy states, combinations thereof, and transitions among such states, as given in Table 4.1. Table 4.1. Hierarchy of designations. Atomic division State Level Term Statistical weight g Specification Specified by L, S, J, M, or L, S, ML, MS Specified by L, S, J, e.g., 4S11 1 Group oflevels specified by L, S 2J (2S +I + 1)(2L + 1) Transition Component (of line) Line Multiplet 56 / 4 SPECTRA Table 4.1. (Continued.) Atomic division Polyad Configuration Statistical weightg Specification Group of terms from one parent term, and with same multiplicity or S Specified by n and I of all electrons Transition Supermultiplet See text Transition array Nowadays, spectroscopists rarely use the tenn polyad. Very complicated level structures arise with the filling of the 3d (iron group), 4d (palladium group), 5d (platinum group), 4f (lanthanides), and Sf (actinides) subshells. Johansson refers to a subconfiguration for all of the levels that result from the addition of an electron (nl) to a parent tenn. For example, if we use S p and L p to designate the spin and orbital angular momentum of the parent, 3d2 (sp L p)nl has five subconfigurations corresponding to the five allowed tenns from d 2 • Similarly, 3d4 (sp L p)nl would have 16 subconfigurations. He uses the tenn supermultiplet to mean all transitions between levels belonging to subconfigurations of opposite parity [4]. 4.2.1 Terms from Various Configurations Table 4.2 gives the multiplicities and orbital angular momenta of the various tenns arising in LS coupling from the configurations listed [2,3]. When a tenn can appear more than once, the number of possible tenns is written below the symbol. Complete shells s2, p6, d 10, f 14, etc., give rise to only 1S tenns. They need not be considered for possible tenns due to outer electrons. Electrons with the same n and I are said to be equivalent. Tenns arising from complementary numbers of equivalent electrons are the same; e.g., tenns from p2 and p4 are the same, since six electrons complete the p shell. The total weight of an electron configuration may be written [2] Here, Wi is the number of (equivalent) electrons with angular momentum Ii. A number of examples are given below. If a single electron with angular momentum I is added to a parent with Lp and Sp, the total weight of the resulting tenns of both resulting multiplicities is g = (4Sp + 2)[(b + 1)2 - a 2 ], where b = ILp + 11 and a = ILp -II. Often, atomic energy levels are not well described by a single electronic configuration. In such cases, configuration interaction or configuration mixing is said to occur. Table 4.2. Allowed terms for equivalent electrons. Configuration Terms Total weight Equivalent s electrons 2 4.3 ELECTRONIC CONFIGURATIONS / 57 Table 4.2. (Continued.) Configuration Total weight Terms Equivalent p electrons 2pO p5 p4 p p2 p3 6 2PDO 15 20 4S0 Equivalent d electrons d d2 d3 d9 d8 d7 2D ISDG 3PF 2PDFGH d4 d6 ISDFGl 10 45 120 2 22 3PDFGH 2 d5 2 2 210 5D 252 2SPDFGHI 3 2 2 2FO f f2 f3 f13 fl2 f11 ISDGI 3PFH 2PDFGHIKL O 4SDFGI O f4 flO ISDFGHIKLN f5 2 2 22 24 f9 423 3pDFGHIKLM 2 2pDFGHIKLMNOO f8 4SPDFGHIKLMO 2344332 2002 6pFH O 5SPDFGHIKL 7F 2SPDF GHIKLMNOQO 4SPDFGHIKLMN O 6pDFGHIO 8,sO ISPDFGHIKLMNQ 4648473422 f7 1001 5SDFGl 3243422 457675532 f6 14 91 364 3pDFGHIKLMNO 659796633 2571010997542 3003 3 2 322 3432 226575533 4.3 ELECTRONIC CONFIGURATIONS Tables 4.3 and 4.4 give the electronic configurations for ground-level atoms [5]. The inner core of electrons is not explicitly shown for heavier elements. Extensive tabulations of energy levels are available [6,7]. Thble 4.3. Ground-level co1!figurations_ L K Atom Is H I He 2 2 2s M N --- 0 2p 3s 3p 3d 4s 4p 4d 5s I Ground level 2SIf2 ISo Li 3 2 Be 4 B 5 2 2 2 2 C N 6 7 2 2 2 2 2 3 0 8 2 2 4 F 9 2 2 5 2SIf2 2p O 1f2 ISo 3 PO 4 s?1f2 3PI 2pO tIf2 0 N Atom 4f p Q 5s 5p 5d 5f 6s 6p 6d 7s Ag 47 I Cd 48 2 Ground level 2S If2 ISO In 49 2 I 2pO Sn 50 Sb 51 2 2 2 3 4.si\f2 I Te 52 53 2 4 2 5 2pO Xe 54 2 6 Cs 55 2 6 1f2 3 PO 3 P2 11f2 2S If2 ISo 58 / 4 SPECTRA 'nIble 4.3. (ContinuetL) K L Atom Is 2s 2p Ne 10 2 2 6 Na 11 2 2 6 2 1 10 Necore Ar 18 2pO )lh 2 6 2 2 Ca 20 Sc 21 1 2D)lh 2 3 2 2 4Fllh 5 5 1 2 6S21h Fe 26 6 2 Co 27 Ni 28 7 8 2 2 4F41h 10 1 2S Ih 11 22 V 23 18 Cr 24 Mn2S Cu 29 Areore 2 2 6 2 6 Ge 32 28 2 3 Se 34 Br 35 2 4 2 5 Kr 36 2 2 6 2pO Ih 2 2 As 33 Rb 37 2 6 Nb 41 10 2pO )lh 2 6 2 6 M042 Te 43 Ru 44 Rh 45 Pd46 Kreore 4 5 2 2 3P2 Sm62 Eu 63 6 7 2 2 Gd64 7 2 Th6S 9 2 Dy66 10 Ho 67 11 2 2 Er 68 Tm69 12 13 2 2 Yb 70 Lu 71 14 14 2 2 SD4 Hf72 14 2 6 3F4 Ta 73 W 74 ISo 31'0 3~ ISo 2 4 1 6Dlh 5 5 7 8 10 1 2 6~lh 1 4F41h 6~lh 4[0 71h ISo 3F2 6S21h Os 76 lr 77 6 7 2 2 4F)lh Pt 78 9 Au 79 14 2 6 10 SD4 2SIh 2 2 1 HS 80 81 2pO Ih 2 2 2 3 46+32 Rn86 2 6 U 92 Soo 3D] n Ra 88 Ae 89 Th90 Pa 91 3H6 2D)lh 2 Fr 87 SIs 2Fflh 5 Pb 82 Bi 83 7Fo 9~ 4F)lh 46+22 SI4 s~lh 2 2 3F2 ISo 6HO 21h 3 4 2 4 2 5 SFs 4/0 41h 2 Po 84 At 85 7S3 IG~ 2 ISo 2D)lh 2 1 2D)lh 2 Re 75 2S Ih 2 2 36 Nd 60 Pm61 4s?lh Sr 38 Y 39 Zr40 3Po 7S3 ISo 2 2 6 Ground level 2 2 3F2 2 2 1 Zn30 Ga 31 8 1 ISo 2 2 Ba 56 3 ISo Q 58 5p 5d 5f 6s 6p 6d 78 Ce 58 2S Ih 2 6 6 4f Pr 59 4s?lh 2 4 2 5 C\ 17 19 2pO Ih Atom p 0 N La 57 ISo 2 2 2 3 P K Ground level 2S Ih 1 AI 13 16 0 ISo 2 S --- 38 3p 3d 4s 4p 4d 58 Mg 12 Si 14 15 N M 14 2 6 10 3Po 4s?lh 2pO )lh 3~ ISo 1 2S Ih 2 6 46+32 2 2 3 ISo ISo 2 2 2D)lh 3F2 2 2 4KSlh sLg 2 4.3 ELECTRONIC CONFIGURATIONS / 59 Table 4.4. Transuranic elements. p 0 Q Ground Atom 5f 6s 6p 93 94 95 4 6 7 2 2 2 6 6 6 2 2 2 96 97 7 9 2 2 6 6 2 2 6Ho Cf 98 10 Es 99 11 2 2 6 6 2 2 4]0 Pm Md No 100 101 12 13 2 2 2 6 6 2 2Fo 102 103 14 14 2 2 6 2 2 2 D 3 1f2 Np Pu Am Cm Bk Lr 7s 6d 6 level 6 L S lf2 7 FO S~lf2 9Do 7 1.12 7 1.12 2 S]s 3H6 3 1.12 ISO Table 4.5 of first ions (Sc II, etc.), is restricted to those ions whose ground levels differ from those of the preceding atom. Table 4.5 gives outer and incomplete shells only. Table 4.5. First ions. Element Configuration Sc Ti 3d4s 3d 24s V 3d4 3d 5 3dS4s 3d6 4s Cr Mn Fe Co Ni Cu Ground level 3 01 500 6 S21/2 3d B 3d9 7 S3 3 F4 202 1/2 3d l0 ISo Zr 4d 2Ss Nb Mo 4d4 4d 5 Tc 4d5 Ss Ru 4 F41/2 Rh 4d 7 4d B Pd 4d9 202 1/2 La Ce 4FII/2 604 '12 Element 4FII/2 5 00 6 S21/2 7 S3 3F4 Configuration 5d 2 4/Sd 2 Sm 4/36s 4/46s 4/56s 4/ 66s Eu Gd 4/76s 4/75d6s Th Dy 4/9 6s 4/106s Ho 4/116s Pr Nd Pm Er 4/ 12 6s Tm 4/136s Yb 4/ 14 6s Ground level 4HO 3 1/2 Element 3F2 W 9~ Au Sd lO 7H~ Th 6tJ27s 5/ 27s 2 4FII/2 Pa U 5/ 37s 2 Np S/57s 4[0 4'12 Pu S/67s 5/77s 6[8 1/2 5[~ 2 3F 2SI/2 SFI 60 1/2 Pt 7Hf BFI/2 4H61/2 5d36s Sd4 6s Ground level Sd 56s 5d6 6s 5d7 6s 5d9 5[2 6[3 1/2 1000 21/2 Ta Configuration Re Os Ir Am 7 S3 604 1/2 5 F5 202 1/2 ISO 3H4 7Hf BFI/2 9~ 60 / 4 4.4 4.4.1 SPECTRA SPECTRUM LINE INTENSITIES Definitions We use the symbol "dimensionless." g Ii!) to mean "dimensionally equal to" or "has dimensions of"; ~ 0 means = (dimensionless) statistical weight for a level = 2J + 1. Subscripts denote levels. f = (dimensionless) oscillator strength, or simply f value. Unless otherwise stated, this is the absorption oscillator strength fabs, related to the emission oscillator strength fern (which is often taken to be negative) by glfabs = -g2fern. Here, gl and g2 are the statistical weights of the lower level and upper level, respectively. gf = weighted oscillator strength = glf12 = -g2izl. gf is symmetrical between emission and absorption. A = Einstein's A ~s-l; spontaneous transition probability (for a downward transition). B12, B21 = Einstein's B; induced transition probability upward and downward. Bu v = probability of transition where U v is the radiation energy density at the frequency v of the transition. Then Buv ~s-l. The B coefficients are sometimes defined with specific intensity Iv, whence BIv ~s-l. S = line strength. Sum of the matrix elements of the electric dipole operator li!)e 2 JxJ 2 • Also used for higher-order radiation (see below). Yel = classical damping constant (~S-l). Yel is the full width at half maximum (FWHM) in units of circular frequency (w = 2rrv) of an absorption line due to a classical oscillator. Y'2 = reciprocal mean life of level 2 = LI A21 + LI B2IU(V21) + L3 B23U(V23)+ collision terms, where level 1 is below and level 3 is above 2. Y = damping constant = VI + Y'2 for transition 1 -+ 2. It is convenient to define damping constants Yv and VA, for use when profiles are expressed in frequency or wavelength units. Then Yv/v = n/)... = Y /w. O'v = atomic cross section (~cm2) near an absorption line. Note: O'A = O'v. Traditionally, O'v is written in terms of y, not Yv. Often a v or a v is used for atomic cross sections. NI = number of atoms per unit volume in level 1 (the lower level). K = NIO'v, the line absorption coefficient, which must be corrected for stimulated emission: Keorr = K[l- exp(-hv/kT)]. vo = frequency at line center. Ri, Rc = Initial and final radial wave functions of the active electron. For bound levels, Ri,C ~ cm- 3/ 2. Commonly, rRi,C == Pi,(, where r = radius. 0' = proportional to radial transition moment (see below), not related to O'v or O'A' S = multiplet strength, scale as given in Table 4.9. E = energy emitted due to spontaneous, bound-bound transitions in all directions, per unit volume and time. 8Ry = photon energy in rydbergs (e 2 /2ao = 2rr2m e e 4 / h 2 ). n* = effective principal quantum number; describes the energy of an atomic level. 4.4 SPECTRUM LINE INTENSITIES / 61 4.4.2 Formulas For a spectral line that arises from a transition between levels a L S J and a' L' S' J', the line strength for a dipole transition is defined as S= L L I(aLSJ Mlexq la' L' S' J' M') 12 (4.1) l{aLSJ MlerC~l)la'L'S' J'M')1 2 . (4.2) MM'q = MM'q Here, a and a' stand for unspecified quantum numbers. q runs from 1 to 3 for the three components of the position vector of the active electron, or equivalently, the three components of the spherical tensor of rank 1, rC~l). The C's are proportional to the spherical harmonics of corresponding order: Consider a simple electronic transition, where there is a single active optical electron (L pi ~ L pi'), where L p stands for the orbital angular momentum of the parent. The greater of I and I' is usually written I>. In a nonrelativistic, single-configuration approximation, the line strength can be written with the help of two Wigner 6 - j symbols [2]: S = (2J x r{~p i, ~ r (10 + 1)(2J' + 1)(2L + 1)(2L' + 1) {~, ~ 2, I> 00 Rjr Rfr2 dr y The line strength S is often taken to be in atomic units (e = ao = me = 1), but that is not the case in the following relations (the B's used here are defined with energy density; we use m == me): g2 A 21 8rr h v 3 = g2~B21 8rr h v 3 = gl ~B12 = 3Yc1g1J12 = -3Yc1g2hl = = 64rr 4 3hJ...3 S12 or 21 8rr 2e 2v 2 3 gI/12, me 8rr 2e 2v 2 8rr 2e 2 Ycl = 3mc3 = 3mCA 2 ' gJ mhv = glf12 = -g2hl = --2 g1 B 12 = rre 8rr 2mv 3h 2 S12, e 8rr 3 gl B12 = g2 B 21 = 3h 2 S12, E f N28rr 2e 2hv3 3 gI/12 me = N2 A 21 hv = -g2 = N2 8rr 2e 2hv3 3 (-hi) me 8rr 2e 2h = N2 mJ...3 (-hi), (Tv rre2 dv = -Jabs, me 2 Kv Y = -rre Jabsme 4rr2 (v - NJ -1 ~ cm , vO)2 + (y /4rr)2 62 I 4 SPECTRA f nl)2 (I p(l»2 ( Rn'l' = > ll' (1 2 = * = nnl 1 412 _ I > 2e2 A2 ">..0 = - 2 .Jl. Ntfabs, mc YA. 7re2 ,,>..dA = --2A~fabsNl' mc (notation of [2]), (Rnl)2 n'l' , ZJ Xion +XHXp - Xnl . The effective principal quantum number n* may be defined for each level with excitation Xnl. The core, or parent excitation, Xp, if present, must be added to the ionization energy Xion. For example, the 2s22p2(1 D)3s level of N I at 12.36 eV (99663 cm- 1) is built on an excited parent in N II. Therefore, in calculating n*, one must add Xp = 1.90 eV to the (first) ionization energy 14.53 eV of N I. 4.4.3 Numerical Relations The following relations are based on the above formulas, which are derived from an approximate, nonrelativistic radiation theory. The numerical factors are given only to four figures. Physical constants are from [8]. Note that the line strength S is in atomic units in the following: = 303.8S/)' = 1.499 x 1O-16g2AA2 (A in A, A in s-I), = 0.003292gfA = 4.936 x 1O-19g2AA3 (A in A, A in s-I), g2A = 2.026 x 1018 S/A3 = 2.678 x 10geiyS = 0.6670 x 10 16 gflA 2 (A in A, A in s-I), gf S 7re 2/mc = 0.02654cm2 s-I, Yel = 2.223 x 1015 /A 2 s-1 87rhv 3 7re 2/mc 2 = 8.853 x 10- 13 cm, (A in A), 3 3 /c = 87rh/A = 0.1665/A (A in A), e2 = 6.460 x 10-36 cm2 esu2 • a5 3 4.4.4 Forbidden Transitions: Electric Quadrupole (E2) and Magnetic Dipole (MI) In astronomical usage, a line is called ''forbidden'' when it violates the rules for an electric dipole (E1)-induced transition. The lines are designated with a bracket notation, e.g., [0 III] for transitions among the low-level, even-parity states of doubly ionized oxygen. El transitions with as ¥= 0 occur frequently and in the astronomical literature are often written with a single bracket. For example, 4.4 SPECTRUM LINE INTENSITIES / 63 Pp the transition 2s2 1So-2s2p 3 at A1909 is written C III]. Such a transition is sometimes called semiforbidden, or spinforbidden. In complex spectra the rule against intercombination of multiplicities is violated so frequently that this notation is not particularly useful, and it is rarely employed. In the formulas below, ex is the fine structure constant (~O), and u is the wave number of the photon (~cm -I ). The gyromagnetic ratio of the electron spin has been assumed to be 2.000 [2]. For magnetic dipole radiation, g2 A 21 = 41l' 2 he 2 u 3 3 2 2 m C = 2.6974 x L 1(y J MIJJI) qMM' L lO-llu 3 + S~I) IY' J' M'} 12 1(y J MIJJI) + S~l) IY' J' M'} 12. qMM' For electric quadrupole radiation, we show the explicit sum over i electrons. These sums are implicit in the symbols JJI) and S~I) above. In practice, only one electron is important. We have 641l'4 e 2a 4 u 5 g2 A21 = = 5h 0 1 L l(yJ Mlr?C~2)(i)IY' 1'M'} 12 qMM'i 1.1200 x 1O-22u 5 L l(yJ Mlr?C~2)(i)IY' J' M'}12. qMM'i 4.4.5 Selection Rules Selection rules for atomic transitions are summarized in Table 4.6, including rules for LS coupling. When levels are not accurately described by single values of L and S, rules involving these quantum numbers are no longer valid. However, even in complex atoms it is often the case that transitions that violate the LS selection rules are weak. Configuration interaction can cause the selection rule on 111 to be violated. An example is found in Si I, >..5621.61 of multiplet 17.01 [9]. This appears to be a jump from 3p4s to 3p4f (111 = 3). The transition occurs because the 3p4s configuration is mixed with 3p3d. Table 4.6. Selection rules for atomic transitions. a Electric Dipole (E 1) AI = ±l, parity change L!.n arbitrary L!.J = 0 ± I, J = 0.,.. J = 0 L!.L=O,±l, L=O+L=O L!.S=O Magnetic Dipole (M 1) L!.J = 0, ±l, J = 0.,.. J = 0 L!.M=O,±l L!.l 0, L!.n = 0, for all electrons L!.S, L!.L =0 = 64 / 4 SPECTRA 1Bble 4.6. (ContinuetL) Electric Quadrupole (E2) aJ =O,±I,±2, 0 ~O,! ~ !,O ~ 1 al = 0, ±2, no parity change an arbitrary aM=O,±I,±2 as = 0, aL = 0, ± I, ±2, L = 0 ~ L = 0, 1 Note a Rules for L and S hold for LS coupling, while those for J are independent of the coupling conditions. 4.4.6 Radial Integrals and Related Calculations The Coulomb approximation [10, 11] to the radial integral for a single electron is still of heuristic interest. It uses the effective principal quantum numbers n*. Let Z be the charge seen by the active electron at large distances from the nucleus. Z = 1 for a neutral species, 2 for a first ion, etc. Set a = (Z/n*). The nonnalizations of the wave functions in the Coulomb approximation are N=~ n* r(n Z + 1 + 1)r(n -I) , where r is the gamma function. We shall use numbers 1 and 2 to distinguish upper and lower levels in the relations below (as above, I> means the greater of the two values, It and 12): U= * 1 v'41; - 1 * Nl(nl,11)N2(n2,h) (2a l)nj (2a2)ni max p *+*+2LG p LCp (al + a2)nt n2 p=o q=o q (1)Cq (2). The coefficients G and C are easily obtained from recurrence relations: Co = 1, . Ck(I)=- (-nj-Ij+k-1)(lj-nj+k)al+a2 k Go = r(nj + ni + 2), 2aj Gk = . Ck-l(I), i = 1,2, Gk-l ---:--.....,;.;..~-- nj +ni +2-k For integral n*'s the coefficients C are 0 for k above n-I-l. Then, if the sum includes all nonvanishing terms, the results are identical with those well known for hydrogen and hydrogenlike ions. The Coulomb approximation usually gives good results when n:1 > 1 + 1 with max < nj + ni - 1. Useful tables are given in [11]. Kurucz and Bell [12] have made extensive calculations of radial integrals for complex atoms using scaled Thomas-Fermi-Dirac potentials. Results from the international "Opacity Project" are becoming available [13]. 4.4.7 Sum Rules The Kuhn-Thomas-Reiche f -sum rule states 4.5 RELATIVE STRENGTHS WITHIN MULTIPLETS / 65 where the summations are for level 1 below the selected level 2, and 3 above that level (including an integral over continuum). z is the number of atomic or ionic electrons. hI is negative and hence for upward transitions L3 123 ~ z. The rule is rigorous for nonrelativistic quantum mechanics, but the sum includes physically unrealistic states. Restricted and approximate forms of the sum rule are of more practical importance, as for more complex spectra where the lines concerned are mainly the lowest members of their series and contain most of the total oscillaator strength. The Wigner-Kirkwood rule for a one-electron jump [2] is " __ ! 1(21 - I} for 1 -+ 1 - I, ~f- 3 2/+1 " f = ! (l + 1)(21 + 3) for 1 -+ 1 + 1 ~ 3 2/+1 (l is the orbital quantum number); for example, Lf = -!, Lf=I, Lf=-~, Lf p -+ ns, s -+ np, d -+ np, p -+ nd. = I~, '"'" The above rule may sometimes be used for complex spectra, but it applies precisely for hydrogen. The J file and J group sum rules refer to a transition array, e.g., sp -++ pp. A J file refers to all transitions that begin or end on a specified level. Let all line strengths S(y' L' s' J', y LSJ} within a transition array be entered in an i x f matrix, with i being the number of initial levels and f the number of final levels. A J file is any single row or column in this matrix. The J file sum rule states that L S(y' L' S' 1', y LSJ} ()( 2J' + 1 1 and L S(y' L' S' J', y LSJ} ()( 2J + 1. l' These two rules are independent of the coupling conditions, but apply only to simple transition arrays, where either the moving electron has no equivalent congeners or the electron configuration with the summed J or J' values does not contain equivalent electrons. A J group consists of all lines in a transition array connecting a level with a given J (e.g., initial) with one with a given J' (e.g., final). The J group sum rule states that the sum of the strengths of the lines in a J group are independent of the coupling conditions. 4.5 RELATIVE STRENGTHS WITHIN MULTIPLETS Table 4.9 gives the relative strengths of lines in multiplets. The notation used here is for LS-coupling multiplets for a transition LS J -+ L' S' J'. It is important to note that the relative strengths apply much more generally to any case where two angular momenta, say iI, and h, couple to a third i3, where h commutes with the dipole operator er [2]. As a result of this generality, these same relative intensity tables may be used for lines in a hyperfine "multiplet" by the following substitution of quantum numbers: J -+ F, L -+ J, and S -+ I, where F is the total angular momentum including the nuclear spin I. Similarly, the relative intensities of what were once called "supermultiplets" may 66 I 4 SPECTRA be computed by making the following exchange: I -+ L, L -+ 1, and S -+ Lp. Here, we assume a single optical electron with angular momentum 1 that couples to a parent core with angular momentum Lp. It therefore turns out that tables [14] giving relative multiplet strengths are unnecessary. The entries are all proportional to (21' + 1)(21 + I)W 2(LL' I I'; IS) = (21' + 1)(21 + 1) {~, ~ I L' }2 Table 4.7. Normal multiplets SP, P D, DF, etc. Jm Jm Jm Jm Jm -I -2 -3 -4 XI Jm -3 Jm -2 Jm - I Jm -4 2:1 YI x2 Y2 x3 2:2 Y3 X4 2:3 Y4 where the W is a Racah coefficient, and the symbol on the right is a Wigner 6 - j symbol [2]. We normalize so that the sum of the entries for a given multiplet is S = (2S + 1) (2L + 1)(2L' + 1). The entries are therefore proportional to the line strengths as defined above and do not contain wavelengthdependent factors. Therefore, they are only approximately proportional to relative line intensities in real (LS-coupling) multiplets. The following qualitative rules describing the intensities in LS multiplets are of practical value. The most intense lines are those where L and I change in the same sense, for example, I -+ I + 1 while L -+ L + 1. These strong lines are called the principal, or sometimes diagonal, lines of the multiplet. In Tables 4.7 and 4.8, their intensities are called Xl, X2, X3, •••• The intensity of the strongest line on the (principal) diagonal is called XI, and it belongs to the line involving the largest I value, called 1m below. With a few exceptions that may be seen in Table 4.9, the intensities diminish down the diagonal. Lines that falloff the main diagonal are called satellite, or off-diagonal, lines. There are two kinds of multiplets to consider, the symmetrical ones (P -+ P, D -+ D, etc.), and "normal multiplets" (L -+ L + 1, such as S -+ P or P -+ D). Since the line strength factors are independent of which level is upper and which is lower, we are free to choose 1m to belong to the largest L. For the symmetrical multiplets, we call the intensities of the lines for which 1m -+ 1m - 1, YI, those for which 1m - 1 -+ 1m - 2, Y2, etc. Lines with identical intensities fallon the complementary side of the diagonal, as shown below. In normal multiplets, there are a second series of satellites with 1m - 1 -+ 1m - 2, etc., which are designated Zh etc. We remark that in a breakdown of LS coupling, the weaker lines typically deviate more strongly from the LS intensities, so that a calculation in LS coupling may yield reasonable results for a line on the main diagonal, but could be badly off for a satellite. Table 4.8. Symmetrical multiplets P P, DD, etc. Jm Jm - I Jm -2 Jm -3 Jm Jm - I xI YI x2 Jm -2 Jm -3 Y2 x3 Y3 Y3 X4 YI Y2 4.5 RELATIVE STRENGTHS WITHIN MULTIPLETS / Table 4.9. Intensities in LS-coupling multiplets. Multiplicity 3 2 s= Xl Xl X2 X3 Xl X2 X3 Xl X2 x3 X4 Xs Yl Y2 Y3 Y4 Ys 10 11 SP 15 18 21 24 27 30 33 3.00 4.00 2.00 5.00 3.00 1.00 6.00 4.00 2.00 7.00 5.00 3.00 8.00 6.00 4.00 9.00 7.00 5.00 10.00 8.00 6.00 11.00 9.00 7.00 12.00 10.00 8.00 13.00 11.00 9.00 9 18 27 36 45 54 63 72 81 90 99 9.00 10.00 4.00 11.25 2.25 12.60 1.60 1.00 14.00 1.25 2.25 15.43 1.03 3.60 16.88 0.88 5.00 18.33 0.76 6.43 19.80 0.67 7.87 21.27 0.61 9.33 22.75 0.55 10.80 2.00 3.75 3.00 5.40 5.00 7.00 6.75 8.57 8.40 10.13 10.00 11.67 11.57 13.20 13.13 14.73 14.67 16.25 16.20 15 30 45 60 75 90 105 120 135 150 165 15.00 18.00 10.00 21.00 11.25 5.00 24.00 12.60 5.00 27.00 14.00 5.25 30.00 15.43 5.60 33.00 16.88 6.00 36.00 18.33 6.43 39.00 19.80 6.88 42.00 21.27 7.33 45.00 22.75 7.80 2.00 3.75 3.75 5.40 6.40 5.00 7.00 8.75 6.75 8.57 10.97 8.40 10.13 13.13 10.00 11.67 15.24 11.57 13.20 17.33 13.13 14.73 19.39 14.67 16.25 21.45 16.20 0.25 0.60 1.00 1.00 2.25 3.00 1.43 3.60 6.00 1.88 5.00 9.00 2.33 6.43 12.00 2.80 7.88 15.00 3.27 9.33 18.00 3.75 10.80 21.00 PP PD DD 25 50 75 100 125 150 175 200 225 250 275 25.00 28.00 18.00 31.11 17.36 11.25 34.29 17.29 8.00 5.00 37.50 17.50 6.25 1.25 40.74 17.88 5.14 0.22 2.22 44.00 18.38 4.37 5.00 47.27 18.94 3.81 0.14 8.00 50.56 19.56 3.38 0.49 11.11 53.85 20.21 3.03 0.95 14.29 57.14 20.89 2.75 1.50 17.50 2.00 3.89 3.75 5.71 7.00 5.00 7.50 10.00 8.75 5.00 9.26 12.86 12.00 7.78 11.00 15.63 15.00 10.00 12.73 18.33 17.86 12.00 14.44 21.00 20.63 13.89 16.15 23.64 23.33 15.71 17.86 26.25 26.00 17.50 35 70 105 140 175 210 245 280 315 350 385 35.00 40.00 28.00 45.00 31.11 21.00 50.00 34.29 22.40 14.00 55.00 37.50 24.00 14.00 7.00 60.00 40.74 25.71 14.40 6.22 65.00 44.00 27.50 15.00 6.00 70.00 47.27 29.33 15.71 6.00 75.00 50.56 31.20 16.50 6.11 80.00 53.85 33.09 17.33 6.29 85.00 57.14 35.00 18.20 6.50 2.00 3.89 3.89 5.71 7.31 5.60 7.50 10.50 10.00 7.00 9.26 13.54 13.89 11.38 7.78 11.00 16.50 17.50 15.00 10.00 12.73 19.39 20.95 18.29 12.00 14.44 22.24 24.30 21.39 13.89 16.15 25.06 27.58 24.38 15.71 17.86 27.86 30.80 27.30 17.50 Yl Y2 Y3 Y4 s= 9 8 12 Zl Z2 Z3 Xl X2 X3 X4 Xs 7 9 Yl Y2 Y3 s= 6 6 Yl Y2 s= 5 3 Yl Zl s= 4 67 68 / 4 SPECTRA Table 4.9. (Continued.) 2 4 3 Zl Xl 0.29 0.40 0.50 1.00 1.00 0.74 1.71 2.40 2.22 X2 x3 X4 x5 X6 X7 Yl Y2 Y3 Y4 Y5 Y6 Y7 Zl Z2 Z3 Z4 Z5 Z6 Z7 4.6 9 10 11 1.00 2.50 4.00 5.00 5.00 1.27 3.33 5.71 8.00 10.00 1.56 4.20 7.50 11.11 15.00 1.85 5.09 9.33 14.29 20.00 2.14 6.00 11.20 17.50 25.00 FF 98 147 196 245 294 343 392 441 490 539 49.00 54.00 40.00 59.06 41.17 31.11 64.17 42.67 28.90 22.40 69.30 44.36 27.56 17.50 14.00 74.45 46.20 26.74 14.40 7.62 6.22 79.62 48.12 26.25 12.25 4.37 0.87 84.81 50.13 25.98 10.67 2.50 3.50 90.00 52.18 25.88 9.45 1.36 0.49 7.88 95.20 54.28 25.90 8.48 0.67 1.60 12.60 100.41 56.41 26.00 7.70 0.26 3.06 17.50 13.19 20.68 23.33 22.00 17.50 10.50 15.00 23.82 27.30 26.25 21.39 13.13 16.80 26.92 31.18 30.33 25.00 15.40 18.59 30.00 35.00 34.30 28.44 17.50 2.00 3.94 3.89 63 126 189 252 315 378 441 504 567 630 693 63.00 70.00 54.00 77.00 59.06 45.00 84.00 64.17 48.21 36.00 91.00 69.30 51.56 37.50 27.00 98.00 74.45 55.00 39.29 27.00 18.00 lO5.oo 79.62 58.50 41.25 27.50 16.88 9.00 112.00 84.81 62.05 43.33 28.29 16.50 7.50 119.00 90.00 65.63 45.50 29.25 16.50 6.88 126.00 95.20 69.23 47.73 30.33 16.71 6.60 133.00 100.41 72.86 50.00 31.50 17.06 6.50 2.00 3.94 3.94 5.83 7.62 5.79 7.70 11.14 10.94 7.50 9.55 14.55 15.71 13.71 9.00 11.38 17.88 20.25 19.25 15.63 10.13 13.19 21.15 24.62 24.38 21.21 16.00 10.50 15.00 24.38 28.88 29.25 26.25 20.63 13.13 16.80 27.57 33.04 33.94 30.95 24.69 15.40 18.59 30.74 37.14 38.50 35.44 28.44 17.50 0.06 0.17 0.21 0.30 0.56 0.50 0.45 1.00 1.29 1.00 0.62 1.50 2.25 2.50 1.88 0.81 2.05 3.33 4.29 4.50 3.50 1.00 2.63 4.50 6.25 7.50 7.87 7.00 1.20 3.23 5.73 8.33 10.71 12.60 14.00 1.41 3.86 7.00 10.50 14.06 17.50 21.00 Yl Y2 Y3 Y4 Y5 Y6 Xl 8 7 49 X2 X3 X4 x5 x6 X7 s= 6 0.11 Z2 Z3 Z4 Z5 s= 5 5.83 7.50 5.60 7.70 10.94 10.50 7.00 9.55 14.26 15.00 12.60 7.78 11.38 17.50 19.25 17.50 13.13 7.00 FG WAVELENGTHS AND WAVE NUMBERS Angstrom units (A) and microns (micrometers, JLm) are used for wavelengths in the tables presented in the following sections. Astronomers often indicate wavelengths in angstrom units by the A symbol. Wavelengths may be truncated after the last unit of an angstrom or they may be rounded off. We have 4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES j 69 tried to follow the latter procedure here, but there is no uniformity in the literature. Thus a line of Ca I at 4226.73 A might be called either >..4226 or >..4227. Wave numbers are almost always given in units of cm- i , although reciprocal microns are occasionally used. Common symbols for wave numbers are v, ii, and a. Many workers use the SI unit nanometer (nm) for wavelengths, 1 nm = 10 A. Wavelengths here are given "in air" for (air) wavelengths greater than 2000 A. Air and vacuum wavelengths are related by the index of refraction of air, n: Avacuum = nAair. An extensive tabulation [15] is based on Edlen's formula for n, n = I + 6432.8 x -8 10 2949810 8 2 10 - a + 146 x + 41 25540 OS 2' x I - a where a is the wave number in em-i. This formula suffices for conversions from air to vacuo when no more than eight-figure accuracy is desired [16]. For shorter wavelengths reciprocal wave numbers, or "vacuum wavelengths" are used. With the advent of space astronomy, some workers have suggested the exclusive use of vacuum wavelengths, but this has not been adopted here. Reader and Corliss [17] give a modem table of wavelengths of the chemical elements. They include lines that are suitable for use in calibration of most spectrographs. Extensive references to wavelength standards are given by Wiese and Martin [18]. 4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES Atomic hydrogen is considered separately here, in the nonrelativistic approximation in Table 4.10. Exact numerical values have been available from the early days of quantum mechanics [19]; they remain of heuristic as well as of practical value. For most cases of astrophysical interest, it is permissible to ignore the electron spin in hydrogen. Each level with a given I is then (21 + 1)- rather than 2(21 + I)-fold degenerate, and the weight of all states belonging to a principal quantum number n is n 2 rather than 2n 2 • The corresponding partition junction at low temperatures is then I and not 2; this must be used in the Boltzmann and Saba formulas when absorption or emission coefficients are calculated. Authors sometimes use a notation that is valid if spin is ignored with statistical weights that take spin into account [19,20]. Transitions may be designated nl ~ n'I', e.g., Is ~ 2p for Lyman ex in absorption. If spin is ignored, then the line strength S = I> (R~?,)2. The values for S in [20] and [21] allow for the spin degeneracy and are twice this value. The Einstein coefficients, line strengths, and f values must be defined in such a way that the intensities or equivalent widths of lines do not depend on whether spin is included in the level-counting scheme. For example, consider the equivalent width W{ of a weak hydrogen absorption line when light passes through a uniform slab of thickness H. If we use the Boltzmann formula to express the population of the lower level Ni as a function of the total population of neutrals NT, we have W{ = rre 2 g'fik -2A5NT-I-I-[1 - exp(hvjkT)]e-xi/kT H. me u(T) 'lltble 4.10. Radial integrals and absorption oscillator strengths Jor hydrogen. Line La LfJ Ly Transition Wavelength (A) (Rn'I' )2 nl Jabs Is-2p Is-3p Is04p 1215.67 1025.72 972.54 1.66479 0.266968 0.092771 0.4162 0.07910 0.02899 70 / 4 SPECTRA Table 4.10. (Continued.) (R,,'I')2 Line Transition Wavelength (A) Ha Ha Ha 2s-3p 2p-3s 2p-3d 6562.74 6562.86 6562.81 9.3931 0.8806 22.5434 0.4349 0.01359 0.6958 Hp Hp Hp 2s-4p 2p-4s 2p-4d 4861.29 4861.35 4861.33 1.6444 0.1462 2.9231 0.1028 0.003045 0.1218 labs ,,1 The factor [1 - exp(h v j kT)] allows for stimulated emission. Spin doubles the value of all statistical weights and the partition function u(T). Therefore, the sum of the gf's for transitions including spin must be double the corresponding sum of the gf's with spin ignored (g, = 21 + 1), in order to keep W{ the same. We use the convention that when a double subscript is written for an I or A value, the first subscript belongs to the initial level. A few authors follow a convention from atomic spectroscopy that the lower level is written first. Spin is ignored in calculating the absorption I values in Table 4.10 condensed from [21]. It is also possible to ignore the I degeneracy of hydrogen, so that only transitions of the form n ~ n' are considered. Let n and I be the initial levels and let n' and I' be the final ones. Then one defines average values of A as follows: Ann' = (ljn 2 ) L(21 + I)Anl-+n'I', II' For example, ~ ( IA 3s-+2p + 3A3p-+2s + 5A3d-+2p)' A similar definition holds for the absorption Inn" but with the weights for the initial, lower level. Thus: A32 = 123 = !(lf2s-+3p + 3/2p-+3s + 3/2p-+3d). Data for the major series in hydrogen from [21] are given in Table 4.11. Table 4.11. Average Einstein A's and absorption I's. Line Transition Wavelength (A) La Lp Ly Llimit Ha Hp Hy HI! HE HS Hlimit Pa Pp Py 1-2 1-3 1-4 1-00 2-3 2-4 2-5 2-6 2-7 2-8 2-00 3-4 3-5 3-6 3-00 1215.67 1025.72 792.54 911.8 6562.80 4861.32 4340.46 4101.73 3970.07 3889.05 3646 18751.0 12818.1 10938.1 8204 PIimit A (s-l) 4.699 5.575 1.278 labs X lOS 107 107 0.4162 7.910 X 10-2 2.899 X 10-2 4.410 X 8.419 X 2.530 X 9.732 X 4.389 X 2.215 X 107 106 106 loS loS loS 0.6407 0.1193 4.467 X 2.209 X 1.270 X 8.036 X X X 8.986 X 106 2.201 X 106 7.783 X loS 10-2 10-2 10-2 10- 3 0.8421 0.1506 5.584 X 10-2 4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES / 71 Table 4.11. (Continued.) Line Transition Wavelength (A) Ba 4-5 BfJ By Blimit 4-6 40512.0 26252.0 21655.0 14584 4-7 4-00 A (s-I) 2.699 7.711 3.041 X X X Jabs 106 105 105 1.038 0.1793 6.549 X 10- 2 In Table 4.12 for La and Ha , the additional states and lines due to electron spin are shown explicitly. The levels are designated with quantum numbers n,l, s, L, S, and J (appropriate to LS coupling). Wavelengths and levels are from [22]. The f and A values were generated from the expression for the line strength given above, using L p = 0 in the appropriate 6 - j symbol, and the numerical constants from [8]. Use of these constants accounts for small differences with other tabulated values. For example, our sum of the gf values for the two La lines is 0.8321, while twice the value for Is-2p given above is 0.8324. In Table 4.13, multiplet numbers are mostly from [23]. They are labeled with u when the ultraviolet table [24] is used. The values of log(gf) given without explicit references were derived from [25]. Asterisks preceding the wavelengths indicate blends, in which case the gf is for the blend as a whole. Accuracy assessments are indicated by letters [21]. References for the table are collected separately at its end. Uncertainties in the range of 25%-50% are indicated by the letter D, those from 10%-25% by a C, 3%-10% by B, 1%-3% by A, and within 1% by AA. The letter E is used for accuracies below 50%. The same scheme is followed for other sources when accuracy estimates are available. Table 4.12. La and Ha transitions with doublet structure. XI (em-I) X2 (em-I) glJI2 2p 2PI/2 2p 2 P3/2 0 0 82258.913 82259.279 0.2774 0.5547 3p 2 PI/2 3p 2P3/2 3s 2SI/2 3s 2SI/2 3d 2D3/2 3d 2D3/2 3d 2D5/2 82258.949 82258.949 82258.913 82259.279 82258.913 82259.279 82259.279 97492.205 97492.313 97492.215 97492.215 97492.313 97492.313 97492.349 0.2898 0.5796 0.02717 0.05434 1.391 0.2782 2.504 Wavelength (A) Lower Upper 1215.6737 1215.6683 Is 2SI/2 Is 2SI/2 6562.2720 6562.7256 6562.7520 6562.9099 6562.710 I 6562.8675 6562.8520 2s 2SI/2 2s 2SI/2 2p 2PI/2 2p 2P3/2 2p 2 PI/2 2p 2P3/2 2p 2P3/2 g2A21 x 10- 8 (s-I) 12.51 25.03 0.4485 0.8970 0.04204 0.08408 2.153 0.4305 3.875 Table 4.13. Atomic oscillator strengths Jor allowed lines. Multiplet Line Atom Transition Hell, Li llI, BeIv, B v, etc. Hydrogen-like ions have nearly the same J values as those for hydrogen. See discussion in [I] and [2] for Sc xXI-Ni XXVIII for higher-order effects. HeI Is2_ls2p Is 2-ls3p Is2_ls4p No. 2u 3u 4u Designation IS_I pO IS_I pO IS_I pO Ji - Jk 0-1 0-1 0-1 A (A) 584.33 537.03 522.21 log(gf) -0.5588 -1.134 I -1.5249 Accuracy AA AA AA Reference [3] [3] [3] 72 I 4 SPECTRA 1Bble 4.13. (Continued.) Multiplet Atom Transition Hel Is2s-ls2p No. (Cont.) 1s2s-ls3p Is2s-1s4p 1s2p-ls3s Is2p-1s4s Is2p-ls3d Is2p-ls4d 1s2p-1s5d 2 4 3 5 10 45 12 47 11 46 14 48 18 51 Is3s-1s3p Is3s-1s4p Line Designation Jj -J" 3S_3pO IS_I pO 3S_3pO IS_I pO 3S_3pO IS_I pO 3pO_3S IpO_IS 3pO_3S IpO_IS 3pO_3D IpO_ID 3 pO_3D IpO_ID 3 pO_3D I pO_I D 3S_3pO IS_I pO 3S_3pO IS_I pO 1-0, 1,2 0-1 1-0, 1,2 0-1 1-0, 1,2 0-1 0, 1,2-1 1-0 0, 1,2-1 1-0 0, 1,2-1,2,3 1-2 0, 1,2-1,2,3 1-2 0, 1,2-1,2,3 1-2 1-0,1,2 0-1 1-0, 1,2 0-1 A (A) *10830 20581 *3889 5016 *3188 3965 *7065 7281 *4713 5048 *5876 6678 *4472 4922 *4026 4388 *42947 74355 *12527 15084 log(gf) Accuracy Reference 0.2088 -0.4243 -0.7135 -0.8200 -l.1119 -l.3085 -0.2037 -0.8373 -l.0216 -l.5873 0.7397 0.3285 0.0436 -0.4427 -0.3737 -0.8866 0.4270 -0.2032 -0.8234 -0.8419 AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] Lil 2s-2p 2s-2p 2S_2pO 2S_2pO Ih-Ilh Ih-Ih 6708 6708 -0.0012 AA -0.3023 AA [3] [3] Bell 2s-2p 2s-2p 1 2S_2pO 1 2S_2pO Ih-Ilh Ih-Ih 3130 3131 -0.1772 AA -0.4783 AA [3] [3] CI 2p3s-2p3p 2 p 2_2s2 p 3 2p2_2p3s 2p 2_2p3d 2p3s-2p3p 2p3s-2p4p 2p3s-2p4p 3 pO_3D 31u 3p_3 sO 3u 3p_3DO 2u 3p_3pO u7 3p_3DO 10 I pO_IS 6 3pO_3p 11 I pO_I P 12 I pO_I D l3 IpO_IS 2pO_2p 2pO_2S 2pO_2D 2pO_2S 2pO_2D 2S_2pO 2pO_2S 2pO_2D 2D_2FO CII 2s 22p-2s2p 2 2s 22p-2s2p 2 2s 22p-2s2p2 2p-3s 2p-3d 3s-3p 3p--4s 3p-3d 3d-4f lu 2u 3u 4u 5u 2 4 3 6 Cm 2s 2-2s2p 2s 2-2s3p 2s3s-2s3p lu IS_I pO 2u IS_1 pO 1 3S_3pO 2-3 2-1 2-3 2-2 2-3 1-0 2-2 1-1 1-2 1-0 10691 0.345 945.6 -0.118 1561 -0.521 1657 -0.285 1278 -0.403 8335 -0.437 4772 -l.866 5380 -l.615 5052 -l.304 4932 -l.658 B C+ A A BB+ C B B B [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] Ilh-Ilh IIh-Ih IIh-2Ih Ilh-Ih Ilh-21h lh-llh Ilh-Ih Ilh-2lh 21h-3 1h 904.1 1037 1336 858.6 687.3 6578 3921 7236 4267 0.224 -0.310 -0.341 -l.284 0.082 -0.026 -0.232 0.298 0.717 B B B B B B B B C+ [3] [3] [3] [3] [3] [3] [3] [3] [3] 0-1 0-1 1-2 977.0 386.2 4647 -0.1200 A+ -0.634 B B+ 0.070 [3] [3] [3] 4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES I 73 Table 4.13. (Continued.) Line Multiplet -h log(gf) Accuracy -0.419 -0.721 -0.391 -0.194 A A AA [3] [3] [3] [3] 40.27 -0.1891 AA [3] 1112-2112 2112-3 112 l1/;rllh 21h-lIh 1199.6 8680 8629 4152 -0.285 0.346 0.Q75 -1.981 B+ B+ B C+ [3] [3] [3] [3] ~1 915.6 1085 5679.6 3995 500.2 -0.782 -1.071 0.250 0.215 0.592 B+ B+ A B+ C+ [3] [3] [3] [3] [3] 991.6 991.5 4097 4515 -0.357 -1.317 -0.057 0.221 B B B B [3] [3] [3] [3] 1-0. 1.2 1-2 765.1 247.2 *3481 4058 -0.2140 -0.486 0.238 -0.088 A+ B B B [3] [3] [3] [3] 2S_2pO 2S_2pO 2S_2pO 2S_2pO 1h-11/2 Ih-Ih 1h-1/2.11/2 1h-11/2 1239 1243 *209.3 4604 -0.505 -0.807 -0.321 -0.278 A A A A [3] [3] [3] [3] NYI Is 2-ls2p IS_lpO ~1 28.79 -0.1712 AA [3] 01 2p4_2p 33s 3 p_3SO Atom Transition CIY 2s-2p 2s-2p 2s-3p 3s-3p CY Is 2-ls2p NI 2p 3_2p 2 3s 2p 23s-2p 23p Designation Ji 2S_2pO 2S_2pO 2S_2pO 2S_2pO 1h-11h Ih-Ih Ih-Ih.11h 1h-11h IS_lpO ~1 2u 1 8 6 4sO_4p 4p_4Do 2p_2pO 4 p_4 sO 3 p_3pO 2p3p-2p3d 2u lu 3 12 19 Nm 2s 2 2p-2s2p 2 2s 22p_2s2 p2 3s-3p 2s2p3s-2s2p3p lu 2pO_2D lu 2pO_2D 1 2 S_2 pO 3 4pO_4D NIY 2s2_2s2p 2s 2-2s3p 2s3s-2s3p 2s3p-2s3d lu IS_I pO 2u IS_lpO 1 3S_3pO 3 1 pO_ID Ny 2s-2p 2s-2p 2s-3p 3s-3p lu lu 2u 2p 23s-2p 24p NIl 2s 22p2_2s2 p 3 2s 22p 2_2s2 p 3 2p3s-2p3p OIV I 3p_3DO 3pO_3D IpO_ID 3D_3Fo 1-1 2-3 1-2 ~ 1Ih-21h 11h- 11/2 1h-11/2 21h-3 1/2 ~1 ~1 1548 1551 *312.4 5801 Reference 3p_3Do 5sO_5 P 3sO_3p 3sO_3p 5p_5Do 4sO_4p 4sO_4p 4p_4DO 4p_4sO 4pO_4D 2-1 2-3 2-3 1-2 1-2 3-4 11/2-21/2 11/2-2112 21fr3 1/2 21/2-11/2 21h-3 1/2 1302 988.8 7772 8446 4368 6158 430.2 834.5 4649 3749 4119 -0.585 -0.634 0.369 0.236 -1.983 -0.409 -0.139 -0.268 0.307 -0.105 0.433 A B A B C B+ B+ B+ B+ B+ B+ [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] [3] 2p3s-2p3p 2p3p-2p3d lu 2u 2 14 3p_3DO 3p_3 pO 3 pO_3 D 3p_3Do 2-3 2-2 2-3 2-3 835.3 703.9 3760 3715 -0.358 -0.293 0.162 0.149 A A C+ C+ [3] [3] [3] [3] 2p-3d 2s 22p-2s2p 2 2s2p3s-2s2p3 p 5u 2pO_2D lu 2pO_2D 3 4pO_4D llh-21/2 llh-21/2 21h-3 1h 238.6 790.2 3386 0.258 -0.401 0.148 B B B [3] [3] [3] 2p 33s-2p 34p 2p 33p_2p 34d 2p 3_2p 23d 2s 2 2 p 3_2s2 p 4 2p 23s-2p 23p 2p 23p-2p 23d Om lu lu 2u 1 )..(A) 2u 5u 1 4 5 10 3u lu 1 3 20 2p 33s-2p 33p OIl No. 2s 22 p 2_2s2 p 3 74 / 4 SPECTRA Table 4.13. (Continued.) Multiplet Atom Transition No. Ov 2s 2-2s2p 2s 2-2s3p 2p3s-2p3p 2p3p-2p3d lu 'S-' pO 2u 'S-' pO 4 3pO_3D Ov, 2s-2p 2s-2p 2s-3p 3s-3p lu 2S_2pO lu 2S_2pO 2u 2S_2pO I 2S_2pO o VII Is 2-ls2p NeI 2p5 3s-2p 5 3p II Designation 3S_3 pO 'S_'pO Line Jj - Jk A(A) log(gf) Accuracy 0-1 0-1 2-3 1-2 629.7 172.2 4124 4159 -0.2905 -0.407 -0.066 -0.356 A+ B B B [3] [3] [3] [3] 'h-lih '/z-'h 'f:z-lih '/z-lih 1032 1038 150.1 3811 -0.576 -0.879 -0.451 -0.349 A A AA [3] [3] [3] [3] 0-1 21.60 -0.1584 AA [3] 2-3 6402 0.345 B 2'12-2'12 3694 0.09 D Reference Nell 2p4 3s-2p4 3p 4p_4pO NevI 2p-3d 2pO_2D 1'/z-2'h 122.7 0.313 D [3] NevIl 2s 2-2s2p 'S_'pO 0-1 465.2 -0.410 C [3] NevIll 2s-2p 2S_2pO 'f:z-lih 770.4 -0.689 B+ [3] NeIX Is 2-ls2p 'S_'pO 0-1 13.45 -0.141 A [3] NaI 3s-3p 3s-3p 3s-4p 3p-4s 3p-5s 2S_2pO 'f:z-I'h '/z-'h 'f:z-lih I'/z-'h 1'12-'12 lih-'h li/z-2'h lih-2'h li/z-2'h 5890 5896 3302 11404 6161 5153 8195 5688 4983 0.104 -0.197 -1.736 -0.163 -1.23 -1.732 0.51 -0.46 -0.962 A A C C C C C C C [3] [3] 0-1 2-1 I"'{} 2-1 2-3 1-2 0, I, 2"'{}, 1,2 2852 5184 11828 3337 3838 8807 *2780 0.29 -0.158 -0.27 -1.l0 0.414 -0.08 0.73 D B D C B D C 2796 2937 2798 *4481 9218 0.09 -0.23 -0.43 0.973 0.26 C C D C C 3p~s 3p-3d 3p-4d 3p-5d MgI 3s 2-3s3p 3s3p-3s4s 3s3p-3s5s 3s3p-3s3d 3s3p-3 p 2 I 2S_2pO 2 2S_2pO 3 2pO_2S 5 2pO_2S 8 2pO_2S 4 2pO_2D 6 2pO_2D 9 2pO_2D lu 2 6 4 3 7 6u 'S-' pO 3pO_3S lu 2u 3u 4 2S_2pO 2pO_2S 2pO_2D 2D_2FO 2 S_2 pO '/z-lih lih-'h 1'12-1'12 1'12,2'12-2'12,3'12 'h-lih 'pO_'S 3pO_3S 3 pO_3D 'pO_'D 3 pO_3 P MgIl 3s-3p 3p-4s 3p-3d 3d-4f 4s-4p MgIX 2s 2-2s2p 'S_'pO 0-1 368.1 -0.493 B Mgx 2s-2p 2s-3p 2S_2pO 2S_2pO '/z-lih '/z-lih 609.8 57.88 -0.775 -0.377 B B MgXI Is 2-ls2p 'S_'pO 0-1 9.169 -0.128 B 3p-4s 4s-5p 3p-3d 2pO_2S 2S_2pO 2pO_2D 1'12-'12 'f:z-lih lih-2'h 3962 6696 3093 -0.34 -1.343 0.263 C C C All 1 5 3 [4] [4] [4] 4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES / 75 Table 4.13. (Continued.) Multiplet Designation Ji -it A (A) log(gf) Accuracy 2u 4u IS_1 pO 3pO_3S 0-1 2-1 1671 1862 0.263 -0.192 B B lu 2 2S_2pO 2S_2pO If2-Ilf2 If2-Ilf2 1855 5696 0.047 0.235 B B 2s 2-2s2p IS_1 pO 0-1 332.8 -0.55 C 3p2-3p4s lu 43u 3 3u 4 5 6 3 p_3 pO ID_lpO IS_lpO 3p_3DO 3pO_3D 3 pO_3 P 3pO_3S 2-2 2-1 0-1 2-3 2-3 2-2 2-1 2516 2882 3906 2217 12031 10827 10585 -0.241 -0.151 -1.092 -0.55 0.41 0.16 -0.19 C C C C D D D Atom Transition No. AlII 3s 2-3s3p 3s3p-3s4s Al III 3s-3p 4s-4p Alx Sil Line 3s 2 3 p2-3s3 p3 3 p4s-3p4p Reference [4] [4] [4] [4] Sill 4s-4p 3d-4f 3s 23p-3s3 p 2 3s 23p-3s3p2 3p-3d 3p-4s 3p-4d 2 3 lu 5u 4u 2u 6u 2S_2pO 2D_2FO 2pO_2D 2 pO_2 P 2pO_2D 2 pO_2S 2pO_2D llz-Ilf2 2 If2-3If2 llz-Ilf2 Ilf2-11f2 111z-21f2 Ilf2-1f2 Ilf2-2 1f2 6347 4131 1808 1195 1265 1534 992.7 0.23 0.463 -2.14 0.49 0.52 -0.28 -0.15 C C D D D C D Si III 3s 2-3s3p 3s4s-3s4p 2u 2 4 IS_lpO 3 S_3 pO IS_1 pO 0-1 1-2 0-1 1207 4553 5740 0.22 0.292 -0.16 B C D [5] Silv 3s-3p 3s-4p 4s-4p lu 2u I 2S_2pO 2S_2pO 2S_2pO llz-llf2 llz-Ilf2 llz-Ilf2 1394 457.8 4089 O.oI B D B [5] -1.34 0.195 [4] SixI 2s 2-2s2p IS_lpO 0-1 303.3 -0.576 C SixII 2s-2p 2S_2pO llz-Ilf2 499.4 -0.845 B [6] SI 3p 34s-3p 34p 5S0_5 P 2-3 9213 0.42 D [4] SII 3s 2 3p 3_3s3p4 lu 4S0_4P Illz-2 112 1260 -1.31 C SIV 3p-4s 5u 2pO_2S Ilf2- 112 554.1 -0.425 C Sv 3s 2-3s3p 3s3p-3s3d lu 3u IS_1 pO 3pO_3D 0-1 0, 1, 2-1, 2, 3 786.5 *661.5 0.165 0.802 B B KI 4s-4p 4s-5p llz-llf2 1/Z-1lf2 7665 4044 0.135 -1.915 B C Cal 4s 2-4s4p 4s4p-4s5s 4s4p-4s6s 4s4p-4s4d 4s4p-4s5d 4s4p-4s6d 4s4p-4p 2 3d4s-3d4p 0-1 2-1 2-1 2-3 2-3 2-3 2-2 3-3 4227 6162 3974 4455 3644 3362 4303 5589 0.243 -0.089 -0.906 0.26 -0.306 -0.578 0.276 0.21 B C C C C C C D 1 2S_2pO 3 2S_2pO 2 3 6 4 9 11 5 21 IS_1 pO 3pO_3S 3pO_3S 3pO_3D 3 pO_3D 3pO_3D 3pO_3p 3D_3 DO 76 I 4 SPECTRA Table 4.13. (Continued.) Multiplet Atom Transition Call 4s~p 3d~p 4p-5s 4~ SCI Til 3d24s-3d24p 3d 34s-3d 34p 3d 34s-3d 24s4p Till VI Designation Jj -Jk A. (A) log(gf) Accuracy 1 2 3 4 2S_2pO 2D_2pO 2pO_2S 2pO_2D Ih- llh 21h-llh I1h- 1h llh-2 1h 3934 8542 3737 3179 0.135 -0.365 -0.15 0.51 e e e e 12 14 15 16 6 4F_4GO 4F_4DO 2 F_2 GO 2F_2FO 2D_2pO 4 1h-5 1h 41h-31h 5672 0.49 4744 0.42 5521 0.29 5482 0.27 4082 -0.57 No. 38 5F_5GO 42 5 F_5 FO 145 5 p_S DO 12 3 F_3 FO 24 3F_3GO 110 3F_3GO 2 7 4F_4 GO 4F_4FO 4 F_4 FO 21 22 27 88 109 14 29 41 125 114 6D_6 pO 6D_6FO 6 D_6 DO 4H_4HO 4 F_4 GO 4F_4 GO 6D_6pO 4D3FO 6Fo_6F 6GO_6H 3d24s_3d 24p 3d 3-3d24p ~4s-3~4p 3d44s-3d 34s4p 3d 34s4p-3d 34s5s 3d 34s4p-3d34s4d Line 31h~lh 3 1h-3 1h 2 1h-llh 5-6 5-5 ~ ~ 4-5 3~ 31~lh 41~lh 41~lh 41h-31h 41h-51h 41~lh 6 112-6 112 41h-5 1h 41h-51h 4112-3 112 31~lh 5 1h-5 1h 6 112-7112 4982 4533 4617 3999 3371 5036 0.504 0.476 0.389 -0.056 0.13 0.130 3361 3235 3323 0.28 0.336 -0.183 4460 -0.15 4379 0.58 4112 0.408 4269 0.65 4545 0.45 3185 0.69 3704 0.18 4091 0.33 5193 0.29 0.97 3695 VII 3d 34s-3d 34p 11 3 p_S DO 5 3F_3Do 25 S p_S DO 2-3 4-3 ~ 3903 3557 4202 en 3d S4s-3dS4p 7S_7 pO Ss_SpO 5G_SHO 5 D-S FO 7S_7 pO SG_S GO 3-4 2-3 6-7 4-5 3-4 6-6 4254 -0.114 5208 0.158 0.67 3964 4351 -0.44 3579 0.409 0.318 3744 41~lh 4041 3807 4031 2795 0.285 0.19 -0.47 0.53 3820 3581 4384 4272 4046 3816 0.119 0.406 0.200 -0.164 0.280 0.237 3d44s2-3d44s4p 3d S4s-3d44s4p Mnl 3d64s-3~4p 3d s4s2-3dS4s4 p Fel 3d74s-3d7 4p 7 38 22 4 43 5 6 2 lu 6 D_6 DO 6D_6FO 6S_6pO 6S_6pO 20 5F_SDO 23 5 F_S GO 41 3F_SGO 42 3F_3GO 43 3 F_3 FO 45 3 F_3 DO 4112-5 112 21h-31h 2112-3 112 5-4 5-6 4-5 4-5 ~ 4-3 -0.89 -0.17 -1.75 Reference [4] D D D D e e+ e+ e+ B e e+ e e+ e+ ee B eee ee eeB B D B B D- e B B e+ B e+ e B+ B+ B+ B+ B+ B [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [2] [2] [2] [2] [2] [7] 4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES / 77 Table 4.13. (Continued.) Multiplet Atom Transition No. Fel (Cont.) 3d 6 4s 2-3d 6 4s4p 4 5 D_5 DO 5 5 D_5 FO 68 5p_5DO 152 7DO_7 D 3d74s-3d 64s4p 3d6 4s4p-3d6 4s5s Designation Line Jj -It A (A) log(gf) Accuracy 4-4 4-5 3-4 5-5 3860 3720 4529 4260 -0.710 -0.431 -0.822 0.077 B+ B+ B+ B [2] [2] [2] [7] Reference Fe II 3d 6 4s-3d6 4p 27 38 4p_4Do 4 F_4 DO 2112-3 112 4112-3 112 4233 4584 -2.00 -2.02 C D [2] [2] COl 3d 84s-3d 84p 22 23 35 5 28 4F_4GO 4F_4FO 2F_2Fo 4F_4 GO 2F_2GO 4112-5 112 4112-4112 3 112-3 112 4112-5 112 3 112-4112 3454 3405 3569 3466 4121 0.38 0.25 0.37 -0.70 -0.32 C+ C+ C C C [2] [2] [2] [2] [2] 19 35 7 25 111 17 130 143 162 194 3 D_3 FO 3-4 2-3 4-5 3-4 5-5 3-3 2-2 4-5 3-4 3-4 3415 3619 3233 3051 5018 3374 4855 5081 5084 5081 -0.06 -0.04 -0.90 -0.12 -0.08 -1.76 0.00 0.13 0.03 0.30 C C C C+ D C D D DD- [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] 112-1112 2112-1112 1112-2112 3248 5106 5218 -0.056 -1.50 0.26 C D D 3d 74s2_3d 74s4p 3d 84s-3d74s4p Nil 3d 94s-3d 94p 3d 84s 2-3d 84s4p 3d94s-3d 84s4 p 3d 84s4p-3d 84s5s 3d 84s4p-3d 84s4d 3d 94p-3d 94d ID_IFo 3F_3GO 3 D_3 FO 5 FO_5 F 3D_5FO 3 pO_3 P 3FO_3G 3DO_3F I FO_IG CuI 4s-4p 3d 94s 2-3dI04p 4p-4d 1 2S_2pO 2 2D_2pO 7 2pO_2D Znl 4s4p-4s4d 4s4p-4s4d 4 6 3 pO_3D IpO_ID 2-3 1-2 3345 6362 0.30 0.158 B C SrI 5s 2-5s5p 2 IS_lpO ~1 4607 0.283 C SrIl 5s-5p 5d-6s 1 2S_2pO 3 2pO_2S 112-1112 1112-112 4078 4306 0.151 -0.11 C D Bal 6s 2-6s6p 2 IS_I pO ~1 5536 0.215 C BaIl 6s-6p 5d-6p 6p-6d 2 4 2S_2pO 2D_2pO 2pO_2D 112-1112 2112-1112 1112-2112 4554 6142 4131 0.163 -0.08 0.441 C D C 3 pO_3S ~1 1-2 2-1 4047 4348 5461 -0.81 -0.92 -0.185 D D C 2-1 4058 -0.18 D HgI 6s6p-6s7s Pbl 6p2-6p7s 3p_3 pO References 1. Martin, G.A., Fuhr, I.R., & Wiese, W.L. 1988, J. Phys. Chern. Ref Data, 17, Suppl. 3 2. Fuhr, I.R., Martin, G.A., & Wiese, W.L. 1988, J. Phys. Chem. Ref Data, 17, Suppl. 4 3. Wiese, W.L., Fuhr, I.R., & Deters, T.M. 1996, J. Phys. Chern. Ref Data Monograph, 7; and other data to be published 4. Wiese, W.L., Smith, M.W., & Miles, B.M. 1969, Atomic Transition Probabilities, Sodium Through Calcium, NSRDSNBS, 22 5. Morton, D.C. 1991, ApJS, 77,119 6. Wiese, W.L., Smith, M.W., & Glennon, B.M. 1966, Atomic Transition Probabilities, H Through Ne, NSRDS-NBS, 4 7. O'Brian, T.R., Wickliffe, M.E., Lawler, I.E., Whaling, W., & Brault, I.W. 1991, J. Opt. Soc. Am., 88,1185 78 / 4 SPECTRA 4.8 NUCLEAR SPIN AND HYPERFINE STRUCTURE: LOW-LEVEL HYPERFINE TRANSITIONS The angular momentum, or spin, of the ground levels of nuclei [26] can be of importance in atomic spectra and structure. Nonzero spins result from unpaired nucleons and occur for some isotopes of most elements. In elements with odd Z, the most abundant isotope will have a nonzero spin, so hyperfine structure is most important for these species. However, secondary (odd-N) isotopes of even-Z elements may make a significant contribution to the overall line shape. If the spin I is taken into account, the total angular momentum of an atomic level is F = J + I. The vectors J and I are added using the same rules as when L and S are added to form J. The quantum numbers F and 1 play analogous roles to J and S. Thus, for a given J and 1 there are 2I + 1 values of F if J > I, and 2J + 1 if 1 > J. The number of elementary states belonging to a level with a given F is 2F + 1, corresponding to the number of possible values of M F, the projection of F on the z axis in units of h. When there should be no ambiguity, MF may be written without the subscript M. Nuclear spin broadens spectral lines and adds 2I + 1 additional states to an atomic system. The first factor, known as hyperfine splitting, may usually be ignored if the resultant width is much smaller than that due to other broadening mechanisms, such as pressure or Doppler broadening. The additional atomic states cancel in the Boltzmann and Saba formulas and usually are not accounted for explicitly. The splitting of atomic levels due to nuclear spin (Il.EM) may be augmented (Il.EQ) if the nucleus has an electric quadrupole moment [27]: + 1) - J(J + 1) - 1(1 + 1)] == !AC, = B[C(C + 1) - jJ(J + 1)/(1 + 1)]. Il.EM = !A[F(F Il.EQ Values of A and B are given by [28]. Nuclear mass effects may be treated as follows. Let P be the momentum of the nucleus with mass M, and let Pi be the momentum of the ith electron. The kinetic energy is then p2 E= 2M We can eliminate P using P + Li Pi = E = P~ + ~2~' I 0, whence (2~ + 2~) ~pr+ ~ .~.Pi ·Pj· I I,J>I The first term is called the normal mass shift and gives rise to well-known displacements of lines in very light elements [29]. The second term, called the specific mass shift, is difficult to calculate [27] but may be measured in the laboratory. It can be significant even for heavy atoms [30]. Finally, nuclear volume, field effects, or isotope shifts occur because the potential at small r departs from a pure llr dependence due to the finite size of the nucleus. Astrophysically important consequences have been documented [31]. While the hyperfine width is difficult to calculate, the relative intensities of lines in a hyperfine multiplet follow readily from the quantum theory of angular momentum. The relative line strengths are written simply with a Wigner 6 - j symbol: S(J'I F' ~ J/ F) ex (2F + 1)(2F' + 1) { i, ~ F}2 J' The relative intensities are identical to those discussed for LS coupling, and the tables of Sec. 4.5 may be used with the substitutions J -+ F, S -+ I, and L -+ J. 4.9 FORBIDDEN LINE TRANSITION PROBABILITIES I 79 The celebrated 21-cm line in atomic hydrogen is an example of a pure magnetic dipole transition. Similar transitions occur in ionized 3He, as well as in deuterium. Results are summarized in Table 4.14, with 1986 constants and transition frequencies from [32]. The formula for magnetic dipole radiation simplifies in this case to Here, S~l) is a spherical tensor, analogous to cf.!), which operates in electron spin space. Quantum numbers Sn and Se describe the spin states of the nucleus and electron. For I H I and 3He II, g F' = 3, while for 2H I it is 4. The sums over M, M', and q are 3/4 for I H I and 3He II and 4/3 for 2H 1. The numerical coefficient is 4.01367 x lO-42 v 3 (cgs). We have neglected the magnetic moment of the nucleus. The ground state orbital functions are not indicated, since they contribute only a trivial multiplicative factor of unity. 4.9 FORBIDDEN LINE TRANSITION PROBABILITIES Most of the lines in Table 4.15 are forbidden in the sense that they involve no change in parity. A few intersystem lines are included. Both magnetic dipole (Ml) and electric quadrupole (E2) lines are possible at the same wavelength in many cases. The dominant radiation is indicated, but the A value is for the sum over all mechanisms, including electric dipole radiation (for intersystem lines). When both magnetic dipole and electric quadrupole transitions are permitted by their selection rules, the Einstein A coefficient for the magnetic dipole will usually dominate for optical transitions. Generally, AmI Aq ~ 3 X lOll la 2 , where a is the wave number of the transition. Typical A values for electric dipole transitions are 105 times larger than their magnetic dipole congeners. Accuracy estimates from [33-36] are indicated where available. The notation is the same as in Sec. 4.7. Table 4.14. Hyperfine transitions. IHI 2HI 3Hen I F' F v (Hz) A21 (s-I) 1/2 I 1/2 Il/2 I 0 1/2 0 1.420405752 x 109 3.273843523 x 108 8.665 649 867 x 109 2.876 x 10- 15 4.695 x 10- 17 6.530 x 10- 13 Table 4.15. Forbidden and intercombination lines. Atom Array He I] [e I] en] e III] [NI] Is 2-1s2p 2p2 2s 22p-2s2 p 2 2s2_2s2p 2p 3 Designation lower-upper IS_3 pO ID_1S 2pO_4p IS_3 pO 4S0_2DO 4sO_2DO Ji-Jk 0-1 2-'{} Il/2-21/2 0-1 Il/:z-Il/2 Ili2-21/2 A (A) 591.4 8727 2325.4 1908.7 5198 5200 A (s-I) Accuracy 1.76 x 10+2 0.634 52.6 114 2.26 x 10- 5 5.77 x 10-6 B B B+ e B MI or E2 Reference [1] E2 Ml E2 [2] [2] [2] [2] [2] 80 / 4 SPECTRA Table 4.15. (Continued.) Atom Array [Nil] 2p2 Nil] NIlI] NIY] [01] [011] [0 Ill] Om] OIY] OY] [FlY] [Ne Ill] 2s 22p2_2s2p3 2s 22p2_2s2p 3 2s 22p-2s2p 2 2s 2-2s2p 2p4 2p 3 2p2 2s 22p2_2s2 p 3 2s 22p2_2s2 p 3 2s 2 p_2s2p2 2s 2-2s2p 2p2 2p4 Designation lower-upper Jj-h ID_IS 3p_I S 3p_I S 3p_ID 3p_ID 3p_ID 3p_3p 3p_3p 3p_3p 3 p_5So 3 P_5S0 2pO_4p IS_3 pO ID-IS 3p_I S 3p_I S 3p_ID 3p_ID 3p_ID 3p_3p 3p_3p 3p_3p 2DO_2pO 2Do_2pO 2Do_2pO 2Do_2pO 4sO_2pO 2sO_2 pO 4sO_2DO 4 sO_2 DO ID_ 1S 3p_1D 3p_1D 3p_1D 3p_3p 3p_3p 3p_3p 3 p_5sO 3p_5sO 2pO_4p IS_3 pO 3p_1D ID-IS 3p_I S 3P_ 1S 3p_1D 3p_1D 3p_1D 3p_3p 3p_3p 3p_3p 2-0 2-0 1-0 1-2 2-2 0-2 1-2 0-2 0-1 2-2 1-2 lih-2lh 0-1 2-0 2-0 1-0 2-2 1-2 0-2 1-0 2-0 2-1 2lh-lih 1112-1112 2112-112 11h-lh lih-lih 11h-lh lih-2lh lih-lih 2-0 1-2 2-2 0-2 1-2 0-2 0-1 2-2 1-2 1112-2112 0-1 2-2 2-0 2-0 1-0 2-2 1-2 0-2 1-0 2-0 2-1 A (A) 5755 3071 3063 6548 6583 6527 121.8/Lm 76.45/Lm 205.3/Lm 2143 2139 1749.7 1486 5577 2958 2972 6300 6364 6392 145.5/Lm 44.06/Lm 63.19/Lm 7320 7331 7319 7330 2470 2470 3729 3726 4363 4959 5007 4931 51.81/Lm 32.66/Lm 88.18/Lm 1666 1661 1401.2 1218.3 4060 3342 1794 1815 3869 3967 4012 36.02/Lm 1O.86 /Lm 15.55/Lm A (s-I) 1.17 1.40 x 3.15 x 9.20 x 2.73 x 5.45 x 7.40 x 9.69 x 2.07 x 1.27 x 5.49 x 3.08 x 1.02 x 1.26 2.42 x 7.54 x 5.65 x 1.82 x 8.60 x 1.75 x 1.34 x 8.91 x 9.91 x 5.34 x 5.19 x 8.67 x 5.22 x 2.12x 3.06 x 1.78 x 1.71 6.21 x 1.81 x 2.41 x 9.76 x 3.17 x 2.62 x 5.48 x 2.20 x 1.47 x 3.68 x 9.25 x 2.72 1.88 2.02 0.159 4.92 x 9.60 x l.l5 x 2.19 x 5.97 x MI Accuracy orE2 B B B B B B B C B BBc+ B B+ 10-4 c+ 10- 2 B+ 10-3 B+ 10- 3 B+ 10-7 B+ 10-5 B+ 10- 10 c+ 10-5 B+ 10- 2 B 10- 2 B 10- 2 B 10- 2 B 10-2 c+ 10- 2 c+ 10- 5 C 10-4 C B 10-3 B 10- 2 B 10-6 c+ 10-5 B+ 10- 11 B+ 10-5 B+ 10+2 B 10+2 B 10+3 10+3 B 10- 2 B B B A A 10-2 A 10-6 B+ 10- 3 B+ 10-8 B 10- 3 A 10-4 10-2 10-4 10- 3 10-7 10-6 10- 13 10-6 10+2 10+ 1 102 10+3 E2 E2 MI MI MI E2 MI E2 E2 E2 E2 MI MI MI E2 MI E2 MI E2 E2 E2 E2 MI MI E2 MI E2 MI MI E2 MI E2 MI MI E2 E2 MI MI MI E2 MI E2 MI Reference [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [3] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] 4.9 FORBIDDEN LINE TRANSITION PROBABILITIES / 81 Table 4.15. (Continued.) Atom [NeIv] Array 2p 3 Designation lower-upper 2DO_2pO 2 DO_2 pO 2DO_2pO 2DO_2pO 4S0_2 pO 4S0_2pO 4S0_2DO 4S0_2DO 2DO_2pO [Nev] Nev] Si III] [S I] [S II] [S III] 2p2 2s 2 2p2_2s2 p 3 2s 2 2 p 2_2s2 p 3 3s 2-3s3p 3p4 3p 3 3p2 SIll] 3s 3 p2_3s3 p 3 [CI III] [CI IV] 3p 3 3p2 [ArIII] 3p4 ID_1S 3p_ID 3p_ID 3p_ID 3p_3p 3p_3p 3p_3p 3 P_5S0 3 p_5sO IS_3 pO ID_1S 2Do_2pO 2 DO_2 pO 2Do_2pO 2DO_2pO 4 sO_2 pO 4sO_2pO 4 SO_2 DO 4S0_2DO ID_1S 3p_I S 3p_I S 3p_ID 3p_ID 3p_ID 3p_3p 3p_3p 3p_3p 3 P_5S0 3 p_5sO 4sO_2Do ID-1S 3p_ID 3p_ID ID-1S 3p_I S 3p_ I S 3p_ID 3p_ID 3p_ID 3p_3p 3p_3p 3p_3p Ji-Jk 2lh-llh ll/:z--llh 2lh-Ih Ilh-lh llh-llh Ilh-lh llh-2lh ll/:z--llh Ilh-lh 2-0 2-2 1-2 0--2 1-2 0--2 0--1 2-2 1-2 0--1 2-0 2lh-Ilh Ilh-Ilh 2 1/:z-- lh Ilh-lh llh-llh Ilh-lh 1l/:z--21h I Ih-IIh 2-0 2-0 1-0 2-2 1-2 0--2 1-2 0--2 0--1 2-2 1-2 ll/:z--llh 2-0 1-2 2-2 2-0 2-0 1-0 2-2 1-2 0--2 1-0 2-0 2-1 A (A) 4714 4724 4716 4726 1602 1602 2424 2422 4726 2973 3426 3345 3300 MI A (s-I) 0.380 0.421 0.105 0.372 1.23 0.499 4.12 x 5.76 x 0.372 2.89 0.351 0.126 2.44 x 4.59 x 14.33 JLm 9.008 JLm 5.12 x 1.28 x 24.25 JLm 6.06 x 1146 2.37 x 1137 1.67 x 1892 7725 1.53 10320 0.179 10287 0.133 7.79 x 10370 0.163 10336 4069 0.225 9.06 x 4076 2.60 x 6716 8.82 x 6731 2.22 6312 1.05 x 3797 3722 0.796 5.76 x 9531 2.21 x 9069 5.82 x 8830 2.07 x 18.71 JLm 4.61 x 12.00 JLm 4.72 x 33.48 JLm 7.32 x 1729 2.66 x 1713 4.83 x 5538 2.80 5323 7.23 x 7531 0.179 8046 2.59 5192 4.17 x 3005 3.91 3109 0.314 7136 8.23 x 7751 2.15 x 8036 5.17 x 21.83 JLm 6.369 JLm 2.37 x 8.992JLm 3.08 x Accuracy B B B B B 10-4 10- 3 10-5 10- 3 10- 9 10- 3 10+3 10+3 10+4 B c+ C B B B B B A B+ A or E2 Reference MI MI [2] [2] [2] [2] [2] [2] [2] [2] [I] [2] [2] [2] [2] [2] [2] [2] [I] [ I] [3] [I] [I] [ I] [ I] [ I] [I] [I] [I] [ I] [ I] E2 MI MI MI E2 MI MI E2 MI MI E2 MI E2 MI E2 E2 10-2 10- 2 10-4 10-4 10- 2 10-2 10-2 10-6 10- 3 10- 8 10-4 103 103 10- 3 10-2 10-2 10- 2 10-5 10- 3 10-6 10- 2 MI E2 E2 MI MI E2 E2 E2 E2 MI MI MI E2 MI E2 MI MI E2 MI MI E2 E2 MI MI MI E2 MI E2 MI [ 1] [ I] [I] [I] [I] [I] [I] [ I] [3] [3] [I] [I] [I] [ I] [ I] [ I] [I] [I] [I] [I] [ I] [I] [ I] 82 I 4 SPECTRA 'Dable 4.15. (Continued.) Atom Array [ArIV] 3p 3 [ArV] [Arx] 3p2 2 p5 [ArXIV] [Klv] 2p 3p4 [Cav] [CaxII] [CaxIII] [Caxv] 3p4 2p5 2p4 2p2 [Fell] 3d64s-3d7 3d64s-3d54s 2 3d7 -3d64s [Fe III] 3d6 [Fe IV] [Fe v] 3d5 )d4 [Fe VI] 3d 3 [Fe VII] 3d2 [Fe x] [Fe XI] 3p 5 3p4 [Fe XIII] 3p2 [Fe XIV] [Fe xv] 3p 3s3p Designation lower-upper Jj-J" 2DO_2pO 2 DO_2 pO 2 DO_2pO 2 DO_2pO 4sO_2pO 4sO_2pO 4sO_2DO 4sO_2DO ID-1S 3p_IS 3p_I S 3p_ID 3p_ID 3p_ID 3p_3p 3p_3p 3p_3p 2 pO_2 pO 21frl lh llh-llh 21h-Ih llh-Ih llh-llh IIh-Ih llh-2lh 1Ih-I Ih 2-0 2-0 1-0 2-2 1-2 0--2 1-2 0--2 0--1 llh-Ih 2 pO_2 pO ID_1S 3p_ID 3p_ID 3p_ID 2 pO_2 pO 3p_3p 3p_3p 3p_3p 6D-4 p 6D_4 F 6D-6S 6D-6 S 4D-2p 4F_4 G 5D_3 F 5D-3 p 4G_4 F 5D-3 p2 5 D-3 F2 4F_4p 4F_2G 3F_3p 3F-ID lh-llh 2-0 1-2 2-2 2-2 Ilh-Ih 2-1 1-2 0--1 3 1h-21h 41h-4lh 41h-21h 3 1h-21h Ih-Ih 41h-5 1h 4-4 3-2 5 lh-4lh 3-2 4-4 41h-21h 41h-4lh 4-2 2-2 3-2 11h-lh 1-2 2-1 0--1 1-2 2-2 Ih-llh 1-2 2pO_2pO 3p_ID 3p_3p 3p_3p 3p_3p 3p_ID 2pO_2pO 3 pO_3 pO A(A) 7237 7171 7331 7263 2854 2868 4711 4740 4626 2786 2691 7006 6435 6133 7.903 1Lm 4.9281Lm 13.09lLm 5533 4412 4511 6795 6102 5309 3328 4087 5446 5694 4890 4416 4287 4359 5528 4244 4658 5270 4907 3895 3891 5677 5176 5276 5721 6087 6375 3987 7892 10747 10798 3389 5303 7059 A (s-I) 0.598 0.789 0.119 0.603 2.11 0.862 1.77 x 2.23 x 3.29 5.69 x 6.55 0.476 0.204 3.50 x 2.72 x 1.24 x 7.99 x 1.06 x MI Accuracy or E2 Reference 10-3 10-2 10-2 10-5 10-2 10-6 10-3 10+2 1.04 x 10+2 3.18 0.203 0.838 1.90 4.87 x 10+2 3.19 x 10+2 7.9 x 10+ 1 9.4 x 10+1 0.36 0.46 1.5 1.1 0.12 0.90 0.44 0.40 0.32 0.71 0.74 0.052 0.62 0.050 0.36 0.58 69.2 9.5 4.36 x 10+1 1.4 x 10+ 1 9.86 7.5 x 10+ 1 6.01 x 10+ 1 3.80 x 10+ 1 B A E E E E E E D D E D D E D E D D B DC+ C+ C+ E C+ C+ MI MI E2 MI MI Ml E2 Ml E2 E2 Ml MI Ml E2 Ml E2 MI MI [1] Ml E2 Ml Ml Ml Ml Ml Ml Ml MI Ml E2 E2 MI E2 Ml Ml E2 Ml Ml E2 Ml E2 MI Ml Ml MI Ml Ml Ml Ml Ml Ml [4] [1] [4] [4] [1] [1] [1] [I] [1] [1] [1] [1] [1] [1] [1] [1] [I] [1] [1] [1] [4] [1] [4] [4] [4] [4] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] [5] 4.10 SPECTRA OF DIATOMIC MOLECULES / 83 Table 4.15. (Continued.) Atom Array [Ni II] [Ni III] [Ni XII] [NiXIII] 3d9_3d 8 (3 F)4s 3d 9_3d 8 (3 P)4s 3d 8 3p 5 3p4 [Nixv] 3p2 [Nixvl] 3p Designation lower-upper Ji-Jk 2D_2F 2D_4p 3F_3p 2pO_2pO 3p_ID 3p_3p 3p_3p 3p_3p 2pO_2pO 2 1h-2 Ih 2 1h-2 Ih 4-2 11h-Ih 1-2 2-1 0-1 1-2 1/2-11/2 ).. (A) 6668 4326 6000 4231 3637 5116 6702 8024 3601 A (s-I) Accuracy 0.099 0.35 0.050 2.37 x 10+2 1.8 x 10+ 1 1.57 x 10+2 5.65 x 10+ 1 2.27 x 10+ 1 1.92 x 10+2 E E E B E C+ C+ C+ C+ M1 orE2 Reference E2 E2 E2 M1 M1 M1 M1 M1 Ml [5] [5] [5] [5] [5] [5] [5] [5] [5] References 1. Mendoza, C. 1983, in Planetary Nebulae, edited by D.R. Flower, lAU Symposium No. 103 (Reidel, Dordrecht), p.143 2. Wiese, W.L., Fuhr, 1.R., & Deters, T.M. 1996, J. Phys. Chem. Ref. Data Monograph, 7; and other data to be published 3. Morton, D.C. 1991,ApJS, 77,119 4. Kaufman, v., & Sugar, I. 1986, J. Phys. Chem. Ref. Data SeT., 15,321 5. Fuhr, I.R., Martin, G.A., & Wiese, W.L. 1988, J. Phys. Chem. Ref. Data SeT., 17, Suppl. 4 4.10 SPECTRA OF DIATOMIC MOLECULES 4.10.1 General Remarks Realistic calculations of astronomical spectra today involve the use of extensive databases such as HITRAN [37], RADEN [38], or the material assembled by Kurucz [39]. The proceedings of IAU Commission 14 [40,41] describe these sources and contain additional material, also covering polyatomic molecules. Recent texts [42,43] treat diatomic molecules. 4.10.2 Approximate Wave Function It is often assumed that the total wave function of a diatomic molecule may be written as a product containing electronic, vibrational, rotational, and nuclear spin components: 1/1 = 1/Ie1/lv1/lr1/ln. A more general situation is considered below. Traditionally, electronic spin is included in 1/Ie, but the nuclear spin wave functions are written separately. In the simplest cases, 1/Iv and 1/Ir are the functions describing the quantum oscillator and rotator. The latter are spherical harmonics. Sophisticated treatments of 1/Iv use realistic potential functions. In general, the rotational function 1/Ir may include electronic angular momentum. In this case, 1/Ir is described by symmetrical top wave functions [43,44]. For the rotational functions to have the proper behavior with respect to parity operations, it is often necessary to use linear combinations of symmetrical top functions. 4.10.3 Quantum Numbers and Notation Angular momentum vectors L and S have the same meanings as for atoms. These, and other (e.g., J) angular momenta, are often loosely referred to by the associated quantum numbers (L, S, J). R or 0 = angular momentum of nuclear (end over end) rotation. R = 0, I, .... N = total angular momentum apart from spin; formerly called K. 84 / 4 SPECTRA = total electron spin; (2S + I) is given as a pre-superscript. = projection of S on internuclear axis (can be positive or negative). J = total angular momentum exclusive of nuclear spin. A = component of electron orbital angular momentum along one internuclear axis, symbolized by 1:: (A = 0), n (A = I), f1 (A = 2), .... g = IA + 1:: I. A + 1:: is used as a term subscript (e.g., 4n_I/2, 4n3/2). I = total nuclear spin. F = total angular momentum including nuclear spin [not F(J); cf. below]. M = projection of vector J (MJ) or F (MF) on the z axis of the laboratory S 1:: coordinate system. F(J) = rotational energy in cm- I , FI, F2, .... A = spin-coupling constant; tabulated by [45] in footnotes. Y = AI Bv describes intermediate coupling; smalllYI =* case (b). v = vibrational quantum number, v = 0, I, . .. . Te = equilibrium electronic energy (or ''term value") in cm- I . G(v) = vibrational energy in em-I. voo = wave number of the 0--0 band of a band system. +, - describe the parity of electronic wave functions of 1:: states, viz., 1::+ and 1::-, with respect to reflection in plane of nuclei. g, u describe the parity of electronic wave functions in homonuclear diatomic molecules with respect to inversion of electronic coordinates. +, - describe the total parity of 1/1e 1/1v 1/1r for rotational levels with respect to inversion of all coordinates in the laboratory frame. s, a describe the parity of 1/Ie1/lv1/lr1/ln of homonuclear molecules with respect to exchange of two nuclei. 4.10.4 Angular Momenta and Hund's Cases [42-44,46,47] The quantum numbers A, 1::, and g all derive from the projection of vectors and are similar in nature to the numbers ML, Ms, and MJ of atoms. In the nomenclature of molecular spectroscopy, only positive values of these projections are commonly used. However, just as in the atomic case, positive and negative projections occur, and it is often necessary to employ both signs in the theoretical description of a molecular state. Case (a): J =L + S + R. The projection ofL, whose absolute magnitude is called A, is well defined, as is the projection of S, called 1::. Unlike atoms, molecules have their full multiplicity, and A ± 1:: is . · e.g., 4n 5/2, 4n 3/2, 4n 1/2, 4n -1/2. wntten as a sub scnpt, Case (b): L + R = N (formerly called K). N + S = J. Rotational levels, which may be labeled by the quantum number N, are split into 2S + I sublevels if N > S, and 2N + I sublevels if S > N. Case (c): L + S = J a . The quantum numbers A and 1:: are not "good," but the projection of Ja on the internuclear axis, g, is well defined. N + Ja = J, the total angular momentum. Case (c) is common for heavier molecules. 4.11 ENERGY LEVELS I 85 Case (d): L + R = N as in case (b), but the energy splitting due to spin and orbital angular momentum is very small. The vector J = S + N does not differ significantly from N, and energy levels are proportional to BvR(R + 1). 4.11 ENERGY LEVELS Approximate energy levels (in cm -1) may be calculated from the following formulas: Bv = + G(v) + F(J), We(v + !) - WeXe(V + !)2 + ... , J(J + I)Bv - J2(J + 1)2 D v , Be - ae(v + !) + ... , Dv De. T = Te G(v) = F(J) = ~ For accurate work it is necessary to consult relations specialized for individual molecules (see [45]). Electron spin manifests itself on molecular energy levels in a variety of ways that are not easily described by general formulas (see [44]). The splitting of 2n levels due to spin, for example, may be approximately described by the formulas below. Here, F1 and F2 refer to the levels with J = N + and J respectively. Y = AI B, as above. ! !, F1(1) = Bv F2(J) = Bv [(1 + [(1 + + !)2 + Y(Y - 4)A2] + ... , + !J4(J + !)2 + Y(Y - 4)A2] + ... . !)2 - A2 - !J4(1 !)2 - A2 Levels with A > 0 are twofold degenerate (±IML I). Rotation can lift this degeneracy, giving rise to A -doubled pairs of levels with opposite parity. See [42,48] for additional comments and notation (a, b, c, d, e, f> used to describe rotational levels. 4.11.1 Molecular Constants Tables 4.16 and 4.17 give the more important constants for selected electronic states of some common diatomic molecules of astrophysical interest. These constants are sufficient for approximate and heuristic work. For example, one may use them to locate lower-order bands and define their character (red or violet degredation). Accurate work would require the use of more elaborate formulas than can be written with these constants alone. Higher-order constants may be found in the papers cited. Table 4.16. Selected constants for diatomic molecules. a State Te We WeXe Be ae De re (A) 1.599 1.115 3.053 1.994(-2) 1.656(-2) 4.644(-2) 1.03 1.29 0.74 IH2. D8 = 4.478075 eV C In.. 2p1l" B IE;t2poX 1Etls0-2 100089.8 91700.0 0.0 2444.66 1357.19 4402.93 65.58 20.15 123.07 31.324 19.984 60.847 86 / 4 SPECTRA Table 4.16. (Continued,) State Te We d 3 ng BIIEt Bid c 3 E'! Ainu b 3 Eg a3nu xlEt 20024.597 15409.139 12082.336 9124.212 8391.408 6435.736 718.318 0.0 1788.2220 1424.119 1407.465 2085.899 1608.199 1470.415 1641.32959 1855.014 WeXe 12C2, Dg D2ni b 4 ni a 4 E+ B2E+ A2ni X 2 E+ 54486.3 44317 (36400) 25753.22 9243.308 0.0 1004.71 1148 (1400) 2160.38 1813.235 2068.648 a'3E+ a 3nr XIE+ 55825.~ 48686.70 0.0 1228.60 1743.41 2169.814 x2ni 0.0 3737.761 Be ae De re (A) 0.01907 0. 1175 0.016816 0.01255 0.016969 0.016312 0.0166625 0.01801 6.72(-6) 6.86(-6) 6.319(-6) 6.517(-6) 6.509(-6) 6.196(-6) 6.463(-6) 6.964(-6) 1.27 1.38 1.39 1.21 1.32 1.37 1.31 1.24 = 6.296 eV 16.4574 2.5711 11.4794 18.623 12.060 11.155 11.65195 13.555 1.755523 1.4810 1.463685 1.921 1.616628 1.49864 1.632365 1.82010 12C 14 N, Dg = 7.74eV 8.78 18.1 (20) 17.74 12.751 13.097 1.162 1.170 0.013 0.016 7(-6) 1.50 1.49 1.96879 1.71562 1.8997832 0.01996 0.01712 0.017372 6.58(-6) 6.129(-6) 6.406(-6) 1.15 1.23 1.17 0.01892 0.01904 0.0175 6.41(-6) 6.36(-6) 6.121(-6) 1.3523 1.20574 1.128 0.7242 19.38(-4) 0.96966 12C 16 0, Dg 10.468 14.36 13.2883 160 I H, Dg 84.8813 = 11.108 eV 1.3446 1.69124 1.9313 = 4.392 eV 18.910g Note aUnits are cm- I except as indicated. The power of ten to be applied to the entry for De is shown in parentheses. References: H2 [1-4]; C2 [5-15]; CO [1,16]; CN [17-21]. References 1. Huber. K.P.• & Herzberg. O. 1979, Molecular Spectra and Molecular Structure N. Constants ofDiatomic Molecules (Van Nostrand. New York) 2. Dabrowski, I. 1984. Can. J. Phys., 62.1639 3. Abgrall. H .• Roueff. E., Launay. F.• Roucin. J.-Y., & Subtil, J.-L. 1993. J. Mol. Spectrosc.• 1S7, 512 4. Balakrishnan. A .• Smith, & Stoicheff. B.P. 1992. Phys. Rev. Len.• 68. 2149 5. Douay. M .• Nietmann. R .• & Bernath, P.P. 1988.1. Mol. Spectrosc., 131. 250. 261 6. Prasad. C.V.V.• & Bernath. P.F. 1994,ApJS, 426, 812 7. Davis. S.P., Abrams. M.C .• Phillips. 10., & Rao. M.L.P. 1988. J. Opt. Soc. Am.. B5, 2280 8. Oalehouse. D.C .• Brault, J.W.• & Davis, S.P. 1980.ApJ. 42. 241 9. Simard, B .• & Hackett, P.A. 1991, J. MoL Spectrosc.• 148, 128 10. Phillips, J.O. 1973, ApJS. 26, 313 11. Hocking. W.H.• Gerry, M.C.L., & Merer, A.J. 1979. Can. J. Phys., 57. 54 12. Veseth. L. 1975. Can. 1. Phys.• 53. 299 13. Urdahl. R.S., Bao, Y.. & Jackson. W.M. 1991, J. Chem. Phys. Len., 178,425 14. Amiot. C .• Chauville. J.• & Maillard, J.-P. 1979. J. Mol. Spectrosc.• 75. 19 15. Davis. S.P.• Abrams. M.C .• Sandalphon, X.x.. Brault, J.W., & Rao. M.L.P. 1988, J. Opt. Soc. Am., B5, 1838 16. Eidelsberg. M .• Roncin. J.-Y, LeFloch, A., Launay, F., Letzelter. C .• & Rostas, J. 1987, J. Mol. Spectrosc., 121. 309 17. Ito. H .• Ozaki. Y.• Suzuki. K., Kondow. T., & Kuchitsu. K. 1992, J. Chem. Phys., 96. 4195 18. Huang. Y., Barts. S.A., & Halpern, J.B. 1992.1. Phys. Chem., 96.425 19. Ito, H .• Ozaki. Y.• Nagata, T .• Kondow. T.• & Kuchitsu. K. 1984, Can. J. Phys., 62, 1586 20. Prasad. C.V.V.• & Bernath. P.P' 1992. J. Mol. Spectrosc.• 156, 327 21. Kotlar. A.J .• Field, R.W., Steinfeld, J.I.. & Coxon, J.A. 1980. J. Mol. Spectrosc.• 80. 86 v.. 4.12 TRANSITIONS I 87 Table 4.17. Selected constants continued: nO.a State TO We WeXe Be re (A) ae De 0.489888 0.063062 6.627(-7) 1.69 0.506223 0.00318 6.97(-7) 1.67 0.003145 6.918(-7) 1.66 48n 16 0, Dg = 6.87 eV C3 a3 C3 a2 C 3al B3n2 B3nl B3nO bln A3~4 A3~3 A3~2 E3n2 E3nl E3nO dlI;+ ala x3a3 x3a2 x3al [19536.63] [19441.47] [19341.68] [16266.797] [16247.951] [16255.986] [14721.14] [14365.60] [14193.69] [14019.43] [12016.13] [11925.26] [11840.15] [5667.10] [3448.32] [202.6177] [97.8177] 0.0 838.2567 4.7592 [863.563] 919.7593 867.7799 4.2799 3.9422 0.507390 924 5.1 [0.5155] 1023.0585 1018.273 1009.1697 4.8935 4.521 4.5640 0.549320 0.537602 0.535431 1.65 0.003348 0.002916 0.003022 6.337(-7) 5.9(-7) 6.32(-7) 1.60 1.62 1.62 Note aUnits are cm- l except as indicated. The power of ten to be applied to the entry for De is shown in parentheses. For no the square brackets indicate that To is given rather than the usual Te. These apply to the v = 0 vibrational level. The constants We, etc., are the same for the levels split by spin-orbit interaction. References: TiO [1-4]. References 1. Gustavsson, T., Amiot, C., & Verg~, J. 1991, J. Mol. Spectrosc., 145, 56 2. Hildebrand, D.L. 1976, Chern. Phys. Lett., 44, 281 3. Merer, AJ. 1989,Annu. Rev. Phys. Chern., 40, 407 4. Brandes, G.R., & Galehouse, D.C. 1985, J. MoL Spectrosc., 109, 345 4.12 TRANSITIONS The upper level is written first, for both absorption and emission. Symbols describing the upper level have a single prime, while a double prime is used for the lower level. 4.12.1 Rotation and Vibration Rotational transitions in emission or absorption are assigned to P, Q, and R branches designated as follows for dipole radiation: P: J" ~ l' = J" - 1, Q: J" ~ J' R: J" ~ l' = J", = J" + 1. Transitions forbidden for electric dipole radiation can give rise to lines in an 0 branch (1" ~ J' = 1" - 2) and an S branch (JII ~ J' = J" + 2). In case (b), when the spin splitting is small with respect to the rotational separation of the energy levels, one can have P-, Q-, and R-form branches whose nomenclature depends on N ' and Nil. For 88 / 4 SPECTRA example, a line in a P-fonn Q branch would arise when J' *+ J", but N" *+ N' = N" - l. It would be labeled P Q. The branch labels also contain subscripts. The symbol Q Rl2 would designate a transition in a Q-fonn R branch from a lower level labeled F2 to an upper Fl. See [49] for additional notation. A common designation of rotational lines uses the J value of the lower level. Thus R(O) arises in transitions between J' = 1 and J" = 0 (in absorption from J" = 0 and in emission from J' = 1). Since J' = 0 *+ J" = 0 is forbidden for electric dipole radiation, Q(O) does not occur. The corresponding wave number is, however, called the band origin, voo or voo. Vibrational transitions are designated by the corresponding quantum numbers. For example, the (0-0) band means a transition from v' = 0 to v" = O. The quantum number for the upper vibrational state is written first. 4.12.2 Electronic Transitions In the spectra of diatomic molecules line strengths are defined in the same way as for atomic transitions, by a sum over the degenerate elementary states of both the upper and lower levels, which are labeled by M' and M": SPJ" = L i(1/IM'lp.I1/IM"} 12. M'M" This "line strength" is symmetrical in the upper and lower levels. The electric dipole moment, here written as 1£, is the sum of the electric moments (charge times displacement) of the electrons and nuclei. This vector must be in the fixed or laboratory frame. For convenience, it is transfonned to the frame of the molecule with the help of Euler angles. In practice, for a given transition, only one electron is important. The line strength for an electronic transition may be written as a product of three factors [50,51] The quantity Re is called the electronic transition moment. Its definition, consistent with the HonlLondon factor S (see below), is such that IRel = I{A'S':E'lzIA"S":E"}I, !:!.A = 0, = I(A'S':E'I (x ± iy)/-hIA"S":E)I, !:!.A = ±1, L Sp JII = (2 - 8o, A' 80, A" )(2S + 1)(21 + 1). This nonnalization [50] holds for absorption or emission. In the fonner case, the value of J on the right-hand side is J", while in the latter it is J'. The Kronecker 8 functions are zero if A' or A" is not equal to zero, and are unity otherwise. Consider a given J (J' or J"). It is necessary to sum the rotational strengths S for all allowed transitions from the (2 - 80,A)(2S + 1) levels with a given J for which transitions are allowed. Thus the sum extends over more than one energy level in general and includes lines with the same J that arise from A doubling. If A doubling is present in both upper and lower levels, the number of allowed lines is exactly twice that which would result if there were no degeneracy. However, if only one of the upper or lower levels is doubled, the resulting number of allowed lines is the same as if neither upper nor lower were doubled because of the selection rule on parity. The sum of these strengths may not equal the theoretical value for low levels where the full spin multiplicity (oflevels) has not developed [43]. 4.13 SELECTION RULES: DIPOLE RADIATION / 89 The recommended nonnalization follows naturally if the rotational strengths are written with n - j symbols [47,52]. Thus for Hund's case (a), we have S = (2J' + 1)(2J" + 1) (~ 0" ~ 0' J" -0" )2 The symbol in the large parentheses is a Wigner 3 - j symbol. This fonnula also holds for cases (c) and (d), in the latter instance with the replacement of 0 by A. These cases are of less importance for molecules of astrophysical interest. For case (b), it is necessary to decouple the electron spin, and this introduces a 6 - j (curly bracket) symbol: S = (2J ,+ 1)(2N,+ 1)(2J"+ 1)(2N,,{N' + 1) J" 1 S N"}2 (N'A' J' 1 A" - A' N" -A" )2 Pure Hund cases are only approximations to the more general description of molecular levels by intermediate coupling. Intensity fonnulas have been given by various authors, e.g., [53-55], and Whiting [56] has published a program for the S's consistent with the above summation rules. We recommend use of the Whiting code for all but I:-I: transitions, which are inherently case (b). It is often useful to have guides to the rotational structure of electronic transitions. In addition to the basic reference [44] useful diagrams may be found in [49, 51, 57]. Oscillator strengths and Einstein coefficients are related to S J' J" by the same fonnulas as for atoms (Sec. 4.4). 4.13 SELECTION RULES: DIPOLE RADIATION Many selection rules for diatomic molecules can be inferred from the properties of the n - j symbols of Sec. 4.12; the relevant 3 - j or 6 - j symbol will vanish for the forbidden transition. For example, we can infer for electric dipole radiation fl.J = 0, ±1 with J = 0 ~ J = O. Similarly, we have fl.0 = 0, ±l for case (a) and fl.A = 0, ±1 for case (b). Case (b) also has fl.N = 0, ±1 and N = 0 ~ N = O. The 3 - j symbol vanishes if N' = N" while A' = A" = 0; consequently, fl.N = 0 is forbidden for I: ~ I: transitions [case (b)]. Similarly fl.J = 0 for 0 = 0 ~ 0 = 0 [case (a)]. The total spin operator commutes with the dipole moment; consequently, fl.S is forbidden for electric dipole radiation. In case (a), where I: is well defined, we also have fl. I: = O. Symmetry of the electronic wave functions prevent I: + from combining with I: -, while symmetry of the overall wave functions prevent positive-positive and negative-negative transitions. For homonuclear molecules gerade-gerade and ungerade-ungerade transitions are prohibited, while symmetric-antisymmetric rotational transitions cannot occur. 4.13.1 Parameters for Selected Electronic Transitions Table 4.18 gives parameters for line-strength calculations in a few diatomic band systems of astrophysical interest. The material is primarily for heuristic use. For detailed calculations it is necessary to consult the sources cited. Entries are primarily from the RADEN database [38]. The first three columns identify the systems and give wavelength ranges, following [58]. A very useful table of persistent band heads is given in [59]. The fourth column contains the band origin for the 0-0 band. The following columns provide information relevant to line-strength calculations. Entries are for r-centroid [Re(rv'v")] and ab initio [Re(r)] calculations. The fonner are used with Franck~ondon factors (qv'v") while the latter involve an integration of Re(r) over the vibrational wave functions. The final column of the table gives square of the transition moment for the 0-0 band, by the two methods, with vibration included. A superscript a in this column indicates R50 = R;(roo)qoo, while b indicates R50 = I{v' = OIRe(r)lv" = 0)12. Comet tail CO+ ",,5015-6450 H4700-6100 H2680-5450 H2800-5900 "i..3 020-3 680 U1950-3400 A 2n-x 2E+ Second positive C 3 n u-B 3 n g First negative B 2Et -x 2Et A 3n_x 3E- y system A 2E+_X 2n MgH N2 N+ 2 NH NO 44080.5 44200.2 29776.76 25566.04 29671.0 19278.4 17837.8 99120.17 HI 028-1 239 LaO H2 90203.55 ",,955-1674 A 2n_x 2E+ Lyman B I Et-X lEt Werner C Inu-x lEt B 2E+_X 2E+ H2 20407.6 64 748.48 HI 115-1544 (abs.) ",,2006-2785 (emiss.) 4th positive A In_x IE+ CO ",,3080-8500 25797.84 H3440-4600 Violet B2E+ - X 2 E+ eN 1.1091 0.9999 1.0559 0.1639 1.0995 0.6636 1.8424 0.944 1.7270 0.4545 1.184 3 1.1783 0.0037 0.%24 0.1217 0.8937 0.8604 1.1806 0.0422 1.1658 0.1150 1.2062 0.9180 9117.38 Red system A 2n_x2E+ H4370-15050 23217.5 H4314-4890 (A) 0.7244 1.2938 0.5445 roo qoo 1.2913 0.9907 1.1313 0.4957 25969.19 CN CH Deslandresd'Azambuja C Ing-A Inu A 2 6-X 2 n H3390-4110 19378.44 i..i..3 400-7 850 Swan d 3ng-Q 3nu C2 (cm- I ) Ii(J() Approx. range (A) System Molecule Re(rv'v") = (1.86±0.17)(1...{}.51rv'v") forrv'v" = 1.05-1.35 A. Re(r) = 0.887 exp[-3.30(r - 0.95)] for r = 0.95-1.40 A. Re(rv'v") = (12.12 ± 0.01)(1-1.63Irv'v" +0.70rv'v") for rv'v" = 0.97-1.16 A. Re (r) = 1.051 + 0.203 3r...{}.4646r 2 for r = 0.85-2.65 A. (Re) = 0.210 ± 0.006. See (7) for Re(r), r = (1.25-20.0)"0. Re(rv'v") = (26.8± 1.5)(I-2.8986r v'v" +2. 749 9r~, v,,"'{}·8597r~, v") for rv'v" = (1.0-1.20)"0' See (8) for Re(r), r = (1.6-2.4)"0' See [2] for R.(r), r = (1.0-12)"0' See [6] for Re(r), r = (1.0-10.0)"0' Re(rv'v") = 348(-1 + 1.74275rv'v" -0.9%36r;,v" + 1.8803r~,v") for rv' v" = 1.6-2.1 A. (Re) = 1.22 (Re) = 0.280 ± 0.008. See (2) for R.(r), r = (1.3-4.0)"0' R.(rv'v") = (0.19±0.03)(1 +0.571rv'v") forrv'v" = 1.05-1.27 A. See (3) for R.(r), r = (1.4-4.0)"0' Re(rv'v") = (0.72 ± 0.02)(I-{J.03rv'v") for rv'v" = 0.95-1.35 A. See (3) for Re(r), r = (1.6-4.0)"0' Re(rv'v") = (2.94 ± 0.15)(1...{}.68rv'v") for r v'v" = 1.0-1.3 A. See (4) for R.(r), r = (1.8-8.0)"0' See [5] for R.(r), r = (1.4-3.1)"0' Re(rv'v") = (2.380±0.28)(I-0.52r v'v") for r v' v" = 1.12-1.50 A. See [I). Figure of Re(r) for r = (2.0-3.5)ao. Recommended electronic transition moment (e"O) Table 4.18. Parameters for molecular transition strengths. (e"O)2 0.0026b O.044la 0.0463b 0.0031 a 0.326b 0.325a 0.25b 0.24a 1.42a 2.23a 0.D785b 0.0054~ 0.0371b 0.00158 b 0.427b 0.0386a 0.0426b 0.442a 0.D78a 0.084b 0.0511 a 0.54b O.44la Rfu > ~ ~ () tr1 "C en .f;>. ........ \0 0 ),),3863-4278 A 2t;_X 2n a system; SiH no a system; ZrO 21631.48 21548.46 21536.36 16033.81 15741.31 15426.78 14163.00 14095.88 14019.43 16722.75 16294.72 17420.2 19334.03 19343.66 19341.68 17840.6 24193.04 32402.39 49358.15 "00 (em-I) (A) 1.7448 1.7564 0.973 1.6448 0.9950 1.7940 0.3130 1.633 I 0.672 1.6590 0.9152 1.6313 0.7191 1.0080 0.9932 1.5459 0.4092 For band (15.0) 0.000272 1.3107 0.9067 roo qOO (Continued.) 0.085a = 0.52. See (10). for Re(r) for r = (2.8-3.8)ao. 2.63b 0.97 b 3.33a 5.24a 4.63 a 0.084a = 1.83. = 2.7. = 2.25. See (10). for Re(r). r = (2.8--3.8)"0' (Re) (Re) (Re) (Re) Re (r v' v") = (102 ± 25) exp( - 2.57rv' v" ) for r v'v" = 1.58-1.72 A. 0.062I a O.OlOgb 0.00953a For (15.0) band 0.000 175a Re(rv'v") = 1.86-0.8069,v'v" for rv'v" = 1.30--2.16 A. Re(rv'v") = (0.42 ± 0.01)(I.0--0.75r v'v") for r v' v" = 0.8-1.2 A. See (9) for Re (,)., = (1.3-4.4)ao. (Re) = 0.25 ± 0.03. R& (e"O)2 Recommended electronic transition moment (e"O) References I. Chabalowski, C.F., Peyerimhof, S.D., & Buenker, R.1. 1983, J. Chern. Phys., 81. 57 2. van Dishoeck, E. 1987, J. Chern. Phys., 86,196 3. Bauschlicher, C.w., Langhoff, S.R., & Taylor, P.R. 1988, ApJ. 332, 531 4. Kirby, K., & Cooper, D.L. 1989, J. Chern. Phys., 90, 4895 5. Marian, C.M., Larsson, M.• Olsson, B.1., & Sigray, P. 1989, J. Chern. Phys., 130, 361 ApJ. 332, 531 6. Dressler, H., Wolniewicz, L. 1985, J. Chern. Phys., 82, 4720 7. Kirby, K.P., & Goldfield, E.M. 1991, J. Chern. Phys .• 94. 1271 8. Langhoff, S.R., Bauschlicher, C.W., & Partridge. H. 1988, J. Chern. Phys.• 89. 4909 9. Bauschlicher, C.W., & Langhoff, S.R. 1987, J. Chern. Phys., 87, 4665 10. 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Leckrone, D.S., Wahlgren, G.M., & Johansson, S. 1991, ApJ, 377, L37 32. Hinds, E.A. 1988, in The Spectrum of Atomic Hydrogen: Advances, edited by G.W. Series (World Scientific, Singapore) 33. Fuhr, J.R., Martin, G.A., & Wiese, WL. 1988, J. Phys. Chern. Ref Data. SeT., 17, Suppl. 4 34. Kaufman, v., & Sugar, J. 1986, J. Phys. Chem. Ref Data. SeT., 15, 321 35. Morton, D.C. 1991, ApJS77, 119 36. Wiese, WL., Fuhr, I.R., & Deters, T.M., 1996, J. Phys. Chem. Ref Data Monograph, 7 37. Rothman, L.S., Gamache, R.R, Tipping, R.H., Rinsland, C.P., Smith, M.A.H., Benner, D.C., Malathy Devi, V., Flaud, I.-M., Brown, L.R, & Toth, RA. 1992, J. Quant. Spectrosc. Rad. Transf, 48, 469 38. Kuznetsova, L.A. et al. 1993 (Russian) J. Phys. Chem., 67,11 39. Kurucz, R.L. 1994, in Molecules in the Stellar Environment, Lecture Notes in Physics, edited by U.G. If1)rgensen (Springer, Berlin), Vol. 428, p. 282; see also Kurucz CD-ROM No. 15 (Smithsonian Ap. Obs., Cambridge, MA), 1993 40. Parkinson, W.H. 1992, in Atomic and Molecular Data for Space Astronomy, Lecture Notes in Physics, edited by P.L. Smith and W.L. Wiese (Springer, Berlin), Vol. 407,p.149 41. If1)rgensen, U.G. 1994, in Molecules in the Stellar Environment, Lecture Notes in Physics, edited by U.G. If1)rgensen (Springer, Berlin), Vol. 428, p. 29 4.13 SELECTION RULES: DIPOLE RADIATION / 93 42. Bernath, P. 1995, Spectra of Atoms and Molecules (Oxford University Press, Oxford) 43. Zare, R.N. 1988, Angular Momentum (Wiley, New York) 44. Herzberg, G. 1950, Spectra of Diatomic Molecules, 2nd edited by (Van Nostrand, New York) 45. Huber, K.P., & Herzberg, G. 1979, Molecular Spectra and Molecular Structure Iv. Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York) 46. Gordy, W., & Cook, R.L. 1984, Microwave Molecular Spectroscopy (Wiley, New York) 47. Judd, B. 1975, Angular Momentum Theory for Diatomic Molecules (Academic Press, New York), see pp. 184186 48. Brown, J.M., Hougen, J.T., Huber, K.-P., Johns, J.W.C., Kopp, I., Lefebvre-Brion, H., Merer, A.J., Ramsay, D.A., Rostas, J., & Zare, R.N. 1975, J. Mol. Spectrosc., 55,500 49. Tatum, J.B. 1967,ApJS, 24, 3 50. Whiting, E.E., Schadee, A., Tatum, J.B., Hougen, J.T., & Nicholls, R.W. 1980, J. Mol. Spectrosc., SO, 249 51. Morton, D.C. 1994, ApJS, 95,301 52. Edmonds, A.R. 1960, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton) 53. Schadee, A. 1964, Bull. Astron. Netherlands, 17, 311 54. Kovacs, I. 1969, Rotational Structure in the Spectra of Diatomic Molecules (Elsevier, Amsterdam) 55. Whiting, E.E., Paterson, J.A., Kovacs, I., & Nicholls, R.W. 1973, J. Mol. Spectrosc., 47, 84 56. Whiting, E.E. 1973, NASA Tech. Note D-7268 57. Herzberg, G. 1971, The Spectra and Structure of Simple Free Radicals (Cornell University Press, Ithaca) 58. Rosen, B. 1970, Spectroscopic Data Relative to Diatomic Molecules (Pergamon, New York) 59. Pearse, R.W.B., & Gaydon, A.G. 1976, The Identification of Molecular Spectra, 4th ed. (Chapman and Hall, London) Chapter 5 Radiation J.J. Keady and D.P. Kilcrease 5.1 5.1 Radiation Quantities and Interrelations. . . . . . . .. 95 5.2 Refractive Index and Average Polarizability. . . . .. 100 5.3 Absorption and Scattering by Particles. . . . . . . .. 102 5.4 Photoionization and Recombination . . . . . . . . . . 106 5.5 X-Ray Attenuation . . . . . . . . . . . . . . . . . . . . 109 5.6 Absorption of Material of Stellar Interiors. . . . . .. 110 5.7 Absorption of Material of the Solar Photosphere. .. 114 5.8 Solar Photoionization Rates . . . . . . . . . . . . . .. 114 5.9 Free-Free Absorption and Emission . . . . . . . . .. 115 5.10 Reflection from Metallic Mirrors . . . . . . . . . . .. 117 5.11 Visual Photometry . . . . . . . . . . . . . . . . . . . .. 117 RADIATION QUANTITIES AND INTERRELATIONS The quantitative concepts of radiation are defined [1] in terms of /, the flux of radiation at a given point in a given direction across a unit surface normal to that direction per unit time and per unit solid angle. This is called specific intensity, or simply intensity. The flux of radiation through a unit surface is the sUrface flux, or flux density, :F = 1/ cos 4:71" e dw, where e is the angle between the ray and the outward normal and integration is in all directions. 95 96 I 5 RADIATION The emittance is the flux of radiation emitted from a unit surface, r f21r I = cos () d w for isotropic radiation 7t I, where in this case the integration is over the outward hemisphere. The radiation density is u = (lIe) { I dw J4rr = (47tje)i. The radiation quantities per unit frequency and wavelength ranges are written lv, 1)., rv, etc.: I I). dA = f Iv dv = f I). dA, v2 e = -2 Iv = -Iv, A e A2 AI). e = --dv = -"2dv, e v = vlv, e = Av. The linear absorption coefficient is Ks: dl jds = -KsI. The scattering coefficient as. is similar to the absorption coefficient but applies to the radiation scattered. It is used in the sense that Ks - as represents absorption and transference into heat. The mass absorption coefficient is Km (the subscript is usually omitted): dl jds = -PKml, where P is the density. The atomic or particle absorption coefficient or cross section is a: dljds = -Nal, where there are N atoms or particles per unit volume and a represents the effective area over which the incident radiation if fully absorbed. The emission coefficient j is the radiant flux emitted per unit volume and unit solid angle. For uniform scattering, j = (a j47t) { J4rr I dw, where the first term represents scattering and the integral represents incident radiation. For scattering by electrons, atoms, molecules, where () is the angle between incident and scattered light. I is assumed to be unpolarized, and the scattered radiation when viewed at the angle () is polarized with intensity proportional to cos 2 () in the plane of scattering and proportional to I in the direction perpendicular to the plane of scattering. 5.1 RADIATION QUANTITIES AND INTERRELATIONS I 97 The optical thickness or depth is r = f f Ks ds = pKm ds. The source function is S = jlKs. The intensity emitted from an absorbing medium is 1= f j exp{-r) ds = f S exp{-r) dr. We show two forms of the Kirchoff law: (a) In a volume element, jv = Ks.vBv{T), where Bv(T) is blackbody intensity at temperature T. (b) At a surface element, Iv = AvBv{T), where Av is the fraction of incident radiation absorbed, i.e., I - Av is the reflection coefficient and analogous to albedo. The atomic polarizability a is the induced dipole moment per unit electric field (& for a steady or low-frequency field): & = 4a5 L in I{vnI cRoo)2 n = 5.927 x 10- 25 = 7.138 x 10-23 L in/{vnlcRoc,)2 cm3 n L inA~ cm 3 (A in jlm), n where vn/cRoo is the frequency in rydbergs of lines connecting the ground level and in is the corresponding oscillator strength. For scattering, as = (128rr 5 /3)N{vlc)4a 2 = (128rr 5 13A4)Na 2 = 1.3057 x 1020 Na 2 IA 4 (A in jlm). The index of refraction is n: n-I=2rrNa = 1.688 x lO20a at STP. 98 / 5 RADIATION The molecular refraction is R n2 - 1 M 41l' =- - = -Noa, n2 + 2 p 3 where M is the molecular weight, p is the density, and No is the Avogadro number. The radiation constants are Cl = 21l'hc2 = 3.74177 x 10-5 ergcm2 s-I, C2 = hc/ k = 1.43877 cmK. The Stefan-Boltzmann constant is U = 21l' 5 k 4J(15c 2 h 3 ) = 1l'4CJ J(l5ci) = 5.6705 x 10-5 ergcm- 2 s- 1 K- 4 . The blackbody emittance is The blackbody intensity is The radiation density u in a cavity at temperature T is In a medium of refractive index n, B u = n 2 (u/1l')T 4, = n 3 (4u/c)T 4 , with similar factors applying for the Planck law with nv and n).,. The photon emission constant is p = 41l'~(3)c/c~ = 1.520486 x where ~ (n) is the Riemann zeta function. 10 11 photonscm- 2 s- 1 K- 3 , 5.1 RADIATION QUANTITIES AND INTERRELATIONS / 99 The photon flux from a unit blackbody surface is Blackbody radiation is unpolarized, hence the intensity of radiation linearly polarized in a specific direction will be half the value quoted in the formulas. The Planck function in wavelength units is (C/4)UA = rr BA =:FA = 2rrhc2 A-5 /(e hc / HT = ClA -5 /(e C2 / AT - 1) - 1) (A in cm), where U A , B A , and:FA are the radiation density, intensity, and emittance for unit wavelength ranges. The Planck function in frequency units is The photon distribution law is NA = 2rrCA -4 /(e C2 / AT - 1), N v = 2rrc-2v2/(ehv/kT - 1), where NA and N v are the emittance of photons per squared centimeter per second and per unit wavelength and frequency ranges, respectively. The Rayleigh-Jeans distribution (for the red end of the spectrum) is :FA = 2rrckTA -4 = (Cl/C2)TA -4, :Fv = 2rrc- 2kTv 2 = 2rrkTA -2. The Wien distribution (for the violet end of the spectrum) is :FA :Fv = 2rrhc2A-5e-C2/AT = ctA-5e-C2/AT, = 2rrhc-2v3e-hv/kT. Wien law: The wavelength of maximum:FA or BA is Amax: TA max = 0.201405 2C2 = 0.28978 cm K. The wavelength of maximum photon emission is Am: TAm = 0.2550571c2 = 0.36697 cmK. The frequency of maximum :Fv or Bv is Vm: Tc/v m y = 0.354429Oc2 = 0.50994cmK. The three numerical constants above are l/y in y e- Y ), respectively. = 3(1 - = 5(1 - e- Y ), y = 4(1 - e- Y ), and 100 / 5 RADIATION S.2 REFRACTIVE INDEX AND AVERAGE POLARIZABILITY The refractive index and polarizability of atomic and molecular gases are given in Tables 5.1 and 5.2, where n is the refractive index at STP, n - 1 = A(1 + BP..2) (A in Itm), and a is the polarizability at low frequency. Table 5.1. Refractive index and polarizability of atomic gases. a [1] Atom (10- 25 em3) H He Li Be C N 0 Ne Na Mg Al Si P S 6.67 2.05 243 56 17.6 11.0 8.03 3.95 236 106 83.4 53.8 36.3 29.0 n (D lines) A (units of 10-5) B (units of 10- 3) 1.0000350 3.48 2.3 a [1] Atom CI Ar K Ca Se n 1.0000671 6.6 2.4 V Cr Mn Fe Co Ni Cu Zn (10- 25 em3) 21.8 16.4 434 250 169 136 114 68 86 75 68 65 61 71 n(D lines) A (units of 10-5) B (units of 10- 3) 1.0002837 27.92 5.6 Reference 1. Miller. T.M., & Bederson. B. 1977,Adv. Atom. Mol. Phys. 13. 1 Table 5.2. Refractive index of molecular gases. B (units of 10-3) Molecule n (D lines) A (units of 10-5) Air H2 1.0002918 1.0001384 1.000272 1.000297 1.000254 28.71 5.67 13.58 7.52 26.63 5.01 29.06 7.7 516 (rodio fioq.) ~ N2 H2O Molecule n (D lines) CO2 CO NH3 NO CI4 1.0004498 1.000334 1.000375 1.000297 1.000441 A (units of 10-5 ) B (units of 10- 3) 43.9 32.7 37.0 28.9 6.4 8.1 12.0 7.4 The refractive indices quoted in Table 5.3 are relative to air at 15 0 C. The temperatures of the media are about 180 C and the temperature coefficients quoted are the change of D-line refractive index for a 10 C temperature rise. Manufacturers' reports must be consulted for indices that are accurate enough for optical design. The table also gives the spectral limits (A in Itm) within which the absorption is less than 2.72cm- 1 (i.e., 1 cm transmission> 37%). ).. 0.23 2.2 0.23 4 +0.000014 1.58 1.515 1.499 1.491 1.486 1.483 1.481 1.479 1.476 1.91 1.722 1.683 1.666 1.657 1.652 1.648 1.643 1.626 +0.000005 Extr. ray Ord. ray 0.32 2.2 -0.000001 1.557 1.531 1.522 1.517 1.513 1.511 1.507 1.496 BSC crown 1.650 1.627 1.616 1.61O 1.605 1.600 DF flint 0.13 9.0 0.17 3.6 1.663 1.589 1.567 1.558 1.553 1.550 1.548 1.544 1.528 Extr. ray 0.17 3.6 -0.000006 Quartz -0.000005 1.651 1.579 1.558 1.549 1.544 1.541 1.539 1.536 1.520 1.42 1.495 1.455 1.442 1.437 1.434 1.432 1.430 1.429 1.424 1.398 1.303 -0.00001 Ord. ray Fluorite CaF2 References I. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. I, Sec. 34; 2, Sec. 35; 3, Sec. 36 2. Garton, W.R.S. 1966, Adv. Atom. Mol. Phys. 2,93 0.37 2.8 +0.000003 Glass Note For information on atmospheric refraction, see Table 5.2. Limits [2) Low).. High).. Temp. coef. IO 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 2 5 (~m) Calcite Table 5.3. Refractive indices of optical media [1,2). 0.16 21 -0.000003 1.550 1.489 1.471 1.463 1.458 1.455 Fused silica 0.20 17 -0.00004 1.792 1.602 1.568 1.552 1.543 1.538 1.535 1.532 1.526 1.519 1.494 Rock salt 1.14 < 0.2 -0.00008 1.423 1.358 1.343 1.336 1.332 1.330 1.328 1.325 1.315 Water VI o ...... -- >< ~ l' ..... ..... > tD N ..... ol' > ::0 '"C tTl > o ::0 ~ tTl 1::1 > Z ~ tTl Z 1::1 - <:tTl ~ > (j ::0 'Tl tTl :;d tv 102 / 5 5.3 RADIATION ABSORPTION AND SCATTERING BY PARTICLES For scattering of free electrons, U e (Thomson scattering) is [2] ue where 8Jl' =3 e 2)2 ( mc2 (1 - 2 mchv2 ) = 0.66524 x 10-24 (1 - 2 hv mc 2 ) 2 cm , is the (exponential) scattering coefficient per electron (Sec. 5.1) with the relativistic term At the high densities and temperatures found in stellar interiors, further corrections due to correlations and thermal motion may be required [3,4]. For Rayleigh scattering of atoms or molecules, Ue 2hv/mc 2 . 32Jl'3 (n - 1)2 Us = 3N = 3.307 x A.4 10 18 (n 6 + 3~ 6-7~ - 1)28/A.4N cm- I (A. in ILm), where N is the number of atoms or molecules per unit volume, n is the refractive index of the medium, is the linear scattering coefficient, and 8 = (6 + 3M/(6 - 7~) = depolarizing factor [5, 6]. ~ = 0.030 for N2 and 0.054 for 02 [7]. The Rayleigh scattering cross section of an atom or a molecule is Us U (n - 1)2 = 32Jl' 38 a 3A.4 = N l.306 x = 128Jl'5 8a2 3A.4 10 8a /A.4 cm 20 2 2 (A. in ILm), where the polarizability a = (n - 1)/(2Jl' N). For atomic scattering at some distance from any absorption line, Ua = 8Jl' 3 (~)2 mc 2 (" 112V2 2 ~ v - v2 2 12 )2, where 112 is the oscillator strength (1 is the ground level when excitation is low). For the absorption of small particles (spherical) of radius a in terms of Jl'a 2 [5], the efficiency factors (Q = u/Jl'a 2) for extinction, scattering, absorption, and radiation pressure are Qext' Qsca, Qabs, and Qpr, respectively, with Qext Qpr = Qsca + Qabs, = Qext - (cose}Qsca, where (cos e) is the forward asymmetry of scattering [8]. For large objects Qext =2.0 of which l.0 is intercepted and l.0 scattered with (cos e) = l.0. The extinction coefficient k is related to the complex dielectric constant E through E = EI ± iE2 = (n ± ik)2. Here n is the refractive index and El, E2, n, and k are real. k and n are therefore given by k} 1 2 + (2)1/2 = E ]1/2 n = _[(E ../i 1 2 ,- 1 . 5.3 ABSORPTION AND SCATTERING BY PARTICLES / 103 For measurements performed in vacuum, with 21l' a/A coefficient is related to the indices of refraction via Qabs « 21l' Qext ---;;- ~ --;- = T 1 everywhere, the measured extinction 24nk (n 2 - k 2 + 2) + 4n 2k 2 • See Tables 5.4-5.10, extinction efficiency factors for various compounds. The mean particle radius for the spheroids in the amorphous carbon sample was 40 A. Table 5.4. Extinction efficiency factor Qext for water droplets as a function ofparticle rodius and wavelength [1). A (p,m) a = 0.31J,m 1.0 IJ,m 3.0 IJ,m 10.0 IJ,m A (p,m) a = 0.31J,m 1.0 IJ,m 3.0 IJ,m 10.0 IJ,m 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.80 2.00 2.10 2.20 2.30 2.50 2.60 2.70 2.75 2.80 2.90 2.95 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.75 3.83 4.00 1.39 1.07 0.80 0.58 0.44 0.35 0.28 0.23 0.18 0.15 0.099 0.067 0.054 0.043 0.035 0.022 0.0127 0.0136 0.0477 0.1754 0.4178 0.458 0.423 0.293 0.159 0.0806 0.0429 0.0264 0.0189 0.0130 0.0114 0.0114 2.79 3.37 3.76 3.90 3.89 3.60 3.41 3.08 2.83 2.56 2.07 1.65 1.45 1.25 1.09 0.69 0.33 0.189 0.297 0.940 1.65 1.74 1.76 1.79 1.93 1.52 1.21 0.944 0.763 0.569 0.497 0.428 2.47 2.13 1.95 2.37 2.68 2.80 2.28 2.04 1.86 1.83 2.09 2.87 3.16 3.51 3.67 3.66 2.61 1.58 1.61 2.58 2.45 2.44 2.49 2.67 2.74 3.14 3.53 3.97 3.99 3.84 3.76 3.58 2.07 1.99 2.05 2.14 2.18 2.05 2.25 2.25 2.01 2.27 2.11 2.13 2.42 2.46 2.28 2.34 1.96 2.26 2.34 2.23 2.21 2.21 2.22 2.24 2.26 2.33 2.42 2.17 1.97 2.38 2.66 2.80 4.50 4.66 4.80 5.00 5.26 5.50 5.80 6.00 6.05 6.40 7.00 7.50 8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50 12.00 12.50 13.00 13.50 14.00 15.00 16.00 17.50 18.00 20.00 30.00 100.00 0.0182 0.0197 0.0180 0.0131 0.0098 0.0111 0.026 0.076 0.083 0.030 0.022 0.021 0.020 0.020 0.020 0.021 0.025 0.031 0.044 0.063 0.083 0.091 0.103 0.107 0.114 0.123 0.104 0.086 0.080 0.061 0.037 0.014 0.342 0.319 0.291 0.242 0.189 0.162 0.177 0.39 0.419 0.215 0.145 0.120 0.106 0.097 0.091 0.087 0.094 0.112 0.155 0.220 0.286 0.317 0.360 0.376 0.400 0.434 0.371 0.309 0.289 0.223 0.129 0.048 3.02 2.88 2.76 2.56 2.22 1.93 1.50 1.95 2.02 1.95 1.47 1.19 1.02 0.886 0.734 0.596 0.509 0.487 0.547 0.706 0.884 0.992 1.13 1.20 1.29 1.44 1.38 1.30 1.29 1.23 0.528 0.149 2.46 2.26 2.21 2.02 1.85 2.02 2.65 2.40 2.38 2.30 2.73 3.09 3.24 3.30 3.21 2.95 2.50 2.08 1.78 1.83 1.97 2.09 2.20 2.26 2.32 2.42 2.51 2.64 2.71 2.92 2.75 0.758 Reference 1. Irvine, W.R., & Pollack, J.B. 1968, Icarus, 8, 324 Table 5.5. Extinction efficiency factor Qextfor ice particles as afunction ofparticle rodius and wavelength [1). A (IJ,m) a = 0.31J,m 1.0 IJ,m 3.01J,m 10.0 IJ,m 0.95 1.00 1.20 1.50 2.00 2.35 0.572 0.49 0.295 0.158 0.063 0.029 2.92 3.80 3.35 2.52 1.52 0.94 2.41 2.66 2.28 1.82 3.10 3.77 2.02 2.08 2.15 2.24 2.35 1.96 A (IJ,m) 3.60 3.80 3.90 4.00 4.10 4.20 a =0.3IJ,m 1.0 IJ,m 3.01J,m 10.0 IJ,m 0.025 0.017 0.018 0.019 0.021 0.023 0.76 0.52 0.46 0.41 0.38 0.35 3.91 3.70 3.51 3.28 3.04 2.84 2.04 2.57 2.63 2.64 2.43 2.30 104 I 5 RADIATION Table 5.5. Continued. ). (/Lm) a = 0.3/Lm 1.0/Lm 3.0/Lm 1O.0/Lm ). (/Lm) a=0.3/Lm 1.0/Lm 3.0/Lm 1O.0/Lm 2.40 2.45 2.50 2.55 2.60 2.625 2.65 2.800 2.85 2.90 2.95 3.00 3.05 3.075 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 0.025 0.022 0.019 0.016 0.013 0.012 0.012 0.027 0.066 0.177 0.306 0.377 0.514 0.547 0.511 0.379 0.244 0.151 0.1096 0.0817 0.0608 0.046 0.035 0.029 0.823 0.724 0.626 0.522 0.433 0.397 0.364 0.261 0.360 0.675 0.986 1.151 1.516 1.63 1.69 2.30 2.23 2.10 1.91 1.74 1.50 1.16 0.97 0.85 3.81 3.73 3.58 3.35 3.09 2.96 2.79 1.84 1.68 1.78 1.92 2.00 2.22 2.28 2.36 2.54 2.57 2.62 2.78 2.92 3.14 3.62 3.87 3.94 1.93 2.12 2.46 2.71 2.58 2.36 2.18 2.07 2.31 2.19 2.14 2.14 2.18 2.19 2.20 2.25 2.26 2.26 2.25 2.25 2.36 2.37 2.19 2.06 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.70 6.00 6.40 6.70 7.00 8.00 9.00 10.00 11.00 12.00 15.00 20.00 40.00 62.00 100.00 150.00 0.027 0.032 0.036 0.031 0.023 0.Dl8 0.Dl5 0.014 0.026 0.048 0.040 0.039 0.033 0.021 0.019 0.020 0.038 0.039 0.019 0.005 0.017 0.016 0.0027 0.00057 0.34 0.33 0.32 0.28 0.23 0.20 0.17 0.16 0.16 0.23 0.19 0.18 0.15 0.10 0.08 0.07 0.15 0.16 0.076 0.019 0.058 0.055 0.009 0.002 2.67 2.46 2.31 2.17 2.02 1.86 1.73 1.61 1.20 1.31 1.11 1.02 0.92 0.67 0.51 0.33 0.77 1.25 0.80 0.21 0.20 0.18 0.028 0.007 2.16 2.11 2.10 2.10 2.06 2.16 2.27 2.39 2.95 2.73 2.86 2.89 2.96 3.01 2.74 1.76 2.79 3.00 3.58 3.06 1.37 1.02 0.17 0.04 Reference 1. Irvine, W.R., & Pollack, J.B. 1968, Icarus, 8, 324 Table 5.6. Extinction efficiencies for amorphous carbon [I, 2].a ). (/Lm) Qext/a (em-I) ). (/Lm) Qext/a (em-I) ). (/Lm) Qext/a (em-I) 0.12 0.13 0.14 0.15 0.16 0.18 0.20 0.22 0.23 0.25 5.12[5] 3.21[5] 2.02[5] 2.18[5] 1.84[5] 1.47[5] 1.43[5] 1.56[5] 1.63[5] 1.60[5] 0.27 0.30 0.50 0.70 1.00 1.60 2.00 3.13 4.00 5.00 1.49[5] 1.28[5] 7.07[4] 4.81[4] 3.52[4] 2.14[4] 1.69[4] 1.05[4] 7.96[3] 6.06[3] 7.14 10.00 15.40 20.00 30.50 50.80 70.50 101.00 205.00 289.00 4.49[3] 3.18[3] 1.74[3] 1.35[3] 8.80[2] 5.38[2] 4.04[2] 3.17[2] 1.66[2] 1.19[2] Note aNumbers in square brackets denote powers of 10. References 1. Bussoletti, E. et al. 1987, AclAS, 70, 257 2. Maron, M. 1990,ApS&S, 172, 21 5.3 ABSORPTION AND SCATTERING BY PARTICLES / Table 5.7. Extinction efficiency factor Qextfor graphite as ajunction ofparticie radius and wavelength [I].a = O.OIJLm A (JLm) a 0.12 0.15 0.18 0.20 0.21 0.215 0.2175 0.22 0.225 0.23 0.24 0.26 0.28 0.30 0.33 0.365 0.4861 0.6562 0.80 1.00 1.40 0.425 0.244 0.512 0.995 1.51 1.25 1.22 Ll7 1.01 0.88 0.63 0.40 0.31 0.25 0.20 0.160 0.093 0.058 0.043 0.030 0.017 = O.OIJLm 0.1 JLm A (JLm) a 2.58 2.32 2.49 2.83 2.92 3.03 3.06 3.08 3.11 3.13 3.12 3.02 2.98 3.01 3.09 3.11 3.34 2.65 1.88 1.09 0.45 2.00 3.00 4.00 5.00 6.00 9.00 10.00 11.00 11.52 11.54 12.00 20.00 40.00 60.00 80.00 100.0 200.0 400.0 700.0 1000.0 2000.0 l.oo[ -2] 5.37[ -3] 3.44[-3] 2.43[-3] 1.83[ -3] 4.65[-6] 9.00[-4] 8.21[ -4] 2.98[-3] 8.82[-4] 7.60[-4] 6.91[-4] 6.51[-4] 4.28[-4] 2.77[-4] 1.89[ -4] 5.24[-5] 1.40[ -5] 4.71[-6] 2.33[-6] 5.87[-7] 0.1 JLm 0.19 0.084 0.048 0.032 0.024 1.23[-2] 1.07[-2] 9.61[ -3] 3.13[-2] 1.01[ -2] 8.78[-3] 7.45[-3] 6.87[-3] 4.41[-3] 2.80[-3] 1.9O[ -3] 5.13[-4] 1.29[-4] 4.24[-5] 2.08[-5] 5.22[-5] Note aNumbers in square brackets denote powers of 10. Reference I. ~ne,B.L. 1985, ApJS, 57, 587 Table 5.S. Extinction efficiencies for silicon carbide [I]. a A (JLm) 0.10 0.20 0.40 0.78 0.99 1.96 3.09 3.97 4.69 6.02 7.10 8.39 Qext!a (em-I) A (JLm) Qext/a (em-I) A (JLm) Qext!a (em-I) 3.46[6] 7.65[4] 1.29[4] 8.85[4] 8.13[3] 7.01[3] 4.15[3] 2.55[3] 1.66[3] 6.97[2] 4.83[2] 4.03[2] 9.12 9.90 10.14 10.37 10.61 10.86 ILlI 11.37 11.63 11.90 12.17 12.45 4.24[2] 9.65[2] 1.66[3] 3.06[3] 5.76[3] 9.35[3] 1.37[4] 1.45[4] 1.04[4] 7.30[3] 4.84[3] 3.31 [3] 12.74 13.04 13.34 13.65 13.96 14.29 15.30 22.00 36.90 52.00 103.3 205.3 2.53[3] 1.94[3] 1.50[3] Ll8[3] 9.69[2] 7.96[2] 5.76[2] 3.23[2] 1.57[2] 9.74[1] 3.79[1] 1.23[1] Note aNumbers in square brackets denote powers of 10. Reference 1. Pegourie, B. 1988, A& A, 194, 335 105 106 / 5 RADIATION Table 5.9. Extinction efficiency factors Qextfor silicate as afunction ofpanicle radius and wavelength [1].a A (JLm) 0.12 0.14 0.16 0.20 0.23 0.30 0.40 0.55 a = O.OlJLm 0.943 0.51 0.154 0.032 0.0146 1.09[-2) 7.99[-3) 5.76[-3) 0.1 JLm 2.56 2.62 2.67 3.13 3.98 3.41 2.26 0.78 A (JLm) 1.00 1.65 2.00 2.60 3.00 4.00 5.00 6.00 a = O.OIJLm 3.22[-3] 4.19[-4] 2.25[-4] 9.40[-5] 5.75[-5] 2.06[-5] 8.64[-4] 9.95[-4] 0.1 JLm 0.11 3.18[ -2] 2.31[ -2] 1.67[ -2] 1.46[ -2] 1.14[-2] 1.01[ -2] 1.00[ -2] Note aNumbers in square brackets denote powers of 10. Reference 1. rhr.Une,B.L. 1985, ApJS, 57, 587 Table 5.10. Extinction efficiencies for silicate for A > 6 JLm [1].a A (JLm) 7.0 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 Qext/a (em-I) A (JLm) Qext/a (em-I) A (JLm) 1.04[3] 3.26[3] 6.75[3] 1.20[4] 1.32[4] 1.20[4] 1.05[4] 8.38[3] 6.80[3] 5.58[3] 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 23.0 25.0 3.74[3] 2.79[3] 3.08[3] 3.70[3] 4.34[3] 4.70[3] 4.62[3] 4.19[3] 3.06[3] 2.57[3] 27.5 30.0 40.0 50.0 80.0 100.0 200.0 500.0 1000.0 2000.0 Qext/a (em-I) 2.10[3) 1.75[3] 9.80[2) 6.15[2] 2.26[2] 1.41[2] 3.40[1] 5.38 1.34 3.36[-1] Note aNumbers in square brackets denote powers of 10. Reference 1. rhr.Une,B.L. 1985, ApJS, 57, 587 5.4 5.4.1 PHOTOIONIZATION AND RECOMBINATION Photoionization Fit Parameters for Ground States The following parameters are taken from [9] and are used in the fonnula for the photoionization cross section: where ET is the threshold energy in eV and aT is the threshold cross section, divided by 1.0 x 10- 18 cm2 . The fitting coefficients R and s are found in Table 5.11. 5.4 PHOTOIONIZATION AND RECOMBINATION / 107 Table S.11. Photoionization cross-section fits [l]. Parent Resulting ion ET aT R s H(2S) He(IS) He+(2 S) Cep) C+ep) C2+(IS) C3+eS) N~S) N+(3p) N 2+(2p) N3+(IS) N*(2S) Oep) 0(3p) 0(3p) 0+ (4S) 0 2+(3 P) 03+ (2p) 04+(IS) 05+ (2S) Ne(IS) Ne+(2p) Ne+(2 P) Ne+(2 P) Ne2+(3 P) Ne2+(3 P) Ne2+ep) Ne3+(4S) Ne4+ep) Ne5+eS) Ne5+ep) H+(IS) He+(2S) He2+(IS) C+(2P) C 2+(IS) C 3+(2S) c4+('S) N+(3p) N 2+(2p) N3+(IS) N"+(2S) N5+(IS) 0+ (4S) O+eD) 0+(2p) 0 2+(3 P) 03+(2p) 04+(IS) 05+ (2S) 06+(IS) Ne+(2p) Ne2+(3p) Ne2+(ID) Ne2+(IS) Ne3+(4S) Ne3+(2D) Ne3+(2p) Ne4+ep) NeS+ep) Ne6+(IS) Ne6+(IS) 13.6 24.6 54.4 11.3 24.4 47.9 64.5 14.5 29.6 47.5 77.5 97.9 13.6 16.9 18.6 35.2 54.95 77.4 113.9 138.1 21.6 41.1 42.3 47.99 63.74 68.8 71.5 97.2 126.5 138.1 157.96 6.30 7.83 1.58 12.2 4.60 1.60 0.68 11.4 6.65 2.06 1.08 0.48 2.94 3.85 2.26 7.32 3.65 1.27 0.78 0.36 5.35 4.16 2.71 0.52 1.80 2.50 1.48 3.11 1.40 0.36 0.49 1.34 1.66 1.34 3.32 1.95 2.60 1.00 4.29 2.86 1.63 2.60 1.00 2.66 4.38 4.31 3.84 2.01 0.83 2.60 1.00 3.77 2.72 2.15 2.13 2.28 2.35 2.23 1.96 1.47 1.00 1.15 2.99 2.05 2.99 2.00 3.00 3.00 2.00 2.00 3.00 3.00 3.00 2.00 1.00 1.50 1.50 2.50 3.00 3.00 2.00 2.10 1.00 1.50 1.50 1.50 2.00 2.50 2.50 3.00 3.00 2.10 3.00 Reference 1. Osterbrock, D.E. 1974, Astrophysics o/Gaseous Nebulae (Freeman, San Francisco) 5.4.2 Photoionization of Light Hydrogenic Ions A semiempirical expression [10] for the photoionization cross section per K -shell electron for hydrogenic light elements is given by a= v a6 291f2 (_EI)4 (T/f3y)3 3a 2Z5 hv [1 + ~4 y(y - 2) y +1 (1 __I_In 11 +- 13)] exp(-4T/arccot 13 1 - exp( T/), -21fT/) 2f3y2 where T/ = [-EI/(hv + El)]1/2. EI is the negative binding energy of the Is electron, v is the electron velocity, and 13 = ~ = [(hv y = (1 - 13 2)-1/2 = c + El)2 + 2(hv + El)mc2]1/2 + El +mc2 1 + (hv + El)/mc 2, hv '" [2(hv + Ed/mc2]1/2 '" aZ/T/, a:::: 1/137.036. 108 / 5 5.4.3 RADIATION Radiative Recombination Given an absorption coefficient all for a particular level, microscopic reversibility demands that the recombination cross section into that same level be given by gi (hv)2 u(v) = - - - - - all. gi+l (mcv)2 This is the Milne relation. Here gi is the statistical weight for the particular level or term i in the recombined ion, gi+ 1 is that of the original ion. Using the Milne relation and the above analytic form for the photoionization cross section, the recombination rate coefficient can be expressed as [9] ai(T)= 4 g. /--' v7r gi+I (m 2k )3/2 T eET / kT E3 t2 aT [REs -2(ET/kT)+(1-R)Es -3(ET/kT)], m c where En (x) is the exponential integral function. If s is noninteger, the relation En (x) -+ x n - I r (1 n, x) can be used, where r(a, x) is the incomplete gamma function. Recombination into excited states is generally at least as, if not more, important than recombination into the ground state. If the excited state can be approximated as hydrogenic (often a good approximation), then the cumulative recombination coefficient a(n) for principal quantum number n and higher is a(n) = L~=n an' and is given in Table 5.12 as a function of temperature for the first four values of n for Z = 1 [9]. For an arbitrary ionic charge Z, a(n; Z, T) = Za(n; I, T /Z2). Table S.12. Recombination coejJicients a(n) in cm3 5- 1 for hydrogen [1]. n 1250K 2500K 5000K lOOOOK 20000K 1 2 3 4 1.74[-12] 1.28[-12] 1.03[-12] 8.65[-13] 1.10[-12] 7.72[-13] 5.99[-13] 4.86[-13] 6.82[-13] 4.54[-13] 3.37[-13] 2.64[-13] 4.18[-13] 2.60[-13] 1.83[-13] 1.37[-13] 2.51[-13] 1.43[-13] 9.50[-14] 6.83[-14] Reference 1. Osterbrock, D.E. 1974, Astrophysics of Gaseous Nebulae (Freeman, San Francisco) Recombination into the nth hydrogenic level can be written as (taking s = 3 and R = 1) (m 4 gi )3/2 Ef E /kT an = - - - - --aTe T EI(ET/kT) . gi+I 2kT m 3c2 ..;;r Note that exp(x)EI (x) ~ l/x for x > 5. The threshold photoionization cross section aT can be obtained from the table of photoionization cross-section fitting parameters or from the Kramers-Gaunt formula: aT (Kramers & Gaunt) = .J3 8h2 3gn 2 3 37r m ce2Z2 where g is the Gaunt factor [11] given in Table 5.13. = 7.907 x 10- 18 n~ cm2 , Z 5.5 X-RAY ATTENUATION / 109 Table 5.13. Bound-free Gaunt/actors/or the hydrogen atom [11. Configuration g at absorption edge g level average Is 0.80 0.96 0.88 1.14 1.14 0.73 1.3 1.3 0.80 0.89 2s 2p 3s 3p 3d 4s 4p 4d 0.92 0.94 4/ 5 6 0.95 0.96 0.97 7 Reference 1. Gaunt, J.A. 1930. Philos. Trans. 229. 163 5.4.4 Dielectronic Recombination For dielectric recombination into ion X+, with excited state x+* and charge Z, we have the Burgess formula [12] for the recombination coefficient ad, ad where = 3.0 x 10-3 T- 3/ 2 f A(x)B(Z)exp[-xC(Z)/T] cm3 s-I, f is the oscillator strength for the transition X+ x = 2[E(X H ) - E(x+)]f[(Z -+ X+* with T in K and + I)Eo], £0 + 0.105x + B(Z) = [Z(Z + 1)5/(Z2 + 13.4)] 1/2, A(x) = x 1/ 2 /(1 C(Z) = 1.58 x 5.5 == 27.2 eV, x > 0.05, 0.015x 2 ), Z :::: 20, lOS (Z + 1)/ [1 + 0.015Z 3/(Z + 1)2] , xC(Z)/T ;$ 5.0. X-RAY ATTENUATION The smoothed fits in Table 5.14 provide an approximate representation ("-' 10% or better) to both the Henke experimental data [13] and to relativistic calculations [14] for the photoionization cross section u (1 barn = 10-24 cm2 ). The photon energy E is measured in keY, and n logI0[u(barn/atom)] =L m=O am (log 10 E)m. 110 / 5 RADIATION Table 5.14. Cold material X-ray attenuation (total cross section) fits. a H He C N 0 Na Mg AI Si S Ar E range (IreV) n ao a} 0.1089-8.0470 8.0470-44.77 0.1086-8.0470 0.0305-0.2885 0.2888-30.000 0.0105-0.4027 0.4031-32.20 0.0305-0.5374 0.5380-30.320 0.0415-0.0708 0.0724-1.079 1.0800-9.886 0.0305-0.0574 0.0576-0.0824 0.0824-1.3113 1.3130-30.921 0.0305-0.0813 0.0815-0.1144 0.1144-1.5680 1.5690-30.000 0.0305-0.1087 0.1089-0.1300 0.1303-1.8470 1.849-30.800 0.0394-0.1740 0.1742-0.1932 0.1996-2.4772 2.479-31.970 0.0504-0.1085 0.1085-0.2497 0.2653-3.2002 3.2033-32.200 5 2 5 3 4 4 4 4 5 5 5 3 3 4 5 4 3 4 5 4 4 4 4 4 4 3 4 4 4 3 4 3 1.000266 -0.1057762 2.596995 3.113512 4.641890 3.653780 4.880570 3.851303 5.087381 2.522877[2] 4.372625 5.551365 1.819299 0.7597808 4.556145 5.664605 1.516313 4.047249[2] 4.713295 5.732064 4.653385 1.704974[3] 4.842629 5.818893 4.862989 -3.287565[2] 5.105629 5.957286 0.1038804 3.766572 5.325805 6.236304 -2.874876 -8.314851[-2] -3.278818 -3.093789 -2.929378 -2.036035 -2.726891 -2.158767 -2.624299 7.578575[2] -2.803046 -2.508414 -3.725268 2.040 594[2] -2.709325 -2.340560 -5.356061 1.227899[3] -2.629794 -2.167852 1.585146 5.668094[3] -2.691588 -2.084606 1.407408 -9.238824[2] -2.701358 -1.944676 0.1580149 -3.816305 -2.604915 -2.427534 a2 1.337216 -5.823671[-2] -0.5054382 -0.3919827 0.5928674 -0.3171900 0.7451610 -0.3410862 8.701549[2] -0.7833634 -0.2958825 -0.9686183 2.000915[2] -0.6249299 -0.6420745 -1.787405 1.261952[3] -0.4217032 -0.7593566 4.064835 6.305044[3] 0.1273064 -0.8070467 4.580753 -6.359921[2] -0.2269985 -0.8396531 0.1802517 -1.506623 -0.4119090 -0.1853513 a3 a4 0.6905931 -0.2734547 0.6372270 0.3444271 0.3640990 0.4291417 6.076411[ -2] 0.5485890 -0.1972559 4.394 846[2] -1.137645 65.19285 -1.125062 0.2357794 4.319780[2] -1.136888 0.2548878 1.700534 2.337491[3] 0.8214728 0.2611724 2.192223 0.2442756 82.19558 -0.7944890 -0.9611755 -1.261846 0.6971264 0.2465677 6.544871 0.4831536 Note aNumbers in square brackets denote powers of 10. See Sec. 5.4 for a semiempirical equation for hydrogen and hydrogenic ion cross sections. 5.6 ABSORPTION OF MATERIAL OF STELLAR INTERIORS The opacity of stellar interiors is usually expressed as the Rosseland mean of the mass absorption coefficient K. Tabulations are available [15,16] for a wide range of compositions expressed by X, Y, and Z. Tables 5.15-5.17 give 10g1OK incm2 g-1 as a function oflog 10 p where density p is in gcm-3 and temperature T in units of 10-6 K. These tables are based on interpolations of data in [15]. 5.6 ABSORPTION OF MATERIAL OF STELLAR INTERIORS / 111 Table S.lS. Hydrogen Rosseland mean opacity loglO K [1]. Ta logp = -10.0 -9.0 -8.0 -7.0 -6.0 0.006 0.007 0.008 0.009 0.010 0.011 0.012 0.014 0.016 0.D18 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.070 0.080 0.090 0.100 0.120 0.150 0.200 0.250 0.300 0.400 0.500 0.600 0.800 1.000 1.200 1.500 2.000 2.500 3.000 4.000 5.000 6.000 8.000 10.00 15.00 20.00 30.00 40.00 60.00 80.00 100.0 -1.67 -0.66 0.18 0.71 0.85 0.76 0.60 0.31 0.12 -0.01 -0.08 -0.15 -0.17 -0.21 -0.27 -0.32 -0.35 -0.37 -0.38 -0.40 -0.40 -0.40 -0.40 -1.41 -0.49 0.33 1.01 1.42 1.56 1.50 1.19 0.89 0.68 0.52 0.30 0.21 0.15 0.07 -0.02 -0.11 -0.18 -0.24 -0.31 -0.35 -0.37 -0.38 -0.39 -0.40 -0.40 -1.00 -0.19 0.54 1.20 1.71 2.05 2.21 2.16 1.91 1.68 1.48 1.17 1.00 0.89 0.78 0.65 0.50 0.35 0.21 0.00 -0.14 -0.22 -0.28 -0.34 -0.37 -0.39 -0.40 -0.40 -0.40 -0.61 0.16 0.82 1.40 1.89 2.27 2.57 2.86 2.86 2.73 2.56 2.25 2.06 1.92 1.78 1.62 1.43 1.21 1.01 0.66 0.39 0.19 0.05 -0.13 -0.26 -0.35 -0.38 -0.39 -0.40 -0.40 -0.40 -0.40 -0.40 -0.13 0.57 1.15 1.65 2.09 2.46 2.77 3.22 3.48 3.57 3.55 3.37 3.19 3.04 2.88 2.67 2.44 2.20 1.97 1.56 1.22 0.94 0.71 0.37 0.07 -0.17 -0.28 -0.33 -0.37 -0.39 -0.39 -0.40 -0.40 -0.40 -0.40 -0.40 Note -0.40 -0.41 -0.41 -0.41 -0.41 -0.41 -0.40 -0.40 -0.41 -0.41 -0.41 -0.42 -0.42 -0.38 -0.39 -0.40 -0.41 -0.41 -0.42 -0.42 -0.43 -0.44 -0.28 -0.33 -0.36 -0.38 -0.40 -0.41 -0.42 -0.43 -0.44 -0.46 -0.47 -0.49 -5.0 2.36 2.68 2.98 3.47 3.82 4.07 4.23 4.35 4.29 4.15 3.96 3.72 3.46 3.20 2.96 2.53 2.17 1.86 1.60 1.17 0.72 0.26 0.02 -0.13 -0.27 -0.33 -0.36 -0.39 -0.39 -0.40 -0.40 -0.40 -0.40 -0.40 0.00 -0.14 -0.22 -0.31 -0.35 -0.39 -0.41 -0.43 -0.44 -0.46 -0.47 -0.49 aUnits of 106 K. Reference 1. Iglesias. C.A .• Rogers. EI .• & Wilson. B.O. 1992. ApJ. 397. 717 -4.0 -3.0 -2.0 -1.0 0.0 1.45 1.10 0.62 0.32 0.13 -0.10 -0.21 -0.27 -0.33 -0.37 -0.38 -0.39 1.07 0.79 0.40 0.17 0.02 -0.13 -0.25 -0.31 -0.34 0.85 0.60 0.34 0.07 -0.08 -0.17 1.06 0.68 0.41 0.23 0.49 0.25 -0.07 -0.22 -0.35 -0.40 -0.44 -0.47 -0.49 0.43 0.14 -0.16 -0.29 -0.41 -0.45 -0.48 -0.01 -0.29 -0.42 -0.48 -0.17 -0.35 4.96 5.10 5.07 4.90 2.56 2.11 1.60 1.01 0.61 0.34 0.03 -0.14 -0.22 -0.32 -0.35 -0.37 -0.39 -0.40 -0.40 -0.40 0.60 0.34 0.16 -0.05 -0.17 -0.31 -0.37 -0.41 -0.43 -0.46 -0.47 -0.49 112 / 5 RADIATION Table 5.16. Helium Rosseland mean opacity 10g1O K [1]. Ta 0.006 0.007 0.008 0.009 0.010 0.011 0.012 0.014 0.016 0.Ql8 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.070 0.080 0.090 0.100 0.120 0.150 0.200 0.250 0.300 0.400 0.500 0.600 0.800 1.000 1.200 1.500 2.000 2.500 3.000 4.000 5.000 6.000 8.000 10.00 15.00 20.00 30.00 40.00 60.00 80.00 100.0 logp = -10.0 -5.79 -4.95 -4.13 -3.36 -2.71 -2.04 -1.49 -0.82 -0.74 -0.83 -0.88 -0.93 -0.73 -0.53 -0.60 -0.64 -0.66 -0.68 -0.67 -0.67 -0.67 -0.67 -0.68 -0.70 -9.0 -8.0 -5.81 -5.14 -4.43 -3.73 -2.99 -2.31 -1.67 -0.72 -0.33 -0.37 -0.51 -0.72 -0.64 -0.28 -0.20 -0.34 -0.45 -0.52 -0.57 -0.61 -0.62 -0.62 -0.62 -0.65 -0.68 -0.69 -5.71 -5.13 -4.52 -3.94 -3.24 -2.43 -1.76 -0.68 -0.01 0.24 0.19 -0.17 -0.27 0.02 0.39 0.43 0.17 -0.03 -0.16 -0.33 -0.42 -0.46 -0.47 -0.49 -0.56 -0.66 -0.69 -0.69 -0.70 -0.70 -0.70 -0.70 -0.71 -0.71 -0.70 -0.70 -0.70 -0.71 -0.71 -0.71 -0.72 -7.0 -3.15 -2.41 -1.73 -0.65 0.13 0.62 0.86 0.72 0.46 0.52 0.85 1.17 1.19 0.95 0.69 0.35 0.15 0.02 -0.06 -0.15 -0.23 -0.45 -0.59 -0.65 -0.69 -0.69 -0.70 -0.70 -0.70 -0.66 -0.68 -0.69 -0.70 -0.71 -0.71 -0.72 -0.73 -0.74 -6.0 1.49 1.36 1.24 1.34 1.63 1.90 1.98 1.83 1.40 1.11 0.93 0.80 0.63 0.47 0.12 -0.21 -0.42 -0.60 -0.66 -0.68 -0.69 -0.70 -0.70 -0.70 -0.70 -0.53 -0.60 -0.64 -0.68 -0.69 -0.71 -0.72 -0.73 -0.74 -0.76 -0.77 -0.79 -5.0 2.39 2.57 2.69 2.57 2.26 2.03 1.89 1.68 1.48 1.03 0.52 0.13 -0.30 -0.49 -0.58 -0.66 -0.68 -0.69 -0.70 -0.70 -0.70 -0.70 -0.19 -0.36 -0.46 -0.57 -0.63 -0.69 -0.71 -0.72 -0.74 -0.75 -0.77 -0.79 Note aUnits of 106 K. Reference 1. Iglesias. e.A.. Rogers, F.J.• & Wilson. B.G. 1992.ApJ. 397, 717 -4.0 3.04 2.83 2.58 2.04 1.45 0.97 0.32 -0.06 -0.28 -0.50 -0.60 -0.64 -0.67 -0.69 -0.70 -0.70 0.43 0.15 -0.05 -0.29 -0.43 -0.59 -0.66 -0.71 ~0.73 -0.75 -0.77 -0.79 -3.0 -2.0 -1.0 0.0 2.41 1.91 1.18 0.68 0.32 -0.10 -0.33 -0.46 -0.57 -0.64 -0.67 -0.69 1.58 1.17 0.60 0.22 -0.03 -0.27 -0.47 -0.56 -0.62 1.02 0.68 0.32 -0.05 -0.26 -0.40 0.65 0.34 0.09 0.29 0.04 -0.31 -0.48 -0.63 -0.69 -0.74 -0.77 -0.79 0.24 -0.07 -0.39 -0.54 -0.68 -0.74 -0.77 -0.22 -0.51 -0.64 -0.72 -0.40 -0.57 5.6 ABSORPTION OF MATERIAL OF STELLAR INTERIORS I 113 Table 5.17. Solar composition (X = 0.73, Z = 0.018) Rosseland mean opacity log lO iC [1]. Ta logp = -10.0 -9.0 -8.0 -7.0 -6.0 0.006 0.007 0.008 0.009 0.010 0.011 0.012 0.014 0.016 0.018 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.070 0.080 0.090 0.100 0.120 0.150 0.200 0.250 0.300 0.400 0.500 0.600 0.800 1.000 1.200 1.500 2.000 2.500 3.000 4.000 5.000 6.000 8.000 10.00 15.00 20.00 30.00 40.00 60.00 80.00 100.0 -1.77 -0.78 0.05 0.55 0.67 0.61 0.47 0.24 0.13 0.04 -0.04 -0.13 -0.12 -0.14 -0.21 -0.26 -0.31 -0.34 -0.35 -0.36 -0.37 -0.36 -0.33 -1.53 -0.62 0.20 0.88 1.27 1.41 1.35 1.06 0.82 0.66 0.54 0.33 0.25 0.25 0.20 0.09 0.00 -0.09 -0.15 -0.22 -0.25 -0.27 -0.26 -0.19 -0.04 -0.20 -1.10 -0.32 0.42 1.08 1.60 1.94 2.08 2.00 1.76 1.56 1.39 1.14 0.97 0.92 0.90 0.81 0.66 0.50 0.38 0.18 0.06 0.00 -0.04 -0.05 0.09 -0.01 -0.24 -0.38 -0.46 -0.62 0.07 0.72 1.30 1.80 2.20 2.48 2.74 2.71 2.56 2.40 2.15 1.97 1.85 1.80 1.74 1.62 1.43 1.25 0.95 0.74 0.60 0.50 0.38 0.38 0.33 0.02 -0.19 -0.40 -0.44 -0.45 -0.44 -0.45 0.00 0.52 1.08 1.59 2.03 2.41 2.71 3.14 3.36 3.42 3.37 3.20 3.06 2.94 2.83 2.73 2.62 2.47 2.29 1.96 1.70 1.51 1.36 1.18 0.99 0.84 0.53 0.24 -0.18 -0.37 -0.40 -0.44 -0.44 -0.44 -0.44 -0.45 -0.46 -0.46 -0.47 -0.47 -0.47 -0.47 -0.43 -0.45 -0.46 -0.47 -0.47 -0.48 -0.48 -0.26 -0.38 -0.43 -0.46 -0.46 -0.47 -0.48 -0.49 -0.50 0.29 -0.03 -0.22 -0.38 -0.43 -0.46 -0.48 -0.49 -0.50 -0.52 -0.54 -0.56 -5.0 2.33 2.65 2.95 3.40 3.71 3.94 4.08 4.16 4.11 4.03 3.92 3.78 3.63 3.47 3.32 3.02 2.76 2.56 2.39 2.15 1.90 1.56 1.25 0.97 0.48 0.05 -0.20 -0.34 -0.38 -0.39 -0.40 -0.45 -0.46 -0.47 0.82 0.50 0.23 -0.11 -0.27 -0.39 -0.44 -0.49 -0.50 -0.52 -0.54 -0.56 Note aUnits of 106 K. Reference 1. Iglesias, e.A., Rogers, F.l., & Wilson, B.G. 1992, ApJ, 397,717 -4.0 -3.0 -2.0 -1.0 0.0 3.66 3.12 2.74 2.45 2.03 1.76 1.49 0.93 0.52 0.27 0.05 -0.11 -0.25 -0.36 2.52 2.26 2.06 1.74 1.43 1.15 0.83 0.48 0.26 0.05 2.23 2.03 1.87 1.65 1.29 0.98 0.73 2.10 1.78 1.50 1.24 0.72 0.48 0.11 -0.09 -0.32 -0.42 -0.50 -0.53 -0.55 0.53 0.22 -0.11 -0.28 -0.44 -0.50 -0.54 -0.30 -0.44 -0.51 -0.18 -0.37 4.80 4.93 4.95 4.88 3.93 3.75 3.58 3.44 3.17 2.85 2.42 2.05 1.77 1.34 0.94 0.53 0.05 -0.15 -0.25 -0.29 -0.35 -0.42 -0.44 1.19 0.88 0.64 0.29 0.06 -0.21 -0.32 -0.44 -0.49 -0.52 -0.54 -0.56 114 I 5 RADIATION The opacity due to electron scattering alone for a completely ionized plasma, with hydrogen mass fraction X, is given by Ke = 0.200(1 + X) [17]. 5.7 ABSORPTION OF MATERIAL OF THE SOLAR PHOTOSPHERE The Rosseland mean opacity for the solar photosphere including diatomic species is given by Table 5.18, as loglO K with Kin cm2 g-I. The assumed microturbulent velocity is 2 km/s. Table 5.18. Solar photospheric Rosseland mean opacity log 10 K [I]. T (10- 6 K) logp = -10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 0.0021 0.0030 0.0040 0.0050 0.0062 0.0071 0.0081 0.0093 0.0100 0.0126 0.0158 0.0200 0.0316 0.0398 0.0501 0.0631 0.0708 0.0794 0.0891 0.1000 -5.31 -4.12 -3.42 -2.83 -1.60 -0.70 0.15 0.61 0.66 0.35 0.07 -0.08 -0.17 -0.23 -0.32 -0.36 -0.35 -0.36 -0.37 -0.37 -5.27 -3.66 -2.72 -2.42 -1.34 -0.53 0.33 1.05 1.27 1.24 0.78 0.49 0.20 0.16 -0.03 -0.21 -0.26 -0.28 -0.30 -0.31 -5.16 -3.04 -2.00 -1.74 -0.92 -0.21 0.54 1.29 1.61 2.05 1.73 1.34 0.87 0.83 0.62 0.26 O.ll 0.01 -0.06 -O.ll -4.95 -2.49 -1.38 -0.92 -0.43 0.19 0.83 1.48 1.79 2.56 2.64 2.35 1.83 1.71 1.54 Ul 0.87 0.66 0.50 0.38 -4.61 -2.14 -0.84 -0.14 0.17 0.65 1.20 1.76 2.03 2.81 3.28 3.29 2.92 2.71 2.50 2.09 1.84 1.61 1.39 1.21 -4.03 -1.94 -0.38 0.47 0.85 U8 1.63 2.11 2.33 3.04 3.63 4.01 3.98 3.80 -3.12 -1.72 -O.ll 0.86 1.43 1.72 2.10 Reference I. Kurucz, R.L. 1992, Rev. Mexicana Astron. Af., 23, 181 5.8 SOLAR PHOTOIONIZATION RATES The solar photoionization rates are calculated as [18] R= fvooo C1v(v)Fv dv, where C1v (V) is the photoionization cross section having threshold vo and Fv is the solar flux. The unattenuated photoionization rate for the quiet and active Sun for some monatomic species, at heliocentric distance 1 AU, is shown in Table 5.19. Table 5.19. Solar photoionization rate R in s-1 [1].a Species Quiet Sun Active Sun Species Quiet Sun Active Sun HH He 14. 7.3[-8] 5.2[-8] 14. 1.9[ -7] 2.2[-7] o (IS) 2.0[-7] 2.1[-7] 1.6[-5] 7.5[-7] 9.5[-7] 1.7[-5] F Na (expt.) 5.9 FREE-FREE ABSORPTION AND EMISSION / 115 Table 5.19. (Continued.) Species Quiet Sun Active Sun C (3 P) C (ID) C (IS) N 4.1[-7] 3.6[-6] 4.3[-6] 1.9[-7] 2.1[-7] 1.8[ -7] 1.0[-6] 1.0[-5] 1.2[-5] 6.3[-7] 8.5[-7] 7.4[-7] o (3p) o (ID) Species Na(theor.) S(3 P) S(I D) S(IS) Cl K Quiet Sun Active Sun 5.9[-6] 1.1[-6] 1.1[-6] 1.0[-6] 5.7[-7] 2.2[-5] 6.6[-6] 2.6[-6] 2.6[-6] 2.5[-6] 1.5[-6] 2.3[-5] Note aNumbers in square brackets denote powers of 10. Reference 1. Huebner, W.E, Keady, 1.1., & Lyon, S.P. 1992, AP&SS, 195, 1 5.9 FREE-FREE ABSORPTION AND EMISSION The free-free linear absorption coefficient [19,20] is 4:rr Z2 e6 g = - - - -2- . -NeNj 3 Ks 3.J3 hcm = 1.802 x = 6.686 x v v (K in expcm- 1) 1014(Z2g/v3v)NeNj (v in cm/s) 1O- 18 Z 2 gA 3 NeNi/v (A in cm), where v is the electron velocity, g is the Gaunt factor representing the departure from Kramers's theory, Z is the ionic charge, and Ne and Nj are the electronic and ionic densities in cm- 3 . The mean lIv is (2m/:rrkT) 1/2, whence Ks = 3.692 x = 1.370 x 108Z2gT-l/2v-3NeNj 1O-23Z2A3gNeNi/TI/2 (A in cm). The effective linear absorption coefficient K' after allowance for stimulated emission is K' = 3.692 x 108 [1 - exp( -hv/ kT)]Z2 gT -l/2 v -3 NeNj. For small hv/ kT (= 1.438/AT), e.g., for radio waves, 8(:rr) 1/2 - K' - - - 3 6 e6 Z2 g N N· c(mkT)3/2 v2 e I = 0.017 8Z 2gv- 2T- 3/ 2NeNj = 1.98 x 1O-23Z2gA2NeNjT-3/2 (A in cm). The Gaunt factor for radio waves is [19,21] g = 10.6 + 1.90 log lO T - 1.26 log10 Zv. Gaunt-factor calculations incorporating relativistic effects and electron degeneracy can be found in [22,23]. The temperature parameter y2 is defined by y2 = Z] Ry/kT, 2 = Z·J Zj 1.579 x lOS K T =1 (forR), (T in K). Zj =2 (for He), 116 I 5 RADIATION For -3 :5 10g10 y2 :5 2.0 we list in Table 5.20 approximate Gaunt factors for both hydrogen and helium, where TJ (defined as the chemical potential divided by kT) is the degeneracy parameter and u == hv/kT. Table 5.20. Relativistic thermally averaged free-free Gaunt factors. logu 1/ -4.0 -3.5 -3.0 -2.0 -1.4 -1.0 -0.7 -0.2 0.0 = -6.0 -2.0 0.0 1.0 2.0 3.0 5.5 4.89 4.26 3.03 2.37 1.95 1.69 1.30 1.17 5.13 4.55 3.97 2.84 2.22 1.85 1.59 1.25 1.13 3.77 3.35 2.95 2.14 1.69 1.42 1.25 1.03 0.96 2.77 2.48 2.18 1.61 1.28 1.10 0.96 0.83 0.80 1.94 1.74 1.54 1.15 0.93 0.80 0.72 0.63 0.62 1.36 1.22 1.09 0.82 0.67 0.58 0.52 0.47 0.46 These smoothed numbers are least accurate ('" 1{}-20%) for large u and small log 10 y2 (~ -3), improving to a few percent for smaller u and larger 10g10 y2. For larger u, Gaunt factors for hydrogen and helium can differ significantly [22,23]. When degeneracy is not important (TJ :5 -4, say), g ~ { .J3 In (~) , r 1r u-0 .4 ru = 1.781 foru« 1, for u ~ 1. The free-free emission (bremsstrahlung) per unit solid angle, volume, time, and frequency range is iv = K~Bv (black body) 6 (m )1/2 (hV) gexp - kT NeNi 16 (1r)1/2 e Z 2 ="3 6" c3m 2 kT = 5.444 x 1O-39 Z 2gexp (- ;~) T- 1/ 2 N eNi ergcm-3 s-1 sr- 1 Hz- 1 (T in K, N in cm- 3). The free-free emission from a cosmic plasma is iv = 6.2 x 10-39 g exp ( - ;~ ) T- 1/ 2 f N; dV erg s-1 sr- 1 Hz-I (T in K, Ne in cm- 3), where J N; dV (integrated over volume) is called the emission measure. The integrated free-free emission is 41r f iv 641r 1r 1/2 e6Z2 (kT) 1/2 dv = -3hc3 m -;;; gNeNi (6") = 1.426 x 10-27 Z 2 T 1/ 2 gNe Ni ergcm- 3 s-l. For a completely ionized plasma with solar abundance [24], Li NiNeZl ~ 1.4N;, and thus 41r f iv dv = 2.0 x 10-27 gT I / 2 f N; dV erg s-l. 5.11 VISUAL PHOTOMETRY / 117 Free-free absorption from neutral atoms: For highly polarizable target atoms, an approximation for the thermally averaged free-free absorption coefficient valid for long wavelength and low temperature is [25] k = 1.62 x 10- 19 N eN aa l / 2 )..3T(1 - e-hc/J...kT) cm- I , where Ne(Na ) are the number of free electrons (neutral atoms) per cm3 , a is the polarizability (cm3), ).. is the wavelength (cm), and T is the temperature (K). The validity criterion is O.633/a < e < 2/a l / 3• where the free-electron kinetic energy e is measured in Rydbergs and a is in units of a3. 5.10 REFLECTION FROM METALLIC MIRRORS In Table 5.21, no attempt has been made to differentiate between different methods of deposition [26]. Table 5.21. Reflectionfrom metallic mirrors. >.. (tt m) Ag AI Speculum Hg Ni Cu Au Si Pt Steel W (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 0.20 0.22 0.24 0.26 0.28 20 25 27 27 23 72 58 61 35 40 42 40 39 34 34 31 29 28 18 27 32 34 34 68 68 68 68 67 20 29 35 37 38 24 27 30 33 36 15 16 18 20 21 0.30 0.32 0.34 0.36 0.38 12 7 63 82 82 83 83 84 44 48 51 54 56 67 69 71 73 39 41 43 45 47 29 30 32 34 36 35 33 33 33 34 65 61 56 50 41 39 40 42 43 45 39 41 46 49 44 23 25 27 30 34 85 86 87 88 89 88 87 58 61 63 65 66 67 74 74 73 73 74 74 75 50 57 61 63 65 67 69 38 42 47 60 74 82 85 34 37 51 84 89 93 35 30 30 30 30 30 30 48 56 59 60 61 63 66 51 55 57 57 56 55 56 38 45 49 52 51 52 53 85 93 96 97 98 70 70 73 82 89 92 70 73 89 92 96 98 95 97 98 99 99 70 74 81 91 95 59 63 77 99 29 28 28 28 28 56 60 87 95 98 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.80 1.00 2.0 5.0 10.0 77 82 85 90 91 92 93 94 95 97 98 98 99 99 78 81 82 82 26 33 38 68 72 82 89 92 64 84 92 96 77 90 93 Reflections in the EUV [27, 28] are strongly dependent on the details of deposition, the age of the surface. and the reflection angle. No summary can be made. 5.11 VISUAL PHOTOMETRY Units of visual photometry are given in Chapters 2 and 15. For values of the relative visibility factor K>.. for normal brightness (about 5x 10-4 stilb or greater). the photopic curve (international) (cone vision 118 / 5 RADIATION at fovea) is given in Table 5.22 [29]. This and the following table are actually one-dimensional tables so that the last column and first row entry of the first table applies to a wavelength of 3 900 A. Table 5.22. Relative visibility factors. )" (A) 3000 4000 5000 6000 7000 0 100 200 300 400 500 600 700 0.0004 0.323 0.631 0.0041 0.0012 0.503 0.503 0.0021 0.0040 0.710 0.381 0.00105 0.0116 0.862 0.265 0.00052 0.023 0.954 0.175 0.00025 0.038 0.995 0.107 0.000 12 0.060 0.995 0.061 0.00006 0.091 0.952 0.032 0.00003 800 900 0.00004 0.139 0.870 0.017 0.000 12 0.208 0.757 0.0082 The equivalent width of the K)" curve is J K)" dJ... = 1068 A. The mechanical equivalent of light (experimental) [29] is K)" lumens == 0.00147 W. The luminous energy (in lumergs) is 680 J K).,e)., dJ..., where e)., dJ... is the element of energy in joules. 1 lumen (5550 A radiation) = 4.11 x 10 15 photons s-I, 1 nanolambert (5550 A radiation) = 1.31 x 106 photons s-I cm- 2 sr- I . The number of lumens L entering a telescope of diameter D in cm for a star of visual apparent magnitude V near the zenith (clear conditions) is IOgiO L = 2 IOgiO D - O.4V - 9.86. For relative visibility for dark-adapted eyes (about 10-7 stilb or less), the scotopic curve (rod vision) is given in Table 5.23. Table 5.23. Relative visibility factors. )" (A) 0 100 200 300 400 500 600 700 800 900 4000 5000 0.0185 0.900 0.0490 0.000 11 0.040 0.985 0.0300 0.076 0.960 0.0175 0.132 0.840 0.0100 0.212 0.680 0.0058 0.302 0.500 0.0032 0.406 0.350 0.0017 0.520 0.228 0.00087 0.650 0.140 0.00044 0.770 0.083 0.00021 6000 7000 For dark-adapted eyes, 1 lumen at 5100 A (scotopic) == 0.00058 W. The quantum thresholds for a single scintillation with most favorable conditions for human eye are 4 quanta in 0.15 s (absorbed) and 60 quanta in 0.15 s (incident). The threshold intensity for a large steady source [30] is 1.4 x 10- 10 stilb. The size of the retinal image for l' arc is 4.9 J1,m. The eye resolving power::::: l' ::::: 5 J1,m at fovea. 5.11 VISUAL PHOTOMETRY I 119 Density of rods and cones in the retina [29]: Rods 30 x 106 rods/sr = 2.7 rods/(minutes of arc)2, Cones 1.2 x 106 cones/sr = 0.1 cones/(minutes of arc)2. The density of cones in the fovea::::: 50 x 106 cones/sr. The equivalent diameter of the fovea region containing no rods [31] is 10 40'. The diameters of individual cones are 2 J.£m == 25" (variable). The diameters of individual rods are 1 J.£m == 12". The approximate brightness of common objects is given in Table 5.24 [32]. Table 5.24. Object and brightness (stilb). Candle Acetylene (Kodak burner) Welsbach (high-pressure) mantle Thngsten lamp filament Sodium vapor lamp Mercury vapor lamp (high pressure) Arc crater (plain carbon) Clear blue sky Overcast sky Zenith Sun 0.6 10.8 25 800 70 150 16000 0.2-0.6 0.3-0.7 165000 Table 5.25 gives approximate albedos for common objects. Table 5.25. Approximate albedos [1. 2]. White cartridge paper Magnesium oxide (or carbonate) Black cloth Black velvet 0.80 0.98 0.012 0.004 References 1. Walsh. 1.W.T. Photometry. 3rd ed. (Dover. New York). p. 529 2. Houston. R.A. 1924. Treatise on Light (Longmans. London) REFERENCES 1. Allen. C.W. 1973. Astrophysical Quantities. 3rd ed.• Sec. 35 (Athlone Press. London) 2. Allen. C.W. 1973. Astrophysical Quantities. 3rd ed.• Sec. 37 (Athlone Press. London) 3. Sampson. D.H. 1959. Api. 129. 734 4. Boercker. D.B. 1987. Api. 316. L95 5. van de Hulst, H.C. 1957. Light Scattering by Small Particles (Wiley. Chapman and Hall. New York) 6. Stergis. C.G. 1966. I. Arm. Ten: Phys.• 28. 273 7. Penndorf.R.1957.1. Opt. Soc. Am.. 47. 176 8. Irvine. W.R. 1965. I. Opt. Soc. Am.. 55.16 9. Osterbrock. D.E. 1974. Astrophysics of Gaseous Nebulae (Freeman. San Francisco) 10. Huebner. W.F. 1986. Physics of the Sun. Vol. I. edited by P. Sturrock (Reidel. Dordrecht) 11. Gaunt. I.A. 1930. Phi/os. Trans .• 229. 163 12. Burgess. A. 1965.ApJ.141. 1588 13. Henke. B.L. et al. 1982. At. Data Nucl. Data Tables. 27. 1 14. Saloman. E.B .• & Hubbell. 1.H. 1986. X-Ray Attenuation Coefficients (Total Cross Sections): Comparison of the Experimental Data Base with the Recommended 120 I 15. 16. 17. 18. 19. 20. 21. 22. 23. 5 RADIATION Values of Henke and the Theoretical Values of Scofield for Energies between 0.1-100 keY, U.S. Dept. of Commerce Report No. NBSIR 86-3431 Iglesias, C.A., Rogers, F.I., & Wilson, B.G. 1992, ApJ, 397,717 Rogers, F.I., & Iglesias, C.A. 1992, ApI, 7, 507 Cox, A.N. 1965, in Stellar Structure, 3rd ed., edited by L.H. Aller & D.B. McLaughlin (University of Chicago Press, Chicago), 195 Huebner, W.F., Keady, JJ., & Lyon, S.P. 1992, AP&SS, 195, 1 Allen, C.W. 1973, Astrophysical Quantities, 3rd ed., Sec. 43 (Athlone Press, London) Spitzer, L. 1962, Physics of Fully Ionized Gases, 2nd ed. (lnterscience, New York), p. 148 Chambe, G., & Lantos, P. 1971, Sol. Phys., 17,97 !toh, N., Nakagawa, M., & Kohyama, Y. 1985, ApJ, 294, 17 Nakagawa, M., Kohyama, Y., & ltob, N. 1987, ApJ Supp., 63, 661 24. Grevese, N., & Anders. E. 1991. in Solar Interior and Atmosphere, edited by A.N. Cox, W.C. Livingston, M.S. Matthews (University of Arizona Press, Tucson), p. 1227 25. Hyman, H.A., Kivel, B., & Bethe, H.A. 1973, Inverse Neutral Bremsstrahlung for Highly Polarizable Atoms, AVCO-Everett Research Laboratory Report No. SAMSO-TR-73-98 26. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed., Sec. 45 (Athlone Press, London) 27. Hass, G., & Tousey, R., 1958, J. Opt. Soc. Am., 49, 593 28. Garton, W.R.S. 1966,Adv. Atom. Mol. Phys., 2, 93 29. Allen, C.W. 1973, Astrophysical Quantities. 3rd ed., Sec. 46 (Athlone Press. London) 30. Pirenne, M.H. 1961, Endeavour. 20,197 31. Martin, L.C. 1948, Technical Optics (Pitman. London), pp. 1, 144 32. Walsh, I.W.T. Photometry. 3rd ed. (Dover, New York). p.529 Chapter 6 Radio Astronomy Robert M. Hjellming 6.1 6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . 121 6.2 Abnospheric Window and Sky Brightness . . . . . . . 123 6.3 Radio Wave Propagation ............................... 125 6.4 Radio Telescopes and Arrays ............................ 128 6.5 Radio Emission and Absorption Processes ............ 131 6.6 Radio Astronomy References ............................ 140 INTRODUCTION Radio astronomy is defined by three things. First is the range of frequencies that constitute the radio windows of the Earth's atmosphere, ranging roughly from 20 MHz to 1000 GHz. Second are the astronomical objects that emit radio waves with sufficient strength to be detectable at the Earth; some emit by thennal processes, but most are seen because of the emission from relativistic electrons (cosmic rays) interacting with local magnetic fields. Third, radio radiation behaves more like waves than particles (photons), allowing the measurement of both amplitude and phase of the radiation field. The capability to measure phase gives radio interferometry the capability to do the highest resolution imaging of astronomical objects currently possible in astronomy. The variety and number of radio sources is so large that in Table 6.1 we merely summarize a number of source catalogs devoted to these topics. 121 122 I 6 RADIO ASTRONOMY Table 6.1. List of radio soun:e catalogs. 1YPe of Source Contents 4C Radio Survey [1, 2] Bologna B2 Sky Survey [3-5] Bologna B3 Sky Survey [6, 7] 20 cm N. Sky Catalog [8] 6 cm Gal. Plane Survey [9] 6 cm South & Tropical Surveys [10, 11] 11 cm All Sky Catalog [12] 11 cm N. Sky Catalog [13] Bright Galaxies [14] 20 cm Gal. Plane Survey [15] 21 cm Gal. Plane Survey [16] Galaxy III [17,18] Atlas of Galactic III [19] Molecular lines [20, 21] Pulsars [22] Opt. Pos. Radio Stars [23] 20 cm Radio Sources 8 > _5° [24,25] 4844 56 cm sources > 2 Jy, _7° !: 8 !: 800 408 MHz, 21.7° !: 8 !: 40° 408 MHz, 37° !: 8 !: 47° 365, 1400,4850 MHz, 0 !: 8 !: 75° Parkes 64 m, Ibl !: 2°, I = 190° - 360° - 40° Parkes 64 m, -78° !: 8 !: _10° Bright sources 6483 sources, Ibl !: 5°,240° !: I !: 357° All radio data pre-1975, normal galaxies VLA B Conf. Survey Eff. 100m, Ibl !: 4°,95° !: I !: 357° Galaxies, Vradial !: 3000 kmls 21 cm H emission line profiles Frequencies, other molecular data Catalog of known pulsars 221 radio stars 1400 MHz sky atlas References 1. Pilkington, J.D.H., & Scott, P.P. 1965, Mem. R.A.S., 69, 183 2. Gower, J.P'R., Scott, P.F., & Willis D. 1967, Mem. R.A.S., 71, 144 3. Colla, G. et al. 1970, A&AS, 1, 281 4. Colla, G. et al. 1972, A&AS, 7, 1 5. Colla, G. et al. 1973, A&AS, 11,291 6. Fanti, C. et al. 1974, A&AS, 18, 147 7. Ficcara, A., Grueff, G., & Tomesetti, G. 1985, A&AS, 59, 255 8. White, R.L., & Becker, R.H. 1992, ApJS, 79, 331 9. Haynes, R.P., Caswell, J.L., & Simons, L.W.J. 1978, Aust. J. Phys. SuppL, 48,1 10. Griffith, M.R. et al. 1994, ApJS, 90, 179 11. Wright, A.E. et al. 1994, ApJS, 91, III 12. Wall, J.V., & Peacock, J.A. 1985, MNRAS, 216,173 13. Fiirst, E. et al. 1990, A&AS, 85, 805 14. Haynes, R.F., Caswell, J.L., & Simons, L.W.J. 1978, Aust. J. Phys. Suppl., 45, 1 15. Zoonematkermani, S. etal. 1990, ApJS, 74,181 16. Reich, W., Reich, P., & Fiirst, E. 1990, A&AS, 83, 539 17. Tully, R.B. 1988, Nearby GaJoxies Catalog (Cambridge University Press, Cambridge) 18. Huchtmeier, W.K., & Richter, O.-G. 1989, A General Catalog of III Observations of Galaxies: The Reference Catalog (Springer-Verlag, New York) 19. Hartman, D., & Burton, W.D. 1995, Atlas of Galactic III (Cambridge University Press, Cambridge) 20. Lovas, F.J. 1992, J. Phys. Chem. Ref. Data, 21,181 21. Lovas, F.J., Snyder, L.E., & Johnson, D.R. 1979, ApJS, 41, 451 22. Taylor, J.H., Manchester, R.N., & Lyne, A.G. 1993, ApJS, 66, 529 23. R6quieme, Y. & Mazurier, J.M. 1991,A&AS, 89, 311 24. Condon, JJ., Broderick, JJ., & Seielstad, G.A. 1989, AI, 97, 1064 25. Condon, J.J., Broderick, JJ., & Seielstad, G.A. 1991, AI, 102, 2041 Other information and images from surveys can be obtained from Internet pages maintained by the Nationa1 Center for Super Computing Applications (NCSA) Astronomy DigitaJ Image Library (ADIL, http://imagelib.ncsa.uiuc.edulimagelib.htm1) and the Nationa1 Radio Astronomy Observatory (NRAO, http://info.aoc.nrao.edu). More extensive radio (and other) cataJogs can be found from Internet pages for the NASA Astrophysics Data System (http://adswww.harvard.edulindex.htm1). In Figure 6.1 schematic radio spectra representative of a variety of continuum radio sources are plotted in the form of flux density (in units of Jy Jansky 10-23 ergs cm-2 s-1 Hz-I 10-26 W m- 2 Hz-I) as a function offrequency. The sources and spectra in Figure 6.1 are schematic = = = 6.2 ATMOSPHERIC WINDOW AND SKY BRIGHTNESS / 123 10' 'va Sun 10' Sky Background 10' Jupiter (radiation belts) 10' 10' 3: roo , x u: Crab Pulsar ""'(unpulsed) M31 10' 10' 10' BLLac 10" SS433 Crab Pulsar Cyg X-3 (non-flaring) (pulsed) 10-' 10-' Antares 10 100 1000 10000 Figure 6.1. Radio spectra of various types of sources in the form of flux density as a function of frequency v. indicators of typical behavior for a wide variety of objects. Major solar-system radio sources are the active Sun, the quiet Sun, the Earth's Moon, Mars, the surface of Jupiter, and Jupiter's radiation belts. Stellar system sources are: pulsars, with the pulsed and unpulsed (dashed line) emission from the Crab pulsar; the partially ionized coronal emission of the red supergiant Antares; and the X-ray binaries SS433 and Cyg X-3 (quiescent). The optically thick and thin portions of the radio spectrum of the ionized gas from an HII region is indicated for the Orion Nebula. Cas A is a remnant of a supernova explosion in our Galaxy; and the Crab nebula spectrum is representative of the relatively rare plerion, i.e., nebulosities energized by pulsars. The radio spectrum for M31, the Andromeda nebula, is representative of spiral galaxy behavior. Strong radio galaxies are represented by Cyg A and Virgo A; BL Lac is a blazar, while 3C273 and 3C295 are strong quasars. Defining the convention that the spectral index ex is the power law index for the flux density, Sv ex: va, then positive spectral indices indicate optically thick emission while negative spectral indices indicate optically thin emission. Spectral indices near zero indicate optically thin emission for thermal sources, while similarly flat spectra for synchrotron radiation sources indicate optically thick emission from a wide range of optical depths. 6.2 ATMOSPHERIC WINDOW AND SKY BRIGHTNESS 6.2.1 Atmospheric Window The low-frequency end of the radio window is set by ionospheric absorption. Since the ionosphere has diurnal variations, solar cycle variations, variations depending upon the effect of particle storms impacting the atmosphere, and variations with Earth latitude and longitude, the lowest frequency where the atmosphere is transparent varies considerably over the range 10 to 30 MHz. From that lowfrequency cut-off, up to about 22 GHz, the Earth's atmosphere does not absorb radio waves, although variation in the index of refraction affects the phase of incoming radio waves at the higher frequencies. 124 / 6 RADIO ASTRONOMY I I f)' 1 r- c: /' 111 I I I - f'T c: o .L: \(\ ..c: I a. f/) o E .:( -1mmPWV - - 8mmPWV o 0.01 0.1 ~ \1 \ \1 \ I Q) - \ I I ~ I- I \ I I a. f/) I ~ IA" 1'\ I ~ co I I 1 I I 1 10 \ I I ~ \~ \ I ~ 100 1000 o o ~I 200 I 1/ 1 d Ii 400 ~ ~ II J 600 800 1000 Frequency [GHz] Wavelength [cm] Figure 6.2. The radio window for the Earth's atmosphere shown in terms of plots of atmospheric transparency as a function of both wavelength and frequency. The solid line is for excellent conditions with 1 mm PWV and the dashed line is for nonnal conditions with 8 mm PWV. At the lowest frequencies plasma effects in the ionosphere induce variable Faraday rotation in incoming radio waves. In Figure 6.2 we plot models for the transparency of the Earth's atmosphere for two values of precipitable water vapor (PWV), 1 and 8 mm, representing extremely low and normal levels, respectively. 6.2.2 Surface Brightness and Brightness Temperature All astronomy is based upon measurements of surface brightness on the celestial sphere: Iv (a, /), t), where t is time, (a,/» is position specified by right ascension and declination, v is frequency, and I is the specific intensity which can be any of the four Stokes parameters. The surface brightness of a black body of temperature T is Bv = (2hv3/c2)(1/[ehv/kT - 1]), where h and k are the Planck and Boltzmann constants. For small values of h v f kT, the Rayleigh-Jeans approximation is valid, and Bv(T) ~ 2kT f).. 2; this is valid at longer radio wavelengths. For reasons related to the antenna measurement equation, radio astronomy often uses brightness temperature rather than surface brightness to describe measurements, where the brightness temperature is Tb == )..2 2kBv. (6.1) Equation (6.1) is often used even when black body or long wavelength approximations are not applicable. Because of this, the concept of radiation temperature (Tr == [hvf k]/[e hv/ kT - 1]) is commonly used; where T is a "true" physical temperature. 6.2.3 Sources of Background Radiation At each wavelength there are sources of background radiation detectable by radio telescopes, principally the Earth's atmosphere, the cosmic radiation background, and diffuse emission from our 6.3 RADIO WAVE PROPAGATION / -E 100000 ... 1;) E 100 ~ 10 0 on 1 .... ~o )( - .s:::; C) ''::: 0.001 co 0.0001 I° . 0.1 0.01 11 I'I I I'r [I II I II 11\1 I I I Earth's II II ( Atmosphere I ItI ( I I ! I \/ 't I ,\./ 1000 'l' en en CD c::: Galactic . . .Background 10000 0 .. Galactic e; . ............... a..ackground ..e /'/ 100 .................... y 10 1 0.1 ° ~O~· . ./ .. o I __ -0·0-0 . 100 Wavelength [cm] 10 g .... CD :::l ~ CD 10 a. E CD ~ en en CD c::: 1 Cosmic Bac 1 100 125 - .c 0) ''::: co 0.1 Wavelength [cm] Figure 6.3. Apparent brightness (left) and brightness temperature (right) plotted as a function of wavelength for: the Earth's atmosphere (dashed line, model; open circle, measurements); cosmic background radiation from COBE (solid line) and other instruments (filled circles); and galactic background radiation (dotted line). Galaxy. In Figure 6.3 we plot data and models for these sources of radiation. At wavelengths shorter than ~ I cm the Earth's atmosphere dominates the background, while above 13 cm the galactic background dominates. Between 1 and ~ 13 cm the cosmic background dominates. However, in many cases man-made interference, or solar radio emission, can be more important "background emission," particularly at wavelengths longer than 10 cm. 6.3 6.3.1 RADIO WAVE PROPAGATION Radiators-Absorbers, Fields, and Coupling Equations Radiation measurement at radio wavelengths allows direct measurement of the amplitude and phase of electromagnetic fields; this is the reason radiation field analysis in radio astronomy is usually done in terms of fields. If we identify a distant point in a radio source with the vector R, and the location of the oscillating current element with the vector, the fields between the two points are proportional to the propagator [1] e21rivIR-rl/c Pv(r) = IR - rl ' (6.2) so by Huygens' Principle, and the fact that all radiation appears as if it originates from the celestial sphere, the field on the celestial sphere at r is the superposition Ev(r) = f E(R) e21rivIR-rl/c IR-rl dS, (6.3) where d S is a surface element on the celestial sphere. The radiation flux for propagating fields is determined by the real part of the Poynting flux averaged over time, so (Sr) = (E x H) = Re(EeHcp - Et/JHe)/2 = EeHt/J. The power dP at distance r 126 / 6 RADIO ASTRONOMY passing through solid angle dO = dA/r 2 is the Poynting flux through dA at distance r. From the field distribution over the surface of an antenna we compute d P / dO which allows us to calculate the important properties of antennas. The normalized antenna pattern is defined by P.( n e, t/J )_ - dP/do. (dP /do.)max (6.4) so an infinitesimal current element has Pn(e, t/J) = sin2 e. The beam solid angle of an antenna is Oa = f41r Pn(e, t/J) dO, and the directivity is D = 4rr/o.a [2]. For real antennas we integrate over the collecting surface and from that compute d P / dO. from which antenna parameters may be computed. 6.3.2 Radio Noise and Detection Limits The measured quantities for radio telescopes are total power or correlated total power at some point in the signal path of the electronics. This is one of the sources of the predominance of using temperature as a measurement variable, because of Nyquist's law which relates the total power Pa to an antenna temperature Ta by Pa = 4kTa '&v, (6.5) where k.&v is the frequency range (or bandwidth) over which the total power measurement is made. Pa is the measure of the sum of the power due to radiation sources external to the antenna and the power generated in the antenna and its electronics system. In modern systems the latter is dominated by the receiver temperature, but is generally called system temperature (Tsys) which constitutes an irreducible minimum level of noise in the measured signal. The power being measured is that of a fluctuating voltage, originally induced by the external electric fields in the form of oscillating currents in the antenna's collecting surface, which radiate with a focus on either a feed at the prime focus of the antenna or on one or more subreflectors directed at a feed. The feed absorbs radiation and produces an output signal which is transferred to an electronic receiver followed (usually) by a complicated series of amplifiers, frequency converters, and other electronics elements. Then the fluctuating total power is then measured over a specific frequency range with a bandwidth (.&v), and over a specific time interval .&t. For a system temperature Tsys the noise component of the measured signal is .&Tnoise = Tsys ~, v.&v.&t (6.6) which indicates how noise changes with bandwidth and integration time. The same principle applies in the case of interferometry where signals are either added or (almost all the time) correlated (or multiplied), so it is the correlated power from two antennas that is being measured. The noise component of the system temperature is usually the limiting factor in the measurements being made. The fundamental limit to electronic noise temperatures is the quantum limit: h v / k = O.048vGHz K, where VGHz is the frequency in units of GHz. Real system temperatures must be above this limit. In the 1990s the state of the art of modern electronics is roughly capable of producing noise temperatures of 4hv/ k. It is expected that at the beginning of the twenty-first century noise temperatures will be'" 2hvj k, but it is unlikely that they will ever get very close to the quantum limit. 6.3.3 Effects of Ionosphere, ISM, and Source Environment Because radio signals are best dealt with by an analysis based upon electric fields, one should think of radio sources as three-dimensional regions radiating electric fields. Once radiation that will eventually 6.3 RADIO WAVE PROPAGATION / 127 reach a radio telescope on, or near, the Earth is produced, one then must think of propagation phenomena which affect these fields. Absorption and re-radiation by free electrons, ions, and atomic or molecular species can change the original radiation field into one modified by many effects. One can decompose this process into propagation effects: inside radio sources; in the intergalactic and interstellar medium (IGM and ISM); in the interplanetary medium of the solar system; and in the Earth's atmosphere and ionosphere. The ionized component of the intervening medium between a radio source and an observing telescope affects propagation by introducing time delays and Faraday rotation. The time of arrival of a pulse of radiation is tpulse = JoL ds / vgroup where L is the propagation path length, ds is a segment of the line of sight, and vgroup is the group velocity. The delay per unit frequency introduced by the electron concentration Ne is approximated by e2 dtpul se '" -- = dv 41l'Eomcv 3 lL 0 Neds. (6.7) The pulsed emission of radio pulsars allows the measurement of the changing time of arrival of a pulse with frequency, so the dispersion measure, Dm = JoL Ne ds, is routinely measured for the lines of sight to pulsars in our galaxy. If coexistent with magnetic fields, the same electrons that cause propagation delays induce Faraday rotation of the field vectors by an angle tP = i.. 2Rm where i.. is the wavelength. Rm is the rotation measure, which depends on the product of the local electron density, Ne , and the component of the magnetic field parallel to the line of sight, BII, and is given by Rm = 8.1 x 105 f NeBIl ds (6.8) in units of radians/m2, where BII is in Gauss, Ne is in cm- 3, ds is in parsecs, and the integral is over the path length along the line of sight. An estimate for the magnitude of these effects in can be made using mean values for the Galactic ISM such as (Ne ) ~ 0.003 cm- 3, BII ~ 2 JLG, and typically Rm '" -181 cot bl cos(l - 94°) radians/m2, where I and b are the galactic longitude and latitude. The scattering of radiation from electrons in the ISM, which produces interstellar scintillation, also has the effect of increasing the apparent size of point sources of radio emission. This effect produces an angular size due to scintillation which is roughly 7.Si.. 11/5 milliarcsec for Ibl ~ 0.°6, O.S(I sinbD- 3/ 5i.. 1l / 5 milliarcsec for 0.°6 < Ibl < 4°, 13(1 sinbl)-3/5i.. 11 / 5 milliarcsec for ISo> Ibl > 4°, and lSi.. 2/.J1 sinbl milliarcsec for Ibl > ISO, where b is the galactic latitude and i.. is the wavelength in meters. At long wavelengths, and for source line of sights close to the Sun, the solar corona and solar wind contribute very strongly to propagation delay, Faraday rotation, and scintillation. This can be estimated from the above formulas by Ne ~ (1.SSR- 6 + 2.99R- 16 ) x 10 14 m- 3 for R < 4, and Ne ~ S x lOll R- 2 m- 3 for 4 < R < 20, where R is the radial distance from the center of the Sun. The scattering size for an unresolved radio source due to the interplanetary medium is approximately SO(i../ R)2 arcmin where i.. is in meters. The ionosphere of the Earth is a major, and highly variable, contributor of electrons along the line of sight that affects the propagation of radio waves at long wavelengths. Figure 6.4 shows typical, but idealized, distributions of the ionospheric electron density for night and day, during sunspot maximum, and at temperate latitudes. The troposphere of the Earth's atmosphere also has the effect of absorbing the radiation from distant sources. If 10, v is the surface brightness of a source seen from outside the Earth's atmosphere, and t'o,v is the optical depth at the zenith, then at a zenith angle (z) I(z , v) =],0 ,v e-To.vX(z) , (6.9) 128 I 6 RADIO ASTRONOMY 1012 Day ~ §. ... E 8 c: 10 10 0 0 c: e t) CD F F1 c: 1011 0 ~ c: E 109 jjj 108 100 1000 Height [km] Figure 6.4. The electron concentration profile of the Earth's ionosphere for day and night plotted against height above the Earth's surface, at solar maximum, and at mid-latitudes. where X (z) is the relative air mass in units of the air mass at the zenith. To first order, X (z) ~ sec(z) = 1/ cos z. For X < 5 the formula X (z) = -0.0045+ 1.00672 sec z-0.OO2234 sec 2 z-O.OOO 624 7 sec3 z has an error less than 6 x 10-4 • Also, t'o,v ~ 0.12, 0.05, and 0.04 at 20,6, and 2 cm, but can be very large and variable at mm wavelengths. Even more important than air mass in affecting radio observations are the delay and scattering effects in the Earth's troposphere that produce the radio equivalent of seeing disks. However, since the 1970s radio astronomers have devised algorithms that allow so-called self-calibration of phase variations produced by the troposphere for radio interferometry measurements with four or more antennas in an array. Phase self-calibration by interferometric arrays are methods by which one can, for any observed field with a strong source, solve for the differences in atmospheric phase variations over each antenna, and then remove these phase variations from interferometric data. 6.4 6.4.1 RADIO TELESCOPES AND ARRAYS Properties of Antennas The normalized antenna pattern Pn(O, cp) (Equation (6.4» is used to define many of the important antenna properties. Although real antenna patterns cannot be exactly described by a mathematical function, many are close to that for a uniformly illuminated circular aperture of diameter D for which Pn (0) = {2J' ~ r 9) } T 8m 2, (6.10) smO where Jl is a first-order Bessel function. In Table 6.2 we list various definitions of antenna and source properties that depend upon the antenna pattern, and give the approximate values for uniform circular 6.4 RADIO TELESCOPES AND ARRAYS / 129 apertures. Since some of the directly measured quantities for radio sources are dependent upon the antenna pattern, some of these are also listed in Table 6.2 [2]. Table 6.2. Antenna propenies. Quantity Definition Uniform Circular Ap. Source solid angle Qs Effective source solid angle Q s = fsource Pn (e, t/J) dQ Surface brightness (Bv) = Half power beam width Pn(E>HPBW) Beam width at first nulls Pn(E>BWFN) Beam solid angle QA = f4:n: Pn(e, t/J) dQ = fsource dQ fmain lobe Bv(e, t/J)Pn dQ r Jmain lobe Pn dQ = 1/2 =0 E>HPBW E>BWFN = 1.02(J,./D) = 58°(J,./D) = 2.44(J,./ D) = 140 (J,./ D) 0 = fmain lobe Pn(e, t/J)dQ Main beam solid angle QM Directivity 4n/QA Effective area Ae=J,.2/QA Aperture efficiency "A = Ae/(n D2 /4) Beam efficiency "M = QM/QA 6.4.2 Major Radio Telescopes and Arrays There are many tens of radio telescope systems in the world that are, have been, or are about to be, important in radio astronomy. Many are listed in Table 6.3, where the size of the telescope or array, its main operational wavelengths, and its type or specialized role may be listed in abbreviated form. For a complete list of most of these telescopes and arrays, see [3]. Table 6.3. Radio observatories. Name of Observatoryllnst. Location Description Australia Tel. Nat. Facility Basovizza-Solar Radio Stn. Bleien Radio Ast. Obs. Culgoora, Australia Parkes, Australia Trieste, Italy Zurich, Switzerland Caltech Submillimeter Obs. Crawford Hill Obs. Mauna Kea, Hawaii Holmdel, New Jersey Decameter Wave Radio Obs. Deep Space Network Sta. Gauribidanur, India Goldstone, California Deep Space Network Sta. Robledo, Spain Deep Space Network Sta. Tidbinbilla, Australia 6 km EW Arr. 1 + (6) 22 m; 0.3-24 em 64 rn; 0.7-75 em 10 m; 38-130 em solar 5 rn; 30-300 em solar 7 rn; 10-300 em solar 10.4 rn; 1.3 mm-350 /.Lm 7 m Hom Thnable; 21 em 7 m Thnable; 1.3-3 mm 1.5 km T Arr.; 200-900 em 34 m; 3.6-13 em 70 m; 3.6-13 em 34 m; 3.6-13 em 70 m; 3.6-13 em 34 m; 3.6-13 em 70 m; 3.6-13 em 130 / 6 RADIO ASTRONOMY 1Bble 6.3. (Continued.) Name of ObservatorylInst. Location Description Dominion Radio Astro. Obs. Penticton. BC. Canada Dwingeloo Radio Obs. Eur. Incoh. Seatt. Fac. Dwingeloo. Netherlands Kinma, Sweden F1eurs Radio 'leI. Five College Radio Ast. Obs. Giant Metrewave Radio Tel. Hat Creek Radio Ast. Obs. Haystack Obs. Hiraiso Solar-Terr. Res. Ctr. Humain Radio Ast. Stn. F1eurs. NSW. Aus. Quabbin Res .• Mass. Pune District, India Cassel. California High TIme Resolving 'leI. Interplanetary Scint. Obs. Instituto Argentino de Rad. Inst. de Radio Astron. Mill. Nanjing. China Toyakawa, Japan Parque Pereya Iraola, Arg. P1ateau de Bore. France Pico Veleta, Spain F1eurs. NSW. Aus. Atibaia, Brazil 600mEW Arc. 49m;21.90em 26 In; 18-21 em 2S m; 6-29 em 32m; 32 em 440 x 120m; 130 em EW Arc. 325.8m+614m;21 em 13.7 m; 1-7 mm 2S km Irr. Arc. 3645 m; 21-790 em 3+ (3) T Arc. 6m; 1-7 mm 36 m; 0.7-18 em 210m+6m+ I m; 300-950 em 7.5 m; SO em solar T Arc. 48 4 m; 74 em solar 2 In; 3.2 em solar 100 x 20 m; 92 em 230 m; 17-21 em 0.4 km T Arc. (3) IS m; 1.3-4 mm 30 m; 0.8-4 mm 2.5 m+ 12-Yagi; 6.11.20. 120 em 13.7 m; 0.3-28 em 1.5 m; 4.3 em solar IS m; 1.3 mm-300 I'm 26m;3-ISOem 1.5 m; CO 2.6 mm Line 26 m; 0.7-90 em 32 m; 1.3-20 em VLBI T Parab. Cyl.; 74 em 14 m; 0.3-1.3 em 1570 x 12 m EW Cyl. Par.; 36 em 14 m; 30-SO em pulars 26 m; 2.5-SO em 5 km EW Arc. (4) 13 m; em A305 m; A- > 6em 14m;mmA43 In; 1.3-600 em 100 m; 0.7-90 em 12 m; 0.9-7 mm 1-35 km Y Arc. (27) 2S m; 0.7-90 em SOOO km Arc. 10 2S m; 0.7-90 em VLBI 22mAnt. 0.5 km T Arc. 16 1.2 m, 1.8 em solar TArcI76m.l90em 45 m, 0.26-3 em 0.7 km T Arc. (5) 10 m, 0.25-1.3 em 32 m; 0.3-1.3 em VLBI 134 km Irr. MERLIN Arc. 7 Ant.: 76 m; 5-200 em 38 x 26 m Par.; 1.3-200 em 38 x 26 m; 17-370 em 2S m; 6-200 em 2S In; 1.3-200 em 2S m; 1.3-2OOem 2S In; 1.3-200 em 13 In; 20-50 em pulsars 2.5 m; 2.5-4 mm 2.5 m; 1.3mm IPS F1eurs Solar Obs. ltapetinga Radio Obs. Westford, Massachusetts Nakaminato. Ibaraki. Japan Humain, Belgium James Clerk Maxwell 'leI. Kashima Space Res. Ctr. Kisaruzu College Obs. Maryland Point Obs. Staz. Rad. di Medieina Mauna Kca, Hawaii Metsahovi Obs. Radio Sta. Molonglo Obs. Synth. 'leI. Mount Pleasant Radio Obs. Metslihovi. Finland Hoskinstown. NSW. Aus. Cambridge, 'Thsmania, Aus. Mullard Radio Ast. Obs. National Astro. and Ion. Obs. National Obs. Ast. Center National Radio Ast. Obs. Cambridge, England Arecibo. Puerto Rico Yebes. Spain Green Bauk, West Va. NRAO mm 'lelescope Very Large Array Very Long Baseline Array Netherlands Found. Res. Ast. Nobeyama Solar Radio Obs. Kitt Peak, Arizona Socorro. New Mexico Nobeyama Radio Obs. Nobeyama, Japan Nobeyama, Japan Noto. Sicily England Jockell Bauk, Cheshire Jockell Bauk, Cheshire Wardle, Cheshire Defford, Worchestershire DarnhaII. Cheshire Knockin. Shropshire Pielanere. Cheshire Jockell Bauk, Cheshire F1oirac. France Plateau de Bore. France Noto Radio Ast. Sta. Nuffield Radio Ast. Labs. Obs. de Bordeaux Obs. de Grenoble Kashima, Japan Kisaruza ehiba, Japan Riverside. Maryland Medicina, Italy Socorro. New Mexico Dwingeloo. Netherlands Nobeyama, Japan 6.5 RADIO EMISSION AND ABSORPTION PROCESSES / 131 Table 6.3. (Continued.) Name of Observatoryllnst. Location Description Obs. fur Solare Astr. Obs. Radioastron. de Maipu Ohio State Radio Obs. Ondrejov Ast. Obs. Tremsdorf, Germany Maipu, Chile Delaware, Ohio Ondrejov, Czech. Onsala Space Obs. Onsala, Sweden Ooty Radioteleseope Ooty Synthesis Radiotelescope Owens Valley Radio Obs. Ootacamund, India Purple Mountain Obs. Purple Mt. Obs. Solar Fac. Delingha, China Nanjing, China Puschino Radio Ast. Sta. Puschino, Russia Radioobs. Effelsberg RATAN-600 Solar Radiospec. Obs. Sta. de Rad. de Naneay Effelsberg, Germany Zelenehukskaya, SU Ravensburg, Germany Naneay, Franee Swedish-ESO Subrnm. Tel. Tonantzintla Solar Radio Int. Toyokaya Obs. La Silla, Chile Puebla, Mexieo Toyokawa, Japan U. of Mieh. Radio Obs. URAN-l Interferometer UTR-2Array Westerbork Synth. Rad. Tel. YunnanObs. Dexter, Miehigan Kharkov, SU Kharkov, SU Westerbork, Netherlands Kunming, China 1.5 + 4 + 10.5 m + Vagi; 3.2-750 em 160 x 73 m; 670 em 100 x 30 m; 1.9 em 3 m; 1.5-3 em solar 7.5 m; 37-120 em solar 7.5 m; 25-300 em solar 20 m; 3.7-270 em 25 m; 30-260 em 530 x 30 m Par. Cyl.; 90 em (ORT) + 8 23 x 9 m; 90 em 0.4 km T Arr. (4) 10 m; 1.3-3 mm 40 m; 0.7-90 em Arr. of 2 27 m; 4-30 em 13.7 m; 0.3,1.3 em 1.5 m; 3.2-11 em solar 2 m; 6 em solar 22 m Tel. Cross-type 1 km decimetrie array 18 acre decimetrie phased array 100 m; 0.6-49 em 0.6 em eircle of 895 elem.; 0.8-30 em 7 m + 8 dipoles; 30-1000 em 161m Parab.; 3.2 em 24 Parab.; 67-200 em solar 16 + 2 Parab.; 67-200 em solar 299 x 40 m; 9-21 em 144 Con. Log. Per.; 380-2000 em 15 m; 0.8-3 rnm 2 1.1 m Parab.; 4 em solar 0.85 m; 3.2 em solar 1.5 m; 8 em solar 2 m; 14 em solar 3 m; 2.8 em solar 3 arrays; 3.2,7.8 em solar 25 m;em>.. Linear Arr, Xed dipoles; 1200-3000 em T Arr 1800 x 54 m + 900 x 54 m; 1200-3000 em 4 km EW Arr. 10 + (4) 25 m; 6-90 em 2.5,3,3.2, & 10 m; 8.1-130 em Big Pine, California 6.5 RADIO EMISSION AND ABSORPTION PROCESSES 6.5.1 Source Models and Prediction of Observables The relationship between the emission and absorption coefficients, which are used to describe the microphysics of radiation processes, and the theoretical quantities corresponding to the direct observables, is important in discussing the principle physical processes in radio astronomy. There are three principal observables: surface brightness Bv (and the related brightness temperature Tb,v), the integrated flux density Sv for a source with a closed boundary of solid angle Qsource, and Vv the 132 / 6 RADIO ASTRONOMY coherence (or visibility) function measured by radio interferometers. All are computed as integrals over the true sky brightness, or specific intensity, lv, and are given by Jsource Iv dOsource r Bv = Jsource dO source (6.11) ' (6.12) (where the approximation is valid for the Rayleigh-Jeans limit and most radio wavelengths) and Vv(u, v) = ff Iv(a, 8)Pn (a - ao, 8 - 80)e- 21ri/A,[Lj-Lk)·[s(a.8)-so(ao.&o)] dO, (6.13) where Lj and Lk are vector locations of antennas j and k, and 5 is a unit vector pointing to locations on the celestial sphere such as (a, 15) or the reference position (ao,80). For a spherically symmetric brightness distribution the latter equation simplifies to a Hankel transform: Vv(u, v) = f Iv «() P n «()Jo(27rq()27r() d(), (6.14) where (Lj - Lk) . (5 - SO)/A = ux + vy + WZ, q = (u 2 + v 2 + w 2 )1/2 '" (u 2 () = (x2 + y2 + z2)1/2 ~ (x2 + y2)1/2. In Table 6.4 a number of models and the associated observables are listed. + v 2 )1/2, and Table 6.4. Observables for simple source models. Tb(8)/ Tb,max Sv(Jy) Vv(q)/Sv Gaussian e-4 In 2(916s)2 Tb.max(K)8~ (arcsec) e-(1I' 24In2)(q6s)2 Uniform disk I, 8 ~ Bu/2 0,8> Bu/2 Tb,max(K)~ (arcsec) Limb-brightened 28u/(~ Model (shot glass) '''Ibin'' ring - 1360A,2(cm) 196 lA,2(cm) 8 2), Tb.max(K)~ (arcsec) 98U 2(cm) 2JI (1TqBu)/(1TqBu)a sin(1TqBu)/(1TqBu) 8 ~Bu/2 0,8> Bu/2 420Tb.max(K)~ (arcsec) 8(8 -Bu/2) A,2(cm) JO(1TqBu) Note a I n is a Bessel function of order n, and assuming that source is at the center of the field, then 8 rid (d is the distance to the object) and Bu is the half-intensity point in these spherically symmetric models. = The resolution of an instrument of size D is set by diffraction theory to be A/ D, and for radio astronomy the best resolution of an antenna is determined by its diameter (Dm in units of meters) and the shortest wavelength it can observe ('" [surface rms]/16). For arrays the size is the maximum separation of antennas (Dun in units of kIn). Thus C\ Oresolution A ,Acm = - = 34 - D Dm = 2" -Acm -. Dun (6.15) 6.5 RADIO EMISSION AND ABSORPTION PROCESSES / 133 The resolution of the instrument and the characteristics of the radio source, which we will discuss in terms of the models in Table 6.4, together with the other parameters determining the sensitivity of the antenna or array, determine the minimum surface brightness that can be detected. For modern paraboloid-shape antennas the 50" detection level for flux density during a time interval Lltsec is O"detection = 20 Tsys ( 2 FK/JyDm I .J LlVMHz Lltsec ) (6.16) Jy, where FK/Jy is a fixed, empirically determined constant for each antenna-receiver combination, while for an array of N antennas of this size, O"detection = 2.5Tsys ( 2 TJcEaDm 1 .JLl VMHz LltsecN (N - ) 1)/2 Jy, (6.17) where TJe is the correlator efficiency (0.82 for 3-level correlations), Ea is the aperture efficiency (~ 0.5 for simple paraboloids, but 0.6--0.7 for specially designed antennas), LlVMHz is the bandwidth in MHz, and Lltsec is the integration time in seconds. 6.5.2 Thermal Free-Free and Free-Bound Transitions For thermal bremsstrahlung radiation, the emission and absorption coefficients jvP and KvP are proportional to p2, where P is the mass density. The source function jv!K v , at radio wavelengths, is the Planck function for an electron temperature Te. Thermal bremsstrahlung or free-free radiation processes are caused by interactions between free electrons and positive ions in a partially or fully ionized plasma. The emission coefficient for free-free emission is given by jrf,vP = 5.4 x 10-39 N;Tel / 2 gffehv/kTe ~ 7.45 x 10- 39 N;Teo.34v-0.ll, (6.18) where we have used 3 1/2 [ Te3/2)] ~ -0.34 -O.ll 17.7 + In ( -v= 1.38 x Te vaHz gff(V, Te) = --;- (6.19) for the free-free Gaunt factor, with an approximation valid at radio wavelengths [4, 5]. In (6.18)(6.19), Ne is the electron concentration in units of cm- 3 , and Te is the electron temperature. The Planck function relates the emission and absorption coefficients for black body radiation, i.e., SV 3 jv = -Kv = -2hv 2C 1 h /kT. eVe - 1 ~ (V)2 , == 2kTr (V)2 = 2kTe c c (6.20) where the approximation that the radiation temperature Tr ~ Te is valid for longer radio wavelengths, but becomes invalid at mm wavelengths. For bound-free transitions the emission coefficient and Gaunt factor are given by 00 3 2 n - 3gfb(V = 1 72 x 10-33 Ne2 r.l 'fb .PV · e / " ~ , r.e, n)eI57890/n2Te , (6.21) n=m where n is the principal quantum number and m is the integer portion of (3.789 89 x 10 15 Hz/v) and gbf(V, Te, n) where Un = n 2 (v/3.289 89 x = 1+ 0.1728(u n - 1) 0.0496(u~ + 1Un + 1) n(u n + 1)2/3 n(u n + 1)4/3' 10 15 Hz) [6]. (6.22) 134 / 6 6.5.3 RADIO ASTRONOMY Spectral Lines-Thermal Bound-Bound Transitions For bound-bound transitions between any two levels with energies En = E 1•...• Eionization and statistical weights gn. radiation absorption and emission involves photons of energy hVnm = Em - En. The properties of a line transition are determined by the Einstein coefficients Amn. Bmn. and Bnm. which are related by and (6.23) The emission and absorption coefficients for line transitions are (6.24) and (6.25) where 4Jnm (vmn ) and 4Jmn (vmn ) are absorption and emission "line" profile functions. which are usually equal to each other. Note that in general the source function can be expressed as Sv nm = .ibb,vnm = 2hv2 3 ( Kbb,vnm c 1 ) . N ngn4Jmn(vmn ) _ 1 N mgm4Jmn(vnm ) (6.26) If the line is in Local Thermodynamic Equilibrium (LTE) with temperature T. then Nn/Nm (gn/gm)exp(hvnm/kT) andS Kbb,LTE,vnm = Bv so ,/,. ( Vnm ) [1 = hV41l'nm Nm Bnm'f'mn e -hvnm1kT] . = (6.27) Most of the known spectral lines from molecules in the interstellar medium have been detected at radio wavelengths. Many are in Table 6.5. For current lists and information about the parameters of various molecular species see the Internet URL http://spec.jpl.nasa.gov. 18ble 6.5. Known interstellar molecules. Name of molecule Chemical symbol Wavelength region Date and telescope of discovery methyladyne cyanogen radical rnethyladyne ion hydroxyl radical ammonia water formaldehyde carbon monoxide hydrogen cyanide cyanoacetylene hydrogen methanol formic acid formyl radical ion CH CN CH+ OH NH3 H2O H2CO CO HCN HC3N H2 CH30H HCOOH HCO+ 4300 A 3875A 4232A 18cm l.3cm l.4cm 6.2cm 2.6mm 3.4mm 3.3cm 1013-1108 A 36cm 18cm 3.4mm 1937 - Mt. Wilson 2.5 m 1940 - Mt. Wilson 2.5 m 1941 - Mt. Wilson 2.5 m 1963 - Lincoln Lab. 26 m 1968 - Hat Creek 6 m 1968 - Hat Creek 6 m 1969-NRA043 m 1970 - NRAO 11 m 1970-NRAO 11 m 1970-NRA043 m 1970 - NRL rocket 1970-NRA043 m 1970-NRA043 m 1970-NRAO 11 m 6.5 RADIO EMISSION AND ABSORPTION PROCESSES / Table 6.5. (Continued.) Name of molecule Chemical symbol Wavelength region Telescope of discovery fonnamide carbon monosulfide silicon monoxide carbonyl sulfide methyl cyanide isocyanic acid methyl acetylene acetaldehyde thiofonnaldehyde hydrogen isocyanide hydrogen sulfide methanimine sulfur monoxide diazenylium ethynyl radical methylamine NH2CHO CS SiO OCS CH3CN HNCO CH3CCH CH3CHO H2CS HNC H2S CH2NH SO N2H+ C2H CH3NH2 dimethyl ether ethanol sulfur dioxide silicon sulfide vinyl cyanide methyl fonnate nitrogen sulfide cyanamide cyanodiacetylene formyl radical acetylene cyanoethynyl radical ketene cyanotriacetylene nitrosyl radical confirmed ethyl cyanide cyano-octatetra-yne methane nitric oxide butadiynyl radical methyl mercaptan isothiocyanic acid thioformyl radical ion protonated carbon dioxide ethylene cyanotetraacetylene silicon dicarbide propynylidyne methyl diacetylene methyl cyanoacetylene tricarbon monoxide silane protonated HCN (CH3}z0 CH3CH20H 6.5cm 2.0mm 2.3mm 2.7mm 2.7mm 3.4mm 3.5mm 28cm 9.5cm 3.3mm 1.8mm 5.7cm 3.0mm 3.2mm 3.4mm 3.5mm 4.1 mm 9.6mm 2.9-3.5 mm 3.6mm 2.8,3.3 mm 22cm 18cm 2.6mm 3.7mm 3.0cm 3.5mm infrared 3.4mm 2.9mm 2.9cm 3.7mm 1.9mm 2.7-4.0mm 2.9cm infrared 2.0mm 2.6-3.5mm 3mm 3mm 3mm 3mm infrared many (cm) many(mm) many (3 mm) several (cm) several (cm) 2cm infrared 3,2, I mm 1971-NRA043 m 1971 - NRAO II m 1971 - NRAO II m 1971-NRAO II m 1971- NRAO II m 1971- NRAO II m 1971-NRAO II m 1971-NRA043 m 1971 - Parkes 64 m 1971 - NRAO II m 1972 - NRAO II m 1972 - Parkes 64 m 1973 - NRAO II m 1974 - NRAO II m 1974 - NRAO II m 1974-NRAO 11 m 1974 - Tokyo 6 m 1974-NRAO II m 1974-NRAO II m 1975-NRAOllm 1975 - NRAO II m 1975 - Parkes 64 m 1975 - Parkes 64 m 1975 - Texas 5 m 1975 -NRAO II m 1976 - Algonquin 46 m 1976 - NRAO II m 1976 - KPNO 4 m 1976-NRAO II m 1976-NRAO II m 1977 - Algonguin 46 m 1977 - NRAO II m 1990 - FCRAO 14 m 1977 - NRAO II m 1977 - Algonguin 46 m 1977 - KPNO 4 m 1978-NRAO II m 1978-NRAO II m 1979-BTL 7 m 1979-BTL7m 1980-BTL 7 m 1980-BTL7m 1980 - KPNO 4 m 1981 - Algonquin 46 m 1984-BTL 7 m 1984-BTL7m 1984 - Haystack 37 m 1984 - Haystack 37 m 1984 - Haystack 37 m 1984-KPN04m 1984 - NRAO 12 m 1984 - Texas 5 m 1985 -many 1985 -KAO 1985 - KAO 1986 - NRAO 12 m 1990 - CSO 10 m cyclopropynylidene hydrogen chloride protonated water confirmed SOz SiS CH2CHCN CH3OCHO NS NH2CN HCSN HCO C2H2 C3N H2CCO HC7N HNO CH3CH2CN HC9N C14 NO C4H CH3SH HNCS HCS+ HOCO+ C214 HCllN SiC2 C3H CH3C4H CH3C3N C30 Si14 NCNH+ C3H2 H2D+ ? HCl? H3 0 + 3,2mm 0.62mm 0.48mm 1.0mm 0.8mm 135 136 I 6 RADIO ASTRONOMY Table 6.5. (Continued.) Name of molecule Chemical symbol Wavelength region Telescope of discovery pentynylidyne radical hexatriynyl radical phosphorus nitride CSH radio radio 3,2,1 mm 1986 - IRAM 30 m 1986 - IRAM 30 m 1986 - NRAO 12 m 1986-FCRAO 14m 1986 - Nobeyama 45 m 1986 - Nobeyama 45 m 1987 - IRAM 30 m 1987 -IRAM 30m 1987 - IRAM 30 m 1987 -IRAM 30m 1987-IRAM30m 1987 - IRAM 30 m 1988 - Nobeyama 45 m 1988 - NRAO 43 m 1989-IRAM 30 m 1989 - Nobeyama 45 m 1989 - NRAO 43 m 1989 - Nobeyama 45 m 1989 - IRAM 30 m 1990 - IRAM 30 m 1990 - NRAO 43 m 1990 - IRAM 30 m 1990 - NRAO 12 m 199O-CSO 10m 1991 - IRAM 30 m 1991-Nobeyama45 m 1991-NRA043 m 1992 - Nobeyama 45 m 1992-NRAO 12 m 1992 - Nobeyama 45 m 1992 - Nobeyama 45 m 1993 - Nobeyama 45 m 1993-CSO 1993-NRAO 12m,CSO 1993 - NRAO 12 m 1993 - NRAO 12 m, CSO 1994 - NRAO 12 m 1995 - NRAO 12 m 1995 - Nobeyama 45 m 1996 - IRAM 30 m 1996 - IRAM 30 m 1996-UKIRT 1997 - NASA 34 m 1997 - NRO, SEST, Haystack 1997 - ISO acetone sodium chloride aluminum chloride potassium chloride aluminum ftuoride methyl isocyanide cyanomethyl radical C2S C3S (CH3hCO? NaCI AICI KCl AlF CH3NC CH2CN silicon carbide propynal SiC HCCCHO phosphorus carbide propadienylidene SiC4 CP H2CCC butatrienylidene silicon nitride silylene (pend. conf.) carbon suboxide isocyanoacetylene sulfur oxide ion ethinylisocyanide magnesium isocyanide protonated HC3NH+ carbon monoxide ion sodium cyanide nitrous oxide magnesium cyanide prot. formaldehyde octatetraynyl radical octatetraynyl radical protonated hydrogen hexapentaenylidene ethylene oxide hydrogen ftouride 6.5.4 YiH PN H2CCCC SiN SiH2 ? HCCN C20 HCCNC SO+ HNCCC MgNC NC3H+ NH2 CO+ NaCN CH20+ N20 MgCN H2COH+ CSH C7H Hj H2C6 C-C2~O HF 3,7mm 3,7mm 3.4mm 2,3mm 2,3mm 2,3mm 2,3mm 3mm 6.5mm 1.3cm 2mm 8mm 1.6cm 3.5,7.5mm 1.2,3.0mm 3mm 1.4cm many (3 mm) 1.1,1.4 mm 0.8,1.0mm 3mm 7mm 1.3cm 7mm 1.3,3mm 1.1,0.8,0.64 cm radio radio 0.645mm 1.3,O.8mm 3,2.4mm 0.8-4.0mm 2.0-4.0mm radio radio radio radio IR-3.67 f.Lm K-band K, Q, 3 mm,l mm 121.7 f.Lm Magneto-Bremsstrahlung Emission and Absorption The other radiation process of dominant importance in radio astronomy is magneto-bremsstrahlung emission and absorption which results from the interaction between fast-moving electrons and the ambient magnetic field. There are three major varieties of magneto-bremsstrahlung emission. When the moving electrons are very relativistic, the emission process is the very efficient, highly beamed synchrotron emission which dominates the emission from many galactic and most extragalactic ra- 6.5 RADIO EMISSION AND ABSORPTION PROCESSES / 137 dio sources. However, in some stars and certain solar system environments, two other magnetobremsstrahlung processes occur when the moving electrons are nonrelativistic or only mildly relativistic. When mildly relativistic (}'Lorentz == (1 - (v/c)2)-1/2 ~ 2-3) electrons undergo interactions with magnetic fields, the emission process is called gyro synchrotron, which is much less beamed and much less efficient at producing radio emission than synchrotron processes; however, it tends to be highly circularly polarized, a characteristic commonly found in stellar radio emission. Even less efficient is the magneto-bremsstrahlung resulting from less relativistic particles, with YLorentz :s 1, which is called cyclotron or gyro resonance emission. The details of nonrelativistic (cyclotron) and mildly relativistic (gyro synchrotron) emission and absorption processes are more complicated than the highly relativistic case. They are summarized by [7], and extensively discussed by [8] and [9]. Much of the analysis of radio source data uses very simple models for the behavior of synchrotron radiating sources. This section summarizes formulas used in such analysis. We assume that the density of relativistic electrons can be described by a power law distribution in energy, N(E) = K E-Y in the energy range E to E + dE, where y is a constant. If these electrons are mixed in with a uniform distribution of magnetic fields of strength H, which can be described as having uniformly random directions on a large scale, then the emission and absorption coefficients are given by jvP = 1.35 x 1O-22 a (y)K H(y+l)/2 ( 636 . : 1018)(Y-l)/2 and (6.28) (6.29) where H is in gauss and all other variables are in cgs units, so that the source function is _ 2 -jv . 84 S v -- Kv x 10-30a(y)2y/2H-I/2 -v 5/2 erg s -I cm -3 g(y) (6.30) [10]. Table 6.6 gives some of the values of the functions a(y), g(y), the brightness temperature source function Ts , and the angular size (80) of a uniform source with flux density So and magnetic field HmG in units of milligauss. Table 6.6. Incoherent synchrotron emission constants. Y 1.0 15 2.0 2.5 3.0 4.0 5.0 a(y) g(y) a 0.283 0.147 0.103 0.0852 0.0742 0.0725 0.0922 0.96 0.79 0.70 0.66 0.65 0.69 0.83 0.0 0.25 0.50 0.75 1.0 1.5 2.0 T. -1/2 HI/2 sVGHz 1.9 1.0 6.6 4.9 3.6 2.3 1.7 x x x x x x x mG 1012 K 1012 K 10" K 10" K 10" K 10" K 10" K e oS-I/2 H- 1/ 4 5/4 0 mG vGHz 0.015 mas 0.021 mas 0.026 mas 0.030 mas 0.035 mas 0.044 mas 0.051 mas The specific intensity is given by (6.31) where dTv = KvP ds in the above integral, which is along the line of sight of length L. 138 / 6 RADIO ASTRONOMY We see from (6.30) that the important case where jv/Kv is constant occurs if the magnetic field is unifonn in strength and geometry. Equations (6.28)-(6.30) also tell us that for the optically thick and thin limits, Iv is proportional to H- 1/ 2v 5/ 2 and K H(y+l)/2 v -(y-l)/2 L, respectively, where L is a line-of-sight path length. Defining the spectral index a by Sv ex: va, then a 2.5 and -(y - 1)/2 in the optically thick and thin limits, respectively. The values of a in the latter case for various values of y are listed in Table 6.6. The evolution of the relativistic electron energy distributiop N(E, t) is the primary factor in the evolution or synchrotron radiation sources. In its most general fonn this evolution is described by = aN(E, t) at + a[ dE] aE N(e, t)Tt = r(E, T) - A(E, t), (6.32) where r(E, T) and A(E, t) are functions describing particle "injection" and "escape," with escape time scales T, respectively. Usually r and A are zero, as they will be for all models discussed below, or applies to only small portions of the radio sources. The equation for evolution of N (E, t) is supplemented by the energy loss equation: dE dt = q,(E) = _~ _ TJE _ ~E2, (6.33) where the first two terms are due to losses by ionization in the ambient, medium, and free-free interaction with this medium. The last tenn, which is usually the most important, includes both energy loss due to synchrotron radiation and energy loss due to inverse Compton scattering off photons in the local radiation field. The coefficients of the first two tenns in (6.33) are: ~ ~ 3.33 x 1O-20nH (6.27 + In (m~2 ) ) + 1.22 x 10-20n e (73.4 In (m~2 ) and TJ ~8x 1O- 16nHne (0.36 + In (m~2)) , - In ne ) (6.34) (6.35) where nH is the concentration of neutral hydrogen atoms and ne is the concentration of thermal electrons. For synchrotron radiation losses ~synch ~ 2.37 x 10-3 Hi, where Hl.. is the magnetic field perpendicular to the velocity vector of the radiating relativistic electron. The time scale for synchrotron losses is tsynch == E/(-dE/dt) = 1/(~synchE) '" (5.1 x 108 /Hi)(mc 2/E) s. Synchrotron radiation losses dominate in regions with large magnetic fields and low radiation fields. For inverse Compton losses ~IC ~ 3.97 x 1O-4 urad, where Urad is the radiation energy density. Inverse Compton losses dominate when brightness temperature approaches Tb ~ 10 12 K. Above 10 12 K all relativistic electrons loss their energy rapidly due to this process. For steady-state synchrotron radiation sources where one assumes A(E, t) = A(E), and N(E, t) = N(E), and aN/at = 0, the relativistic particle energy equation has the solution N(E) = q,-I(E) J A(E)dE. So if one can assume a power law for the particle injection, A(E) = AoE-Y, then (6.36) The relativistic particle spectra and observable radio spectrum for such steady-state radio sources can be described by three segments of power laws as shown in Figure 6.5. The principle effect of more complex models is replacement of the sharp spectral breaks with smooth transitions. 6.5 RADIO EMISSION AND ABSORPTION PROCESSES / 139 a=-(y-l)/2 y log N(E) y+ 1 logE , ionization losses : free-free losses, synchrotron + inverse , : compton losses ,, a absorption / absorption a + 112 log V Figure 6.5. Relativistic particle (top), and observable flux density (bottom), spectrum for steady-state synchrotron radiation sources. The changes in slope indicate regions where ionization, free-free, and synchrotron (+ inverse Compton) losses dominate. By each curve segment is the power law index for the energy and flux density spectra. External or self-absorption can occur at any point in the flux density spectrum; two possibilities are indicated in the figure. A synchrotron radio source with losses only due to synchrotron radiation has an energy loss equation d(E- l )/dt = {synch which leads to a spectrum described by E = Eo/[1 + {synch(t - to)Eo]. Then if at t = to, N(E) = NoE-Y, then at later times N(E) = NoE-Y(1 - {synchEtV-l for E < ET(t), and N(E, T) = 0 for E > ET(t), where ET(t) = 1/({syncht). The frequency above which synchrotron losses dominate is Vb ~ BG:usst~ GHz. Time-dependent synchrotron radiation source models with complex geometry and complex energy loss mechanisms require extensive computation. However in the case of simple geometries and only adiabatic losses the evolution of the flux density of a radio source can be expressed in analytic or nearanalytic equations. For a spherical region which "suddenly" has a distribution of relativistic particles given by No = KoE-Y and which expands with an outer radius r2(t) the flux density of the source is described by the quantities in Table 6.7 [11-13]. An analogous model can be expressed for a conical jet with ejection of adiabatically expanding plasma [13]. The jet ejection parameters are such that at an initial distance Zo the radius of the cross section of the jet is ro Get Mach number Mo = zo/ ro) and the relativistic particle density is No. The quantities that determine the flux density for an observer for whom the jet is oriented at an inclination angle e are in Table 6.7; for a continuous jet Z2 = 00 and Zl = zo; however, a time-dependent jet which starts ejection with velocity V2 at time tstart and ends ejection with velocity VI at time tstop is described by the same equations with the necessary time dependence in the limits of integral for the flux density. Table 6.7. Radio source models-{)niy adiabatic energy losses. TO Expanding sphere Conical jet E = Eo(r2/ro)-1 H = Ho(r2/ro)-2 K = Ko(r2/ro)-(y+2) E = Eolr2(Z2)/rOr 2/ 3 H = HO[r2(Z2)/rO]-1 Ko[r(Z2)/rOr 2(y+2)/3 K = 0.038g(y)(3.5 x 109 )y KoHci Y+ 2)/2 ro = same 140 / 6 RADIO ASTRONOMY Table 6.7. (Continued.) Expanding sphere Hr; r > 20) Hr; r < 20) Conical jet =1 = 0.66584 + 0.09089r - 0.009989r2 + 0.0005208r 3 > 20) r < 20) ~(r; r ~(r; - 0.00001268r4 + 0.000000115r 5 , rv = rO ( r )-<2Y+3) ( v )-<Y+4)/2 - rO - Vo -0.65y n-1/2. 5/2 ",,3 Sv -- 142 . e O,mG vGHz "'mas r' v Sv r2(t; E cons.) r2(t; Mom. cons.) sm(E» rO JzZI2<~i 1; 3/ 2 [1 - exp( -r~)H(r~) dl; r2(t; free exp.) / = rO ( iOt )2 5 t ) vo = SOMO ( ~) 5/2 sin(E» = rO (~) = rO ( iO = 0.78517 + 0.06273r - 0.007242r2 + 0.0003905 r 3 - 0.00000973r4 + 0.OOOOOOO9r 5 = (~) (~)-<Y+4)/2 [r2(Z2) ]-<7Y+8)/6 x r2(t; freeexp.) =1 1/4 r2(t; E cons.) = rO z )1/2 ( Z~ r2(t; Mom. cons.) = ro (~~) 1/3 Z2 ZI 6.6 = rO G~) = v2 (t = vI (t - tstart) tstop) RADIO ASTRONOMY REFERENCES Table 6.8 gives further references for radio astronomy. Table 6.8. List of radio astronomy references. Topic Reference Radio astronomy research field reviews Properties of radio telescopes Interferometry and aperture synthesis Aperture synthesis Observation-oriented radio astronomy textbooks Synchrotron radiation physics Radio astrophysical theory General astrophysical theory (1) (2) (3) [4,5) [6,7) (8) (9) (10) References 1. Verschuur, V.L., & Kellermann, K.I. 1988, Galactic and Extragalactic Radio Astronomy (Springer-Verlag, New York) 2. Christiansen, W.N., & Hogbom, I.A. 1985, Radio Telescopes (Cambridge University Press, Cambridge) 3. Thompson, A.R., Moran, I.M., & Swenson, G.w. 1986, Interferometry and Synthesis in Radio Astronomy (Wiley, New York) 4. Perley, R.A., Schwab, F.R., & Bridle, A.H. 1989, Synthesis Imaging in Radio Astronomy, A.S.P. Conference Series, 6 5. Cornwell, T.I., & Perley, R.A. 1991, Radio Interferometry: Theory, Techniques, and Applications, A.S.P. Conference Series, 19 6. Rohlfs, K. 1986, Tools of Radio Astronomy (Springer-Verlag, Berlin) 7. Krause, J.D. 1986, Radio Astronomy, 2nd ed. (Cygnus-Quasar Books, Powell) 8. Ginzburg, V.L., & Syrovatskii, S.I. 1965, Ann. Rev. Astron. Astrophys., 3, 297 9. Pacholczyk, A.G. 1970, Radio Astrophysics (W.H. Freeman, San Francisco) 10. Longair, M.S. 1981, High Energy Astrophysics: an informal introduction for students of physics and astronomy (Cambridge University Press, Cambridge) 6.6 RADIO ASTRONOMY REFERENCES I I 141 REFERENCES 1. Clark, B.G. 1989, Synthesis Imaging in Radio Astronomy, A.S.P. Conference Series, 6, p. I 2. Christiansen, W.N., & H6gbom, I.A. 1985, Radio Telescopes (Cambridge University Press, Cambridge) 3. Price, R.M. et al. 1989, Radio Astronomy Observatories (National Academy Press, Washington, DC) 4. Karzas WJ., & Latter, R. 1961,ApJS, 6,167 5. Hjellming, R.M., Wade, C.M., Vandenberg, N.R., & Newell, R.T. 1979, AI, 14,1619 6. Aller, L.H. & Liller, W. 1968, Nebulae and Interstellar Matter, edited by B. Middlehurst & L.H. Aller (Univer- sity of Chicago Press, Chicago), Chapter 9 7. Dulk,G.A. 1985,ARA&:A.13. 169 8. Kundu. M.R. 1965. Solar Radio Astronomy (Interscience. New York) 9. Zheleznyakov, v.v. 1970. Radio Emission of the Sun and Planets (Pergamon Press. Oxford) 10. Ginzburg, V.L., & Syrovatskii. S.I. 1965. ARA&:A. 3. 297 11. vander Laan,H. 1966. Nature. 211. 1131 12. Kellermann, K.I. 1966. ApJ. 146.621 13. Hjellming, R.M., & Iohnston. KJ. 1988. ApJ. 328, 600 Chapter 7 Infrared Astronomy A.T. Tokunaga 7.1 7.1 Useful Equations; Units . . . . . . . . . . . . . . . . . 143 7.2 Atmospheric Transmission. . . . . . . . . . . . . . .. 144 7.3 Background Emission. . . . . . . . . . . . . . . . . .. 146 7.4 Detectors and Signal-to-Noise Ratios. . . . . . . . .. 148 7.5 Photometry (J.. < 30 #Lm) . • . • • . . . . • . . . . • .. 149 7.6 Photometry (J.. > 30 #Lm) . . . . . . . . . • . • . . • .• 154 7.7 Infrared Line List . . . . . . . . . . . . . . . . . . . .. 155 7.8 Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 158 7.9 Solar System . . . . . . . . . . . . . . . . . . . . . . .. 161 7.10 Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 163 7.11 Extragalactic Objects. . . . . . . . . . . . . . . . . .. 164 USEFUL EQUATIONS; UNITS The Planck function in wavelength units B). (J..~m = 2hc2J.. -5 /(e hc / kAT - in #Lm; T in K) is 1) = 1.1910 x 108J..;~/(eI4387.7/).,.mT - 1) Wm- 2 #Lm- 1 sr-I. The Planck function in frequency units (v in Hz) is Bv = 2hv3c-2/(ehv/kT - 1) = 1.4745 x 10-SO v 3 /(e4.79922xIO-IJ v/T _ 1) Wm- 2 Hz-I sr-I. 143 144 / 7 INFRARED ASTRONOMY The Rayleigh-Jeans approximation (for hv «kT) is B)" = 2ckT)..-4 = 8.2782 x 103 TP"!m Wm- 2 JLm- l sr- l , Bv = 2c- 2kTv 2 = 3.0724 x 10-40 Tv 2 Wm- 2 Hz- l sr- l . The Stefan-Boltzmann law is The wavelength of maximum B)" (Wien law) is Amax = 2898/T, Amax in JLm. The frequency of maximum Bv is Vmax = 5.878 x 10 10 T, Vmax in Hz. The conversion equations (0 in sr) are F)" = OB)", Fv = OBv, F)" = 3.0 x 1014 Fv/A~m' Other units are 1 Jansky (Jy) = 10-26 Wm- 2 Hz-l. Units details are given in Table 7.1. Table 7.1. Units [1-4]. Units Radiometric name Astronomical name Luminosity Flux Wsr- I Wm- 2 sr- 1 Wm- 2 IL m - l ; Wm- 2 Hz-I Wm-2ILm-1 sr-I; Wm- 2 Hz-I sr- I Flux Irradiance; radiant exitance Intensity Radiance Spectral irradiance Spectral radiance Intensity Flux density Surface brightness; specific intensity References 1. Boyd, R.W. 1983, Radiometry and the Detection of Optical Radiation (Wiley, New York) 2. Dereniak, B.L., & Crowe, D.G. 1984, Optical Radiation Detectors (Wiley, New York) 3. Wolfe, W.L., & Zissis, G.J. 1985, The Infrared Handbook. rev. ed. (Office of Naval Research. Washington, DC) 4. Rieke. G.H. 1994. Detection of Light; From the Ultraviolet to the Submillimeter (Cambridge University Press. Cambridge) 7.2 ATMOSPHERIC TRANSMISSION The major atmospheric absorbers and central wavelengths of absorption bands are H20 (0.94, 1.13, 1.37, 1.87,2.7,3.2,6.3, A > 16 JLm); C02 (2.0,4.3, 15 JLm); N20 (4.5, 17 JLm); CR4 (3.3,7.7 JLm); 03 (9.6 JLm). See Figures 7.1 and 7.2. For atmospheric transmission at airborne and balloon altitudes, see [6,11]. For water-vapor measurements at observatory sites, see [12-14]. For atmospheric extinction, see [2, 15-17]. 7.2 ATMOSPHERIC TRANSMISSION I 145 1.0 0.8 C 0 '00 0.6 'E 0.4 C 0.2 u .;:: 1.0 C/) C/) ca .... 0.0 +-' Q) .c c.. en 6 0.8 0.6 0 E 0.4 ~ 0.2 0.0 N 10 6 20 Wavelength (~m) Figure 7.1. Atmospheric transmission from 0.9 to 30 JLm under conditions appropriate for Mauna Kea, Hawaii. Altitude = 4.2 km, zenith angle = 300 (air mass = 1.15), precipitable water vapor overhead = 1 mm. AI AA = 300 for 1-6 JLm and 150 for 6-30 JLm. Spectra are calculated by Lord [1]. The infrared filter band passes are shown as horizontal lines; see Table 7.5 for definitions. Note that the filter transmission is modified by the atmospheric absorption. For the atmospheric transmission at Kitt Peak, see [2]. For ESO, see [3]. See also [4]. f... -?flc ". 60 'E 40 C/) c ca .... ~ 1000 80 0 '00 en 5000 100 ·. ·. :: 500 400 w I •• .. W 300 250 =1 mm (Mauna Kea) =5 mm (Kitt Peak) .. ..'" . ..'.' . .' .' .' ..'.'.' · .... ..'.'• ··· .. ' 20 0 .: (...... (~m) ' ' '' 0 5 10 15 20 25 30 35 40 u (em -1) Figure 7.2. Atmospheric transmission from 0.25 to 3 mm, adapted from [5]. The precipitable water vapor is denoted by w. See also [6-9]. For the South Pole. see [10]. 146 I 7.3 7.3.1 7 INFRARED ASTRONOMY BACKGROUND EMISSION Background Emission Sources Table 7.2 gives the background emission from a ground-based telescope. The main background emission sources are shown in Figure 7.3. Where specified they are blackbody functions reduced by a multiplying factor €. In most cases, only the minimum background levels are plotted. OH GBT ZSL ZE GBE SEP CST CBR OH airglow. Average OH emission of 15.6 and 13.8 mag arcsec- 2 at J and H, respectively [18-21]. Ground-based telescope thermal emission, optimized for the thermal infrared and approximated as a 273 K blackbody with € = 0.02. Emission from the Earth's atmosphere at 1.525ILm is shown [22]. Zodiacal scattered light at the ecliptic pole, approximated as a 5 800 K blackbody with € = 3 x 10- 14 (based on data from [23]). Zodiacal emission from interplanetary dust at the ecliptic pole, approximated as a 275 K blackbody with € = 7.1 x 10-8 . Based on observations from the Infrared Astronomical Satellite (IRAS) [24]. Galactic background emission from interstellar dust in the plane of the Galaxy. In the plane of the Galaxy away from the Galactic Center, it can be approximated by a 17 K blackbody and € = 10-3 [25,26]. South ecliptic pole emission as measured by the Cosmic Background Explorer (COBE) spacecraft [27]. Cryogenic space telescope, cooled to 10 K with € = 0.05. Cosmic background radiation, 2.73 K blackbody with € = 1.0 [28]. Table 7.2. Combined sky, telescope, and instrument background emission at the 3.0 m IRTF (1).a Band A(JLm) dA Surface brightness (mag arcsec- 2) Band A(/Lm) dA J H Ks K 1.26 1.62 2.15 2.21 0.31 0.28 0.35 0.39 15.9 13.4 14.1 13.7 L L' M' M 3.50 3.78 4.78 4.85 0.61 0.59 0.22 0.62 Surface brightness (mag arcsec- 2) 4.9 4.5 0.3 -0.7 Note aTelescope emissivity at the time of the observations was about 7%. Reference 1. Shure, M. et al. 1994, Proc. SPIE. 2198, 614 7.3.2 OU Emission Spectrum The OH emission is often given in Rayleigh units. To convert to other units, use the following equations, with A/Lm in ILm [29]: 1 Rayleigh unit = 10 10 /4K photons s-1 m- 2 sr- 1 = 1.5808 X lO- lO /A/Lm Wm- 2 sr- 1, 7.3 BACKGROUND EMISSION / 147 Frequency (cm-1 ) 10000 c: 1000 10 100 1.0 0 'iii 0.8 0.6 0.4 0.2 (J) 'E (J) c: ~ l- 0.0 f" u Q) (J) 10° ::-I ... 108 ~ tU (J) I' E 106 =l 10-2 ')IE I(J) 10-4 104 -z ~ ~ [0"< « ...o (J) c: 0 0 10-6 102 [0> :> ..c: a. -e- 100 1 100 10 Wavelength (~m) Figure 7.3. Top: Transmission of the Earth's atmosphere at Mauna Kea (4.2 km), airborne (14 km), and balloon altitudes (28 km), adapted from [6]. Bottom: Background emission sources. The surface brightness is calculated from NqJ = fA,."mB).../(hc) = 1.41 x 10 16 fAj;!/(eI4387.7/AjLmT - 1) (A,."m in J.Lm, T in K). The intensity is derived from A,."mBA = 8.45 x 10-9 N qJ • ~ == = = =:~ 1.10 1.15 1.20 1.25 1.45 1.30 1.50 1.55 1.65 1.70 1.60 1.75 1.80 ~ 1 .95 2.00 2.05 2.10 Wavelength <14m) 2.15 2.20 Figure 7.4. Observed OR airglow spectrum adapted from [30]. See also [19,31-34,29]. 148 / 7 INFRARED ASTRONOMY 1 Rayleigh unit/A = 1.5808 x 1O-6 /AJ.tffi Wm- 2 J,Lm- 1 sr- I = 3.7184 x 1O- 17 /AJ.tffi Wm- 2 J,Lm- 1 arcsec- 2 . The OR airglow spectrum is given in Figure 7.4. 7.4 DETECTORS AND SIGNAL-TO-NOISE RATIOS Tables 7.3 and 7.4 list the basic detector types for infrared observations. Table 7.3. Basic detector types and typical useful wavelength ranges [1-4]. Material Typea Si Ge HgCdTe PtSi InSb Si:As PO PO PO SO PO mc Wavelength range (J.tffi)b <1.1 < 1.8 1-2.5 1-4 1-5.6 6-27 Material Typea Si:Sb Ge:Be Ge:Ga Ge:Ga GeorSi mc PC PC PC (stressed) TO (bolometer) Wavelength range (J.tffi)b 14-38 30-50 40-120 120-200 200-1000 Notes apO = photodiode, PC = photoconductor, SO = Schottky diode, mc = impurity band conduction photoconductor [also known as blocked impurity band (Bm) photoconductor]; TO = thermal detector. bThe HgCdTe long-wavelength cutoff is determined by the Hg/Cd ratio and can be extended to 25 J.tm. References 1. Rieke, G.H. 1994, Detection of Light: From the Ultraviolet to the Submillimeter (Cambridge University Press, Cambridge) 2. Fazio, G.G. 1994, Infrared Phys. Technol., 35, 107 3. Herter, T. 1994, in Infrared Astronomy with Arrays, edited by I. McLean (Kluwer Academic, Dordrecht), p. 409 4. Haller, E.E. 1994, Infrared Phys. Technol., 35, 127 For an object that is distributed over n pixels, the signal photocurrent for photodiodes, photoconductors, and Schottky diodes is [35] I>s = ATT/GAF>..ll.A/(hc) = ATT/G(ll.A/A)Fv / h electrons s-I, n where is is the photocurrent from an individual pixel, A (m 2 ) is the telescope collecting area, T is the transmission of instrument, telescope, and atmosphere, T/ is the detector quantum efficiency, G is the photoconductive gain (= 1 for a photodiode; ::::: 0.5 for a photoconductor), ll.A/A is the fractional spectral bandwidth, F>.. (W m- 2 J,Lm- 1 ) = QsourceB>.. = source flux density, and Fv (W m- 2 Hz-I) = QsourceBv = source flux density. The background photocurrent per pixel is ibg = ATT/GNtjJll.AQpix electrons s-l, where NtjJ (photons s-l m- 2 J,Lm- 1 arcsec- 2 ) is the background surface brightness and Qpix (arcsec 2 ) is the solid angle on the sky viewed by one pixel. 7.5 PHOTOMETRY (A. < 30 j.Lm) I 149 The RMS noise per pixel is [ N r2 + xG(is + ibg + idc) t ]1/2 electrons, where N r (electrons) is the detector read noise, idc (electrons s-l) is the detector dark current, t (s) is the integration time, and x = 1 for a photodiode or !BC photoconductor or x = 2 for a photoconductor. The signal-to-noise ratio before sky subtraction is An alternative signal-to-noise ratio equation including the noise introduced by sky subtraction is [36]: SIN = Nobj[Nobj + npix(1 + npixlnbg)(N; + Nbg + Ndc + NJig)]-1 / 2, where Nobj is the total number of signal electrons from the object (= Lis t), npix is the number of pixels summed for the object, nbg is the number of pixels summed for the sky subtraction, N r is the read noise in electrons per pixel, Nbg is the sky background in electrons per pixel (= xGibgt), Ndc is the dark current in electrons per pixel (= xGidct), and Ndig is the digitization noise in electrons per pixel (usually negligible). Table 7.4. Far-infrared heterodyne detectors [1,2]. Type Schottky diode Superconducting-insulator-superconducting (SIS) Wavelength range (J.l.ffi ) 100-300 300-3000 References 1. Phillips, T.O. 1988, in Millimetre and Submillimetre Astronomy, edited by R.D. Wolstencroft and W.B. Burton (Kluwer Academic, Dordrecht), p. 1 2. White, OJ. 1988, in Millimetre and Submillimetre Astronomy, edited by R.D. Wolstencroft and W.B. Burton (Kluwer Academic, Dordrecht), p. 27 For a heterodyne receiver [37], where Ts is the source temperature (K), TN is the equivalent Rayleigh-Jeans noise temperature (K) of the receiver, and f::J. v (Hz) is the channel width of the radio integrator. 7.5 PHOTOMETRY (A. < 30 j.Lm) There is no common infrared photometric (radiometric) system. As a result, filter central wavelengths, filter bandwidths, and instrumental responses are different at each observatory, as are the effects of the atmospheric transmission. The flux density of Vega established by Cohen et al. [38] is presented in Table 7.5. It is based upon an atmospheric model for Vega and the flux density calibration at 0.555 6 JLm given by Hayes [39]. It is consistent with ground-based absolute flux density measurements to within .::: 20" of the measurement errors. 150 / 7 INFRARED ASTRONOMY Table 7.5. Filter wavelengths, bandwidths, and flux densities for Vega. a b Filter name Aiso (/Lm) D.A c (/Lm) V J H Ks K 0.5556d 1.215 1.654 2.157 2.179 3.547 3.761 4.769 8.756 10.472 11.653 20.130 0.26 0.29 0.32 0.41 0.57 0.65 0.45 1.2 5.19 1.2 7.8 L L' M 8.7 N 11.7 Q FA (Wm- 2 /Lm- l ) 3.44 3.31 l.l5 4.30 4.14 6.59 5.26 2.ll 1.96 9.63 6.31 7.18 x x x x x x x x x x x x 10-8 10-9 10-9 10- 10 10- 10 10- 11 10- 11 10- 11 10- 12 10- 13 10- 13 10- 14 Fv (Jy) 3540 1630 1050 667 655 276 248 160 50.0 35.2 28.6 9.70 N,p (photons s-I m- 2 /Lm- I ) 9.60 2.02 9.56 4.66 4.53 l.l7 9.94 5.06 8.62 5.07 3.69 7.26 x 1010 x x x x x x x x x x x 1010 109 109 109 109 108 108 107 107 107 106 Notes aCohen et al. [I] recommend the use of Sirius rather than Vega as the photometric standard for A > 20 /Lm because of the infrared excess of Vega at these wavelengths. The magnitude of Vega depends on the photometric system used, and it is either assumed to be 0.0 mag or assumed to be 0.02 or 0.03 mag for consistency with the visual magnitude. bThe infrared isophotal wavelengths and flux densities (except for Ks) are taken from Table 1 of [1], and they are based on the UKIRT filter set and the atmospheric absorption at Mauna Kea. See Table 2 of [1] for the case of the atmospheric absorption at Kitt Peak. The isophotal wavelength is defined by F(Aiso) = J F(A)S(A) dA/ J S(A) dA, where F(A) is the flux density of Vega and S(A) is the (detector quantum efficiency) x (filter transmission) x (optical efficiency) x (atmospheric transmission) [2]. Aiso depends on the spectral shape of the source and a correction must be applied for broadband photometry of sources that deviate from the spectral shape of the standard star [3]. The flux density and Aiso for Ks were calculated here. For another filter, K', at 2.11/Lm, see [4]. cThe filter full width at half maximum. dThe wavelength at V is a monochromatic wavelength; see [5]. References 1. Cohen, M. et al. 1992, AJ, 104, 1650 2. Golay, M. 1974, Introduction to Astronomical Photometry (Reidel, Dordrecht), p. 40 3. Hanner, M.S., et al. 1984,AJ, 89,162 4. Wainscoat, R.J., & Cowie, L.L. 1992, AJ, 103,332 5. Hayes, D.S. 1985, in Calibration of Fundamental Stellar Quantities, edited by D.S. Hayes, et al., Proc. IAU Symp. No. III (Reidel, Dordrecht), p. 225 Absolute calibration. (a) For 1.2-5 J,tm, see [40]. (b) For 10-20 J,tm, see [41]. Photometric systems and standard star observations. For AAO, 1.2-3.8 J,tm, see [42]; for CIT, 1.23.5 J,tm, see [43]; for ESO, 1.2-3.8 J,tm, see [44]; for ESO, 1.2-4.8 J,tm, see [45]; for IRTF, 10-20 J,tm, see [46]; for KPNO, 1.2-2.2 J,tm, see [47]; for MSO, 1.2-2.2 J,tm, see [48]; for OAN, 1.2-2.2 J,tm, see [49]; for SAAO, 1.2-3.4 J,tm, see [50]; for UA, IRTF, WIRO, 1.2-20 J,tm, see [51]; for UKIRT, 1-2.2 J,tm, faint standards, see [52]; for WIRO, 1.2-33 J,tm, see [53]. Color transformations. For JHKLI.!M; SAAO-Johnson, SAAO-ESO, SAAO-AAO, AAO-MSO, AAO-CIT, see [17]; for JHKLM; ESO-SAAO; ESO-AAO; ESO-MSSSO; ESO-CTIO, see [44]; for JHK; OAN-CIT, OAN-AAO, OAN-ESO, OAN-Johnson, see [49]; for JHKL; SAAO-ESO, SAAOAAO, SAAO-MSSSO, SAAO-CTIO, see [50]; for JHKL; CIT-AAO, CIT-SAAO, CIT-Johnson, see [54]; for JHKLM; Johnson-ESO, Johnson-SAAO, see [55]; for JHK; CIT-IRTF, CIT-UKIRT, CIT-CTIO, CIT-ESO, CIT-KPNO, CIT-HCO, CIT-AAO, CIT-Johnson/Glass, see [56]. Acronyms. AAO = Anglo-Australian Observatory; CIT = California Institute of Technology; CTIO = Cerro Tololo Inter-American Observatory; ESO = European Southern Observatory; HCO = 7.5 PHOTOMETRY (). < 30/Lm) / 151 Harvard College Observatory (Mt. Hopkins); !RTF = NASA Infrared Telescope Facility; KPNO = Kitt Peak National Observatory; MSO = Mt. Stromlo Observatory; MSSSO = Mt. Stromlo/Siding Springs Observatory; OAN = San Pedro Martir National Observatory; SAAO = South African Astronomical Observatory; UA = University of Arizona; UKIRT = United Kingdom Infrared Telescope; WIRO = Wyoming Infrared Observatory. Tables 7.6-7.8 give intrinsic colors and effective temperatures for stars. Thble 7.6. Intrinsic colors and effective temperatures for the main sequence (class V).a Spectral type V-K J-H H-K K-L 09 09.5 BO Bl B2 B3 B4 B5 B6 B7 B8 B9 AO A2 -0.87 -0.85 -0.83 -0.74 -0.66 -0.56 -0.49 -0.42 -0.36 -0.29 -0.24 -0.13 0.00 0.14 0.38 0.50 0.70 0.82 1.10 1.32 1.41 1.46 1.53 1.64 1.96 2.22 2.63 2.85 3.16 3.65 3.87 4.11 4.65 5.28 6.17 7.37 -0.14 -0.13 -0.12 -0.10 -0.09 -0.08 -0.07 -0.06 -0.05 -0.03 -0.03 -0.01 0.00 0.02 0.06 0.09 0.13 0.17 0.23 0.29 0.31 0.32 0.33 0.37 0.45 0.50 0.58 0.61 0.66 0.67 0.66 0.66 0.64 0.62 0.62 0.66 -0.04 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 -0.01 0.00 0.00 0.00 0.01 0.02 0.03 0.03 0.04 0.04 0.05 0.05 0.05 0.06 0.06 0.08 0.09 0.11 0.11 0.15 0.17 0.18 0.20 0.23 0.27 0.33 0.38 -0.06 -0.06 -0.06 -0.05 -0.05 -0.05 -0.05 -0.04 -0.04 -0.04 -0.04 -0.03 0.00 AS A7 FO F2 F5 F7 GO 02 04 06 KO K2 K4 K5 K7 MO Ml M2 M3 M4 M5 M6 om 0.02 0.03 0.03 0.03 0.04 0.04 0.05 0.05 0.05 0.05 0.06 0.07 0.09 0.10 0.11 0.14 0.15 0.16 0.20 0.23 0.29 0.36 K-L' 0.00 0.01 0.02 0.03 0.03 0.03 0.04 0.04 0.05 0.05 0.05 0.05 0.06 0.07 0.10 0.11 0.13 0.17 0.21 0.23 0.32 0.37 0.42 0.48 K-M 0.00 om 0.03 0.03 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.00 -0.01 -0.02 -0.04 Tefl 35900 34600 31500 25600 22300 19000 17200 15400 14100 13000 11800 10700 9480 8810 8160 7930 7020 6750 6530 6240 5930 5830 5740 5620 5240 5010 4560 4340 4040 3800 3680 3530 3380 3180 3030 2850 Notes aColors given in the Iohnson-Glass system as established by Bessell and Brett [1]. References used: 0, B, [2]; A, F, 0, K, [1]; K. M, [3]. Did not use K-M from [2] because there is a large offset compared to [1]. Approximate uncertainties (one standard deviation): ±0.02 (O-K); ±0.03 (M). bTeff is an average of values from the following sources: for 0, B, [4]; for B, A, F, 0, K, [5]; for B, 0, K. [6]; for A, F, [7]; for A, F, 0, K, [8]; for A, F, 0, [9]; for 0, K, [10]; for K, M, [3]; for M, [11], [7], [12]. Approximate uncertainties (one standard deviation): ±1000 K (09-B2); ±250 K (B3-B9); ±100 K (AO-M6). References 1. Bessell, M.S., & Brett, I.M. 1988, PASP, 100,1134 152 / 7 INFRARED ASTRONOMY 2. Koomneef, J. 1983, A&A, 128, 84 3. Bessell, M.S. 1991, AJ, 101, 662 4. Vacca, W.O. et aI. 1996,ApJ, 4(;0, 914 5. Popper,D.M. 1980, ARA&A, 18, 115 6. Bohm-Vitense, E. 1981'ARA&A, 19,295 7. Bohm-Vitense, E. 1982,ApJ, 255, 191 8. Blackwell, D.E. et aI. 1991, A&A, 245, 567 9. Fernley, J.A. 1989, MNRAS, 239, 905 10. Bell, R.A., & Gustafsson, B. 1989, MNRAS, 236, 653 11. Jones, H.R.A et aI. 1995, MNRAS, 277, 767 12. Leggett, S.K. et aI. 1996, ApJS, 104, 117 1Bble 7.7. Intrinsic colors and effective temperatures for giant stars (class m). a Spectral type V-K J-H H-K K-L K-L' K-M Terf 1.75 2.05 2.15 2.16 2.31 2.50 2.70 3.00 3.26 3.60 3.85 4.05 4.30 4.64 5.10 5.96 6.84 7.80 0.37 0.47 0.50 0.50 0.54 0.58 0.63 0.68 0.73 0.79 0.83 0.85 0.87 0.90 0.93 0.95 0.96 0.96 0.07 0.08 0.09 0.09 0.10 0.10 0.12 0.14 0.15 0.17 0.19 0.21 0.22 0.24 0.25 0.29 0.30 0.31 0.04 0.05 0.06 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.12 0.13 0.15 0.17 0.18 0.20 0.05 0.06 0.07 0.07 0.08 0.09 0.10 0.12 0.14 0.16 0.17 0.17 0.19 0.20 0.21 0.22 0.00 -0.01 -0.02 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 -0.10 -0.12 -0.13 -0.14 -0.15 5910 5190 5050 4960 4810 4610 4500 4320 4080 3980 3820 3780 3710 3630 3560 3420 3250 GO G4 G6 G8 KO Kl K2 K3 K4 KS MO Ml M2 M3 M4 M5 M6 M7 Notes aColors given in the Johnson-Glass system as established by Bessell and Brett in [1]. APf,roximate uncenainties (one standard deviation): ±o.02. Teff is an average of values from the following sources: for G, K, M, [2]; for K, M, [3]; for G, K, [4]; for G, K, M, [5]. Approximate uncertainties (one standard deviation): ±50 K (G2-KS); ±70 K (MO-M6). For 0 and B stars, see [6]. References 1. Bessell, M.S., & Brett, J.M. 1988, PASP, 100, 1134 2. Ridgway, S.T. et aI. 1980,ApJ, 235,126 3. Di Benedetto; G.P', & Rabbia, Y. 1987,A&A, 188,114 4. Bell, R.A., & Gustafsson, B. 1989, MNRAS, 236, 653 5. Blackwell, D.E. et aI. 1991, A&A, 245, 567 6. Vacca, W.O. etal. 1996,ApJ, 4(;0, 914 1Bble 7.8. Intrinsic colors and effective temperatures for supergiant stars (class I). a Spectral type V-K J-H H-K K-L Tetf 09 BO Bl B2 B3 B4 -0.82 -0.69 -0.55 -0.40 -0.28 -0.20 -0.05 -0.04 -0.03 -0.04 -0.03 -0.01 -0.13 -0.10 -0.06 0.00 0.03 0.01 -0.08 -0.07 -0.07 -0.07 -0.05 -0.01 32500 26000 20700 17800 15600 13900 7.5 PHOTOMETRY ().. < 30 JLffi) / 153 Table 7.8. (Continued.) Spectral type V-K J-H H-K K-L Tetf B5 B6 B7 B8 B9 AO Al A2 A5 G8 KO Kl K2 K3lab K5Iab MOlab Mllab M2Iab M3Iab M4Iab -0.13 -0.07 0.01 0.07 0.13 0.19 0.26 0.32 0.48 0.64 0.75 0.93 1.21 1.44 1.67 1.99 2.15 2.28 2.43 2.90 3.50 3.80 3.90 4.10 4.60 5.20 0.01 0.04 0.06 0.07 0.08 0.09 0.11 0.12 0.13 0.15 0.18 0.22 0.28 0.33 0.38 0.43 0.46 0.49 0.52 0.59 0.67 0.73 0.73 0.73 0.74 0.78 0.00 -0.02 -0.02 -0.02 -0.02 -0.02 -0.01 -0.01 0.02 0.04 0.05 0.06 0.07 0.08 0.09 0.11 0.12 0.13 0.13 0.13 0.14 0.18 0.20 0.22 0.24 0.26 0.02 0.03 0.04 0.05 0.06 0.07 0.07 0.08 0.07 0.06 0.06 0.07 0.07 0.08 0.08 0.09 0.10 0.11 0.12 0.15 0.18 0.20 0.22 0.24 0.26 0.28 13400 12700 12000 11200 10500 9730 9230 9080 8510 7700 7170 6640 6100 5510 4980 4590 4420 4330 4260 4130 3850 3650 3550 3450 3200 2980 MOIb Mllb M21b M31b M41b 3.80 3.90 4.10 4.60 5.20 0.76 0.76 0.76 0.77 0.81 0.18 0.20 0.22 0.24 0.26 0.12 0.14 0.16 0.18 0.20 MOIa Mila M2Ia M3Ia M4Ia 3.80 3.90 4.10 4.60 5.20 0.61 0.61 0.61 0.62 0.66 0.18 0.20 0.22 0.24 0.26 0.27 0.29 0.31 0.33 0.35 FO F2 F5 F8 GO G3 Notes aColors given in the Johnson-Glass system as established by Bessell and Brett [I]. References used: For 0, A, [2]; for A, F. G, K. [3]; for K, M. [4]. Approximate uncertainties (one standard deviation): ±0.03. bTeff is an average of values from the following references: For O-M. [5]; for 0K, [6]; for O. B. [7]. Approximate uncertainties (one standard deviation): ±1000 K (09-B2); ±250 K (B3-B9); ±200 K (A-M). References 1. Bessell. M.S .• & Brett. J.M. 1988, PASP.l00. 1134 2. Whittet, D.C.B., & van Breda, I.G. 1980, MNRAS, 192.467 3. Koomneef. J. 1983.A&A.128. 84 4. Elias. J. et al. 1985. ApJS. 57, 91 5. Schmidt-Kaler, Th. 1982. in Landolt-Biirnstein. New Series, edited by K. Schaifer & H.H. Voigt (Springer-Verlag. Berlin). Vol. V1I2b. p. 451 6. Bohm-Vitense. E. 1981. ARA&A.19. 295 7. Remie. H .• & Lamers. HJ.G.L.M. 1982. A&A. lOS. 85 154 / 7 INFRARED ASTRONOMY 7.6 PHOTOMETRY (A > 30 jlm) The primary flux density calibrator for ground-based submillimeter and millimeter observations is Mars [57]. The main secondary calibrators are Uranus [58,59] and Jupiter [5, 59, 60]. Other secondary calibrators consist of astronomical sources [59,61]. Instrument details for the IRAS satellite are given in Table 7.9. Table 7.9. InfraredAstronomical Satellite (IRAS) summary injormation. a Effective wavelength (#Lm) 12 25 60 100 Bandwidth (FWHM) (#Lm) 'JYpicai detector field of view, (in scan) x (cross scan) (arcmin) Point Source Catalog, with 2 coverages, 90% completeness limits (Jy)b Faint Source Catalog median 90% completeness limits (Jy)b 7.0 11.15 32.5 31.5 0.76 x 4.55 0.76 x 4.65 1.51 x 4.75 3.03 x 5.05 0.45 0.64 0.18 0.29 0.26 Notes aIRAS observations are sensitive to dust with T > 25 K. For IRAS catalogs, see [1, 2]. bCompleteness limits vary according to the amount of sky coverage obtained. References 1. Infrared Astronomical Satellite (lRAS) Catalogs and Atlases, 1988, ed. Joint IRAS Science Working Group (U.S. Government Printing Office, Washington, DC), Vols. 1-7 2. The Infrared Processing & Analysis Center (IPAC) WWW Home Page (bttp://www.ipac.caltecb.eduJ) bas numerous databases and information on IRAS catalogs The following formulas give the IRAS four-band and two-band fluxes. For galactic sources [62] Fir(7 - 135/Lm) = 1.0 x 1O-14(20.653fI2 + 7.538/25 + 4.578160 + 1.7621100) Wm- 2. For extragalactic sources [63,64] Fir(8 - 1000 /Lm) Ffir(43 - 123 /Lm) = = 1.8 x 1O- 14 (13.48fI2 1.26 x 10- 14 (2.58160 + 5.16/25 + 2.58160 + 1100) Wm-2, + fIoo) Wm-2, where 112, /25, 160, and fIoo are the IRAS flux densities in Jy at 12, 25, 60, and 100 /Lm. These formulas are approximations based on assumptions about the intrinsic source spectrum and dust emissivity. It is recommended that the original references be consulted for details. The luminosity (in solar luminosities) is where D is in pc and Fir,fir is in W m- 2. The far-infrared emission-radio emission correlation [65] is q where fI.4 GHz = log{[Ffir/(3.75 x 10 12 Hz)]/it.4 GHz} is the 1.4 GHz flux density in W m- 2 Hz-I. = 2.14, 7.7 INFRARED LINE LIST / 155 7.7 INFRARED LINE LIST Table 7.10 presents data for a sample of infrared lines. Table 7.10. Selected infrared lines. A (ttm)a 1.00521 1.01264 1.0833 1.09411 1.11286 1.1290 1.16296 1.16764 1.252 1.25702 1.28216 1.31682 1.47644 1.52647 1.58848 1.61137 1.6189 1.62646 1.64117 1.64400 1.68111 1.68778 1.69230 1.70076 1.73669 1.74188 1.81791 1.87561 1.94509 1.95756 1.9634 2.03376 2.040 2.04065 2.05869 2.06059 2.08938 2.09326 2.1127 2.12183 2.13748 2.14380 2.16612 2.18911 2.20624 2.20897 2.22329 2.24772 2.26311 v (cm-I)a Species Transitionb Referencec 9948.17 9875.18 9231.2 9139.85 8985.84 8857.4 8598.75 8564.28 7987.0 7955.30 7799.34 7594.03 6773.05 6551.08 6295.29 6205.92 6177.0 6148.32 6093.21 6082.73 5948.45 5924.94 5909.12 5879.74 5758.08 5740.94 5500.82 5331.60 5 141.15 5108.40 5093.2 4917.01 4902.0 4900.39 4857.45 4852.99 4786.11 4777.23 4733.4 4712.91 4678.41 4664.61 4616.55 4568.07 4532.59 4527.00 4497.84 4448.96 4418.69 HI Hell Hel HI Fell n = 7-3 (Pa.S) n =5-4 2 p 3p o_2s 3S n = 6-3 (pay) b 4 GS/2-z4F3/2 3d 3Do_3p3p n = 7-5 n = 11-6 3PI _ 3 P2 [1,2,3] [1,3] [1,3] [1,2,3] [4,5,6] [2,3,4] [1,3] [1,7] [8,9, 10, 11] [4,5,6] [1,2,3] [3,6] [1,3] [1,2,3] [1,2,3] [1,2,3] [12] [12] [1,2,3] [4,5,6] [1,2,3] [4,5,6] [1,7] [3,6] [1,2,3] [3,6] [1,2,3] [2,3] [1,2,3] [13, 14] [9, 10, 15] [14, 16] [9, 10] [17] [3, 18] [5,6, 18] [5,6, 16] [17] [3,6] [14, 16] [18] [18] [2,3, 16] [1,7] [16, 19,20] [16, 19,20] [14, 16] [14, 16] [19] 01 Hell Hell lSi IX] [Fe II] HI 01 Hell HI HI HI CO OH HI [Fe II] HI Fell Hell Hel HI Fell HI HI HI H2 lSi VI] H2 [AlIX] H3+ Hel Fell Fell H3+ Hel H2 MgII MgII HI Hell Nal Nal H2 H2 Cal a 4n-, /2--a 6D9/2 n = 5-3 (PafJ) 4s 3So_3p 3 P n = 9-6 n = 19-4 (BrI9) n = 14-4 (8rI4) n = 13-4 (Br13) v = 6-3 band head v = 2--0 Pld(15) n = 12-4 (BrI2) a 4n-, /2--a 4F9/2 n = 11-4 (Br11) c4F9/2-z4F9/2 n = 12-7 4d 3D _ 3p 3p o n = 10-4 (BrIO) c 4 F7/2-Z 4 n-, /2 n = 9-4 (Br9) n = 4-3 (Paa) n = 8-4 (Br8) v = 1--0 S(3) 2PI/2-2p3/2 v = 1-0 S(2) 2po 2po 3/2- 1/2 v = 2V2(2)--O; (4, 6, +2}-(3, 3) 2p Ipo_2s IS c 4FS/2-Z 4F3/2 c 4F3/2-Z 4F3/2 v = 2V2(2)--O; (7, 9, +2}-(6, 6) 4s 3S_3 p 3po v = 1-0 SO) 5 p 2Pf/2-5s 2SI/2 5p 2Pl/2-5s 2SI/2 n = 7-4 (Bry) n = 10-7 4p 2Pf/2-4S 2SI/2 4p 2Pl/2-4s 2SI/2 v = I-OS(O) v = 2-1 SO) 4f 3Ff-4d 3D2 156 I 7 INFRARED ASTRONOMY Table 7.10. (Continued.) (em-If A. (p.mf II 2.26573 2.29353 2.32265 2.34327 2.34531 2.34950 2.35167 2.35246 2.38295 2.40659 2.41344 2.42373 2.4833 2.49995 2.62587 2.62688 3.0279 3.03920 3.09169 3.133 3.29699 3.41884 3.48401 3.50116 3.52203 3.6246 3.64592 3.661 3.69263 3.7240 3.74056 3.80741 3.8462 3.935 3.95300 4.0045 4.02087 4.03781 4.04900 4.05226 4.17079 4.64931 4.65378 4.65748 4.67415 4.68262 4.69462 5.0531 6.634 6.985 7.642 8.99135 10.51 10.521 12.2786 12.3720 4413.58 4360.09 4305.42 4267.54 4263.84 4256.22 4252.30 4250.87 4196.48 4155.25 4143.47 4125.87 4026.9 4000.08 3808.26 3806.80 3302.6 3290.34 3234.48 3192.0 3033.07 2924.97 2870.26 2856.20 2839.27 2758.9 2742.79 2731.0 2708.10 2685.3 2673.40 2626.46 2600.0 2541 2529.72 2497.2 2487.02 2476.59 2469.75 2467.76 2397.63 2150.86 2148.79 2147.08 2139.43 2135.55 2130.10 1979.0 1507 1432 1309 1112.18 951.5 950.48 814.425 808.283 Species Transitionb Referencec Cal CO CO CO CO CO CO CO CO H2 H2 H2 lSi VII] H2 HI H2 [Mgvm] HI Hell OH HI Hell Hell HI HI H2 HI [Alvl] HI H2 HI H2 H2 [Silx] H3+ SiO HI Hel Hel HI HI CO HI CO CO CO H2 H2 [Nill] 4f 3F:-4d 3D3 [19] [16] [16] [21] [21] [21] [21] [16] [16] [13,14] [13,14] [13,14] [9,10,15] [14,22] [2,22] [14,22] [8, 9, 10, 15] [2] [3] [23] [2, 24] [3,24] [3,24] [2,24] [2,24] [25,26] [2,25] [8-10] [2,25] [26] [2] [14,27] [26,27] [9,10,15] [28] [29] [2,16] [3,30] [30] [2, 16] [2,16] [31] [2, 16] [31] [31] [31] [14] [14,26] [32] [33] [9,10] [33,34] [33] [11,32] [14] [2] [Arn] [NevI] [Arm] [SIV] [COli] H2 HI = II = II = II = II = II = II = II = II = II = II = II 2-0 band head 3-1 band head 2"'{)R(1) 2"'{)R(0) 2-OP(1) 2-OP(2) 4-2 band head 5-3 band head 1-OQ(l) 1...{)Q(2) I...{)Q(3) 3PI_3~ II = 1...{)Q(7) n = 6-4 (Brp) II = 1"'{)0(2) 21'.0 2po 3/2- 1/2 n = 10-5 (PfE) n=7-6 II = 1"'{), K=9 multiplet n = 9-5 (PfB) n = 25-11 n = 17-10 n = 24-6 (Hu24) n = 23-6 (Hu23) II = 0...{) S(15) n = 19-6 (Hu19) 3PI _3~ n = 18-6 (Hu18) II = 0...{) S(14) n = 8-5 (Pfy) II = 1"'{)0(7) II = 0...{) S(13) 3PI_3PO II = "2(1)...{); (1, 0, -1)-(1,0) 1I=2-0bandhead n = 14-6 (HuI4) 5f3F°-4d 3D 5g IG~f I FO; 5g 3G~f 3 FO n = ~(Bra) n = 13-6 II = l"'{)R(1) n = 7-5 (PfP) II = 1...{)R(0) II = 1...{)p(1) II = 1...{)p(2) II = 0...{) S(9) II = 0...{) S(8) a 2D)/2-<l2DS/2 2po 21'.0 1/2- 3/2 2Pj/2-2PI/2 3PI_3~ 21'.0 2po 3/2- 1/2 a 3F3-<l3F4 II = 0...{) S(2) n =7-6(Hua) 7.7 INFRARED LINE LIST / Table 7.10. (Continued.) ).. (/Lm)Q v (cm-I)Q Species Transitionb Referencec 12.8135 780.424 [Nell] 642.7 587.032 534.387 411.256 386.5 354.374 298.67 192.99 174.47 [Nem] H2 [S m] [Nev] [OIV] H2 [S m] [Om] [Nm] 2po 2po 1/2- 3/2 3PI_3P2 v=O-OS(l) 3P2_3PI 3PI_3PO 2PJ/2-2PI/2 v = O-OS(O) 3PI_3PO [33,34] 15.56 17.0348 18.7130 24.3158 25.87 28.2188 33.482 51.816 57.317 63.1837 77.059 88.355 119.23 119.44 121.898 124.65 145.526 157.741 162.81 205.178 370.415 371.65 609.135 158.269 129.77 113.18 83.872 83.724 82.0358 80.225 68.7162 63.3951 61.421 48.7382 26.9967 26.907 16.4167 [01] CO [Om] OH OH [NIl] NH3 [01] [CII] CO [NIl] [CI] CO [CI] 3~_3pI 2po 2po 3/2- 1/2 3PI_3~ J = 34-33 3PI_3PO 2n3/2 J = 5/2-312 2n3/2 J = 512-312 3P2_3PI K = 3, J = 4-3, a - s 3PO_3PI 2po 2po 3/2- 1/2 J = 16-15 3PI_3PO 3P2_3PI J=7~ 3PI_3PO [33] [l4] [34,35] [34,35] [33] [14] [35,36] [33,35] [33] [37] [37] [33,35] [37] [37] [33,38] [37] [33] [33] [37] [38] [33] [39] [33] Notes Q Vacuum wavelengths and frequencies are given. bTransition shown is (upper level}-{Iower level). cBecause of space limitations, only a few transitions of each species are shown; see references for additional lines. 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Gautier m, T.H. et al. 1976, ApJ, 207, LI29 14. Black, J.H., & van Dishoeck, E.F. 1987, ApJ, 322, 412 15. Reconditi, M., & Oliva, E. 1993, A&A, 274, 662; Oliva, E. et al. 1994, A&A, 288, 457 16. Scoville, N. et al. 1983, ApJ, 275, 201 17. Drossart, P. et al. 1989, Nature, 340, 539; see also Kao, L. et al. 1991, ApJS, 77,317 18. Simon, M., & Cassar, L. 1984, ApJ, 283, 179 19. Kleinman, S.G., & Hall, D.N.B. 1986, ApJS, 62, 501 no, 157 158 I 7 INFRARED ASTRONOMY 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 7.8 Martin, W.C., & Zalubas, R. 1981, J. Phys. Chern. 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SPIE, 1946,238 Watson, D.M. 1984, in Galactic and Extragalactic Infrared Spectroscopy, edited by M.E Kessler and I.P. Phillips (Reidel, Dordrecht), p. 195; Townes, C.H., & Melnick, G. 1990, PASP, 102, 357 Colgan, S.W.I. et al. 1993, ApJ, 413,237 Howe, I.E. et al. 1993, ApJ, 410, 179 H: Wynn-Williams, C.G. 1984, in Galactic and Extragalactic Infrared Spectroscopy, edited by M.E Kessler and I.P. Phillips (Reidel, Dordrecht), p. 133 H2: Schwartz, R.D. et al. 1987, ApJ, 322, 403; Black, I.H., & van Dishoeck, E.E 1987, ApJ, 322,412 CO: Goorvitch, D. 1994,ApJS, 95, 535 Solar atlases: Livingston, W., & Wallace, L. 1991, An Atlas of the Solar Spectrum in the Infraredfram 1850 to 9000 cm- 1 (1.1-5.4/Lm), NSO Technical Report No. 91-001 (NOAO, Thcson); Wallace, L., & Livingston, W. 1992, An Atlas of a Dark Sunspot Umbral Spectrum fram 1970 to 8640 cm- 1 (1.16-5.1 /Lm), NSO Technical Report No. 92-001 (NOAO, Thcson) Infrared spectra: Iourdain de Muizon, M. et al. 1994, Database of Astronomical Infrared Spectroscopic Observations (University of Leiden, Leiden) Infrared wavelength calibration: Outred, M. 1978,1. Phys. Chern. Ref Data Ser., 7, 1; Rao, K.N. et al. 1966, Wavelength Standards in the Infrared (Academic Press, New York) DUST For the infrared interstellar reddening law, see [66--69]. The total to selective absorption ([66-68], for R = Av IE(R - V) Av IE(1 - K) Av /E(V - K) AdE(1 - K) The color excess ratio [67] = 5.82 ± 0.1, = 1.13 ± 0.03, = 2.4(A)-1.75 Av IE(H - K) (for 0.9 < A = 3.1) is = 15.3 ± 0.6, < 6/Lm). is E(l - H)/E(H - K) = 1.70 ± 0.05. The ratio of visual extinction to silicate band optical depth A v / t"Si Av /t"Si = 19 ± 1 = 11 ± 2 (t"Si) [68,70,71] (local interstellar medium), (Galactic Center region). is 7.8 DUST / e-o 1ii :x: -i - ~ 1crU + 159 + J: Z > ~1cr- ~ .IRAS -COBEFIRAS 100 10 A (11m) Figure 7.5. Emission spectrum of interstellar dust. Adapted from [78]. See also [26,79,80]. The average visual extinction to the Galactic Center region is 34 mag [72] and to individual sources it ranges from 23 to 35 mag [67]. The extinction cross section per H nucleus in the local interstellar medium [68] is The interstellar linear polarization [73-75]: P(A)/ P rnax = exp[ -K In2(Arnax/A)] P(A) ex: A-{3, (for A < 2 JLm), f3 = 1.6 - 2.0 (for 2 < A < 5 JLm), where P(A) is the percentage polarization, Prnax is the maximum percentage polarization occurring at Amax, and K = 0.01 ± 0.05 + (1.66 ± 0.09)Arnax. Table 7.11 and Figure 7.5 present data on the interstellar dust emission. Table 7.12 presents farinfrared dust properties. Dlble 7.11. Average galactic diffuse emission [1].a 3.5 4.9 12 25 0.21 0.13 0.80 0.41 60 100 140 240 0.88 2.0 3.8 2.5 Note aFor galactic latitudes _60 to _40 and +40 to +60 . Emission is highly variable on small spatial scales [1, 2]. References 1. Bernard, J.P. et al. 1994, A&A, 291, 1.5 2. Cutri, R.M., & Latter, W.B., editors, 1993, The First Symposium on the Infrared Cirrus and Diffuse Interstellar Clouds, ASP Conf. Set. (ASP, San Francisco), Vol. 58 160 / 7 INFRARED ASTRONOMY The dust mass estimate from the 100 JLm flux density is Mdust = 4.81 x 10- 12 /100 D2(eI43.88/Td - 1) M 0 , where 1100 is the 100 JLm flux density in Jy, D is the distance in pc, and Td is the dust temperature in K. The derivation follows from [76], using a mass absotption coefficient of 2.5 m 2 kg- 1 at 100 JLm. The dust mass absotption coefficient at submillimeter wavelengths is estimated in [68,76,77]. The equilibrium dust temperature of a particle with albedo A at a distance r (in pc) from a source of luminosity L (in L0) is Te = 0.612(1 - A)0.25 L 0.25 r -0.5 K. The nonequilibrium emission from extremely~mall particles is discussed in [81-83]. Table 7.12. Galactic dust properties at 140-240 I'm Mean values in the galactic plane (lbl < 1°) [I].a Inner galaxy Quantity Dust temperature (K) 240 I'm optical depth Total FIR radiance (Wm- 2 sr- 1 ) Gas-to-dust ratio FIR luminosity perHmass (L0/M0) (270° < t < 350°; 10° < t < 90°) Outer galaxy 20± I (5.0 ± 2.0) x 10-3 (3.7 ± 0.3) x 10-5 17± I (9.5 ± 3.0) x 10-4 (2.4 ± 0.2) x 10-6 19± I (3.0 ± 1.0) x 10- 3 (2.0 ± 0.2) x 10-5 140±50 3.0±0.3 190±60 0.9±0.1 160±60 2.0±0.2 (90° < t < 270°) Entire galaxy Note aData from the Cosmic Background Explorer (COBE) satellite; for additional information, see the COBE WWW Home Page: http://www.gsfc.nasa.gov/astrolcobelcobe_home.html Reference I. Sodroski, T.J. et al. 1994, ApJ, 428, 638 Spectral features of dust and ice in the infrared are listed in Table 7.13. Table 7.13. Major dust and ice features [1-7]. 3.08 3.29,6.2,7.7, 8.65, 11.25 4.62 4.67 6.0 6.85 ~9.7 ~ 11.2 1l.5 ~ 18 ~34 43 Identification Where observed H20 ice Aromatic hydrocarbonsa Molecular clouds; OH-IR stars H II regions, planetary nebulae, reflection nebulae, young and evolved stars, starburst galaxies Molecular clouds Molecular clouds Molecular clouds Molecular clouds H II regions, molecular clouds Circumstellar shells; planetary nebulae OH-IRstars H II regions; Galactic center Planetary nebulae; carbon stars OH-IRstars "X-CN" CO ice H20 ice CH30H + other Amorphous silicates SiC H20 ice Amorphous silicates MgS (7) H20 ice Note aThe nature of the "aromatic hydrocarbons" is not known precisely [7]; it is commonly assumed to be polycyclic aromatic hydrocarbons (PAHs). 7.9 SOLAR SYSTEM / 161 References 1. Willner, S.P. 1984, in Galactic and Extragalactic Infrared Spectroscopy, edited by M.P. Kessler and J.P. Phillips (Reidel, Dordrecht), p. 37 2. Roche, P.P. 1989, in Proc. 22nd ESLAB Symp. on Itifrared Spectroscopy in Astronomy, ESA SP290,p.79 3. Tokunaga, A.T., & Brooke, T.Y. 1990, Icarus, 86, 208 4. Whittet, D.C.B. 1992, Dust in the Galactic Environment (Institute of Physics, Bristol), p. 147 5. Allamandola, LJ. et al. 1989, ApJS, 71, 733 6. Uger, A., & d'Hendecourt, L. 1987, in Polycyclic Aromatic Hydrocarbons and Astrophysics, edited by A. Uger et al. (Reidel, Dordrecht), p. 223 7. Sellgren, K. 1994, in The First Symposium on the Infrared Cirrus and Diffuse Interstellar Clouds, edited by R.M. Cutri and W.B. Latter, ASP Conf. Ser. (ASP, San Francisco), Vol. 58, p. 243 7.9 SOLARSYSTEM The solar colors are [84] J - H = 0.310, H - K = 0.060, K - L = 0.034, L - M = -0.053, v- K = 1.486. Solar analogs [85] are 16 eyg B, VB64, HD 105590, HR 2290. The blackbody temperature of an object without an atmosphere in the solar system is Tb = 278.8(1 - A)O.25 r -0.5 K, where A is the albedo and r is the distance from the Sun in AU. For thermal emission from asteroids, see [86-88]. For the infrared spectra of planetary atmospheres, see [89-92]. For the infrared spectra of comets, see [93,94]. For near-infrared spectra of satellites, see [95,96]. For near-infrared spectra of asteroids, see [97,98]. The infrared magnitudes and colors of many solar system objects are given in Table 7.14. 'Dlble 7.14. Magnitudes o/selected solar system bodies. Q Object Ref. V(l,O)b I1Ve V-J J-H H-K K-L V-N 11 10 J2 Europa (L) J2 Europa (T) 13 Ganymede (L) J3 Ganymede (T) J4 Callisto S2 Enceladus S3 Tethys S4Dione S5Rhea S6 Titan S8 Iapetus (L) S8 Iapetus (T) Ul Ariel U2Umbriei U3 Titania U40beron [1-4] [1-5] [1-5] [1-5] [1-5] [1-5] -1.68 -1.37 0.15 0.3 5.69 10.26 142e 0.13 0.5 0.1 0.3 0.2 0.0 0.00 -2.24 -2.35 -1.90 -1.44 -1.01 < -0.5 130e -0.95 1.9 0.7 0.88 0.1 -1.3 2.4 0.6 1.7 2.4 1.3 1.6 0.08 -0.35 -0.53 -0.08 -0.07 0.07 -0.24 -0.16 -0.12 -0.24 -0.38 0.05 -0.13 -0.04 -0.09 -0.14 -0.14 9.29 8.81 0.15 0.35 -0.31 -0.37 -0.10 -0.07 -0.27 -0.05 -0.20 -0.20 -0.05 -0.31 0.4 -0.11 0.21 0.25 0.20 0.20 4.70 3.91 -2.08 1.3 1.2 1.4 1.0 7.26 11.72 152e [6-8] [4,6,7] [4,6,7] [4,5,8,9] [4, 10--13] [13-15] [13-15] [4, 16] [7,9] [4,7,9] [7,9] 1.5 1.06 0.9 0.8 1.06 0.2 1.60 0.8 1.20 1.30 1.30 1.35 -1.6 -1.7 V-Q 8.5 6.3 10.4 10.0 10.4 T (K)d 137e 761 162 / 7 INFRARED ASTRONOMY Table 7.14. (Continued.) Object Ref. V(1,O)b t::..V c V-J J-H H-K Nl Triton Pluto, Charon 1 Ceres 2 Pallas 3 Juno 4 Vesta [5,8, 17, 18] [17, 19-21] [22-28] [22-28] [22-28] [22-28] -1.0 -0.76 3.72 4.45 5.73 3.55 1.3 1.3 1.2 1.2 0.31 -0.01 0.31 0.21 1.4 0.17 -0.24 -0.36 0.05 0.04 0.05 0.01 0.30 0.04 0.16 0.22 0.12 K-L V-N V-Q 10.0 9.9 8.7 8.4 > 8.2 > 9.9 12.8 12.4 12.0 11.2 T (K)d 38d 558 245 h 270h 230h 250h Notes a Average magnitude given unless indicated otherwise; (L) = leading hemisphere, (T) = trailing hemisphere. Approximate filter wavelengths: V (0.55 ~m), J (1.25 ~m), H (1.65 ~m), K (2.2 ~m), L (3.45 ~m), N (10 ~m), Q (20 ~m); see references for details. bV(1,O) absolute visual magnitude at a distance of 1 AU from the Earth and 1 AU from the Sun at 0° phase angle. The apparent visual magnitude of an object is V(r, t::.., a) = V(I, 0) + Ca + 5Iog(rt::..), where r is the heliocentric distance and t::.. is the geocentric distance (both in AU), C is the phase coefficent in mag deg- 1, and a is the phase angle (deg). The opposition effect, occurring when a ~ 0°, is not included in this table. c t::.. V visual light curve amplitude (peak to peak). d TB = brightness temperature; TS = surface or subsolar temperature. = = eTB (lO~m). f TB (100 ~m). 8TB (60~m). hTS (10 ~m). RefereDc:es 1. Morrison, D. et aI. 1976,ApJ, 2fY1, L213 2. Morrison, D. 1977, in Planetary Satellites, edited by J.A. Burns (University of Arizona, Tuscon), p. 269 3. Morrison, D., & Morrison, N.D. 1977, in Planetary Satellites, edited by J.A. Bums (University of Arizona, Tuscon), p.363 4. Morrison, D., & Cruikshank, D.P. 1974, SSRv, 15,641 5. Hartmann, W.K. et al. 1982, Icarus, 52, 377 6. Franz, O.G., & Millis, R.L. 1975, Icarus, 24, 433 7. Cruikshank, D.P. 1980, Icarus, 41, 246, and private communication 8. Cruikshank, D.P. et al. 1977,ApJ, 217,1006 9. Brown, R.H. et al. 1982, Nature, 300, 423 10. Andersson, L.B. 1977, in Planetary Satellites, edited by J.A. Burns (University of Arizona, Tucson), p. 451 11. 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McCheyne, R.S. et al. 1985, Icarus, 61, 443 7.10 STARS I 163 7.10 STARS Molecular features seen in cool stars are listed in Table 7.15. 1Bb1e 7.15. Molecular bands in cool stars [1, 2]. Wavelength range (ILm) Selected references dv dv 1.5-4.7 1.7-2.5 1.3-3.6 [3,4.5.6.7.8.9] [3] [10. II] CN C2 A 2n_x2E b I n,,-x I E+ (Phillips) A' 3Eg -X' fn" (Ballik-Ramsey) <4 <2.5 [3.4.6. 12. 13. 14. 15] [3. 6. 14. 16] C3,CS II] 4-5 2-5.7.1.14 2.5-4.14 4-4.2. 8.0-8.3 1.6-2.0.3.1-4.0 3.3-4.0 3.8-4.0 [12. 17, 18] [13. 15. 16. 19] [13. 16. 19] [9.20.21.22.23] [8.22.24] [3.22] [22.23] Molecule Bands CO H2 H2O = 1,2,3 = I (quadrapole vib-rot) 11]. 2V2. V2 + II] - V2. V2 + 11], VI + V2 HCN C2H2 SiO OH CH CS V2. 11], 2V2. 3V2. 2VI 11]. vs. VI + Vs dv = 1.2 dv = 1.2 dv= 1 dv=2 + V2 References 1. Merrill. K.M .• & Ridgway. S.T. 1979,ARA&A.I7. 9 2. Tsuji. T. 1986. ARA&A. 24, 89 3. Lambert, D.L. et aI. 1986. ApJS. 62. 373 4. Thompson. R.1. et aI. 1972. PASP. 14. 779 5. Ridgway. 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For the infrared star count models, see [103-105]. Useful catalogs are found in [106--109]. For near-infrared spectra of young stars, see [110-118]. For spectral energy distributions of young stellar objects and pre-main sequence stars, see [119-124]. Figure 7.6 shows the color-color diagram for stars. 164 / 7 INFRARED ASTRONOMY / 1.5 J: I ..., 1.0 0.5 0.0 7.11 7.11.1 0.5 H-K 1.0 1.5 Figure 7.6. Color-color diagram for various classes of stars, adapted from [17]. The dark line indicates the location of G5 to M6 main sequence dwarf and giant stars. The dashed lines indicate the boundary for most carbon-rich stars; the carbon long-period variable (LPV) stars lie to the right. The oxygenrich (M type) LPV stars fall within the boundary of the solid line, and the LPV stars with periods greater than 350 days are to the right and overlap the carbon-rich LPV stars. The supergiant M stars (SG) lie in a region below and to the right of the giant sequence. The arrow indicates the direction of the interstellar reddening. EXTRAGALACTIC OBJECTS Energy Distributions and Colors Infrared energy distributions of galaxies vary widely. Representative examples may be found in [125,126]. At least five different physical causes have been identified for the continuum infrared emission from galaxies: (a) Photospheric emission from evolved stars (usually dominant in the 1-3 /Lm region) [127, 128]: Mean colors of elliptical galaxies (CIT photometric system): V -K = 3.33 mag; J-H = 0.69 mag; H-K = 0.21 mag. Molecular absorption bands in elliptical galaxies H20 (1.95 /Lm) = 0.12 mag; CO (2.3 /Lm) =0.16 mag. For additional near-infrared colors, see [129-132]. (b) Dust shells around evolved stars [133]: This is the main cause of 10-12 /Lm emission in elliptical galaxies, for which /v(l2 /Lm) =0.13/v(2.2 /Lm). Units of /v are Jy. (c) Emission from interstellar dust [134,135]: Transiently heated "small" grains dominate at about 10 /Lm; "large" grains in thermal equilibrium dominate at 50-100 /Lm. A typical energy distribution from dust emission in a starburst galaxy normalized to 60 /Lm is /v(l2 /Lm) =0.035; /v(25 /Lm) =0.18; /v(60 /LID) = 1.0; /v(loo /Lm) = 1.41 [136]. (d) Seyfert nucleus: Seyfert galaxies exhibit infrared emission from dust heated by the central source, as well as emission from starburst or nonthermal components. Seyfert galaxies tend to be most prominent at 60 /Lm, but energy distributions vary widely. The IRAS 25-60 /Lm spectral slope has been found useful for selecting Seyfert galaxies [137, 138]. (e) Blazar component: Nonthermal, approximately power-law emission (fv oc va). Mean values are a(1 /Lm) = -1.42 ± 0.95; a(10 /Lm) = -1.12 ± 0.47; a(loo /Lm) = -0.88 ± 0.43; a(l mm) = -0.18 ± 0.42 [139]. For far-infrared colors of extragalactic objects, see [125, 140-143]. 7.11 EXTRAGALACTIC OBJECTS / 7.11.2 165 Statistics of Galaxies at Infrared Wavelengths Galaxy number counts at 2.2 ILIn. The number of galaxies per square degree per magnitude is [144]: dN /dK where a =0.67 for 10 < K < 17, a = 4000 x lOa(K-l7), =0.26 for 17 < Luminosity function at 60 /-Lm [125,145], magnitude interval at 60 /-Lm is K < 23, and K = 2.2 /-Lmmag. The density of galaxies per cubic megaparsec per log(p) = -3.2 - a (log[vLv(60 /Lm)] - 1O.2}, = = where vLv(60 /-Lm) is given in units of L 0 , and a 0.8 for 10g[vLv(60 /Lm)] < 10.2 and a 2.0 for 10g[vLv(60 /Lm)] > 10.2. Ho is assumed to be 75 Ian s-1 Mpc-l. The total infrared energy output of the local universe from 8 to 1000 /-Lm is 1.24 x 108 L0 Mpc- 3 [146], ACKNOWLEDGMENTS Many people have helped with their comments and suggestions. I thank in particular the following persons for valuable comments and contributions to this chapter: E. Beckiin, M. 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Teays 8.1 8.1 Ultraviolet Wavelengths . . . . . . . . . . . . . . . . . 169 8.2 Ultraviolet Astronomy Satellite Missions . . . . . .. 170 8.3 Significant Atlases and Catalogs . . . . . . . . . . . . 172 8.4 Interstellar Extinction in the Ultraviolet . . . . . . .. 174 8.5 Commonly Observed Ultraviolet Emission Lines .. 175 8.6 Ultraviolet Spectral Classification. . . . . . . . . . .. 178 8.7 Ultraviolet Spectrophotometric Standards. . . . . .. 180 ULTRAVIOLET WAVELENGTHS The Earth's atmosphere is an efficient absorber of ultraviolet radiation, and so astronomical observations in this wavelength regime are pretty well limited to space-based instruments. As such, I adopt the nomenclature that "ultraviolet" refers to the wavelengths in the region from the atmospheric cutoff at ~ 3200 A down to 100 A. (The tenns ''far ultraviolet" and "extreme ultraviolet" are frequently used to refer to the shorter end of the ultraviolet wavelength range, but the usage has not been consistent in the literature. Generally one thinks of the far ultraviolet as referring to wavelengths shorter than that of the Lyman limit at 912 A, and the extreme ultraviolet as being the region between 912 and 100 A.) Note that wavelengths given in this chapter will always be vacuum ones. In the past ultraviolet wavelengths shorter than 2000 A were expressed as vacuum values, while those longward of this were given with regard to wavelengths in air. This convention has been continued in the International Ultraviolet Explorer (IUE) Project, but is currently being changed in their newest pipeline processing system, and eventually the entire archive will make use of only vacuum wavelengths. Newer missions such as the Hubble Space Telescope (HST) and Extreme Ultraviolet Explorer (EUVE) are using vacuum wavelengths exclusively. This practice conforms to Resolution C15 of the 21st General Assembly of the International Astronomical Union. Equation (8.1) is the algorithm for calculating the index of refrac169 170 I 8 ULTRAVIOLET ASTRONOMY tion (n) of standard air as a function of vacuum wavelength. This algorithm was derived by Edlen [1], and was the one officially adopted by the International Astronomical Union (IAU) [2]. The wavelength in air is the vacuum wavelength divided by the index of refraction: -5 n = 1 + 6.4328 x 10 + 2.94981 x 10-2 146 x 108 _ (T2 2554.0 x 10-4 x 108 _ (T2 ' + 41 (8.1) where (T represents the wave number in vacuum, expressed in reciprocal A. 8.2 ULTRAVIOLET ASTRONOMY SATELLITE MISSIONS There have been numerous balloon and rocket flights devoted to ultraviolet astronomy, as well as various short-term studies, such as those conducted from manned space missions. The first ultraviolet spectrum of the Sun was obtained in 1946 using a captured V2 rocket, while the first stellar ultraviolet observations took place during 1955-1957. The first stellar ultraviolet spectrophotometry, by Stecher and Milligan [3], was accomplished by a rocket-borne instrument, while the first ultraviolet stellar spectroscopy (i.e., wavelength resolution sufficient to resolve individual spectral lines) was achieved in a 1965 rocket flight [4]. A balloon-borne stellar spectrograph first examined the very important Mg II resonance doublet in 1971 [5]. The principal long-term ultraviolet astronomy missions are summarized in Table 8.1. Note that the extensive number of missions that have been devoted to ultraviolet solar studies have not been included in the table. The first column in Table 8.1 gives the mission's name or acronym. OAO-2 stands for the second satellite in the Orbiting Astronomical Observatory series (the first having failed). It was the first instrument to carry out an extensive survey of the ultraviolet sky. The fourth satellite in this series was named Copernicus. It made substantial contributions to our understanding of the interstellar medium, hot stars, and stellar chromospheres. The lU-I mission (named after the launch vehicle-a Thor Delta) was a European Space Agency (ESA) mission which had two ultraviolet experiments on board, including the S2/68 Ultraviolet Sky Survey Telescope. lUI's primary legacy is the catalog of ultraviolet fluxes, which is cited in Table 8.2. ANS, the Astronomy Netherlands Satellite, had one ultraviolet experiment. Though well known for their spectacular success in planetary encounter missions, each of the two Voyager spacecraft have an ultraviolet spectrometer (UVS) that has been used for stellar spectroscopy, now that the primary mission objectives are completed. IUE, the International Ultraviolet Explorer, was a joint project of NASA, ESA, and the British SERC. It was originally intended for a three-year mission, but it continued to operate for over 18 years. One of the first major international satellites, IUE was operated in real-time from NASA's Goddard Space Flight Center for 16 hours per day, and from the ESA tracking station near Madrid for the remaining 8 hours. It is in an eccentric geosynchronous orbit. RiJntgensatellit (ROSAT) is primarily an X-ray mission, but it has a wide field camera which operates in the ultraviolet wavelength range and has been used to produce an all-sky survey. The Hubble Space Telescope contains a battery of instruments, most with a number of configurations, which operate at ultraviolet wavelengths. For example, the Goddard High Resolution Spectrograph (GHRS) had a number of gratings and echelle cross-dispersers, which have not been detailed specifically in the table, rather representative ranges have been listed. These instruments, referred to by their acronyms in Table 8.1, are the GHRS, Faint Object Spectrograph (FOS), Wide FieldIPlanetary Camera (WFIPC), Faint Object Camera (FOC), High Speed Photometer (HSP), and the Space Telescope Imaging Spectrograph (STIS). 8.2 ULTRAVIOLET ASTRONOMY SATELLITE MISSIONS I 171 Table 8.1. Major long-term ultraviolet astronomy missions. Spect. resol. Tel. apert. Mission Operational dates (cm) Instrument OA0-2 I 2J07/68-211 3173 20 20 20 20 20 20 40 30 30 30 30 Photometer Photometer Photometer· Photometer Photometer Photometer Nebular photometer Vidicon Vidicon Vidicon Vidicon Spectrometer Spectrometer Copernicus TD-I 8121172-12131180 3/12172-1/9/80 80 27.5 Spectrometer Spectrometer Spectrometer Spectrometer A (A) (A) 1430 Reference [1] 1550 1910 2460 2980 3320 I 200-4 000 1850-3600 1160-1850 12 22 912-1500 0.05 912-1645 1640-3185 1480-3275 0.2 0.01 0.04 Photometer Spectrophotometer 2740 [2] [3] 1350-2550 ANS 8/30174-6/14177 22 Photometer Photometer Photometer Photometer Photometer ISSO 1800 2200 2500 3300 WE 1/26/78-9/30/96 45 Echelle spectrograph Spectrograph 1145-3230 1150-3300 0.2 6 [5.6] HST 4/24/90- 240 OHRS FOS WFIPC 1110-3200 1150-7000 I 200-10000 1200-6500 I 150-8000 I 150-10 000 0.01-3.5 1.2-7 [7] FOe HSP STIS ROSAT EUVE 6/1190- 6/7/92- aa aa aa aa IIf aa aa Wide field camera Wide field camera Wide field camera Wide field camera Scanning photometer Scanning photometer Scanning photometer Deep survey Spectrometer Spectrometer Spectrometer [4] [8] 60-140 112-200 150-220 530-720 [9] 44-360 44-360 400-750 40-385 70-190 140-380 280-760 0.5 1 2 Note a See text for aperture discussion. References I. Code. A.S .• Houck. T.E .• McNall, J.F.• Bless. R.C .• & Lillie. C.F. 1970. ApJ. 161. 377 2. Rogerson. J.B .• Spitzer. L .• Drake. J.F•• Dressler. K .• Jenkins. E.B .• Morton. D.C.• & York. D.O. 1973. ApJ. 181.97 3. Jamar. C .• Macau-Hercot, D .• Monfils. A.. Thompson. 0.1.• Houziaux. L •• & Wllson, R. 1976. Ultraviolet Bright-Star Spectrophotometric Catalogue (ESA. Paris) 172 / 8 ULTRAVIOLET ASTRONOMY Wesselius, P.R., van Duinen, RJ., de Jonge, A.R.W., Aalders, J.W.G., Luinge, W., & Wildeman, K.J. 1982, A&AS, 49, 427 Kondo, Y., editor, 1987, Exploring the Universe with the IUE Satellite (Reidel, Dordrecht). Newmark, J.S., Holm. A.V., Imhoff, C.I., Oliversen, N.A., Pitts, R.E., & Sonneborn, G. 1992, NASA IUE Newslett., 47,1 Bless, R.C. 1992, in The Astronomy and Astrophysics Encyclopedia, edited by S.P. Maran (Van Nostrand, New York), pp. 912915 8. Pye, J.P', Watson, M.G., Pounds, K.A., & Wells, A. 1991, in Extreme Ultraviolet Astronomy, edited by R.F. Malina and S. Bowyer (pergamon, New York), p. 409 9. EUVE Guest Observer Center 1992, EUVE Guest Observer Program Handbook (Appendix G of NASA NRA 92-0SS-5) 4. 5. 6. 7. This configuration will change as a result of servicing missions for HST. The Extreme Ultraviolet Explorer (EUVE) is still in opemtion at the time of writing. The ROSAT and EUVE missions provided the first extensive and detailed look at this wavelength regime. HST and EUVE are in low-Earth orbits. Column 2 of Table 8.1 gives the mission's opemtional dates (the first date is the launch date, and so science opemtions will have begun somewhat later). Column 3 gives, when applicable, the size of the telescope objective (in cm) for the satellite or specific instrument. The notation "a" is used for the ROSAT and EUVE instruments to indicate that the matter of aperture is not as stmightforward in the case of those instruments. They make use of various types of segmented filter masks which allow a given instrument to make use of a specific fraction of the aperture. Column 4 indicates the type of instrument, and column 5 gives the experiment's wavelength range (for spectrogmphic and spectrophotometric instruments) or the effective and/or centml wavelength (for photometric instruments). Column 6 gives the approximate avemge spectml resolution (in A) for spectrographic instruments. (This will, of course, vary with wavelength in each instrument, so the entries in column 6 are intended to be representative only.) Finally, column 7 lists a representative reference which gives information about the mission. 8.3 SIGNIFICANT ATLASES AND CATALOGS Table 8.2 gives titles and references for some of the more important catalogs and atlases of ultraviolet astronomical data. Table 8.2. Important atloses and catalogs of ultraviolet data. The Variation of Galactic Interstellar Extinction in the Ultraviolet [1] Atlas of the Wavelength Dependence of Ultraviolet Extinction in the Galaxy [2] IUE-ULDA Access Guide No.2: Comets [3] ANS Ultraviolet Photometry, Catalogue of Point Sources [4] An Atlas of Extreme Ultraviolet Explorer (EUVE) Sources [5] IUE Low-Dispersion Spectra Reference Atlas. Part 1. Normal Stars [6] IUE Ultraviolet Spectral Atlas of Selected Astronomical Objects [7] Ultraviolet Bright-Star Spectrophotometric Catalogue [8] Supplement to the Ultraviolet Bright-Star Spectrophotometric Catalogue [9] Catalogue of Stellar Ultraviolet Fluxes [10] Ultraviolet Photometry from the Orbiting Astronomical Observatory. XXXII. An Atlas of Ultraviolet Stellar Spectra [11] IUE Ultraviolet Spectral Atlas [12] IUE Ultraviolet Spectral Atlas [13] The Extreme Ultraviolet Explorer Stellar Spectral Atlas [14] Spectral Synthesis in the Ultraviolet. I. Far-Ultraviolet Stellar Library [15] An Atlas of High Resolution IUE Ultraviolet Spectra of 14 Wolf-Rayet Stars [16] The Hopkins Ultraviolet Telescope Far-Ultraviolet Spectral Atlas ofWolf-Rayet Stars [17] International Ultraviolet Explorer Atlas of 0 Type Spectra from 1200 to 1900 A [18] Ultraviolet Spectral Morphology of the 0 Stars. ll. The Main Sequence [19] P Cygni and Related Profiles in the Ultraviolet Spectra of O-Stars [20] 8.3 SIGNIFICANT ATLASES AND CATALOGS / Table 8.2. (Continued.) An Atlas of Ultraviolet P Cygni Profiles [21] Identification of Lines in the Satellite Ultraviolet: The Spectrum of Tau Scorpii [22] Spectral Classification with the International Ultraviolet Explorer: An Atlas of B-Type Spectra [23] The IUE Spectral Atlas of1\vo Normal B Stars: 1r Ceti and v Capricorni (l25-198nm) [24] Identification Lists of the Far UV Spectra of 7 Solar Chemical Composition Main Sequence Stars in the Spectral Range B2-B9.5 [25] A Catalog of 0.2 AResolution Far-Ultraviolet Stellar Spectra Measured with Copernicus [26] The Copernicus Ultraviolet Spectral Atlas of Vega [27] The Copernicus Ultraviolet Spectral Atlas of Sirius [28] Early Type Strong Emission-Line Supergiants of the Magellanic Clouds: A Spectroscopic Zoology [29] Chromospheric Mg II Emission in A5 to K5 Main Sequence Stars from High Resolution IUE Spectra [30] Atlas of High Resolution IUE Spectra of Late-Type Stars. 2500-3230 A[31] The Spectra of Late-Type Dwarfs and Sub-Dwarfs in the Near Ultraviolet. I. Line Identifications [32] Outer Atmospheres of Cool Stars. VII. High Resolution Absolute Flux Profiles of the Mg II h and k Lines in Stars of Spectral Types F8 to M5 [33] UV Fluxes of Pop II Stars [34] IUE Low Dispersion Observations of Symbiotic Objects [35] A Far-Ultraviolet Atlas of Symbiotic Stars Observed with IUE. I. The SWP Range [36] A Spectrophotometric Atlas of White Dwarfs Compiled from the IUE Archives [37] Ultraviolet Observations of Cataclysmic Variables: The IUE Archive [38] A Catalogue of Low-Resolution IUE Spectra of Dwarf Novae and Nova-Like Stars [39] An Atlas of UV Spectra of Supernovae [40] UV Observations of SN 1987a [41] International Ultraviolet Explorer Atlas of Planetary Nebulae. Central Stars. and Related Objects [42] UV Spectra of the Central Stars of Large Planetary Nebulae [43] A Survey of Ultraviolet Interstellar Absorption Lines [44] Galactic Interstellar Abundance Surveys with IUE. II. 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Special Pub. No.1 Beckman, J.E., Crivellari, L., & Selvelli, P.L. 1982, A&AS, 47, 295 Stencel, R.E., Mullan, D.J., Linsky, J.L., Basri, G.S., & Worden, S.P. 1980, ApJS, 44, 383 Cacciari, C. 1985, A&AS, 61, 407 Sahade, J., Brandi, E., & Fountenla, J.M. 1984, A&AS, 56, 17 Meier, S.R., Kafatos, M., Fahey, R.P., Michalitsianos, A.G. 1994 ApJS, 94,183 Wegner, G., & Swanson, S.R. 1991, ApJS, 75, 507 Verbunt, E 1987, A&AS, 71, 339 La Dous, C. 1990, Space Sci. Rev., 52, 203 Benvenuti, P., Sanz Fernandez de Cordoba, L., Wamsteker, W., Macchetto, E, Palumbo, G.e., & Panagia, N. 1982, ESA Special Pub. No. 1046 Kirschner, R.P., Sonneborn, G., Crenshaw, D.M., & Nassiopoulos, G.E. 1987,ApJ, 320, 602 Feibelman, W.A., Oliversen, N.A., Nichols-Bohlin, J., & Garhart, M.P. 1988, NASA Ref. Pub. No. 1203 Kaler, J.B., & Feibelman, W.A. 1985,ApJ, 297, 724 Bohlin, R.e., Hill, J.K, Jenkins, E.B., Savage, B.D., Snow, Jr., T.P., Spitzer, Jr., L.S., & York, D.G. 1983, ApJS, 51,277 Van Steenberg, M.E., & Shull, J.M. 1988, ApJS, 67, 225 Blades, J.C., Wheatley, J.M., Panagia, N., Grewing, M., Pettini, M., & Wamstecker, W. 1988, ApJ, 334, 308 Rosa, M., Joubert, M., & Benvenuti, P. 1984, A&AS, 57,361 Cassatella, A., Barbero, J., & Geyer, E.H. 1987,ApJS, 64, 83 Longo, G., & Capaccioli, M. 1992, IUE-ULDA Access Guide No.3: Normal Galaxies, ESA SP-1152 Maoz, D., Filippenko, A.V., Ho, L.C., Macchetto, ED., Rix, H.-W. & Schneider, D.P. 1996, ApJS, 107, 215 Kinney, A.L., Bohlin, R.C., Calzetti, D., Panagia, N., & Wyse, R.EG. 1993, ApJS, 86, 5 Courvoisier, T.J.-L., & Paltani, S. 1992, IUE-ULDA Access Guide No.4: Active Galactic Nuclei, ESA SP-1l53 Chapman, G.N.E, Geller, M.J., & Huchra, J.P. 1985, ApJ, 297, 151 Kinney, A.L., Bohlin, R.e., Blades, J.e., & York, D.G. 1991, ApJS, 75, 645 INTERSTELLAR EXTINCTION IN THE ULTRAVIOLET Since interstellar extinction is significantly stronger in the ultraviolet than at visual wavelengths, correcting for its effects is very important. The most prominent feature in the ultraviolet extinction curves is a broad peak centered at ~ 2 175 A. Equation (S.2) [6] gives some useful analytic functions which can be used to determine AJ.. in the ultraviolet. Equation (S.2) is broken into three wavelength domains, and is parametrized in terms of a , the wave number expressed in microns: 2.70 ~ a ~ 3.65, AJ../EB-V = 1.56 + I.04Sa + [(a _ 1.01 4.60)2 + 0.2S0], (S.2a) 8.5 COMMONLY OBSERVED ULTRAVIOLET EMISSION LINES / 3.65::: a ::: 7.14, AA/EB-V = 2.29 + O.848a + [(a 7.14::: a ::: 10, AA/EB-v = 16.17 - 3.20a 1.01 _ 4.60)2 + 0.280]' + 0.2975a 2 • 175 (8.2b) (8.2c) Savage and Mathis [7] adopt 3.1 for the value of Av /E(R-v), while Seaton [6] uses 3.2. More detailed information is available in the review by Savage and Mathis [7], and additional references concerning ultraviolet extinction as a function of location in the sky are cited in Table 8.2. 8.S COMMONLY OBSERVED ULTRAVIOLET EMISSION LINES Table 8.3 (which is an expanded version of one given in Wu et al. [8]) gives a list of some of the more prominent ultraviolet emission lines observed in astronomical objects. The organization of Table 8.3 is as follows. Column 1 gives the wavelength (in A) of the line, using the convention that a reasonably precise value (to 0.01 A) is given for single lines, while an approximate value is given for lines formed of closely spaced individual lines of a given element. This value corresponds to the approximate location of the (blended) line which would be seen in low-resolution spectra, such as those taken in IUE's low-dispersion mode. In cases where there is a spectral region which contains a large number of lines due to a single element, then the range of wavelengths is given in column 1. In the cases of multiple lines, column 4 gives more accurate wavelengths for the individual components that may be present. Column 2 specifies the ion which is the source of the emission line, while column 3 lists the type of objects in which this emission line is generally observed. The abbreviations used in column 3 to specify object type are given at the bottom of Table 8.3. Table 8.3. Emission lines commonly found in ultraviolet spectra. A (A)O Ion lYpe of object where observed b Individual components in multiplets 538 584.33 834 916 On Hel Om Nn C SSO C C 537.83,538.26,538.32,539.13 933.4 977.02 1033 1066.66 1085 SVI Cm OIV Arl Nn SNR SNR SNR SSO,C C 1175 Cm WR, PN, CS, SS 1199 Sm SSO 1215.67 1240 HI Nv 1247.38 1256 1279 Cm Sn CI (all sources) PN, SS, WR, CV, XRB, SN, m, N,SQ,SNR SS,WR SSO TI,LTS 1299 1304 1309 Si m 01 Si n sS,m, TI RS, LTS, N, SQ, C PN 832.93,833.74,835.29 915.61,915.96,916.02,916.10,916.35, 916.70,916.71 1031.93, 1033.82, 1037.62 1083.99, 1 084.56, 1 084.58, 1085.53, 1085.55, 1085.70, 1085.12 1174.93,1175.26,1175.59,1175.71, 1 175.99, 1 176.37 1190.21, 1194.06, 1194.46, 1197.56, 1200.97,1201.73,1202.13 1 238.82, 1 240.15, 1 242.80 1250.58, 1253.81, 1256.12, 1259.52 1276.48, 1276.75, 1277.19, 1277.25, 1277.28, 1277.46, 1277.51, 1277.55, 1277.72, 1277.95, 1279.06, 1279.23, 1279.50, 1279.89, 1280.14, 1280.33, 1 280.36, 1 280.40, 1 280.60, 1 280.85 1 298.89, 1 298.96 1302.17,1303.49,1304.86,1306.03 1304.37, 1307.64, 1309.28 176 I 8 ULTRAVIOLET ASTRONOMY Table 8.3. (ContinuetL) A (A)a Ion 'IYPe of object where observed b Individual components in multiplets 1335 CII 1334.53. 1335.31. 1335.66. 1335.71 1342 1371.29 1394 OIV Ov SiIV TI. PN. LTS. RS. WR, ev. N. SNR.C CS. SS. WR. XRB 1397-1407 OIV 1402.77 Si IV 1460 CI PN. LTS. RS. TT. XRB. CV. IV. N.SQ TI 1473 SI RS.LTS 1483.32 1486 1487 1550 NIV SI NIV CIV ~.SS.WR.N 1561 CI 1574.77 1577 1602 1640 Nev CIll Nelv Hell 1641.31 1657 01 1663 o III 1670.79 1710 1718.55 1728.94 1750 AlII Sill NIV SIll NIll 1760 1815 1814.63 1860 1882.71 1892.03 CII Si II NellI AlIll Si III Si III 1900.29 1908.73 SI CIll 1914.70 1993.62 2321.67 2326 SI CI LTS.m ~. LTS.mI. SN. N. SQ. SNR TI. PN. LTS. mI. SN. N. SQ. SNR RS. LTS. SN.mI TI. PN. LTS. WR. mI. N. SN. SQ.ELG RS.LTS RS.LTS CII RS.LTS.SQ CI o III 1342.99. 1343.51 ~.CS.SS.XRB.SNR ~. LTS. RS. TT. XRB. ev.lV. N.SQ PN.SS.N RS.LTS PN. SS. WR. N. SNR TI. PN. LTS. SS. N. WR. CV. m. XRB. SQ. SNR C 1393.76.1396.75.1398.13 1397.23. 1399.78. 1401.16. 1404.81. 1407.38 1459.03. 1463.34. 1467.40. 1467.88. 1468.41 1472.97. 1473.02. 1473.01. 1473.99. 1474.38. 1474.57. 1478.50 1485.62. 1487.15 1 486.50. 1 487.89 1548.20.1550.77 1560.31. 1560.68. 1560.71. 1561.05. 1561.34. 1561.37. 1561.44 ~.N SS ~.N.SS TT. PN. LTS. RS. WR. XRB. SQ. SNR RS. LTS. SS. N C. RS. LTS. TT 1576.48. 1577.30. 1577.89 1 601.50. 1601.68 1640.47. 1640.49 ~. 1656.28. 1656.93. 1657.01. 1657.38. 1657.59. 1657.91. 1658.12 1660.81. 1666.15 ~.WR 1710.83. 1711.30 WR. SQ. N. LTS.mI. SS. SNR m.LTS PN. WR. XRB. CV. N SSO WR. TT. mI. N. SN. SNR ~ TT. PN. RS. LTS 1746.82. 1748.65. 1749.67. 1752.16. 1754.00 1760.47. 1760.82 1808.01. 1816.93. 1817.45 ~.N 1 854.72. 1862.79 1906.68. 1908.73. 1909.60 ~ 2324.21.2325.40.2326.11.2327.65. 2328.84 8.5 COMMONLY OBSERVED ULTRAVIOLET EMISSION LINES / 177 Table 8.3. (Continued.) Ion Type of object where observed b Individual components in multiplets 2328-2414 Fe II LTS. IT 2328.11.2333.52.2338.73.2344.21. 2344.70.2345.00.2349.02.2359.83. 2365.55.2367.59.2374.46.2381.49. 2382.77.2383.79.2389.36.2394.98. 2396.15.2396.36.2399.97.2405.16. 2405.62.2407.39.2411.25.2411.80. 2414.05 2329.23 2335 2381.13 2424 2471.04 2511.96 2586-2632 Sill Si II He II Ne IV all He II Fe II RS.LTS PN PN SQ PN. SN.HIl PN LTS. IT. N. MSG 2664.06 2696.92 2724.00 2734.14 2764.62 2783.03 2786.81 2794 2800 Hel He I Hel Hel Hel Mgv Arv MgIl MgIl 2829.91 2838 2852.96 2854.48 2869.00 2928.34 2933 2945.97 2950.07 2973.15 2978 3005.36 3024.33 3046 3068 3109 3133.77 3188.67 3204.03 Hel CII MgI Arlv Arlv Mgv MgIl Hel MnIl PN PN PN PN PN.HIl PN PN PN PN. LTS. RS. IT. ELG PN.HIl PN PN.HIl PN PN PN PN PN PN.IT C PN PN PN PN PN PN PN. IT. N. LTS PN PN 01 NIII ArIII alII am NIl ArIII alII Hel He II 2335.12.2335.32.2344.92.2350.89 2422.51.2425.15 2586.65.2599.15.2600.17.2607.87. 2611.41.2612.65.2614.61.2618.40. 2621.19.2622.45,2626.45,2629.08, 2631.83, 2632.11 m. N. SQ. 2798.81,2791.59 2796.35. 2803.53 2837.54. 2838.44 2929.49,2937.36 2973.43,2979.70 3043.91,3048.02 3 063.72. 3071.44 3109.16,3110.06 Notes aWavelengths (in vacuum) are taken from: Aller. L.H. 1984, Physics o/Thermal Gaseous Nebula (Reidel. Dordrecht); Kelly. R.L. 1979, Atomic Emission Lines in the Near Ultraviolet; Hydrogen through Krypton. NASA Tech. Memo. No. 80268; Kelly, R.L. 1987. Atomic and Ionic Spectrum Lines Below 2000 A: Hydrogen through Krypton (American Chemical Society. New York); Kelly. R.L. & Palumbo. LJ. 1973, Atomic and Ionic Emission Lines Below 2000 Angstroms (Naval Research Lab.• Washington. DC); Koppen. J.• & Aller. L.H. 1987. in Exploring the Universe with the IUE Satellite. edited by Y. Kondo (Reidel. Dordrecht). p. 589; and Morton. D.C. 1991. ApJS. 77. 119. bThe astronomical objects where these lines are frequently seen in emission are noted by the abbreviated code in column 3. They are: C. comets; CS. carbon stars; CV. cataclysmic variables (N.B. novae have a separate listing); ELG. emission line galaxies; HIl. H II regions; m. interacting binaries; LTS.late-type stars; MSG. massive supergiants; N. novae; PN. planetary nebulae; RS. RS CVn stars; SQ. Seyfert galaxies and QSOs; SN. supernovae; SS. symbiotic stars; SSO. solar system objects; IT. T Tau stars; WR. Wolf-Rayet stars; XRB. low-mass X-ray binaries. 178 / 8 8.6 ULTRAVIOLET ASTRONOMY ULTRAVIOLET SPECTRAL CLASSIFICATION Studies of spectral classification of 0 and B stars based on ultraviolet spectra have been made using Copernicus data and the extensive IUE archive. Low-dispersion spectra were used by Heck et al. [9], Heck [10], and laschek and laschek [11]. High-dispersion studies have been conducted by Snow and Morton [12], Walborn and Panek [13], Walborn et al. [14], Walborn and NicholsBohlin [15], Massa [16], Bates and Gilheany [17], Prinja [18], and Rountree and Sonneborn [19]. For detailed quantitative comparisons, the papers by Massa and Prinja are convenient, because they give tables and/or figures which show the equivalent widths as a function of spectral type or temperature. Prinja [18] gives two useful fonnulas relating equivalent widths (Wa) in rnA to effective temperature. The most sensitive diagnostic for 0 stars temperatures is Si III A1299: log(Wa ) = 17.89 - 3.43 log Teff. (3) For B stars, the Si II ),,1265 is the most sensitive temperature indicator [16]: log(Wa ) = 20.57 - 4.21 log Teff. (4) The infonnation in Table 8.4 is taken from these studies. Table 8.4 gives the approximate wavelength and identification for classification lines in its first two columns, and summarizes their changing characteristics as a function of spectral type and luminosity in the final column. (More accurate wavelengths can be found in Table 8.3.) Table 8.4. Lines useful for spectral classification of 0 and B stars. A (A) Ion Comments 1175 C 1216 HI 1240 Nv 1247 C 1255 1264 Fev Si II 1 300 Si III 1310 Si II 1336 CII 1339 OIV 1371 Ov In low dispersion this blend of six lines (U 1174.933-1176.370) is seen to increase from 04 to a maximum at B I, and disappears at B6 into the Ly a wing. In high dispersion one can see dramatic P Cygni profiles for all supergiants from 04 I-BO.5 Ia, for bright giants as late as 09.5, and for giants as late as OS. When not affected by interstellar or circumstellar components has a half-width at half-maximum which increases from lO A at 09 to 100 A at BS. AI.. 1239, 1243 show wind profiles in most 0 stars. Shows a dependence on luminosity at 09.5, since the stellar wind effects have declined by then. Blended with Fe II AI.. 1246.S, 1247.S, and can be severely affected by emission component of NY J..l240 P Cygni lines in luminous stars. Generally increases in strength from early to late O. Strongest in early B (BO-Bl), and then slowly declines. The ratio C III 1..1247/0 IV 1..1339 depends on luminosity class, being higher for more luminous stars. This ratio can be as large as 4 between supergiants and main-sequence stars at a given temperature (Prinja, R.K. 1990, MNRAS, 246, 392). The comparison of this line with Si II 1..1265 shows a slight dependence on luminosity class (N.B.: can be affected by a reseaux mark in high-dispersion IUE spectra). Decreases from 03 to 07. Becomes visible at Bl; at B1.5 it is clearly present but weaker than 1..1247; at B2 it is as strong as J..l247; and by B4 it is much stronger. Continues to increase through B9. Does not show any luminosity effect. Probably the most sensitive diagnostic of 0 star temperatures. Increases sharply from 03 to B2, then levels out in strength from B2 to B5. Useful diagnostic in B stars. It is weaker than 1..1300 at B2, greater than or equal to 1300 at B3-B4, and dominates the spectrum at B5-BS. Doublet, which increases from BO to a maximum at BS. The wind profiles achieve maximum strength at B I-B2 Ia. There is a very strong interstellar contribution to this line. Shows a well-defined temperature sequence for luminosity classes I and V in 0 stars, decreasing as temperature declines. Generally only the 1..1339 line is used in this doublet, since the J..l343 line is blended with a nearby Si III line (as well as lying in an awkward location in IUE echelle spectra). This line declines from 03 until it disappears at 07. III III 8.6 ULTRAVIOLET SPECTRAL CLASSIFICATION I 179 Table 8.4. (Continued.) A (A) Ion Comments 1400 Si IV 1428 CIII 1430 1453 1485 1527 1533 1550 Fev Blend Si" Si" Si" CIV 1608 Fe" 1640 He" 1655 1670 CI AI" 1718 NIV 1723 AI" 1750 NIII 1859 Al III 1862 AI" 1891 Fe '" 1926 1967 Fe III Fe III Blend of the A1394 and AI403 lines of Si IV. In low-dispersion spectra this blended pair is a useful luminosity indicator for late 0, and a spectral type discriminator for B. First strongly visible in lowdispersion spectra at 07, and gets stronger as surface gravity decreases. In high dispersion, at 06.5 lines display stellar wind effects which increase with luminosity, from none at V to a full P Cyg profile at Ia. At 09.5 the doublet shows no stellar-wind effect in luminosity classes v-m, but it develops gradually as a function of luminosity from classes II through Ia. In the B stars, Si IV is strong in BO and Bl and decreases in strength until it disappears at about B6. The intensity ratio Si IV A1400/C IV A1550 is very sensitive to the 0 star spectral type, being R:: 1 at 06, and greater than 1 for 06.5-09.7. (In low dispersion the A1426 and A1428 lines are blended, though they are never especially strong. They increase from 04 to a maximum at B1.) Especially fine discriminator in the 07-Bl region, where it can be compared to A1430. The ratio A1429/A1430 = 1 for this Fe v doublet between 03 and 04, and declines at 05 and later. In low dispersion, has a maximum at 04 and disappears at BO. Blend of three lines. First present at B2 and becomes stronger through B9. Absorption feature becomes prominent in late B. Absorption feature becomes prominent in late B. Resonance doublet is one of the most prominent UV lines. Strong in 0 stars, decreasing from 03 to B2 (in dwarfs) where it disappears. If seen in mid-B, indicates a supergiant. Saturated P Cyg profiles from 03-06, declining at 07. Continues to show strong wind absorption through 09, becoming purely photospheric at B1. At the transition type 09.5 there is an increase in strength with luminosity class. A large collection of Fe "lines exist in the AA 1~161O region. These blends increase in strength with increasing luminosity, while showing little temperature effect. In 0 stars there is a noticeable interstellar component. Present throughout the 0 star regime, is still strong at BO, still noticeable, but declining in BO.5-B I, weak at B 1.5, and weak to absent at B2. Increases in strength as spectral type gets later. It is a prominent line in B5-B9. Becomes prominent in late B (N.B.: there is frequently a strong interstellar line seen in 0 stars, due to this ion). Unsaturated subordinate line which shows P Cyg profiles through 06, then declines in strength with increasingly later spectral type. It is still strong at BO, much less prominent at BO.5, and weak to absent at B 1. At BO it is stronger in giants than dwarfs. Blend. The components are at AA 1719.44, 1721.24, 1721.27, 1724.95, 1724.98. Line strength increase with luminosity in B stars. Doublet at AA 1748, 1752. The strength of both lines increases between 03 and 04, and the ratio A1748/A1752 increases dramatically between 03 and 04. The pair remains distinct through BO, but starts to weaken at BO.5, and disappears as B1. Doublet at AA 1855, 1862. Purely interstellar in 0 stars. In B stars increases with increasing luminosity class. There is a strong wind maximum at B 1-2 la. Strong in 0 stars. Blended with A1855 in low-resolution spectra. Shows an increased strength with increased luminosity class. Present in early B stars. Shows a positive luminosity effect. There are many Fe III lines in this wavelength region. The use of this line and others below is most generally useful in low-dispersion spectra. Similar to A1891. Similar to A1891. The ultraviolet is particularly suitable for classifying 0 and B stars, due to the strong fluxes for these objects in that wavelength regime. Difficulties with classifying OB stars include the contamination of some lines by strong interstellar components, and the fact that ultraviolet resonance lines are frequently severely affected by stellar winds. Snow and Morton [12] found that all 0 and B supergiants exhibited mass loss, with P Cygni profiles being seen to as late as B 1. For bright giants and giants, strong P Cygni profiles were noted as late as 09.5 and 09, respectively, and all main-noted sequence 0 stars showed evidence of mass loss. A further complication is that the wind profiles of some B supergiants have been found to be variable. Exactly how much of the dispersion in wind line strengths is due to variations in the intrinsic stellar properties, and how much is due to variability or abundance anomalies, is uncertain [17, 20]. 180 / 8 8.7 ULTRAVIOLET ASTRONOMY ULTRAVIOLET SPECTROPHOTOMETRIC STANDARDS Spectrophotometric calibration has always been a thorny problem for long-term ultraviolet satellite missions. Early efforts tended to focus on using hot subdwarfs as reasonably line-free continuum sources, which were not generally variable, and had very small or negligible interstellar reddening. The current IUE absolute calibration is based on comparison with the earlier measurements of some baseline standard stars made by OAO-2 and TO-I, and normalized to the flux values for the fundamental calibration star, T/ UMa. The stars used were HD 60753, BD + 75° 325, HD 93521, BD + 33° 2642, and BD + 28° 4211 for the low-dispersion data, while Cas, }.. Lep, and r Sco were used for the high-dispersion data. It should be noted that both Cas and T/ UMa have shown some indications of microvariability [21]. A more complete list of IUE standards can be found in [22], while the HST standards are cited in [23]. More recently a shift has been made to using hot DA (i.e., essentially pure helium) white dwarfs as fundamental calibrators. The reasoning behind this is that the models for these stars are very simple and well understood, as well as being unaffected by spectral lines. The ruE' Project's Final Archive is making use of white dwarfs for their new absolute calibration. The EUVE used this approach from the very beginning. The fundamental calibrator that is being used is G19lB2B. Table 8.5 lists some of the ultraviolet standard stars that have been used in common by many missions. Columns 1 and 2 give the star's catalog number and common name, while columns 3 and 4 list the star's coordinates. Columns 5 and 6 give the spectral type and visual magnitude, while column 7 indicates which missions have observed this star for calibration purposes. s s Table 8.5. Selected ultraviolet spectrophotometric standard stars. CatalogID Common name HD 2151 HD3360 BPM 16274 Feige 11 HD 10144 HD 11636 HD 15318 GD50 HZ4 LB227 HZ2 Gl91B2B HD32630 HD34816 HD35468 HD35580 HD38666 PG0549 + 158 HD45557 HD49798 HD60753 CD -310 4800 HD 61421 HD66811 BD+75° 325 HD 80007 AGK +81 0 266 BD +48 0 1777 HD87901 Feige 34 13 Hyi ~Cas a Eri f3Ari ~2 Cet TJAur ALep yOri Pic JL Col GD71 Ie aCMi ~ Pup 13 Car a Leo a(2000) 8(2000) Sp. Type V 00:25:45.4 00:36:58.3 00:50:03.2 01:04:21.6 01:37:42.9 01:54:38.3 02:28:09.5 03:48:50.1 03:55:21.7 04:09:28.8 04:12:43.5 05:01:31.0 05:06:30.8 05:19:34.4 05:25:07.8 05:22:22:2 05:44:08.4 05:52:27.5 06:24:13.7 06:48:04.6 07:33:27.3 07:36:30.2 07:39:18.1 08:03:35.1 08:10:49.3 09:13:12.1 09:21:19.1 09:30:46.6 10:08:22.3 10:39:36.7 -77:15:16 +53:53:49 -52:08:17 +04:13:38 -57:14:12 +20:48:29 +08:27:36 -00:58:30 +09:47:19 +17:07:54.4 +11:51:50 +52:45:48 +41:14:04 -13:10:37 +06:20:59 -56:08:04 -32:19:27 +15:53:17 -60:16:52 -44:18:59 -50:35:04 -32:12:45 +05:13:30 -40:00:12 +74:57:58 -69:43:02 +81:43:29 +48:16:26 +11:58:02 +43:06:10 G2IV B2IV DA BOVI B3Vpe A5V B9m DA DA DA DA DA B3V BO.5IV B2m B8-9V 09.5 IV DA AOV sd06 B3IV 08 AI F5 IV-V 05f 05p A2IV sdO OVI B7V DO 2.80 3.68 14.2 12.06 0.46 2.64 4.29 14.06 14.52 15.34 13.86 11.78 3.17 4.29 1.64 6.11 5.17 13.04 5.80 8.30 6.69 10.50 0.38 2.26 9.54 1.68 11.92 10.37 1.35 11.18 Observed by" H OTAVI H OIH OCTI OTI H H H H H VllIE OTAI OTAI OTI TI VIH VIE TI VIH TIH AI OCTAl OCTVIH OTAVIH OTI AIH AI OCTAVIH VIH 8.7 ULTRAVIOLET SPECTROPHOTOMETRIC STANDARDS / 181 Table 8.5. (Continued.) Catalog ID HD93521 HD 100889 HD 103287 HZ21 PG 1254 + 223 HZ 44 Grw +70° 5824 HD 120315 HD 121263 HD 122451 HD 125924 HD 128801 HD 137389 HD 137744 BD +33°2642 HD 142669 HD 145454 0153-41 HD 149438 HD 149757 HD 155763 HD 164058 HD 172167 HD 172883 HD 177724 HD 186427 HD 196519 HD 197637 HD 201908 LDS749B BD +28°4211 G93-48 HD209952 NGC7293 HD214680 HD 214923 PG2309+ 105 Feige 110 Common name o Crt yUMa GD 153 TJUMa s Cen fJ Cen lOra p Sco r Sco s Oph s Dra Y Ora aLyr s Aql 16 Cyg B vPav aGru 10 Lac s Peg GD246 a(2000) 10:48:23.5 11:36:40.8 11.53:49.8 12:13:56.4 12:57:04.5 13:23:35.4 13:38:51.8 13:47:32.4 13:55:32.3 14:03:49.5 14:22:43.0 14:38:48.1 15:22:37.1 15:24:55.7 15:51:59.9 15:56:53.0 16:06:19.5 16: 17:55.4 16:35:52.9 16:37:09.5 17:08:47.1 17:56:30.4 18:36:56.3 18:39:52.7 19:05:24.5 19:41:52.0 20:41:57.1 20:36:00.6 21:05:29.2 21:32:15.8 21:51:11.1 21:52:25.3 22:08:13.9 22:29:38.5 22:39:15.6 22:41:27.7 23:12:35.3 23:19:58.4 1YPe 8(2000) Sp. +37:34:13 -09:48:08 +53:41:41 +32:56:31 +22:12:45 +36:08:00 +70:17:09 +49:18:48 -47:17:18 -60:22:23 -08:14:54 +07:54:44 +62:02:50 +58:57:58 +32:56:55 -29:12:50 +67:48:36 -15:35:49 -28:12:58 -10:34:02 +65:42:53 +51:29:20 +38:47:01 +52:11:46 +13:51:48 +50:31:03 -66:45:39 +79:25:49 +78:07:35 +00:15:14 +28:51:52 +02:23:24 -46:57:40 -20:50:13 +39:03:01 +10:49:53 +10:50:27 -05:09:56 09Vp B9.5 Vn AOVe 00 DA sdO DA B3V B2.5 IV Blm B2IV B9 AOpSi K2m B2IV B2IV-V AOVn DA BOV 09.5Vn B6m KSm AOV AOpHg AOVn G1.5 V B9m B3 B8Vn DB sdOp DA B7IV PNN 09V B8V DA DOp V 7.04 4.70 2.44 14.68 13.4 11.66 12.77 1.86 2.55 0.61 9.70 8.80 5.98 3.29 10.81 3.88 5.44 13.42 2.82 2.56 3.17 2.22 0.03 6.00 2.99 6.20 5.15 6.78 5.91 14.67 10.51 12.74 1.74 13.51 4.88 3.40 13.10 11.82 Observed by" TAVIH IH IH H VIE VH H OCTVIH OCTAl H TAl TAl TAl H OTAIH OTAI TI VIH OCTAVI OCTVIH OCTAl H OCTAVIH TI OTAI IH TAl TI on H OTAVIH H OCTI VIH OCTAl H !HE H Note aObservations were made of these standards by many of the ultraviolet astronomy missions, and they are listed in column 7, where the letters refer to 0 = OAO-2, C = Copernicus, T = TO-I, A = ANS, V = Voyager UVS, I = ruE, H = HST, E = EUVE. REFERENCES Edlen, B. 1953, JOSA, 43, 339 Oosterhoff, P.T. 1957, Trans. IAU, 9, 202 Stecher, T.P., & Milligan, J.E. 1962, ApJ, 136, 1 Morton, D.C., & Spitzer, L. 1966, ApJ, 144, 1 Kondo, Y., Giuli, T., Modisette, J.L., & Rydgren, A.E. 1972,ApJ, 176, 153 6. Seaton, M.J. 1979, MNRAS, 187,73 7. Savage, B.D., & Mathis, J.S. 1979, ARA&A, 17, 73 8. Wu, C.-c. et al. 1992, 1UE Ultraviolet Spectral Atlas of Selected Astronomical Objects, NASA Tech. Memo. 1. 2. 3. 4. 5. No. 1285 9. Heck, A., Egret, D., Jaschek, M., & Jaschek, C. 1984, lUE Low-Resolution Spectra Reference Atlas: Part 1. Normal Stars (ESA, Paris) 10. Heck, A. 1987, in Exploring the Universe with the IUE Satellite, edited by Y. Kondo (Reidel, Dordrecht), p. 121 II. Jaschek, C., & Jaschek, M. 1987, The Classification of Stars (Cambridge University Press, Cambridge) 12. Snow, Jr., T.P., & Morton, D.C. 1976, ApJS, 32, 429 13. Walborn, N.R., & Panek, R.J. 1984, ApJ, 286, 718 182 I 8 ULTRAVIOLET ASTRONOMY 14. Walborn, N.R., Nichols-Bohlin, J., & Panek, R.J. 1985, IUE Atlas of O-Type Spectra from 1200 to 1900 A, NASA RP-1155 15. Walborn, N.R., & Nichols-Bohlin, J. 1987, PASP, 99, 40 16. Massa,D.1989,A&A,224,131 17. Bates, B., & Gilheany, S. 1990, MNRAS, 243, 320 18. Prinja, R.K. 1990, MNRAS, 246, 392 19. Rountree, J., & Sonneborn, G. 1991, ApJ, 369, 515 20. Massa, D., Altner, B., Wynne, D., & Lamers, H.J.G.L.M. 1991, A&A, 242, 188 21. Taylor, B.J. 1984, ApJS, 54, 259 22. P6rez, M.R., Dliversen, N.A., Garhart, M.P., & Teays, T.J. 1990, in Evolution in Astrophysics: IUE Astronomy in the Era of New Space Missions, edited by E.J. Rolfe (ESA, Noordwijk), p. 349 23. Thrnshek, D.A., Bohlin, R.C., Williamson, R.L., Lupie, D.L., & Koorneef, J. 1990, ApJ, 99, 1243 Chapter 9 X-Ray Astronomy Frederick D. Seward 9.1 .. 183 9.1 Useful Conversions 9.2 Characteristic X-Ray Transitions 184 9.3 Emission Mechanisms and Spectra 184 9.4 Transmission of X-Rays Through the Interstellar Medium 194 9.5 Cosmic X-Ray Sources. 9.6 Diffuse Background . 9.7 X-Ray Astronomy Missions .. 198 203 .. . . .. . . 205 USEFUL CONVERSIONS = 1.6021 x 10-9 erg = 1.6021 x 10- 16 J: the kilo-electron-volt. = 12.398 [A (A)r l : the energy of a photon. = 0.862T (l07K): the characteristic energy, kT, of a thennal source. = 2.998 x 1018 [A(A)r l = 2.418 x 1017 E (keV). = 1.160 x 107 [kT (keV)]. 1 (keV) E (keV) E (keV) v (Hz) T (K) 1/.L1y = 10-29 ergcm-2 s-I Hz- I = 10-32 W m-2 Hz-I: the micro-Jansky. Spectra are usually presented as the dependence of spectral irradiance (spectral flux density) I, on wavelength A (A), frequency v (Hz), or photon energy E (keV or erg). To convert from one to the other: h(ergcm- 2 s-I A-I) = 3.336 x = 5.034 x 183 1O- 19 v2 (Hz) I v (ergcm- 2 s-I Hz-I) 107 E 2 (erg) Ie(ergcm- 2 s-Ierg-I), 184 / 9 X-RAY ASTRONOMY = 3.336 x = 6.626 x Ie (keYcm- 2 s-I key-I) = 1.509 x I v (ergcm- 2 S-I Hz-I) = 5.034 x N p (photoncm- 2 s-I key-I) 9.2 1O- I9 )..2(A) h(ergcm- 2 s-I A-I) 10-27 Ie (keY cm-2 s-I key-I), 1026 Iv (ergcm- 2 s-I Hz-I) 107)..2 (A) h(ergcm- 2 s-I A-I), = Ie (keY cm- 2 s-I key-I)E-I(keY). CHARACTERISTIC X-RAY TRANSITIONS Energies of absorption edges and emission lines are given in Table 9.1. All energies are in keV. 9.3 EMISSION MECHANISMS AND SPECTRA 9.3.1 Continuum Models X-ray spectra have historically been compared to three simple models that imply emission from: (a) high-energy electrons moving in a magnetic field; (b) thermal electrons in an optically thin plasma with temperature, T > 3 x 107 K; and (c) thermal radiation from an optically thick object. These spectra are: (a) Power law, I (E) = AE-a , a = spectral index. (b) Thermal bremsstrahlung, I(E, T) = AG(E, T)Z2neni(kT)-I/2e-E/kT. Densities of electrons and positive ions are ne and ni, respectively, and G is the Gaunt factor, a slowly varying function with increasing value as E decreases [1,2]. When E « kT, G ~ 0.55In(2.25kT/E), and when E "" kT, G ~ (E/kT)-O.4 is an adequate approximation [3]. When electrons are relativistic, the Gaunt factor can be approximated as G = [0.9 + 0.75(kT /mc 2)](E/ kT)-I/4 + 1.9(kT /mc 2)(E/ kT)-I/6 + 3.4(kT /mc 2)2(E/ kT), an approximation better than 20% in the range (kT /mc 2) :::: I, (E/ kT) :::: 6 [4]. (c) Blackbody radiation, Early observations were usually well fit using these simple models. Spectra of actual sources are, of course, more complex. There are emission lines, absorption edges, and, usually, scattering and absorption in material surrounding, or close to, the sources. Observations with high spectral resolution and good counting statistics, or those covering a broad spectral range, require more complex models for good fits [5]. 9.3 EMISSION MECHANISMS AND SPECTRA Table 9.1. Energies of characteristic lines and edges [1]. K series Z K(ab) IH 2He 3Li 4Be 5B 6C 7N 80 9F lONe 11 Na 12Mg 13 AI 14Si 15 P 16 S 17 CI 18Ar 19K 20Ca 21 Sc 22 Ti 23V 24Cr 25Mn 26 Fe 27 Co 28Ni 29Cu 30Zn 31 Ga 32Ge 33 As 34Se 35Br 36Kr 37Rb 38 Sr 39Y 40Zr 41Nb 42Mo 43Tc 44Ru 45Rh 46Pd 47Ag 48 Cd 49 In 0.0136 0.025 0.055 0.112 0.192 0.283 0.399 0.531 0.687 0.867 1.072 1.305 1.559 1.838 2.142 2.472 2.822 3.202 3.607 4.038 4.496 4.965 5.465 5.989 6.540 7.112 7.709 8.333 8.979 9.659 10.368 11.104 11.868 12.658 13.474 14.322 15.201 16.105 17.037 17.998 18.986 20.002 21.054 22.118 23.224 24.350 25.514 26.711 27.940 K{33 K{3, Kfh Ku, KU2 9.656 10.365 11.099 11.862 12.650 13.467 14.312 15.183 16.082 17.013 17.967 18.949 19.962 21.002 22.070 23.169 24.295 25.452 26.639 27.856 0.052 0.110 0.185 0.277 0.392 0.525 0.677 0.848 1.041 1.253 1.486 1.740 2.013 2.307 2.622 2.957 3.313 3.691 4.090 4.510 4.951 5.414 5.898 6.403 6.929 7.477 8.046 8.637 9.250 9.885 10.542 11.220 11.922 12.648 13.393 14.163 14.956 15.772 16.612 17.476 18.364 19.276 20.213 21.174 22.159 23.170 24.206 1.486 1.739 2.012 2.306 2.620 2.955 3.310 3.687 4.085 4.504 4.944 5.405 5.887 6.390 6.914 7.460 8.026 8.614 9.223 9.854 10.506 11.179 11.876 12.596 13.333 14.095 14.880 15.688 16.518 17.371 18.248 19.147 20.070 21.017 21.987 22.980 23.998 1.067 1.295 1.553 1.829 2.136 2.464 3.190 3.589 4.012 4.460 4.931 5.426 5.946 6.489 7.057 7.648 8.263 8.904 9.570 10.263 10.259 10.976 10.980 11.724 11.718 12.437 12.494 13.282 13.289 14.102 14.110 14.959 14.949 15.822 15.833 16.723 16.735 17.651 17.665 18.603 18.619 19.587 19.605 20.595 20.615 21.631 21.653 22.695 22.720 23.787 23.815 24.907 24.938 26.057 26.091 27.233 27.271 / 185 186 I 9 X - RAY ASTRONOMY Table 9.1. (Continued.) K series Z 50Sn 51 Sb 52 Te 53 I 54Xe 55 Cs 56Ba 57 La 58Ce 59Pr 60Nd 61 Pm 62Sm 63Eu 640d 65Th 66Dy 67Ho 68Er 69Tm 70Yb 71 Lu 72Hf 73 Ta 74W 75Re 76 Os 77 Ir 78Pt 79 Au 80Hg 81 Tl 82Pb 83 Bi 84 Po 85 At 86Rn 87Fr 88Ra 89Ac 90Th 91 Pa 92U 93Np 94Pu 95 Am 96Cm 97Bk 98Cf K(ab) 29.200 30.491 31.813 33.169 34.582 35.959 37.441 38.925 40.449 41.998 43.571 45.207 46.835 48.515 50.240 51.996 53.789 55.615 57.483 59.390 61.332 63.304 65.351 67.414 69.524 71.662 73.860 76.112 78.395 80.723 83.103 85.528 88.006 90.572 93.112 95.740 98.418 101.147 103.927 106.759 109.649 112.581 115.603 118.619 121.760 124.876 128.088 131.357 134.683 K{33 K{31 K{32 Kal 28.439 29.674 30.939 32.234 33.556 34.913 36.298 37.714 39.163 40.646 42.159 43.705 45.281 46.896 48.547 50.221 51.949 53.702 55.485 57.293 59.141 61.037 62.969 64.938 66.940 68.983 71.065 73.190 75.355 77.567 79.809 82.104 84.436 86.819 89.231 91.707 94.230 %.791 99.415 102.084 104.813 107.576 110.387 28.481 29.721 30.990 32.289 33.619 34.981 36.372 37.795 39.251 40.741 42.264 43.818 45.405 47.030 48.688 50.374 52.110 53.868 55.672 57.506 59.356 61.272 63.222 65.212 67.233 69.298 71.401 73.548 75.735 77.971 80.240 82.562 84.922 87.328 89.781 92.287 94.850 97.460 100.113 102.829 105.591 108.409 111.281 113.725 116.943 120.350 122.733 126.490 127.794 29.104 30.388 31.698 33.036 34.408 35.815 37.251 38.723 40.226 41.767 43.327 44.929 46.566 48.248 49.952 51.715 53.500 55.315 57.204 59.085 60.974 62.956 64.969 67.001 69.089 71.219 73.390 75.606 77.864 80.172 82.530 84.933 87.351 89.846 92.383 94.974 97.622 100.307 103.051 105.849 108.699 111.605 114.587 118.057 120.350 123.960 126.490 130.484 133.290 25.267 26.355 27.468 28.607 29.774 30.968 32.188 33.436 34.714 36.020 37.355 38.718 40.111 41.535 42.989 44.474 45.991 47.539 49.119 50.733 52.380 54.061 55.781 57.523 59.308 61.130 62.990 64.885 66.821 68.792 70.807 72.859 74.956 77.095 79.279 81.499 83.768 86.089 88.454 90.868 93.334 95.852 98.422 100.781 103.300 105.949 108.737 111.676 114.778 Ka2 25.040 26.106 27.197 28.312 29.453 30.620 31.812 33.028 34.273 35.544 36.841 38.165 39.516 40.895 42.302 43.737 45.200 46.692 48.213 49.764 51.345 52.956 54.602 56.267 57.972 59.708 61.476 63.276 65.112 66.978 68.883 70.820 72.792 74.802 76.851 78.930 81.051 83.217 85.419 87.660 89.938 92.271 94.649 %.844 99.168 101.607 104.168 106.862 109.699 19K 20Ca 21 Sc 22 Ti 23V 24Cr 25Mn 26 Fe 27 Co 28Ni 29Cu 30Zn 310a 320e 33 As 34Se 35Br 36Kr 37Rb 38 Sr 39Y 40Zr 41Nb 42Mo 43Tc 44Ru 45Rh Z 0.400 0.463 0.530 0.604 0.682 0.754 0.842 0.929 1.012 1.100 1.196 1.300 1.420 1.530 1.653 1.794 1.920 2.067 2.216 2.369 2.547 2.698 2.866 3.054 3.236 3.419 L[(ab) LY3 1.697 1.817 1.936 2.060 2.187 2.319 2.455 2.741 2.890 2.763 2.915 1.286 LP4 0.585 0.654 0.721 0.792 0.866 0.941 1.023 1.107 1.197 1.294 1.388 1.490 1.596 1.706 1.826 1.947 2.072 2.201 2.334 2.473 LP3 L[ series 1.596 1.756 1.866 2.007 2.145 2.307 2.465 2.625 2.795 2.996 3.146 LU(ab) 2.964 3.143 2.302 2.461 2.623 0.350 0.407 0.460 0.520 0.583 0.652 0.721 0.794 0.872 0.952 1.044 1.134 1.249 1.360 1.477 LYI 0.345 0.400 0.458 0.519 0.583 0.649 0.718 0.791 0.869 0.950 1.034 1.125 1.218 1.317 1.419 1.526 1.636 1.752 1.871 1.995 2.124 2.257 2.394 2.536 2.683 2.834 LPI LII series L series Table 9.1. (Continued.) 2.382 2.519 1.542 1.649 1.761 1.876 1.9% 2.120 0.262 0.306 0.353 0.401 0.453 0.510 0.567 0.628 0.694 0.762 0.832 0.906 0.984 1.068 1.155 1.244 1.399 LI'/ 0.346 0.403 0.454 0.513 0.574 0.641 0.709 0.799 0.855 0.932 1.021 1.117 1.218 1.325 1.436 1.550 1.675 1.806 1.940 2.079 2.223 2.371 2.520 2.677 2.837 3.003 Lm(ab) 2.835 3.001 2.219 2.367 2.518 LP2 La2 0.341 0.395 0.452 0.511 0.573 0.637 0.705 0.776 0.851 0.930 1.012 1.098 1.188 1.282 1.379 1.480 1.586 1.692 1.694 1.804 1.806 1.922 1.920 2.042 2.040 2.163 2.166 2.289 2.293 2.424 2.554 2.558 2.692 2.696 Lal LIII series 2.252 2.376 1.482 1.582 1.685 1.792 1.902 2.015 0.260 0.303 0.348 0.395 0.446 0.500 0.556 0.615 0.678 0.743 0.811 0.884 0.957 1.036 1.120 1.204 1.293 Ll \0 -...l 00 ..... ...... > :;:0 >-l (") tr1 '"C CJ') I:::) > Z en ~ en ...... > Z :t (") tr1 0 Z ~ en ...... en ~ ...... tTl UJ 46Pd 47 Ag 48 Cd 49 In 50Sn 51 Sb 52Te 53 I 54Xe 55Cs 56Ba 57 La 58Ce 59Pr 60Nd 61 Pm 62Sm 63Eu 64Gd 65Th 66Dy 67Ho 68Er 69Tm 70Yb 71 Lu 72Hf Z 3.617 3.806 4.019 4.237 4.465 4.698 4.939 5.188 5.452 5.720 5.955 6.267 6.549 6.846 7.126 7.448 7.737 8.069 8.376 8.708 9.083 9.395 9.776 10.116 10.486 10.867 11.264 LI(ab) 7.485 7.795 8.104 8.422 8.752 9.086 9.429 9.778 10.141 10.509 10.889 5.552 5.808 6.073 6.340 6.615 6.900 3.749 LYJ 4.649 4.851 5.061 5.276 5.497 5.721 4.716 4.926 5.143 5.364 5.591 5.828 6.070 6.317 6.570 6.830 7.095 7.369 7.650 7.938 8.229 8.535 8.845 9.162 6.195 6.438 6.686 6.939 7.203 7.470 7.744 8.024 8.312 8.605 8.904 3.045 3.203 3.367 3.535 3.708 3.886 4.069 4.257 L{J4 3.072 3.234 3.401 3.572 3.750 3.932 4.120 4.313 L{J3 LI series 3.330 3.524 3.727 3.938 4.156 4.381 4.612 4.852 5.100 5.358 5.624 5.891 6.165 6.443 6.722 7.018 7.312 7.624 7.931 8.252 8.621 8.919 9.263 9.618 9.978 10.345 10.739 LII(ab) 5.279 5.530 5.788 6.051 6.321 6.601 6.891 7.177 7.479 7.784 8.100 8.417 8.746 9.087 9.424 9.778 10.142 10.514 3.328 3.519 3.716 3.920 4.130 4.347 4.570 4.800 LYI 4.619 4.827 5.041 5.261 5.488 5.721 5.960 6.205 6.455 6.712 6.977 7.246 7.524 7.809 8.100 8.400 8.708 9.021 2.990 3.150 3.316 3.487 3.662 3.843 4.029 4.220 L{JI LII series L series Table 9.1. (Continued.) 5.588 5.816 6.049 6.283 6.533 6.787 7.057 7.308 7.579 7.856 8.138 4.141 4.330 4.524 4.731 4.935 5.145 2.660 2.806 2.956 3.112 3.272 3.436 3.605 3.780 LTJ 3.173 3.351 3.537 3.730 3.929 4.132 4.341 4.557 4.781 5.011 5.247 5.483 5.724 5.968 6.208 6.466 6.717 6.983 7.243 7.515 7.850 8.071 8.364 8.648 8.943 9.241 9.561 Lm(ab) 4.935 5.156 5.383 5.612 5.849 6.088 6.338 6.586 6.842 7.102 7.365 7.634 7.910 8.188 8.467 8.757 9.047 9.346 3.l7l 3.347 3.528 3.713 3.904 4.100 4.301 4.507 LfJ2 2.838 2.984 3.133 3.286 3.443 3.604 3.769 3.937 4.109 4.286 4.465 4.650 4.839 5.033 5.229 5.432 5.635 5.845 6.056 6.272 6.494 6.719 6.947 7.179 7.414 7.654 7.898 Lal Lm series 4.272 4.450 4.633 4.822 5.013 5.207 5.407 5.607 5.816 6.024 6.237 6.457 6.679 6.904 7.132 7.366 7.604 7.843 2.833 2.978 3.126 3.279 3.435 3.595 3.758 3.925 La2 4.994 5.176 5.361 5.546 5.742 5.942 6.152 6.341 6.544 6.752 6.958 3.794 3.953 4.124 4.287 4.452 4.632 2.503 2.633 2.767 2.904 3.044 3.188 3.335 3.484 LI == >< 0 Z 0 :;tI til ~ > ~ I >< :;c 1.0 ...... 00 00 - 8111 82Pb 83Bi 84 Po 85 At 86Rn 87Fr 88Ra 89Ac 90Th 91 Pa 92U 93Np 94Pu 95 Am 96Cm 97Bk 98Cf BOHg 73Th 74W 75Re 76 Os 17Ir 78Pt 79 Au Z 11.680 12.098 12.522 12.965 13.424 13.892 14.353 14.846 15.344 15.860 16.385 16.935 17.490 18.058 18.638 19.233 19.842 20.470 21.102 21.756 22.417 23.095 23.793 24.503 25.230 25.971 LI(ab) 19.503 20.094 20.709 21.336 21.979 18.354 11.276 11.672 12.080 12.498 12.922 13.359 13.807 14.262 14.734 15.215 15.708 9.486 9.817 10.158 10.509 10.866 11.233 11.608 11.993 12.388 12.791 13.208 13.635 14.065 14.509 14.973 15.442 15.929 16.423 16.927 17.452 17.986 18.537 19.103 LfJ3 Llseries L}/'3 15.640 16.101 16.573 17.058 17.553 18.060 14.745 9.211 9.524 9.845 10.174 10.509 10.852 11.203 11.561 11.929 12.304 12.689 13.083 L{34 11.139 11.542 11.955 12.383 12.824 13.273 13.733 14.209 14.698 15.198 15.708 16.244 16.784 17.337 17.904 18.480 19.078 19.692 20.311 20.947 21.596 22.263 22.944 23.640 24.352 25.080 Ln(ab) 10.893 11.284 11.683 12.093 12.510 12.940 13.379 13.828 14.289 14.762 15.245 15.741 16.249 16.768 17.300 17.845 18.405 18.979 19.565 20.164 20.781 21.414 22.061 22.703 23.389 24.070 Ln 9.342 9.671 10.008 10.354 10.706 11.069 11.440 11.821 12.211 12.612 13.021 13.445 13.874 14.313 14.768 15.233 15.710 16.199 16.699 17.217 17.747 18.291 18.849 19.399 19.961 20.557 L{31 Ln series L series Thble 9.1. (Continued.) 14.507 14.944 15.397 15.874 16.330 13.661 8.427 8.723 9.026 9.335 9.649 9.973 10.307 10.649 10.992 11.347 11.710 LT/ 9.881 10.204 10.531 10.869 11.215 11.564 11.918 12.284 12.657 13.035 13.418 13.817 14.215 14.618 15.028 15.442 15.865 16.300 16.731 17.167 17.614 18.053 18.526 18.990 19.461 19.938 Lm(ab) 15.621 16.022 16.425 16.837 17.252 17.673 18.096 18.529 18.983 14.448 14.839 9.650 9.960 10.274 10.597 10.919 11.249 11.583 11.922 12.270 12.621 12.978 13.338 L/h 8.145 8.396 8.651 8.910 9.174 9.441 9.712 9.987 10.267 10.550 10.837 11.129 11.425 11.725 12.029 12.338 12.650 12.987 13.288 13.612 13.942 14.276 14.615 14.953 15.304 15.652 Lal Lm series 8.086 8.334 8.585 8.840 9.098 9.360 9.626 9.896 10.171 10.448 10.729 11.014 11.303 11.596 11.893 12.194 12.499 12.807 13.120 13.437 13.757 14.082 14.409 14.740 15.080 15.418 La2 11.117 11.364 11.616 11.887 12.122 12.381 10.620 7.172 7.386 7.602 7.821 8.040 8.267 8.493 8.720 8.952 9.183 9.419 9.662 LI 00 \0 ..- '- > ~ ~ n ttl ~ en 0 > Z til ~ ....Ztil > n ::t: ttl 0 Z ~ ....til~ ....til ttl \0 w 190 / 9 X-RAY ASTRONOMY Table 9.1. (Continued.) M series Mv series MN series Z 57 La 58Ce 59Pr 60Nd 61 Pm 62Sm 63Eu 640d 65Th 66Dy 67Ho 68Er 69Tm 70Yb 71 Lu 72Hf 73Ta 74W 75 Re 76 Os 77Ir 78Pt 79 Au 80Hg 81 Ti 82Pb 83 Bi 84 Po 85 At 86Rn 87Fr 88Ra 89Ac 90Th 91 Pa 92U MN(ab) 0.851 0.902 1.004 1.108 1.221 1.280 1.390 1.515 1.578 1.718 1.793 1.871 2.116 2.202 2.291 2.385 2.485 2.586 2.687 3.491 3.728 MfJ Mv(ab) Mal Ma2 1.809 1.775 1.773 2.041 2.122 2.206 2.295 2.389 2.484 2.579 1.980 2.050 2.123 1.975 2.046 2.118 2.270 2.345 2.422 2.265 2.339 2.416 3.332 2.996 3.082 3.170 2.986 3.072 3.159 0.854 0.902 0.949 0.996 1.100 1.153 1.209 1.266 1.325 1.383 1.443 1.503 1.567 1.631 1.697 1.765 1.835 1.906 1.978 2.053 2.127 2.204 2.282 2.362 2.442 2.525 3.145 3.239 3.336 3.552 Reference 1. Woldseth. R. 1973. X-Ray Energy Spectroscopy (Kevex Corp .• Burlingame. CA) 9.3.2 Line Emission When the source is "thin" and T < 3 X 107 K, the dominant radiation mechanism is line emission. Elemental abundances [6] and temperature determine which lines are strongest. In the X-ray band, lines from H-like and He-like ions and from ions of 0 and Fe are usually prominent. Figures 9.1 through 9.3 show the relative numbers of selected ions as a function of temperature [7]. Collisional eqUilibrium is assumed. Some sources, however, have ages smaller than the time required to achieve equilibrium. Young supernova remnants are the most obvious examples. In these cases, the ion populations are quite different from those expected at the temperature indicated by the continuum radiation. Emission from such nonequilibrium models has been calculated [8]. 9.3 EMISSION MECHANISMS AND SPECTRA / o 1oJ: -.3... C N 0 S Ar Ne Ca 2 I 3 & &.5 7 LogT Figure 9.1. Concentration of hydrogen-like ions versus temperature. JJ I LogT Figure 9.2. Concentration of helium-like ions versus temperature. 8 191 192 I 9 X-RAY ASTRONOMY o Fe XVII Fe IX -0.5 z J I -1 -1.5 8 8.5 LogT o Fe XXV Fe XVII -0.5 z J I -1 -1.5 7 7.5 8 LogT Figure 9.3. Concentration of iron ions versus temperature. Above: low temperatures; below: high temperatures. 9.3 EMISSION MECHANISMS AND SPECTRA I 193 -21.5 i . -22 -23.5 8 8.5 Lo, T 7 7.5 8 Figure 9.4. Power radiated from a low-density plasma. Table 9.2 gives the power from a low-density plasma, with solar abundances, in units of 10- 23 ergs em3 s-l. Figure 9.4 plots these data. Table 9.2. Power radiatedjrom a low-density plasma [1]. logT < O.IOkeV 0.10-0.28 0.28-1.00 1.00-3.00 3.0-10.0 5.500 5.600 5.700 5.800 5.900 6.000 6.100 6.200 6.300 6.400 6.500 6.600 6.700 6.800 6.900 22.75 13.71 11.66 9.84 8.69 8.93 8.82 8.25 6.15 3.35 1.75 1.00 0.60 0.37 0.29 0.49 0.92 1.52 1.90 1.96 1.85 1.49 1.08 0.79 0.56 0.42 0.36 0.37 0.45 0.55 0.00 0.02 0.12 0.37 0.79 1.29 1.67 1.82 1.89 1.87 1.85 1.99 2.28 2.51 2.20 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.03 0.09 0.20 0.35 0.52 0.72 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 > 10.0 Total 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 23.24 14.66 13.30 12.11 11.44 12.07 11.98 lU5 8.84 5.81 4.12 3.55 3.59 3.85 3.78 194 I 9 X-RAY ASTRONOMY Table 9.2. (Continued.) logT 7.000 7.100 7.200 7.300 7.400 7.500 7.600 7.700 7.800 7.900 8.000 < O.lOkeV 0.38 0.43 0.34 0.26 0.20 0.16 0.14 0.12 O.lO 0.09 0.08 0.10-0.28 0.28-1.00 1.00-3.00 3.~lO.0 0.53 0.35 0.23 0.18 0.16 0.15 0.14 0.13 0.12 0.12 0.11 1.28 0.67 0.52 0.48 0.47 0.46 0.44 0.43 0.41 0.39 0.37 0.89 0.89 0.80 0.71 0.67 0.65 0.63 0.62 0.62 0.61 0.60 0.03 0.07 0.12 0.20 0.30 0.41 0.55 0.68 0.81 0.93 1.02 > lO.O 0.00 0.00 0.00 0.00 om 0.02 0.05 0.11 0.20 0.32 0.48 Total 3.11 2.41 2.01 1.83 1.81 1.85 1.96 2.lO 2.26 2.46 2.66 Reference 1. Raymond, J.C. 1992, current version of code described by Raymond, J.C., & Smith, B.W. 1977, ApJ,35, 419 9.3.3 X-Ray Sources for In-Flight Calibration The best-known X-ray spectrum is that of the Crab Nebula. It has small angular extent, and for our purpose, is not time variable (the pulsar contribution is only'" 5% in the soft X-ray band and the diffuse nebula is probably only slowly decreasing in flux). It has a simple power-law spectral continuum. The Crab spectrum between 3 and 30 keY is I(E) = (9.7 ± l)E-l.l0±·03 keY cm- 2 s-1 keV- 1 [9]. Below 3 keV this spectrum is decreased by interstellar absorption, which is not well measured. Most observations fall within the range NH = (2 - 3.5) 1021 atomscm- 2 (Morrison and McCammon abundances). Other sources which, because of small angular extent, simple spectra, and constant flux, are suitable for calibration purposes are: the supernova remnant G21.5-0.9, the clusters AI795 and A40I, and, probably, the white dwarf HZ43. The supernova remnant NI32D in the Large Magellanic Cloud is in a favorable location (close to the ecliptic pole) and often used, but has a thermal spectrum with detailed spectral structure. x 9.4 TRANSMISSION OF X-RAYS THROUGH THE INTERSTELLAR MEDIUM The transmission of X-rays through interstellar gas (which is cold and atomic) depends on column density, usually expressed as the number of hydrogen atoms cm-2 , NH, and elemental composition. Two models with different elemental composition and absorption cross sections have been used extensively in the literature: that of Brown and Gould (BG) [10], and that of Morrison and McCammon (MM) [11]. The BG gas contains H, He, C, N, 0, Ne, Mg, Si, S, and Ar. The MM gas contains these same elements with updated cross sections [12] plus Ca, Fe, and Ni. Figure 9.5 shows the relative importance of these elements. At 0.7 keY, for example, half the absorption is in O. At 10 keY, half the absorption is in Fe. Since very little of the absorption occurs in H, the use of NH is somewhat misleading. This is sometimes referred to as the number of "equivalent H atoms" cm-2. 9.4.1 Transmission of the MM Gas Figure 9.6 shows graphs of transmission through the MM gas over a large range of column densities. Only photoelectric absorption has been considered. Compton scattering will become important at energies above 5 keY, so 1024 atoms cm- 2 is the highest column density shown. The two prominent absorption edges are 0 K at 0.53 keY and Fe K at 7.1 keY. 9.4 TRANSMISSION OF X-RAYS I 195 900. - 500.... N E c.J :; 400. - '0 > 300. ..,,: . LaJ b 200. 100. o. tw::::r::u~0~.1==r:::i::::W:J:IJ::It1.0~:::I:=c::i:I:b;;;;;;;~1o. PHOTON ENERGY ( keV) Figure 9.S. X-ray absorption coefficient versus energy for the ISM. The structure is caused by atomic absorption edges [11]. 1 0.9 0.6 0.7 r:: 0 0.6 ·s 0.5 'iii UI UI r:: <\I s... E-< 0.4 0.3 0.2 0.1 0 0.1 1 Pholon Energy (keV) 10 Figure 9.6. Transmission versus energy for various interstellar medium column densities. 196 / 9 X-RAY ASTRONOMY I: 0 S S a:I 23 U () :::;;! I I: 0 .s::I'll 22 1-0 0 :::;;! N I S () 21 I'll S .....0 ~ :.: Z 20 QO ..2 0.1 1 E. (keV) Figure 9.7. Conversion of the parameter Ea to column density. 9.4.2 Comparison of Different Models In order to compare published analyses, a conversion between different absorption-measure models is needed. Table 9.3 gives a comparison between the measured BG and MM column densities. The conversion is not precise because the BG and MM transmission curves do not have the same shape. Transmission through the column densities in Table 9.3 cross at '" 0.5, but the BG transmission curve is steeper at low NH, and the MM curve is steeper at high NH. In early work, the parameter Ea was used to quantify observed absorption. The transmission Tr through interstellar gas was expressed as T.r -- e -(Ea/ E)8/3 . Figure 9.7 gives the conversion of Ea to MM column density. It is assumed that the measurement is made over that energy range where Tr drops from 0.8 to 0.2, and there is some ambiguity when the o or Fe absorption edge falls in this range. The value of the conversion factor at these energies will depend on the characteristics of the X-ray detector used to make the observation. Table 9.3. Equivalent transmission column densities for MM and BG gas. Model MMgas 8Ggas Ea Column 1 x 10 19 0.90 x 1019 0.080 1 x 1020 1.18 x 1020 0.187 1 x 1021 1 x 1022 1.15 x 1021 -0.50 1.25 x 1022 1.41 1 x 1023 0.95 x 1023 3.4 1 x 1024 0.80 x 1024 9.8 9.4 TRANSMISSION OF X-RAYS / 9.4.3 197 Relation to Optical Extinction An empirical relation between X-ray absorption and optical extinction has been noted. Using diffuse supernova remnants as calibrators, the relationship to extinction, A v, and to color excess, E B - v, were found to be: NH/Av NH/ EB-V = 1.9 x = (5.9 1021 atomscm- 2 mag- 1 [13], ± 1.6) x 1021 atomscm- 2 mag- 1 [14]. Agreement with Copernicus observations of absorption in atomic (HI) and molecular (H2) hydrogen is quite good. The average measured column density toward 100 stars (90 closer than 2 kpc) is ROSAT (Rontgensatellit) observations of bright, strongly absorbed sources have given a measure of both soft X-ray absorption and of the brightness and extent of dust-scattering halos, a direct relation between dust and gas. The result is NH/Av = 1.79±O.03 x 1021 atomscm- 2 mag- 1 [16]. Table 9.4. Conversion of count rate to millicrab. ILJy. and energy flux. Satellite Vela5B Uhuru Ariel V HEAO-I Einstein EXOSAT Tenma Ginga ROSAT ASCA XTE BeppoSAX Chandra Instrument survey survey Al A2 (1 keY band) A4 (channel A) HRI !PC MPC ME GSPC(A+B) LAC HRI PSPC SIS GIS PCA HEXTE MECS HPGSPC PDS HRC-I ACIS-I Crab rate (counts-I) 40 [1] 947 [2] 403 [3.4] 13 600" [5] 575 [6] 11.2 [7] 120 [8] 684 [8] 1383 [8] 1740 [9] 1640 [10] 10500 [11] 362 [12] 964 [12] 1020 [12] 890 [12] 11800 [12] 200 [12] 328 [12] 334 [12] 210 [12] 1200 [12] 3200 [12] 1 count s-I = erg cm- 2 coune l 27 ILJy @ 5 keY 1.15 JL1y @ 5 keY 2.70 ILJy @ 5 keY 0.080 ILJy @ 5 keY 4.8 ILJy @ 2 keY 21 ILJy @ 20 keY 23 JL1y @ 2 keY 4.0 JL1Y @ 2 keY 0.79 ILJy @ 5 keY 0.63 JL1y @ 5 keY 0.66 ILJy @ 5 keY 0.104 ILJy @ 5 keY 7.6 ILJy @ 2 keY 2.8 ILJy @ 2 keY 1.07 ILJy @ 5 keY 1.22 ILJy @ 5 keY 0.092 ILJy @ 5 keY 1.2 JL1Y @ 20 keY 3.3 ILJy @ 5 keY 0.71 ILJy @ 20 keY 1.13 ILJy @ 20 keY 2.3 ILJy @ 2 keY 0.34 JL1Y @ 5 keY 4.5 x 1.6 x 5.3 x 2.7 x 2.7 x 6.8 x 1.6 x 2.8 x 1.6 x 2.1 x 2.2 x 2.8 x 3.7 x 1.4 x 3.3 x 3.8 x 3.1 x 9.0 x 8.1 x 7.8 x 9.5 x 2.8 x 1.1 x 10- 10 10- 11 10- 11 10- 12 10- 11 10- 10 10- 10 10- 11 10- 11 10- 11 10- 11 10- 12 10- 11 10- 11 10- 11 10- 11 10- 12 10- 11 10- 11 10- 11 10- 11 10- 11 10- 11 Note QHEAO-l A 1 rates are cataloged in counts cm -2 s-l; to convert, use area = 3 300 cm2 . References 1. Priedhorsky, W.C., Terrell, J. & Holt, S.S. 1983, ApJ, 270, 233 2. Forman, W. et aI. 1978, ApJS, 38, 357 Energy range (keV) 3-12 2--6 2-10 1-20 0.5-3 13-25 0.5-4 0.5-4 1--6 1-20 1-20 2-20 0.5-2.4 0.5-2.4 0.4-12 0.4-12 1-20 12--60 1.3-10 4-34 13-80 0.4-10 0.4-10 198 I 9 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 9.5 9.5.1 X-RAY ASTRONOMY Warwick, R.W. et al. 1981, MNRAS, 197, 865 McHardy,I.M. et al. 1981, MNRAS, 197, 893 Wood, K.S. et al. 1984, ApJS, 56, 507 Nugent, 1.1. et al. 1983, ApJS, 51, 1 Levine, A.M. et al. 1984, ApJS, 54, 581 Seward, F.D. 1990, ApJS, 73, 781 White, N. 1992, the ME catalog accessed through the HEASARC online database Koyama, K. et al. 1984, PASJ, 36, 659 Thmer, M.l.L. et al. 1989, PASJ, 41, 345 PIMMS program. 1997, NASAlGSFC HEASARC online software COSMIC X-RAY SOURCES AU-Sky Surveys Sensitive surveys have been completed by Uhuru (2-6 keY) [17]; Ariel V (2-18 keV) [18, 19]; HEAO1 (1-20 keY) [20]; Einstein in the slew mode (0.2-4 keY) [21]; and ROSAT (0.2-2.4 keY) [22]. Table 9.4 gives sensitivities of the survey instruments. Figure 9.8 shows the 842 sources found by HEAO-l. HEAO-l also covered lower [23] and higher [24] energy bands and, because of its lO-year coverage, the Vela 5B data are unique [25]. Count rates from these surveys and from other missions can be converted to spectral irradiance assuming a Crab-like spectrum [a well-known power law (see Sec. 9.3.3) modified by absotption below 3 keY and with no spectral flux below 0.4 keY]. The Crab spectral irradiance at 2,5, 10, and 20 keY is 2750, 1090, 510 and 238 J,£Jy. The energy flux per count listed in Table 9.4 was calculated using a Crablike spectrum, including interstellar absotption. This conversion is reasonable for most sources with absorbing column> 5 x loW atomscm- 2 • For soft sources and the Einstein and ROSAT detectors, which have appreciable sensitivity down to 0.1 or 0.2 keY, the energy conversion factors in Table 9.4 can be an order of magnitude too large. 9.5.2 Types of Sources Tables 9.5-9.10 give characteristics of sources in several broad categories, and are by no means complete. They include some of the brightest sources and others chosen to illustrate the variety of objects in each category [26]. Thble 9.5. Brightest X-ray emitting supernova remnants [1]. Galactic coordinates 184.6-5.8 74.3-8.5 263.5-2.7 260.4-3.4 111.7-2.1 120.1+1.4 Flux density Name Flux density O.2-4keV (millicrab) Crab Nebula Cygnus Loop VelaXYZ PuppisA Cassiopeia A TychoSNR 1000 965 760 365 89 32 1000 Note 4LY = light year = 0.31 parsec ~ 1 x 1016 m. Reference 1. Seward, F.D. 1990, ApJS, 73, 781 1.5-1OkeV (millicrab) 10 39 26 80 20 LX (Ly4) X-ray diameter (arcmin) O.2-4keV (ergs-I) 6500 2500 1500 6500 8000 8000 2 160 420 50 4 8 3x 2x 3x 6 x 1x 3 x Distance 1037 1036 1035 1036 1037 1036 X-ray Pulsar and Be S.... Biliary X Per Remnant suc:,O:va Cyg X-3 Binary X-ray and l-ray Source ~-~ Virgo Cluster of Galaxies Slack Hole Candidale Burster Figure 9.8. The HEAO-l X-ray sky [20]_ PKS 2155-304 Bl lacerlae Object Active Galaxy GX 339-4 NGC 6624 I- 1 l,L*=-'I', ,=r=-=:-Y' .I" ."I", ! ~ ...~.....: -.;t NGC 4151 lMC large MageilanlC Cloud Acerellng BlIlanes in Vela X-I Binary X-ray Pulsar MXB 1659-29 Bursler EX Hya Cataclysmic Vanable (U Gem) \0 \0 \0 - .... CIl trl ~ ("} c::: CI.l ~ o ~ I ><: ("} &::: ..... oCIl (') VI 200 I 9 X-RAY ASTRONOMY Table 9.6. Selected X-ray emitting stars. Name Capella (a Aur) HZ 43 Algol (fJ Per) Wolf 630 24UMa ProxCen YYGem EEri EQPeg ('Ori aCen E Ori aTri Sirius (a CMa B) Flux density 0.2-4 keY [1] (millicrab) type 6.1 2.2 1.8 1.1 0.70 0.70 0.67 0.63 0.60 0.58 0.58 0.44 0.35 0.34 G8V+FV WD B8V M4V+MSV GlV MSV MY K2V MY 09.51 KSV+G2V BOI F2V WD Stellar LX [2] O.2-4keV (erg s-1) Distance (LyQ) 2.0 4 x 5x 2.0 1.0 2.5 4 x 2.0 6 x 3.5 3.2 2.0 3.2 6x 44 210 100 20 80 4.3 50 10.8 20 1600 4.4 1500 60 8.6 x UpO 1031 1030 x 1029 x 1030 x 1027 1029 x 1028 1028 x 1032 x 1027 x 1032 x 1029 1028 Note QLY = light year = 0.31 parsec ~ 1 x 1016 m. References 1. Harris, D.E. et aI. 1990, The Einstein Observatory Catalog of fPC X-Ray Sources, NASA TM 108401, Vol. I, 24 2. Vaiana, G.S. et aI. 1981, ApJ, 245, 163 Table 9.7. Selected X-ray emitting normal galaxies [1, 2]. Galaxy Type NGC507 NGC720 NGC4382 NGC4472 M31 NGC253 M81 M82 SO E SO FJSO Sb Sc Sb Irr Flux density 0.2-4 keY [1] (millicrab) DistanceQ (MLyb) O.2-4keV (ergs-1) 0.46 0.10 0.032 0.73 2.3 0.31 0.35 0.88 320 105 90 90 2.2 10 11 11 1.1 2.2 5.2 1.1 3.6 7.4 1.3 3.5 LX x x x x x x x x 1043 1(1'1 1040 1042 1039 1039 1040 1040 Notes Q HO = 50 kIn s-1 Mpc-1 , qO = 0.5. bMLY = one million light years =0.31 x 106 pc ~ 1 x 1022 m. References 1. Fabbiano, G., Kim, D.-W., & Trinchieri, G. 1992, ApJS, BO, 531 2. Harris, D.E. et aI. 1990, The Einstein Observatory Catalog of fPC X-Ray Sources, NASA TM 108401, Vol. I, p. 24 SSCyg CygX-2 CygX-3 CygX-I SgrX-4 Her X-I GX339-4 Rapid Bur GX5-1 Vela X-I CenX-3 CenX-4 CirX-1 ScoX-1 LMCX-3 Name VI341 Cyg SS433 VI357Cyg V404Cyg VI521 Cyg AC211 V1727Cyg AM Her HZ Her V821 Ara V616Mon UYVol UGem GPVel V779Cen V822Cen BRCir V818Sco KZTrA V801 Ara V725Tau = 73.2 79.9 65.0 91.6 90.6 87.3 11.3 181.4 273.6 210.0 280.0 199.2 263.1 292.1 332.2 322.1 359.1 321.8 332.9 345.0 58.2 338.9 354.8 5.1 77.9 2.8 39.7 -2.6 -32.1 -6.5 -19.3 23.4 3.9 0.3 23.9 0.0 23.8 -13.1 -4.8 2.5 37.5 -4.3 -0.2 -.0 25.9 -7.9 -2.2 3.1 -2.2 0.7 -27.3 -3.0 -7.1 -11.3 b Galactic coordinates 250 [5] 300[4] 20000 [6] 850[4] 17000[5] 20[7] 310[4) 1200[1) 160[7] 350[5] 250 [5] 1300[4] 3 [8] 320 [5] 10[4] 1175 [5) 20000 [9] 380 [5] 6 [1) 20[5) 4[8) 750 [7] 2700 [4] 25 [5] 125000 [4] 30[1] Max Fl. Den. 2-lOkeV (millicrab) 3.09h O.l9h 13.1 d 5.60d 6.47d 4.79h 17.1 h 5.24h 6.50h 9.84d 11.3 15.8 16.4 8.2 14.7 14.2 8.9 12.7 12.2 18.5 17.5 14.4 13.0 15.5 III d 1.70d 7.75 h 3.82h 4.22h 8.96d 2.09d 15.1 h 16.6d 18.9h 0.69h 3.80h 2.61d 1.70d 14.8h POrb 8.9 16.7 11.2 16.9 9.0 6.9 13.3 12.8 (mag) V Max. = = 9 1.24 7.7 25 283 4.84 104 (s) Pspin HMXB HMXB LMXB LMXB CV HMXB HMXB LMXB LMXB LMXB LMXB LMXB LMXB LMXB LMXB LMXB LMXB CV LMXB HMXB HMXB LMXB HMXB LMXB LMXB CV LMXB [3] Type = Bright at 0.25 keY; WD+M5V In GC NGC 6624; Bur BH ?;jets BH+09.7Iab Tr; BH+(KOIIl-V) NS+Helium star In GC MI5;Bur Tr; ADC; Bur; Triple? Bright 0.25 keY; DN; WD+K5V NS+(ASIIl to FlIII) Bur Tr; BH+F1V; Eel; jets Eel; NS+(BOV to roV) BH? In GC Liller I, type II Bur Tr; NS+09.7Ile In LMC; BH+B3Ve Tr;BH+K5V Eel; ADC; Bur Bright 0.25 keY; DN; WD+M5V Eel; NS+BO.51b NS+06.5Il-IIl; Eel Tr; Bur; NS+K5V Tr; Bur Comment = = = = = = = = 1. van Paradijs, I. 1995, in X-Ray Binaries, edited by W. Lewin, I. van Paradijs, and E.P.I. van den Heuvel, (Cambridge University Press, Cambridge) p. 536 2. Ritter, H. 1987,A&AS, 70, 335 3. Bradt, H., & McClintock, I. 1983, ARA&A, 21, 3 4. Warwick, R.W. et aI. 1981, MNRAS, 197, 865 5. Forman, W. et aI. 1978, ApI, 38, 357 6. Conner, I.P., Evans, W.O., & Belian, R.O. 1969, ApI, 157, Ll57 7. McHardy, 1M. et aI. 1981, MNRAS, 197, 893 8. Wood, K.S. et aI' 1984, ApIS, 56, 507 9. Makino, F. 1989, IAU Circular No. 4786 References = Note aHMXB high-mass X-ray binary; LMXB low-mass X-ray binary; CV cataclysmic variable; ON dwarf nova; Bur Burster; GC globular cluster; Tr transient; NS neutron star; LMC Large Magellanic Cloud; BH black hole; Eel eclipse; ADC accretion disk corona; WD white dwarf. 3A0535+26 4U0538-64 3A0620-00 EXOO748-676 H0752+22 4U09OO-40 4U1II8-60 1455-31 4U1516-56 4U1617-15 4UI626-67 4U1636-53 GROJl655-40 4U1656+35 4U1658-48 1730-335 4U1758-25 4U1814+49 4U1820-30 3AI909+048 4U1956+35 GS2023+338 4U2030+40 4U2129+12 4U2129+47 IH2140+433 4U2142+38 Source Optical counterpart Thble 9.8. Selected X-ray emitting accretion-powered binaries [I, 2].a 0 tv - ...... tI.I ttl (") ::0 c::: 0 C/.l ~ I :;;c (") ....3: >< tI.I 0 (') VI 10 202 / 9 X-RAY ASTRONOMY Table 9.9. The brightest X-ray emitting clusters of galaxies [1]. Flux density 2-lOkeV (millicrab) Cluster Source A426 (Perseus) Ophiuchus Cluster M87 (Virgo) A1656 (Coma) Centaurus Cluster A2199 A496 A85 4U0316+41 4U 1708-23 4U 1228+12 4U 1257+28 4U 1246-41 4U 1627+39 4U0431-12 4UOO37-1O 47 c Redshift z 0.0183 0.028 0.0037 0.0235 0.0107 0.0305 0.0316 0.0518 30 22d 15 5 4 3 3 Distancea Lx (MLyb) 2-lOkeV (ergs-I) 360 550 73 460 210 600 620 1000 1.4 2.5 3 9 6 3 3 8 x x x x x x x x l(f5 1045 1043 1044 1043 1044 1044 1044 Notes a HO = 50kms- 1 Mpc-I, qo = 0.5. bMLY = one million light years 0.31 x 106 pc R: 1 x 1022 m. cIncludes the nucleus of the galaxy NGC1275 and diffuse emission from the Cluster. dIncludes the active nucleus and diffuse emission from M87, and emission from the surrounding Vugo Cluster. = Reference 1. Forman, W. et aI. 1978, ApJS, 38, 357 Table 9.10. Sekcted X·ray emitting active galDxies. Flux den. 2-10keV Name (millicrab) 2E 189 IH0244+OO1 2E 1007 4U0432+05 2E2195 4U 1206+39 IH 1226+022 IH 1226+128 2E2900 4U 1322-42 4U 1414+25 2E4066 lH 1937-106 lH 2156-304 MRK348 NGC 1068 Q0420-388 3C120 M81 NGC4151 3C273 M87 3C279 CenA NGC5548 E1821+643 NGC6814 PKS 2155-304 1.3 [I) 0.8[2) 0.02 [3] 2.3 [3) 0.16 [1] 4.3 [3) 3.1 [2) 22.4e [3) 0.23 [I) 8.4[3) 1.7 [3) 0.80[1) 1.9 [2) 8.4[2) Redshift z 0.014 0.0037 3.12 0.033 0.0006 0.0033 0.158 0.0037 0.538 0.0008 0.0017 0.297 0.005 0.17 Disla (MLyb) 270 73 80000 650 11.7 65 3200 73 11000 15.6 33 6200 98 3500 LX 2-lOkeV (ergs-I) Ix 9x 2x 2x 5x 4x 6x 3x 6x 5x 4x 7x 4x 2x 'JYpe 1043 S~ert2.hl~yobKUred 1041 1046 1044 1039 1042 104S 1043 104S 104 1 104 1 104S 1042 1046 Seyfert 2. Compton thick High redshift quasar Superlum VLBI radio galc Low luminosity AGNd S~ert 1.5 Radio loud quasar Radio galaxy OVV (Blazar)/ y-rays Radio galaxy ~ertl Radio quiet quasar ~ett 1. hl~yvariable BLLac Notes aHO 50kms- 1 Mpc-l,qO =0.5. bMLY one million light years = 0.31 x 106 pc R: 1 x 1022 m. cVLBI = very long baseline interferometry. d AGN active galactic nucleus. eIncludes diffuse emission from M87 and from Vugo cluster. f OVV = optically violent variable. = = = References 1. Harris, D.E. et aI. 1990, The Einstein Obs. Catalog of [PC X-Ray Sources, NASA TM 108401, Vol. 1. p.24 2. Wood, K.S. et aI. 1984, ApJS, 56, 507 3. Forman, W. et aI. 1978. ApJS, 38. 357 9.6 DIFFUSE BACKGROUND / 203 3 -........ III :: I 1 .IIC I III I -S CI ...... ~ .IIC ...... .3 III ., CI c:: l fit .1 f.... + CI III Q. III .03 HEAO-l A2 HEAO-l A.4 3 10 30 10Q Photon Energy [keVJ 300 1000 Figure 9.9. The diffuse background spectrum above 3 keV [28]. 9.6 DIFFUSE BACKGROUND Above 3 keY, surface brightness fluctuations of the high-latitude extragalactic diffuse background, measured in 5° x 5° blocks, are less than 2% above those expected from an extrapolation of the observed distribution of sources [27]. The spectrum from the HEAO-IA2 detectors is one of the best measured in astrophysics and, in the range 3-50 keY, is given by I(E) = 7.8E-0.2ge-EI40 keY cm-2 s-l sCI keV- l [28]. Figure 9.9 shows the HEAO-l A2 and A4 data. Statistical error for the A2 instrument is less than the width of the heavy solid line. The lighter curve is an empirical fit to all the data and is I (E) = { 7.877E-O.2ge-EI41.13, E < 6OkeV, 1652E-2 + 1.75E-0.7, E > 60 keY [29]. In the range 2-60 keY there is an additional component of 2%-10% associated with the galactic plane. Intensity is concentrated in the plane and is strongest in the direction of the center [30]. Below 2 keV there is structure in the background at all latitudes, which changes appreciably with energy. Both absorption and local emission contribute to this structure. Figure 9.10 shows the background at 0.25 keV. Similar maps are available from 0.13 to 2.2 keY [31,32]. ! Figure 9.10. The diffuse background at keV measured by ROSAT [32]. Two bright sources, the Cygnus Loop (74, -8) and the Vela supernova remnant (263, -3) are also clearly visible. Color bar values are 10-6 counts s-1 arcrnin- 2 . 100 300 600 900 1200 1500 -< a-:: 0 z 0 ~ til "":l > ~ ~ I >< 1.0 ........ ~ 9.7 X-RAY ASTRONOMY MISSIONS / 9.7 205 X-RAY ASTRONOMY MISSIONS Characteristics of some prominent X-ray satellites are given in Tables 9.11 and 9.12. Table 9.11. Some X-ray astronomy satellites [I, 2). Energy range b (keV) Satellite Country Launch Last data Typea Vela 5A,B Uhuru OSO-7 Copernicus ANS Ariel-V SAS-3 HEAO-I Einstein Hakucho Tenma EXOSAT Spartan 101 Ginga KVANT Granat ROSAT Astro-I OXS ASCA Alexis RXTE lXAE 8eppoSAX Chandra USA USA USA USAlUK Netherlands UK USA USA USA Japan Japan ESA USA Japan USSR USSR Germany USA USA Japan USA USA India Italy USA May 69 Dec. 70 Sep.71 Aug. 72 Aug. 74 Oct. 74 May 75 Aug. 77 Nov. 78 Feb. 79 Feb. 83 May 83 June 85 Feb. 87 June 87 Dec. 89 June 90 Dec. 90 Jan. 93 Feb. 93 Apr. 93 Dec. 95 Mar. 96 Apr. 96 Jul. 99 June 79 Jan. 75 May 73 Dec. 80 July 76 Mar. 80 Apr. 80 Jan. 79 Apr. 81 Apr. 85 Nov. 85 Apr. 86 June 85 Oct. 91 Scanning, small SC Scanning, large PC Scanning, PC Pointed, small concentrator Pointed, PC, Bragg crystal Scanning, pointed, ASM, large PC Scanning, RMC, large PC Scanning, very large PC, SC Pointed, telescope, PC, HRI, Si detector Scanning, RMC, large PC Scanning, GSPC, ASM Pointed, small telescope, large PC PC Pointed, large PC Pointed, GSPC, SC, coded mask Pointed, Coded masks, ASM Scanning, pointed, telescope, PC, HRI Pointed, BBXRT collector, Si detector, Spectrometer to study background Pointed, telescope, CCO, GSPC Scanning, small multilayer telescopes Pointed, large PC, large SC, ASM Pointed, large PC, ASM Pointed, GSPC, SC, WFC (3) Pointed, telescope, CCO, HRI, gratings Dec. 90 Jan. 93 3-12 2-10 1-40 0.2-10, 0.2-{).6 2-40 2-10 1.5-10 1-20 0.2-4 0.1-2,2-20 2-10 0.05-2.0, 1.5-10 2-10 1.5-30 2-30 40-100,0-1300 0.1-2.5 0.3-12 0.15-{).28 0.4-12 0.06-{).1O 2-50, 15-200 2-18 0.1-300 Notes a ASM = all-sky monitor; BBXRT = broad-band X-ray telescope; CCD = charged coupled detector; GSPC = gas scintillation proportional counter; HRI = high resolution, channel plate detector; PC = proportional counter; RMC = rotating modulation collimator; SC = scintillation counter; WFC = wide field camera. bThese data apply to the main survey instrument(s). Since most satellites carried several detectors, data were usually collected over a broader energy range than that specified here. The range for a given detector also depends on source strength. Since the background obscures the higher-energy photons from weaker sources, this range is larger for strong sources than for weaker sources. References 1. Bradt, H., Ohashi, T., & Pounds, K.A. 1992, ARA&A, 30, 391 2. Charles, P.A., & Seward, F.D. 1995, Exploring the X-Ray Universe (Cambridge University Press, Cambridge) 3. Boella, G. et al. 1997, A&AS, 122, 299 fible 9.12. Characteristics of X-ray telescope mirrors. Mission Aperture diameter (cm) Einstein EXOSAT ROSAT ACSA (4 mod.) Chandra 58 28 83 34 (1 mod.) 123 Mirrors Geometric area (cm2) Field (arcmin diam.) Reflection angles (arcmin) Focal length (m) Mirror coating Highest energy (keV) On-axis resolution (arcsec) 4 nested 2 nested 4 nested 120 nested (1 mod.) 4 nested 350 80 1140 1300 (4 mod.) 1145 60 120 120 40 <ID-70 9(}...11O 83-135 14-42 3.45 1.09 2.4 3.5 Ni Au Au Au 4.5 2 2.4 12 4 18 3 180 30 27-52 Ir 10 10.0 0.5 206 / 9 X-RAY ASTRONOMY ACKNOWLEDGMENTS Information and advice for this section was kindly supplied by M. Elvis, G. Fabbiano, ER. Harnden Jr., J.P. Hughes (Fig. 9.6), C. Jones, J. McClintock, J. McDowell, J. Raymond (Figs. 9.1-9.4), W. Tucker, D. Worrall, and M. Zombeck at the Harvard-Smithsonian Center for Astrophysics, E. Boldt and S. Snowden (Fig. 9.10) at the Goddard Space Flight Center, D. Gruber of the University of California, San Diego (Fig. 9.9), D. Cox and D. McCammon of the University of Wisconsin (Figs. 9.5 and 9.10), H. Bradt at MIT, and K. Wood of the Naval Research Laboratory (Fig. 9.8). REFERENCES 1. Karzas, W., & Latter, R. 1961, ApJS, 6, 157 2. 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Barcons and A. Fabian (Cambridge University Press, Cambridge), p. 1I5 29. Gruber, D. 1992, in Proceedings of the International Workshop on the X-Ray Background, edited by X. Barcons and A Fabian (Cambridge University Press, Cambridge), p. 44 30. Iwan, D. et al. 1982, ApJ, 260, III 31. McCammon, D. et al. 1983, ApJ, 269, 107 32. Snowden, S. L. et al. 1997, ApJ, 485, 125 Chapter 10 y-Ray and Neutrino Astronomy R.E. Lingenfelter and R.E. Rothschild 10.1 10.1 Continuum Emission Processes . . . . . . . . . . . .. 207 10.2 Line Emission Processes . . . .. 208 10.3 Scattering and Absorption Processes ..... ... 213 10.4 Astrophysical y-Ray Observations . . . . . .. ... 216 10.5 Neutrinos in Astrophysics .. . . . . . . . . . . . . .. 235 10.6 Current Neutrino Observatories .......... ....... .. 237 CONTINUUM EMISSION PROCESSES Important processes for continuum emission at y-ray energies are bremsstrahlung, magnetobremsstrahlung, and Compton scattering of blackbody radiation by energetic electrons and positrons [1-6]. 10.1.1 Bremsstrahlung The bremsstrahlung luminosity spectrum of an optically thin thermal plasma of temperature T in a volume V is [3] where the index of refraction is assumed to be unity, m is the electron mass, Z is the mean atomic charge, ne and nj are the electron and ion densities, and the Gaunt factor g(v, T) ~ (3kT j1rhv)I/2 for hv > kT and T > 3.6 x lOSZ 2 K, or L(V)brem ~ 6.8 x 1O-38 Z 2n enjVg(v, T)T- 1/ 2 exp(-hvjkT) ergs- l Hz-I. 207 208 / 10 y-RAY AND NEUTRINO ASTRONOMY 10.1.2 Magnetobremsstrahlung The synchrotron luminosity spectrum of an isotropic, optically thin nonthermal distribution of relativistic electrons with a power-law spectrum, N(y) = NoY-S, interacting with a homogeneous magnetic field of strength, H, is [5] 08 (3 3 L(v)s ch ~ ~ yn 3mc2 or __ e_ )(S-I)/2 4rrmc V NoH(S+I)/2 v (1-S)/2 L(V)synch ~ 3.60 x 10- 23 V NoH(S+1)/2(4.2 x 106 /v)(S-I)/2 ergs-I Hz-I. 10.1.3 Compton-Scattered Blackbody Radiation The Compton-scattering (cs) luminosity spectrum of an optically thin, isotropic nonthermal distribution of relativistic electrons with a power-law spectrum, N(y) = NOY-S, interacting with blackbody photons having a temperature T is [5] L(v) cs ~ 4e4 -3m2c3 ( h ) (3-S)/2 -V MOWbbT(S-3)/2v(I-S)/2 3.6k or where Wbb is the energy density of the blackbody radiation. 10.2 LINE EMISSION PROCESSES Important processes for line emission at y-ray energies are electron-positron annihilation, nuclear deexcitation, decay of radio nuclei, and radiative capture (see Tables 10.1-10.3). 10.2.1 Electron-Positron Annihilation Radiation Positron annihilation can occur either via a direct interaction with a free electron or via positronium formed by charge exchange with a bound electron or by radiative combination with a free electron (e.g., [7-12]). See Figure 10.1. Direct annihilation (da) leads to line emission, e+ e- ~ 2y, at a mean energy, Te« 107 K, 107 < Te < 1010 K, Te> 1010 K, where m e c 2 =510.9991 keVand Te is the temperature of the annihilating electrons and positrons. The direct-annihilation line spectrum can be approximated by a Gaussian with a linewidth [12] r da ~ 0.87(Te/104 K)o.so keY, for Te « 109 K, and at higher temperatures the width [10] r da ~ kTe, for Te » 109 K. The cross section for direct annihilation of a positron of energy ymec2 with an electron at rest [1] is + + _ 30T (y2 4y 1 u(Y)da - 8(y + 1) y2 _ 1 In(y c:;:-: + V y- - 1) - y +3 ) JY2=1 ' where the Thomson cross section, O'f = 8rr e4 / (3m 2c 4 ) = 0.6652 barn (b). 10.2 LINE EMISSION PROCESSES / 209 10.10 'j U 1&1 ...::E II) U 10. 11 >t: II) Z 1&1 10. ,2 Q ~ 1&1 c:I a: 10.,1 ~ ~ ..... II) 1&1 ~ ~ a: 10"'14 10.15 102 10'5 10· 10' 10' lOT 10' T(K) Figure 10.1. Positron-annihilation rates in a thennal medium per unit density as a function of temperature, for annihilation directly with free electrons (Rda/ne) or with bound electrons (Rda/nH), and via positronium fonnation by radiative combination with free electrons (Rrc/ne) or by charge exchange with neutral hydrogen (Rce/nH), from [8]. Annihilation via positronium formation leads to line emission only from the singlet parapositronium, para-Ps ~ 2y, which forms 25% of the time. The mean energy of the positronium line, hvps = m ec 2 - (R/4n2), where the Rydberg R = 0.0136 keY, and n is 1 for the ground state. The parapositronium annihilation line spectrum can be approximated by a Gaussian with a linewidth r rc ~ 0.80(T /104 K)O.44 keY for radiative combination (re), valid at least from 8000 to 106 K, and a Gaussian linewidth r ce ~ 6.4 keV for charge exchange (ee), since the parapositronium mean life of'" 10- 10 s is much less than the energy loss time [12]. The total number of 511 keV line photons emitted per positron annihilation, Y511/e+ =2- 1.5/ps , where Ips is the fraction of positrons that annihilate via positronium. Annihilation via positronium formation leads to three-photon continuum emission from the triplet orthopositronium, ort ho- P s ~ 3y, which forms 75% of the time. The spectrum [7] of this emission is P(hvh y = (1T 2 _ 2 9)mec2 (17(1 -17) (2 _ 17)2 + 2(1 -17) 2(1 - 17)2 172 In(1 - 17) - (2 _ 17)3 In(1 - 17) where 17 = h v / mc2 is the photon energy, and the spectrum is normalized to unity. 2 - 17) + -17- , 210 I 10 y-RAY AND NEUTRINO ASTRONOMY Thble 10.1. Nucleardeexcitation y-ray lines.a,b Energy (MeV) Emission mechanism Excitation processes Mean life (s) 0.4291 0.4776 7Be..o· 429 ~ g.s. 7Li*0.478 ~ g.s. 0.7183 lOB*o.718 ~ g.s. 0.8468 56Fe*O.847 ~ g.s. 1.2383 56Fe*2.085 1.2745 22Ne*1.275 ~ g.s. 1.3685 24Mg*1.369 ~ g.s. 1.4083 55Fe*I.408 ~ g.s. 1.4084 1.4341 54Fe*I.408 ~ g.s. 52Cr*1.434 ~ g.s. 1.6336 2oNe*1.634 ~ g.s. 1.6352 14N*3.948 .... 14N*2.313 1.7790 28Si*I.779 ~ g.s. 1.8086 26Mg*l.809 ~ g.s. 2.2302 32S*2.230 ~ g.s. 2.3126 14N*2.313 4He(a, n)7Be* 4He(a, p)7Li* 4He(a, n)7Be(€)7Li*(1O%) 12C(p, x)lOB* 160(p, x)lOB* 12C(p, x)lOC(e+)lOB* 160(p, x)lOC(e+)lOB* 56Fe(p, p,) 56 Fe* 56Fe(p, n) 56 Co(e+; €) 56 Fe* 56Fe(p, p,) 56 Fe* 56Fe(p, n)56Co(e+; €)56Fe*(67%) 22Ne(p, p')22Ne* 22Ne(a, a')22Ne* 22Ne(p, n)22Na(e+; €)22Ne* 24Mg(p, x)22Na(e+; €)22Ne* 2SMg(p, x)22Na(e+; €)22Ne* 28Si(p, x)22Na(e+; €)22Ne* 24Mg(p, p,) 24 Mg* 24Mg(a, a,) 24 Mg* 28Si(p, x) 24 Mg* 56Fe(p, pn)55Fe* 56Fe(p, 2n)55Co(e+; €)55Fe*(18%) 56Fe(p, x)54Fe* 56Fe(p, x)52Cr* 56Fe(p, x) 52 Mn*(e+; €)5 2Cr* 56Fe(p, x)52Mn(e+; €)52Cr* 20Ne(p, p') 2O Ne* 2ONe(a, a')2oNe* 20Ne(p, n)20Na(e+)20Ne*(80%) 24Mg(p, x)20Ne* 28Si(p, x) 2oNe* 14N(p, p') 14 N* 14N(a, a') 14 N* 160(p, x)14N* 28Si(p, p,) 28 Si* 28Si(a, a,) 28 Si* 32S(p, x)28Si* 26Mg(p, p,) 26 Mg* 26Mg(a, a,) 26 Mg* 26Mg(p, n) 26 A1(e+; €) 26 Mg* 27 A1(p, pn)26Al(e+; €) 26 Mg* 28Si(p, x)26 A1(e+; €) 26 Mg* 32S(p, p,) 32 S* 32S(a, a,)32S* 14N(p, p')14N* 14N(a, a') 14 N* 14N(p, n) 14 O(e+)14N* 160(p, x)14N* 160(p, x) 14 O(e+)14N* 1.9 x 10- 13 1.1 x 10- 13 6.6 x 106 1.0 x 10-9 1.0 x 10-9 27.78 27.78 9.1 x 10- 12 9.6 x 106 1.0 x 10- 12 9.6 x 106 5.2 x 10- 12 5.2 x 10- 12 1.2 x 108 1.2 x 108 1.2 x 108 1.2 x 108 1.9 x 10- 12 1.9 x 10- 12 1.9 x 10- 12 5.5 x 10- 11 9.1 x 104 1.2 x 10- 12 9.8 x 10- 13 1.8 x 103 7.0 x lOS 1.0 x 10- 12 1.0 x 10- 12 6.4 x 10- 1 1.0 x 10- 12 1.0 x 10- 12 6.9 x 10- 15 6.9 x 10- 15 6.9 x 10- 15 6.8 x 10- 13 6.8 x 10- 13 6.8 x 10- 13 6.9 x 10- 13 6.9 x 10- 13 3.2 x 1013 3.2 x 1013 3.2 x 1013 2.4 x 10- 13 2.4 x 10- 13 9.8 x 10- 14 9.8 x 10- 14 101.9 8.7 x 10- 14 ~ ~ 56Fe*O.847 g.s. 101.9 10.2 LINE EMISSION PROCESSES / 211 Table 10.1. (Continued.) Energy (MeV) Emission mechanism Excitation processes Mean life (s) 2.6138 2ONe~.248 -+ 2~e*1.634 2.7412 2.7540 24Mg~·123 -+ 3.7365 4Oea*3.737 -+ g.s. 4.4380 12C~·439 -+ g.s. 9.2 9.2 9.2 9.2 1.8 3.5 3.5 6.8 6.8 6.1 6.1 6.1 6.1 6.1 6.1 4.4439 II B ~.445 -+ g.s. 5.1049 14N*5.106 -+ g.s. 6.1291 160*6.130 -+ g.s. 6.8778 28Si*6.879 -+ g.s. 6.9174 16 0*6.919 -+ g.s. 7.1152 160*7.117 -+ g.s. 2ONe(p, p')~e* ~e(a, a')20Ne* 24Mg(p, x)20Ne* 28Si(p, x)20Ne* 160(p, p') 160* 24Mg(p, p') 24Mg* 24Mg(a, a')24Mg* 4OCa(p, p')40Ca* 4Oea(a, a')40Ca* 12C(p, p,)12C* 12C(a, a,) 12C* 14N(p, x) 12C* 14N(a, x) 12C* 160(p, x) 12C* 160(a, x) 12C* 12C(p,2p)lIB* 12C(a,x)IIB* 14N(p, p')14N* 14 N (a, a') 14N* 160(p, x)14N* 160(a, x) 14N* 160(p, p,) 160* 160(a, a') 160* 2ONe(p, x) 160* 28Si(p, p')28Si* 28 Si(a, a,)28 Si* 160(p, p,) 16 0* 160(a, a') 160* 160(p, p,) 160* 160(a, a,) 160* 160*8.872 -+ 160*6.130 24Mg*I.369 1.1 1.1 6.3 6.3 6.3 6.3 2.7 2.7 2.7 2.6 2.6 6.8 6.8 1.2 1.2 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 10- 14 10- 14 10- 14 10- 14 10- 13 10- 14 10- 14 IO-Il IO-Il 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 15 10- 15 10- 12 10- 12 10- 12 10- 12 10- 11 10- 11 10- 11 10- 12 10- 12 10- 15 10- 15 10- 14 10- 14 Notes aUpdaled from Ramaty, R., Kozlovsky, B., & Lingenfelter, R.E. 1979, ApJS, 40, 487, with data from Firestone, R.B. et al. 1996, Table of Isotopes (Wiley, New York). bBecause of recoil the observed y-ray energy hv' = hV(l-hv/2Mc2), where hv is the transition energy and M is nuclear mass. Table 10.2. Nucleosynthetic radioactive decay lines. a Radioactive decay Dominant decay mean life Line energy (MeV) Branching ratio (%) 8.80 days 0.1584 0.8119 0.7500 0.2695 0.4805 1.5618 98.8 86.0 49.5 36.5 36.5 14.0 212 / 10 y-RAY AND NEUTRINO ASTRONOMY Table 10.2. (Continued.) Dominant decay mean life Line energy (MeV) Branching ratio 48V(e+; €)48Ti 23.0 days 0.9835 1.3121 0.5110 100. 96.6 50.0n c 56Co(e+; €)5 6 Fe 111.3 days 0.8468 1.2383 0.5110 2.5986 1.7715 1.0379 (3.244) (2.029) 99.9 68.4 21.7 19.0n c 17.4 15.5 14.1 12.4 11.3 1.1155 0.0080 50.6 34.2 0.1221 0.1365 0.0144 85.5 48.9 10.3 9.5 Radioactive decay (O.OO64}b 65Zn(e+; €)6 5Cu 352.4 days 57 Co(€)57Fe 392.1 days (O.OO64) (%) 22Na(e+; €)22Ne 3.754yr 1.2745 0.5110 99.9 89.4n c 125Sb(e-) 125Te 3.979yr (0.0274) 0.4279 0.6006 0.6360 0.4634 62.1 29.4 17.8 11.3 10.5 44Ti(€)44Sc 91 ±4yr 0.0679 0.0783 (0.0041) 1.1570 0.5110 100 99.3 16.7 99.9 94.0n c 44Sc(e+; €)44Ca (0.236 day) 6OFe(e-)60Co 6OCo(e-)60Ni 2.2 x 106 yr (7.60 yr) 0.0586 1.3325 1.1732 26 AJ(e+; €) 26 Mg 1.03 x 106 yr 1.8086 0.5110 99.7 82.1n c 4OK(€)40Ar 1.84 x 109 yr 1.4608 10.7 2.0 100 99.9 Notes aBased on data from Browne E., & Firestone, R.B. 1986, Table of Radioactive Isotopes (Wiley, New York), Firestone, R.B. 1996, Table of Isotopes (Wiley, New York), and Norman, E.B. et at. 1997, Nuc. Phys., A621, 92 for the 44Ti mean-life. bBracketted ( ) line energies are the mean of two or more close lines. cThe number of 0.5110 MeV photons per positron annihilation, n = 2-1.5/ps, where fps is the fraction of annihilation occurring via positronium formation. 10.3 SCATTERING AND ABSORPTION PROCESSES / 213 Table 10.3. Radiative capture y-ray lines. a Radiative capture Thermal cross section (b) Line energy Branching ratio (MeV) (%) 0.332 2.2233 100 2.6 0.0144 7.6316 7.6456 0.3525 5.9205 6.0185 1.7252 64 30 24 12 9 9 9 iH(n, y)2H 56Fe(n, y)57 Fe Note aBased on data Nuclear Data Group, 1973, Nuclear Level Schemes A = 45 through A = 257 from Nuclear Data Sheets (Academic Press, New York). 10.3 SCATTERING AND ABSORPTION PROCESSES y-Ray emission spectra can be modified by several processes: photoelectric absorption, electronpositron pair production, Compton scattering, and Landau-level electron scattering in intense magnetic fields [1-4, 13-21]. See Figure 10.2. 10.3.1 Photoelectric Absorption The cross section for photoelectric absorption of a photon by the ejection of a K -shell electron from an atom of nuclear charge Z is [1] a(hv)K = 5 4(mc2)5 (y2 _ 30'[Z a 2 hv 1)3/2 1 x{-4+ y(y-2) [ 1In (y+JY2=1)]) 3 y+1 2yJY2=1 y_Jy 2-1 ' where the Thomson cross section, 0'[ ejected electron y = 1 + hv/mc2. 10.3.2 = 81re 4 /(3m 2e4 ) = 0.6652 b, and the Lorenz factor of the Pair Production The cross section for electron-positron pair production (pp) by a photon in the presence of a nucleus of charge Z is [14] 3aZ20'[[7 (2hV) 109] a(hv)pp = 21r gin mc2 - 54 for no screening when 1 « hv/mc2 « 1/aZ I / 3 , and a(hv)pp 2 = 3aZ21r 0'[ [7gin (183) 1] for complete screening when hv/mc2 » 1/aZ I / 3 . ZI/3 - 54 214 / 10 y-RAY AND NEUTRINO ASTRONOMY ! I I 10' ~ 'Leo, , rOo 1 = f}".~ ..e . -ti c: I 'v ~ 10·· 10·' 10·~ ~ '\ ::- ~ I 1,/ ~~ ,+; 1\ " ' \ '0 , , .0. 1 ,I \ Photon )" (MeV) 100:').a .v 1,0' I Photon Energy (MeV) 10 I' 1\ r\ I '\ I \ 10" II '~ ~ 10·' .. ~ 'v II.a ~ ~, .v .... ~I L' ~\ ~ ~~ ..a ". k"e ,.-ff JI Y. I. Photon E:nergy (MeVl 1 ..a .v r' I Photon Energy (MeV) I' Figure 10.2. Macroscopic cross sections for y-ray attenuation by photoelectric absorption, Compton scattering and pair production in hydrogen, air, NaI, and Ge, as a function of photon energy from [21]. The cross section for electron-positron pair production by the interaction of two photons of energy hv and hv' when hvhv' > m 2 c4 is [1] 10.3 SCATTERING AND ABSORPTION PROCESSES / 215 The attenuation coefficient for electron-positron pair production by a photon in a strong magnetic field, in the limit h 2 v 2 /2m 2e 4 B* » 1 with B* = B/4.414 x 1013 G, is [15] R1y where X 10.3.3 == ame = --B* sine = 2h ( 4) { 0.377 exp - 3x 06 . X -1/3 , , x« 1, X» 1, (hv/2me 2 )B* sin e and the threshold energy is 2me 2 / sin e. Compton Scattering The cross section for Compton scattering (cs) of photons by electrons is [13] + 2) In(21] + 1) + 2:1 + ~4 ----:;;z- 3O'f [( 21] a(hv)cs = 81] 1- 2(21] 1] + 1)2 ' where 1] = h v / me 2 is the initial photon energy. The angular distribution of the scattered photons, in terms of the scattering angle 41, is j(cos41) = 3O'f [(1 8a(hv)cs + 1] + 1]2 - 1] cos (1)(1 + cos 2 (1) - 21]2 cos 41] 3 · (l + 1] -1] cos (1) The energy of the Compton-scattered photon h v' relative to the initial photon energy h v is r = hv'hv = 1/(1 + 1] -1] cos (1), and the energy distribution of the Compton-scattered photons is j(r) = 3O'f [ 1 (1Jr + r - 1)2] r - 1+ - + 2 2 81]a(hv)cs r 1] r ' for 1/(21] + 1) ::s r ::s 1, corresponding to scattering angles 0 0 ::s 41 ::s 1800 , and j (r) = 0 for other values of r. In a magnetic field, where the electron energies are quantized in Landau states, the total scattering cross section for unpolarized photons in the Thomson limit is [16] where e and h v are the angle and energy of the incident photon with respect to the magnetic field in the electron rest frame, and hVB = eB/me is the cyclotron frequency. When (hv/ hVB)B > 10 12 G, relativistic effects modify the cross section [17, 18]. 10.3.4 Cyclotron Absorption In a magnetic field, the cross section for absorption of photons by electron scattering from ground state to higher Landau levels is [19] a~s(e) = arr21; 2 e 2 En e- z Zn-1 ( ~(hv - hvn ) (n _ I)! (1 Z) + cos2 e) + ;; sin2 e , 216 I 10 y-RAY AND NEUTRINO ASTRONOMY where Z = h 2v 2 sin 2 ()j2me 2B*, En = (m 2e4 + h 2v 2 cos 2 () 1013 G. The photons are absorbed at the resonant energies In the nonrelativistic limit, nB* = nBj4.414 x + 2nB*m2e4) 1/2, and B* = Bj4.414 X 1013 G« I, the absorption cross section is [20] 1 + cos2 () (n-I)! ' where photons are absorbed at hannonics h Vn = neB j me. 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS The v-ray sky is extremely variable. Unlike the sources seen at longer wavelengths, most of the astrophysical v-ray sources have been seen only in their transient emission. Out of roughly a thousand v-ray sources less than 10% are relatively steady, persistent sources. The latter include a wide variety of sources such as the Sun, supernova remnants, the interstellar medium, and the cosmic background emission, but they are mostly compact objects: radio pulsars, accreting neutron stars, and blackhole candidates, ranging from stellar mass objects in our own galaxy to s~pennassive, active galactic nuclei. TOTAL CRAB EMISSION 10-' 10" +11is _ _ 1981 + \ 1 PerMgsfeid et 111.1979 ling el Ill. 1979 <> Toar and Seward 1974 + Dolan et at. 1977 I (arpenle, et 01. 1967 + Gruber and ling. 1977 I Helmken and HoffOllM. 1973 ~ P. Mandrou 10-" 10-" 10-u et al.1977 + Baker et at. 1973 I Portier et Ill. 1973 + W,lson et at. 1977 t Haymes el at. 1966 ~Sct01lelder et al. 1975 c::J KllIffen et al.1974 (OS- B Db..,.,alians IpWarI IBemett et at. 19771 Walraven et at. 1975 + + ...... totat (rab ILichti et al.19801 --- White et al.19BO 10-"1O'':.1~-'-'-~1O:':-r-~~~1O':r-'-'-~'''''1O",,4,-'-...........u.u.~10:-'--'-'-'''''''''~'''-'''''''''''~101 - Ey [keV) Figure 10.3. Total Crab Nebula and pulsar emission from 10 keY to 2 GeV. The Crab flux is the de facto standard for the expression of source fluxes, e.g., 10 milliCrabs. This figure is provided to relate Crab fluxes at various energies to the more useful photonscm- 2 s-1 -lkeV. The plot is from Graser, U., & SchOnfelder, V. 1982, ApJ, 263, 677, and references to observations contained within the plot can be found in that paper. 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 217 The vast majority of y-ray sources, however, have been seen only briefly for times as short as a few milliseconds to as much as 1000 s. These are collectively known as y-ray bursts, but because of their diverse properties, they may arise from a variety of sources and processes. General reviews of astrophysical y-ray sources are given in [22-25]. Figure 10.3 displays the famous Crab Nebula spectrum. Many y-ray bursts are reviewed in [26-31]. The locations and properties of selected galactic and extragalactic y-ray sources are listed in Tables 10.4-10.9 and basic data on the major hard X-ray and y-ray instruments are included in Tables 10.10-10.12. Table 10.4. Selected galactic sources> 100 keY. Source name 1YpeQ periodb aC XPersei 0352+308 XRBe 835 s 58.06 +30.90 0422+328 BHC Crab (total) 0531+219 Crab (pulsar) 0531+219 0535+262 .s III d Dist. e flux! 163.08 -17.14 0.35 4 x 10- 5 1 x 10-5 64.63 +32.79 165.89 -11.91 2 2 x 10- 2 2 x 10- 3 1 x 10-4 SNRand Pulsar 82.88 +21.98 184.56 -5.79 2 8 6 5 5 2 6 2 x x x x x x x Pulsar 0.0332 s 82.88 +21.98 184.56 -5.79 2 1x 1x 2x 6x 5x 2x 2x 1x 3x XRBe 104 s 84.06 +26.32 181.47 -2.54 1.8 I x 10-2 5 x 10-5 SNh 83.96 -69.30 279.71 -31.94 50 0.87 bII SN1987A 0536-693 (in LMC) 0620-00 BHC 95.05 -0.32 209.96 -6.54 Geminga 0630+178 Pulsar 0.2371 s 97.75 +17.81 195.14 +4.27 < O.4t Lum. g Refs. 30keV 100 keY 8 x 1032 2 x 1033 [l] 30keV 100 keY 300 keY 1 x 1037 1 x 1037 6 x 1036 [2] [2] [2] 10- 3 10-4 10-5 10-6 10- 8 10- 11 10- 13 30keV 100 keY 300 keY 1 MeV 10 MeV 100 MeV lGeV 5 5 3 4 2 5 2 x x x x x x x 1036 1036 1036 1036 1036 1035 1035 [3] [3] [3] [3] [3] [3] [3] 10- 3 10-4 10-5 10-7 10-9 10- 11 10- 13 10- 15 10- 21 30keV 100 keY 300 keY 1 MeV 10 MeV 100 MeV lGeV IOGeV 1 TeV 7x 8x 1x 5x 4x 2x 2x 8x 2x 1035 1035 1036 1035 1035 1035 1035 1034 1033 [4] [3] [3] [3] [3] [3] [3] [5] [6] 30keV 100 keY 6 x 1036 3 x 1035 [7] [7] 2 x 10-4 4 x 10-5 7 x 10-6 30keV 100 keY 300 keY 1 x 1038 2 x 1038 3 x 1038 [8] [8] [8] 3 x 10-3 2 x 10-4 30keV 100 keY 4 x 1035 3 x 1035 [9] [9] 3 x 10- 11 6 x 10- 13 100 MeV 1 GeV <6x1033 < 2 x 1034 [10] [10] Energy [I] 218 / 10 y-RAY AND NEUTRINO ASTRONOMY Table lOA. (Continued.) Source 1'ype'I aC III d 8 bll name perioob Vela (pulsar) 0833-45 Pulsar 0.0892s 128.40 -45.05 1009-45 BHe 1055-52 Nova Muscae 1124-684 Dist.e Flux! 263.58 -2.82 0.5 4x 2x 1x 3x 6x 1x 2x 153.37 -45.06 275.85 +9.35 3t 1 x 10-4 7 x 10-6 Pulsar 164.50 -52.45 286.00 6.65 l.53 BHe 17l.08 -68.40 295.31 -7.07 1509-58 Pulsar 0.1502 s 227.50 -58.95 1543-47 BHe 10-1 10-1 10-8 10-9 10- 10 10- 10 10- 12 Energy Lum.g 1032 1033 1033 1034 1034 1034 1034 [11] [11] [11] [12] [12] [12] [12] lookeV 300keV 2 x 1036 1 x 1036 [13] [13] 2 x 10- 12 100 MeV 1 x 1034 [14] It 4 x 10-3 2 x 10-4 1 x 10-5 30keV lookeV 300keV 7 x 1035 4 x 1035 2 x 1035 [15] [15] [15] 320.33 -1.16 It 3 x 10-5 4 x 10-6 8 x 10-1 30keV lookeV 300keV 5 x 1033 8 x 1033 1 x 1034 [16] [16] [16] 235.96 -47.56 330.92 +5.43 4 8 x 10-3 2 x 10-4 30keV lookeV 2 x 1031 6 x 1036 [17] lookeV 300keV 3 MeV 10 MeV 30 MeV 100 MeV lOeV 2x 1x 5x 2x 3x 5x 8x Refs. [17] 1655-40 BHe 253.50 -39.85 344.98 +2.46 3.2 2 x 10-4 1 x 10-5 lookeV 300keV 4 x 1036 2 x 1036 [13] [13] Her X-I 1656+354 LMXB l.24 s 254.01 +35.42 58.15 +37.52 5 1 x 10-3 1 x 10-5 3 x 10-20 30keV lookeV 1 TeV 4 x 1036 5 x 1035 1 x 1035 [18] [18] [6] OX 339-4 1659-487 BHe 254.76 -48.72 338.94 -4.33 lOt 2 x 10- 3 2 x 10-4 1 x 10-5 30keV lookeV 300keV 4 x 1031 4 x 1031 2 x 1031 [17] [17] HMXB 255.14 -37.78 347.76 +2.17 l.7 1 x 10- 3 3 x 10-5 30keV lookeV 5 x 1035 2 x 1035 [19] [19] BHe 256.29 -25.03 358.59 +9.06 lOt 2 x 10-3 1 x 10-4 30keV lookeV 3 x 1031 2 x 1031 [20] [20] 1706-44 Pulsar O.I024s 256.52 -44.42 343.10 -2.68 l.82 7 x 10- 12 1 x 10- 13 100 MeV lOeV 3 x 1034 6 x 1034 [5] [5] 1716-249 BHe 259.94 -24.97 0.20 +6.99 2.4 4 x 10-4 2 x 10-5 lookeV 300keV 5 x 1036 2 x 1036 [13] [21] [21] 1700-37 NovaOph '77 1705-250 [17] [13] Terzian 2 1724-308 LMXB 26l.08 -30.76 356.32 +2.30 14t 2 x 10-4 3 x 10-5 40keV lookeV 1 x 1031 1 x 1031 OX 1+4 1728-247 LMXB 114s 262.15 -24.70 l.9O +4.87 lOt 2 x 10- 3 4 x 10-5 30keV lookeV 3 x 1031 8 x 1036 [19] [19] BHe 264.48 -29.52 358.97 +0.52 lOt 1 x 10-3 4 x 10-4 30keV lookeV 2 x 1031 8 x 1031 [22] [22] 1737.9-2952 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS I 219 Table lOA. (Continued.) aC Source ~ name III d bll Dist.e Flux! Energy Lum. 8 Refs. 1740.7-2942 BHC 265.18 -29.71 359.12 -0.10 lOt 5 x 10-4 7 x 10-5 1 x 10-5 40 keY 100 keY 300 keY 2 x 1037 1 x 1037 2 x 1037 [23] [23] [23] ''Galactic Center" 1742-294 BHC 266.24 -29.38 359.89 -0.71 lot 3 x 10-3 1 x 10-4 2 x 10-5 30 keY 100 keY 300 keY 5 x 1037 2 x 1037 3 x 1037 [24] [24] [25] 1743-322 XRT 265.44 -32.21 357.13 -l.61 lot 6 x 10-4 4 x 10-5 30 keY 100 keY 1 x 1037 8 x 1036 [19] [19] GX5-1 1758-250 LMXB 269.51 -25.08 5.08 -l.02 lOt 8 x 10-4 4 x 10-5 30 keY 100 keY 1 x 1037 8 x 1036 [19] [19] 1758-258 BHC 269.53 -25.74 4.52 -1.36 lOt 4 x 10-4 6 x 10-5 3xlO-6 30 keY 100 keY 300keV 7 x 1036 1 x 1037 5 x 1036 [25] [25] [25] 1915+105 BHC 288.80 +10.95 45.37 -0.22 12.5 8 x 10-5 2 x 10-6 100 keY 300 keY 3 x 1037 6 x 1036 [13] [13] CygX-l 1956+350 BHC 299.04 +35.05 7l.29 +3.12 2.5 9x 1x 4x 1x 10-3 10- 3 10-5 10-5 30keV 100 keY 300 keY 1 MeV 1x 1x 4x 1x 1037 1037 1036 1037 [26] [26] [27] [27] 2000+25 BHC 300.18 +25.10 63.38 -3.00 2t 2 x 10- 3 2 x 10-4 2 x 10-5 30 keY 100 keY 300keV 1 x 1036 2 x 1036 1 x 1036 [28] [28] [28] 2023+338 BHC 305.53 +33.71 73.13 -2.09 2t 1 x 10-2 1 x 10-3 1 x 10-4 30 keY 100 keY 300 keY 7 x 1036 8 x 1036 7 x 1036 [13] [13] [13] CygX-3 2030+407 HMXB .307.52 +40.76 79.76 +0.77 lOt 1x 2x 5x 2x 30keV 100 keY 1 TeV 1 PeV 2x 4x 1x 4x [18] [18] [6] [6] 10- 3 10-5 10-20 10-26 1037 1036 1036 1035 Notes aBHC, black hole candidate; HMXB, high mass X-ray binary; LMXB, low-mass X-ray binary system; SN, su~ova; SNR, supernova remnant; XRBe denotes Be star plus collapsed object binary system; XRT, X-ray transient. Pulsar periods in seconds are from Taylor, J.H., Manchester, R.N., & Lyne, A.G. 1993, ApJS, 88, 529, and an update to be found at pulsar.princeton.edu. Binary pulse periods are from Nagase, F. 1989, PAS!, 41, l. cCelestial coordinates in degrees from Wood, K.S. et al. 1984, ApJS, 56, 507, except for SNl987A (West, R. 1987, ESO Workshop on the SN1987A, 5); A0620-00 (Boley, F.I. et aI. 1976, ApJ, 203, Ll3); Geminga (Bignami, G.F. et al. 1983, ApI, 272, L9); Vela Pulsar (Forman, W.R. et al. 1978, ApJS, 38,357); Nova Muscae (West, R. 1991, IAU Cire. No. 5165); GRSI227+0229 (Jourdain, E. et al. 1991,lnt. Cosmic Ray Corif., 1, 173); PSRI509-58 (Princeton Pulsar List, 1992); AI524-62(Murdin,P.etaI. 1977,MNRAS, 178, 27);4UI700-37 (Forman, W.R.etal. 1978,ApIS, 38,357); PSRI706-44 (Princeton Pulsar List, 1992); Terzian 2 (Hertz, P.L., & Grindlay, J.E. 1983, ApJ, 275, 105); 1740.7-2942 (Hertz, P.L., & Grindlay, J.E. 1984,ApJ, 278,137); GRSI758-258 (Sunyaev, R. et al. 1991, Sov. Astron. Lett., 17, 50); Briggs Source (Briggs, M.S. et aI. 1995, ApJ, 442, 638); GS2QOO+25 (Tsunemi, H. et aI. 1989, ApI, 337, LSI); GS2023+338 (Wagner, R.M. et al. 1989, IAU Cire. No. 4783). d Galactic coordinates in degrees. e All distances in kiloparsecs. Those marked with a dagger (t) are assumptions, some of which are based on optical limitations and some of which are unknown in which case the value of 10 kpc is used. Known distance references are Crab (Trimble, V. 1968, AI, 73, 535); X Persei (Brucato, RJ., & Kristian, J. 1972, ApI, 173, L105); A0535+26 (Giangrande, A. et al. 1980, A&AS, 40, 289); SNl987A (Arnett, W.D. et al. 1989, ARA&A, 27, 629); A0620-00 (Oke, 220 I 10 y-RAY AND NEUTRINO ASTRONOMY J.B. 1977,ApJ,lI7,181); Vela (Grenier, IA etal. 1988,A&A, 204,117); A1524-62 (Murdin, P. etal. 1977,MNRAS, 178,27); Her X-I (Bahcall, NA 1973, Sixth Texas Symp., 224,178); 4U1700-37 (Bradt, H.V., & McClintock, J.E. 1983, ARA&A, 21, 13); Terzian 2 (Malkan, M.A. et al. 1980, ApJ, 237, 432); OX 1+4 (Davidsen, A.E et al. 1977, ApJ, 211,866); Cyg X-I (Margon, B.H. et al. 1973, ApJ, 185, L117); Cyg X-3 (Breas, L.L.E. et al. 1973, NaturePS, 242, 66). f Observed flux in photonslcm2 s keY. gInferred luminosity per logarithmic interval assuming isotropic emission, E2 x (Flux) = E2 (keV2) x Distance2 (kpc2) x Flux (photJcm2 s keY) x 2 x 1035 erg/s In E. hpeak flux from supernova explosion in the Large Magellanic Cloud (LMC). 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Process LineE (MeV) FWHM (keV) Redshifted Redshifted Redshifted Redshifted Redshifted Blueshifted Backscattered Backscattered 0.511 0.511 0.511 0.430 0.480 0.481 0.404 0.413 0.500-2.0 0.170 0.19 2 3 < IOC 100 240 60 3 15 Line source Max. flux (phJcm2 s) Lum. (ergls) 1.5 x 1O-3a 2 x 10-3 2 x 10- 2 100 1 x 10-2 6 x 10- 3 7 x 10- 3 7 x 10-3 2 x 10-2 7 x 10-4 2 x 10-3 7 I 5 2 6 6 2 6 2 2 7 Refs. e± Annihilation Radiation 12 40 Interstellar gas BH? near ocb Solar flares OBS0526-66 IE 1740.7-2942 Nova Muscae CrabPulsar transient IOJune74 transient Cygnus X-I BH?nearOCb Nova Muscae x x x x x x x x x x x 1036 1037 1019 1043 1037 1035d 1036 1035d 1037 1034 lO34d [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [6] 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / Table 10.5. (Continued.) LineE (MeV) FWHM (keV) ~9 44SC(EY, ,8+y)44Ca 26Al(,8+y)26Mg 0.847 1.238 2.598 3.244 0.122 0.068 0.078 l.l57 1.809 5.4 4He(a, n)7Be* 4He(a, p)7Li* 56Fe(p, p'y) 12C, 160(p, x)IOB* 56Fe(p, p'y) 24Mg(p, p'y) 20Ne(p, p'y) 28Si(p, p'y) 12C(p, p'y) 160(p, p'y) 0.429 0.478 0.847 1.023 1.238 1.369 1.634 1.779 4.438 6.129 25 c 30C 5c 30C 7c 15c 22c 20c 97 c 114c IH(n, y)2H 2.223 2.223 1.790 5.947 < O.lc Process Line source Max. flux (phJcm2 s) Lum. (erg/s) I x 10- 3 Ix 10-3 3xlO-4 2xlO-4 4x 10-5 4xlO- 5 4xlO- 5 4xlO- 5 4 6 4 3 3 4 5 8 8 x x x x x x x x x 1038 1038 1038 1038 1036 103 3 1033 1034 1036 [II] [II] [12] [12] [l3] [14] [l4] [15] [16] 6 7 4 2 6 I 3 4 I I x x x x x x x x x x 1019 10 19 10 19 10 19 10 19 1020 1020 1020 1021 1021 [17] [17] [2] [2] [2] [2] [2] [2] [2] [2] I 6 I 2 x x x x 1022 1036d 1037d 1037d [2, 18] [8] [8] [8] Refs. Radioactive Decay 56Co(EY, ,8+y) 56 Fe 57Co(Ey)57Fe 44Ti(EY)44Sc Supernova 1987A Supernova 1987A Supernova 1987A Supernova 1987A Supernova 1987A SN Remnant CasA SN Remnant CasA SN Remnant CasA Interstellar medium ~Il ~26c ~32c ~ ~ ~ IC 2c 2c ~3OC 4.5 x 1O-4a Nuclear Excitation Solar flares Solar flares Solar flares Solar flares Solar flares Solar flares Solar flares Solar flares Solar flares Solar flares 3 3 I 5 I 2 4 5 5 4 x x x x x x x x x x 10- 2 10-2 10- 2 10- 3 10- 2 10- 2 10- 2 10- 2 10-2 10-2 Neutron Capture Redshifted 56Fe(n, y)57 Fe Redshifted 70 95 25 Solar flares IOJune74 transient IOJune74 transient IOJune74 transient ~I 1.5 x 10- 2 3 x 10- 2 1.5 x 10- 2 Notes aper radian of longitude in the Galactic Plane. bBlack hole? Near Galactic Center. cTheoreticai widths for unresolved lines. dFor a nominal distance of I kpc. References I. 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(deg) 8 (deg) I (deg) b (deg) Centroid (keV) FWHM (keV) Field (10 12 G) Refs. 3.1 ±0.6 4.3 ±0.9 1.0 [I] 28.5 ±0.5 52.6 ± 1.4 11.0 ± 0.9 1O±3 2.5 [2] 184.56 -5.79 73.3 ± 1.000·b <4.9 6.7 [3] 83.95 +26.29 181.09 -3.24 ~55 4.3 [4] Xray Binary 135.53 -40.56 263.06 3.93 25.6±0.9 57.9± 1.0 7.2±2.6 24.0± I 2.2 [5] Cen X-3 1119-603 Xray Binary 170.31 -60.62 292.09 0.34 28.5 ±0.5 6.3 ± 2.0 2.5 [6] 1538-522 Xray Binary 235.60 -52.39 327.42 +2.16 20.9 ± 0.2c 5.1 ± 0.3c 1.7 [7] 4Ul626-67 1627-673 Xray Binary 248.07 -67.46 321.79 -13.09 ~7± Ib ~3 [8] Source name Object type IX 0115+634 Xray Binary 19.82 +63.82 126.00 +1.11 12.1 ±0.2 22.6±0.4 0332+530 Xray Binary 53.75 +53.18 146.05 -2.19 NP0531 0531+219 Pulsar 83.63 +22.01 0535+262 Xray Pulsar Vel X-I 0900-403 ~11O ~ 18 ± Ib 36.5 ± 1.0 15 7±2.8 34.7 ±0.9c 12.0± 2.OC 2.9 [9] ~ Her X-I 1656+354 Xray Binary 254.46 +35.34 58.15 +37.52 1907+097 Xray Binary 287.41 +9.83 43.74 0.48 20.0± 1.0 4.1 ± 2.6 1.7 [10] CepX-4 2137+579 Xray Binary 324.88 +57.99 99.68 +4.06 30.5 ±0.4 15.0 ± 1.4 2.6 [II] GRB870303 y burst 20.4 ± 0.7 40.6±2.6 3.5 ±2.7 12.3 ±6.3 ~ 1.7 [12] GRB880205 y burst 19.3 ±0.7 38.6± 1.6 4.1 ± 2.2 14.4±4.6 ~ 1.7 [12] GRB890929 y burst 26.3 ± 1.5 46.6± 1.7 75+4·5 . -4.1 ~ 2.1 [13] Notes °Transient line seen between 73 and 79 keY. bErnission line. CLine centroid and width are observed to vary with pulse phase. 12.7:t~ 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 223 References 1. Nagase, F. et al. 1991, ApJ, 375, LA9 2. Makishima, K. et aI. 1990, ApJ, 365, L59 3. Ling, J.C. et aI. 1979, ApJ, 231, 896; Ayre, C.A. et aI. 1983, MNRAS, lOS, 285 4. Grove, J.E. et aI. 1995, ApJ, 438, L25; Maisack, M. et aI. 1997, AM, 325,212 5. Makishima, K., & Mihara, T. 1992, Frontiers ofX-Ray Astronomy (University Academy Press, Tokyo) p. 23; Mihara, T. 1995, Thesis, University of Tokyo; Kretschmar, P. et aI. 1997, AM, 325, 623; DaI Fiume, D. et aI. 1998, Nuc Phys B Proc. Suppl., 69, 145 6. DaI Fiume, D. et aI. 1998, Nuc Phys B Proc. Suppl., 69, 145 7. Clark, G.W. et aI. 1990, ApJ, 353,274 8. Pravdo, S.H. et aI. 1979,ApJ, 231, 912; Orlandini, M. 1998, ApJ, 500, L163 9. Mihara, T. et aI. 1990, Nature, 346,250 10. Makishima, K., & Mihara, T. 1992, Frontiers of X-Ray Astronomy (University Academy Press, Tokyo) p. 23; Mihara, T. 1995, Thesis, University of Tokyo 11. Mihara, T. et aI. 1991, ApJ, 379, L61 12. Murakami, T. et aI. 1988, Nature, 335, 234 13. Yoshida, A. et aI. 1991, PASJ, 43, L69 Table 10.7. y-Ray burst source positions < 100 arcmin 2.a ,b Burst source Date (yrmo day) Time (s) GBSoolO-16O GBS0026-630 GBS0117-289 GBS0502+118 GBS0526-661 GBS0615-461 GBS0625-346 GBS0653+ 793 GBS0702+388 GBS0723-271 GBS0813-326 GBS0836-189 GBS0847-361 GBS0912-51O GBS 1028+459 GBSl104-229 GBS1156+652 GBS1205+239 GBS1257+592 GBS1327+375 GBS1330-164 GBSI4OO-468 GBS1407+353 GBS1412+789 GBS1450-693 GBS 1528+ 196 GBS1625-583 GBS 1630-765 GBS 1703+006 GBS1730+491 GBS1756-261 GBS1806-207 7911 16 98010ge 78 11 19 970228d 790305bc 790313 791014 970508d 9803 2~ 91 11 09 920501 980326d 9203 11 910522 790329 91 11 18 971214d 781124 971227d 920720 920517 790307 91 11 04 790613 970402e 9701 lie 910717 7901 13 78 11 21a 960720 910421 790107c 51400 4341 34021 10681 57125 62636 40412 78106 13478 12458 76695 76733 08423 44036 80512 68252 84041 14130 30187 11524 11875 80330 54282 50755 80352 35040 16378 27360 05736 41813 33246 20155 F>30keV (erglcm2 ) 10-4 10-6 10-4 10-5 10- 3 10-5 10- 5 10- 6 10- 5 10- 6 10-5 10-6 10-4 10-5 10-5 10- 5 10- 5 10- 5 10- 7 10-5 10-5 10-4 10-5 10-7 ~ 10- 5 ~ 10- 5 7 x 10-6 I x 10-4 9 x 10- 5 3 x 10- 6 4 x 10- 6 1 x 10- 6 2x 4x 3x 1x 1x 6x 1x 4x 5x 7x 4x 1x 1x 3x 7x 5x I x 4x 7x 2x 4x 2x 1x 4x ex (deg) 8 (deg) (deg) b (deg) Error box (arcmin2) 3.20 6.48 19.72 75.43 81.51 94.1 96.7 103.37 105.65 110.8 123.34 129.14 131.8 137.9 157.8 166.0 179.13 181.94 194.31 201.8 202.6 210.69 211.8 213.1 222.53 232.06 246.3 249.2 256.4 262.65 268.9 272.17 -15.69 -63.02 -28.64 +11.78 -66.08 -46.1 -34.6 +79.29 +38.84 -27.1 -32.59 -18.86 -36.1 -51.0 +45.6 -22.9 +65.20 +23.65 +59.40 +37.5 -16.4 -46.99 +35.3 +78.9 -69.33 +19.60 -58.3 -76.6 +0.5 +49.10 26.1 -20.41 82.85 307.50 228.50 188.91 276.09 253.8 242.6 134.94 178.12 240.6 250.80 242.37 257.8 271.9 169.9 272.9 132.02 229.93 121.55 89.2 316.3 315.37 64.4 118.0 313.11 29.63 328.1 314.7 20.7 75.76 51.5 10.0 -75.46 -53.86 -83.75 -17.95 -33.24 -25.0 -19.7 +26.71 +18.65 -5.6 +0.96 +13.03 +4.5 -1.9 +56.6 +33.6 +50.95 +79.54 +57.71 +77.2 +45.5 +14.15 +71.9 +37.7 -8.84 +53.39 -6.3 -19.2 +23.6 +33.09 +23.2 -0.24 4 50 8 2 0.05 24 82 28 3 6 4 80 4 4 41 20 48 48 7 6 12 10 16 0.8 2 28 10 78 ~ 100 28 ~ 100 6 224 / 10 y-RAY AND NEUTRINO ASTRONOMY Table 10.7. (Continued.) Burst source Date (yrmoday) Time (s) F>30keV (erglcm2) GBS1808+593 GBS181O+314 GBSI847+728 GBS 1900+ 145 GBS1912-577 GBS 1926+036 GBS2ooo-427 GBS2006-216 GBS2142-414 GBS2252-025 GBS231 1+319 GBS2311-499 GBS2320+128 970828e 790325b 920711 790324c 920406 790331 920525 7811 O4b 7906 22 7911 05b 790504 790406 920325 63877 49500 58166 58010 09915 76172 12427 58667 02665 48862 31464 42447 62261 _10-5 5 x 10-5 8 x 10-6 1 x 10-6 1 x 10-4 8 x 10-5 1 x 10-4 3 x 10-4 7 x 10-5 1 x 10-5 6 x 10-6 1 x 10-6 3 x 10-5 (deg) 8 (deg) (deg) (deg) Error box (arcmin2) 272.13 273.0 281.8 286.83 288.0 292.0 300.0 302.2 326.4 343.55 348.4 348.51 349.9 +59.13 +31.4 +72.8 +9.45 -57.7 +3.7 -42.7 -21.5 -41.2 -2.26 +32.1 -49.66 +12.8 87.95 58.2 103.7 43.08 339.0 40.4 357.2 21.1 0.3 69.45 99.9 336.03 90.8 +28.45 +21.6 +26.1 +0.81 -25.3 -6.4 -30.1 -26.2 -49.6 -52.51 -26.3 -60.74 -44.3 0.8 2 100 7 4 20 6 14 - 100 35 58 0.3 7 a b Notes aQuiescent X-ray counterparts have been suggested for the three repeater burst sources GBS0526-661, GBS1806-207 and GBSI900+145, which are associated with supernova remnants N49, GlO.0-0.3, and G42.8+O.6 (see note c below and Rothschild, R.E., & Lingenfelter, R.E. 1996, High Velocity Neutron Stars and Gamma-Ray Bursts (AlP, New York». No quiescent counterparts have been identified for the "classical" bursts, but fading afterglow sources have been seen following several bursts (see note d) and underlying "host" galaxies have been reported. bLocations (2000 coordinates) for bursts prior to 1990 are based on catalog of Atteia, J.L. et al. 1987, ApJS, 64, 305, and ftuences from Mazets, E.P. et al. 1981, Ap&SS, SO, I, except as follows: GBS1550+762 data from Hueter, G.J. 1987, Ph.D. Dissertation, University of California, San Diego; GBS1806-207 position from Atteia, J.L. et al. 1987, ApJ, 320, LlI0, and private communication; GBS 1900+ 145 position also from Mazets, E.P. et al. 1981; GBS0746-672 data from Katoh, T. et al. 1984, in AlP Conf. Proc. 115, 390; locations of bursts after 1990 are from Hurley, K., private communication on behalf of the 3rd Interplanetary Network; and from BeppoSAX burst detections listed in notes d and e. Fluences are from Third BATSE Catalog (Meegan, C.A. et al. 1996, ApJS, 106, 65, and the online update of that catalog. cRepeaters: 17 bursts have been observed from the source GBS0526-661 (Golenetskii, S.V. et al. 1979, SOy. Astron. Lett., 13, 166) associated with supernova remnant N49 in LMC and possibly an X-ray source at a 05h26mO.55 s, .5 -66°4'35.56" (Rothschild, R.E., Kulkarni, S.R., & Lingenfelter, R.E. 1994, Nature, 368, 432); > 100 bursts from GBS1806-204 (Atteia, J.L. et al. 1987, ApJ, 320, Ll05; Laros, J.G. et al. 1987, ApJ, 320, L111) associated with Galactic supernova remnant GlO.0-0.3 and an X-ray source at a 18h8m4O.34s , 8 -20°24'41.67" (Murakami, T. et al. 1994, Nature, 368, 127), and six bursts from GBSI900+145 (Mazets, E.P. et al. 1979, SOy. Astron. Lett., 5, 343; Kouveliotou, C. et al. 1993, Nature, 362,728; Hurley, K. etal. 1994, ApJ, 431, L31) associated with Galactic supernova remnant G42.8+0.6 and possibly an X-ray source ata Igh7m 17s, 8 +9°19'18" (Vasisht, G. et al. 1994,ApJ, 431, L35). dFading optical sources have been observed for GRB0502+118 (Costa, E. et al. 1997, IAU Circ. No. 6572) at V = 21.3 discovered 0.9 days after burst at a 05 hOl m46.61 s, 8 +11°46'53.4" (van Paradijs, I. et al. 1997, Nature, 386,686); GRB0653+793 (Heise, J. et al. 1997, IAU Cire. No. 6654) at V = 20.5 discovered 1.28 days after burst at a O6h53 m49.43 s, 8 +79°16'19.6" (Bond 1997, IAU Circ. No. 6654) and red-shifted absorption lines observed with z = 0.835 (Metzger, M.R., et al. 1997, Nature, 387. 878); GBS0702+388 (in't Zand, J. et al. 1998, IAU Circ. No. 6854) at 250 ILJy at 8.4 GHz discovered 2.9 days after burst at a 07h02m38.0217OS, .5 +38°50'44.0170" (Taylor, G.B. et al. 1998, GeN. No. 40) and at K = 21.4 after 4 days (Metzger, M.R. et al. 1998, IAU Cire. No. 6874) GBS0836-189 (Celidonio, G. et al. 1998, IAU Cire. No. 6851) at R = 21.7 discovered 0.5 days after burst at a 8h36m34.28s, 8 -18°51'23.9" (Groot, P.J. et al. 1998, IAU Cire. No. 6852) GRB1156+652 (Heise, J. et al. 1997, IAU Circ. No. 6787) at I = 21.2 discovered 0.5 days after burst at a 11 h56m26.4s, .5 +65°12'00.5" (Halpern, J. et al. 1997, IAU Circ. No. 6788) and red-shifted emission lines observed with z = 3.4 (Kulkarni, S. et al. 1998, Nature, 393, 35) GBS1257+592 (Piro. L. et al. 1997, IAU Cire. No. 6797) at R = 19.5 discovered 0.6 days after burst at a 12h57m 1O.6s, .5 +59°24'43" (Castro-Trrado, A.J. et al. 1997, IAU Circ. No. 6800) eNo fading optical sourees were observed for GBS0026-630 (in't Zand, J. et al. 1998, IAU Cire. No. 6805) with I < 21 (Sahu, K.C., & Sterken, C. 1998,lAU Cire. No. 6808) GBS1450-693 (Piro. L. et al. 1997, IAU Circ. No. 6617) with V < 22.5 (Pedersen, H. et al. 1997, IAU Circ. No. 6628) GBS1528+196 (in't Zand, J. et al. 1997, IAU Cire. No. 6569) with R < 22.6 (Castro-Trrado, A.J. et al. 1997, IAU Circ. No. 6598) GBS1808+593 (Murakami, T. et al. 1997, IAU Cire. No. 6732) with R < 24.5 (Odewahn, S.C. et al. 1997, IAU Circ. No. 6735) 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 225 Table 10.8. y -Ray burst propenies. a Property Observed values Energy range ~ Comments References "Soft" Repeating Bursts 1 keV-l MeV y-yopacity constraints with E 2: 25 keY Redshifted e- e+ Annihilation radiation [ 1] Energy spectra rf>(hv) ex exp(-hv/E) Emission features ~ Rise times Size < 60km [3] Durations As short as 0.2 ms ~ 1O-2_~ 102 s Periodicity 8.0 s ~23ms Burst GB790305b Burst GB790305b [3,4] [5] Source Off-center in Supernova remnants high-velocity neutron stars? [6] Energy range ~ Energy spectra rf>(hv) rf>(hv) 430keV [1] [2] [1] "Classical" Bursts Eo 1 keV-20 GeV ~ (hv)S (hv)S 50-1000 keY ~ ~ y-yopacity constraints with s :5 -1 for (hv)S < Eo with s :5 -2 for (hv)S > Eo [7] [9] [8] Absorption features 20-50keV Cyclotron absorption ~ few 10 12 G fields Rise times As short as 0.2 ms ~ 1O-2_~ 104 s Size < 60km (V/Vmax ) (cos8) Galactocentric angle 8 0.33 ±0.01 Spatially nonuniform [ 11] -0.01 ±0.02 Isotropic [11] Source Optical transient and host galaxies? for several bursts at z ~ 0.8-3.4 Durations [10] [7] =0 [12] [12] Note aFor general reviews, see also Higdon, J.c., & Lingenfelter, R.E. 1990, ARA&A, 28, 401; Harding, A.K. 1991, Phys. Rep., 206, 327; Fishman, GJ., & Meegan, C.A. 1995, ARA&A, 33, 415; Rothschild, R.E., & Lingenfelter, R.E. 1995, High Velocity Neutron Star and Gamma-Ray Bursts (American Institute of Physics, New York) 282 pp.; Kouveliotou, C., Briggs, M.E, & Fishman, GJ. 1996, Gamma-Ray Bursts (American Institute of Physics, New York) 1008 pp. References 1. Mazets, E.P. et al. 1981, Ap&SS, SO, 1; Mazets, E.P., & Golenetski, S.V. 1981, Ap&SpPhysRev, 1,205; Mazets, E.P. et al. 1982,Ap&SS, 82, 261; Atteia, J.L. et al. 1987,ApJ, 320, Ll05; Laros, J.G. et al. 1987, ApJ, 320, L111; Murakami, T. et al. 1994, Nature, 368, 127 2. Mazets, E.P. et al. 1982, Ap&SS, 84, 173 3. Cline, T.L. et al. 1980, ApJ, 237, LI 4. Mazets, E.P. et al. 1979, Nature, 282, 587; Barat, C. et al. 1979, A&A, 79, L24 5. Barat, C. et al. 1983, A&A, 126,400 6. Rothschild, R.E., & Lingenfelter, R.E. 1995, High Velocity Neutron Star and Gamma-Ray Bursts (American Institute of Physics, New York) 282 pp.; and previous Table 10.7 7. Mazets, E.P. et aJ. 1981, Ap&SS, SO, 1; Mazets, E.P., & Golenetski, S.V. 1981, Ap&SpPhysRev, 1,205; Meegan, C.A. et al. 1996, ApJS, 106,65; Hurley, K. et al. 1979, Nature, 372, 652 8. Mazets, E.P. et al. 1981, Ap&SS, SO, 1; Band, D. et al. 1993, ApJ, 413, 281; Higdon, J.c., & Lingenfelter, R.E. 1986, ApJ, 307, 197 9. Murakami, T. et al. 1988, Nature, 335, 234; Mazets, E.P. et al. 1982, Ap&SS, 82, 261; Hueter, GJ. 1987, Ph.D. thesis, University of California, San Diego 10. Walker, K.c., & Schaefer, B.E. 1998, "Gamma Ray Bursts," AlP Conf. Proc., 428, edited by C. 226 / 10 y-RAY AND NEUTRINO ASTRONOMY Meegan. R. Preece. and T. Kashut (AlP. New York) p. 34 11. Meegan. C.A. et aI. 1996. ApJS. 106. 65 12. See previous Table 10.7 Table 10.9. Extragalactic hard X-ray or y-ray sources. a Source name Object type NGC253 0045-255 Starburst galaxy 4C+15.05 0202+149 0208-512 ab 8 Z de Fluxd Energy Lum. e 11.27 -25.56 0.6 0.0036 2 x 10-3 100keV 5 x 1046 [1] QSO blazar 30.53 +15.00 0.833 3.25 3 x 1O- ge 100 MeV 1 x l(f7 [2] QSO blazar 32.24 -51.25 1.003 6.0 5x 7x 1x 1x 2x 10-8 10-9 10-9 10- 10 10- 11 30 MeV 100 MeV 300 MeV lOeV 30eV 3x 5x 6x 7x 1x 1048 [3] [3] [3] [3] [3] 100 MeV 1 x 1046 [4] l(f7 l(f7 l(f7 l(f7 Refs. 3C66A 0219+428 BLLac 34.88 +42.81 0.833 3.25 1 x 10-91 4C+28.07 0234+285 BLLac 38.73 +28.59 1.213 3.97 3 x 10-91 100 MeV 3 x 1047 [4] 0235+164 BLLac 38.97 +16.40 0.94 5.6 2x 6x 8x 8x 1x 10- 8 10-9 10- 10 10- 11 10- 11 50 MeV 100 MeV 300 MeV lOeV 30eV 3 4 4 5 6 1047 1047 1047 1047 1047 [5] [5] [5] [5] [5] NGC 1275 0316+413 Seyfert-2 49.12 +41.33 0.0172 0.10 2 x 10- 1 3 x 10- 2 5 x 10- 3 30keV 100 keY 300keV 3 x 1044 6 x 1044 1 x 1045 [6] [6] [6] crA26 0336-019 QSO blazar 54.25 -1.94 0.852 3.29 1 x 10-81 100 MeV 5 x 1048 [4] 3C 111 0415+379 Seyfert-l 63.75 +37.90 0.0485 0.283 3 x 10-31 lookeV 5 x 1044 [7] OA 129 0420-014 QSO blazar 65.18 -1.46 0.915 5.5 4 x 10-91 100 MeV 2 x 1047 [2] 3C 120 0433+052 Seyfert-l 67.63 +5.25 0.0330 0.194 3 x 10-31 l00keV 2 x 1044 [7] NRA0190 0440-003 QSO blazar 70.02 -0.39 0.844 3.27 9 x 10-91 100 MeV 4 x 1047 [4] 0454-463 QSO 73.60 -46.34 0.86 5.2 3 x 10-91 100 MeV 1 x 1047 [2] 4C-02.19 0458-020 QSO blazar 74.67 -2.06 2.286 4.98 3 x 10-91 100 MeV 1 x 1048 [4] 0521-365 BLLac 81.00 -36.49 0.055 0.32 2 x 10-91 100 MeV 4 x 1044 [4] x x x x x 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / Table 10.9. (Continued.) Source name Object type Olb 8 z de 0528+134 QSO blazar 82.03 +31.50 2.06 12.4 0537-441 BLLac 84.34 -44.11 MCG 8-11-11 0551+464 Seyfert-I 87.79 +46.43 0716+714 BLLac 109.05 +71.44 OI 158 0735+178 BLLac 113.81 +17.82 0827+243 QSO blazar OJ 49 0829+046 Energy Lum. e 10-7 10- 8 10-9 10- 11 10- 12 30 MeV 100 MeV 300 MeV lGeV 3GeV 8x 6x 3x 1x 8x 1048 1048 1048 1047 [8] [8] [8] [8] [8] 0.894 5.4 2 x 10-9 2 x 10- 10 2 x 10- 11 100 MeV 300 MeV 1 GeV 1 x 1047 1 x 1047 1 x 1047 [9] [9] [9] 0.0205 0.12 2 6 2 6 3 30keV l00keV 300keV 1 MeV 10 MeV 5x 2x 5x 2x 1x 1044 1045 1045 1046 1046 [10] [10] [10] [10] [10] F1uxd 3x 2x 1x 4x 3x x x x x x 10- 1 10- 2 10- 2 10- 3 10-5 ur8 Refs. 2 x 10-9 100 MeV 0.424 2.04 3 x 1O- 9j 100 MeV 4 x 1046 [4] 127.80 +24.05 2.046 4.83 7 x 1O-9j 100 MeV 2 x 1048 [4] BLLac 127.30 +4.66 0.18 0.98 2 x 1O- 9j 100 MeV 5 x 1045 [4] 4C+71.07 0836+710 QSO blazar 129.09 +71.07 2.172 4.92 3 x 1O-9j 100 MeV 1 x 1048 [2] 0917+449 QSO blazar 139.43 +44.91 2.18 4.51 3 x 1O-9j 100 MeV 1 x 1048 [4] MCG -5-23-16 0945-307 Seyfert-2 146.37 -30.72 0.0485 0.283 4 x 1O- 3j lOOkeV 2 x 1043 [7] 4C+55.17 0954+556 QSO blazar 148.56 +55.62 0.909 3.42 5 x 1O-9j 100 MeV 3 x 1047 [4] 0954+658 BLLac 148.74 +65.80 0.368 1.82 2 x 1O- 9j 100 MeV I x 1046 [4] MRK421 1101+384 BLLac 165.42 +38.48 0.0308 0.18 1x 4x 7x 2x 2x 2x 2x 3x 10- 1 10- 2 10-9 10-9 10- 10 10- 11 10- 12 10- 17 j 30keV lOOkeV 50 MeV 100 MeV 300 MeV 1 GeV 3GeV 500GeV 6x 3x I x I x 1x 1x 1x 5x 1044 1045 1044 1044 1044 1044 1044 1043 [11] [11] 2 x 1O- 8j 100 MeV 7 x 1047 [4] 4C+29.45 1156+295 QSO blazar 179.24 +29.52 0.729 2.99 [2] [12] [12] [12] [12] [12] [13] 227 228 / 10 y-RAY AND NEUTRINO ASTRONOMY Table 10.9. (Continued.) Source name Object type NGC4151 1208+396 Seyfert-l WComae 1219+285 ab Z de FJuxd 182.00 +39.68 0.003 0.018 2x 5x 1x 8x BLLac 184.76 +28.51 0.102 0.58 4C+21.35 1222+216 QSO blazar 185.60 +21.66 NGC4388 1223+126 Seyfert-2 185.81 +12.94 3C273 1226+023 QSO 1227+023 Energy Lum. e 30keV 100 keY 300keV 1 MeV 1x 3x 6x 5x 1043 1043 1043 1044 [I 4] [14] [14] [14] 5 x 10-91 100 MeV 4 x 1045 [4] 0.435 2.08 5 x 10-91 100 MeV 7 x 1046 [4] 0.00842 0.051 6 x 10- 31 100 keY 3 x 1043 [7] 186.64 +2.33 0.158 0.95 1x 1x 5x 2x 2x 2x 2x 1x 1x 3x 30keV l00keV 300keV 1 MeV 3 MeV 10 MeV 30 MeV 100 MeV 300 MeV lGeV 2 2 8 3 3 3 3 2 2 5 [15] [I5] [16] [17] [17] [17] [17] [17] [17] [17] QSO 186.83 +2.41 0.57 3.4 3 x 10- 1 2 x 10-2 40keV l00keV 1 x 1048 5 x 1047 [18, 19] [18, 19] 4C-02.55 1229-021 QSO blazar 187.36 -2.13 1.045 3.68 2 x 10-91 100 MeV 1 x 1047 [4] M87 1228+124 NELG 187.08 +12.67 (0.0042) 0.025 1 x 10- 1 6 x 10- 3 30keV l00keV 1 x 1043 7 x 1042 [20] [20] 3C279 1253-055 QSO 193.40 -5.52 0.538 3.2 2x 3x 2x 2x 3x 3x 4x 4x 3 MeV 10 MeV 30 MeV 100 MeV 300 MeV 1 GeV 3GeV IOGeV 4 6 4 4 5 6 7 8 1047 1047 1047 1047 1047 1047 1047 1047 [17] [17] [21] [21] [21] [21] [21] [21] XComae 1257+286 Seyfert-l 194.49 +28.67 0.092 0.55 2 x 10- 1 3 x 10- 2 30keV l00keV 1 x 1046 2 x 1046 [22] [22] 1313-333 QSO blazar 198.33 -33.39 1.21 3.96 2 x 10-91 100 MeV 3 x 1047 [4] CenA 1322-427 Radio galaxy 200.74 -42.71 (0.001825) 0.0073 1x 1x 2x 2x 7x 30keV l00keV 300keV 1 MeV 10 MeV 1x 1x 2x 2x 7x 1043 1043 1043 1043 1043 [23] [23] [23] [24] [24] OP 151 1331+170 QSO blazar 202.79 +17.07 100 MeV 3 x 1047 [4] 8 2.084 4.86 10- 1 10-2 10-2 10- 3 10- 1 10- 2 10- 3 10-4 10-5 10-6 10-7 10- 8 10-9 10- 11 10- 5 10-6 10-7 10-8 10-9 10- 10 10- 11 10- 12 10° 10- 1 10- 2 10- 3 10-5 1 x 10-91 x x x x x x x x x x x x x x x x x x 1046 1046 1046 1046 1046 1046 1046 1046 1046 1045 Refs. 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / Table 10.9. (Continued.) Source name Object type MCG -6-30-15 1314-340 Seyfert-l IC4329A 1346-300 ab z de Fluxd Energy Lum. e 203.26 -34.04 0.00775 0.048 5 x 1O- 3j l00keV 2 x 1(j43 [7] Seyfert-l 206.62 -30.06 0.01605 0.094 7 x 1O- 3j l00keV 1 x 1<J"4 [7] MRK279 1348+700 Seyfert-l 207.97 +69.55 0.0294 0.175 3 x 1O- 3j l00keV 2 x 1<J"4 [7] OQ-OIO 1406-076 QSO blazar 211.58 -7.64 1.494 4.34 1 x 1O-8j 100 MeV 2 x 1048 [4] NGC5548 1415+255 Seyfert-l 214.50 +25.14 0.0168 0.100 4 x 1O- 3j 100 keY 8 x 1043 [7] 1424-418 QSO blazar 216.00 +41.80 1.522 4.37 6 x 1O-9j 100 MeV 1 x 1048 [4] OR-017 1510-089 QSO blazar 227.54 -8.91 0.361 1.79 5 x 1O-9j 100 MeV 5 x 1046 [4] 4C+15.54 1604+159 BLLac 241.21 +15.99 0.357 1.78 4 x 1O-9j 100 MeV 4 x 1046 [4] OS 319 1611+343 QSO blazar 242.95 +34.34 1.401 4.23 7 x 1O- 9j 100 MeV 1 x 1048 [4] 1622-253 QSO blazar 245.68 -25.35 0.786 3.14 7 x 1O-9j 100 MeV 3 x 1047 [4] 1622-297 QSO blazar 246.36 -29.92 0.815 3.21 3 x 1O- 8j 100 MeV 1 x 1048 [4] 4C 38.41 1633+382 QSO 248.38 +38.24 1.814 10.9 10- 8 10-9 10- 10 10- 11 10- 11 10- 12 50 MeV 100 MeV 300 MeV lGeV 3GeV IOGeV 1x 1x 1x 2x 2x 2x 1048 1048 1048 1048 1048 1048 [25] [25] [25] [25] [25] [25] NRA0530 1730-130 QSO blazar 262.56 -13.05 0.902 3.40 1 x 1O- 8e 100 MeV 6 x 1047 [4] 4C+51.37 1739+522 QSO blazar 264.87 +52.22 1.375 4.19 4 x 1O-9j 100 MeV 5 x 1047 [4] ar-68 1741-038 QSO blazar 265.34 -3.81 1.054 3.70 4 x 1O-9j 100 MeV 3 x 1047 [4] 3C 390.3 1845+797 Seyfert-I 281.41 +79.75 0.0561 0.326 3 x 1O- 3j l00keV 7 x 1<J"4 [7] 1933-400 QSO blazar 293.46 -40.08 0.966 3.53 1 x 1O-8j 100 MeV 7 x 1047 [4] NGC 6814 1942-102 Seyfert-l 295.67 -10.32 0.00521 0.030 3 x 1O- 3 j 100 keY 6 x 1042 [7] NRA0629 2022-077 QSO blazar 305.75 -7.76 1.388 4.21 7 x 1O-9j 100 MeV 9 x 1047 [4] 8 2x 6x 7x 8x 1x 1x Refs. 229 230 / 10 y-RAY AND NEUTRINO ASTRONOMY Table 10.9. (Continued.) Source name Object type MRK509 2041-107 Seyfert-I 2052-474 ab z dC Fluxd Energy Lum. e 310.36 -10.91 0.0344 0.203 4 x 10-31 100 keY 3 x 10« [7] QSO blazar 314.52 -46.96 1.489 4.33 3 x 10-91 100 MeV 5 x Hf7 [4] 2155-304 BLLac 328.99 -30.47 0.116 0.655 3 x 10-91 100 MeV 3 x 1045 [4] BLLacertae 2200+420 BLLac 330.16 +42.04 0.0686 0.398 4 x 10-91 100 MeV I x 1045 [4] 2209+236 QSO blazar 332.51 +23.97 1.489 4.33 I x 10-91 100 MeV 2 x 1047 [4] CTA 102 2230+114 QSO 337.53 +11.47 1.037 6.2 4 x 10-9 100 MeV 3 x 1047 [2] 3CR454.3 2251+158 QSO 342.87 +15.88 0.859 5.2 8 x 10-9 100 MeV 4 x 1047 [2] NGC7582 2318-422 Seyfert-2 344.18 -43.23 0.00525 0.033 3 x 10- 31 lOOkeV 6 x 1042 [7] OZ 193 QSO blazar 359.05 +19.64 1.066 3.72 3 x 10- 91 100 MeV 2 x 1047 [4] 2356+196 8 Diffuse background 5 2 I I I 2 x x x x x x IO I /sr lOo/sr IO- I /sr 1O- 2/sr 1O-4/sr 1O-7/sr Refs. [26] [26] [26] [26] [26] [26] 30keV 100 keY 300keV I MeV 10 MeV 100 MeV Notes a Source type, position, and redshiftare from Hewitt, A., & Burbidge, G. 1987,ApJS, 63, I; 1989,ApJS, 69, I; and 1991, ApJS, 75, 297, except for M87 and Cen A from Tully, R. 1988, Nearby Galaxies Catalog (Cambridge University Press, Cambridge) for which the redshifts are corrected for local motion, and for GRS1227+0229 from Grindlay, I.E. 1993,A&AS, 97,113. bPositions in degrees. CDistances in Gpc assume cosmological redshifts with HO = 50 kmls Mpc. d (Gpc) =6 x (I+Z)~-1 (l+z) +1 dFlux in photonslcm2 s MeV at the energy denoted. e Assuming isotropic emission, E2 x (flux) = E2 (keV2) x z2 x [flux (phot./cm)2 sMeV] x 7 x 1045 ergs/sin E. 1 Differential flux determined from integral flux assuming a differential spectrum of the form E- 2 . References I. Bhattacharya, D. et aI. 1992,AlP Conf. Proc., 280, 498 2. Fichtel, C.E. et aI. 1992, AlP Conj. Proc., 280, 461 3. Bertsch, D.L. et aI. 1993, ApJ, 405, L21 4. Hartman, R.C. et aI. 1997, AlP Conf. Proc., 410,307 5. Hunter, S.D. et al. 1992, A&A, 272,59 6. Rothschild, R.E. et aI. 1981, ApJ, 243, L9 7. Kurfess, I.D. et aI. 1995, NATO ASI Series C, 461, 233 8. Hunter, S.D. et aI. 1993, ApJ, 409, 134 9. Thompson, D.L. et aI. 1992, ApJ, 410, 87 10. Perotti, F. et aI. 1981, Nature, 292,133 II. Ubertini, P. et aI. 1984, ApJ, 284, 54 12. Lin, Y.C. et aI. 1993, ApJ, 401, L61 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 231 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. Punch, M. et al. 1992, Nature, 358, 477 Perotti, E et al. 1981, Api, 247, L63 Primini, EA. et al. 1979, Nature, 278,234 Bassani, L. et al. 1991, 22nd Int. Cosmic Ray Can!, 1, 173 Hermsen, W. et al. 1993, A&AS, 97, 97 Bassani, L. et al. 1991, 22nd Int. Cosmic Ray Conf., 1, 173 Grindlay, J.E. 1993, A&AS, 97, 113 Lea, S. et al. 1981, Api, 246, 369 Kniffen, D.A. et al. 1993, Api, 411,133 Bazzano, A. et al. 1990, Api, 362, L51 Baity, W.A. et al. 1981, Api, 244, 429 von Ballmoos, P. et al. 1987, Api, 312, 134 Mattox, J.R. et a1. 1993, Api, 410, 609 Rothschild, R.E. et al. 1983, Api, 269, 423 Table 10.10. Hard X-ray and y-ray instruments in space since 1970. Energy range tl.E/E Field of view resolution Area (cm2 ) Date OSO-7 6-500keV 33% @6OkeV 6.5° 64 1971-73 Peterson UCSD [ 1] Solar X-ray telescope OSO-7 10-350keV 18% @6OkeV 90° x 20° 9.6 1971-73 Peterson UCSD [2] y-ray monitor OSO-7 0.3-10 MeV < 8%@662keV 120° x 70° 45 1971-73 Chupp UNH [3] y-ray telescope SAS-2 30-200 MeV 30° ~ 2° 115 1972-73 Fichtel GSFC [4] Scintillator telescope Ariel-V 26 keV-1.2 MeV 30% @662keV 8° 8 1974--80 Imperial College [5] Celestial X-ray detector y-ray detector OSO-8 15 keV-3 MeV 50% @6OkeV 50MeV-2GeV 40% @ 100 MeV 5° 28 1975-78 [6] 75 1975-82 Frost GSFC Caravane Collaboration A-4LED HEAO-I 15-180keV 25%@6OkeV 1.2° x 20° 206 1977-79 Peterson-Lewin UCSD-MIT [8] A-4MED HEAO-l 0.1-2 MeV 10% @ 1 MeV 16.5° 160 1977-79 Peterson UCSD A-4HED HEAO-l 0.2-10 MeV 1O%@ 1 MeV 40° 120 1977-79 Peterson UCSD C-I germanium spectrometer HEAO-3 50 keV-I0 MeV 0.2% @ 1.8 MeV 30° 64 1979-80 Jacobson JPL [9] GRS SMM 0.3-9 MeV 7%@662keV 180° 310 1979-89 Chupp UNH [10] HXRBS SMM 20-26OkeV 30% @ 122keV 40° 71 1979-89 Frost GSFC [11] HEXE MIR KVANT 15-200keV 30% @6OkeV 1.6° x 1.6° 800 1987- Trumper MPI [12] Pulsar X-I KVANT 50-800keV 3° x 3° 1256 1987- [13] GSPC KVANT 3-100 keY 3%@6OkeV 2.3° ~ Sunyaev IKI Schnopper SRL Instrument Mission Cosmic X-ray telescope ~50% COS-B ~ ~ 30° 1° 150 1987- PI institution Refs. [7] [l4] 232 / 10 y-RAY AND NEUTRINO ASTRONOMY Table 10.10. (Continued.) PI institution Energy range t:.EjE Field of view resolution Area (cm2) Date GRANAT 30 keV-1.3 MeV 8% @511keV 4.7 0 x 4.3 0 0.20 797 1989- Paul-Mandrou CESR-Saclay [15] WATCH GRANAT ~180KeV 4 sr 30 1989- Lund DSRI [l6] ART-P GRANAT 4-100keV 14% @60keV 1.80 x 1.80 0.10 2520 1989- Sunyaev JKI [17] ART-S GRANAT 3-IOOkeV ll% @60keV 2.10 x 2.10 800 1989- Sunyaev IKI [l7] BATSE occultation CGRO 20 keV-1.8 MeV 30%@88keV 211" sr 10 1800 1991- Fishman MSFC [18] OSSE CGRO 50keV-IOMeV 8% @511keV 3.80 x 11.40 2620 1991- Kurfess NRL [19] COMPTEL CGRO 0.8-30 MeV 9%@ 1.3 MeV - I sr - 1.50 45 1991- Schonfelder MPJ [20] EGRET CGRO 20 MeV-30 GeV - 20% 0.1-5 GeV _400 1600 1991- Fichtel GSFC [21] O.lo~.40 1600 1995- Rothschild UCSD [22] 800 199~ Instrument Mission SIGMA HEXTE RXTE 15 KeV-250 KeV 15%@60keV PDS BeppoSAX 15 KeV-300 KeV - 15%60keV _ 10 - 1.40 Refs. [22] TeSRF1IAS References l. Peterson, L.E. 1972, IAU Symp. No. 55,51 2. Harrington, T. et al. 1972, IEEE Trans. NucL Sci., NS-19, 596 3. Higbie, P.R. et al. 1972, IEEE Trans. Nucl. Sci., NS-19, 606 4. Derdeyn, S. et al. 1972, NucL Instrum. Metlwds, 98, 557 5. Engel, A.R., & Coe, MJ. 1977, Space Sci.lnstrum., 3, 407 6. Dennis, B.R. et al. 1977, Space Sci. Instrum., 3, 325 7. Bignami, G.F. et al. 1975, Space Sci. Instrum., 1, 245 8. Jung, G.V. 1989, ApJ, 338, 972; Knight, F.K. 1982, ApJ, 260, 538 9. Mahoney, W.A. et al. 1980, Nucl.lnstrum. Methods,178, 363 10. Forrest, D.J. et al. 1980, Solar Phys., 65, 15 11. Orwig, L. et al. 1980, Solar Phys., 65, 25 12. Reppin, C. et al. 1985, in Nonthermal and Very High Temperature Phenomena in X-ray Astronomy, edited by G.C. Perola and M. Salvati (Instituto Astronomico, Roma) p. 279 13. Sunyaev, R. et al. 1990, Adv. Space Sci., 10,41 14. Smith, A. 1985, in Nonthermal and Very High Temperature Phenomena in X-ray Astronomy, edited by G.c. Perola and M. Salvati (lnstituto Astronomico, Roma) p. 271 15. Paul, J.A. et al. 1991, Adv. Space Res., 11, (8) 289 16. Lund, N. 1991, Adv. Space Res., 11, (8) 17 17. Sunyaev, R. et al. 1990, Adv. Space Res., 10, (2) 233 18. Fishman, G.J. et al. 1992, NASA Conj. Publ. 3137,26 19. Kurfess, J.D. et al. 1991, Adv. Space Res., 11, (8) 323 20. Schonfelder, V. 1991, Adv. Space Sci., 11, (8) 313 21. Kanbach, G. et al. 1988, Space Sci.lnstrum., 49, 69 22. Rothschild, R.E. et al. 1998, ApJ, 496, 538 23. Frontera, F. et al. 1997, A&AS, 122,357 10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / Table 10.11. y -Ray burst instruments. Trigger Satellite Dates Orbit" Detectors Energy range (MeV) Time resolution (s) Time (s) Energy (MeV) Refs. 0.2-1 ::: 0.016 0.25. 1.5 0.0341.1.5 [I] Vela 5AlB Vela6AIB 5/69-3/84 GC &-10 em3 CsI Helios-2 In&-I2f79 H 21.5 em3 CsI > 0.1 ::: 0.004 0.004 0.032 0.250 > 0.1 [2] Solrad-II AlB 4n&-6n7 GC 2-43 em3 CsI 0.2-2 ::: 0.0003 0.625 0.2-2 [3] Signe-3 6n7-3n8 GC 950 em2 CsIb > 0.06 0.008 0.1-1.6 0.03--6 0.000 5-0.02 ::: 0.05 0.32 0.1 ~ HEAO-I 8n7-2f79 GC 2000 em2 CsIb 280em2 NaI 3300em2 PC Prognoz-6 9n7-3n8 G 63 em2 NaI 750 em2 CsIb 16 em3 NaI 0.08-1 > 0.3 0.02-> 0.3 ::: 0.002 4 0.25 ICE 8n8-3/87 H 22em2 NaI 0.D2-1.25 ::: 0.004 35 em3 Ge 0.2-3 0.001 V 2-36em 3 NaI 0.1-2 ::: 0.012 2~3em3 NaI &-50em2 NaI 0.1-2.5 0.03-2 (ISEE-3) PVO 5n8-9/92 [4] 0.3 0.13-1.7 [5] [5] [6] 0.02 0.0841.4 [7] [7] [7] 0.000250.008 0.000 130.001 0.132-1.25 [8] 0.2-3 [9] 0.25, 1,4 0.1-2 [10] > 0.002 ::: 0.016 0.02 0.25, 1.5 0.0841.4 0.0541.15 [11] [12] Venera 11/12 (Konus) 9n8-1/80 H Prognoz-7 Iln8~9 G 63 em2 NaI 750 em2 Cslb 0.1-2.5 > 0.1 ::: 0.002 0.002 0.25 0.0841.4 [7] [7] Venera 13114 (Konus) 11/81-4183 H 2~3 em2 NaI &-50em2 NaI 0.05-1 0.03-2 ::: 0.002 ::: 0.004 0.25 0.25,1.5 0.0841.4 0.0541.15 [11] Prognoz-9 7/83-2/84 G 2-178 em2 NaI 0.04-8 ::: 0.016 0.5,2 0.07341.966 [14] Ginga 2/87-11/91 GC 6Oem2 NaI 63em2 PC 0.0 I 44l.40 0.0024).030 0.031 0.031 0.25, 1,4 1,4 0.01441.4 0.00241.03 [15] [15] GRANAT -SIGMA -SIGMA -WATCH -Konus-B -Phebus 12/89- G 800em2 NaI 8-2400 em2 CsI 4-30 em2 NaI/CsI &-314 em2 NaI &-573 em3 BOO 0.03-2 0.1-1 0.00&-0.18 0.Dl-8 0.1-100 ::: 0.000008 ::: 0.000 I 0.002 ::: 0.00003 0.25,2 0.25,2 0.004-32 0.25,1.5 0.008 0.03-2 0.1-1 0.00&-0.18 0.0541.2 0.075-1.6 [16] [16] [17] [18] [19] Ulysses 11190- H 41 em2 CsI 0.0154).150 ::: 0.008 0.125-4.0 0.01541.150 [20] Compton GRO BATSE-LAD BATSE-SD 4/91- GC 8-2025 em2 NaI 8-127 em2 NaI 0.03-1.9 0.Dl5-11O ::: 0.000002 0.000 128 0.06, 0.25, I 0.0&-0.3 [21] [21] BeppoSAX WFC 4/9&- 2-250em2 Xe 0.0024).028 0.0005 0.00241.028 [22] 12/89-2190 GC Notes aG, geocentric; GC, geocentric circular; H, heliocentric; V: venuscentric. b Anticoincidence shield used as burst detector, References I. Kiebesadel, RW, et ai, 1973, ApJ, 182, L85 2. Cline, T.L. et aI. 1979, ApJ, 229, IA7 3. Laros, J.G. et aI. 1977, Nature, 267,131 [13] 233 234 I 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14. 10 y-RAY AND NEUTRINO ASTRONOMY Chambon. G. et al. 1979. X-Ray Astronomy (Pergamon. Oxford). p. 509 Hueter. G.J. 1987. Ph.D. thesis. University of California, San Diego VVood.~S.etal. 1984.~S.S6.507 Chambon. G. et al. 1979. Space Sci.lnstrum.. 5. 73 Anderson, R.D. et al. 1978. IEEE Trons.• GE-16. 157 Teegarden. B .• & Cline. T.L. 1980. Api. 236. 1.67 Klebesadel. R.VV. et al. 1980. IEEE Trons.• GE-18. 76 Barat. C. et al. 1981. Space Sci. Instrum.. 5. 229 Mazets. E.P. et al. 1981. Ap&:SS. 80. 3 Mazets. E.P. et al. 1983. AlP Conf. Proc. No. 101. 36 Boer. M. et al. 1986. Adv. Space Sci.• 6. 97 15.M~. T.etal. 1989.P~.41.405 16. Guerry. H. et al. 1986. Adv. Space Sci.. 6. 103 17. Brandt. S. et al. 1990. Adv. Space Sci.• 10. 239 18. Golenetskii. S.V. et al. 1991. Adv. Space Sci.• 11. 125 19. Terekhov. o. et al. 1991. Adv. Space Sci.. 11. 129 20. Hurley. K. et al. 1992. A&ASS. 92.401 21. Fishman, G.J. et al. 1989. Proc. Gamma Ray Observatory Sci. Workshop. 2-39 22. Jager. R. et al. 1997. A&AS. 125, 557 Table 10.12. Very-high-energy and ultrahigh-energy y-ray experiments: Atmospheric Cherenkov and particle arrays.a Array Country Lat. (deg) Long. (deg) Elev. (kID) Themis Albuquerque Mt. Hopkins Narrabri Haleakala Pachmarchi Gulmarg Potchefstroom White Cliffs Crimea Beijing Plateau Rosa Gran Sasso TIbet TienShan Ooty Mt. Hopkins La Palma Mt. Aragats South Pole Mt. Norikura Dugway Mt. Chacaltaya Cygnus Baksan Kolar Haverah Park AkenoRanch Moscow Buckland Park Janzos France USA USA Australia USA India India South Africa Australia Ukraine China Italy Italy China Kirghiz India USA Spain Armenia Antarctica Japan USA Bolivia USA Kab-Ba1kar India UK Japan Russia Australia New Zealand 43N 35N 32N 31S 21N 23N 35N 27S 32S 45N 40N 46N 42N 30N 42N 11N 32N 29N 40N 90S 36N 40N 16S 36N 43N 13N 54N 35N 56N 35S 41N IVV 107VV 111W 145E 156W 78E 77E 27E 143E 34E 117E 8E 14E 90E 75E 77E l11W 18VV 44E OW 137E 112W 68W I06VV 43E 78E lW 138E 37E 138VV 172E 1.5 1.5 2.3 0.21 3.0 Area (104 rn2) 1.1 2.7 1.4 0.16 0.6 1.0 3.5 2.0 4.2 3.3 2.2 2.3 2.2 3.2 2.5 2.8 1.5 5.2 2.1 1.7 0.9 0 0.9 0 0 0.9 3.5 1 10 2.0 0.5 0.5 -0.5 4 -1 =s1 - 2125 >0.5 >8 0.5 1.66 > 1 -1 1.0 > 0.23 Threshold (TeV) 0.1 0.2 0.3 0.3 0.5 0.5 1 1 1 1 1 10 10 10 100 100 100 100 100 100 100 100 200 200 300 500 500 1000 1000 1000 1000 a9 (deg) 0.1 1.4 5.5 1 0.8 3 3 1 1 1 1 1 0.5-1 1-3 1 1.5 1.5 1 3 3 2.5 2 Began 1986 1986 1983 1986 1985 1987 1985 1985 1986 1986 1987 1981 1988 1990 1974 1984 1985 1986 1987 1988 1988 1989 1986 1986 1984 1984 1986 1981 1982 1984 1988 Note aBased on Weekes, T.C. 1988. Phys. Rep.• 160,1; Yodh. G. 1992. private communication; and Stepanian. A.A. 1992. private communication. 10.5 NEUTRINOS IN ASTROPHYSICS / 235 10.5 NEUTRINOS IN ASTROPHYSICS by Wick C. Haxton Perhaps the original motivation for studying astrophysical neutrinos was the prospect of directly probing the interior of our Sun: neutrinos produced as a byproduct of nuclear fusion pass undistorted through the outer layers of the Sun, carrying in their flux and spectrum a detailed memory of the nuclear reactions that produced them. As the competition between the three cycles comprising the pp chain (the process that dominates solar burning of four protons into 4He) depends sensitively on the solar core temperature Te , one can deduce Te by measuring the various components of the solar neutrino flux. Results from the 37 Cl detector, which has operated for nearly 30 years, and from three more recent experiments, SAGE and GALLEX (radiochemical detectors containing 71Ga) and Kamioka IIIIII (an active water Cerenkov detector sensitive to higher energy solar neutrinos), have revealed some surprises. The results are consistent with a flux of high-energy 8B neutrinos reduced to about 50% of the standard solar model value and a greatly suppressed flux of neutrinos produced from electron capture on 7Be. This is a surprising pattern because a reduction in Te tends to suppress the 8B solar neutrino flux more than the 7Be flux, not less. In fact, detailed fits seem to show that the 7Be neutrinos must be completely absent to account the experimental results. One popular explanation for this puzzle is the phenomenon of neutrino oscillations: if neutrinos have nonzero masses and mix (so that the electron, muon, and tauon neutrinos are not identical to the mass eigenstates, but linear combinations of these), solar electron neutrinos can oscillate into muon neutrinos and escape detection. While once it was thought that neutrino oscillations would most likely produce only a small reduction in the solar electron neutrino flux, it was discovered about a decade ago that oscillation effects can be greatly enhanced within the Sun. This phenomenon, known as the Mikheyev-Smimov-Wolfenstein or MSW mechanism, arises because the effective masses of neutrinos change when the neutrinos pass through matter. The MSW solution that best reproduces the results of the 37 Cl, SAGEIGALLEX, and KamiokalIlIII experiments is consistent with oscillations of a very light electron neutrino into a muon neutrino with a mass of about 0.003 electron volts (eV). Two new detectors, SuperKamiokande and the Sudbury Neutrino Observatory (SNO), should be able to confirm or rule out neutrino oscillations as a solution to the solar neutrino problem. SuperKamiokande is an enormous (22.5 kiloton fiducial volume) Ultrapure water Cerenkov detector located in a Japanese mine. It began operations in the Spring of 1996. By making a precision measurement of the spectrum of recoil electrons following neutrino--electron scattering, the experimentalists hope to find subtle distortions characteristic of the MSW mechanism. SNO, which should be fully operational by the end of 1998, is a Canadian-US-UK detector located deep within a nickel mine in Sudbury, Ontario. The inner volume of this water Cerenkov detector contains heavy water. Reactions on the deuterium nuclei provide separate charged and neutral current signals. Thus, in addition to spectrum distortions, the experimentalists hope to measure directly the neutrinos of a different flavor that are generated by the MSW mechanism. SuperKamiokande, SNO, and similar detectors are sensitive to another source of neutrinos, those produced in the atmosphere by the interactions of cosmic rays impinging on the Earth. For some years most such detectors have found a puzzling result, an unexpected ratio of muon neutrino to electron neutrino events given our understanding of cosmic ray neutrino production. Very recently the SuperKamiokande group, by comparing upward- to downward-going neutrinos, have claimed that this anomaly is definitive evidence for neutrino oscillations and thus of massive neutrinos. Another source of neutrinos is associated with one of the most spectacular events in astrophysics, the sudden collapse of the core of a massive star. This collapse triggers the ejection of the star's mantle, producing the spectacular display known as a supernova. However 99% of the energy released in such 236 / 10 y-RAY AND NEUTRINO ASTRONOMY a collapse, an enormous 3 x 1053 ergs, is invisible optically as it is carried by an intense three-second burst of neutrinos emitted by the cooling protoneutron star forming at the star's center. We were extremely fortunate to have two large water Cerenkov detectors, Kamioka II and 1MB, operating at the time of Supernova 1987A. The free protons in water absorb electron antineutrinos, emitting relativistic positrons that can be detected readily in such detectors. In each detector approximately 10 events were detected from a star that collapsed in the Large Magellanic Cloud 150000 light years from earth. The characteristics of the detected neutrinos-the number of events, the spectrum, the duration of the neutrino pulse--were in good accord with supernova theory. There were no detectors operating that had the necessary characteristics and sensitivities to record the electron neutrinos or the muon and tauon neutrinos and antineutrinos. This was unfortunate because supernova electron neutrinos may hold the key to one of the central problems in cosmology, the dark matter. Studies on a variety of astrophysical scales-galaxies, clusters of galaxies, etc.-indicate that at least 90% of the mass in the Universe is dark, not emitting or absorbing electromagnetic radiation. Most estimates of the dark matter lead to a minimum mean density in the Universe of 20% of the closure density, the density that would keep the Universe from expanding forever. As the standard theory of big bang nucleosynthesis argues that at least some of this dark matter is nonbaryonic, massive neutrinos seem a natural explanation for this component. In partiCUlar, a heavy tauon neutrino with a mass of about 5-10 e V could comprise an important fraction of the dark matter and would also help to explain how galaxies and other structures in the Universe formed. Such a mass is quite consistent with a theoretical model for generating neutrino masses known as the seesaw mechanism. If the solar neutrino problem involves oscillations between the electron neutrino and a 0.003 eV muon neutrino, then the seesaw mechanism predicts that the tauon neutrino mass might be in the range required to explain large scale structure. How can one test the hypothesis of a tauon neutrino mass of a few eV? Just as the densities available in the Sun enhance oscillations between electron and muon neutrinos, the much larger densities found near the core of a supernova can enhance oscillations between electron neutrinos and massive tauon neutrinos. Because the tauon neutrinos emitted by a supernova tend to be substantially more energetic than supernova electron neutrinos, such oscillations would produce an anomalously energetic electron neutrino spectrum. Thus the detection of these electron neutrinos could demonstrate that massive tauon neutrinos make up an important component of the dark matter. As the standard model of electroweak interactions cannot accommodate massive neutrinos, such a discovery would also have a profound impact on particle physics. Neutrinos also play a crucial role in nuclear astrophysics. Arguments based on big-bang nucleosynthesis provided early evidence that there were only a few (three or four) light neutrino flavors, a result now beautifully confirmed by measurements of the width of the Zoo Neutrinos govern much of the nucleosynthesis that occurs in a supernova. For example, the process of rapid neutron capture, by which about half of the heavy elements and all of the transuranics are synthesized, is now believed to depend on conditions in the hot bubble that resides just above the surface of the protoneutron star. The entropy and neutron/proton ratio in this bubble are largely determined by neutrino interactions. Neutrinos also directly synthesize nuclei like 19F and 11 B by scattering off the neon and carbon in the mantle of the collapsing star. The subsequent supernova explosion is the mechanism by which these newly synthesized metals are ejected into the interstellar medium. Finally, there is an enormous density of very low energy neutrinos-about 300/cm3-throughout the Universe, a relic of the big bang similar to the background microwave photons. Recent precision measurements of the microwave background allow us to look backward to the time of recombination, when electrons condensed on nuclei to form neutral atoms, providing a snapshot of conditions in the early Universe, 100000 years after the big bang. Were we ever to find a method to detect the relic neutrinos, this would provide a probe of the Universe at the time the neutrinos decoupled from matter, early in the first minute in the history of the Universe. Detection of these relic neutrinos is likely to remain a challenge for many decades. 10.6 CURRENT NEUTRINO OBSERVATORIES / 237 10.6 CURRENT NEUTRINO OBSERVATORIES by Thomas J. Bowles Table 10.13 lists the existing neutrino observatories and a description of each one. Some of these are still under development. 'Illble 10.13. Existing 1II!utrino observatories. Detector Main aims" target Depth (mweY' Scnsorsc Detection techniques Remarks Antan:tica Hell 9000m2 1800-2400 Cerenkov Under development SN,HEII "'1000 LS HEII,NO 330 tons 250m2 140 ton 4000 LS One of the oldest IJIIdcqround neutrino observatories Experiment no longer in operation SN 100 ton ND,SN 150 ton 5000 NO,SN 90 ton 5000 NO,SN 912 ton 4850 AMANDA Baksan, Caucusus Russia Homestake Mine S. Dakota Artyomovsk Ukraine Mt. Blanc, Italy NUSEX Mt. Blanc, Italy LSD Frejus France Gran Sasso, Italy MACRO Gran Sasso, Italy LVD Greece NESTOR Hawaii DUMAND Lake Baikal, Siberia NT·200 Soudan, Minnesota SOUDAND Soudan, Minnesota MINOS Kolar Gold Fields (2) India Kamiokande ''Size'' of LS Plastic tubes in limited streamer mode LS Experiment no longer in operation Flasb chambers, Experiment no longer in operation Geiger tubes Experiment no longer in operation SN,HEII 3240m2 3800 LS, streamer tubes SN,HEII I 800 ton 3800 LS, streamer tubes HEll I x 104m2 3700 Cerenkov Under development HEll 2 x 104m2 4700 Cerenkov Under development HEll 500m2 1000 Cerenkov "NT' stands for neutrino telescope NO,HEII 1100 ton 7200 Honeycomb Iron calorimeter NO,HEII,LB drift chamber 10000 ton 7200 Honeycomb drift chamber Full operation began in 1996 Iron calorimeter Under development Experiment no longer in operation NO,HEII 140 ton 7200 NO,SN,HEII 4500 ton 2400 Proportional counters, calorimeter Cerenkov NO,SN, NEII,LB NO,SN,HEII 50000 ton 2400 Cerenkov HOOton 1580 Cerenkov Homcstake Mine, S. Dakota Homestake mine S. Dakota Baksan, Russia SAGE Gran Sasso, Italy Borexino sol 615 ton Radiochemical sol 100 tons sol 6OtonsGa 4900 (percbloretbylene) 4900 (Nal solution) 4815 sol 300 tons 3800 LS \Ix +e- ~ "'x +eDetects 7Be neutrinos Gran Sasso, Italy GALLEX Gran Sasso, Italy GNO Gran Sasso, Italy ICARUS sol 30tonsGa 3800 Radiochemical Detects p-p neutrinos sol 30 tons Ga 3800 Radiochemical Detects p-p neutrinos sol,NO,LB 1600 tons 3800 Liquid argon Operation began in 1998 TIDlC production chamber Under development Japan SuperKamiokande Japan IMB,Ohio Radiochemical Radiochemical Detected II. from SN I 987a Detects 8B neutrinos Experiment no longer in operation Detects 8B neutrinos Operational in 1996 Detected ". from SN I 987a Experiment no longer in operation 37Cl + ". -+ 37 Ar+.Detects 7Be and 8B neutrinos 1271 + II. -+ 127Xe +.Detects 7 Be and 8B neutrinos 710a+ II. -+ 37 Ar+.Detects p-p neutrinos Operational in 2001 Experiment completed in 1997 238 I 10 y-RAY AND NEUTRINO ASTRONOMY Table 10.13. (Continued.) Main "Size" of Depth SensorsC Detector aims" taIget (mwe)b Detection techniques Remarks Sudbury, Canada sol,SN Cerenkov v. +d ..... p + P +evx+d ..... n+p+vx vx+c + e- -+ Vx + ev.+d ..... n+n+e+ Operational in 1998 SNO Notes aSN, supernova bursts; ND, nucleon decay; HEv, high-energy neutrinos; sol, solar neutrinos; LB, long baseline experiment using an accelerator neutrino source. b mwe, meters water equivalent. cSensors means detectors of neutrino secondaries, e.g., muons; LS, liquid scintillator; Cerenkov light from charged secondaries is observed by photomultipliers. ACKNOWLEDGMENTS We wish to thank Ed Chupp, Carl Fichtel, Gerry Fishman, Alice Harding, Wick Haxton, Jim Higdon, Kevin Hurley, John Lams, Chip Meegan, Larry Peterson, Reuven Ramaty, A. Stepanian, and Trevor Weekes for valuable comments and contributions. REFERENCES 1. Heitler, W. 1954, The Quantum Theory of Radiation (Clarendon Press, Oxford) 2. Jauch, J.M., & Rohrlich, F. 1976, The Theory of Photons. and Electrons (Springer-Verlag, Berlin) 3. Rybicki, G.B., & Lightman, A.P. 1979, Radiative Processes in Astrophysics (Wiley, New York) 4. Lang, K.R. 1980, Astrophysical Formulae (SpringerVerlag, Berlin). 5. Felten, J.E., & Morrison, P. 1966,ApJ, 146,686 6. Blumenthal, G.R., & Gould, RJ. 1970, Rev. Mod. Phys., 42,237 7. Ore, A., & Powell, J.L. 1949, Phys. Rev. 75,1696 8. Bussard, R.W. et al. 1979, ApJ, 228, 928 9. Zdziarski, A.A. 1980, Acta Astron., 30, 371 10. Rarnaty, R., & Meszaros, P. 1981, ApJ, 250, 384 11. Gould, R.J. 1989, ApJ, 344, 232 12. Guessoum, N. et al. 1991,ApJ, 378,170 13. Klein, 0., & Nishina, Y. 1929, Z Phys. 52, 853 14. Marmier, P., & Sheldon, E. 1969, Physics ofNuclei and Particles (Academic Press, New York) 15. Erber, T. 1966, Rev. Mod. Phys., 38, 626 16. Canuto, V. et al. 1971, Phys. Rev. D, 3, 2303 17. Bussard, R.W. et al. 1986, Phys. Rev. D, 34, 440 18. Daugherty, J.K., & Harding, A.K. 1986, ApJ, 309, 362 19. Harding, A.K., & Daugherty, J.K. 1991, ApJ. 374, 687 20. Canuto, V., & Ventura, J. 1977, Fund. Cosmic Phys., 2, 203 21. ChUpp, E.L. 1972, Gamma-Ray Astronomy (Reidel, Dordrecht) 22. Rarnaty, R., & Lingenfelter, R.E. 1982, Ann. Rev. Nucl. Part. Phys., 32, 235 23. Bignami, G.F., & Hemsen, W. 1983, ARA&A, 21, 67 24. ChUpp, E.L. 1984, ARA&A, 22, 359 25. Rarnaty, R., & Lingenfelter, R.E. 1994, Chapter 3 in High Energy Astrophysics (World Scientific, New York), p. 32 26. Harding, A.K. 1991, Phys. Rep, 206, 327 27. Higdon, J.C., & Lingenfelter, R.E. 1991, ARA&A, 28, 401 28. Fishman, G.J., & Meegan, C.A. 1995, ARA&A, 33, 415 29. Rothschild, R.E., & Lingenfelter, R.E. 1995, High Velocity Neutron Star and Gamma-Ray Bursts (American Institute of Physics, New York), 282 pp. 30. Kouveliotou, C., Briggs, M.F., & Fishman, G.J. 1996, Gamma-Ray Bursts (American Institute of Physics, New York), 1008 pp. 31. Rees, M.J. 1998, Proc. 18th Texas symposium ReL Astrophys.. edited by A.V. Olinto, J.A. Frieman, and D.N. Schramm (World Scientific, Singapore) p. 34; Rees, M.J. 1999, NucPhys B, Proc. SuppL, 69681 Chapter 11 Earth Gerald Schubert and Richard L. Walterscheid 11.1 Oblate Ellipsoidal Reference Figure . . . . . . . . .. 240 11.2 Mass and Moments oflnertia . . . . . . . . . . . . .. 240 11.3 Gravitational Potential and Relation to Products oflnertia . . . . . . . . . . . . . . . . . . . . 241 11.4 Topography. . . . . . . . . . . . . . . . . . . . . . .. 243 11.5 Rotation (Spin) and Revolution About the Sun . . .. 244 11.6 Gravity. . . . . . . . . . . . . . . . . . . . . . . . . .. 245 11.7 Geoid. . . . . . . . . . . . . . . . . . . . . . . . . . .. 245 11.8 Coordinates. . . . . . . . . . . . . . . . . . . . . . .. 246 11.9 Solid Body Tides . . . . . . . . . . . . . . . . . . . . . 246 11.1 0 Geological Time Scale . . . . . . . . . . . . . . . . .. 248 11.11 Glaciations......................... 251 11.12 Plate Tectonics ...................... 252 11.13 Earth Crust . . . . . . . . . . . . . . . . . . . . . . . .. 252 11.14 Earth Interior 255 11.15 Earth Atmosphere, Dry Air at Standard Temperature and Pressure (STP) ....................... ...... 257 11.16 Composition of the Atmosphere . . . . . . . . . . . . 258 11.17 Water Vapor . . . . . . . . . . . . . . . . . . . . . . . . 259 11.18 Homogeneous Atmosphere, Scale Heights and Gradients . . . . . . . . . . . . . . . . . . . . . . . 259 Regions of Earth's Atmosphere and Distribution with Height . . . . . . . . . . . . . . . .. 260 11.19 239 240 / 11.1 11 EARTH 11.20 Atmospheric Refraction and Air Path . . . . . . . . . 262 11.21 Atmospheric Scattering and Continuum Absorption. 265 11.22 Absorption by Atmospheric Gases at Visible and Infrared Wavelengths . . . . . . . . . . . . . . . . 268 11.23 Thermal Emission by the Atmosphere . . . . . . . .. 270 11.24 Ionosphere......................... 271 11.25 Night Sky and Aurora . . . . . . . . . . . . . . . . . . 279 11.26 Geomagnetism ...................... 282 11.27 Meteorites and Craters . . . . . . . . . . . . . . . . .. 285 OBLATE ELLIPSOIDAL REFERENCE FIGURE [1,2] Equatorial radius a = 6.378136 x 106 m. Polar radius e = 6.356753 x 106 m. Mean radius Re = (a 2 e)I/3 = 6.371000 x 106 m. Length of equatorial quadrant = 1.001875 x 107 m. Length of meridional quadrant = 9.985164 x 106 m. Ellipticity or Flattening (a - e)/a = 1/298.257 = 0.0033528. Eccentricity e = (a 2 - e 2)1/2/a = 0.081818. Surface Area = 21l' {a 2 + e 2(1 _e2/a 2) -1/2 In [ale + (a 2le2 _ 1) 1/2]} = 5.100657 X 1014 m2 . Volume = 11.2 MASS AND MOMENTS OF INERTIA [1-3] ~1l'a2e = 1.083207 x 1021 m3 . Earth mass Me = 5.9737 x 1024 kg. Moon-Earth mass ratio MMoonlMe = 0.012300034. Sun-Earth mass ratio M01 Me = 332946.038. Earth mass multiplied by the gravitational constant: GMe = 3.98600441 x 10 14 m3 s-2, (GMe)I/2 = 1.996498 x 107 m3/ 2 S-I. Earth mean density Pe = 5514.8 kg m- 3 . Moments of inertia (see below): about rotation axis C = 8.035 8 x 1037 kg m2 , average about equatorial axis (A + B)/2 = 8.009 5 x 1037 kg m2 , dynamical ellipticity or flattening {C - (A + B) 12} IC = 0.0032729, 11.3 GRAVITATIONAL POTENTIAL AND PRODUCTS OF INERTIA / lz = {C - (A + B) 12} IMea2 = C I Mea2 = 0.33078, Me a2 = 2.43014 x 1038 kg m 2 . 241 1.082626 x 10-3 , 11.3 GRAVITATIONAL POTENTIAL AND RELATION TO PRODUCTS OF INERTIA [1-3] The gravitational potential is u= G~e 11 + ~ (;y to Pi (sin</» [Ci cosmA + Si sinmA]}, = radial distance from Earth center of mass, Pi = fully normalized associated Legendre polynomials, r i.e., the mean square value of Pi (sin </»(cos mA, sinmA) over a spherical surface is unity, Pi = {(2-8 m .o)(21+ 1)[(l-m)!/(I+m)!]}lj2 pr, where pr is the ordinary associated Legendre polynomial, = degree and order of normalized spherical harmonic Pi (sin </>)(cos mA, sinmA), </> = latitude, A = longitude, Ci, Si = coefficients in spherical harmonic expansion of Earth's gravitational potential using fully t, m normalized functions. C? ct st = = = O. Table 11.1 gives the With coordinate system origin at the center of mass values of the zonal coefficients in a spherical harmonic expansion of the gravitational potential using fully normalized functions. C? Table 11.1. Zonal coefficients C? 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. -484.165 0.53952 -0.14951 0.048883 0.054065 0.035629 -0.021555 -0.0061891 0.0085246 0.019924 C? in units of 10-6. 3. 5. 7. 9. II. 13. 15. 17. 19. C? 0.95720 0.068343 0.091301 0.026862 -0.049464 0.040 112 0.0032275 0.017427 -0.0021551 Table 11.2 gives values of the coefficients Ci, Si in a spherical harmonic expansion of the gravitational potential using fully normalized functions. Note that C~ = 0 and S~ = O. 242 / 11 EARTH I, m cIm' 2,2 2.439, 3, 1 2.0277, 4,1 4,4 Table 11.2. Coefficients Cj, 8j in units of 10-6. I, m cI'm 0.2492 3,2 0.9045, -0.5362, -0.1888, -0.4734 0.3094 4,2 5,1 5,4 -0.0583, -0.2956, -0.0961 0.0497 6, 1 6,4 -0.0769, -0.0868, 7,1 7,4 7, 7 8r I, m cr, 8Im -0.6194 3,3 0.7203, 1.4139 0.3502, 0.6630 4,3 0.9909, -0.2009 5,2 5,5 0.6527, 0.1738, -0.3239 -0.6689 5,3 -0.4523, -0.2153 0.0270 -0.4713 6,2 6,5 0.0487, -0.2673, -0.3740 -0.5368 6,3 6,6 0.0572, 0.0097, 0.0094 -0.2371 0.2749, -0.2756, 0.0010, 0.0975 -0.1238 0.0241 7,2 7,5 0.3278, 0.0013, 0.0932 0.0186 7,3 7,6 0.2512, -0.3588, -0.2153 0.1517 8,1 8,4 8, 7 0.0236, -0.2463, 0.0675, 0.0588 0.0702 0.0751 8,2 8,5 8,8 0.0776, -0.0250, -0.1242, 0.0660 0.0895 0.1202 8,3 8,6 -0.0178, -0.0649, -0.0863 0.3091 9,1 9,4 9, 7 0.1461, -0.0101, -0.1190, 0.0200 0.0190 -0.0970 9,2 9,5 9,8 0.0225, -0.0171, 0.1871, -0.0336 -0.0538 -0.0024 9,3 9,6 9,9 -0.1613, 0.0639, -0.0481, -0.0760 0.2226 0.0987 10,1 10,4 10, 7 10,10 0.0815, -0.0853, 0.0076, 0.0998, -0.1303 -0.0787 -0.0034 -0.0225 10,2 10,5 10,8 -0.0913, -0.0510, 0.0401, -0.0511 -0.0511 -0.0917 10,3 10,6 10,9 -0.0086, -0.0371, 0.1243, -0.1550 -0.0784 -0.0380 8Im -1.4001 A simplified expression for the gravitational potential is GM$ U ~ - { 1- r L (a)1 -r 11 PI (sin</» 00 1=2 I , where PI is the Legendre polynomial of degree I. Values of the zonal coefficients 11, defined by 1 ~ 2, are given in Table 11.3. Table 11.3. Zonal coefficients II, in units of 10- 6. II 2. 4. 6. 8. 10. 1082.626 -1.6186 0.5391 -0.2015 -0.2478 II 3. 5. 7. 9. 11. -2.533 -0.2267 -0.3536 -0.1171 0.2372 11.4 TOPOGRAPHY / 243 1Rble 11.3. (Continued.) J, J, -0.1781 0.1161 0.003555 -0.0051853 -0.12758 12. 14. 16. 18. 20. -0.2084 -0.01797 -0.10310 0.013459 13. 15. 17. 19. The relation of the second degree coefficients in a spherical harmonic expansion of the gravitational potential to products of inertia Iij is ~-o -'V 5 C2 = h = Me1a2 { 133 - III +2 h2} ' The principal products of inertia 111,122,133 are often denoted A, B, C with C > B > A or 133 > 122 > Ill, III = A = 8.0094 x 1037 kg m 2 , 122 = B = 8.0096 x 1037 kg m2, 133 = C = 8.0358 x 1037 kgm2 . 11.4 TOPOGRAPHY [2,4,5] The topography of solid Earth, T, is: T (in 103 m) 1 LL 00 = Pi(sincp) [CTi cosmA + STi sinmA]. 1=0 m=O Pi (sin cp), cp, A are defined in the expression for the gravitational potential in Section 11.3. The coefficients are given in Table 11.4. 1Rble 11.4. Values o/the coejJicients CTj and STj (in units 0/103 m). l.m CTj. 0.0 -2.3890. STj l.m CTj. STj l.m CTj. STj 1.0 0.6605. 1. 1 0.6072. 0.4062 2.0 0.5644. 2.1 0.3333. 0.3173 2.2 0.4208. 0.0839 3.0 3.3 -0.1683. 0.1299. 3.1 -0.1518. 0.1244 3.2 0.4477. 0.4589 0.5733 244 / 11 EARTH Table 11.4. (Continued.) I,m CTi, -0.2563 0.4703 4,2 -0.3928, 0.0716 -0.0406, 0.5254, -0.0770 -0.0654 5,2 5,5 -0.0216, -0.0549, -0.1577 0.2276 0.0013, 0.1960, -0.0171 -0.1737 6,2 6,5 0.0247, -0.1076, -0.1323 -0.2075 I,m CTi, STi I,m CTi, 4,0 4,3 0.3162, 0.3761, -0.1291 4,1 4,4 -0.2241, -0.6387, 5,0 5,3 -0.5514, 0.1232, 0.0386 5,1 5,4 6,0 6,3 6,6 0.2567, 0.0601, 0.0354, 0.1865 0.0282 6,1 6,4 STi STi Area = 5.100657 x 10 14 m2 . Land area = 1.48 x 1014 m2 . Water area = 3.62 x 10 14 m 2 . Continental area including margins = 2.0 x 1014 m2 . Mean land elevation = 825 m. Mean ocean depth = 3770 m. 11.5 ROTATION (SPIN) AND REVOLUTION ABOUT THE SUN [1,2,6,7] Rotational period with respect to fixed stars = 24hoomoos.0084 mean sidereal time, = 23h56m 04s.098 9 mean solar time. Mean angular velocity = 7.292115 x 10-5 rad s-l, 15.041067 arcsec s-l. Equatorial rotational velocity = 465.10 m s-l. Centrifugal acceleration at equator = 3.39157 x 10-2 m s-2. Angular momentum = wC = 5.8598 x 1033 m2 kg s-l. Rotational energy = iCw2 = 2.1365 x 1029 J. The general precession in longitude per Julian century for J2ooo.0 is p = 5 029'~096 6, where p is the long period motion of the mean pole of the equator about the pole of the ecliptic with a period of about 26,000 years. The general precession is due to the gravitational torques of the Sun, Moon, and planets on the Earth's dynamical figure. Nutations are the motions of the Earth's rotation axis with respect to inertially fixed axes. Nutation includes the general precession and shorter period motions. A nutation induced by the Moon has a period of 18.6 years and an amplitude of about 9 arcsec. The gravitation of the Sun causes the lunar orbit to precess with respect to the plane of the ecliptic with a period of 18.6 years. Smaller nutations have periods of a solar year and a lunar month and harmonics thereof. Length of Day (LOD) variations comprise an overall linear increase from tidal dissipation (of about 1 to 2 ms per century). There are large irregular fluctuations with amplitudes of milliseconds and time scales of decades, and smaller oscillations with shorter time scales. LOD variations with periods of a year and less are generally attributable to exchange of angular momentum between the solid Earth and the atmosphere-ocean system and to effects of solid Earth and ocean tides. LOD fluctuations with decade time scales may be due to angular momentum exchange between the solid Earth and the liquid outer core. Polar motion or wobble is the motion of the solid Earth with respect to the spin axis of the Earth. Polar motion is dominated by nearly circular oscillations at periods of one year, the annual wobble with an amplitude of about 100 milliarcseconds, and at about 434 days, the Chandler wobble with an amplitude of about 200 milliarcseconds. The Chandler wobble is a free oscillation of the Earth; its 11.6 GRAVITY / 245 excitation mechanism is uncertain. Other components of polar motion occur over a wide range of time scales from weeks to thousands of years. Loading of the solid Earth by the redistribution of mass in the atmosphere, oceans, groundwater, and ice caps contributes to polar motion. Mean orbital speed = 2.97848 x 104 m s-l. Mean centripetal acceleration = 5.9301 x 10-3 m s-2. Mean distance from Sun = 1.000 001057 AU = 1.49598029 x 1011 m. Mean eccentricity of orbit about the Sun = 0.016708617. Obliquity of the ecliptic at J2000.0 = 23°26'21".4119. 1 AU = 1.495978706 6 x 1011 m. Light time for 1 AU = 499.004 78353 s. 11.6 GRAVITY [5, 7] Gravity includes the gravitational attraction of the Earth's mass and the centrifugal acceleration of the Earth's rotation. Surface gravity on reference ellipsoid g(m s-2) = 9.806 21 - 0.02593 cos 2</> + 0.000 03 cos 4</> = 9.78031 + 0.05186sin2 </> - 0.00006sin2 2</>. </> is the geodetic latitude of point p, i.e., the angle between the equator of the reference ellipsoid and the normal from p to the ellipsoid. Gravity anomalies are actual values of g minus the reference g given above. A practical unit for the measurement of gravity anomalies is the mgal = 10-5 m s-2. Reference equatorial gravity = 9.78031 m s-2. Reference polar gravity = 9.832 17 m s-2. Reference gravity at </> = 45° = 9.806 18 m s-2. Gravitation at the equator = GMe/a2 = 9.79829 m s-2. Centrifugal acceleration at equator/gravitation at equator = 3.46139 x 10-3 . Variation of g with altitude at the Earth's surface = 0.3086 x 10-5 s-2 = 3.086 mm s-2 km- 1 = 0.3086 mgal m- 1. g decreases by 3.086 mm s-2 per kilometer of elevation at the Earth's surface. Gravity anomalies corrected for altitude, i.e., evaluated on the reference ellipsoid, are known as free-air gravity anomalies. 11.7 GEOID [2,5,7] The gravity potential is the sum of the gravitational potential U (see above) and the centrifugal potential 2 r2 cos2 </>, where is the mean angular velocity. The geoid is the equipotential of gravity that coincides with mean sea level in the oceans. The geoid lies generally below the topography. The height of the geoid N is given with respect to a reference ellipsoid with the observed flattening of the Earth 1/298.257 and with the Earth's equatorial radius 6378.136 km. The equation of the reference ellipsoid is r = a{1 + [(2/ - /2)/{1 - f)2] sin2 </>}-1/2, where / is the flattening. With / = 1/298.257 !w w r = a { 1 + 0.67395 sin2 </> ~a { 1 - 0.33698 sin2 </> r 1/2 + 0.17033 sio4 </>} . 246 / 11.8 11 EARTH COORDINATES [7] = 692".74 sin 2rjJ - Geodetic latitude (rjJ) - geocentric latitude (rjJ') 1".16 sin 4rjJ. Geocentric latitude of a point p is the angle between the equator of the reference ellipsoid and a line from p to the center of the ellipsoid. Geodetic latitude is defined above. 10 oflatitude = 110.575 + 1.110 sin2 rjJ, 103 m. 10 oflongitude = (111.320 + 0.373 sin2 rjJ) cos rjJ, 103 m. tan rjJ , = (l-e 2 )Nt/>+h Nt/> +h tan rjJ . e is the eccentricity of the reference ellipsoid f is the flattening of the ellipsoid. Nt/> is the ellipsoidal radius of curvature in the meridian Nt/> = (1 - a e 2 ' 2,/,.)1/2' SIn 'Y' h is the height of a point p above the reference ellipsoid. With f = 1/298.257, e 2 = 6.694385 x 10-3 , e 2 « 1, Nt/> ~ a, tan rjJ' ~ tan rjJ (1 - e2 + e2 ~ ) ~ tan rjJ (0.993306 + 1.049583 x 1O- 9 h(m)) . 11.9 SOLID BODY TIDES [7,8] The tidal potential due to the gravitation of the Sun and the Moon UT is the gravitational potential of these bodies expressed in the coordinate system of the Earth's gravitational potential, but without the I = 1 spherical harmonic terms. These I = 1 terms determine the orbital motion of the Earth. The tidal potential is a differential gravitational potential. Each spherical harmonic component of the tidal potential has contributions with different periods and amplitudes. Table 11.5 lists contributions to the I = 2 tidal potential, the dominant tidal component. Table U.5. Periods and amplitudes for the l = 2 tidal potential. m Tidal contribution Period Long Period m=O Lunar nodal tides Sa Ssa Mm Mf 18.613 years 365.26d 182.62 d 27.555 d 13.661 d (Amplitude) g-I, 10- 2 m 2.79 0.49 3.10 3.52 6.66 11.9 SOLID BODY TIDES / 247 Table 11.5. (Continued.) m m Tidal contribution 0, P, S, Diurnal m =I 23.934 h 23.869 h 23.804 h 26.22 12.20 0.29 36.88 0.29 0.52 12.658 h 12.421 h 12. h 11.967 h 12.10 63.19 29.40 8.00 25.819 h 24.066 h 24.h K, IV, 4>, Semi-Diurnal m=2 (Amplitude) g-', 10- 2 m Period N2 M2 S2 K2 The perturbation in the Earth's second degree gravitational potential at the surface of the Earth due to tidal deformation of the Earth's interior is the product of the second degree tidal potential evaluated at the Earth's surface with the second degree potential Love number k. The product of the second degree body tide displacement Love number h with the second degree component of UT / g evaluated at the Earth's surface gives the tidally induced radial displacement of the surface. Southward and eastward displacements of the tidally deformed surface of the Earth are given in terms of the body tide displacement Love number I by -I aUT --g ae and aUT g sine ~' respectively, where e is colatitude, A is eastward longitude, and g, UT and its derivatives are evaluated at the Earth's surface. Second degree contributions are understood here. Second degree tidal effects on surface gravity and surface tilt are represented by the gravimetric factor Ii = 1- ~k+ h 1} = 1+k - and the tilt factor h, respectively, similar to the above. Table 11.6 gives these Love numbers for a model of the Earth. Table 11.6. Second degree Love numbers for a spherical. rotating. ellipsoidal. elastic. oceanless Earth. m Tidal contributions k h 0 Any long period tide 0.299 0.606 0, P, S, 0.298 0.287 0.280 0.256 0.603 0.581 0.568 0.520 K, B 1/ 0.0840 1.155 0.689 0.0841 0.0849 0.0853 0.0868 1.152 1.147 1.l44 1.132 0.689 0.700 0.707 0.730 248 I 11 EARTH Table 11.6. (Continued.) Tidal contributions m 2 k h 8 1/ 0.523 0.660 0.692 "'I ell I 0.466 0.328 0.937 0.662 0.0736 0.0823 1.235 1.167 Any semi-diurnal tide 0.302 0.609 0.0852 1.160 Values of the Love numbers for the real Earth are strongly modified by ocean tides and slightly modified by anelasticity in the solid Earth. 11.10 GEOLOGICAL TIME SCALE [9] Age of Earth = 4.5 - 4.7 Ga Oldest Geological Dates: Rocks at Isua in southern West Greenland have yielded dates of metamorphic events at about 3750Ma. Sand River gneisses in the Limpopo belt of Southern Africa have been dated at about 3800 Ma. Detrital zircons from Western Australia have yielded dates of about 4200 Ma, indicative of preexisting crust. Table 11.7 gives dates of various geologic eras in the Phanerozoic eon, and Table 11.8 gives dates in the Precambrian eon. Table 11.9 lists the major geological and biological events in the Earth's history. Table 11.7. The Phanerozoic Eon (Present-570 Million Years Ago). Period Duration Cenozoic Era Quaternary Sub-Era Holocene Epoch Pleistocene Epoch Tertiary Sub-Era Neogene Period Pliocene Epoch Miocene Epoch Paleogene Period Oligocene Epoch Eocene Epoch Paleocene Epoch Mesozoic Era Cretaceous Period Senonian Epoch Gallic Epoch Neocomian Epoch K2 Gulf Epoch KI Jurassic Period J3, Maim Epoch J2, Dogger Epoch ]I, Lias Epoch Triassic Period Tr3Epoch Tr2Epoch Trl, Scythian Epoch Present-65 Ma Present-1.64 Ma Present-O.01 Ma 0.01-1.64 Ma 1.64-65Ma 1.64-23.3 Ma 1.64-5.2Ma 5.2-23.3Ma 23.3-65Ma 23.3-35.4 Ma 35.4-56.5 Ma 56.5-65Ma 65-245Ma 65-145.6Ma 65-88.5Ma 88.5-131.8 Ma 131.8-145.6 Ma 65-97Ma, 97-145.6 Ma) 145.6-208 Ma 145.6-157.1 Ma 157.1-178 Ma 178-208Ma 208-245Ma 208-235Ma 235-241.1 Ma 241.1-245 Ma 11.10 GEOLOGICAL TIME SCALE Table 11.7. (Continued.) Period Duration Paleozoic Era Permian Period Zechstein Epoch Rotliegendes Epoch Carboniferous Period Pennsylvanian Subperiod Gzelian, Kasimovian, Moscovian, Bashkirian Epochs Mississippian Subperiod Serpukhovian, Visean, Tounaisian Epochs Devonian Period D3 Epoch D2 Epoch D,Epoch Silurian Period Pridoli, Ludlow, Wenlock, Llandovery Epochs Ordovician Period Bala Subperiod Ashgill, Caradoc Epochs Dyfed Subperiod Llandeilo, Llanvirn Epochs Canadian Subperiod Arenig, Tremadoc Epochs Cambrian Period Merioneth Epoch St. David's Epoch Caerfai Epoch 245-570Ma 245-290Ma 245-256Ma 256--290Ma 290-362.5 Ma 290-323 Ma 323-362.5 Ma 362.5-408.5 Ma 362.5-377.5 Ma 377.5-386 Ma 386--408.5 Ma 408.5-439 Ma 439-51OMa 439-464Ma 464-476 Ma 476--51OMa 510-570 Ma 510-517 Ma 517-536 Ma 536--570Ma Table 11.8. The Precambrian Eon (570-4550-4570 Ma)a. Period Duration Sinian Era Vendian Period Sturtian Period Riphean Era Karatau Period Yurmatin Period Burzyan Period Animikean Era Gunflint Period Huronian Era Cobalt, Qurke Lake, Hough Lake, Eliot Lake Periods Randian Era Ventersdorp, Central Rand, Dominion Periods SwazianEra Pongola, Moodies, Figtree, Onverwacht Periods Isuan Era HadeanEra Imbrian (pars) Period Nectarian Period Pre-Nectarian Period Cryptic Division 570-800Ma 570-6IOMa 610-800Ma 800-1650Ma 800-1050Ma 1050-1350 Ma 1350-1650 Ma 1650-2200 Ma 1650-2200 Ma 2200-2400-2500 Ma 2400-2500-2800 Ma 2800-3500 Ma 3500-3800 Ma 3800-4550-4570 Ma 3800-3850 Ma 3850-3950 Ma 3950-4150 Ma 4150-4550-4570 Ma Note aThe Precambrian is also divided as follows: Proterozoic Eon (570-2500 Ma); Pt3 (570-900 Ma), Pt2 (900-1600 Ma), Pt, (1600-2500 Ma) Subeons; Archean Eon (2500-4000 Ma); Ar3 (2500-3000 Ma), Ar2 (3000-3500 Ma), Ar, (3500-4000 Ma) Subeons; Priscoan Eon (4000-4550-4570 Mal. / 249 250 I 11 EARTH Table 11.9. Major "events" in Earth history. Event Homo sapiens, Neanderthal man, Homo erectus, Australopithecus africanus, worldwide glaciations Approximate age (Ma, million years ago) 0-3 Ma Gulf of California opens, Calabria collides Italy-Sicily 3-5 Ma Mediterranean desiccation, Panama collides NW Columbia, Red Sea Opens 5-10 Ma FA (First Appearance) Hipparion (horse), FA hominids, Sivapithecus, Kenyapithecus, Khabylies collides Africa 10-15 Ma Andaman Sea opens, South China Sea spreading ceases, Calabria rifts SE from Sardinia, Corsica-Sardinia collide Apulia, Main Himalayan Orogeny 15-20 Ma Okinawa trough opens, Japanese Sea opens, Corsica-Sardinia parts France, East African and Red Sea rifting begins, BalearicslKhabalirs rift from Iberia 20-25 Ma Norwegian Sea opens east of Jan Mayen, Main Alpine Orogeny South China Sea opens, Scotia Sea opens Drake Passage opens, Caribbean Plate moves east 25-30 Ma 30-35 Ma Late Eocene extinction, FA proboscideans (mastodons, elephants), early anthropoids, Labrador SeaJBaffin Bay cease spreading, Jan Mayen Ridge rifts from Greenland 35-45 Ma FA rodents, Cuba collides Bahama Bank, India Eurasia collision begins, Indian-Australian plates united, Eurasia Basin opens, Norwegian Sea opens, Tasman Sea opens 45-55 Ma FA horses, FA grasses, mammals diversify, FA primates 55-60 Ma North Atlantic lavas, Indian Ocean spreads northwest of Seychelles, Yucatan Basin opens as Cuba moves north, Laramide Orogeny 60-65 Ma Terminal Cretaceous extinction, Deccan lavas 65-70 Ma FA early grasses, LA (last appearance) pteridosperms (seed ferns) 70-75 Ma Cretaceous anoxic event, Labrador Sea opens, India-Madagascar separate, Australia parts Antarctica 85-95 Ma FA diatoms (one-cell marine organisms), equatorial Atlantic opens, Bay of Biscay opens, Iberia parts Grand Banks 105-120 Ma FA angiosperms (flowering plants), South Atlantic opens, East Indian Ocean opens, India parts from Australia-Antarctica, FA placental mammals 125-135 Ma FA birds, Paleo Tethys closed 145-155 Ma India-Madagascar Antarctica separate, Gulf of Mexico opens, Neo-Tethys opens, central Atlantic opens, East Gondwana (India, Australia, Antarctica) parts West Gondwana (Africa, South America) 155-170 Ma Karoo volcanism 185-195 Ma Early mammals, terminal Triassic extinction, Rifting between Gondwana and Laurasia 205-215 Ma Iran, Crete, 1\Jrkey part from Gondwana, FA dinosaurs, Siberian lavas 235-250 Ma Gondwana Laurasia collide, Appalachian Ocean finally closed 265-280 Ma Iran, Tibet rift from Gondwana, FA conifers 280-300 Ma FA winged insects, FA pelycosaurs (early mammal-like reptile) 300-320 Ma South China rifts from Gondwana, FA sharks 350-380 Ma FA wingless insects, tims, Iapetus Ocean finally closed 380-400 Ma FA lungfish, land plants, jawed fish, North China rifts from Gondwana 400-430 Ma 11.11 GLACIATIONS I 251 Table 11.9. (Continued.) Approximate age (Ma, million years ago) Event Ediacaran metazoans (soft body multicell animals), Skilogalee microbiota, Grenvilian Orogeny 570-1000 Ma Keweenawan, Mackenzie Volcanics, Duluth Muskox intrusives, Oldest megascopic algae (Iarge-celled algae), algal coals 1100-1400 Ma Hudsonian and Penokean Orogenies, FA common red beds, Sudbury intrusion, Banded iron fonnations, Oxygen buildup in atmosphere 1700-2000 Ma Bushveld intrusion, Gunflint microbial structures in chert, Hammersley & Fortescue biota, Kenoran Orogeny 2000-2500 Ma FA red beds, Ventersdorp biota, Stilwater volcanics and intrusives 2500-2800 Ma Kaap Valley Granite, Fig Tree Group with bacteria and blue green algae, Barberton Gneisses 3200-3300 Ma FA stromatolites (bacterial algal mats) in Onverwacht Group and Australia "" 3400 Ma Amitsoq & Kaapvaal gneisses, evidence life well established (carbon isotopic ratios) "" 3800 Ma Basin formation on the Moon 3800-4200 Ma Zircons from early crust 4200-4300 Ma Lunar melting and differentiation of anorthositic crust "" 4500 Ma Accretion of Earth and Moon 11.11 4500-4600 Ma GLACIATIONS [9-11] The geological record contains evidence of major glaciations as listed in Table 11.10. Table 11.10. Ages and locations of major glaciations. Age(Ma) Locations 0-15, Holocene, Pleistocene 250-380, Pennian, Carboniferous, Devonian 430-450, Silurian, Ordovician 600, Vendian 650,Sturtian 800, Sturtian 900, Karatau 2300-2400, Huronian 2800, Randian, Swazian Antarctica, North America, Eurasia Gondwana Gondwana China, North Europe, North and South America Eurasia, South Africa, Australia Australia, North America, South Africa Africa Notth America, South Africa South Africa Some glaciations may be related to plate tectonics, e.g., Gondwana moved over the South Pole in the Paleozoic. The Quaternary glaciations (most geologically recent glaciations) may be related to cyclical changes in the Earth's orbital motion about the Sun and in the motion of the Earth's rotation axis (Milankovitch or astronomical theory of ice ages). The tilt of the Earth's equator to the ecliptic varies from 21.5 0 to 24.5 0 with a period of about 41,000 years. The eccentricity of the Earth's orbit varies with periods of about 100,000 years and 400,000 years and the Earth's axis of rotation wobbles with a period of about 22,000 years. Pleistocene glaciations have occurred cyclically with a period of about 252 I 11 EARTH lOS years. 'JYpically there has been a relatively slow glaciation phase lasting about 9 x 104 years and a relatively fast deglaciation phase lasting about 104 years. The last deglaciation event of the current ice age began about 18,000 years ago and ended about 7000 years ago. 11.12 PLATE TECTONICS [5, 12] Earth's outer shell is divided into units known as tectonic plates that behave essentially rigidly on geological time scales. Plates move with respect to each other and the underlying mantle which defonns like a very viscous fluid on geological time scales. Tectonic plates comprise the lithosphere or rbeologically stiff outer shell of the Earth. Plates are separated by four types of boundaries: (1) midocean ridges or sites of seafloor spreading and generation of new oceanic crust; (2) subduction zones or sites of plate submergence into the mantle; (3) transfonn faults or sites of fault-parallel relative horizontal motion or sliding; and (4) collisional zones or sites of horizontal convergence characterized by strong defonnation and mountain building. Nonrigid defonnation of the lithosphere occurs mainly at plate boundaries. Major tectonic plates include Eurasia, Pacific, Antarctic, North America, South America, Africa, Australia, Philippine, Arabia, Nazca, Cocos, Caribbean, and Juan de Fuca. Plate motions are well described by rigid body rotations of the plates about axes through the center of the Earth and intersecting the surface at poles of rotation generally located remotely from the plates (Euler'S theorem). The angular velocity vector of plate rotation is known as the Euler vector. Each plate rotates counterclockwise relative to the fixed Pacific plate (PA). These main plates are given in Table 11.11. Table 11.11. NUVEL-l Euler vectors ofplate rotJJtion. Latitude of rotation pole Plate Africa,AF Antarctica, AN Arabia,AR Australia, AU Caribbean, CA Cocos, CO Eurasia,EU India, IN Nazca,NZ North America, NA South America, SA Juan de Fucao Philippine" ON 59.16 64.315 59.658 60.080 54.195 36.823 61.066 60.494 55.578 48.709 54.999 35.0 O. Longitude of rotation pole °E -73.174 -83.984 -33.193 +1.742 -80.802 -108.629 -85.819 -30.403 -90.096 -78.167 -85.752 +26.0 -47. Magnitude of rotation rate w(deg. Myr-l) 0.9695 0.9093 1.1616 1.1236 0.8534 2.0890 0.8985 1.1539 1.4222 0.7829 0.6657 0.53 1.0 Note °Listed Euler vectors are not part of the NUVEL-l model. 11.13 EARm CRUST [5, 11] The crust is the outennost layer of the Earth. The rocks of the crust are chemically and physically distinct from underlying mantle rocks; the major distinction between crust and mantle is compositional. Crustal rocks are less dense than mantle rocks and contain greater concentrations of heat-producing radiogenic elements. The base of the crust is defined by a discontinuity in the depth profiles of seismic velocities known as the Mohorovici~ discontinuity or Moho. 11.13 EARTH CRUST / 253 There are two major subdivisions of the crust-the oceanic crust and the continental crust. Both types of crust generally consist of a sediment layer, an upper layer, and a lower layer. The average properties of these crustal layers are given in Table 11.12. Table 11.12. Average properties of oceanic and continental crust. Property Sediment layer thickness (km) Upper layer thickness (km) Lower layer thickness (km) Total thickness (km) AreaJ abundance (%) Volume abundance (%) Heat flow (mW m- 2) Bouguer anomaly (mgal)Q up. upper layer (km s-l)b up. lower layer (Ian s-l)b Oceanic Continental 0-1 1.5(0.7-2) 5(3-7) 7(5-15) 59 21 78 250 5.1 6.6 17(1()""20) 21(15-25) 36(3()""80) 41 79 56.5 -100 6.1 6.8 ()""5 Notes QBouguer anomaly = free air gravity anomaly (see above) -2rrGpch (a correction for the gravitational attraction of topography with elevation h and density Pc. G is the universal gravitational constant). b up = velocity of seismic P or compressional waves; 1 mgal = 10- 2 mm s-2. Seismic shear velocities of crustal rocks Us are about 3.7 km s-1 The average composition of the oceanic crust is primarily that of a tholeiitic basalt (Table 11.13). Oceanic tholeiitic basalt is extruded and intruded at mid-ocean ridges as a consequence of pressurerelease melting of upper mantle material that rises beneath the ridges. Oceanic basalts undergo varying degrees of alteration by reactions with seawater and hydrothermal fluids especially at and near midocean ridges. The average composition of the upper layer of the continental crust is similar to that of granodiorite. The lower layer of the continental crust may be largely similar to mafic granulites in composition though a more felsic composition is possible. Whereas the oceanic crust is produced in a one stage melting of the upper mantle, continental crustal rocks involve mUltiple melting events. Table 11.13. Estimated average composition of the oceanic and continental crust (excluding sediments). Continental crust Upper Lower. mafic Lower, felsic Oceanic crust Oxides (in weight %) Si02 Ti02 AI203 FeOT MgO CaO Na20 K20 MnO P20 5 65.5 0.5 15.0 4.3 2.2 4.2 3.6 3.3 0.1 0.2 49.2 1.5 15.0 13.0 7.8 10.4 2.2 0.5 0.2 0.2 61.0 0.5 15.6 5.3 3.4 5.6 4.4 1.0 0.1 0.2 49.6 1.5 16.8 8.8 7.2 ll.8 2.7 0.2 0.2 0.2 254 / 11 EARTH Table 11.13. (Continued.) Continental crust Upper Lower, mafic Lower, felsic Oceanic crust Trace Elements (in ppm) Rb Ba Sr La Yb Zr Nb U Th Cr Ni llO. BOO. 325. 30. 2.0 220. 25. 2.5 II. 35. 20. 2. 50. 500. 10. 1.0 30. 3. 0.1 0.3 200. 150. 4. 60. IBO. 3.5 2.7 100. 5. 0.2 0.6 230. BO. 10. 7BO. 570. 20. 1.2 200. 5. 0.1 0.5 90. 60. Properties of the main crustal rocks are given in Table 11.14. Table 11.14. Properties of crustal rocks. ab Rock Density (kg m- 3) Young's modulus (10 11 Pa) Shear modulus (10 11 Pa) Poisson's ratio Thermal conductivity Wm- I K- 1 Thermal expansivity 10-5 K- 1 Sedimentary Shale Sandstone Limestone Dolomite Marble 2100-2700 2200-2700 2200-2800 2200-2BOO 2200-2BOO 0.1~.3 0.14 0.1~.6 0.~.3 O.~.B 0.2~.3 Gneiss Amphibole 2700 3000 0.~.7 Basalt Granite Diabase Gabbro Diorite Anorthosite Granodiorite 2950 2650 2900 2950 2Boo 2750 2700 O.~.B 0.3 0.~.7 0.2~.3 0.8-1.1 0.6-1.0 0.3~.45 O.~.B 0.3~.35 0.B3 0.35 0.5~.9 0.3~.5 0.~.9 0.2-0.35 0.2-0.3 0.25-0.3 0.1-0.4 1.2-3 1.5-4.2 2-3.4 3.2-5 2.5-3 3. 2.4 Metamorphic 0.1~.35 0.~.15 0.5 - 1.0 0.4 2.1-4.2 2.5-3.B Igneous 0.2~.35 0.25 0.1-0.25 0.25 0.15-0.2 0.25 1.3-2.9 2.4-3.B 1.7-2.5 1.9-2.3 2.8-3.6 1.7-2.1 2.6-3.5 Notes aThe specific heats of crustal rocks are all approximately I kJ kg-I K- 1 . bMean density of the continental crust = 2750 kg m- 3. Mean density of the oceanic crust = 2900 kg m- 3 . The radioactive heat sources in the Earth's interior are listed in Table 11.15. 2.4 1.6 11.14 EARTH INTERIOR / 255 Table 11.1S. Radiogenic heat production rates per unit mass H and half-lives '1"1/2 of the important radioactive isotopes in the Earth's interior. a Isotope or element 238U 235U U 232Th 40K K ~antleconcentration H (Wkg- I ) 9.37 5.69 9.71 2.69 2.79 3.58 x x x x x x 10-5 10-4 10-5 10-5 10-5 10-9 '1"1/2 (Gyr) (kg kg-I) 4.47 0.704 25.5 x 10-9 1.85 x 10- 10 25.7 x 10-9 1.03 x 10-7 3.29 x 10-8 2.57 x 10-4 14.0 1.25 Note aU is 99.27% by weight 238U and 0.72% 235U. Th is 100% 232Th. K is 0.0128% 4OK. Assumes kg K/kg U = 104, kg Th/kg U = 4, and H = 6.18 x 10- 12 W kg-I in present mantle. [I] Reference 1. Turcotte D.L., & Schubert, G. 1982, Geodynamics (Wiley, New York) The abundances of uranium, thorium and potassium in the Earth and meteorite rocks is given in Table 11.16. Table 11.16. Representative concentrations (by weight) ofheatproducing elements in several rocks and chondritic meteorites. a Concentrations Rock Depleted Peridotites Tholeiitic Basalt Granite Chondritic ~eteorites U (ppm) 0.012 0.1 4. 0.013 Th(ppm) K(%) 0.035 0.35 17. 0.04 0.004 0.2 3.2 0.078 Note aRadiogenic elements are highly concentrated in the continental crust. 11.14 EARTH INTERIOR [13] The structure of the Earth's interior has been detennined mainly from seismology. Table 11.17 summarizes the values of the physical properties of a spherically symmetric model of the Earth as a function of radius from the center of the Earth based on seismological data. The major divisions of the solid Earth model are the core (radius r = 0 to 3480 km), the mantle (r = 3480 to 6346.6 km), and the crust (r = 6346.6 to 6368 km). The model core is divided into a solid inner core (r = 0 to 1221.5 km) and a liquid outer core. The model mantle is divided into the lower mantle (r = 3480 to 5701 km) and upper mantle (5701 to 6368 km). Subregions of the model mantle are the D"-layer at the base of the mantle (r = 3480 to 3630 km), the transition zone in the mid-mantle (r = 5701 to 5971), the seismic low velocity zone (r = 6151 to 6291 km) and the lithosphere or lid (r = 6291 to 6346.6 km). Similar tenns are used to describe regions of the real Earth whose radial thicknesses are not so readily defined. The real Earth is, of course, laterally heterogeneous. 256 I 11 EARTH Table 11.17. Physical properties of the Earth's interior according to PREM (Preliminary Earth Reference Model). a (ms- I ) P (kg m- 3) Ks (m s-I) /L (GPa) (GPa) v P (GPa) g (m s-2) 200. 400. 600. 800. 1000. 1200. 1221.5 11266.20 11255.93 11237.12 11205.76 11161.86 11105.42 11036.43 11028.27 3667.80 3663.42 3650.27 3628.35 3597.67 3558.23 3510.02 3504.32 13088.48 13079.77 13053.64 13010.09 12949.12 12870.73 12774.93 12763.60 1425.3 1423.1 1416.4 1405.3 1389.8 1370.1 1346.2 1343.4 176.1 175.5 173.9 171.3 167.6 163.0 157.4 156.7 0.4407 0.4408 0.4410 0.4414 0.4420 0.4428 0.4437 0.4438 363.85 362.90 360.03 355.28 348.67 340.24 330.05 328.85 0 0.7311 1.4604 2.1862 2.9068 3.6203 4.3251 4.4002 Outer core 1221.5 1400. 1600. 1800. 2000. 2200. 2400. 2600. 2800. 3000. 3200. 3400. 3480. 10355.68 10249.59 10122.91 9985.54 9834.96 9668.65 9484.09 9278.76 9050.15 8795.73 8512.98 8199.39 8064.82 O. O. O. O. O. O. O. O. O. O. O. O. O. 12166.34 12069.24 11946.82 11809.00 11654.78 11483.11 11292.98 11083.35 10853.21 10601.52 10327.26 10029.40 9903.49 1304.7 1267.9 1224.2 1177.5 1127.3 1073.5 1015.8 954.2 888.9 820.2 748.4 674.3 644.1 O. O. O. O. O. O. O. O. O. O. O. O. O. 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 328.85 318.75 306.15 292.22 277.04 260.68 243.25 224.85 205.60 185.64 165.12 144.19 135.75 4.4002 4.9413 5.5548 6.1669 6.7715 7.3645 7.9425 8.5023 9.0414 9.5570 10.0464 10.5065 10.6823 D" 3480. 3600. 3630. 13716.60 13687.53 13680.41 7264.66 7265.75 7265.97 5566.45 5506.42 5491.45 655.6 644.0 641.2 293.8 290.7 289.9 0.3051 0.3038 0.3035 135.75 128.71 126.97 10.6823 10.5204 10.4844 Lower mantle 3630. 3800. 4000. 4200. 4400. 4600. 4800. 5000. 5200. 5400. 5600. 13680.41 13447.42 13245.32 13015.79 12783.89 12544.66 12293.16 12024.45 11733.57 11415.60 11065.57 7265.97 7188.92 7099.74 7010.53 6919.57 6825.12 6725.48 6618.91 6563.70 6378.13 6240.46 5491.45 5406.81 5307.24 5207.13 5105.90 5002.99 4897.83 4789.83 4678.44 4563.07 4443.17 641.2 609.5 574.4 540.9 508.5 476.6 444.8 412.8 380.3 347.1 313.3 289.9 279.4 267.5 255.9 244.5 233.1 221.5 209.8 197.9 185.6 173.0 0.3035 0.3012 0.2984 0.2957 0.2928 0.2898 0.2864 0.2826 0.2783 0.2731 0.2668 126.97 117.35 106.39 95.76 85.43 75.36 65.52 55.90 46.49 37.29 28.29 10.4844 10.3095 10.1580 10.0535 9.9859 9.9474 9.9314 9.9326 9.9467 9.9698 9.9985 5600. 5701. 11065.57 10751.31 6240.46 5945.08 4443.17 4380.71 313.3 299.9 173.0 154.8 0.2668 0.2798 28.29 23.83 9.9985 10.0143 5701. 5771. 10266.22 10157.82 5570.20 5516.01 3992.14 3975.84 255.6 248.9 123.9 121.0 0.2914 0.2909 28.83 21.04 10.0143 10.0038 5771. 5871. 5971. 10157.82 9645.88 9133.97 5516.01 5224.28 4932.59 3975.84 3849.80 3723.78 248.9 218.1 189.9 121.0 105.1 90.6 0.2909 0.2924 0.2942 21.04 17.13 13.35 10.0038 9.9883 9.9686 5971. 6061. 6151. 8905.22 8732.09 8558.96 4769.89 4706.90 4643.91 3543.25 3489.51 3435.78 173.5 163.0 152.9 80.6 77.3 74.1 0.2988 0.2952 0.2914 13.35 10.20 7.11 9.9686 9.9361 9.9048 Lowvelocity zone 6151. 6221. 6291. 7989.70 8033.70 8076.88 4418.85 4443.61 4469.53 3359.50 3367.10 3374.71 127.0 128.7 130.3 65.6 66.5 67.4 0.2796 0.2796 0.2793 7.11 4.78 2.45 9.9048 9.8783 9.8553 Lid 6291. 8076.88 4469.53 3374.71 130.3 67.4 0.2793 2.45 9.8553 Region Inner core Transition zone Radius (kIn) O. vp Vs 11.15 EARTH ATMOSPHERE, DRY AIR AT STP / 257 Table 11.17. (Continued.) Region Crust Ocean Radius (Ian) (ms- I ) (ms- I ) P (kgm- 3) Ks /.L (GPa) (GPa) v 6346.6 8110.61 4490.94 3380.76 131.5 68.2 0.2789 0.604 9.8394 6346.6 6356. 6800.00 6800.00 3900.00 3900.00 2900.00 2900.00 75.3 75.3 44.1 44.1 0.2549 0.2549 0.604 0.337 9.8394 9.8332 6356. 6368. 5800.00 5800.00 3200.00 3200.00 2600.00 2600.00 52.0 52.0 26.6 26.6 0.2812 0.2812 0.337 0.300 9.8332 9.8222 6368. 6371. 1450.00 1450.00 O. O. 1020.00 1020.00 2.1 2.1 O. O. 0.5 0.5 0.300 9.8222 9.8156 vp Vs P (GPa) O. g (m s-2) Note a Ks is the bulk modulus, /.L is the shear modulus, and v is Poisson's ratio. 11.15 EARTH ATMOSPHERE, DRY AIR AT STANDARD TEMPERATURE AND PRESSURE (STP) [14, 15] Standard temperature To = 273.15 K. Standard pressure po = 1013.250 x 102 Pa = 1013.25 mbar. Standard gravity gO = 9.806 65 m s-2. Mass density of air PO = 1.2928 kg m- 3. Molecular weight Mo 28.964 x 10-3 kg mole-I. Mean molecular mass mo 4.810 x 10-26 kg. Molecular root-mean-square velocity (3RTo/ MO)I/2 = 4.850 x 102 m s-I. Speed of sound (ypo/ PO)I/2 = (y RTo/ MO)I/2 = 3.313 x 102 m s-I. Specific heat at constant pressure C p 1005 J kg-I K- 1. Specific heat at constant volume C v = 717.6 J kg-I K- I . Ratio of specific heats y cp/c v 1.400. Number density of air No = 2.688 x 1025 m- 3. Molecular diameter a = 3.65 x 10- 10 m. Mean free path L = 1/(2 1/ 21r N( 2 ) = 6.285 x 10-8 m. Coefficient of viscosity = 1.72 x 10-5 Pa s. Thermal conductivity = 2.41 x 10-2 W m- I K- 1. Refractive index n = = = = (n -1) xl 06 = 288.15 (64.328 + 29498.1 x 10-6 146 x 10-6 -a 2 = -27-3-.1-5 a = 1/)..(m). Rayleigh scattering (molecular) volume attenuation coefficient k = 321r 3 1.06--4 (n 3N)" 1)2. 255.4 x 10-6 ) + -:-4-1-x-1O---;;6"---a~2 . 258 I 11.16 11 EARTH COMPOSITION OF THE ATMOSPHERE [14, 16-21] Table 11.18 gives the composition of the atmospheric gases. 'Dlble 11.18. Gases in the well-mixed atmosphere. Gas Nl ~c H2 0def ArB C~c NeB He' CM4 h KrB code s~de H2i N2 0i 03 dek Xe8 N02d HN03d Node CFCl3' CF2Cl2' Notes Molecular weight 28.013 31.999 18.015 39.948 44.010 20.183 4.003 16.043 83.80 28.010 64.06 2.016 44.012 47.998 131.30 46.006 63.02 30.006 137.37 120.91 = Fraction of dry air at surface volume percent 78.08 20.95 2 x 10-6 - 3 x 10-2 9.34 x 10-3 3.45 x 10-4 18.2 x 10-6 5.24 x 10-6 1.72 x 10-6 1.14 x 10-6 1.5 x 10-7 3 x 10- 10 5.0 x 10-7 3.1 x 10-7 3.0-6.5 x 10-8 8.7 x 10-8 2.3 x 10- 11 5 x 10- 11 3 x 10- 10 2.8 x 10- 10 4.8 x 10- 10 weight percent Column amount (atm-cm)a 75.52 23.14 3 x 10-6 - 5 x 10-2 12.9 x 10-3 5.24 x 10-4 12.7 x 10-6 0.724 x 10-6 0.95 x 10-6 3.30 x 10-6 1.5 x 10-7 7 x 10- 10 0.35 x 10-7 4.7 x 10-7 5.0-11 x 10-8 39.4 x 10-8 3.9 x 10- 11 11 x 10- 11 3 x 10- 10 13 x 10- 10 20 x 10- 10 6.24 x loS 1.67 x loS 1760 7470 276 14.6 4.2 1.3 0.91 0.089 1.1 x 10-4 0.4 0.25 0.343 0.07 2.0 x 10-4 3.6 x 10-4 3.1 x 10-4 2.2 x 10-4 3.8 x 10-4 = a 1 ann-cm thickness of gas column when reduced to STP 2.687 x 1023 molecules m- 2 . Gases are well mixed (constant fractional amount with altitude) in the troposphere unless otherwise noted. Column amounts are nominal mid-latitude values [1, 2, 3]. Values for fractional amounts are from [I, 2, 3, 4, 5]. bPbotochemical dissociation in the thermosphere (see Table 11.20 for definition of thermosphere). Well mixed at lower levels [4]. cPhotochemical dissociation above 95 kIn. Well mixed at lower levels [4]. d Considerable tropospheric vertical variation in the fractional amount. Very dry above the tropopause [1, 2]. See Table 11.20 for definitions of troposphere and tropopause. eFactor of 102 or more local variability related to local sources such as anthropogenic pollution and geothermal activity [I, 2,4,5, 6]. fFractional amounts are 1% extremes [1]. 'Well mixed up to...., 110 kIn (turbopause). Diffusive separation at higher levels [4]. hDissociated in the mesosphere (see Table 11.20 for definition of mesosphere). Well mixed at lower levels [4, 7]. iIncrease with altitude in the mesosphere because of dissociation of H20. Minimum value in the stratosphere (see Table 11.20 for definition ofstratosphere) [1,7]. iDissociated in the stratosphere and mesosphere [4]. kRange in fractional amount refers to monthly averages [5]. 'Dissociated in the stratosphere [4]. References 1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office, Washington DC) 2. Anderson, G.P. et al. 1986, AFGL-TR-86-0110, Atmospheric Constituent Profiles 10-120 kIn, Air Force Geophysics Laboratory (now Air Force Research Laboratory). 3. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London) 4. Goody R.M., & Yung, Y.L. 1989, Atmospheric Radiation: Theoretical Basis, 2nd ed. (Oxford 11.18 HOMOGENEOUS ATMOSPHERE, SCALE HEIGHTS AND GRADIENTS / 259 University Press, New York) 5. Watson, R.F. et al. 1990, Greenhouse gases and aerosols, in Climate Change: The [PCC Scientific Assessment edited by J.T. Houghton, G.H. Henkins, and J.H. Ephraums (Cambridge University Press, New York) 6. Logan, J.A. et al. 1981, J. Geophys. Res., 86, 7210 7. Allen, M., Lunine, J.I., & Yung, Y.L. 1984, J. Geophys. Res. 89,4841 11.17 WATER VAPOR [22,23] The water vapor pressure in saturated air is given in Table 11.19. Table 11.19. Water vapor pressure e in saturated air. Over pure water T(°C) e (Pa) -30 50.88 -20 125.4 -10 286.3 0 610.8 10 1227 20 2337 30 4243 40 7378 Over ice T(°C) e (Pa) -30 37.98 -20 103.2 -10 259.7 0 610.7 Water vapor density (perfect gas law) = (2.167 x 1O-3 eff) kg m- 3 with T in K and e the water vapor pressure in Pa. 1 cm precipitable water = 1245 cm STP water vapor. Density of moist air (perfect gas law) = 3.484 x lO-\p - 0.378e)/T (kg m- 3 ) with P the total pressure, p the water vapor pressure, e in Pa, and T in K. Mean change of water vapor pressure with height h log(eh/eo) = -h/2, h ::s 7.2 km 7.2 km::s h ::s 13.6 km. = -(h - 2.16)/1.4, h eh eo = height above surface (km). = water vapor pressure at height h. = water vapor pressure at surface. 11.18 HOMOGENEOUS ATMOSPHERE, SCALE HEIGHTS AND GRADIENTS [17] The scale height of the atmosphere (height for e-fold change of pressure in an isothermal atmosphere) RT/g = R*T/MWg = 2.93 x 1O- 2 T (km), where R is the gas constant of dry air = 287.05 J kg- 1 K- 1 , R* is the universal gas constant = 8.314 kJ K- 1 kmole- 1, MW is the molecular weight of dry air = 28.964 kg kmole- 1, g is the acceleration of gravity = 9.8 m s-2, and T is in K. Height of homogeneous atmosphere. (An idealized abnosphere of finite height, constant temperature equal to the surface temperature, and constant density equal to the surface density.) = H = R*T/MWg. 260 / 11 Surface Air T Hkm EARTH eC) -30 7.11 -15 7.55 o 7.99 15 8.43 30 8.87 Mass of atmosphere per m2 = 1.035 x 104 kg. Total mass of Earth's atmosphere = 5.136 x 10 18 kg. Moment of inertia of the Earth's atmosphere = 1.413 x 1032 kg m2 . Magnitude of the dry adiabatic temperature gradient g / c p (c p is the specific heat at constant pressure = 1005 J kg-I K- I for dry air) = 9.75 K km-I. Mean temperature gradient in troposphere = -6.5 K km-I. Mass per unit area of 1 atm-cm of gas of molecular weight MW = 4.462 x 1O-4 MW(kg m- 2 ) where MW is in kg kmole- I . 11.19 REGIONS OF EARTH'S ATMOSPHERE AND DISTRIBUTION WITH HEIGHT [14, 17,24] The Earth's atmospheric layers are detailed in Table 11.20. Table 11.20. Atmospheric layers and transition levels. Height, h Layer (km) Characteristics Troposphere Tropopause Stratosphere Stratopause Mesosphere Mesopause Thermosphere Exobase Exosphere Ozonosphere Ionosphere Homosphere Heterosphere 0-11 11 Weather, T decreases with h, radiative-convective equilibrium Temperature minimum, limit of upward mixing of heat T increases with h due to absorption of solar UV by 03, dry Maximum heating due to absorption of solar UV by 03 T decreases with h Coldest part of atmosphere, noctilucent clouds T increases with h, solar cycle and geomagnetic variations 11-48 48 48-85 85 85-exobase 500-1000km > exobase 15-35 km > 70km < 85km > 85km Region of Rayleigh-Jeans escape Ozone layer (full width at e- 1 of maximum) Ionized layers Major constituents well-mixed Constituents diffusively separate Radiation belts Inner belt Outer belt r / R(B at magnetic equator Magnetosphere In direction of Sun Bow shock in direction of Sun In direction normal to ecliptic r / R(B at magnetic equator ,..., 1.3-2.4 ,..., 3.5-11 10 12 18 Profiles of physical quantities in the atmosphere are given in Table 11.21. 11.19 REGIONS OF EARTH'S ATMOSPHERE / 261 Table 11.21. Altitude profiles of mean physical conditions at latitude 45 0 [1]. Altitude (km) logP (Pa) T (K) logp (kgm- 3 ) logN (m- 3 ) Ha (km) loglb (m) 0 1 2 3 4 5 6 8 10 15 20 30 40 50 60 70 80 90 100 110 120 150 220 250 300 +5.006 +4.95 +4.90 +4.85 +4.79 +4.73 +4.67 +4.55 +4.42 +4.08 +3.74 +3.08 +2.46 +1.90 +1.34 +0.72 +0.022 -0.74 -1.49 -2.15 -2.60 -3.34 -4.07 -4.61 -5.06 -5.84 -6.52 -7.50 -8.12 288 282 275 269 262 256 249 236 223 217 217 227 250 271 247 220 199 187 195 240 360 634 855 941 976 996 999 1000 1000 +0.0881 +0.0460 +0.00286 -0.0413 -0.087 -0.133 -0.180 -0.279 -0.384 -0.71 -1.05 -1.73 -2.40 -2.99 -3.51 -4.08 -4.73 -5.47 -6.25 -7.01 -7.65 -8.68 -9.59 -10.22 -10.72 -11.55 -12.28 -13.51 -14.45 25.41 25.36 25.32 25.28 25.23 25.19 25.14 25.04 24.93 24.61 24.27 23.58 22.92 22.33 21.81 21.24 20.58 19.85 19.08 18.33 17.71 16.71 15.86 15.28 14.81 14.02 13.34 12.36 11.74 8.4 8.3 8.1 7.9 7.7 7.5 7.3 6.9 6.6 6.4 6.4 6.7 7.4 8.0 7.4 6.6 6.0 5.6 6.0 7.7 12.1 23. 36. 45. 51. 60. 69. 131. 288. -7.2 -7.1 -7.1 -7.0 -7.0 -7.0 -6.9 -6.8 -6.7 -6.4 -6.0 -5.4 -4.7 -4.1 -3.6 -3.0 -2.4 -1.6 -0.85 -0.10 +0.52 +1.52 +2.38 +2.95 +3.41 +3.80 +4.89 +5.86 +6.49 400 500 700 1000 Notes a H = pressure scale height (km). bl = mean free path (m). Reference 1. COESA, u.s. Standard Atmosphere 1976, (Government Printing Office, Washington DC) Variations in physical quantities during the day and during the solar cycle are given in Table 11.22. Table 11.22. Diurnal and solar cycle variations from mean values [1]. ab Altitude (km) 200 500 1000 Diurnal ±~p 6.0 46. 43. Solar Diurnal (%) 33 84 71 Solar HN(%) 6.2 44. 25. 32 80 51 Diurnal ±~p 12.3 52. 35. Solar Diurnal (%) Solar ±~T(K) 45 87 64 59 121 122 145 207 207 Diurnal Solar HMW (kg kmol)-l 0.041 0.49 0.99 0.32 1.62 1.40 Notes a ~ is the maximum departure in absolute value from mean values. bValues obtained from the Mass Spectrometer Incoherent Scatter (MSIS) model for the following conditions. Diurnal: Solar Activity Index FIO.7 = 150, geomagnetic activity index Ap = 10, day of year = 91, latitude = 45°N ; Solar: Maximum FIO.7 = 200, minimum FIO.7 = 75, Ap = lO,dayofyear = 91, latitude = 45°N, local time of day = O9OOh. Reference I. Hedin, A.E. 1983, J. Geophys. Res. A, 88, 170 262 I 11 EARTH Composition and other atmosphere profile data are given in Table 11.23. Table 11.23. Mean molecular weight. composition and molecular collision frequency \I [1, 2]. a Altitude (kIn) 100 150 200 300 400 500 700 1000 Composition (% by volume) AI 0 He MW (kgkmol- i ) N2 02 28.44 24.18 21.55 18.11 16.42 15.23 10.63 4.48 77. 61. 42. 17. 6.0 1.9 0.1 <0.05 19. 5.6 3.0 0.8 0.2 < 0.05 < 0.05 < 0.05 3.4 34. 55. 81. 91. 90. 55. 5.7 <0.05 < 0.05 .01 0.8 2.7 8.2 43. 88. 0.8 0.1 < 0.05 <0.05 <0.05 <0.05 <0.05 <0.05 H < 0.05 <0.05 <0.05 < 0.05 <0.05 0.2 1.6 6.7 log(\I) \I ins- i 3.42 1.36 0.59 -0.377 -1.143 -1.796 -2.66 -3.12 Note aQuantities obtained from the MSIS model for the following conditions: Solar activity index FIO.7 = ISO, geomagnetic index Ap = 10, day of year = 91, latitude = 45°N, and local time of day = 0900 h. References 1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office, Washington DC) 2. Hedin, A.B. 1983, J. Geophys. Res. A, 88, 170 11.20 ATMOSPHERIC REFRACTION AND AIR PATH The refractive index n of dry air at pressure Ps = 1 0l3.25 x 102 Pa and temperature Ts is given by (ns _ 1) x 106 = 64.328 + 29498.1 x 10-6 + 255.4 x 10-6 , 146 x 10-6 - u 2 41 x 10-6 - u 2 = 288.15 K where u = A-I and A is the vacuum wavelength in nm [15]. For other temperatures and pressures the refractive index is found from n - 1 = (pTslpsT)(ns - 1). Water vapor reduces the refractive index by where Pw is the partial pressure of water vapor [15]. Refractive index of air for radio waves [25] (n - 1) x 106 = 0.776: - 0.056 P; + 3.75 x 103 ~~ . Atmospheric refraction R is defined by R == Zt - Za, where Zt is true zenith distance and Za is apparent zenith distance. The constant of refraction Ro is n5 - 1 Ro = - - 2 2no where no refers to n evaluated at PO = 0.000 292 6 = 60.35" , = 10l3.25 x 102 Pa and To = 273.15 K. 11.20 ATMOSPHERIC REFRACTION AND AIR PATH / 263 For n = no refraction is [26] Rno ~ Ro tan Zt, Rno ~ = Ro Zt ;S 80°, (2.06 0.0589 + (rr/2 _ Z') - 3.71 ), For other temperature and pressure conditions Table 11.24 presents refraction data for the atmosphere. Table 11.24. Refractive index n and refraction R versus wavelength A. a A(nm) 200 220 240 260 280 300 320 340 360 380 400 450 500 550 600 650 700 800 900 1000 1200 1400 1600 1800 2000 3000 4000 5000 7000 10000 (nd - 1) X 341.9 329.4 321.2 315.3 310.9 307.6 304.9 302.7 301.0 299.5 298.3 295.9 294.3 293.1 292.2 291.5 290.9 290.1 289.6 289.2 288.7 288.4 288.2 288.1 288.0 287.7 287.7 287.6 287.6 287.6 106 -(nw - 1) 0.19 0.20 0.20 0.21 0.21 0.22 0.22 0.22 0.22 0.22 0.22 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 X 106 (n - 1) X 341.7 329.2 321.0 315.1 310.7 307.2 304.7 302.5 300.8 299.3 298.1 295.7 294.1 292.9 292.0 291.3 290.7 289.9 289.4 289.0 288.5 288.2 288.0 287.9 287.8 287.5 287.5 287.4 287.4 287.4 106 R (arcsec) 70.44 67.87 66.18 64.96 64.06 63.34 62.82 62.37 62.02 61.71 61.46 60.97 60.64 60.39 60.20 60.06 59.94 59.77 59.67 59.58 59.48 59.42 59.38 59.36 59.34 59.28 59.28 59.26 59.26 59.26 Note aRefractive index nd is for dry air at To = 273.15 K and Po = 1 013.25 X 102 Pa and the correction nw for water vapor is for Pw = 550 Pa. For other temperatures and pressures multiply nd - 1 by PTo£ POT and for other vapor pressures multiply nw - 1 by Pw/PO' Refraction R = (n - 1)/(2n 2 ) ;::;: n - 1 in arc seconds. For radio waves and dry air with Po = 1013.25 x 102 Pa, To = 273.15 K, nd is (nd -1) x 106 The correction nw for water vapor with Pw = 550 Pa is (nw - 1) x 106 = 30.2. The refractive index n is (n - 1) x 106 = 318.2. = 288.0. 264 / 11 EARTH Transmission data for atmosphere components are in Table 11.25. Table 11.25. Atmosphere transmission-;;zbsoroerlscatterer [I, 2, 3, 4, 5, 6, 7, 8, 9, 10]. }.. (I-£m) H2O C~ 03 H2O continuum Molecular scattering AerosolsD Other Total 10.00 7.50 5.00 4.00 3.00 2.00 1.00 0.90 0.80 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.38 0.36 0.34 0.32 0.30 0.28 0.26 0.24 0.22 0.20 0.971 0.126 0.415 0.994 0.462 0.828 0.990 0.790 0.967 0.943 0.981 0.990 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.723 0.994 0.970 0.980 0.565 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.525 0.0014 0.0000 0.0000 0.851 1.000 0.999 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.978 0.959 0.972 0.990 0.999 1.000 1.000 1.000 0.986 0.765 0.037 0.0000 0.0000 0.0000 0.0000 0.055 0.946 0.280 0.728 0.983 0.859 0.982 1.000 0.990 1.000 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.991 0.987 0.979 0.964 0.952 0.934 0.908 0.867 0.802 0.698 0.641 0.572 0.492 0.399 0.298 0.196 0.105 0.040 0.0083 0.0005 0.977 0.983 0.979 0.975 0.966 0.961 0.862 0.836 0.811 0.787 0.765 0.744 0.723 0.689 0.657 0.627 0.615 0.604 0.592 0.578 0.564 0.551 0.538 0.526 0.514 0.502 0.999" 0.993cd 1.000 O.906e 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.759 0.025 0.294 0.837 0.376 0.441 0.846 0.645 0.767 0.709 0.699 0.659 0.637 0.591 0.527 0.438 0.394 0.345 0.287 0.177 0.0062 0.0000 0.0000 0.0000 0.0000 0.0000 Notes DLowtran rural aerosol model. bTrace gasses. cTrace gasses (0.999). dHN03 (0.934). eN2 continuum. References 1. Anderson, G.P. et at. 1986, AFGL-TR-86-0110, Atmospheric Constituent Profiles 10-120 km, Air Force Geophysics Laboratory (now Air Force Research Laboratory). 2. Kneizys, F.X. et at. 1983, AFGL-TR-0187, Atmospheric TransmittancelRadiance: Computer Code LOWTRAN6, Air Force Geophysics Laboratory (now Air Force Research Laboratory) 3. McClatchey, R.A. et at. 1973, AFCRL-TR-73-0096, Atmospheric Absorption Line Parameters Compilation, Air Force Cambridge Research Laboratory (now Air Force Research Laboratory) 4. Rothman, L.S. & McClatchey, R.A. 1976, Appl. Optics, IS, 2616 5. Rothman, L.S. 1978, Appl. Optics, 17,507 6. Rothman, L.S. 1978,Appl. Optics, 17, 3517 7. Rothman, L.S. 1981,Appl. Optics, 20, 791 8. Rothman, L.S. 1981,Appl. Optics, 20, 1323 9. Rothman, L.S. 1983,Appl. Optics, 22, 1616 10. Rothman, L.S. 1985, Appl. Optics, 22, 2247 11.21 ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION / 265 11.21 ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION by David Crisp At wavelengths shorter than about 300 nm, scattering and continuum absorption by gases and airborne particles (aerosols) renders the Earth's atmosphere virtually opaque to incoming radiation. The depth of penetration of ultraviolet radiation is shown in Figure 11.1. For cloud-free conditions, Rayleigh scattering by the atmosphere's principal molecular constituents, N2 and 02, accounts for the majority of the scattering, while continuum absorption is produced primarily by 02 and 03. The extinction (scattering and absorption) at these wavelengths obeys the Beer-Bougher-Lambert law, which states that the intensity 1 at wavelength A and altitude z is given by I(z, e, A) = 1(00, e, A) exp{-M(e)r(z)}, 1(00, e, A) is the intensity at the top of the atmosphere at zenith angle e, M(e) is the air-mass factor (M(e) ~ sec for for < 800 ) , and r(z) is the vertical extinction optical depth e e r(z) roo = L Jo m i=l N(i, z)O'(i, z) dz, 0 N(i, z) is the altitude-dependent number density (particles m- 3 ) and O'(i, z) is the effective extinction cross section of a particle (molecule or aerosol m2 ). 200 +--N2"0_ °2 150 NO· + = w E ...°2--. • 100 N·2 0 ::;) ~ S t < SO LYMAN <1 a so 100 150 200 2SO 300 WAVELENGTH (nm) Figure 11.1. Depth of penetration of solar radiation as a function of wavelength. Altitudes correspond to an attenuation of 1/e. The principal absorbers and ionization limits are indicated. 266 I 11.21.1 11 EARTH Rayleigh Scattering The Rayleigh scattering cross section per molecule O"R()..) is given by 8 is the depolarization factor and ng is the wavelength-dependent refractive index of air. The Rayleigh scattering optical depth for air can be approximated by O"R().. ) ~ 0.(08569)..-4 (1 + 0.(0113)" -2 + 0.000 13)..-4) pI PO, P is the pressure (mbar) at altitude z, and PO = 1013.25 mbar is the sea-level pressure. The slight difference from the).. -4 dependence is introduced by the wavelength dependence of ng [27]. 11.21.2 Aerosol Extinction The continuum absorption and scattering by aerosols cannot be specified uniquely because the aerosol abundance, composition, and size distribution can vary dramatically with location and time. However, representative global-annual-average values of the wavelength-dependent aerosol extinction optical depths have been derived for climate modeling studies. Tropospheric aerosols considered in these models include sea salt, sulfates, natural dust, hydrocarbons, and other more minor constituents. The stratospheric aerosols include sulfuric acid and silicates from volcanic eruptions, ammonium sulfates and persulfates and ammonium hydrates. The integrated aerosol optical depths above sea-level (0 kID), 3 kID, and 12 kID from one such modeling study [28] are shown in Figure 11.2. For hazy conditions, actual values of optical depth can be more than an order of magnitude larger. The wavelength dependence of the optical depths results from the particle size distribution (particles usually produce the most extinction at wavelengths 1Ir' 1 10 100 W...wIongIh (jAm) Figure 11.2. The calculated aerosol optical depth of the atmosphere. 11.21 ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION / 267 comparable to their radius) as well as wavelength-dependent variations in the complex refractive indices of these materials. 11.21.3 Continuum Absorption by Gases at UV and Visible Wavelengths Molecular oxygen 02 and ozone 03 are the principal continuum absorbers at ultraviolet and visible wavelengths. The principal 02 features include the ionization continuum at}.. < 120 nm, the Schumann-Runge continuum at 140 < }.. < 180 nm, the Schumann-Runge bands at 180 < }.. < 200 nm, and the Herzberg continuum at}.. > 200 nm [29]. Several other gases, such as H20, C02, N20, and N02 also contribute absotption at these wavelengths. The wavelength-dependent absotption optical depths for these gases can be derived from their cross sections once their number densities are known. If we neglect the temperature dependence of the gas continuum cross sections, the column-integrated optical depths can be simplified further and expressed as the product of the mean cross section, and the gas column abundance X which can be derived from the pressure-dependent gas mixing ratios, r(p), X = tx) N(z)dz = Ao /-Lag 10 {P r(p')dp', 10 Ao is Avogadro's number (6.02 x 1023 molecules mol-I), /-La is the molecular weight of air (~ 29 kg kmol- I ), g is the gravitational acceleration, and p is pressure. The wavelength-dependent, column-integrated optical depth is then given by r(}..) = a(}..)X. Global-annual average gas mIxmg ratio profiles for the gases mentioned above are shown in Figure 11.3. Column abundances derived from these profiles are included in Table 11.26. Global-Annual-Avera 0.000 1 r-r----.:==r--.:.::..:.:.;.::::.=--.:..r:.=~:...-:::~....:.::.:.::.::,::.::L.:~::..:::..:::........,-___, ,, ,, , \ 0.0010 \ , \ , \ I ~ ! ~ Q. 0.0100 I ,:03 ,,. CO 2 10 Volume Mixing Ratio Figure 11.3. Global annual average gas mixing ratios. 268 I 11 EARTH Table 11.26. Column abundances of atmospheric gases. Gas 02 03 H20 C02 N20 N02 11.22 X (molecules cm- 2) 4.47 7.97 8.12 7.04 6.36 1.27 x 1024 x 1018 x 1022 x 102 1 x 1018 x 1016 ABSORPTION BY ATMOSPHERIC GASES AT VISIBLE AND INFRARED WAVELENGTHS by David Crisp At wavelengths longer than 500 run, the principal sources of abnospheric extinction are the vibrationrotation bands of gases. Unlike the slowly-varying ultraviolet gas absorption features described in the previous section, these bands consist of large numbers of narrow, overlapping absorption lines. Because the cores of these lines can become completely opaque while their wings remain much more transparent, the absorption within these bands does not strictly obey the Beer-Bougher-Lambert absorption law, except in spectral regions that are sufficiently narrow to completely resolve the individual line profiles « 0.1 cm-1). The absorption coefficients within vibration-rotation bands also vary much more strongly with pressure and temperature than those at ultraviolet wavelengths. The absorption by these gases has therefore been characterized by an effective vertical optical depth. Figures 11.4-11.6 show the vertical optical depth above sea level (top, thick line) and above a high-altitude site, e.g., Mauna Kea Observatory in Hawaii (z = 4 km, p = 600 mbar, lower thin line). These synthetic spectra were generated with an abnospheric line-by-line model. This model employs a spectral resolution adequate to completely resolve the individual absorption lines (0.1 to 10-4 cm -I), but the spectra shown here were then smoothed with a rectangular slit function with a full-width of 10 cm- I (Figure 11.4) or 5 cm- I (Figures 11.5 and 11.6). These figures therefore do not resolve individual absorption lines. Absorption line parameters for all gases are from the HITRAN database [30]. Vertical Optical Depth 10.000 ".-~-,-~~~----,--'-~~.!.,--,--~~~----, H,O 0, H,O H,O H,O H,O "~ 0 g 0.100 =E,. 0 0.010 0.001 0.4 0.6 Wavelength (1=) 0.8 Figure 11.4. Vertical optical depth versus wavelength. 1.0 11.22 ABSORPTION BY ATMOSPHERIC GASES I 269 H K L 3 2 Wavelength L' 4 (/UI1) 6 5 Figure U.5. Vertical optical depth for near-infrared wavelengths. co, H,O H,O 1.0 5 10 15 Wavelength (/UI1) 20 25 Figure 11.6. Vertical optical depth at long wavelengths. Figure 11.4 confirms that Rayleigh scattering and 03 continuum absotption dominate the extinction optical depth at wavelengths less than 0.5 ILm. At longer wavelengths, water vapor is the principal absorber with its strongest features near 0.7, 0.82, and 0.94 ILm. 02 also has four significant bands between 0.65 and 1 ILm. This figure also illustrates the advantage of working at a high-altitude site, where the atmospheric pressure and scattering optical depth are only 60% of their sea level values. Much less of an advantage is seen within the strong gas absotption bands, which are opaque even at the high-altitude site. Figure 11.5 shows that water is also the principal absorber at near-infrared wavelengths between 1 and 6 1LDl, with very strong bands centered near 1.1, 1.38, 1.88, 2.7, and beyond 6 ILm. C02 is the next most important absorber at these wavelengths, with strong bands near 2.0, 2.7, and 4.3 ILm, and much weaker absotption near 1.22, 1.4, 1.6, 4.0, 4.8, and 5.2 ILm. Other trace gases including CF4 (2.4 and 3.3lLm),03 (3.3,3.57, and 4.7 ILm), and N20 (2.1, 2.2, 2.47,2.6,2.9, and 4.7 ILm) also produce some extinction at these wavelengths. Water vapor absotption continues to dominate the spectrum at wavelengths beyond 5 ILm (Figure 11.6). The most prominent water vapor bands at thermal wavelengths are the V2 fundamental centered near 6.3 ILm and the rotation band beyond 20 JLm, but this gas contributes significant 270 / 11 EARTH absorption throughout this wavelength region. For example, the far wings of water vapor lines in the V2 and rotation bands provide much of the absorption in the atmospheric window regions near 8.5 and 12 /Lm. Within these windows, the high-altitude site (thin solid line) has up to a factor of 5 less absorption than the sea-level site (thick solid line), because the H20 absorption coefficients at these wavelengths are very strong functions of pressure (proportional to density-squared), and the high-altitude site is above the majority of the water vapor. C02 and 03 are the next most important absorbers at thermal wavelengths, with strong features near 15 and 9.6 /Lm, respectively. Cf4, N20, and N02 also have strong absorption bands at these wavelengths, but their bands are largely obscured by the stronger water vapor bands. 11.23 THERMAL EMISSION BY THE ATMOSPHERE by David Crisp The atmosphere emits as well as absorbs thermal radiation. This emission can enhance the sky brightness significantly at some wavelengths and reduce the detectability of faint astronomical sources. The intensities of the downwelling thermal radiance at a zenith angle of 21 0 are shown for a sea-level site (solid line), and a high-altitude site, e.g., Mauna Kea, Hawaii (z = 4 km, p = 600 mbar, dotted line) in Figures 11.7 and 11.8. At wavelengths within strong absorption bands, the atmosphere emits almost like a black body. Within the atmospheric window regions centered near 3.5 and 10 /Lm, the atmosphere emits much less radiation. The downward thermal radiation above a high-altitude site is substantially less than over the sea-level site because the overlying atmosphere is both cooler and less opaque. Downward Thermal Radiance 2 3 4 Wavelength (JLm) 5 6 Figure 11.7. Downward thermal radiance in the near-infrared part of the spectrum. 11.24 IONOSPHERE / 271 Downward Thermal Radiance 10.0 ,.... E ::l.. "... >-E"' 1.0 "~ '-' Gl 0 ~ !\ c: 0 'i5 0 0:: 0.1 II ! 5 10 15 Wavelength (J.Lm) 25 20 Figure 11.S. Downward thennal radiance at long wavelengths. 11.24 IONOSPHERE [17,31] The Earth's ionosphere is the partially ionized part of its atmosphere. It is divided into layers or regions, the main ones being the D, E, F1, and F2 regions, based principally on the altitude (z) profile of the electron density ne (the number of electrons per unit volume). Ionospheric structure, ne(z), varies strongly with time of day and month, latitude and solar activity. At night, the D and F1 regions vanish, the E region weakens considerably, and the F2 region tends to persist at reduced intensity. Table 11.27 summarizes the characteristics of the ionospheric layers. The quantities are explained in the text below the table. Table 11.27. Propenies of daytime ionospheric /ayers at middle and low latitudes. Quantity R Approx. altitude range (lan) Approx. height of max. ne (lan) Range of max. ne (m- 3) fo (MHz), X = 0, Max. ne (m- 3), X = 0, q(m- 3 s- I ) Layer thickness (lan) jqdz (m- 2 s-I) Ionizing emission at Sun Surface (photons m -2 s-I) 0 100 0 100 0 100 0 100 0 100 D E F1 60--95 At top 108_10 10 0.2 0.28 5.0 x 108 109 2 x loS 105-160 105-110 1011 3.3 3.82 1.35 x 10 11 l.81 x 10 11 5 x 108 109 25 4 x 1013 2.5 x 1013 160--180 170 1011 _10 12 4.25 5.34 2.24 x 10 11 3.54 x 10 11 7 x 108 l.5 x 109 60 3 x 1013 9 x 1013 > 180 200-400 10 12 6.9 1l.95 5.91 x lOll l.77 x 10 12 108 3 x 108 300 5 x 1017 12 x 1017 18 x 10 17 40 x 10 17 14 x 1013 40 x 1013 15 l.2 x 1013 F2 9 x 1013 272 / 11 EARTH Table 11.27. (Continued.) R Quantity D 4 x 1020 E F2 1018 2 x 10 16 1015 10- 12 300 a-Chapman layer 10- 14_10- 13 900 Chapman layer 4 x 10- 14 1100 Anomalous. strongly variable 10- 15 3 7 x loS 10- 3 400 3 x 103 Neutral density at height of maximum ne (m- 3 ) T at height of max. ne (K) Behavior 180 Regular Recombination coefficient a (m3 s-l) Attachment (3 (s-I). day Vej (s-l) Ven (s-l) FI 10- 3 200 250 3 x 10-4 400 10 fo = critical frequency = maximum plasma frequency of an ionospheric layer = (e 2(maximum ne)/41r2€Ome)I/2, me = electron mass, e = electron charge, 100 = permittivity of free space, ne = electron number density. (fo (Hz»2 = 80.5 (maximum ne (m- 3». R = Wolf sunspot number = k(f + 10 g) , f = total number of spots seen, g = number of disturbed regions (either single spots or groups of spots), k = a constant for a particular observatory. q = ionization rate = rate of production of ion-electron pairs per unit volume (derived, e.g., from the Sun's spectrum and ionospheric absorption coefficients). = recombination coefficient, rate of electron loss by recombination = anjn e (nj = number density of ions) = an; (normally, nj = ne). Electron loss rate an; has units of number per unit volume per unit time. a a-Chapman layer = idealized model of an ionospheric layer, single species neutral atmosphere with constant scale height H, solar radiation absorption ()( neutral gas number density, absorption coefficient is constant, q = qmoexp(1 - ZI - (secx)e- Z'), z' = (z - zmo)/H, Z is altitude, Zmo is the height of maximum production rate when the Sun is overhead (X = 0), qmo is the production rate at Zmo (when X = 0), X = solar zenith angle, production = loss, q = an;, ne = ne (Zmo) exp (1 - ZI - e- z' sec X), qm is the maximum production rate = qmo cos X, Zm is the height of maximum production = Zmo + H In (sec X), ne(Zm) = ne(Zmo) cosl/2 X. ! {3 = attachment coefficient, rate of electron loss by attachment to neutral particles to form negative ions = {3ne (neutral species number density» ne). {3 has units of inverse time. {3-Chapman layer = similar to a- Chapman layer except for electron loss which occurs by attachment, q = {3ne, ne = ne(Zmo) exp(1 - ZI - e-z' sec X), ne(Zm) = ne(Zmo) cos X. dne/dt =q - an; - {3ne, usually either a or {3. 11.24 IONOSPHERE Vei, Ven = collision frequency of mean electron with ions, and neutral particles. Ven (S-I) = (6.93 x lOSn(N2) number densities in m- 3 . WB (rad s-I) + 4.37 x lOSn(02)) u, u is electron energy in J, n(N2) and n(02) are = gyrofrequency = QB/m, Q (T), m = charged particle mass (kg). = charge on particle (C), B = magnetic flux density (rads- I )/21l'. fB (Hz) = WB (rad s-I) for an electron = 1.759 x 1011 B (T). !B 1 273 WB (Hz) for an electron = 2.799 x 1010 B (T). WN (rad s-I) plasma frequency = (nee2/Eome) 1/2, e = charge on an electron. l/1 = Faraday rotation ionosphere = rotation of the polarization angle of a radio wave propagating through the is the speed of light, B is a unit vector in the direction of B, dl is a path increment along the wave propagation direction, integration is along the path of the radio wave, cu is the circular frequency of the wave, f is the frequency of the wave in Hz, /LO is the permeability of fn-.e space, H is the magnetic field strength (A m- I ), all units are SI, it is assumed that cu » CUB, the formula is approximate for cross-field propagation but accurate to within a few degrees of the normal to B, the rotation follows the right-hand rule. Photon efficiency of ionization,., is the ratio of the rate of production of ion-electron pairs (number m- 3 s-I) to the total number of photons absorbed per unit volume and per unit time. Ionization of atomic species yields one ion-election pair for every 5.45 x 10- 18 J absorbed. Accordingly, C n "' = 1 8 5.45 x 10- 1 J/(hc/A) = 36.5/A (nm), 2 < A < lOOnm, h is Planck's constant and A is the wavelength of the radiation. For A < 2 nm,,., is approximately 20. 274 I 11.24.1 11 EARTH Ionosphere as a Whole The total electron content of the ionosphere is I == forx ne dz, where z is altitude. More generally, I can be defined as a line integral along an arbitrary path. Typically, I is about 10 17 electrons m- 2 . The equivalent thickness or slab thickness t' of the ionosphere is t' I == ---. maxne This is the thickness of a hypothetical layer with uniform electron density equal to the maximum value of ne and total electron content equal to I. Typically, t' is about 250 Ian. 11.24.2 Effects of Earth Curvature The factor sec X in the formulas for ionization and absorption should be replaced by Ch(x, X) to account for Earth curvature, where x = (a + z) I H, H = scale height, a = Earth radius, z = altitude, and X is the zenith angle. Curvature effects of the atmosphere are listed in Table 11.28. Table 11.28. Thefunction Ch(x. x).a Q x= sec X = 50 100 200 400 800 1000 Note a Q =: (a 30° 1.155 45° 1.414 Ch(x. X) 60° 75° 2.000 3.864 80° 5.76 85° 11.47 90° 1.148 1.151 1.153 1.154 1.154 1.155 1.389 1.401 1.407 l.4ll 1.412 1.413 1.901 1.946 1.972 1.985 1.993 1.994 4.19 4.70 5.10 5.38 5.55 5.59 5.82 7.07 8.28 9.33 10.15 10.35 8.93 12.58 17.76 25.09 35.46 39.65 3.228 3.473 3.646 3.742 3.800 3.812 95° 00 16 30 68 220 1476 + zo)/ H. zo = altitude of maximum ionization rate. 11.24.3 International Reference Ionosphere (IRI) IRI is an empirical reference model of ionospheric electron density, electron and ion temperatures, and ion composition recommended by COSPAR (Committee on Space Research) and URSI (International Union of Radio Science). It is updated bi-yearly; the 1990 model is used below. IRI is distributed by the National Space Science Data Center and World Data Center A for Rockets and Satellites (NSSDCIWDC-A-R&S) in Greenbelt, Md. IRI is available online on SPAN (Space Physics Analysis Network) now called NSI-DECNET (NASA Science Internet) and can be accessed interactively on NSSDC's Online Data Information Service (NOmS) account. Tables 11.29 to 11.36 give data about this IRI ionosphere model. 11.24 IONOSPHERE Thble 11.29. IRI-90 electron density. a Noon z (km) ne (m- 3) 65 70 75 80 85 90 95 100 8.3 2.1 3.7 5.1 1.1 1.2 5.2 1.1 x x x x x x x x ne/ne F2(max) 3 7 1.3 1.8 3.7 4.0 1.8 3.7 107 108 108 108 109 1010 1010 1011 Midnight x x x x x x x x ne (m- 3) ne/ne F2(max) 0 0 0 0 x x x x 0 0 0 0 x x x x 10-4 10-4 10-3 10-3 10-3 10-2 10- 1 10- 1 2.6 4.8 1.6 1.6 108 108 109 109 Note aLatitude = 45°, Longitude = 260o E, R = 0, Day X = 21.6° (Noon), 111.6° (Midnight). 2.3 4.2 1.4 1.4 = 10-3 10- 3 10- 2 10-2 6/22, F10.7 = 63.8, Thble 11.30. IRI-90 electron density. a Midnight Noon z (kIn) ne (m- 3) 2.7 6.7 1.2 1.6 3.4 3.3 1.1 1.8 65 70 75 80 85 90 95 100 x x x x x x x x 108 108 109 109 109 10 10 1011 1011 ne/ne F2(max) 4x 1x 1.7 x 2.4 x 5.0 x 4.8 x 1.6 x 2.6 x 10-4 10-3 10-3 10-3 10-3 10-2 10- 1 10- 1 ne (m- 3) ne/ne F2(max) 0 0 0 0 x x x x 0 0 0 0 x x x x 2.6 4.8 2.8 3.9 Note X 6 1.1 6.2 8.8 108 108 109 109 aLatitude = 45°, Longitude = 260o E, R = 150, Day 21.6° (Noon), 111.6° (Midnight). = = 10-4 10-3 10-3 10- 3 6/22, FlO.7 = Thble 11.31. IRI-90 electron tknsity.a 6122 3121 9123 12122 R=O ne ne ne ne (70km) (SOkm) (9Okm) (1ookm) 1.9 x 4.5 x 1.0 x 9.5 x 108 108 1010 1010 ne ne ne ne (70km) (SOkm) (9Okm) (lookm) 5.9 x 1.4 x 2.9 x 1.6 x 108 109 1010 1011 2.1 5.1 1.2 1.1 6.7 1.6 3.3 1.8 x x x x 108 108 1010 1011 1.8 x 4.4 x 1.0 x 9.5 x 108 108 1010 1010 1.5 3.8 8.0 7.0 x x x x 108 108 109 1010 x x x x 108 109 1010 1011 1.6 4.1 9.0 1.0 x x x x 108 108 109 1011 R = 150 Note x x x x 108 109 1010 1011 5.8 1.0 2.9 1.6 = aTune = Noon, Latitude = 45°, Longitude = 260o E, FlO.7 63.8 (R 0), 193 (R 150), X 44.5°(3121), 21.6°(6122), 45.4°(9123), 68.5°(12122), units of ne are number m- 3. = = = 193, / 275 276 / 11 EARTH Table 11.32. IRI-90 electron density. a 45 60 90 75 R=O ne ne ne ne (70km) (80km) (90km) (lOOkm) 1.5 3.8 8.0 7.0 ne ne ne ne (70km) (80km) (90km) (lOOkm) 1.6 4.1 9.0 1.0 X X X X 108 108 109 1010 1.2 3.7 6.0 3.8 R X X X X 108 108 109 1011 X X X X 108 108 109 1010 o o 4.7 4.4 X X 108 109 = 150 1.2 3.7 6.3 5.4 X X X X 108 108 109 1010 o o 4.7 6.3 X X 108 109 1.6 3.8 3.4 4.0 X X X X 108 108 109 109 Note aTime = Noon, Longitude = 260o E, FlO.7 = 63.8 (R = 0), 193 (R = 150), X = 68.5°(45°N), 83.5°(600 N), 98.5°(75°N), 113.5°(900 N), Day = 12/22, units of ne are number m- 3. Table 11.33. IRJ-90 model ionosphere. a 100 200 300 400 500 600 700 800 900 1000 1.08 2.74 2.40 1.11 4.63 2.41 1.61 1.28 1.14 1.07 X X X X X X X X X X 1011 1011 1011 1011 1010 1010 1010 1010 1010 1010 Tn (K) Tj (K) Te (K) 0+ 786 821 822 822 822 822 822 822 822 786 1011 1237 1513 1813 2113 2413 2712 3012 1419 2689 2831 2835 2846 2936 3042 3148 3254 23 99 100 96 88 80 69 59 50 o H+ He+ 0 0 0 0 4 10 18 28 37 45 0 0 0 0 0 1 2 3 4 5 48 21 52 56 o o o 0 0 0 0 o o o o o 1 0 0 0 Note aLatitude = 45°, Longitude = 260o E, R = 0, Day = 6/22, FlO.7 = 63.8, X = 21.6°, Time = Noon, Tn = neutral temperature, Tj = ion temperature, Te = electron temperature, ion composition is given in percent. Table 11.34. IRJ-90 model ionosphere. a 100 200 300 400 500 600 700 800 900 1000 1.79 3.92 6.85 6.25 4.63 3.29 2.51 2.10 1.89 1. 77 X X X X X X X X X X 1011 lOll lOll lOll lOll 1011 lOll 1011 lOll lOll Tn (K) 11 (K) Te (K) 0+ 1187 1361 1385 1389 1390 1390 1390 1390 1390 1187 1361 1385 1513 1813 2113 2413 2712 3012 1421 2689 2831 2835 2846 2936 3042 3148 3254 59 100 100 96 88 80 69 59 50 o H+ He+ 0 0 0 0 4 10 18 28 37 45 0 0 0 0 0 58 6 o o o 1 o 2 3 4 5 o o o o 42 35 0 0 0 0 0 0 0 0 Note aLatitude = 45°, Longitude = 260o E, R = 150, Day = 6/22, FlO.7 = 193, X = 21.6°, Time = Noon, Tn = neutral temperature, Tj = ion temperature, Te = electron temperature, ion composition is given in percent. 11.24 IONOSPHERE Table 11.35. IRl-90 model i01Wsphere. a Noon ne (m- 3) Til (K) Tj (K) Te (K) %0+ %H+ %He+ Midnight Noon R=O 2.87 x lOll 9.07 x 1010 815 692 817 899 2076 1010 53b 42c 0 0 0 0 Midnight R= 150 5.94 x 1011 3.70 x 1010 1090 1314 1090 1314 2076 1090 99 99 0 0 0 0 Note aLatitude 45°, Longitude 260o E, Day 6/22, FlO.7 63.8 (R 0), 193 (R 150), Til neutral temperature, Tj ion temperature, Te electron temperature, Altitude 250 kin, X 21.6° (Noon), 111.6° (Midnight). bThe other ions in this case are 46% NO+ and 1% cThe other ions in this case are 57% NO+ and 1% = = = = = = = = = = = ot. ot. Table 11.36. IRI-90 model ionosphere. a Date 3nI 6122 9123 12122 3.27 x 1011 773 864 1882 76 0 0 0 23 4.27 x lOll 687 802 1780 95 0 0 0 5 8.60 x lOll 1219 1219 1882 95 0 0 0 5 1.63 x 1012 1089 1089 1782 95 0 0 0 5 R=O ne (m- 3) Til (K) Tj (K) Te (K) %0+ %H+ %He+ %ot %NO+ 3.07 x 1011 777 867 1882 76 0 0 0 23 2.87 x lOll 815 899 2076 53 0 0 1.15 x 1012 1221 1221 1882 95 0 0 0 5 5.94 x 1011 1314 1314 2076 99 0 0 0 0 46 R ne (m- 3) Til (K) Tj (K) Te (K) %0+ %H+ %He+ %ot %NO+ = 150 Note a Latitude 45°, Longitude 260°, FlO.7 63.8 (R 0), 193 (R 150), Til neutral temperature, Tj ion temperature, Te electron temperature, Altitude 250 kID, X 44.5°(3121), 21.6°(6122), 45.4°(9123), 68.5°(12122). = = = = = = = = = / 277 278 I 11.24.4 11 EARTH Irregularities of Ionospheric Behavior [31] Storm Magnetic Storm F-Region Ionospheric Storm 11.24.5 A severe departure from normal behavior lasting from one to several days. A magnetic storm consists of three phases: (1) an increase of magnetic field lasting a few hours; (2) a large decrease in the horizontal component of magnetic field building up to a maximum in about a day; (3) a recovery to normal over a few days. The initial phase (1) is caused by the compression of the magnet sphere by a burst of solar plasma. The main phase (2) is due to the ring current in the magnetosphere which flows around the Earth from east to west. This storm is characterized by an initial positive phase of increasing electron density lasting a few hours followed by a main or negative phase of decreasing ne. The ionosphere gradually returns to normal over one to several days during the recovery phase. Sq Current System The Sq current system is an ionospheric current system due to neutral winds blowing ions across magnetic field lines. The Sq winds and currents are driven by solar (S) tides under quiet (q) geomagnetic conditions. The winds have speeds of tens of meters per second and associated electric fields are a few millivolts per meter. The Sq currents produce daily magnetic field variations at the Earth's surface. Node of EW currents is at latitude 38°. Current between node and either pole or equator (at equinox and zero sunspots) = 5.9 x 104 A. 11.24.6 Magnetic Indices [31] K p is based on the range of variation within 3 hour periods of the day observed in the records from about a dozen selected magnetic observatories. The K p value for each 3 hour interval of the day is reported on a scale from 0 (very quiet) to 9 (very disturbed). Integer values are subdivided into thirds by use of the symbols + and -. The K p scale is quasi-logarithmic. ap-similar to K p , but a linear scale of geomagnetic activity. The value of a p is approximately half the range of variation of the most disturbed magnetic component measured in n T. The relation between Kp and Ap is shown in Table 11.37. Table 11.37. Relation between K p and ap. Kp ap 0 0 1 3 2 7 3 15 4 27 5 48 6 80 7 140 8 240 9 400 Ap is a daily index, the average of a p over a day. AE is a geomagnetic index measuring the activity level of the auroral zone, particularly valuable as an indicator of magnetic substorms. L Kp is the sum of the eight Kp values over a UT day. 11.25 NIGHT 11.25 SKY AND AURORA / 279 NIGHT SKY AND AURORA [17,32-36] The units for expressing the night sky brightness of spectroscopic features (lines or bands of restricted extent in wavelength) are: 1 Rayleigh = R = = 106 photons emitted in 41r sr per cm2 vertical column per sec 1.58 x 1O-7 A-I J m- 2 sr- I s-I at zenith (A in nm) = 1.95 x 10-7 nit for A = 555 nm. I Photon = 1.986 x 1O- 16 A-I J (A in nm) I mv = 10 star deg- 2 near 550 nm through clear atmosphere = 3.6 x 10-2 R nm- I = 7.1 x 10-7 nit (for a bandwidth of 100 nm). Components of the night sky brightness are given in Table 11.38. Table 11.38. Night sky brightness. Source (near zenith) Airglow Atomic lines Bands and continuum Zodiacal light (away from zodiac) Faint stars, m > 6 (galactic pole) (mean sky) (gal. equator) Diffuse galactic light Total brightness (zenith, mean sky) (15° lat, mean sky) Photographic 10th mag stars 30 60 16 48 140 10 145 190 Visual deg -2 Photometry 10-5 nit 40 50 100 30 95 320 20 290 380 3 4 6 2 7 23 I 21 28 Color index of night sky C ~ 0.7 (C = B - V - 0.11, where B is the apparent magnitude at 555 nm and V is the apparent magnitude at 435 nm). Airglow variation with latitude: Generally brighter at middle and high latitudes than at low latitudes, a factor of ~ 2 increases with latitude for some emissions [35]. Airglow variation with solar cycle activity: Good correlation with sunspot activity for 01 red line (630 nm), ambiguous evidence for variation in green line (557.7 nm) [35]. Van Rijin function: Off-zenith path length through a spherically symmetric airglow layer is increased relative to the zenith viewing by a factor where r is the Earth's radius, h is the height of the emitting layer above the Earth's surface, and z is the zenith angle. The full moon brightness is 1100 tenth magnitude stars per square degree in the photographic spectral region and 100 in the visual band. For other phases of the Moon multiply by cfJ(a), where a is the phase angle, the angle between the Sun and Earth seen from the Moon, and cfJ(a) is the phase law or the change of the Moon's brightness with a(cfJ(O) = 1) [17]. The sky brightness during twilight is given in Table 11.39. 280 I 11 EARTH Table 11.39. Variation ofsky brightness throughout twilight relmive to 0° solar depression angle [1]. Solar depression angle 0° 6° 12° 18° Log relative brightness 0 -2.7 -4.7 -5.8 Reference 1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London) Table 11.40 lists the night sky emissions from various components. Table 11.40. Spectral emissions in the night sky [1, 2, 3, 4, 5]. a Intensity Emitter OI OI OI OI OI OI NI NI NI NIl Nal In In Call Lil N2 N2 N2 N2 N2 ~2 Oz Oz Oz Oz 0+ 2 OR OR OR OR NOz NOy ReI A,etc. Night Twilight Aurora run R R kR 557.7 630.0-636.4 297.2 130.4-135.6 777.4 844.6 1040 346.6 519.9 VIS.andFUV 589.0-589.6 summer winter 656.3 121.6 393.3-396.7 670.8 IR 250 100 180 1000 100 2-100 6 30±2O 10 12 6 1 0.1-2 45 150 13 10 BUV NUV,VIS. 630-890 300-400 864.5 1270 1580 VIS.,IR 1580 VIS. 8342 Total 500-650 MUV 1083 < 100 R to > 500 R night to night variation Sporadic enhancements in tropical nightglow ICBmAurora Observed from satellites, ICB m Aurora ICBmAurora ICBmAurora ICBmAurora NaD, Strong seasonal variation 30 200 15 2500 1 1 10 100 1000 5000 Ha La 150 30 880 110 200-400 55 2000 UV FUV Blue Remarks 100 1000 1500 500 6000 20000 150 630 60 1200 2500 26 150000 130 2000 4.5 x 106 250 20-60 1st positive, ICB m Aurora 2nd positive, ICB m Aurora LBR bands, ICB m Aurora VK bands, ICB m Aurora BR, WK, ICB m Aurora, rough value deduced from photometer data 1st negative, ICB m Aurora M, ICB m Aurora Hertzberg hands Atm. (0-1), ICB m Aurora Atm. (0-0), not seen at ground, ICB m Aurora IR Atm, ICB m Aurora 1st negative, ICB m Aurora (4-2) Strongest bands are in NIR (5-0)(7-1) (8-2) (9-3) bands (6,2)band Nightglow continuum ICBmAurora 1000 Note aLBR = Lyman-Birge-Ropfield, M = Meinel, VK Ropfield,lCB m = 01(557.7) = 100 kR [1,2,3,4]. = Vegard-Kaplan, WK = Watson-Koontz. BR = Birg~ 11.25 NIGHT SKY AND AURORA I 281 References 1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London) 2. Vallance Jones, A. 1974, Aurora (Reidel, Boston) 3. Roach, F.E., & Gordon, J.L. 1973, The Light o/the Night Sky, (Reidel, Boston) 4. Krassovsky, V.I. et al. 1962, Planet. Space Sci., 9, 883 5. Chamberlain, J.W. 1961, Physics o/the Aurora and Airglow, (Academic Press, New York) Zone of maximum auroral activity = 60-75 0 geomagnetic latitude [32]. Seasonal variation: Minima in auroral frequency at solstices, maxima at equinoxes (approximately a factor of 2 increase from minima to maxima as seen from Yerkes Observatory) [36]. Table 11.41 gives details of the types of aurorae. Thble 11.41. Auroral heights [1, 2]. Aurora Height Lower border strong aurora Lower border weak aurora Average value Average height of maximum emission Vertical extents Upper extremity 95km 114km 105-108km IlOkm 20-40km frequently> 200 km Type c (normal aurora) Sunlit upper extremity 700 km (1000 km in extreme cases) Type b: red lower border Type d (red overall) lower border 250km 8~I00km References I. Allen, C. W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London) 2. Meinel, A.B. et al. 1954, J. Geophys. Res., 59, 407 The proton input needed to produce auroral Ha is given in Table 11.42. Table 11.42. Flux o/monoenergetic protons required to produce 10 kR o/Ha in the zenith [l]. Initial energy keV Minimum penetration height km 130 27 8.5 100 110 120 photons Proton fiux cm- 2 s-I Total incident energy fiux eVcm- 2 s-I 60 27 7 1.6 x 108 5 x 108 14 x 108 2.1 x 1013 1.4 x 1013 1.2 x 1013 Ha Reference 1. Chamberlain, J.W. 1961, Physics o/the Aurora and Airglow (Academic Press, New York) Auroral International Coefficients of Brightness: I.C.B. I II III IV 557.7 brightness 557.7 brightness 557.7 brightness 557.7 brightness = = = = 1 kR ~ 10-4 nit, 10 kR ~ 10-3 nit, 100 kR ~ 10-2 nit, 1000 kR ~ 10- 1 nit. 282 / 11 EARTH 11.26 GEOMAGNETISM [37-39] The geomagnetic field arises from sources both interior and exterior to the solid Earth, including electric currents in the liquid outer core and the ionosphere and the magnetization of crustal rocks. Models of the global magnetic field are intended to describe the field originating in the core (the main field). The description of the main field is based on a spherical harmonic description of the potential V(r, rp, t) for magnetic induction B(r, 8, rp, t) e, B = -VV, where r, 8, rp are spherical polar coordinates and t is time. The spherical harmonic expansion of V is V(r, e, rp, t) = a 1+1 aLL C:·) L 1 _ {gi(t) cosmrp + hi(t) sinmrp} pr(cos8), 1=1 m=O where a is the mean radius of the Earth (a = 6371.2 km), L is the truncation level of the expansion, and the pr (cos e) are Schmidt quasi-normalized associated Legendre functions, i.e., the integral of pr squared over all solid angles is 41f/(21 + 1). The quantities gi(t) and hi(t) are known as Gauss geomagnetic coefficients; they vary with time over a broad range of time scales from less than a year to hundreds of millions of years. The core dynamo responsible for generating the main magnetic field is fundamentally time dependent in its behavior. If the small electrical conductivity of the mantle is neglected, then the above representation of the main geomagnetic field can be used to extrapolate the surface field down to the core-mantle boundary. The components of the magnetic field are given by Br av L = -a; = L a 1+2 L(l + 1) (;-) 1 {gi(t)cosmrp _ + hi(t) sinmrp} pr(cos8), 1=1 m=O 1 aV a Be=-;:-ae=-LLC:-) L 1 1+2 1=1 m=O 1 BtfJ = - - .-8 r SID av !l..l. u." = {gi(t)cosmrp+hi(t)sinmrp} LL -r L 1 (a)/+2 1=1 m=O d pm d~ {gi(t)sinmrp -hi(t)cosmrp} (cos 8), mpm(cos8) I. sm 8 . Magnetic field observations are generally described in terms of the quantities: X Y = - Be = north magnetic field component, = BtfJ = east magnetic field component, = - Br = vertically downward magnetic field component, H = (X 2 + y2)1/2 = horizontal magnetic field intensity, F = (X 2 + y2 + Z2)1/2 = total magnetic field intensity, 1= arctan(Z/ H) = magnetic inclination, D = arctan(Y / X) = magnetic declination. Z Historically, there has been much discussion of the westward drift of the main field or components thereof, particularly the nondipole part of the field (see below). While some features of the field may participate in a westward drift, the secular variation of the main field is more complex than a simple westward drift. 11.26 GEOMAGNETISM 11.26.1 / 283 Geomagnetic Dipole The contributions to V of the I = 1 terms in the spherical harmonic representation of V are from magnetic dipoles situated at r = 0 and oriented along the coordinate axes. a 3 cosO 0 r2 a 3 cos f/> sin 0 gl is the potential of a magnetic dipole in the +z-direction (along the Earth's rotation axis), gl is the potential of a magnetic dipole in the +x-direction (along the Greenwich meridian), a 3 sin f/> sin 0 1 hI r2 is the potential of a magnetic dipole in the +y-direction. r2 1 The total dipole potential Vdipo1e is the sum of the above terms. The total dipole magnetic field Bdipole = - V Vdipole has components B~pole = ~3 (g? cosO + sin8(g} cosf/> + hI sinf/») , B:pole dipole BI/> = ~: (g? sinO - cosO(g} cosf/> + hI sinf/») • a 3 1· I = 3(gl smf/> - hi cosf/». r The magnetic dipole moment m has magnitude The magnetic dipole moment pierces the surface of the Earth at colatitude 8m and longitude f/>m, given by lim ~ aICtan { «(g1)2 +gtl>2)1/2}, ~ ~ aICtan (;1). Table 11.43 lists the values of m/47ra 3 • 8m• and f/>m for the years 1945-1990. The orientation and magnitude of the centered. tilted. magnetic dipole from the I = 1 terms in the spherical harmonic representation of the main field is given in Table 11.43. 1Bble 11.43. Orientation and magnitude o/the centered. tilted. magnetic dipole. (m/4na 3 ). l04nT Colatitude of Geomagnetic Pole (8m• degrees) Longitude of Geomagnetic Pole (I/>m. degrees)" 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 3.122 3.118 3.113 3.104 3.095 3.083 3.070 3.057 3.043 3.032 11.53 11.53 11.54 11.49 11.47 11.41 11.31 11.19 11.03 10.87 291.5 291.2 290.8 290.5 290.1 289.8 289.5 289.2 289.1 288.9 Note aEast from the Greenwich meridian. 284 / 11 EARTH The time rate of change of the magnetic dipole is obtained by differentiating the above expressions for m, em, and <Pm with respect to time. 11.26.2 Eccentric Dipole The Cartesian coordinates (xo, YO, zo) of the eccentric dipole that best represents the main field are given by a(LJ - gfT) xo----...:"...".. - 3(m/4rra 3 )2' YO = a(L2 - h~ T) 3(m/4rra 3 )2' zo = a(Lo - g?T) 3(m/4rra 3 )2' where 11.26.3 Dipole Coordinate System A coordinate system with its z-axis along the direction of the centered, tilted dipole is the dipole coordinate system or the geomagnetic coordinate system. The pole of this coordinate system is located at em, <Pm, given above. This is the geomagnetic pole or dipole pole. If &J is a vector in the dipole coordinate system and:!. is a vector in the standard coordinate system, then where R is the rotation matrix with elements R - =[ em cos <Pm -sin <Pm sin em cos <Pm COS cos em sin <Pm cos <Pm sin em sin <Pm -sin em] o cos em . 11.26.4 Magnetic Dip-Poles A magnetic dip-pole is a location at which the horizontal magnetic field is zero. At the north and south dip-poles the magnetic potential has its maximum and minimum values, respectively. Table 11.44 gives the coordinates of the dip-poles at different times. 11.27 METEORITES AND CRATERS / 285 1Bble 11.44. Coordinotes oj the magnetic dip-poles. Year Latitude (N) Longitude (W) North Dip-Pole 1831.4 1904.5 1948.0 1962.5 1973.5 70"05' 70"30' 73°00' 75°06' 76°00' 96°46' 95°30' 100"00' 100"48' 100"36' South Dip-Pole 1841.0 1899.8 1909.0 1912.0 1931.0 1952.0 1962.1 11.26.5 75°05' 72°40' 72°55' 71°10' 70"20' 68°42' 67°30' 154°08' 152°30' 155°16' 150°45' 149°00' 143°00' 140"00' Centered, TOted Dipole Field [39] Vertical magnetic field at geomagnetic poles, at r = a, = 2 (4:a 3 ) = 6.064 x 104 nT. Horizontal magnetic field at geomagnetic equator, at r = a, = 41ra ~3 = 3.032 x l04nT. In the dipole coordinate system m V = 41rr2 cos9mag _ a 3 cos 9mag - r2 (~) 41ra 3 ' V(r = a) = (4':3)acOS9mag, where 9mag is the magnetic colatitude. Numerical values are for the IGRF (1991 Revision). 11.27 METEORITES AND CRATERS [17,40--44] Classes of meteorites (natural objects of extraterrestrial origin that survive passage through the atmosphere) and statistics on falls and finds are given in Table 11.45. Falls refer to meteorites that were seen to fall; they are usually recovered soon after fall. Finds refer to meteorites that were not seen to fall but were found and recognized subsequently. Meteorites are broadly classified into stones, irons (pure metal, essentially nickel-iron alloy), and stony-irons. Additional classifications are required because of the great diversity of objects in these broad classes. Stony meteorites are divided into chondrites (meteorites containing distinctive features known as chondrules with compositions very similar to that of the solar photosphere for all but the most volatile elements) and achondrites (differentiated meteorites with compositions considerably different from the Sun). 286 I 11 EARTH Table 11.45. Meteorite classes and statistics on/ails andfinds [1]. Findsa Fall frequency Class Chondrites CI CM CO CV H L LL EH EL Other Anchondrites Eucrites Howardites Diogenites Ureilites Aubrites Shergottites Nakhlites Chassignites Anorthositic breccias Stony-irons Mesosiderites Pal1asites Irons lAB IC IIAB IIC lID lIE IIF IIIAB mCD IIIE IIIF IVA IVB Other irons Non-Antarctic Antarcticc 0.60 2.2 0.60 0.84 33.2 38.3 7.9 0.84 0.72 0.36 0 5 2 4 347 286 21 3 4 3 0 34 6 5 671 224 42 6 1 3 3.0 2.2 1.1 0.48 1.1 0.24 0.12 0.12 8 3 0 6 1 0 2 0 13 4 9 9 17 2 0 0 0 0 0 6 3 0.72 0.36 22 34 2 6 0 5 0 3 1 1 8 2 0 0 3 0 13 0.73 0.08 0.45 0.05 0.09 97 11 60 7 12 13 4 189 19 13 6 52 12 175 4 0 6 0 0 0 0 0 0 0 0 1 0 0 Falls (%)h 5 18 5 7 276 319 66 7 6 3 25 18 9 4 9 2 1 1 O.lO 0.03 1.42 0.14 0.10 0.05 0.39 0.09 1.32 Notes aData for finds are given to provide an indication of available material. The unusual conditions in the Antarctic favor the recovery of large numbers of meteorites without the selection biases of non-Antarctic regions (e.g., in nonAntarctic regions, stony meteorites, especially anchondrites are more easily confused with terrestrial rocks than iron meteorites). The statistics for Antarctic finds, therefore, more closely resemble those of falls than non-Antarctic finds. In fact, several rarer classes are overrepresented in the Antarctic collections. biron-meteorite fall statistics calculated from finds, scaled to percentage of total iron-meteorite falls. cus finds in the Antarctic. In addition, > 6000 meteorites have been recovered from the Antarctic by Japanese teams. Reference 1. Sears, D.W.G., & Dodd, R.T. 1988, in Meteorites and the Early Solar System, edited by J.F. Kerridge and M.S. Matthews (University of Arizona Press, TUcson, Arizona),pp. 3-31 11.27 METEORITES AND CRATERS 11.27.1 / 287 Meteorite Infall Rates Fall of meteorites large enough to be seen and found, ~ 2 meteorites per day over the whole Earth. The cumulative flux of meteoroids F in the vicinity of the Earth-Moon system is given by F ( = 7.9(m (kg))-1.16, # ) 1()6 km2 yr 10- 10 < m < 105 kg, where F is the number of meteoroids with mass greater than m per 106 km2 per year. Accordingly, meteoroids with masses greater than about 6 kg will arrive in the vicinity of the Earth-Moon system at a rate of about one per 106 km2 per year. 11.27.2 Meteorite Masses The most probable size of found meteorites for iron is 15 kg and for stones 3 kg. Meteoroid masses before entry to the Earth's atmosphere are ~ 100 kg. The mass of the greatest known meteorite (Hoba, an iron meteorite) is 6 x 104 kg. 11.27.3 Cratering Efficiency Mass displaced from crater/mass of impactor = cratering efficiency = 0.2 (1.612g L)-0.65 , Vi g = gravity(m s-2), L = projectile diameter (m), Vi 11.27.4 = impact velocity (m s-I). Crater Diameter Scaling Relations for Terrestrial Craters [42] D = 0.0133W 1/ 3.4 + 1.51p;!2 p~I/2 L, D = 1.8p~l1p~I/3g-0.2Lo.13WO.22, D -- 0 .2Pp1/6 PT-1/2 W O. 28 ' D > 1 km • rv All units in the above formulas are SI. D = diameter of a transient impact crater, pp PT W = impactor density, = target density, = impactor energy, L = impactor diameter. Formulas valid for vertical impacts. Energy of 1 kiloton of TNT = 4.2 x 10 12 J. 288 / 11.27.5 11 EARTH Crater Dimensions Rim height hR above original ground surface of many fresh (unrelaxed) lunar, terrestrial, explosion, and laboratory impact craters with diameter (rim to rim), D ;S 15 km, hR (m) = 0.036(D (m»1.014. For craters with D > 15 km on the Moon (collapsed craters) hR (m) = 0.236(D (m))0.399. Crater depth H (rim to floor) of fresh lunar craters with diameter D ;S 11 km H (m) = 0.196(D (m»l.01. Crater depth of collapsed lunar craters H (m) = l.044(D (m))0.301 11 km < D < 400 km. Crater depth of simple" (relatively young) terrestrial impact craters (e.g., Meteor Crater, Arizona) H (m) = 0.14(D (m))1.02. Crater depth of collapsed or complex terrestrial impact craters H (m) = 0.27(D (m))0.16. Estimated cratering rate from relatively young « 120 Myr) large craters on the North American and European cratons (5.4 ± 2.7) x 10- 15 km- 2 yr- 1 for D ~ 20km. Estimated cratering rate from smaller craters on a nonglaciated area in the U.S. (2.2 ± 1.1) x 10- 14 km- 2 yr- 1 for D ~ lOkm. Important impact craters are listed in Table 11.46. Table 11.46. Terrestrial impact structures [1]. Diameter Age (Ian) (Myr) Name Latitude Longitude Amguid, Algeria Aouelloul, Mauritaniaa Araguainha Dome, Brazil Azuara, Spain Barringer, Arizona, USAa Bee Bluff, Texas, USA Beyenchime-Salaatin, Russia Bigatch,}(azakhstan Boltysh, Ukraine Bosumtwi, Ghana Boxhole, Northern Territory, Australiaa B.P. Structure, Libya Brent, Ontario, Canadaa 26°05'N 20° 15'N 16°46'S 41°01'N 35°02'N 29°02'N 71°50'N 48°30'N 48°45'N 06°32'N 004°23'E 012°41'W 052°59'W ()()()055'W 1l100l'W 099°51'W 123°30'E 082°00'E 032°lO'E 001°25'W 0.45 0.37 40. 30. 1.2 2.4 8. 7. 25. 10.5 < 0.1 3.1 ±0.3 < 250 < 13O 0.025 <40 < 65 6±3 l00±5 1.3 ± 0.2 22°37'S 135°12'E 024°20'E 078°29'W 0.18 2.8 3.8 < 120 450±30 25° 19'N 46°05'N 11.27 METEORITES AND CRATERS Table 11.46. (Continued.) Name Campo del Cielo. Argentina (20)"b Carswell. Saskatchewan. Canada Charlevoix. Quebec, Canada Clearwater Lake East, Quebec, Canada Clearwater Lake West, Quebec, Canada Connolly Basin, Western Australia, AustraliaQ Crooked Creek, Missouri. USA Dalgaranga, Western Australia, AustraiiaQ Decaturville, Missouri, USA Deep Bay. Saskatchewan, Canada Dellen, Sweden Eagle Butte, Alberta, Canada E1' gygytgyn, Russia Flynn Creek. Tennessee, USA Glover Bluff. Wisconsin. USA Goat Paddock. Western Australia, Australia Gosses Bluff. Northern Territory, Australia Gow Lake, Saskatchewan, Canada Gusev. Russia Haughton. Northwest Territories, Canada Haviland, Kansas, USAQ Henbury, Northern Territory, Australia (14)"b Holleford, Ontario, Canada De Rouleau, Quebec, Canada Dintsy, Ukraine Dumetsy, Estonia Janisjlirvi, Russia Kaalijlirvi, Estonia (7)"b Kaluga, Russia Kamensk, Russia Kara, RussiaQ Karla, Russia Kelly West, Northern Territory, Australia Kentland, Indiana, USA Kjardla, Estonia Kursk, Russia Lac Couture, Quebec, Canada Lac La Moinerie. Quebec, Canada Lappajlirvi, FiniandQ Liverpool, Northern Territory, Australia Logancha, Russia Logoisk, Byelorussia Lonar, India Diameter Age Latitude Longitude (Jan) (Myr) 27°3S'S 5s027'N 47°32'N 061°42'W 109°30'W 0700 lS'W 0.09 37. 46. 117±S 36O±25 56°05'N 074°07'W 22. 290±20 56°13'N 074°30'W 32. 290±20 23°32'S 37°50'N 124°45'E 091°23'W 9. 5.6 <60 320±SO 27°43'S 37°54'N 117°05'E 092°43'W 0.21 6. <300 56°24'N 61°55'N 49°42'N 67°3O'N 36°17'N 43°5S'N 102°59'W 016°32'E lI0030'W 172°05'E OS5°4O'W OS9°32'W 12. 15. 10. 23. 3.S 6. 100 ± 50 109.6± I < 65 3.5 ±0.5 36O±20 < 500 I So 20'S I 26°4O'E 5. < 50 23°50'S 132° 19'E 22. 142.5±0.5 56°27'N ""54°N I04°29'W ""22°E 5. 3. < 250 65 75°22'N 37°35'N OS9°4O'W 099°10'W 20. 0.011 24°34'S 44°2S'N S0041'N 49°06'N 57°5S'N 61°5S'N 5so24'N 54°30'N 4S°2O'N 69°10'N 57°54'N 133°10'E 076°3S'W 073°53'W 029° 12'E 025°25'E 030°55'E 022°4O'E 036° 15'E 040° 15'E 065°00'E 04S°00'E 0.15 2. 4. 4.5 O.OS 14. 0.11 15. 25. 60. 10. 550± 100 <300 395±5 0.002 69S±22 0.004 3S0± 10 65 57±9 10 19°30'S 40045'N 57°00'N 51°4O'N 600OS'N 132°50'E OS7°24'W 022°42'E 036°00'E 075°2O'W 2.5 13. 4. 5. S. < 550 <300 51O±30 250±SO 425±25 57°26'N 63°09'N 066°36'W 023°42'E S. 14. 4OO±50 77±4 12°24'S 65°30'N 54°12'N 134°03'E 095°5O'E 027°4S'E 076°31'E 1.6 20. 17. 1.83 150± 70 50±20 40±5 0.05 I~SS'N 21.5 ± 1.2 / 289 290 / 11 EARTH Table 11.46. (Continued.) Diameter Age (Myr) Name Latitude Longitude Machi, Russia (5)b Manicouagan, Quebec, Canada Manson, Iowa, USA Middlesboro, Kentucky, USA Mien, Swedena Misarai, Lithuania Mishina Gora, Russia Mistastin, Newfoundland, and Labrador, Canada Monturaqui, Chilea Morasko, Poland (7)ab New Quebec, Quebec, Canada Nicholson Lake, Northwest Territories, Canadaa Oasis, Libya Obolon', Ukraine Odessa, Texas, USA (3~b Ouarkziz, Algeria Piccaninny, Western Australia, Australia Pilot Lake, Northwest Territories, Canada Popigai, Russia Puchezh-Katunki, Russia Red Wing Creek, North Dakota, USA Riacho Ring, Brazil Ries, Germanya Rochechouart, Francea Rogozinskaja, Russia Rotmistrovka, Ukraine Siiliksjiirvi, Finlanda Saint Martin, Manitoba, Canada Serpent Mound, Ohio, USA Serra da Canghala, Brazil 57°30'N 51°23'N 42°35'N 36°37'N 56°25'N 54°00'N 58°4O'N 116°00'E 068°42'W Q94°31'W 083°44'W 014°52'E 023°54'E 028°00'E 55°53'N 23°56'S 52°29'N 61° 17'N 063°18'W Q68°17'W 016°54'E 073°4O'W 28. 0.46 0.1 3.2 38±4 1 0.01 <5 62°4O'N 24°35'N 49°30'N 31°45'N 29°00'N 102°41'W 024°24'E 032°55'E 1Q2°29'W 007°33'W 12.5 11.5 15. 0.168 3.5 <400 17°32'S 128°25'E 7. 60°17'N 71°30'N 57°Q6'N 111°Q1'W l11°00'E 043°35'E 6. 100. 80. 47°36'N 07°43'S 48°53'N 45°30'N 58° 18'N 49°00'N 61°23'N 51°47'N 39°Q2'N 08°05'S 42°42'N 3Q036'N 46°07'N 61°Q2'N 48°40'N 46°18'N 63°Q2'N 103°33'W 046°39'W 010037'E OOO056'E Q62°00'E 032°00'E 022°25'E 098°32'W 083°24'W 046°52'W 072°42'E 102°55'W 134°4O'E 014°52'E 087°OO'W 138°52'E Q21°35'E 9. 4. 24. 23. 8. 2.5 5. 23. 6.4 12. 2.5 16°30'S 59°31'N 48°41'N 126°00'E 117°38'W OlOo 04'E 5. 25. 3.4 95±7 14.8±0.7 15°12'S 46°36'N 44°Q6'N 33°19'N 133°35'E 081°11'W 109°36'E Q04°Q2'E 24. 140. 1.3 1.75 <472 1850± 150 <30 <3 25°50'S 22°55'N 48°Q1'N 27°36'N 69°18'N 120055'E 010024'W 033°05'E 005°07'E 065° 18'E 28. 1.9 8. 6. 25. 1685 ±5 2.5 ±0.5 330±30 <70 57±9 Shunak,~tan Sierra Madera, Texas, USA Sikhote Alin, Russia (122)ab Siljan, Sweden Slate Island, Ontario, Canada Sobolev, Russiaa Soderfjiirden, Finland Spider, Western Australia, Australia Steen River, Alberta, Canada Steinheim, Germany Strangways, Northern Territory, Australiaa Sudbury, Ontario, Canada Thbun-Khara-Obo, Mongoliaa Thlernzane,Algeria Teague, Western Australia, Australia Tenoumer, Mauritania Ternovka, Ukraine Tm Bider, Algeria Ust-Kara, Russia (kIn) 0.3 100. 32. 6. 5. 5. 2.5 13. 0.0265 52. 30. 0.05 5.5 < 1 210±4 61 ±9 <300 118±3 395 ± 145 <360 215 ±25 < 70 <360 440±2 39±9 183±5 200 14.8±0.7 160±5 55±5 14O±20 < 330 225 ±40 < 320 <300 12 100 368± 1 < 350 <600 11.27 METEORITES AND CRATERS I 291 Table 11.46. (Continued.) Diameter (km) Age (Myr) Name Latitude Longitude Upheaval Dome, Utah, USA Veevers. Western Australia, Australiaa Vepriaj. Lithuania Vredefort, South Africa Wabar. Saudi Arabia (2~b Wanapitei Lake. Ontario. Canadaa Wells Creek, Tennessee. USA West Hawk Lake. Manitoba, Canada Wolf Creek. Western Australia, Australiaa Zeleny Gai. Ukraine Zhamanshin. Kazakhstan 38°26'N 1()9°54'W 22°58'S 55°06'N 27°OO'S 21°30'N 125°22'E 024°36'E 027°30'E Oso028'E 0.08 8. 140. 0.097 <450 160±30 1970± 100 46°44'N 36°23'N osoo44'W 087°4O'W 8.5 14. 37±2 200± 100 49°46'N 095°11'W 2.7 l00±SO 19°IO'S 48°42'N 48°24'N 127°47'E 035°54'E O6Oo48'E 0.85 1.4 10. 120±2O 0.75±0.06 5. Notes a Structures with meteoritic fragments or geochemical anomalies considered to have a meteoritic source. bSites with multiple craters, with (n) indicating number of craters. Diameter given corresponds to largest crater. Reference 1. Grieve. R.A.P. 1987. Ann. Rev. Earth Planet. Sci.• IS. 245 There is increasing acceptance of the importance of impacts in the evolution of the Earth and planets. Examples of possible impact-related events in the Earth's history include the fonnation of the Moon by a Mars-sized impactor early in the Earth's evolution and the Cretaceous-Tertiary extinctions (about 65 Ma) by the effects of an impactor of mass about 1015 kg, energy about 1023 J, and diameter about 100 km. REFERENCES 1. Lerch. F.J. et aI. 1992. NASA Technical Memorandum 10455S Geopotential Models of Earth from Satellite Tracking and Altimeter and Surface Gravity Observations GEM-TI and GEM-TIS 2. Cazenave. A. 1994. American Geophysical Union Handbook of Physical Constants (American Geophysical Union, Washington. DC) 3. International Earth Rotation Service Standards. Central Bureau of IERS (Observatoire de Paris) 4. ETOPO 5 Data Base (distributed by NOAA), 1986. (National Geophysical Data Center. Boulder. CO) 5. Thrcotte DL.• & Schubert, G. 1982. Geodynamics (Wiley. New York) 6. Dickey, J.O. 1994. American Geophysical Union Handbook of Physical Constants (American Geophysical Union. Washington. DC) 7. ExplmuJtory Suppkment to the Astronomical Almanac. edited by P.K. Seidelmann 1992. (University Science Books. Mill Valley. CA) 8. Wahr. J. 1994. ArMrican Geophysical Union Handbook of Physical 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. Constants (American Geopbysical Union, Washington. DC) Harland, W.B. et al. 1990. A Geologic 7irMscale 1989 (Cambridge University Press, Cambridge) Imbrie. J. 1985, J. GeoL Lond.. 142. 417 Condie. K.C. 1989. Plate Tectonics and Crustal Evolution (Pergamon Press. Oxford) DeMets. C. et al. 1990. Geophys. J. Int.• 101.425 Dziewonski. A.M. & Anderson. D.L. 1981. Phys. Earth Planet. Int.• 15. 297 COESA, U.S. Stmu.llJrdAtmosphere 1976. (Government Printing Office. Washington, DC) EdI6n. B. 1953. J. Opt. Soc. ArM!:, 43, 339 Anderson. G.P. et aI. 1986. AFGL-TR-86-0110. Atmospheric Constituent Profiles 10-120 km, Air Forr:e Geophysics Laboratory (now Air Force Research Lab0ratory). Allen. C.W. 1973. Astrophysical Quantities, 3rd ed. (Athlone Press. London) Goody R.M .• & Yung, Y.L. 1989, Atmospheric Radi- 292 I 11 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. EARTH ation: Theoretical Basis, 2nd ed. (Oxford University Press, New York) Watson, R.P. et al. 1990, Greenhouse gases and aerosols, in Climate Change: The IPCC Scientific Assessment, edited by J.T. Houghton, G.H. Henkins, and J.H. Ephraums (Cambridge University Press, New York) Logan, J.A. et al. 1981, J. Geophys. Res., 86, 7210 Allen, M., Lunine, 1.1., & Yung, Y.L. 1984, J. Geophys. Res., 89, 4841 Smithsonian Meteorological Tables, 5th rev. 1949, (Smithsonian Institution Press, Washington, DC) Walterscheid, R.L., DeVore J.G., & Venkateswaran, S.V. 1980, J. Atmos. Sci., 37, 455 Champion, K.S.W., Cole, A.E., & Kantor, A.J. 1985, Standard and reference atmospheres, in Handbook of Geophysics and the Space Environment, edited by A.S. Jursa (Air Force Geophysics Laboratory, Available from National Technical Information Service, ADA 167_ 1985). Smith E.K. Jr., & Wientraub, S. 1953, Institute ofRadio Engineers Proc., 41, No.8, 1035 Berman, A.L., & Rockwell, S.T. 1992, New Optical and Radio Frequency Angular Troposphere Refraction Models for Deep Space Applications, NASA TR-321601 Hansen, J.E., & Travis, L.D. 1974, Space Sci. Rev. 16 Toan, O.B., & Pollack, J.B. 1976, J. Appl. Met. 15 Brasseur, G., & Solomon, S. 1986, Aeronomy of the Middle Atmosphere: Chemistry and Physics of the Stratosphere and Mesosphere, 2nd ed. (Kluwer Academic, Amsterdam) Rothman, L.S. et al. 1992, JQSRT, 48, 469 31. Hargreaves, J.K. 1992, The Solar-Terrestrial Environment (Cambridge University Press, Cambridge) 32. Vallance Jones, A. 1974, Aurora (Reidel, Boston). 33. Roach, F.E., & Gordon, J.L. 1973, The Light of the Night Sky (Reidel, Boston) 34. KrassovskY, V.I. et al. 1962, Planet. Space Sci., 9, 883 35. Chamberlain, J.W. 1961, Physics of the Aurora andAirglow (Academic Press, New York) 36. Meine1, A.B. et al. 1954, J. Geophys. Res., 59, 407 37. Bloxham, J. 1995, Global Earth Physics: A Handbook of Physical Constants. T.J. Ahrens, Editor, AGU Reference Shelf 1. American Geophysical Union, Washington,DC) 38. Langel, R.A. 1987, in Geomagnetism, edited by J.A. Jacobs (Academic Press, Orlando), Vol. I, p. 249 39. 1992 IAGA Division V, Working Group 8, IGRF, 1991 Revision, EOS Trans. American Geophys. Union, 73, 182 40. Sears, D.W.G., & Dodd, R.T. 1988, in Meteorites and the Early Solar System, edited by J.P. Kerridge and M.S. Matthews, (University of Arizona Press, Tucson, AZ), pp.3-31 41. Wasson, J.T. 1985, Meteorites-Their Record of Early Solar System History (W.H. Freeman, New York) 42. Me1osh, H.J. 1989, Impact Cratering-A Geologic Process, (Oxford University Press, New York) 43. Pesonen, L.J., Terho, M, & Kukkonen, T.T. 1993, Physical properties of 368 meteorites: Implications for meteorite magnetism and planetary geophysics, Proc. NIPR Symp. Antarct. Meteorites, 6, 401 44. Grieve, R.A.F. 1987, Ann. Rev. Earth Planet. Sci., IS, 245 Chapter 12 Planets and Satellites David J. Tholen, Victor G. Tejfel, and Arthur N. Cox 12.1 Planetary System . . . . . . . . . . . . . . . . . . . . . 293 12.2 Orbits and Physical Characteristics of Planets . . . . 294 12.3 Photometry of Planets and Asteroids. . . . . . . . .. 298 12.4 Physical Conditions on Planets . . . . . . . . . . . .. 300 12.5 Names, Designations, and Discoveries of Satellites 302 12.6 Satellite Orbits and Physical Elements. . . . . . . .. 303 12.7 Moon. . . . . . . . . . . . . . . . . . . . . . . . . . .. 308 12.8 Planetary Rings . . . . . . . . . . . . . . . . . . . . . . 311 12.1 PLANETARY SYSTEM Total mass of planets [I] Total mass of satellites [2] Total mass of asteroids Total mass of meteoric and cometary matter Total mass of entire planetary system Total angular momentum of planetary system Total translational kinetic energy of planetary system Total rotational energy of planets 293 446.6M e {M e = 5.9742 x 1027 g) 6.2 x 1026 g = O.I04M e 1.8 x 1024 g = 0.000 301M e 1O-9 M e 2.669 x 103° g = 446.7M e 3.148 x Hfo gcm2 s-1 1.99 x 1042 erg 0.7 x 1042 erg = 0.00134M 0 294 I 12 PLANETS AND SATELLITES Invariable (Laplacian) plane of the solar system [1,3] with respect to the ecliptic and equinox of J2ooo.0 Longitude of ascending node Inclination North pole longitude North pole latitude with respect to the equator and equinox of 12000.0 (International Celestial Reference Frame) Longitude of ascending node Inclination North pole right ascension North pole declination Gaussian period of comet or asteroid where a is the sernimajor axis of orbit in AU 12.2 107°34' 57~'7 1°34' 43~'3 17°34' 57~'7 88°25' 16~'7 3°51' 09~'4 23°00' 32~'0 273°51' 09~'4 66°59' 28~'0 1.000 040 27a 3 / 2 tropical years ORBITS AND PHYSICAL CHARACTERISTICS OF PLANETS The orbital elements in Tables 12.1 and 12.2 are given in [3]. They are given with respect to the mean ecliptic and equinox of J2ooo.0 at the epoch J2000 (JD 2451545.0). The longitudes of the ascending node, n, and perihelion, W, are measured from a mean y, the intersection of the ecliptic and equator. Therefore, W = n + w, where w is the argument of perihelion measured from the ascending node along the orbit. L, the planet longitude for noon January 1,2000, is also measured the same way from the mean y. For the Earth, data are given for the Earth-Moon barycenter. Thble 12.1. Planetary orbit data [l]. Semimajor axis of orbit Planet (AU) (106 km)Q Mercury l;! Venus 9 0.38709893 0.72333199 1.000000 II 1.52366231 5.20336301 9.53707032 19.19126393 30.06896348 39.48168677 57.909175 108.20893 149.59789 227.93664 778.41202 1426.7254 2870.9722 4498.2529 5906.3762 Earth Mars Jupiter Saturn Uranus Neptune Pluto 6 <1 4 I) 0 W I? Period Sidereal (Julian years) Synodic (days) 0.24084445 0.61518257 0.99997862 1.880711 05 11.85652502 29.42351935 83.74740682 163.7232045 248.0208 115.8775 583.9214 779.9361 398.8840 378.0919 369.6560 367.4867 366.7207 Mean daily motion (deg.) Mean orbit vel. (kms-l) 4.09237706 1.60216874 0.98564736 0.52407109 0.08312944 0.03349791 0.01176904 0.006020076 0.003973966 47.8725 35.0214 29.7859 24.1309 13.0697 9.6724 6.8352 5.4778 4.7490 Note aCalculated using 1 AU = 1.4959787066 x 1011 rn. Reference 1. Explanatory Supplement to the Astronomical Almanac 1992, edited by P.K. Seidelrnann (University Science, Mill Valley. CA). pp. 316, 704 12.2 ORBITS AND PHYSICAL CHARACTERISTICS OF PLANETS I 295 Table Planet Eccentricity e (2000.0) [1.2] Inclination to ecliptic i (2000.0) [1.2] (deg.) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto 0.20563069 0.00677323 0.01671022 0.09341233 0.04839266 0.05415060 0.04716771 0.00858587 0.24880766 7.00487 3.39471 0.00005 1.85061 1.30530 2.48446 0.76986 1.76917 17.14175 12~ Additional planetary orbit data. Planet L 2000.0 Jan. 1.5 [1,2] (deg.) Perihelion latest date before 1999 [3] 252.25084 181.97973 100.46435 355.45332 34.40438 49.94432 313.23218 304.88003 238.92881 1998 Dec. 2 1998Sep.7 1998 Jan. 4 1998 Jan. 7 1987 Jul. 10 1974 Jan. 8 1966 May 20 1876Sep.2 1989Sep.5 Mean longitude of ascending node n perihelion if> [1.2] [1.2] "Ta "To (deg.) (deg.) 48.33167 76.68069 -11.26064 49.57854 100.55615 113.71504 74.22968 131.72169 110.30347 -446 -997 -18228 -1020 +1217 -1591 +1681 -151 -37 77.45645 131.53298 102.94719 336.04084 14.75385 92.43194 170.96424 44.97135 224.06676 +574 -109 +1198 +1560 +840 -1949 +1312 -844 -132 Note a T is in centuries. References 1. Explanatory Supplement to the Astronomical Almanac 1992. edited by P.K. Seidelmann. (University Science. Mill Valley. CA). p. 316 2. Lang. K.R. 1991. Astrophysical Data: Planets and Satellites (Springer-Verlag. New York). p. 937 3. Astronomical Almanac (USNO. Government Printing Office) In Table 12.3, the closest approach is at inferior conjunction for Mercury and Venus, at opposition for the other planets. Note that the total mass of the Earth and Moon is 1.012300034 that of the Earth alone. For Venus, Uranus, and Pluto the rotation is retrograde with respect to the orbit. Table 12.4 gives additional physical information for the planets. Table 12.3. Physical characteristics o/planets [I]. Semi-diameter equator at IAU Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto (") 3.37 8.34 8.794 4.69 98.48 83.3 32.7 33.4 1.5 at closest approach (") 5.5 30.1 8.95 23.43 9.76 1.95 1.15 0.04 Radius equator Re (km) 2439.7 6051.8 6378.14 3397 71492 60268 25559 24764 1195 $=1 0.3825 0.9488 1.000 0.5326 11.209 9.449 4.007 3.883 0.180 Ob1ateness Re -Rp Rp Volume $=1 [2] 0.0 0.0 0.00335364 0.00647630 0.0648744 0.0979624 0.0229273 0.0171 0 0.054 0.88 1.00 0.149 1316. 755. 52. 44. 0.005 Reciprocal mass (including satellites) [3] 1/0= I Mass 1027 g (excluding satellites) [1] Mass (excluding satellites) $=1 6023600 408523.71 328900.56 3098708 1047.3486 3497.898 22902.98 19412.24 135000000 0.33022 4.8690 5.9742 0.64191 1898.7 568.51 86.849 102.44 0.013 0.055274 0.81500 1.000000 0.10744 317.82 95.161 14.371 17.147 0.002200 References 1. Explanatory Supplement to the Astronomical Almanac 1992. edited by P.K. Seidelmann (University Science. Mill Valley. CA) 2. Allen. C.W. 1973. Astrophysical Quantities (Athlone Press. London) 3. Standish. E.M. 1995. Report of the IAU WGAS sub-group on numerical standards. In Highlights of Astronomy. edited by I. Appenzeller (Kluwer Academic. Dord:recht) 296 / 12 PLANETS AND SATELLITES Table 12.4. Additional physical characteristics ofplanets [1]. Surface gravity [2] Density (gcm- 3 ) Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto [9] 5.43 5.24 5.515 3.94 1.33 0.70 1.30 1.76 1.1 (cms- 2 ) equator attractive centrifugal 370 887 980 371 2312 896 869 1100 81 -0.0 -0.0 -3.391 -1.706 -224.841 -175.310 -26.195 -29.065 -0.014 Equatorial escape velocity [2] (kIns-l) 4.25 10.36 11.18 5.02 59.54 35.49 21.29 23.71 1.27 Siderealab rotation period (equatorial) [3-8] (day) 58.6462 -243.0187 0.99726968 1.02595675 0.41354 0.44401 -0.71833 0.67125 -6.38718 Inclination of equator to orbit (deg.) 0.0 177.3 23.45 25.19 3.12 26.73 97.86 29.58 119.61 Moment of inertia [2] (MeR~) 0.4 0.34 0.3335 0.377 0.25 0.22 0.23 0.29 Notes aEquatorial Jupiter I: gh5om3OS. High latitudes Jupiter IT: gh55m~3. Deep interior Jupiter m: gh55m29'!37. This deep interior rotation rate is given in the table. bEquatorial Saturn: I lohl4m. High latitudes Saturn: IT loh38m. Deep interior Saturn: loJt3gm24s . m References 1. Exp1muuory Supplement to the Astronomical Almanac 1992, edited by P.K. Seidelmann (University Science, Mill Valley, CA), p. 369 Allen, C.W. 1973, Astrophysical QutUltities (Athlone Press, London) Davies, M.E. et al. 1994, eeL Mech., 63,127 Klassen, K.P. 1976, Mercury's rotation axis and period. Icarus, 28, 469 Shapiro, 1.1., Campben. D.B., & De Campli, W.M. 1979, Nonresonance rotation of Venus? ApJL, 230, L123 Linda!, G.F. et al. 1987, The atmosphere ofUranus-results of radio occultation measurements with Voyager 2. J. Geophys. Res., 92, 14937 7. Warwick et al. 1986, Voyager 2 radio observations of Uranus. Science, 233, 102 8. Warwick et al. 1989, Voyager planetary radio astronomy at Neptune. Science, 246, 498 9. Tholen, D.J. & Buie, M.W. 1997, The orbit of Charon. I. New Hubble space telescope observations. Icarus, 125, 245 2. 3. 4. 5. 6. 12.2.1 Rotation Axes Table 12.5 lists the right ascension and declination of the angular momentum vectors at epoch J2000.0 with the equinox J2ooo.0 for the Sun and the nine planets. Also listed are even more recent and accurate sidereal rotation periods. Those given in Table 12.4 were used for recent Astronomical Almanacs. The reference frame for the coordinates is the mean equator and equinox of J2ooo.0. The rotation periods for Jupiter, Saturn, Uranus, and Neptune with no visible markings on a hard surface refer to their magnetic fields. For information about prime meridians, see [3,4]. Table 12.5. Solar system cartographic dJJta [1]. a Object Sun [1,2] Mercury Venus (deg.) 286~13 281~01 272~76 & (deg.) +63?87 +61?45 +67?16 Sidereal Period (days) 25.38 58.646225 -243.01999 12.2 ORBITS AND PHYSICAL CHARACTERISTICS OF PLANETS / 297 Table 12.5. (Continued.) Object Earth Mars Jupiter Saturn Uranus Neptune Pluto a (deg.) (deg.) O?OO 317%81 268?05 40?589 257?311 299?36 313?02 +90?00 +52?886 +64?49 +83?537 -15?175 +43?46 -9?09 Sidereal Period (days) 8 0.9972696323 1.025 956 754 3 0.413 538 325 8 0.444 009 259 2 -0.7183333333 0.671 2500000 -6.387 24600 References 1. Davies, M.E. et al. 1994, Cel. Mech., 63, 127 2. Carrington. R.C. 1863. Observations of Spots on the Sun (Williams and Norgate. London) 12.2.2 Gravity Fields Table 12.6 gives the spherical harmonic terms in the gravitational potential for the Earth and the outer planets. See Chapter 11 for more details for the Earth. Table 12.6. Coefficients of potential. a Planet Earth Mars Jupiter Saturn Uranus Neptune 12 J3 +0.00108263 +0.001964 +0.014736(1) +0.016298(10) +0.012 +0.003411(10) -0.000 002 54 +0.000036 +0.0000014(50) J4 J6 -0.00000161 -0.000 587(5) -0.000915(40) -0.000 026( + 12/-20) Reference [1] +0.000031(20) +0.000 103(50) [2] [3] [4] [5] Note a Numbers in parentheses are uncertainties in the last digits as given. References 1. Explanatory Supplement to the Astronomical Almanac. 1992, edited by P.K. Seidelmann. (University Science, Mill Valley. CAl. p. 697 2. Campbell, J.K .• & S.P. Synnott 1985. Gravity field of the Jovian system from Pioneer and Voyager tracking data. Astron. J.• 90. 364 3. Campbell. J .K.• & J.D. Anderson 1989. Gravity field of the Saturnian system from Pioneer and Voyager tracking data. Astron. J., 97. 1485 4. Anderson. J.D .• J.K. Campbell. R.A. Jacobson. D.N. Sweetnam. & A.H. Taylor 1990, Radio science with Voyager 2 at Uranus: Results on masses and densities of the planet and five principal satellites. J. Geophys. Res.• 92. 14877 5. 'lYler. G.L.. D.N. Sweetnam. J.D. Anderson. S.E. Borutzki. J.K. Campbell, V.R. Eshleman. D.L. Gresh. E.M. Gurrola. D.P. Hinson. N. Kawashima. E.R. Kurinski. G.S. Levy. G.F. Linda!. J.R. Lyons. E.A. Marouf, P.A. Rosen. R.A. Simpson. & G.E. Wood 1989, Voyager radio science observations of Neptune and Triton. Science. 246. 1466 298 I 12 PLANETS AND SATELLITES 12.2.3 Planetary Magnetic Fields The dipole field strength at the planet surface in units of tesla-mete.-3 are given in Table 12.7. Quadrupole and octapole strengths are the Schmidt nonnalized coefficients relative to the dipole moment. Table 12.7. Planet magnetic,Mlds and angles. Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Dipole 2-6 x 1012 < lOll 7.84 x 1015 < 1012 1.55 x 1020 4.6 x 1018 3.9 x 1017 2.2 x 1017 ? Quadrapole (%) Octapole (%) Angle (deg.) 13 10 10.8 23 14 20 7 10 0 59 47 Reference [1] [2] [3] [4] [5] [6] [7] [8] References 1. Connemey, J.E.P., & N.F. Ness 1988, Mercury's magnetic field and interior. In Mercury edited by Vilas, C.R. Chapman, and M.S. Matthews, (University of Arizona Press, Thcson) pp.494-513 2. Phillips, J.L., & C.T. Russell 1987, Upper limit on the intrinsic magnetic field of Venus. J. Geophys. Res., 92, 2253 3. Barton, C.E. 1989, Geomagnetic secular variation: Direction and intensity. In The EncyclopediD of Solid Earth Geophysics, (Van Nostrand Reinhold, New York) pp. 561-577 4. Russell, C.T. 1978, The magnetic field of Mars: Mars 5 evidence re-examined. Geophys. Res. Len.,S,85 5. Connerney, J.E.P. 1981, The magnetic field of Jupiter: A generalized inverse approach. J. Geophys. Res., 86, 7679 6. Connerney, J.E.P., M.H. Acuna, & N.F. Ness 1984, The Z3 model of Saturn's magnetic field and the Pioneer 11 vector helium observations. J. Geophys. Res., 89, 7541 7. Connerney, J.E.P., M.H. Acuna, & N.F. Ness 1987, The magnetic field of Uranus. J. Geophys. Res., 92, 15379 8. Connemey, J.E.P., M.H. Acuna, & N.F. Ness 1991, The magnetic field of Neptune. J. Geophys. Res., !J6, 19023 12.3 PHOTOMETRY OF PLANETS AND ASTEROIDS Table 12.8 gives the photometry data for the planets and some asteroids. 12.3 PHOTOMETRY OF PLANETS AND ASTEROIDS I 299 Table 12.8. Photometry o/the planets and five asteroids [1,2]. Planet or asteroid Visual geometric albedo Opposition V B-V u-v [1,3,4] VO,O) or H (rnag.)O Mercury 0.106 0.93 0.41 -0.42 Venus 0.65 0.82 0.50 -4.40 Earth Mars Jupiter Saturn 0.367 0.150 0.52 0.47 0.2 1.36 0.83 1.04 0.58 0.48 0.58 -3.86 -1.52 -9.40 -8.88 Uranus Neptune Pluto [5,6] (1) Ceres [7,8,11,12] (2) Pallas [7,8,11,12] (3) Juno [7,8,11,12] (4) Vesta [7,9,11,12] (10) Hygiea [10-12] (243) Ida [10-12] (253) Mathilde [10-12] (433) Eros [7,10-12] (951) Gaspra [10-12] -2.01 -2.70 +0.67c 0.51 0.41 variabled +5.52 +7.84 +15.12 0.56 0.41 0.842d 0.28 0.21 0.31 -7.19 -6.87 -0.81 0.113 0.159 0.238 0.423 0.072 0.238 0.044 +6.78 +7.60 +8.57 +5.73 +9.56 +13.57 +13.39 +lO.28 +13.59 0.72 0.67 0.79 0.81 0.69 0.81 0.48 0.28 0.52 0.66 0.39 0.61 0.92 0.87 0.80 0.77 +3.34 +4.13 +5.53 +3.20 +5.43 +9.94 +lO.2 +11.16 +11.46 Variation of V with phase (a, L in deg.)o.b +0.038a - 2.73 x lO 4a 2 +2.00 x lO-6a 3 +O.OOO9a + 2.39 x lO- 4a 2 -0.65 x lO-6a 3 +0.0100 +0.005a +0.0441 - 2.6 sin b +1.25 sin 2 b +0.0028a 0.037a 0.12 0.11 0.32 0.32 0.46 Notes °For the asteroids the V(1.0) is designated as H, and the phase function is given by the slope parameter G [13]. b a is the phase angle between the Sun and Earth as seen from the planet. I is the Saturnicentric longitude difference of the Sun and Barth and lies between _6° and 6°. b is the Saturnicentric ring latitude of the Earth that lies between -27° and 27°. c V refers to the Saturn disk only. dThe Pluto visual geometric albedo is variable by 30%. The Pluto color is the combination of the planet and its satellite Charon. References 1. Astronomical Almanac, 1998 (USNO, Government Printing Office) 2. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. Athlone Press, London 3. Irvine, W.M. et al. 1968, AJ, 73, 251, 807 4. Harris, D.L. 1%1, in Planets and Satellites, edited by G. Kuiper and B. Middlehurst (University of Chicago, Chicago), p.272 5. Tholen D.J. & Tedesco, B.E 1994, Icarus, 108, p. 200 6. Buie, M.W., Tholen, D.J., & Wasserman L.H. 1997, Separate lightcurves of Pluto and Charon, Icarus, 125, 233 7. Haupt, H. 1951, Min. U.S. Wien, 5, 31 8. Watson, EG. 1956, Between the Planets, rev. ed. (Harvard University Press, Boston) 9. Gehrels, T. 1967, AJ, 72, 929 lO. Tedesco, E.E & Veeder, G.J. 1992, in The lRAS Minor Planet Survey edited by E.E Tedesco, G.J. Veeder, J.w. Fowler, and J.R. Chillemi (Phillips Laboratory, Hanscom Air force Base) 11. Tedesco, E.E, Marsden, B.G., & Williams, G.V. 1990, Minor Planet Circulars 17256-17273 (Smithsonian Astrophysical Observatory, Cambridge) 12. Bowell, E. Hapke, B, Domingue, D. Lumme, K., Peltoniemi, J., & Harris, A.W. 1989, in Asteroids II edited by R.P. Binzel, T. Gehrels, and M.S. Matthews (University of Arizona Press, Tucson) 13. Zellner, B., Tholen, D.J., & Tedesco, E.E 1985, Icarus, 61, 355 300 / 12 PLANETS AND SATELLITES 12.4 PHYSICAL CONDITIONS ON PLANETS by Glenn S. Orton Planetary atmosphere and surface conditions are given in Table 12.9: Te = Effective temperature of the planet. Ta = Atmospheric temperature at the level with pressure 1 bar. Ts = Mean temperature at the solid surface. Ps = Atmospheric pressure at the solid surface for the terrestrial planets and satellites or at visible cloud surface for major planets. H Scale heighL So, Cl = Solid, cloud; for lowest visible surface. = Table 12.9. Planetary and selected satellite atmoSpMTf! and swface conditions. VISible Planet surface Mercury Venus Pluto So Cl So,CI So Cl Cl Cl CI So Moon So 10 Europe Ganymede Callisto TItan [2] Triton [3] So So .So So CI So Earth Mars Jupiter Saturn Uranus Neptune T. (K) -230 -255 -212 124.4±0.3 95.0±0.4 59.1±O.3 59.3±O.8 50-70 Ta (lbar) (K) Ps (bar) H (Ian) 730 288-293 183-268 90 I 0.007-0.010 -0.3 -0.4 15 8 11 19-25 35-50 22-29 18-22 57.8 [1] 8x 10-5 [1] Ts (K) 440 288 165 134 76 73 120-380 99 97 107 117 86 100-140 (300 locd) 1O-6 ? 83 94 38 References 1. Trafton L. & Stern S.A. 1983, Ap. 1., 'Hi7, 872 2. Saturn, 1984, edited by T. Gehrels (University of Arizona Press, 1\icson) 3.Scknce, 1990,250,4979 Compositions of planetary atmospheres are given in Table 12.10. 1.496±O.020 -1.5xl0-5 20-22 10- 5 10- 5 10- 5 10- 9 3 x 10-6 1.5 x 10-4 1.2 x 7x 1x 3x 0.016 2.5 x 10- 6 3 x 10- 7 8 x 10-8 10-9 < 10-6 < 10- 9 10-8 10- 10 10-8 10-6 10-9 (0.7-1.7) x 10-8 :'S 4.5 x 10- 6 3.4 x 10- 7 2 x 10- 9 :'S 1 x 10- 7 :'S 5 x 10- 6 < 10- 9 < 10-6 :'S 1 x 10-4 (0.2-2) x 10- 7 0.94 0.06 (1-3) x 10- 9 (1-4) x 10- 3 :'S 3 x 10- 10 Saturn [2,5,6] :'S 10- 7 ~ 2x 6x :'S 3 x :'S 3 x < 1x ~ 1.1 x 10-5 :'S 6 x 10-6 1 x 10- 10 (2.4 ± 0.5) x 10- 3 :'S 7 x 10-4 :'S 6.5 ± 2.9 x 10- 5 0.863 ± 0.007 0.156 ± 0.006 (1.0 ± 0.4) x 10- 5 (2.3 ± 0.25) x 10- 5 < (8.5 ± 4) x 10-9 < (5 ± 2.5) x 10-9 (1-8) x 10-5 Jupiter [2-4] :'S4xlO- 7 ~ 2 x 10- 6 (6-10) x 10- 5 < 3 x 10- 10 < 5 x 10- 7 :'S 0.02 < 10-4 :'S (0.5-1.2) x 10-8 0.85 0.15 Uranus [2,4,5] <1x ~ 1x 0.85 0.15 10-8 10-6 < (1.5-3.5) x 10- 9 :'S 0.02-0.04 ~6x 10- 7 :'S 5 x 10- 10 Neptune [2,5,7] :'S 2 :'S 2 :'S 2 :'S 4 :'S 4 :'S (0.1-1) :'S (0.1-1) :'S (0.1-1) x x x x x x x x (0--0.25) 10- 6 10- 5 10- 7 10-6 10-7 10-7 10-7 10- 7 :'S (0.4-1.4) x 10-9 2 x 10- 3 1.5 x 10- 9 (0.6-1.5) x 10-4 :'S 0.02-0.10 0.73-0.99 Titan [8] I. Lewis, lS. 1995, Physics and Chemistry of the Solar System (Academic Press, San Diego) 2. Encrenaz, T. & Bibring l-P. 1990, The Solar System (Springer-Verlag, Berlin), 330 pp. 3. Niemann H.B. et al. 1996, Science, 272, 846; Niemann H.B. 1998, JGR, 103, 22831; Folkner, W.M., Woo, R., & Nandi, S. 1998, JGR, 103, 22847; Encrenaz, T. et al. 1996, A&A, 315, L347; Bezard, B. et al. 1998, A&A, 334, L41 4. Encrenaz, T. et al. 1998, A&A, 338, L48 5. Feutchtgruber, H. et al. 1997, Nature 232, 139 6. Griffin, M. et al. 1996, A&A, 315, L389; Davis, G. et al. 1996, A&A, 313, L393; de Graauw, T. et al. 1997, A&A, 321, L43 7. Orton, G.S. 1992, Icarus, 100, 541 8. Science, 1989,246, N4936; Saturn, 1984, edited by T. Gehrels (University of Arizona Press, Tucson); Science, 1990,250, N 4979 References HCN C3 H8 C2f4 HC3N C2N2 CH3NH2 C2~ PH3 CH3D Gef4 C2 H2 HD Xe H2S S02 Kr Ne Ar 2 x 10- 5 3 x 10-4 0.027 1.3 x 10- 3 0.953 2.7 x 10- 3 0.78084 0.20948 3.33 x 10-4 2 x 10- 7 2.0 x 10-6 4 x 10-9 ~ 10- 6 5 x 10- 7 5.24 x 10-6 9.34 x 10- 3 1.818 x 10- 5 1.14 x 10-6 8.7 x 10-8 2 x 10-8 1 x 10-9 0.035 N2 02 CO2 CO Cf4 NH3 H2O H2 He 0.965 3 x 10- 7 Mars [2] Earth [2] Venus [2] Gas Table 12.10. Selected gas components of planetary atmospheres [1]. o w - ........ ...., en > ztr1 r Z '"C o en Z (3 ...., o z o...... n ...... n > r -< en :::c '"C ~ tv - 302 / 12.5 12 PLANETS AND SATELLITES NAMES, DESIGNATIONS, AND DISCOVERIES OF SATELLITES byDanPascu Table 12.11 lists the names, designations, and discoveries of the planetary satellites. Table 12.11. Names, designations, and discoveries [I, 2, 3]. Satellite Name Discovery date Discoverer Earth Moon Mars I II Jupiter I II 1II IV V VI VII VlII IX X Xl XII XlII XIV XV XVI Saturn I II 1II IV V VI VII Vlll IX X Xl XII XIII XIV Phobos Deimos 1877 1877 10 Europa Ganymede Callisto Amalthea Himalia Elara Pasiphae Sinope Lysithea Carme Ananke Leda Thebe Adrastea 1610 1610 1610 1610 1892 1904 1905 1908 1914 1938 1938 1951 1974 1980 1979 Metis 1980 Mimas Enceladus Tethys Dione Rhea Titan Hyperion Iapetus Phoebe Janus Epimetheus Helene Telesto Calypso 1789 1789 1684 1684 1672 1655 1848 1671 1898 1966 196611978 1980 1980 1980 A.Hall A. Hall Galileo Galileo Galilco Ga1ileo E.E.Bamard C. Perrine C. Perrine P. Melotte S. Nicholson S. Nicholson S. Nicholson S. Nicholson C. Kowal S.SynnoUfVoyagerI D. Jewitt, E. DanielsonIVoyager 2 S. SynnoUfVoyager 2 Satellite Name Discovery Discoverer date XV XVI Atlas Prometheus 1980 1980 XVII Pandora 1980 XVIII Pan 1990 Ariel Umbriel Titania Oberon Miranda Cordelia Ophelia Bianca Cressida Desdemona Juliet Portia Rosalind Belinda Puck Calibana 1851 1851 1787 1787 1948 1986 1986 1986 1986 1986 1986 1986 1986 1986 1986 1997 Sycoraxa 1997 Triton Nereid Naiad Thalassa Despina Galatea Larissa 1846 1949 1989 1989 1989 1989 1982 Proteus 1989 W. Lassen G. Kuiper Voyager 2 R. TerrileIVoyager 2 S. SynnoUfVoyager 2 S. SynnoUfVoyager 2 H. Reitsema, W. Hubbard, L. Lebofsky. D. Tholen S.SynnoUfVoyager2 Charon 1978 J. Christy Uranus I II 1II IV V VI VII VlII IX X XI XII XIII XIV XV XVI XVII W. Herschel W. Herschel Neptune G.D. Cassini I G.D. Cassini II G.D. Cassini III C. Huygens IV W. & G. BondIW. Lassen V G.D. Cassini VI W. Pickering VII A. Dollfus R.WalkedJ.Fountain.S.Larson VlII P. Laques, J. Lecacheux Pluto B. Smith. H. Reitsema, I S. Larson. J. Fountain D. Pascu. P.K. Seidelmann, W. Bawn, D. Currie R. TerrilelVoyager 1 S.A. Collins. D. CarlsonIVoyager 1 S.A. Collins. D. CarlsonIVoyager 1 M. ShowaiterlVoyager 2 W. Lassell W. Lassen W. Herschel W.Herschel G. Kuiper R.TerrileIVoyager2 R. TerrileIVoyager 2 Voyager 2 S.SynnoUfVoyager2 S. SynnoUfVoyager 2 S. SynnoUfVoyager 2 S. SynnoUfVoyager 2 S. SynnoUfVoyager 2 S. SynnoUfVoyager 2 S. SynnoUfVoyager 2 B.J. Gladman. P.O. Nicholson. J.A. Burns, JJ. Kavelaars P.O. Nicholson, BJ. Gladman, J .A. Burns, J.J. Kavelaars Note aThe two distant satellites of Uranus. Caliban and Sycorax still have provisional names. They will be accepted or changed at the IAU General Assembly in 2000. References 1. Burns, J.A. 1986, Satellites, edited by J.A. Burns and M.S. Matthews (University of Arizona Press, Tucson) 2. Pasachoff, J. 1998, From the Earth to the Universe, 5th ed. (Saunders College Pub., Fort Worth) 3. Veverka, J.M. 1998, Observers Handbook, edited by R.L. Bishop (University of Toronto Press, Toronto) 12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS / 303 12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS byDanPascu The main orbital and physical elements for the planetary satellites are given in Tables 12.12 and 12.13. For comparison with observations, several factors are related to terrestrial opposition, labeled Op. Synodic periods are relative to the main planet. The inclinations of satellite orbits are complicated by precession around the "proper plane," which is normally close to the planet's equator. Inclinations are measured from the planet's equator and values greater than 90° indicate that the motion is retrograde. The inclination of the Moon to the ecliptic is only 5? 145396. Reciprocal mass of satellite totals: Jupiter Saturn Uranus Neptune Pluto 4831 (Jupiter)-l, 4050 (Saturn)-l, 9571 (Uranus)-l, 4780 (Neptune-I, 8.3 (Pluto)-l, Total mass of all satellites 7.34 x 1026 g. The following commensurabilities exist among the mean motions Jupiter Saturn Uranus nI - ni of planetary satellites [5-7]: + 2n3 = 0, + 4n4 = 0, 3n I + 2n2 = 0, n2 - 2n3 + n4 = O. 3n2 5nl - 10n2 + n3 ns nI - Table 12.12. Planetary satellite orbits [1, 2, 3]. Semimajor axis (10- 3) AU (10 3 Ian) Satellite Max elong. at mean opposition '" Sidereal perioda •b (days) Earth Moon Mars I II Jupiter I II ill IV V VI VII vm IX X Phobos Deimos 10 Europa Ganymede Callisto Amalthea Himalia Elara Pasiphae Sinope Lysithea 384.400 2.5696 9.378 23.459 0.0627 0.1568 025 102 2.8209 4.4854 7.1525 12.5871 1.2099 76.7391 78.4570 157.0878 158.4247 78.3434 218 340 551 10 18 059 6246 6410 12826 12931 6404 422. 671. 1070. 1883. 181. 11480. 11737. 23500. 23700. 11720. 27.321661 0.31891023 1.2624407 1.769137786 3.551181041 7.15455296 16.6890184 0.49817905 250.5662 259.6528 R735. R758. 259.22 304 / 12 PLANETS AND SATELLITES Table 12.12. (Continued) Semimajor axis (10- 3) AU (103 kIn) Satellite Jupiter (Cont.) XI Canne XII Ananke xm Leda XN Thebe XV Adrastea XVI Metis Saturn I II m IV V VI VII vm IX X XI XII xm XN XV XVI XVII XVIII Uranus I II m IV V VI VII vm IX X XI XII xm XN XV XVI XVII Neptune I II m IV V VI VII vm 22600. 21200. 11094. 222. 129. 128. Maxelong. at mean opposition 1/1 151.0717 141.713 2 74.1588 1.4840 0.8623 0.8556 12331 11552 6039 1 13 042 042 Mimas Enceladus Tethys Dione Rhea Titan Hyperion Iapetus Phoebe Janus Epimetheus Helene Telesto Calypso Atlas Prometheus Pandora Pan 185.52 238.02 294.66 377.40 527.04 1221.83 1481.1 3561.3 12952. 151.472 151.422 377.40 294.66 294.66 137.670 139.353 141.700 133.583 1.240 1 1.5910 1.9697 2.5228 3.5230 8.1674 9.9005 23.8053 86.5788 1.0125 1.0122 2.5228 1.9697 1.9697 0.9203 0.9315 0.9472 0.8929 030 038 048 101 125 317 359 935 3451 024 024 101 048 048 022 023 023 021 Ariel Umbriel Titania Oberon Miranda Cordelia Ophelia Bianca Cressida Desdemona Juliet Portia Rosalind Belinda Puck Calibanc Sycoraxc 191.02 266.30 435.91 583.52 129.39 49.77 53.79 59.17 61.78 62.68 64.35 66.09 69.94 75.26 86.01 7169. 12214. 1.2769 1.7801 2.9139 3.9006 0.8649 0.3327 0.3596 0.3955 0.4130 0.4190 0.4302 0.4418 0.4675 0.5031 0.5749 47.29 81.64 014 020 033 044 010 004 004 004 005 005 005 005 005 006 007 856 1526 Triton Nereid Naiad Thalassa Despina Galatea Larissa Proteus 354.76 5513.4 48.23 50.07 52.53 61.95 73.55 117.65 2.3714 36.8548 0.3224 0.3347 0.3511 0.4141 0.4917 0.7864 017 421 002 002 002 003 003 006 Sidereal perioda,b (days) R692. R631. 238.72 0.6745 0.29826 0.294780 0.942421813 1.370217855 1.887 802 160 2.736914742 4.517500436 15.94542068 21.2766088 79.3301825 R550.48 0.6945 0.6942 2.7369 1.8878 1.8878 0.6019 0.6130 0.6285 0.5750 2.52037935 4.1441772 8.7058717 13.4632389 1.41347925 0.3350338 0.376400 0.43457899 0.46356960 0.47364960 0.49306549 0.51319592 0.55845953 0.62352747 0.76183287 R579. R1289. R5.8768541 360.13619 0.294396 0.311485 0.334655 0.428745 0.554654 1.122315 12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS / 305 Table 12.12. (Continued.) Semimajor axis (10- 3) AU (10 3 Ian) Satellite Pluto I Charon 19.6 0.1310 Max elong. at mean opposition '" <001 Sidereal perioda,b (days) 6.38725 Notes a R before the period indicates a retrograde orbit. bTropical periods are given for the Saturn satellites I to VIII. cProvisional names. References 1. 1998 Astronomical Almanac (USNO, Government Printing Office) 2. Jacobson, R.A. 1998, AJ, 115, 1195 3. Owen, W.M., Vaughn, R.M., & Synnott, S. 1991,AJ,101, 1511 Table 12.13. Additional satellite data [I, 2, 3,4]. Orbit Satellite Inclination (deg) Eccentricity Radius (Ian) Mass (1IPIanet) Mass (g) 18.28-28.58 0.05490049 1737.4 0.012300034 7.3483 x 1025 1.654 x lO- S 3.71 x 10- 9 1.063 x 1019 2.38 x 10 1S Earth Moon Mars II Jupiter I II ill IV V VI VII Vill IX X XI XII xm XIV XV XVI Saturn I II ill IV V VI VII VIII Phobos Deimos 1.0 0.9-2.7 0.015 0.0005 13.4 x 11.2 x 9.2 7.5 x 6.1 x 5.2 10 Europa Ganymede Callisto Amalthea Himalia Elara Pasiphae Sinope Lysithea Carme Ananke Leda Thebe Adrastea Metis 0.04 0.47 0.21 0.51 0.40 27.63 24.77 145 153 29.02 164 147 26.07 0.8 0.004 0.009 0.002 0.007 0.003 0.15798 0.20719 0.378 0.275 0.107 0.20678 0.16870 0.14762 0.015 1830.0 x 1818.7 x 1815.3 1565 2634 2403 131.0 x 73.0 x 67.0 85 40 18 14 12 15 10 5 55 x 45 13 x 10 x 8 20 x 20 4.7041 x 10- 5 2.528 Ox 10-5 7.8046x 10- 5 5.6667xlO-5 3.8xlO- 9 5.0xlO-9 4xlO- 1O lxl0- 10 4x 10- 11 4xl0- 11 5x 10- 11 2x 10- 11 3x 10- 12 4xlO- 1O 1 x 10- 11 5x 10- 11 8.9316x 1025 4.799 82x 1025 1.481 86x 1026 1.07593 x 1026 7.2x 102 1 9.5 x 102 1 8.x102O 2.x102O 8.x 10 19 8.x10 19 9.x10 19 4.x10 19 6.x 10 1S 8.x102O 2.x10 19 9.x 10 19 Mimas Enceladus Tethys Dione Rhea Titan Hyperion Iapetus 1.53 0.00 1.86 0.02 0.35 0.33 0.43 14.72 0.0202 0.00452 0.00000 0.002230 0.00 1 00 0.029192 0.104 0.02828 209.1 x 196.2 x 191.4 256.3 x 247.3 x 244.6 535.6 x 528.2 x 525.8 560 764 2575 180 x 140 x 112.5 718 6.60xlO- S Lx 10-7 1.l0x 10-6 1.95 x 10-6 4.06 x 10-6 2.366 7 x 10-4 4xlO- S 2.8x 10-6 3.75x1022 7.x1022 6.27xl023 1.l0xl024 2.31 x 1024 1.345 5 x 1026 2.x1022 1.6 x 1024 306 I 12 PLANETS AND SATELLITES 'nlble 12.13. (Continued.) Orbit Inclination (deg) Satellite Satum(eont.) IX Phoebe X Janus XI Epimetheus XII Helene xm Telesto XIV Calypso XV Atlas XVI Prometheus xvn Pandora xvm Pan U1'Q1IIU I II m IV V VI VII vm IX X XI XII xm XIV XV XVI xvn Neptune I II m IV V VI VII vm Pluto I Ariel Umbriel Titania Oberon Miranda Cordelia Ophelia Bianca Cressida Ina Radius (Ian) Eccentricity 0.14 0.34 0.0 0.16326 0.007 0.009 0.005 0.3 0.0 0.0 0.000 0.003 0.004 110 97.0 x 95.0 x 77.0 69 x 55 x 55 18 x 16 x 15 15 x 12.5 x 7.5 15.0 x 8.0 x 8.0 18.5 x 17.2 x 13.5 74.0 x 50.0 x 34.0 55.0 x 44.0 x 31.0 0.0034 0.0050 0.0022 0.0008 0.0027 0.00026 0.0099 0.0009 0.0004 0.00013 0.00066 0.0000 0.0001 0.00007 0.00012 0.082 0.509 581.1 x 577.9 x 577.7 584.7 788.9 761.4 240.4 x 234.2 x 232.9 13 15 21 31 27 42 54 27 33 77 30 Triton Nereid Naiad Thalassa Despina Galatea Larissa Proteus 157.345 0.000016 0.7512 0.000 0.000 0.000 0.000 0.00139 0.0004 1352.6 170 29: 40: 74 79 104 x 89 218 x 208 x 201 Charon 96.16c Juliet Portia Rosalind Belinda Puck Calibanb Sycoraxb Mass (g) 7xlO- 1O 3.38xlO-9 9.5xlO- 1O 4.x1020 1.92 x loll 5.4x1020 1.55xlO-S 1.35x10-S 4.06x10-S 3.47x10-S 7.6xlO-7 1.35 x 1024 1.17 x 1024 3.53x1024 3.01 x 1024 6.6x1022 2.089 x 10-4 2xlO-7 2.x1022 0.125 1.62 x 1024 10 0.3 0.36 0.14 0.10 4.2 0.08 0.10 0.19 O.ol 0.11 0.07 0.06 0.28 0.03 0.32 139.:za 152.7" Desdemona Mass (lJPlanet) 27.6c 4.74 0.21 0.07 0.05 0.20 0.55 60 593 Notes "Relative to the ecliptic plane. bProvisional names. cRefeIred to the Earth equator of 1950.0 (Nereid) and of J2000 (Charon). References 1. 1998 Astronomical Almanac (USNO, Government Printing Office) 2. Davies, M.E. et al. 1995, CeL Meeh., 63, 127 3. Jacobson,R.A.1998,AI,l1!,1195 4. Owen, W.M., Vaughn, R.M., & Synnott, S. 1991, AI, 101, 1511 2.140x102S 12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS I 307 Rotation and photometric data for many of the planetary satellites are given in Table 12.14. Table 12.14. Satellite rotation and photometric datil [1. 2. 3]. Sidereal period of rotation (d)" Geometric albedo (V)b V(l.O)C v.0d B-V U-B Moon S 0.12 0.21 -12.74 0.92 0.46 Phobos Deimos S S 0.07 0.08 11.8 12.89 11.3 12.40 0.6 0.65 0.18 10 Europa S S S S S 0.4 0.5 0.63 0.67 0.44 0.20 0.07 0.03 0.03 0.10 0.05 0.06 0.06 0.06 0.07 0.04 0.05 0.05 -1.68 -1.41 -2.09 -1.05 7.4 8.14 10.07 10.33 11.6 11.7 11.3 12.2 13.5 9.0 12.4 10.8 5.02 5.29 4.61 14.1 14.84 16.77 17.03 18.3 18.4 18.0 18.9 20.2 15.7 19.1 17.5 1.17 0.87 0.83 0.86 1.50 0.67 0.69 0.63 0.7 0.7 0.7 0.7 0.7 1.3 0.5 1.0 0.9 0.7 0.7 0.22 0.3 0.2" 0.06 0.9: 0.8: 0.7: 1.0: 1.0: 0.8: 0.5: 0.7: 0.5: 3.3 2.1 0.6 0.8 0.1 -1.28 4.63 1.5 6.89 4.4: 5.4: 8.4: 8.9: 9.1: 8.4: 6.4: 6.4: 12.9 11.7 10.2 10.4 9.7 8.28 14.19 11.1 16.45 14.: 15.: 18.: 18.5: 18.7: 18.: 16.: 16.: 0.35 0.19 0.28 0.25 0.27 0.07: 0.07: 1.45 2.10 1.02 1.23 3.6 11.4 11.1 14.16 14.81 13.73 13.94 16.3 24.1 23.8 Satellite Earth Mars I n Jupiter I n m IV V VI vn vm IX X XI XU xm XIV XV XVI Saturn I n m IV V VI vn vm IX X XI XU xm XIV XV XVI xvn xvm UrtUJIIS I n m IV V VI vn Ganymede Callisto Ama1thea HimaIia Elara Pasipbae Sinope Lysithea Carme Ananke Leda Thebe Adrastea Metis Mimas Enceladus Tethys Dione Rhea TItan Hyperion Iapetus Phoebe Janus Epimetheus Helene Telesto Calypso Atlas Prometheus Pandora S S S S S S S S 0.4 S S Pan Ariel Umbriel TItania Oberon Miranda Cordelia Ophelia S S S S S 5.6S 1.30 0.52 0.50 0.55 0.30 0.28 0.34 0.70 0.73 0.71 0.78 1.28 0.78 0.72 0.70 0.28 0.30 0.31 0.38 0.75 0.33 0.30 0.34 0.65 0.68 0.70 0.68 0.28 0.20 308 I 12 PLANETS AND SATELLITES Table 12.14. (Continued.) Sidereal period of rotation (d)il Satellite Uranus (cont.) Bianca vm IX Cressida X Desdemona Juliet XI Portia xn Rosalind Belinda XN Puck XV Calibanf XVI Sycoraxf XVII xm Neptune I II m IV V VI VII vm Geometric albedo (V)b v.0d 0.07: 0.07: 0.07: 0.07: 0.07: 0.07: 0.07: 0.075 0.07: 0.07: 10.3 9.5 9.8 8.8 8.3 9.8 9.4 7.5 23.0 22.2 22.5 21.5 21.0 22.5 22.1 20.2 22.4 20.9 -1.24 4.0 10.0: 9.1: 7.9 7.6: 7.3 5.6 13.47 18.7 24.7 23.8 22.6 22.3 22.0 20.3 0.9 16.8 Triton Nereid Naiad Thalassa Despina Galatea Larissa Proteus S 0.77 0.4 0.06: 0.06: 0.06: 0.06: 0.06 0.06 Charon S 0.5 Pluto I V(1,O)C B-V U-B 0.72 0.65 0.29 Notes a S means the rotation is synchronous with the orbit period. bThe solar V used is -26.75. cThe apparent V magnitude with the planet 1 AU from both Sun and Earth at zero phase angle. dThe apparent mean opposition V magnitude. eBright side 0.5, faint side 0.05. f Provisional names. References I. 1998 Astronomical Almanac (USNO, Government Printing Office) 2. Bums, J.A. 1986, Satellites, edited by J.A. Bums and M.S. Matthews (University of Arizona Press, "lUcson) 3. Veverka, J.M. 1998, Observers Handbook, edited by R.L. Bishop (University of Toronto Press, Toronto) 12.7 MOON Mean distance from Earth [8] Extreme range Mean equatorial horizontal parallax Eccentricity of orbit Inclination of orbit to ecliptic oscillating ±9' with period of 173 d Sidereal period (fixed stars) Mean orbital speed [9] Synodical month (new moon to new moon) 384401 ± 1 krn 356400-406 700 krn 3422%08 0.05490 5° 8' 43~'42 27.321661 1.023 krns- 1 29.530588 12.7 MOON / 309 Tropical month (equinox to equinox) Anomalistic month (perigee to perigee) Nodical month (node to node) Period of Moon's node (nutation period, retrograde) Period of rotation Moon's perigee (direct) [3] Moon's sidereal mean daily motion 27.321582 27.554550 27.212220 days 18.61 Julian years 8.849 Julian years 47434~'889 13?176358 Mean transit interval Main periodic terms in the motion [10] Principle elliptic term in longitude Principle elliptic term in latitude Evection Variation Annual inequality Parallactic inequality where g = Moon's mean anomaly g' = Sun's mean anomaly D = Moon's age u = distance of mean Moon from ascending node Physicallibration [11] Displacement (selenocentric) Period Opticallibration [11] Displacement (selenocentric) Period Surface area of Moon at some time visible from earth Inclination of lunar equator [11] To ecliptic To orbit Moon radii: a toward Earth, b along orbit, c toward pole. Mean Moon radius (b + c)/2 [8] Moon mass [12] Moon semi-diameter at mean distance geocentric topocentric, zenith Mean volume Moon mean density 24h50~47 22 639" sin g 18461" sin u 4586" sin(2D - g) 2370" sin 2D -669" sin g' -125" sin D longitude ±66" 1 yr latitude ±105'' [9] 6yr approximately sidereal lunar 59% 1° 32' 6° 41' 32~'7 1738.2 km 0.272 52 Earth equatorial radius a - c = l.09km a - b = 0.31 km b -c =0.78km M~/81.301 = 7.353 x 1025 g 15' 32% 15' 48~'3 2.200 x lQ25 cm3 3.341 gcm- 3 310 / 12 PLANETS AND SATELLITES Surface gravity Surface escape velocity Moment of inertia (about rotation axis) [13] Moment of inertia differences [13-15] (a + y = fJ) 162.2 cms-2 2.38 kms- 1 0.396Meb2 a = (C - y = B)/ A A)/ B (B - A)/C fJ = (C - = 0.000400 = 0.000628 = 0.000228 A-axis toward Earth, B along orbit, C toward pole. Gravitational potential term [13] Jz = 2.05 X 10-4 Mascons [16] Number of strong mascons on the near side of the Moon 4 exceeding 80 milligals Mean surface temperature [12] +107 C (day), 153 C (night) Temperature extremes [12] -233 C(?), +123 C 29mWm- 2 Flow of heat through Moon's surface [12] Moon's atmospheric density [12] '" 104 molecules cm- 3 (day) 2 x 105 molecules cm- 3 (night) Number of maria and craters on lunar surface with diameters greater than d [8, 17-19] This rule extends from the largest maria (d ~ 1000 km) to the smallest holes (d Lunar surface and photometric data are given in Tables 12.9 and 12.14. Table 12.15 gives the integral phase function for the Moon. Table 12.15. Lunar integral phase function [1]. Phase angle (deg.) Before full Moon After full Moon 0 1.000 0.787 0.603 0.466 0.356 0.275 0.211 0.161 1.000 0.759 0.586 0.453 0.350 0.273 0.211 0.156 10 20 30 40 50 60 70 Phase angle (deg.) Before full Moon After full Moon 80 0.120 0.0824 0.0560 0.0377 0.0249 0.0151 0.111 0.0780 0.0581 0.0405 0.0261 0.0158 0.0093 0.0046 90 100 110 120 130 140 150 Reference 1. Hapke B. 1974, Optical properties of lunar surface. In Physics and Astronomy of the Moon, edited by Zd. Kopal (Academic Press, New York) ~ I cm). 12.8 PLANETARY RINGS / 311 12.8 PLANETARY RINGS 12.8.1 Rings of Jupiter The four rings of Jupiter are described in Table 12.16. Table 12.16. Rings of Jupiter [1]. Distance Ring Halo ring Main ring Gossamer ring (inner) Gossamer ring (outer) Optical depth (krn) (Rj) 100 000--122 ()()() 122000--129 ()()() 129200-182 ()()() 182000--224900 1.40-1.71 I. 71-1.81 1.81-2.55 2.55-3.15 Albedo 3 x 10-6 5 x 10-6 ~0.015 1.0 x 10-7 Reference 1. http://nssdc.gsfc.nasa.gov/planetary/factsheetljupringfact.htrnl, and private communication from G.S. Orton 12.8.2 Rings of Saturn Table 12.17 lists the details of the rings of Saturn. Table 12.17. Rings of Satum a [1,2]. Radius Zone O-ring inner edge C-ring inner edgeb Titan ringlet Maxwell ringlet B-ring inner edge B-ring outer edge Cassini division A-ring inner edgeC Encke gap center A-ring outer edge F-ring center G-ring center E-ring inner edge E-ring outer edge (krn) Distance Rj RS aturn >66900 74658 77871 87491 91975 117507 l.ll 1.239 1.292 1.452 1.526 1.950 122340 133589 136775 140374 170 ()()() 2.030 2.216 2.269 2.329 2.82 3 8 ~180()()() ~480()()() Optical depth Albedo 0.05-0.35 0.12-0.30 0.4-2.5 0.4-0.6 0.05-.015 0.4-1.0 0.2-0.4 0.4-0.6 0.1 1.0 x 10-6 1.5 x 10- 5 0.6 Notes aTotai mass of rings 6 x 10- 8 MS aturn = 3.4 x 1022 g. bThickness of C-ring no more than 10 m. cThickness of A-ring about 50 m. References I. Zebker, H.A. & lYler, G.L. 1984, Science, 223, 396 2. http://nssdc.gsfc.nasa.gov/planetary/factsheetlsatringfact.htrnl 312 I 12 12.8.3 Rings of Uranus PLANETS AND SATELLITES Table 12.18 lists the details of the rings of Uranus. Table 12.18. Rings of Uranus [I, 2, 3]. Radius Zone 6 5 4 ex f3 1/ y 8 A € (kIn) Distance RJRUranus Optical depth 41837 42235 42571 44718 45661 47176 47626 48303 50024 51149 1.637 1.652 1.666 1.750 1.786 1.834 1.863 1.900 1.957 2.006 ~0.3 ~0.5 ~0.3 ~0.4 ~.3 ~0.4- ~1.5+ ~0.5 ~O.I 0.5-2.3 Albedo ~15 ~15 ~15 ~15 ~15 ~15 ~15 ~15 ~15 ~18 x x x x x x x x x x 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10-3 References 1. Stone, E.C. & Miner, E.D. 1986, Science, 233,39 2. AstronomicalAlmanac, 1996 (USNO, Government Printing Office) 3. http://nssdc.gsfc.nasa.gov/planetary/factsheetluranringfact.htrnl 12.8.4 Rings of Neptune Table 12.19 lists the details of the rings of Neptune. Table 12.19. Rings of Neptune [I, 2]. Radius Zone Galle (1989 N3R) LeVerrier (1989 N2R) Lassell (1989 N4R)a Arago (1989 N4R)a Unnamed (indistinct) Adams (1989 NIR)b (kIn) ~41900 ~532oo ~532oo ~572oo 61950 62933 Distance RJ RNeptune 1.692 2.148 2.148 2.310 2.501 2.541 Optical depth Albedo ~0.OOO08 ~0.002 ~O.OOO 15 ~0.0045 ~15 x 10- 3 ~15 x 10- 3 ~15 x 10- 3 ~15 x 10-3 Notes aLeVerrier and Lassell were originally identified as one ring, designated 1989N4R. b Arcs in the Adams Ring with optical depths of 0.12 and albedos of about 0.04 are: Courage, Liberte, Egalite I, Egalit6 2, and Fraternite. References 1. Lang, K.R. 1991, Astrophysical Data: Planets and Satellites, (Springer-Verlag, New York), p. 937 2. http://nssdc.gsfc.nasa.gov/planetary/factsheetlnepringfact.htrnl 12.8 PLANETARY RINGS I 313 REFERENCES 1. Myles Standish. DE 4OS. private communication 2. Robert Jacobson. private communication 3. Exp/QnQtory Suppkment to tIu! Astronomical Almonac 1992. edited by P.K. Seidelmann (University Science. Mill Valley. CA) 4. Davies. M.E. et al. 1994. eeL Meeh.. 63. 127 S. Handbook of the British Astronomy Association (Annual) Roy. A.E. &; Ovenden. M.W. 1954. MNRAS. 114.232 Roy. A.E. &; Ovenden. M.W. 19S5. MNRAS. 115.296 Astrophysical QlIIJIItities. I. Sec. 86; 2. Sec. 69 Lang. K.R. 1991. Astrophysical Data: Pionets and Satellites. (Springer-Verlag. New York) p. 937 10. Landolt-Bomstein Tabks. 1962 (Springer-Verlag. New 6. 7. 8. 9. York). pp. 3. 83 11. Astronomical Almanacs (USNO. Government Printing Office) 12. LwuJr Source Book. 1991. edited by G. Heiken. D. Vaniman. and B.M. French (Cambridge University Press. Cambridge) 13. Cook, A.H. 1970. MNRAS. ISO. 187 14. Goudas. C.L. 1967. AI. 72. 9SS IS. Koziel, K. 1967. Proc. R. Soc. London.. 296. 248 16. Mutch, T.A. 1970. Geology of the Moon (Princeton University Press. Princeton. NJ). pp. SO. 217. 26S 17. Jaffe. L.D. 1969. SSRv. 9. SOS 18. Cross. C.A. 1966. MNRAS. 134.24S 19. Marcus. A. 1966. MNRAS.I34. 269 Chapter 13 Solar System Small Bodies Richard P. Binzel, Martha S. Hanner, and Duncan I. Steel 13.1 13.1.1 13.1 Asteroids or Minor Planets. . . . . . . . . . . . . . .. 315 13.2 Comets. . . . . . . . . . . . . . . . . . . . . . . . . .. 321 13.3 Zodiacal Light . . . . . . . . . . . . . . . . . . . . . .. 328 13.4 Infrared Zodiacal Emission . . . . . . . . . . . . . . . 331 13.5 Meteoroids and Interplanetary Dust. . . . . . . . . .. 333 ASTEROIDS OR MINOR PLANETS Populations and Locations [1-3] Number of minor planets having well-determined orbits, cataloged by permanent designations (numbers) as of 1998, January 1: 8125. Number of known minor planets having less well-determined orbits, cataloged by provisional designations: > 25, 000. Most are located in the Main-belt, between Mars and Jupiter. Semimajor axis, range 2.06 to 3.28 AU, mean a Mean orbital eccentricity: e = 0.142. Mean orbital inclination: i = 7.92 deg. Mean orbital period: 4.40 yr. = 2.68. Number of main-belt asteroids larger than 100 kIn in diameter: 188,50 kIn: 475. Estimated population of main-belt asteroids larger than diameter D (in kIn): 315 316 / 13 SOLAR SYSTEM SMALL BODIES Near-Earth Asteroids (NEAs) are those approaching within 0.3 AU of the Earth's orbit. Atens: a < 1.0 AU, aphelion Q > 0.983 AU. Number known as of 1998, January 1 = 27. Apollos: a ~ 1.0 AU, perihelion q ::s 1.017 AU. Number known as of 1998, January 1 = 213. Amors: a > 1.0 AU, 1.017 < q ::s 1.3 AU. Number known as of 1998, January 1 = 207. Aten and Apollo asteroids have orbits which cross the Earth's orbit. Orbits of many Amor asteroids can evolve to become Earth-crossing. Estimated population of Earth-crossing asteroids having diameter: > 1 kIn: 2100. > 100 m: 320,000. (A size likely to survive passage through the terrestrial atmosphere.) 'JYpical collisional frequency (per object) with Earth, for an NEA having an Earth-crossing orbit: Pj = 2.2 per 109 yr. Mean collision velocity with Earth: Vc = 22.5 kmls. Trojan asteroidsare located in the vicinities of the L4 and L5 Lagrange points of Jupiter. Mean semimajor axis: a = 5.20 AU. Mean eccentricity: e = 0.080. Mean inclination: i = 15.9 deg. Number known as of 1998, January 1: 413. 13.1.2 Magnitudes [4] An asteroid's absolute magnitude, H, is defined as its mean V magnitude (neglecting rotational and aspect variations), if it were observed at a distance r = 1 AU from the Sun, ll. = 1 AU from the Earth, and a phase angle (Earth-object-Sun angle) a = O. For other locations, an asteroid's mean apparent V magnitude can be expressed by V = H(a)+5Iogrll., where H(a) = H - 2.5Iog[(1 - G)4>1 (a) + G4>2(a)]. G is called the slope parameter which accounts for an asteroid's nonlinear change in brightness as a function of phase angle only. 4>1 and 4>2 are described by 4>j = exp{-Aj[tan(a/2)]Bi}; Al = 3.33, BI = 0.63, i = 1,2, A2 = 1.87, B2 = 1.22. An asteroid's diameter D (in kIn) can be estimated by logD = 3.129 - 0.5logp - 0.2H, where p is its geometric albedo in the V passband. An asteroid's Bond albedo, A, is related to the geometric albedo by the phase integral, q, where A=pq, q = 0.290 + 0.684G; o ::s G ::s 1. 13.1 ASTEROIDS OR MINOR PLANETS I 317 13.1.3 Physical Properties [5] Estimated total mass of the asteroids = 1.8 x 1()24 g. Estimated densities for most asteroids, 1.0 - 3.5 g cm- 3. Possible compositions, typical albedos, slope parameters, and color indices for selected taxonomic types of asteroids. C-types: Carbonaceous chondrite, p = 0.05, G = 0.15, B - V = 0.70, U - B = 0.35. S-types: Stony-Iron? Ordinary chondrite?, p = 0.19, G = 0.25, B - V = 0.85, U - B = 0.44. M-types: Metal-rich?, p = 0.10, G = 0.20, B - V = 0.70, U - B = 0.25. Typical rotation period, P '" 9 h. Observed range: 2 to > 1000 h. Typical rotation light curve amplitude variation, l:!.M '" 0.2 mag. Observed range: 0 to > 1 mag. Typical shape, modeled by a triaxial ellipsoid with axes a, b, c, where a> b > c: a:b:c=2:..fi: 1. Lowest energy rotation state occurs about the c-axis. 13.1.4 Data Tables Tables 13.1 and 13.2 give the 100 largest and 147 of the nearest asteroids. Table 13.1. The 100 largest asteroids [1]. No. Name 1 2 4 10 511 704 52 15 87 16 24 31 65 3 324 107 624 532 451 48 19 29 121 423 13 45 Ceres Pallas Vesta Hygica Davida Interamnia Europa Eunomia Sylvia Psyche 94 88 7 702 Themis Euphrosyne Cybcle Juno Bamberga Camilla Hektor Herculina Patientia Doris Fortuna Amphitrite Hermione Diotima Egeria Eugenia Aurora Thisbc Iris Alauda Year of Discovery D (km) 1SOl 1802 1807 1849 1903 1910 1858 1851 1866 1852 1853 1854 1861 1804 1892 1868 1907 1904 1899 1857 1852 1854 1872 1896 1850 1857 1867 1866 1847 1910 913 523 501 429 337 333 312 272 271 264 249 248 245 244 242 237 233 231 230 225 221 219 217 217 215 214 212 210 203 202 a e 2.77 2.77 2.36 3.14 3.18 3.06 3.10 2.64 3.49 2.92 3.13 3.14 3.44 2.67 2.68 3.48 5.18 2.77 3.06 3.11 2.44 2.55 3.44 3.08 2.58 2.72 3.16 2.77 2.39 3.19 0.078 0.234 0.091 0.120 0.178 0.148 0.100 0.185 0.083 0.134 0.134 0.228 0.104 0.258 0.341 0.084 0.024 0.176 0.071 0.069 0.158 0.072 0.143 0.034 0.086 0.083 0.082 0.164 0.230 0.029 P (h) 10.6 34.8 7.1 3.8 15.9 17.3 7.4 11.8 10.9 3.1 0.8 26.3 3.5 13.0 11.1 9.9 18.2 16.4 15.2 6.5 1.6 6.1 7.6 11.2 16.5 6.6 8.0 5.2 5.5 20.6 9.075 7.811 5.342 18.4 5.13 8.727 5.631 6.083 5.183 4.196 8.38 5.531 6.07 7.21 29.43 4.84 6.921 9.405 9.727 11.89 7.445 5.39 6.1 4.622 7.045 5.699 7.22 6.042 7.139 8.36 l!.M (mag) 0.04 0.0~.16 0.12 0.09-{).18 0.06-0.25 0.0~.11 0.09-{).1O 0.4-0.56 0.30-0.62 0.0~.42 0.10-0.14 0.09-{).13 0.04-0.12 0.14-0.22 0.07 0.32-{).52 0.1-1.1 0.08-0.18 0.05-0.10 0.35 0.22-{).35 0.01~.15 0.03 0.06-0.18 0.12 0.08-0.41 0.12 0.08-0.21 0.04-0.29 0.07~.1O 'JYpe P H G U-B B-V G B 0.10 0.14 0.38 0.07 0.05 0.06 0.05 0.19 0.04 0.10 3.32 4.13 3.16 5.27 6.17 6.00 6.25 5.22 6.95 5.99 7.07 6.53 6.79 5.31 6.82 6.SO 7.47 5.78 6.65 6.83 7.09 5.84 7.39 7.48 6.47 7.27 7.55 7.05 5.76 7.23 0.11 0.15 0.34 -0.04 0.02 0.02 0.00 0.20 0.28 0.22 0.10 0.15 0.15 0.30 0.10 -0.17 0.15 0.25 0.20 -0.05 0.10 0.21 0.15 0.68 -0.02 0.15 0.09 0.17 0.51 0.13 0.43 0.29 0.50 0.35 0.36 0.26 0.33 0.46 0.25 0.25 0.35 0.32 0.27 0.41 0.30 0.30 0.24 0.41 0.33 0.43 0.39 0.42 0.39 0.30 0.46 0.27 0.30 0.29 0.48 0.32 0.72 0.66 O.SO 0.69 0.72 0.64 0.66 0.84 0.70 0.70 0.68 0.67 0.67 0.81 0.70 0.70 0.79 0.85 0.65 0.72 0.75 0.83 0.72 0.67 0.75 0.66 0.66 0.66 0.85 0.66 V C C F CF S P M C C P S CP C D S CU CG G S C C G FC CP CF S C 0.07 0.05 0.22 0.05 0.06 0.16 0.07 0.06 0.16 0.04 0.03 0.09 0.04 0.03 0.21 0.05 318 / 13 SOLAR SYSTEM SMALL BODIES Table 13.1. (Continued). No. 375 372 128 6 154 76 130 22 259 776 41 2060 9 120 747 790 566 911 96 194 59 386 54 1437 334 444 241 409 185 11 139 354 804 165 39 89 173 488 536 85 150 238 145 49 117 168 14 51 106 20 1172 137 283 209 361 617 18 211 308 508 895 93 144 196 420 Name Ursula Palma Nemesis Hebe Bertha Freia Elektra Kalliope Aletheia Berbericia Daphne Chirona Metis Lachesis Wmchester Pretoria Stereoskopia Agamemnon Aegle Prokne Elpis Siegena Alexandra Diomedes Chicago Gyptis Germania Aspasia Eunike Parthenope Juewa Eleonora Hispania Loreley Laetitia Julia Ino Kreusa Merapi 10 Nuwa Hypatia Adeona Pales Lomia Sibylla Irene Nemausa Dione Massalia Aneas Meliboea Emma Dido Bononia Patroclus Melpomene Isolda Polyxo Princetonia Helio Minerva Vibilia Philomela Bertholda Year of Discovery D (kin) a e 1893 1893 1872 1847 1875 1862 1873 1852 1886 1914 1856 1977 1848 1872 1913 1912 1905 1919 1868 1879 1860 1894 1858 1937 1892 1899 1884 1895 1878 1850 1874 1893 1915 1876 1856 1866 1877 1902 1904 1865 1875 1884 1875 1857 1871 1876 1851 1858 1868 1852 1930 1874 1889 1879 1893 1906 1852 1879 1891 1903 1918 1867 1875 1879 1896 200 195 194 192 192 190 189 187 185 183 182 180 179 178 178 176 175 175 174 174 173 173 171 171 170 170 169 168 165 162 162 162 161 160 159 159 159 158 158 157 157 156 155 154 154 154 153 153 152 151 151 150 150 149 149 149 148 148 148 147 147 146 146 146 146 3.13 3.14 2.75 2.43 3.18 3.42 3.11 2.91 3.15 2.93 2.76 13.68 2.39 3.12 3.00 3.41 3.39 5.21 3.05 2.62 2.71 2.90 2.71 5.11 3.87 2.77 3.05 2.58 2.74 2.45 2.78 2.80 2.84 3.13 2.77 2.55 2.74 3.14 3.50 2.65 2.98 2.91 2.67 3.08 2.99 3.38 2.59 2.37 3.16 2.41 5.16 3.11 3.04 3.14 3.95 5.23 2.30 3.05 2.75 3.16 3.20 2.75 2.66 3.11 3.41 0.102 0.264 0.126 0.202 0.095 0.169 0.219 0.098 0.112 0.166 0.273 0.380 0.122 0.064 0.343 0.154 0.093 0.068 0.140 0.238 0.117 0.169 0.196 0.046 0.041 0.173 0.103 0.070 0.127 0.100 0.177 0.116 0.138 0.070 0.115 0.181 0.209 0.179 0.090 0.194 0.125 0.089 0.146 0.236 0.023 0.049 0.166 0.065 0.182 0.144 0.104 0.224 0.151 0.067 0.216 0.139 0.218 0.155 0.038 0.023 0.149 0.142 0.233 0.027 0.047 15.9 23.9 6.2 14.8 21.1 2.1 22.9 13.7 10.7 18.2 15.8 6.9 5.6 7.0 18.2 20.6 4.9 21.8 16.0 18.5 8.6 20.3 11.8 20.6 4.7 10.3 5.5 11.2 23.2 4.6 10.9 18.4 15.3 11.2 10.4 16.1 14.2 11.5 19.4 12.0 2.2 12.4 12.6 3.2 14.9 4.6 9.1 10.0 4.6 0.7 16.7 13.4 8.0 7.2 12.7 22.0 10.1 3.9 4.4 13.3 26.1 8.6 4.8 7.3 6.7 P (h) 11M (mag) 16.83 6.58 39 7.274 0.0~.17 0.0~.20 9.98 5.225 4.147 0.15-0.2 0.19-0.58 0.04-0.30 7.672 5.988 0.13-0.23 0.16-0.38 5.078 0.04-0.36 9.4 10.37 7 0.12 0.10 0.13 0.16 0.2-0.4 Type C BFC C S P G M CP C C B S C PC P C D T 15.67 13.69 9.763 7.04 18 0.27 0.1 0.11 0.12 0.3~.42 6.214 0.15 9.03 10.83 7.83 41.8 4.277 7.42 7.6 5.138 11.39 5.93 0.10-0.14 6.875 8.14 8.9 8.1 10.42 0.15 0.09 0.12 0.08 0.1~.20 9.35 7.785 0.04-0.1 0.14-0.25 0.07-0.12 0.18 0.12-0.30 0.19 0.12 0.08-0.53 0.10-0.25 0.04-0.11 8.098 0.17-0.27 6.888 8 0.31 0.20 11.57 0.22-0.35 12.03 0.20 5.97 13.81 8.333 0.10 0.13 0.07-0.33 C CP C C DP C C CP ex C S CP S PC CD S S C C X FC CX C C CG XC C S CU G S D C X C DP P S C T C FCB CU C S P p 0.05 0.04 0.25 0.07 0.02 0.08 0.12 0.03 0.07 0.04 0.04 0.03 0.03 0.04 0.03 0.05 0.04 0.06 0.05 0.02 0.06 0.04 0.06 0.05 0.05 0.15 0.05 0.19 0.04 0.06 0.29 0.16 0.05 0.05 0.04 0.06 0.03 0.03 0.04 0.05 0.04 0.05 0.08 0.08 0.19 0.03 0.04 0.02 0.04 0.03 0.04 0.22 0.05 0.04 0.03 0.02 0.08 0.05 0.18 0.03 H G U-B B-V 7.43 7.33 7.55 5.70 7.09 8.08 6.86 6.50 7.86 7.68 7.16 6.62 6.32 7.73 7.68 8.05 8.15 7.88 7.97 7.66 7.72 7.42 7.70 8.30 7.46 7.85 7.50 7.60 7.73 6.62 7.79 6.32 7.87 7.49 5.94 6.57 7.79 7.83 8.08 7.56 8.32 8.38 8.05 7.91 8.18 7.93 6.27 7.36 7.42 6.52 8.26 8.04 8.73 8.15 8.27 8.17 6.41 7.84 8.18 8.30 8.64 7.47 7.87 6.64 8.35 0.23 0.25 0.15 0.24 0.15 0.44 -0.04 0.22 0.15 0.34 -0.06 0.25 0.29 0.17 0.15 0.15 0.43 0.15 0.15 0.15 0.34 0.68 0.36 0.38 0.68 0.83 0.29 0.47 0.25 0.28 0.39 0.37 0.28 0.51 0.38 0.32 0.30 0.30 0.22 0.34 0.35 0.29 0.40 0.36 0.24 0.36 0.30 0.29 0.34 0.33 0.42 0.29 0.54 0.38 0.31 0.50 0.48 0.32 0.36 0.28 0.28 0.27 0.38 0.36 0.39 0.30 0.38 0.39 0.47 0.47 0.42 0.26 0.33 0.30 0.29 0.19 0.21 0.39 0.36 0.37 0.33 0.70 0.75 0.69 0.67 0.70 0.73 0.70 0.86 0.70 0.71 0.70 0.70 0.77 0.77 0.73 0.67 0.74 0.70 0.70 0.72 0.68 0.69 0.72 0.68 0.85 0.70 0.95 0.71 0.74 0.89 0.88 0.70 0.70 0.69 0.66 0.71 0.73 0.69 0.75 0.68 0.75 0.84 0.77 0.74 0.81 0.73 0.70 0.71 0.69 0.75 0.70 0.85 0.72 0.79 0.73 0.25 0.39 0.46 0.23 0.73 0.72 0.86 0.69 om 0.23 0.15 0.15 -0.06 0.23 0.04 0.28 0.27 0.27 0.15 0.32 0.22 0.15 -0.03 0.14 0.12 0.15 0.15 0.05 0.15 0.51 om 0.39 0.48 0.16 0.09 0.06 0.17 0.26 0.15 0.10 0.15 -0.09 0.15 0.15 0.18 0.03 0.28 0.15 0.15 -0.11 0.08 0.48 0.04 13.1 ASTEROIDS OR MINOR PLANETS / 319 Table 13.1. (Continued). No. 95 489 69 349 762 Name Year of Discovery Arethusa Cornacina Hesperia Dernbowska Pulcova 1867 1902 1861 1892 1913 D (Ian) 145 144 143 143 142 a 3.07 3.16 2.98 2.92 3.16 P (h) e 0.144 0.032 0.169 0.091 0.092 12.9 12.9 8.6 8.3 13.0 AM (mag) 1Ype 8.688 0.24 5.655 4.701 0.20 0.08"'{).47 C C M R F p H 0.06 0.03 0.12 0.34 0.03 7.84 8.36 7.10 5.98 8.58 G U-8 8-V 0.37 0.36 0.23 0.54 0.31 0.71 0.69 0.70 0.93 0.65 0.08 0.15 0.15 0.33 0.50 Note a Object 2060 Chiron is known to exhibit cometary activity, e.g., IAUC 4770, and is catalogued as comet 95p. Reference I. Binzel, R.P., Gehrels, T., & Matthews, M.S., editors, 1989, Asteroids II Database, in Asteroids II (University of Arizona Press, Tucson), pp. 997-1190 Table 13.2. Near-eanh asteroids having permanent designations [l_3].a No. 433 719 887 1036 1221 1566 1580 1620 1627 1685 1862 1863 1864 1865 1866 1915 1916 1917 1943 1980 1981 2059 2061 2062 2063 2100 2101 2102 2135 2201 2202 2212 2329 2340 2368 2608 3102 3103 3122 3199 3200 3271 3288 3352 3360 Name Eros Albert Alinda Ganyrned Arnor Icarus Betu1ia Geographos Ivar Toro Apollo Antinous Daedalus Cerberus Sisyphus Quetzalcoatl Boreas Cuyo Anteros Tezcatlipoca Midas Baboquivari Anza Aten Bacchus Ra-Shalorn Adonis Tantalus Aristaeus 01jato Pele Hephaistos Orthos Hathor Beltrovata Seneca Krok Eger Florence Nefertiti Phaethon UI Seleucus McAuliffe Provisional designation q (AU) a e 1898 DQ 1911 MT 1918 DB 1924TD 1932 EAl 1949MA 1950KA 1951 RA 1929 SH 19480A 1932 HA 1948 EA 1971 FA 1971 UA 1972XA 1953 EA 1953 RA 1968AA 1973 EC 1950 LA 1973 EA 1963 UA 1960UA 1976AA 1977 HB 1978 RA 1936CA 1975 YA 1977 HA 1947 XC 1972 RA 1978 SB 1976 WA 1976 UA 1977RA 1978DA 1981 QA 1982 BB 1981 ET3 1982RA 1983 TB 1982 RB 1982DV 1981 CW 1981 VA 1.133 1.189 1.087 1.226 1.083 0.187 1.119 0.828 1.124 0.771 0.647 0.891 0.563 0.576 0.873 1.081 1.250 1.066 1.064 1.085 0.622 1.256 1.048 0.790 0.701 0.469 0.441 0.905 0.794 0.626 1.119 0.362 0.820 0.464 1.234 1.044 1.188 0.907 1.021 1.128 0.140 1.271 1.102 1.186 0.633 1.458 2.584 2.486 2.658 1.919 1.078 2.195 1.245 1.863 1.367 1.471 2.260 1.461 1.080 1.893 2.537 2.272 2.150 1.430 1.710 1.776 2.651 2.265 0.967 1.078 0.832 1.874 1.290 1.599 2.174 2.292 2.168 2.402 0.844 2.105 2.491 2.152 1.406 1.769 1.574 1.271 2.102 2.032 1.879 2.465 0.223 0.540 0.563 0.539 0.436 0.827 0.490 0.335 0.397 0.436 0.560 0.606 0.615 0.467 0.539 0.574 0.450 0.504 0.256 0.365 0.650 0.526 0.537 0.183 0.349 0.437 0.765 0.299 0.503 0.712 0.512 0.833 0.659 0.450 0.414 0.581 0.448 0.355 0.423 0.284 0.890 0.395 0.458 0.369 0.743 10.8 10.8 9.3 26.6 11.9 22.9 52.1 13.3 8.4 9.4 6.4 18.4 22.2 16.1 41.2 20.4 12.8 23.9 8.7 26.9 39.8 11.0 3.8 18.9 9.4 15.8 1.4 64.0 23.0 2.5 8.8 11.8 24.4 5.8 5.3 15.3 8.4 20.9 22.2 33.0 22.1 25.0 5.9 4.8 21.7 H 1Ype 11.2 16.0 13.8 9.5 17.7 16.9 14.5 15.6 13.2 14.2 16.3 15.5 14.9 16.8 13.0 19.0 14.9 13.9 15.8 13.9 15.5 15.8 16.6 16.8 17.1 16.1 18.7 16.2 17.9 15.3 17.6 13.9 14.9 19.2 15.2 17.5 15.6 15.4 14.2 14.8 14.6 16.7 15.3 15.8 16.3 S S S S C S S S Q S SQ S S S S S S S TCG S C S? SG CSU SQ S QRS E S F S D (Ian) 17 2 5 41 1 2 8 2 7 12 1 2 3 I 10 0.5 3 6 2 13 3 3 3 I I 4 I 2 I 2 I 5 4 I 3 1 2 3 6 3 5 2 3 3 2 Pi (109 yr) Vc (km/s) 1.5 1.8 0.5 3.8 1.8 4.0 2.8 1.3 1.0 2.5 15.4 30.6 30.6 16.7 14.0 17.2 20.3 19.9 26.0 20.9 1.3 3.5 17.8 13.4 3.8 30.7 1.3 7.1 6.5 6.3 2.8 2.5 2.0 2.3 0.1 0.4 1.8 14.0 14.2 16.0 15.8 17.9 25.4 34.8 21.0 26.4 14.8 34.6 23.3 16.3 3.9 2.1 17.3 17.0 1.4 35.0 1.4 21.0 0.7 26.6 Category Arnor Arnor Arnor Arnor Arnor Apollo Arnor Apollo Arnor Apollo Apollo Apollo Apollo Apollo Apollo Arnor Arnor Arnor Arnor Arnor Apollo Arnor Arnor Aten , Apollo Aten Apollo Apollo Apollo Apollo Arnor Apollo Apollo Aten Arnor Arnor Arnor Apollo Arnor Arnor Apollo Arnor Arnor Arnor Apollo 320 / 13 SOLAR SYSTEM SMALL BODIES 1Bble 13.2. (Continued.) No. 3361 3362 3551 3552 3553 3554 3671 3691 3752 3753 3757 3838 3908 3988 4015 b 4034 4055 4179 4183 4197 4257 4341 4401 4450 4486 4487 4503 4544 4581 4596 4660 4688 4769 4947 4953 4954 4957 5011 5131 5143 5189 5324 5332 5370 5381 5496 5587 5590 5604 5620 5626 5645 5646 5653 5660 5693 5731 5751 5786 5797 5828 5836 5863 5869 5879 6037 6047 Name Orpheus Khufu Verenia Don Quixote Mera Amun Dionysus Camillo Epona WilsonHarrington Magellan Toutatis Cuno Ubasti Poseidon Aditi Pan Mithra Pocahontas Cleobulus Xanthus Asclepius Nereus Castalia Ninkasi Eric Brucemurray Ptah Heracles Lyapunov Taranis Sekhmet Zeus Zao Talos Bivoj Tara Tanith Provisional designation (AU) a e 1982HR 1984QA 1983RD 1983 SA 1985 JA 1986EB 1984KD 1982Fr 1985 PA 19861'0 1982XB 1986WA 1980PA 1986 LA 1979 VA 0.819 0.526 1.073 1.209 1.117 0.701 1.003 1.270 0.986 0.484 1.017 0.449 1.043 1.055 1.000 1.209 0.989 2.092 4.233 1.645 0.974 2.196 1.774 1.414 0.998 1.835 1.505 1.926 1.545 2.644 0.323 0.469 0.487 0.714 0.321 0.280 0.543 0.284 0.302 0.515 0.446 0.702 0.459 0.317 0.622 1986PA 1985002 1989AC 1959LM 1982 TA 1987QA 1987KF 1985 TB 1987 SY 1987 SB 1987UA 1989WM 1989 FB 1989 FC 1981 QB 1982 DB 1980WF 1989 PB 1988 TJI 1990MU 1990SQ 1990XJ 6743 P-L 1990BG 1991 VL 1990UQ 1987 SL 1990DA 1986RA 1991IY 1973 NA 1990 SB 1990 VA 1992 FE 19900A 1991 FE 1990SP 1990TR 1992 WD5 1974MA 1993 EA 1988 VP4 1992AC 1991 RC 1980AA 1991 AM 1993 MF 1983 RB 1988 VN4 1992 CHI 1988EG 1991 TBI 0.589 1.226 0.920 0.718 0.523 0.876 0.588 1.117 0.596 0.743 1.217 1.279 0.781 0.657 1.077 0.953 1.081 0.549 1.139 0.555 1.104 1.223 0.818 0.639 0.419 0.810 1.136 1.176 1.228 0.667 0.881 1.080 0.710 0.551 1.247 1.201 0.830 1.205 1.248 0.424 0.527 0.786 1.215 0.187 1.053 0.517 1.143 1.097 1.231 1.154 0.636 0.942 1.060 1.820 2.512 1.980 2.298 1.647 1.835 2.578 1.442 2.200 1.731 2.703 1.042 1.022 2.239 1.490 2.232 1.063 1.370 1.621 2.001 1.565 1.635 1.486 1.835 1.551 2.958 2.163 3.344 0.947 2.433 2.392 0.985 0.927 2.159 2.196 1.355 2.143 1.794 1.786 1.272 2.267 2.104 1.081 1.893 1.698 2.443 2.222 1.812 1.625 1.269 1.454 0.444 0.326 0.634 0.638 0.773 0.468 0.679 0.567 0.586 0.663 0.297 0.527 0.250 0.357 0.519 0.360 0.516 0.483 0.168 0.658 0.448 0.219 0.500 0.570 0.771 0.478 0.616 0.456 0.633 0.296 0.638 0.548 0.279 0.405 0.422 0.453 0.387 0.438 0.304 0.763 0.585 0.653 0.423 0.827 0.444 0.696 0.532 0.506 0.321 0.289 0.499 0.352 q H Type 2.7 9.9 9.5 30.8 36.8 23.4 13.6 20.4 55.6 19.8 3.9 29.3 2.2 10.8 2.8 19.0 18.3 16.8 13.0 16.5 15.8 16.3 14.9 15.5 15.1 19.0 15.5 17.4 18.2 16.0 V 11.2 23.2 0.5 6.8 12.2 40.7 11.9 26.7 5.5 3.0 16.4 2.5 14.1 4.9 37.1 1.4 6.4 8.9 15.6 24.4 17.5 35.0 7.4 36.4 9.2 3.6 19.5 25.4 19.0 49.0 68.0 18.1 14.2 4.8 7.8 3.9 13.5 7.9 6.9 38.0 5.1 11.5 16.1 23.3 4.2 30.0 8.0 19.4 17.9 21.6 3.5 23.5 18.1 14.8 15.3 14.4 14.6 16.2 15.5 15.8 17.2 15.6 17.1 15.6 17.1 20.4 16.0 18.2 19.0 16.9 18.7 14.1 12.6 15.1 17.1 14.1 14.0 17.3 15.2 13.9 15.7 16.5 15.3 13.6 19.7 16.4 17.0 14.7 17.0 14.3 15.4 15.7 17.0 15.8 14.8 17.0 19.1 16.3 13.9 15.5 17.0 17.9 18.7 17.0 V D M S V CF V SQ S S C S S D (km) 1 1 1 18 2 3 2 4 3 4 0.5 3 1 1 4 1 3 3 5 5 2 3 3 1 3 1 3 1 0.5 2 I 0.5 2 1 6 12 4 I 6 6 1 3 6 5 2 3 7 0.5 2 2 4 2 5 3 3 2 3 4 2 1 2 6 3 2 I I 2 Pi (109 yr) Vc (kmIs) 21.0 5.3 14.0 19.8 5.4 1.5 17.4 16.0 1.0 3.0 5.1 1.0 4.0 27.0 22.0 13.4 29.0 14.7 0.8 15.5 1.3 1.0 21.3 27.0 1.5 23.3 6.4 5.5 22.2 18.5 6.6 13.3 0.8 22.5 1.1 4.2 15.5 15.4 21.8 13.1 20.9 18.9 0.6 26.5 3.8 0.6 16.7 26.3 5.8 17.2 2.9 0.5 26.7 40.5 5.4 16.5 1.6 4.0 16.4 17.0 0.9 32.0 1.0 20.1 0.3 0.5 13.2 28.0 8.8 18.3 Category Apollo Aten Amor Amor Amor Aten Amor Amor Apollo Aten Amor Apollo Amor Amor Amor Apollo Amor Apollo Apollo Apollo Apollo Apollo Amor Apollo Apollo Amor Amor Apollo Apollo Amor Apollo Amor Apollo Amor Apollo Amor Amor Apollo Apollo Apollo Apollo Amor Amor Amor Aten Apollo Amor Aten Aten Amor Amor Apollo Amor Amor Apollo Apollo Apollo Amor Apollo Amor Apollo Amor Amor Amor Amor Apollo Apollo 13.2 COMETS / 321 Table 13.2. (Continued.) No. 6050 6053 6063 6178 6239 6455 6456 6489 6491 6569 6611 7025 7088 7092 7236 7335 7336 7341 7350 7358 7474 7480 7482 7753 7822 7839 7888 7889 7977 8013 8014 8034 8035 8037 Name Jason Minos Golornbek Golevka Ishtar Cadmus Norwan Hermesc Provisional designation q (AU) a e 1992AE 1993 BW3 1984KB 1986DA 1989QF 1992 HE 1992 OM 1991 JX 19910A 1993MO 1993 VW 1993 QA 1992AA 1992 LC 1987 PA 1989 JA 1989 RSI 1991 VK 1993 VA 1995 YA3 1992TC 1994 PC 1994 PCl 1988 XB 1991 CS 1994ND 1993 UC 1994 LX 1977 QQ5 I990KA 1990MF 1992LR 1992TB 1993 HOI 1937 UB 1.240 1.010 0.522 1.174 0.676 0.959 1.298 1.011 1.036 1.267 0.873 LOll 1.208 0.744 1.185 0.913 1.195 0.909 0.825 1.095 1.108 1.071 0.905 0.761 0.938 1.047 0.819 0.825 1.189 1.246 0.950 1.082 0.721 1.159 0.618 2.202 2.146 2.216 2.817 1.151 2.241 2.194 2.517 2.508 1.626 1.695 1.476 1.981 2.522 2.717 1.771 2.305 1.842 1.356 2.198 1.566 1.568 1.346 1.468 1.123 2.166 2.436 1.262 2.226 2.198 1.746 1.830 1.342 1.987 1.644 0.437 0.529 0.764 0.583 0.413 0.572 0.409 0.598 0.587 0.221 0.485 0.315 0.390 0.705 0.564 0.484 0.481 0.507 0.391 0.502 0.292 0.317 0.328 0.482 0.165 0.517 0.664 0.346 0.466 0.433 0.456 0.409 0.462 0.417 0.624 H 6.4 21.6 4.8 4.3 3.9 37.4 8.2 2.3 5.5 22.6 8.7 12.6 8.3 17.8 16.4 15.2 7.2 5.4 7.3 4.7 7.1 9.5 33.5 3.1 37.1 27.2 26.0 36.9 25.2 7.6 1.9 2.0 28.3 5.9 6.1 15.4 15.1 15.3 15.1 17.9 13.8 15.9 19.2 18.5 16.5 16.5 18.3 16.7 15.4 18.4 17.0 18.7 16.7 17.3 14.4 18.0 17.2 16.8 18.6 17.4 17.9 15.3 15.3 15.4 16.6 18.7 17.9 17.3 16.6 18.0 Type S M D (Ian) 3 4 3 4 I 7 3 I I 2 2 I 2 3 I 2 I 2 I 5 I I 2 I 1 I 3 3 3 1 0.5 I I I I Pi (109 yr) Vc (km/s) 1.1 28.8 6.4 17.9 2.8 17.5 6.2 5.0 17.0 22.0 16.6 14.1 2.2 21.7 Category Arnor Arnor Apollo Arnor Apollo Apollo Arnor Arnor Arnor Arnor Apollo Arnor Arnor Apollo Arnor Apollo Arnor Apollo Apollo Arnor Arnor Arnor Apollo Apollo Apollo Arnor Apollo Apollo Arnor Arnor Apollo Arnor Apollo Arnor Apollo Notes aCollision probabilities are available only for objects discovered prior to mid-1991. These values are presented only for objects which can evolve into an Earth-intersecting orbit. bObject 4015 Wilson-Harrington is also catalogued as comet 107P. CObject Hermes received a permanent name upon discovery, but is currently lost. References I. IAU Minor Planet Center web page as of 1998 January 1. hnp:/Icfa.www.harvard.edu/cfa/ps/mpc.html 2. The Spaceguard Survey, Report of the NASA International Near-Earth Object Detection Workshop (1992) 3. T. Oehrels, editor, 1994, Hazards Due to Comets and Asteroids, (University of Arizona Press, Tucson) 13.2 13.2.1 COMETS Locations and Populations [6,7,2] The source region for long-period and high-inclination, short-period comets is the Oort cloud. Estimated distance: 103 to 105 AD. Estimated number of comets: 1011_1013. Estimated total mass: 1025 _1027 kg. The primary source for low-inclination, short-period comets is the Kuiper belt. Estimated distance: 30 to 1000 AU. Estimated number of comets: 108_10 12 . 322 / 13 SOLAR SYSTEM SMALL BODIES Estimated total mass: 1022 _1026 kg. Total number known as of 1998, January 1: 60. Short-period comets, defined as orbital period P < 200 yr. Total number known as of 1998, January 1: 193. Average number of apparitions per year: 17. Typical discovery rate per year for new comets: 6. Mean semimajor axis: a = 5.8 AU. Mean orbital eccentricity: e = 0.6. Mean inclination: i = 19 deg. Long-period comets. defined as orbital period P > 200 yr. Total number known as of 1998, January 1: 756. Typical discovery rate per year for new comets: 6. Estimated semimajor axes: 102-105 AU. Typical orbital eccentricity: e '" 1. Inclinations are isotropic. 13.2.2 Magnitudes [6] A comet's absolute magnitude, Ho. is defined as its integrated V magnitude if it were observed at a distance r = 1 AU from the Sun, ~ = 1 AU from the Earth. and zero phase angle. At other distances, a comet's integrated V magnitude can be estimated by v = Ho + 2.5n log r + 5 log ~. Typical range for n: 2 to 8. Average value: n '" 4. For a body with no coma, tail, or emission: n = 2. 13.2.3 Physical Properties [6-8] Nucleus: Diameter range: 1.0-40 km (Halley = 16 x 8 x 7 km). Mass range: 10 14_10 19 g (Halley = 10 17_10 18 g). Density range: 0.1-1.1 g cm-3 (Halley estimates: 0.2 to 1.1 g cm- 3). Estimated albedo range: 0.01-0.05 (Halley = 0.035). Typical rotation period: 12 h (Halley = 2.2 and 7.4 days). Typical dust production rate at 1 AU: 104-106 gls. Typical gas production rate at 1 AU: 1028 _1030 molecules/so Gas/dust expansion rate at 1 AU: 0.5 to 1.0 kmls. Typical dust/gas ratio (by mass): 1.0 to 2.0. Typical mass loss per apparition: 0.05 to 1.0 percent of total mass. Estimated composition of ices: H20 (80%), CO (3-7%), C02 (3%), CH30H (1-6%), plus CH3CN, (H2CO)n, HCN. Estimated composition of grains: Mg-rich silicates. refractory organics. 13.2 COMETS / 323 Coma: Typical radius: 104 _105 kIn. Typical composition: H20, CO, C02, OH, H2CO, CH30H, CH3CN, CN, C2, C3. Hydrogen cloud: TYpical radius: 107 kIn. "TYPical production rate at 1 AU: 1028 _1030 H atoms/so Ion Tail (TYpe I): Typical length: 106 _108 kIn. Direction: anti solar. Principal species: CO+, H20+, cot, OH+, H30+. Dust Tail (Type II): Typical length: 106 _107 kIn. Direction: Initially anti solar, becoming curved as dust particles follow independent orbits. Particle size range: 0.1 to 100 microns. Typical particle composition: silicates and refractory organics. 13.2.4 Comet Data Tables Table 13.3 lists short-period comets with more than one apparition, while Table 13.4 lists those with only one appearance. Table 13.5 gives selected long-period comets. Table 13.6 lists probable cometary nature objects. 1Bble 13.3. Shorr period comets having more than one blown apparition [1]. Comet Name 2P 107pa 26P 79P 96P 45P 73P 25D 5D 41P lOP 9P 46P 71P 88P lID lOOP 83P 37P 116P 103P 54P 81P 7P 6P 57P I04P 31P 76P Enclee Wilson-Harrington Grigg-Skjellerup du Toit-Hartley Macbho1z Honda-Mrkos-Pajdusakova Schwassmann-Wachmann 3 Neujmin2 Brorsen Tuttle-Giacobini-Kresak Tempe12 Tempel I Wntanen Clark Howell Tempel-Swift Hartley I Russell I Forbes WJ.ld4 Hartley 2 de Vico-Swift Wild 2 Pons-Wmnecke d'Arrest du Toit-Neujmin-Delporte Kowal 2 Schwassmann-Wachmann 2 West-Kohoutek-lkemura Perihelion Orbital Longitude Orbital Apehelion date period Perihelion Orbital Longitude (Year) (AU) (AU) (yrs) eccentricity of perihelion ofasc. node inclination 1994.1 1992.6 1992.6 1987.4 1991.6 1990.7 1990.4 1927.0 1879.2 1990.1 1994.2 1994.5 1991.7 1989.9 1993.2 1908.8 1991.4 1985.5 1993.2 1996.7 1991.7 1965.3 1991.0 1989.6 1989.1 1989.8 1991.8 1994.1 1994.0 3.28 4.29 5.10 5.21 5.24 5.30 5.35 5.43 5.46 5.46 5.48 5.50 5.50 5.51 5.58 5.68 6.02 6.10 6.13 6.16 6.26 6.31 6.37 6.38 6.39 6.39 6.39 6.39 6.41 0.33 1.00 1.00 1.20 0.13 0.54 0.94 1.34 0.59 1.07 1.48 1.49 1.08 1.56 1.41 1.15 1.82 1.61 1.45 1.99 0.95 1.62 1.58 1.26 1.29 1.72 1.50 2.07 1.58 0.850 0.623 0.664 MOl 0.958 0.822 0.694 0.567 0.810 0.656 0.522 0.520 0.652 0.501 0.552 0.638 0.451 0.517 0.568 0.408 0.719 0.524 0.541 0.634 0.625 0.502 0.564 0.399 0.543 186.3 90.9 359.3 251.6 14.5 325.8 198.8 193.7 14.9 61.6 194.9 178.9 356.2 209.0 234.8 113.4 178.8 0.4 310.5 170.8 174.9 325.4 41.6 172.3 177.1 115.3 189.5 358.2 360.0 334.7 271.1 213.3 309.3 94.5 89.3 69.9 328.7 103.0 141.6 118.2 69.0 82.3 59.7 57.7 291.8 38.9 230.8 334.5 22.1 226.8 25.1 136.2 93.4 139.5 189.1 247.8 126.2 84.2 11.9 2.8 21.1 2.9 60.1 4.2 11.4 10.6 29.4 9.2 12.0 10.6 11.7 9.5 4.4 5.4 25.7 22.7 7.2 3.7 9.3 3.6 3.2 22.3 19.4 2.8 15.8 3.8 30.5 4.09 4.29 4.93 4.81 5.91 5.54 5.18 4.84 5.61 5.14 4.73 4.73 5.15 4.68 4.88 5.22 4.80 5.06 5.25 4.73 5.84 5.21 5.30 5.62 5.59 5.17 5.38 4.82 5.33 324 / 13 SOLAR SYSTEM SMALL BODIES Table 13.3. (Continued.) Comet Name 105P 22P 43P 87P 114P 94P 67P 21P 3D 44P 112P 75P 62P 18P 51P 49P 60P 65P 1I0P 19P 16P 86P 15P 84P 48P 69P 77P 33P 17P 113P 98P 108P 100P 102P 30P 4P 89P 47P 61P 91P 52P 97P 70P 39P 78P 50P 83P 80P II1P 24P 14P 58P 36P 74P 115P 32P 59P 72P 93P 64P 42P 40P 68P 34P 85P 56P 53P Singer Brewster Kopff Wolf-Harrington Bus Wiseman-Skiff Russell 4 Churyumov-Gerasimenko Giacobini-Zinner Biela Reinmuth2 Urata-Niijima Kohoutek Tsuchinshan 1 Perrin~Mrkos Harrington Arend-Rigaux Tsuchlnshan 2 Gunn Hartley 3 Borrelly Brooks 2 Wild 3 Finlay Giclas Johnson Taylor Longmore Daniel Holmes Spitaler Takamizawa Ciffreo Schuster Shoemaker 1 Reinmuth 1 Faye Russell 2 Ashbrook-Jackson Shajn-Schaldach Russell 3 Harrington-Abell Metcalf-Brewington Kojima Oterma Gehrels 2 Arend Gehrels 3 Peters-Hartley Helin-Roman-Crockett Schaumasse Wolf Jackson-Neujmin Whipple Smimova-Chemykh Maury Comas Sola Keams-Kwee Denning-Fujikawa Lovas 1 Swift-Gehrels Neujmin 3 Vaisala 1 Klemola Gale Boethin Slaughter-Burnham Van Biesbroeck Perihelion Orbital Orbital Apehelion Longitude date period Perihelion Orbital Longitude (AU) (AU) (yrs) eccentricity of perihelion ofasc. node inclination (Year) 1992.8 1990.1 1991.3 1994.5 1993.4 1990.5 1989.5 1992.3 1852.7 1994.5 1993.5 1987.8 1991.7 1968.8 1994.6 1991.8 1992.4 1989.7 1994.4 1988.0 1994.7 1994.6 1988.4 1992.7 1990.9 1991.0 1988.8 1992.7 1993.3 1994.1 1991.6 1993.1 1992.7 1992.0 1988.4 1991.9 1994.8 1993.5 1993.9 1990.4 1991.5 1991.0 1994.1 1958.4 1989.8 1991.4 1993.6 1990.5 1996.8 1993.2 1992.7 1987.4 1995.0 1992.6 1994.2 1987.6 1990.9 1978.8 1989.8 1991.2 1993.9 1993.3 1987.6 1938.5 1986.0 1993.5 1991.3 6.43 6.46 6.51 6.52 6.53 6.57 6.59 6.61 6.62 6.64 6.64 6.65 6.65 6.72 6.78 6.82 6.82 6.84 6.84 6.86 6.89 6.91 6.95 6.96 6.97 6.97 7.00 7.06 7.09 7.10 7.22 7.23 7.26 7.26 7.29 7.34 7.38 7.49 7.49 7.50 7.59 7.76 7.85 7.88 7.94 7.99 8.11 8.13 8.16 8.22 8.25 8.42 8.53 8.57 8.74 8.78 8.96 9.01 9.09 9.21 10.6 10.8 10.9 11.0 11.2 11.6 12.4 2.03 1.59 1.61 2.18 1.51 2.22 1.30 1.03 0.86 1.89 1.46 1.78 1.50 1.27 1.57 1.44 1.78 2.47 2.46 1.36 1.84 2.30 1.09 1.85 2.31 1.95 2.41 1.65 2.18 2.13 1.59 1.71 1.54 1.99 1.87 1.59 2.28 2.32 2.35 2.52 1.77 1.59 2.40 3.39 2.35 1.85 3.43 1.63 3.49 1.20 2.43 1.44 3.09 3.57 2.03 1.83 2.22 0.78 1.68 1.36 2.00 1.78 1.77 1.18 1.11 2.54 2.40 0.414 0.543 0.539 0.375 0.568 0.366 0.630 0.706 0.756 0.464 0.588 0.498 0.576 0.643 0.561 0.600 0.504 0.314 0.317 0.624 0.491 0.366 0.699 0.493 0.366 0.466 0.341 0.552 0.410 0.422 0.575 0.543 0.590 0.470 0.503 0.578 Q.400 0.395 0.388 0.343 0.540 0.594 0.393 0.144 0.410 0.537 0.151 0.598 0.139 0.705 0.406 0.653 0.259 0.147 0.522 0.570 0.487 0.820 0.614 0.692 0.586 0.635 0.640 0.761 0.778 0.504 0.553 46.6 162.9 187.0 24.4 171.9 93.0 11.4 172.5 223.2 45.9 21.5 175.7 22.8 166.0 233.5 329.1 203.1 197.0 168.4 353.3 198.0 179.3 322.3 276.5 208.3 355.6 195.7 11.0 23.2 50.2 147.7 358.0 355.7 18.8 13.1 203.9 249.2 348.7 216.6 353.2 138.7 208.0 348.5 354.9 183.5 47.1 231.6 338.3 10.2 57.5 162.3 196.6 201.9 89.0 119.8 45.5 131.8 334.1 73.6 84.8 147.0 47.4 154.5 209.2 11.7 44.1 134.2 192.6 120.9 254.9 182.2 271.7 71.0 51.0 195.4 248.0 296.2 31.9 269.7 96.8 240.9 119.3 122.1 288.3 68.5 287.9 75.4 176.9 72.6 42.4 112.5 117.3 108.9 15.7 69.1 328.0 14.5 124.9 53.7 50.6 340.0 119.8 199.6 42.5 2.7 166.9 248.7 337.3 187.8 154.8 155.8 216.3 356.2 243.3 260.1 92.0 81.1 204.1 163.8 182.5 77.5 176.8 61.1 315.8 41.6 342.4 314.4 150.4 135.1 176.5 67.9 26.5 346.4 149.1 9.2 4.7 18.5 2.6 18.2 6.2 7.1 31.8 12.5 7.0 24.2 5.9 10.5 17.8 8.7 17.9 6.7 10.4 11.7 30.3 5.5 15.5 3.7 7.3 13.7 20.6 24.4 20.1 19.2 5.8 9.5 13.1 20.1 26.2 8.1 9.1 12.0 12.5 6.1 14.1 10.2 13.0 0.9 4.0 6.7 19.9 1.1 29.8 4.2 11.8 27.5 14.1 9.9 6.6 11.7 13.0 9.0 8.7 12.2 9.3 4.0 11.6 10.9 11.7 5.8 8.2 6.6 4.89 5.35 5.37 4.80 5.47 4.79 5.73 6.01 6.19 5.17 5.61 5.30 5.57 5.85 5.59 5.75 5.41 4.74 4.75 5.86 5.40 4.96 6.19 5.44 4.98 5.35 4.91 5.71 5.21 5.25 5.88 5.77 5.96 5.51 5.65 5.96 5.31 5.34 5.31 5.15 5.95 6.25 5.50 4.53 5.61 6.14 4.64 6.46 4.61 6.94 5.74 6.84 5.25 4.81 6.46 6.68 6.42 7.88 7.03 7.43 7.67 7.98 8.09 8.70 8.91 7.70 8.33 13.2 COMETS I 325 Table 13.3. (Continued.) Perihelion Orbital Orbital date period Perihelion Longimde LongibJde Apebelion Orbital (AU) (Year) (yn) (AU) eccentricity ofperibelion ofasc. node inclination Comet Name 92P 63P 8P IOIP 29P 66P 99P 90P 28P 27P 55P 38P 95pb 20D 13P 23P 121P IP 100P 35P Sanguin Wild I Thttle Cbemykh Schwassmann-Wachmann I du Toit Kowall Gehrels 1 Ncujmin 1 Crommelin Tempel-Thttle Stephan-Oterma Chiron Westphal Olbers Brorsen-Metcalf Pons-Brooks Halley Swift-Thttle Herscbel-Rigollet 1990.2 1973.5 1994.5 1992.1 1989.8 1974.2 1992.2 1987.6 1984.8 1984.1 1965.3 1980.9 1996.1 1913.9 1956.5 1989.7 1954.4 1986.1 1993.0 1939.6 12.5 13.3 13.5 14.0 14.9 15.0 15.0 15.1 18.2 27.4 32.9 37.7 50.7 61.9 69.6 70.5 70.9 76.0 135. 155. 1.81 1.98 1.00 2.36 5.77 1.29 4.67 2.99 1.55 0.74 0.98 1.57 8.45 1.25 U8 0.48 0.77 0.59 0.96 0.75 0.663 0.647 0.824 0.594 0.045 0.787 0.233 0.510 0.776 0.919 0.904 0.860 0.383 0.920 0.930 0.972 0.955 0.967 0.964 0.974 162.8 167.9 206.7 263.2 49.9 257.2 174.5 28.5 346.8 195.8 172.6 358.2 339.6 57.1 64.6 129.6 199.0 1l1.9 153.0 29.3 182.5 358.9 270.5 130.4 312.8 22.8 28.8 13.6 347.0 250.9 235.1 79.2 209.4 348.0 86.1 311.6 255.9 58.9 139.4 356.0 18.7 19.9 54.7 5.1 9.4 18.7 4.4 9.6 14.2 29.1 162.7 18.0 6.9 40.9 44.6 19.3 74.2 162.2 113.4 64.2 8.96 9.24 10.3 9.24 6.31 10.9 7.50 9.21 12.3 17.4 19.6 20.9 19.0 30.0 32.6 33.7 33.5 35.3 51.7 56.9 Notes aObject 107P, Wilson-Harrington is also catalogued as minor planet 4015. bObject 95P, Chiron is also catalogued as minor planet 2060. Reference 1. Marsden, B.G., & Williams, G.V. 1995, Catalogue of Cometary Orbits, 10th ed., IAU Central Bureau for Astronomical Telegrams and Minor Planet Center Table 13.4. Short-period comets hoving one known apparition [l]. Comet Name D/1766Gl D/1819 WI P/I994 PI D/1884 OJ D/1886 Kl P/I991 R2 DlI770Ll PIl991 Fl D/1783 WI D/1978 Rl P/I990R2 D/1978 C2 D/1952 Bl P/I991 C2 Helfenzrieder Blanpain Machho1z2 Barnard 1 Brooks 1 Spacewatch Lexell Mrkos Pigott Haneda-Campos DlI892Tl P/I990Rl D/1896R2 D/1918Wl P/I991 SI P/I991 V2 PIl986 WI D/1895 Ql PIl991 CI Dl1984 HI P/I994 Al P/I993 Xl D/1894Fl PIl992 G2 DlI977 CI PIl991 VI Holt~lmstead Tritton Harrington-Wilson Shoemaker-Levy 4 Barnard 3 Mueller 2 Giacobini Schorr McNaught-Hughes Shoemaker-Levy 7 Lovas 2 Swift Shoemaker-Levy 3 Kowal-Mriros Kushida Kushida-Muramatsu Denning Shoemaker-Levy 8 SldlJ-Kosai Shoemaker-Levy 6 Peribelion date (Year) Orbital period (yrs) 1766.3 1819.9 1994.7 1884.6 1886.4 1991.0 1770.6 1991.2 1783.9 1978.8 1990.8 1971.8 1951.8 1990.5 1892.9 1990.9 1896.8 1918.8 1991.4 1991.8 1986.7 1895.6 1990.9 1984.4 1994.0 1993.9 1894.1 1992.5 1976.6 1991.8 4.35 5.10 5.23 5.38 5.44 5.59 5.60 5.64 5.89 5.97 6.16 6.35 6.36 6.51 6.52 6.56 6.65 6.67 6.70 6.72 6.7S 7.20 7.25 7.32 7.36 7.40 7.42 7.47 7.54 7.57 Perihelion (AU) Orbital eccentricity 0.41 0.89 0.75 1.28 1.33 1.54 0.67 1.41 1.46 UO 2.04 1.44 1.66 2.02 1.43 2.08 1.46 1.88 2.12 1.63 1.46 1.30 2.81 1.95 1.37 2.75 U5 2.71 2.85 U3 0.848 0.699 0.750 0.583 0.571 0.511 0.786 0.555 0.552 0.665 0.392 0.580 0.515 0.421 0.590 0.406 0.588 0.469 0.404 0.542 0.592 0.652 0.250 0.483 0.639 0.277 0.698 0.291 0.259 0.706 LongibJde of perihelion 178.7 350.3 149.3 30U 176.9 87.1 225.0 18G.4 354.7 240.5 2.6 147.7 343.0 302.2 170.0 171.0 140.5 279.3 223.2 91.7 71.3 167.8 181.7 338.0 214.5 348.3 46.4 22.4 26.6 333.1 LongibJde ofasc. node 76.3 79.8 246.2 6.8 55.1 153.4 134.5 1.7 58.7 132.2 15.3 300.8 128.5 152.1 208.0 218.9 194.9 119.0 90.2 313.0 283.8 171.8 303.8 249.3 245.9 93.7 85.7 213.4 80.8 37.9 Orbital inclination 7.9 9.1 12.8 5.5 12.7 10.0 1.6 31.5 45.1 5.9 14.9 7.0 16.3 8.5 31.3 7.1 1l.4 5.6 7.3 10.3 1.5 3.0 5.0 3.0 4.2 2.4 5.5 6.1 3.2 16.9 Aphelion (AU) 4.92 5.03 5.27 4.86 4.86 4.76 5.63 4.92 5.06 5.48 4.68 5.42 5.20 4.95 5.55 4.93 5.62 5.21 4.99 5.49 5.69 6.16 4.68 5.59 6.20 4.85 6.46 4.93 4.84 6.58 326 / 13 SOLAR SYSTEM SMALL BODIES Table 13.4. (Continued.) Comet Name P/1989 E3 West-Hartley Shoemaker 2 Shoemaker-Holt 2 Helin-Roman-Alu 2 Mueller I Mueller 3 Shoemaker-Levy 5 Parker-Hartley Mueller 4 Shoemaker-Levy 2 Helin-Lawrence Helin-Roman-Alu 1 Shoemaker-Holt I Brewington Ge-Wang IRAS Mueller 5 Helin Shoemaker 4 van Houlen Bowell-Skiff Kowal-Vavrova Shoemaker 3 Shoemaker-Levy 1 Shoemaker-Levy 9 McNaught-Russell McNaught-Hartley Hartley-IRAS Levy Pons-Gambart Dubiago de Vico Bradfield 2 Vaisala 2 Bamard2 Mellish Bradfield I Wilk 0/1984 WI P/1989 E2 PI1989 Ul P/1987 U2 P/1990 SI P/I991 Tl P/1989 EI P/I992 G3 P/1990 UL3 P/I993 K2 P/1989 T2 P/1987 Ul P/1992 QI PI1988 VI P/1983 M1 P/I993 WI P/1987 G3 P/I99413 0/1960 SI P/1983 C1 P/198313 PI1986 Al P/I990 VI 0/1993 F2 PI1994 Xl P/I994N2 PI1983 VI P/1991 L3 0/1827 M1 0/1921 HI 0/1846 Dl 0/1989 A3 0/1942EA 0/1889 MI 0/1917FI 0/1984 Al 0/193701 Perihelion Orbital Orbital Longitude date period Perihelion Orbital Longitude (yrs) (AU) (Year) eccentricity of perihelion ofasc. node inclination 1988.8 1984.7 1988.6 1989.8 1987.9 1990.6 1991.9 1987.6 1992.1 1990.7 1993.5 1987.8 1988.4 1992.4 1988.4 1983.6 1994.7 1987.6 1994.8 1961.3 1983.2 1983.2 1986.0 1990.7 1994.2 1994.7 1994.9 1984.0 1991.5 1827.4 1921.3 1846.2 1988.9 1942.1 1889.5 1917.3 1984.0 1937.1 7.59 7.84 8.01 8.19 8.45 8.65 8.66 8.85 8.97 9.28 9.45 9.50 9.55 10.7 11.3 13.2 13.8 14.5 14.6 15.6 15.7 15.9 16.9 17.3 17.7 18.4 20.8 21.5 51.3 57.5 62.3 76.3 81.9 85.4 145. 145. 151. 187. 2.13 1.32 2.65 1.93 2.75 3.00 1.98 3.03 2.64 1.84 3.09 3.71 3.05 1.60 2.52 1.70 4.25 2.57 2.94 3.96 1.95 2.61 1.79 1.52 5.38 1.28 2.49 1.28 0.98 0.81 1.12 0.66 0.42 1.29 1.11 0.19 1.36 0.62 0.449 0.666 0.339 0.525 0.338 0.288 0.529 0.292 0.389 0.582 0.309 0.174 0.322 0.671 0.501 0.696 0.261 0.567 0.507 0.367 0.689 0.588 0.728 0.772 0.207 0.817 0.671 0.834 0.929 0.946 0.929 0.963 0.978 0.934 0.960 0.993 0.952 0.981 46.8 55.5 99.8 203.0 4.6 138.0 29.7 244.3 145.4 236.0 92.0 73.5 214.6 343.7 180.5 357.9 100.7 143.7 92.9 23.6 346.3 202.6 97.3 52.0 220.9 218.0 36.0 1.5 329.4 320.0 67.2 79.7 28.4 172.3 272.6 88.7 356.9 58.3 102.7 317.6 5.9 200.7 30.3 226.0 6.0 181.3 43.6 140.1 163.7 216.3 210.4 47.8 176.1 356.9 30.0 216.3 192.2 14.4 169.0 19.5 14.9 310.6 355.0 171.1 312.2 47.1 41.5 19.2 97.4 12.9 194.7 335.2 60.2 121.3 219.2 31.5 15.4 21.6 17.7 7.4 8.8 9.4 ll.8 5.2 29.8 4.6 9.9 9.8 4.4 18.1 11.7 46.2 16.5 4.7 24.8 6.7 3.8 4.3 6.4 24.3 5.8 29.1 17.6 95.7 19.2 136.5 22.3 85.1 83.1 38.0 31.2 32.7 51.8 26.0 Aphelion (AU) 5.59 6.57 5.36 6.19 5.55 5.43 6.45 5.53 6.00 6.99 5.85 5.27 5.95 8.12 7.58 9.45 7.24 9.30 8.99 8.54 10.6 10.1 11.4 ll.8 8.20 12.70 12.60 14.2 26.6 29.0 30.3 35.3 37.3 37.5 54.2 55.1 55.5 64.9 Reference 1. Marsden, B.G., & Williams, G.V. 1995, Catalogue of Cometary Orbits, 10th ed., IAU Central Bureau for Astronomical Telegrams and Minor Planet Center Table 13.5. Selected long-period comets [1, 2]. Comet Name Designation Discovery date (Year) Perihelion (AU) Orbital eccentricity Orbital inclination C/1843 Dl C/1858 Ll C/1882 RI C/1908 Rl C/1956 Rl C/1965 SI C/1969 Yl C/1973 El Great March Comet of 1843 Donati Great September Comet of 1882 Morehouse Arend-Roland Ikeya-Seki Bennett Kohoutek West Bowell lRAS-Araki-Alcock Levy 1843 I 1858 VI 1882ll 1908m 1957m 1965vm 1970ll 1973 xn 1976 VI 1982 I 1983 Vll 1987 XXX 1843 1858 1882 1908 1956 1965 1970 1973 1976 1980 1983 1988 0.005 0.58 0.008 0.95 0.32 0.008 0.54 0.14 0.20 3.36 0.99 1.17 1.000 0.996 1.000 1.001 1.000 1.000 0.996 1.000 1.000 1.057 0.990 0.998 144.3 117.0 142.0 140.2 119.9 141.9 90.0 14.3 43.1 1.7 73.3 62.8 CI1975 VI C/1980 El C/1983 HI C/1988 Fl 13.2 COMETS / 327 Table 13.5. (ContinuetL) Discovery date Comet Cl198811 C/1990 Kl ClI991 C3 C/I992J2 ClI995 01 ClI996B2 Name Designation Shoemaker-Holt 1988m 1990 XX 1990 XIX 1992 XIII Levy McNaught-Russell Bradfield Hale-Bopp Hyakutake (Year) Perihelion (AU) Orbital eccentricity Orbital inclination 1988 1990 1991 1992 1995 1996 1.17 0.94 4.78 0.59 0.91 0.23 0.998 1.000 1.002 1.000 0.996 1.0 62.8 131.6 113.4 158.6 89.4 124.9 References 1. Marsden. B.G .• & Williams. G.V. 1995. Catalogue of Cometary Orbits. 10th ed .• lAU Central Bureau for Astronomical Telegrams and Minor Planets 2. Beatty. 1.K.. & Chaikin. A.• editors. 1990. in The New Solar System (Sky Publishing. Cambridge). p. 292 Table 13.6. Outer solar system objects of probable cometary nature. a,b,c Provisional designation Perihelion (AU) Aphelion (AU) a e 1977 VB 1992 AD 1993 HA2 1994TA 19950W2 1995 GO 1997CU26 8.45 8.67 1l.8 11.7 18.9 6.84 13.1 18.8 31.8 37.4 22.0 31.0 29.3 18.4 13.648 20.226 24.594 16.843 24.916 18.069 15.712 0.381 0.571 0.519 0.304 0.243 0.622 0.169 6.9 24.7 15.7 5.4 4.2 17.6 23.4 6.5 7.0 9.6 11.5 9.0 9.0 6.0 180 150 75 25 100 100 300 Trans-Neptunian Objects 1992 QBI 1993FW 1993RO 1993 RP 1993 SB 1993 SC 1994 ES2 1994EV3 1994GV9 1994JQl 1994JRl 1994JS 1994N 1994TB 1994TG 1994TG2 1994TH 1994 VK8 19950A2 19950B2 1995DC2 1995 FB21 1995GA7 1995 GJ 1995 GY7 1995 HM5 1995 KII 1995 KKI 40.9 41.5 31.5 34.9 26.9 32.3 40.3 40.8 41.0 41.8 34.8 33.0 35.3 27.1 42.3 42.4 40.9 41.7 33.7 40.1 40.8 42.4 34.8 39.0 41.3 29.5 43.5 32.0 47.7 45.5 47.7 43.8 52.4 47.5 50.8 44.7 46.0 46.1 44.1 51.6 35.3 52.6 42.3 42.4 40.9 44.0 38.7 52.5 46.9 42.4 44.2 46.8 41.3 49.3 43.5 47.0 44.298 43.522 39.608 39.329 39.633 39.880 45.530 42.763 43.495 43.959 39.434 42.289 35.251 39.845 42.254 42.448 40.940 42.830 36.181 46.290 43.850 42.426 39.455 42.907 41.347 39.369 43.468 39.475 0.077 0.045 0.205 0.1l4 0.321 0.191 0.1l5 0.046 0.058 0.049 0.1l9 0.219 0 0.321 0 0 0 0.027 0.069 0.134 0.070 0 0.1l9 0.091 0 0.251 0 0.190 2.2 7.8 3.7 2.6 1.9 5.1 1.1 1.7 0.6 3.8 3.8 14.1 18.1 12.1 6.8 2.2 16.1 1.5 6.6 4.1 2.3 0.7 3.5 22.9 0.9 4.8 2.7 9.3 7.0 7.0 8.0 9.0 8.0 7.0 7.5 7.0 7.0 7.0 7.5 8.0 7.0 7.0 7.0 7.0 7.0 6.5 8.0 7.5 7.0 7.5 7.5 7.0 7.5 8.0 6.5 8.5 250 250 150 100 150 250 200 250 250 250 200 150 250 250 250 250 250 300 150 200 250 200 200 250 200 150 300 125 Number Centaurs 2060 5145 7066 Name Chiron Pholus Nessus H D (kIn) 328 I 13 SOLAR SYSTEM SMALL BODIES Table 13.6. (ContinuetL) Number Name Provisional designation Perihelion (AU) Aphelion (AU) a e 1995QY9 1995 QZ9 1995WY2 1995 YY3 1996KVl 1996 KWl 1996KXl 1996KYl 1996RQ20 1996RR20 1996 SZ4 1996TK66 1996TL66 1996T066 1996TP66 1996TQ66 1996TR66 1996TS66 1997CQ29 1997CR29 1997CS29 1997CT29 1997CU29 1997CV29 1997CW29 1997QH4 1997 QJ4 1997 RT5 1997RX9 1997RY6 1997 SZ10 1997TX8 29.2 33.7 40.6 30.7 41.2 46.6 35.7 35.7 39.2 32.8 29.6 42.9 35.1 38.1 26.4 34.6 33.2 38.5 41.2 42.0 43.4 42.3 41.9 40.0 36.3 41.3 34.8 42.2 42.1 41.4 31.6 32.0 51.0 45.8 52.3 48.1 44.7 46.6 43.4 43.3 49.4 47.1 50.1 43.2 134.0 49.3 53.0 44.7 52.1 49.7 47.7 42.0 44.0 44.9 44.8 48.5 42.5 47.4 44.3 42.2 42.1 41.4 47.6 46.6 40.115 39.769 46.432 39.389 42.966 46.602 39.543 39.517 44.291 39.936 39.817 43.035 84.457 43.700 39.703 39.667 42.636 44.100 44.412 41.996 43.703 43.580 43.331 44.227 39.375 44.359 39.568 42.239 42.135 41.360 39.584 39.312 0.271 0.153 0.126 0.221 0.041 0 0.097 0.096 0.115 0.180 0.257 0.004 0.585 0.128 0.335 0.127 0.222 0.126 0.073 0 0.006 0.030 0.034 0.096 0.079 0.070 0.121 0 0 0 0.201 0.186 D H 4.8 19.5 1.7 0.4 8.4 5.5 1.5 30.9 31.6 5.3 4.7 3.3 24.0 27.3 5.7 14.6 12.3 7.4 2.9 20.2 2.3 1.0 1.5 7.8 19.0 12.8 16.0 12.6 29.8 12.4 12.7 9.0 7.5 7.5 7.0 8.5 7.0 7.0 8.5 8.0 7.0 7.0 8.0 7.0 5.0 4.5 6.5 6.5 7.5 6.0 6.5 6.5 5.0 5.0 6.5 7.0 6.5 7.0 7.5 7.0 8.0 7.5 8.5 8.5 (kIn) 200 200 250 125 250 250 125 150 250 250 150 250 600 750 300 300 200 400 300 300 600 600 300 250 300 250 200 250 150 200 125 125 Notes alAU Minor Planet Center web page as of 1998, January 1. URL http://cfa.www.harvard.edU/cfaJpsfmpc.html. bPor explanation of symbols, see section on Minor Planets. CObject 2060 Chiron is known to exhibit cometary activity, e.g., IAUC 4770 and is catalogued as comet 95P. 13.3 ZODIACAL LIGHT The zodiacal light is due to sunlight scattered by the interplanetary dust cloud. Zodiacal light brightness is a function of viewing direction, wavelength, heliocentric distance (r) and position of the observer relative to the dust symmetry plane. The brightness does not vary with the solar cycle [9,10]. A comprehensive review is given in [11]. Table 13.7 presents the surface brightness (radiance) and degree of linear polarization of the zodiacal light at ),,5000 A for an observer at r = 1 AU in the dust symmetry plane as a function of helioecliptic longitude ()., - ).,0) and latitude (fJ) [11-15]. 13.3 ZODIACAL LIGHT Table 13.7. Zodiacal light brightness and polarization. IW) 15 20 25 30 45 60 75 0 2450 .08 1260 .10 770 .11 500 .12 215 .16 117 .19 78 .20 5 2300 .09 1200 .10 740 .11 490 .12 212 .16 117 .19 78 .20 3700 .11 1930 .11 1070 .12 675 .13 460 .14 206 .17 116 .19 78 .20 ).. - )..0(°) 0 5 10 15 10 .13 5300 .13 2690 .13 1450 .13 870 .13 590 .14 410 .15 196 .17 114 .19 78 .20 20 5000 .14 3500 .14 1880 .14 1100 .15 710 .15 495 .15 355 .15 185 .17 110 .19 77 .20 25 3000 .15 2210 .15 1350 .16 860 .16 585 .16 425 .16 320 .16 174 .18 106 .19 76 .20 30 1940 .16 1460 .16 955 .16 660 .16 480 .16 365 .17 285 .17 162 .18 102 .19 74 .20 35 1290 .17 990 710 .17 530 .17 400 .17 .17 310 .17 250 .17 151 .18 98 .20 73 .20 925 .17 735 .17 545 .17 415 .17 325 .18 264 .18 220 .18 140 .19 94 .20 .20 45 710 .18 570 .18 435 .18 345 .18 278 .18 228 .18 195 .18 130 .19 91 .20 70 .20 60 395 .19 345 .19 275 .19 228 .19 190 .19 163 .20 143 .20 105 .20 81 .20 67 .20 75 264 .18 248 .18 210 .18 177 .18 153 .18 134 .19 118 .19 91 .19 73 .19 64 .19 90 202 .16 196 .16 176 .16 151 .16 130 .16 115 .16 103 .17 81 .18 67 .18 62 .19 105 166 .12 164 .12 154 .12 133 .12 117 .13 104 .13 93 .14 75 .15 64 .17 60 .19 120 147 .08 145 .08 138 .09 120 .09 108 .09 98 .10 88 .11 70 .13 60 .15 58 .18 135 140 .05 139 .05 130 .05 115 .06 105 .06 95 .07 86 .08 70 .11 60 .14 57 .17 150 140 .02 139 .02 129 .02 116 .03 107 .03 99 .04 91 .05 75 .08 62 .12 56 .16 165 153 -.02 150 -.02 140 -.01 129 -.01 118 0 110 .02 102 .03 81 .07 64 .11 56 .16 180 180 0 166 -.02 152 -.03 139 -.02 127 -.01 116 0 105 .02 82 .06 65 .11 56 .16 40 9000 72 I 329 330 I 13 SOLAR SYSTEM SMALL BODIES The brightness is given in SIO (V), the equivalent number of tenth visual magnitude solar-type stars per square degree. One SIO (V) = 1.26 x 10-8 W m- 2 sr- 1 Jl,m- 1 at 5000 A. The uncertainty in brightness and polarization is 10% in the bright regions, to 20% in the faint regions. Negative values mean that the direction of polarization lies in the scattering plane. The brightness at the ecliptic pole ({3 = 90°) is 60 SIO (V) and the degree of linear polarization is 0.19 [11, 12]. The component of the solar corona due to scattering by interplanetary dust is known as the F corona. The brightness of the solar F corona in SIO (V) is given in Table 13.8 as a function of elongation (E) [16, 17], for the line of sight in the ecliptic plane (i = 0°) and line of sight in a plane perpendicular to the ecliptic plane (i = 90°). Table 13.8. Brightness a/the solar F corona. 5 3.9 x 106 8.6 x loS 1.2 x loS 10 2.4 x 104 2.6 x 106 4.3 x loS 4.8 x 104 8300 UBV colors of the zodiacal light are given by [15] Iv IB = 1.14 - 4 5.5 x 10- E, 18 - lu = 1.11-5.0 x 10 -4 E, where E ~ solar elongation in degrees. An intensity ratio of 1.0 corresponds to solar color. The dependence of intensity on heliocentric distance for an observer at r AU (0.3 ::: r ::: 1.0) as measured from the Helios probe is [15] I(r) _ -2.3 1(1 AU) - r . The dependence of polarization on heliocentric distance [15] can be approximated by P(r) P(1 AU) = r+O.3. For 1 < r < 3.3 AU, the I (r) is given by I(r) -2.5±O.5 1(1 AU) = r , as measured from Pioneer 10 [18]. The plane of symmetry of the zodiacal light deviates from the ecliptic by a few degrees, causing annual variations of 10%-20% (peak to peak) in the zodiacal light brightness as viewed from Earth. The symmetry plane differs in the inner and outer solar system; at r > 1 AU it is close to the invariant plane where i for r < 1 AU, i = 3°.0 ± 0°.3, g = 87° ± 4°, [19], for r 2: 1 AU, i = 1°.5 ± 0°.4, g = 96° ± 15°, [9], = inclination to the ecliptic and g = ecliptic longitude of the ascending node. 13.4 INFRARED ZODIACAL EMISSION I 331 - I 0-' 10-' 10- 10 10- 10 ~ L 0 ~ ~ E " , N E 0 ~ .-< lL 10-11 10-11 ),~20.9I'm 30 60 90 1 0 1 0 1 0 SOLAR ELONGATION Figure 13.1. Zodiacal emission (radiance) as a function of solar elongation in the ecliptic plane [20]. 0: 1O.9/.LID; 6: 20.9/.LID. 13.4 INFRARED ZODIACAL EMISSION At A ~ 3 J.Lm, thennal emission from the interplanetary dust (zodiacal emission, or ZE) dominates over scattered light. The zodiacal emission at 1 AU has been measured from rockets [20], from the Infrared Astronomical Satellite (IRAS) [21,22], and from the Diffuse Infrared Background Experiment (DIRBE) on the Cosmic Background Explorer (COBE) satellite [23). The observed variation in the 10.9 J.Lm and 20.9 J.Lm radiance along the ecliptic plane is presented in Figure 13.1 [20). Absolute calibration accuracy is approximately 20%. Model fits for assumed radial dust distribution <X r-1. 3 and r-l. O are shown by the dashed and solid lines. Figure 13.2 shows the variation of zodiacal emission with ecliptic latitude at or near E = 90° (Le., in a plane perpendicular to the Earth-Sun line) as determined from survey observations of the IRAS satellite between February and November 1983 [21,24]. Only the smooth component of the ZE is shown, represented by the following slowly-varying empirical function [25]. To remove zodiacal dust bands [22], point sources, and the diffuse emission of the Galaxy, the function was fitted in a lower envelope sense to IRAS scans that extended nearly from one ecliptic pole to the other: 1 (fJ) = 10 - c5J (l - 8fJ I cosec(fJ) I [1 - exp( - fJ 18fJ - (fJ I 8fJ)2 13)]), where 1 (fJ) = brightness at ecliptic latitude fJ, fJ = geocentric ecliptic latitude, 10 = peak brightness, 81 = parameter with units of brightness, and 8fJ = angle parameter characterizing the width of the brightness distribution. The parameter values shown in Table 13.9 represent an annual average of the ZE at E = 90°. The position of peak emission deviates sinusoidally from the ecliptic plane by about two degrees on 332 I 13 SOLAR SYSTEM SMALL BODIES 80 ,, ,, ... , 60 ' .... ., <Il ~ ,~ 40 ., , ,, .s~ ---I 251l1l\ -------- 20 -........ .............. _- .......... -..... _--._-_ ... . o ~~ __ ~ o __- L__ ~ __ ~ __ ~~ __ ~ __ ~ 90 60 30 Ecliptic latitude I ~ I (degrees) Figure 13.2. Intensity of the smooth component of the zodiacal emission as a function of the ecliptic latitude at solar elongation 90 0: annual average from IRAS data [25]. a yearly cycle owing to the Earth's orbital motion in a plane inclined with respect to the approximate symmetry plane of the interplanetary dust; the peak brightness of the ZE near the ecliptic plane, la, and the ecliptic pole brightness, given by 10 - 81 (1- 8{J), similarly vary modestly on an annual cycle [25]. 1Bble 13.9. Empirical function parameters for the ZE at E = 90°. Wavelength Fitted parameter 12ILm 2SlLm 60ILm 10 (MJy sr- I ) 81 (MJysr- l ) 8fJ (degrees) 37 34 15.6 77 70 14.0 31 29 12.0 At 12 and 25 /Lm the diffuse infrared emission of the sky is dominated by zodiacal emission; at 60 /Lm, the ZE becomes less prominent, and by 100 /Lm emission from the galactic plane dominates the appearance of the sky, and the ZE is too weak compared with emission from the Galaxy to permit reliable separation by this method. A linear transfonnation converts the IRAS values in Table 13.9 and Figure 13.2 to the somewhat different DIRBE calibration to an nns accuracy of several percent [26]. (Unlike IRAS, DIRBE has an instrumentally established zero point, an ability to measure electrical and radiative offsets, and superior stray light rejection.) The transformation is given as (DIRBE value) = Gain x (IRAS value) + Offset, where, at 12, 25, and 60 /Lm, respectively, Gain = 1.06, 1.01, and 0.87, and Offset and 0.13 MJy sr- 1• = -0.48, -1.32, 13.5 METEOROIDS AND INTERPLANETARY DUST / 333 13.5 METEOROIDS AND INTERPLANETARY DUST This section deals with the characteristics of meteoroids and interplanetary dust as determined from studies of their ablation or collection in the Earth's atmosphere, and from detections of impacts on spacecraft. The remote sensing of the space dust population through observations of the zodiacal light, or infrared studies such as from IRAS, COBE, ISO, etc., are covered in the preceding section. Solid particles in space smaller than about 10 m in size are termed meteoroids, larger bodies being asteroids. Meteoroids produce meteors (synonym shooting star) when they enter the atmosphere. The term "meteor" encompasses the atmospheric phenomena resulting (optical emission, train of ionization, etc.). Dependent upon composition, entry angle, speed, and density, particles smaller than about 100 JLm in size do not ablate, but remain intact and gradually settle to the Earth's surface. These particles are termed interplanetary dust. Such a size limit is also convenient because the majority of the zodiacal light is the result of scattering by particles in the 10-100 JLm range. The absolute visual magnitude of a meteor (M) is the observed magnitude corrected to a standard height of 100 kIn at the observer's zenith. Meteor activity (i.e., detection rate) is normally expressed in terms of the zenithal hourly rate. Sporadic (nonshower) activity is of the order of 5-10 per hour to M = 6.5, although there is a seasonal variation which depends upon the solar longitude and the observer's latitude. Meteor shower activity may be detectable at rates as low as a few per hour, although most well-known showers have zenithal rates of order 20-50 per hour. The prominent meteor showers, occurring when the Earth passes through a meteoroid stream, are listed in Tables 13.10 and 13.11. Every so often an exceptional shower will occur, with rates up to many thousands per hour being seen. At the time of writing the next such events, termed meteor storms, are anticipated in 1998 and/or 1999 November when the Leonid storm is due. For a more extensive discussion of all of the above, see [27]. Table 13.10. Principal meteor showers. a Radiant Diurnal drift Shower nameb Activity period Solar long.C RA Dec RA Dec Local time of transit Vgd re Peak ZHR Number density! Quadrantids Lyridsg ~ Aquarids Arietids h ~ Perseids h P Tauridsh a Capricomids S ~ Aquarids Perseids i K Cygnids S Taurids N Taurids Orionids Draconids j Leonidsk Geminids Ursidsl JanOI-{)5 Apr 16-25 Apr 19-May 28 May 29-Jun 19 JunOI-17 Jun 07-Jul 07 Jul03-Aug 19 Jul15-Aug 28 Ju117-Aug24 Aug 03-31 Sep 15-Nov 25 Sep 15-Nov 25 Oct02-Nov07 Oct 06-10 Nov 14-21 Dec 07-17 Dec 17-26 283.3 32.1 43.1 230 271 336 +49 +34 -02 +23 +23 +19 -10 -16 +58 +59 +14 +23 +16 +54 +22 +33 +75 +0.4 +1.1 +0.9 +0.7 +1.1 +0.8 +0.9 +0.7 +1.3 +0.3 +0.8 +0.9 +0.7 +0.4 +0.7 +1.0 0 -0.2 0.0 +0.4 +0.6 +0.4 +0.4 +0.3 +0.2 +0.1 +0.1 +0.2 +0.2 +0.1 0 -0.4 -0.1 0 08.5 04.0 07.6 09.9 11.0 11.2 00.0 02.2 05.7 21.3 00.5 00.5 04.3 16.1 06.4 01.9 08.4 39 48 65 35 25 28 20 39 58 22 25 27 65 17 70 33 31 2.2 2.9 2.7 120 20 50 80 8-10 4-5 2.5 3.2 2.6 3.0 2.3 2.3 2.9 2.6 2.5 2.6 3.0 10 20 100 5 10 8 25 150 20-25 10-20 125 50 30 2 25 110 20 1-2 290 80 77 77 97 127 126 139.9 146 221 231 208 197.0 235.2 262.0 270.9 44 62 86 307 339 46 286 50 60 95 262 152 112 217 Notes aCourtesy I. Rendtel, M. Gyssens, P. Roggemans, and P. Brown, International Meteor Organization. All angles are in der.ees, and referred to the 1950.0 equinox. See Table 13.11 for parent comet identifications. cThe solar longitude is that at the time of peak shower activity. d Vg is the geocentric velocity of the meteoroid; the velocity at the top of the atmosphere after acceleration by the Earth is given by V 2 = Vi + 125 (in kmIs). eThe mass index s is related to the population index r by s = 1+ 2.3 log 10 r (see [1] for details). f The number density gives the number of particles of m > 10- 3 g per 109 lan3 [2]. 334 I 13 SOLAR SYSTEM SMALL BODIES gZHR to 90. hDaytime showers. i ZHR > 200 in 1992-94 near parent comet return. j Also known as the Giacobinids; periodic shower with ZHR > 200 occurring near alternate parent comet returns. kMeteor storms anticipated in 1998 and 1999 near parent comet return with ZHR > 1000. 'ZHR to 50. References 1. Hughes. D.W. 1978. in Cosmic Dust. edited by J.A.M. McDonnell (W"lley. New York). p. 123 2. Hughes. D.W. 1987. A&A. 187.879 Table 13.11. Orbits o/meteoroid streams [1]. ne (AU) e" qC (AU) of1 Shower name (0) (D) (0) Quadrantids Lyrids 3.08 28 13 1.6 1.6 2.2 2.53 2.86 28 3.09 1.93 2.59 15 3.51 11.5 1.36 5.70 0.683 0.968 0.958 0.94 0.79 0.85 0.77 0.976 0.965 0.68 0.806 0.861 0.962 0.717 0.915 0.896 0.85 0.977 0.919 0.560 0.09 0.34 0.34 0.59 0.069 0.953 0.99 0.375 0.359 0.571 0.996 0.985 0.142 0.939 170 214 95 29 59 283.3 32.1 43.1 77 77 277 127 306 139.9 146 41 231 28 197.0 235.2 262.0 270.9 72.5 79 163.5 21 0 6 7 27.2 113.8 38 5.2 2.4 163.9 30.7 162.6 23.6 53.6 aa " Aquarids Arietids ~ Perseids fJ Taurids a Capricomids S 8 Aquarids Perseids K Cygnids S Taurids NTaurids Orionids Draconids Leonids Geminids Ursids 246 269 153 152 194 113 292 83 172 173 324 206 if Parent objects 96PlMachholz 1 & 149111 ClI'hatcher (1861 G 1) IPlHalley 96PlMachholz 1 & 149111 2PlEncke & various asteroids 96PlMachholz 1 & 149111 I09P/Swift-Thttle 2PlEncke & various asteroids IPlHalley 21P/Giacobini-Zinner 55Plrempel-Thttle (3200) Phaethon 8PIThttle Notes aa is the semimajor axis. be is the orbital eccentricity. Cq is the perihelion distance. q a(l - e). d (i) is the argument of perihelion. is the longitude of the ascending node (equinox 1950.0). f i is the inclination to the ecliptic. = en Reference 1. Cook. A.F. 1973. in Evolutionary and Physical Properties 0/ Meteoroids. NASA SP-319. edited by C.L. Hemenway and A.F. Cook (NASA. Washington. DC) The above discussion pertains to visual meteors. mostly produced by meteoroids larger than '" 1 cm in size. Fainter meteors may be detected through HFNHF radio wave scattering from their trains of ionization [27,28]. Such meteors are due to smaller meteoroids, typically 100 #LIn-I mm in size. The limiting magnitude is about +15 (corresponding to the micrometeor limit at '" 100 #Lm); radars sensitive to such magnitudes may detect meteors at rates of one per few seconds, and especially powerful radars covering large areas at rates exceeding one per second [29]. It was thought for some years (see [27]) that the deficit of meteors detected in the radar regime (masses 10-6-10-2 g) was due to the reduced ionizing efficiency of low-speed meteoroids (that efficiency varies as '" V 3.5- 4.O, V being the top-of-the-atmosphere velocity), but it is now known that the finite "echo ceiling" [28] of HFNHF radars has led to only those ablating lower than...., 105 km being detected, meaning that the majority ablating higher have been missed, but are detectable using MF radars [29,30]. 13.5 METEOROIDS AND INTERPLANETARY DUST / 335 The magnitude of a meteor is given in [27,28]: M = 40 - 2.5 log 10 (xz, where {xz is the zenithal electron line density (per meter) in the train. There have been many determinations of the relationship between (xz, V, and the initial meteoroid mass m [27,31], both from theory and from observations. The form of the expression is generally given as where the normalizing constant Cl has values typically in the range 2-8 x 10- 10 , x = 0.9-1.1, and y = 3.2-4.0. Dependent upon the velocity, one finds [27]: where C2 = 16-17. This implies that a meteor of zenithal magnitude zero (M = 0) has a mass of ,....,O.I-lg. The above assumed that the mean sporadic meteoroid speed is ,...., 30-40 kmls; in fact the initial analysis of the Harvard Radar Meteor Project results [32] implied that the mean speed, at least for faint radar meteors, is < 20 kmls, but apparently an error was made such that the real mean speed is somewhat higher than 20krn s-I[33]. Particles arriving from heliocentric elliptical orbits may impact the Earth at speeds between 11 and 73 kmls. The composition of meteoroids and dust is still a matter of uncertainty. Spectroscopic observations of meteors indicate highly differentiated material similar to various meteorite classes, whilst dust collection in the stratosphere also indicates compositions similar to meteorite classes although volatile components may have been lost through heating in atmospheric entry; hypervelocity spacecraft impacts are unlikely to leave traces of any but the most refractory components. A variety of recent papers on these topics, and other features of meteoroids and interplanetary dust, may be found in [34-39]. The present state of knowledge indicates that the particles under consideration are largely comprised of meteoritic-type materials (silicates, nickel-iron) but with a significant fraction of heavy organics (kerogens) that are thermodynamically stable over periods of""" 104 yr after release from their parent bodies, but which are destroyed on atmospheric entry. The origin of at least some meteoroids is indicated by the association of various meteor showers with specific comets through orbit similarity [40]. The orbits of meteoroids determined in various surveys are reviewed and cataloged in [41], where evidence linking showers with various Earthcrossing asteroids (see Table 13 .11) is also discussed. Larger meteoroids in the 5-10 m size range may also be cometary fragments [42]. While many meteoroids appear to be of low density (p < 1 glcm3 ), there is also a high-density component with p = 3-8 glcm3 [43], [44]. The evolution of meteoroid streams is reviewed in [45]. The origin of sporadic meteors appears to be gravitational stirring of streams, in particular by Jupiter; small meteoroids and dust are also subject to orbital circularlzationlinspiralling toward the Sun under the influence of the Poynting-Robertson drag force, with various other effects also being significant. Meteoroids tend to end their lives through impacts upon smaller dust particles, their comminution maintaining the interplanetary dust supply (although it is not clear whether the present complex is in balance [46]), which in tum is depleted through collisions, in spiralling, and eventual ejection from the solar system by radiationlsolar wind pressure. The terrestrial mass accretion rate of small meteoroids and dust has been established from impact data collected with the Long Duration Exposure Facility [47] and other satellites [48], the small particle influx being 40 ± 20 x 106 kg per year (see Figure 13.3), in accord with the influx determined by radar 336 I 13 SOLAR SYSTEM SMALL BODIES FIgure 13.3. The logarithmic incremental mass influx to the Earth, in units of loti kg per year per logarithmic mass interval. For these small particles (meteoroids and dust) the peak influx is at "" 10-5 g, and the integral under this curve is "" 40, 000 tonneslyear [47], although larger particles (asteroids and comets) dominate the long-term averaged mass influx [50]. From [47], Figure 4. meteor techniques [29]. The small particle influx can also be measured from ice cores [49]. The influx over the whole mass spectrum (from dust through to large asteroids and comets) is reviewed in [50]. Whilst the interplanetary complex of meteoroids and dust is significant in a number of ways (such as its effect upon atmospheric chemistry and the light it scatters producing a diffuse background), its total mass is only equivalent to an asteroid or comet a few tens of kilometers in diameter. REFERENCES 1. Through Minor Planet Circular 31044. 1997. December 14 2. Marsden. B.G.. & Williams. G.V.. and http://cfa.www.harvard.edu/cfalpslmpc.html 3. The Spaceguard Survey. 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Livingston 14.1 Basic Data . . . . . . . . . . . . . . . . . . . . . . . . . 340 14.2 Interior Model . . . . . . . . . . . . . . . . . . . . . .. 341 14.3 Solar Oscillations .. . . . . . . . . . . . . . . . . . .. 342 14.4 Photospheric-Chromospheric Model . . . . . . . . .. 348 14.5 Spectral Lines . . . . . . . . . . . . . . . . . . . . . .. 351 14.6 Spectral Distribution . . . . . . . . . . . . . . . . . . . 353 14.7 Limb Darkening . . . . . . . . . . . . . . . . . . . . .. 355 14.8 Corona. . . . . . . . . . . . . . . . . . . . . . . . . . .. 357 14.9 Solar Rotation . . . . . . . . . . . . . . . . . . . . . .. 362 14.10 Granulation......................... 364 14.11 Surface Magnetism and its Tracers. . . . . . . . . .. 364 14.12 Sunspots........................... 367 14.13 Sunspot Statistics ..... . . . . . . . . . . . . . . .. 370 14.14 Flares and Coronal Mass Ejections. . . . . . . . . .. 373 14.15 Solar Radio Emission. . . . . . . . . . . . . . . . . .. 375 339 340 I 14.1 14.1.1 14 SUN BASIC DATA Global Solar radius Volume Surface area Solar mass Mean density Gravity at surface Moment of inertia Angular rotation velocity at equator Angular momentum (based on surface rotation) Work required to dissipate solar matter to infinity Sun's total internal radiant energy Escape velocity at solar surface 14.1.2 R0 = 6.95508 ± 0.000 26 x 1010 cm [1] V0 = 1.4122 x 1033 cm3 6.087 x 1022 cm 2 M0 = 1.989 x 1033 g P0 = 1.409 g cm- 3 2.740 x 104 cms- 2 5.7 x 1053 gcm2 2.85 x 10-6 rad s-1 1.63 x 1048 gcm2 s- 1 6.6 x 1048 erg 2.8 x 1047 erg 6.177 x 107 cms- 1 Viewed from Earth Mean equatorial horizontal parallax [2] Mean distance from Earth (A = AU = astronomical unit) Distance at Perihelion Aphelion Semidiameter of Sun At mean Earth distance Oblateness: Semidiameter equator-pole difference [3,4] Solid angle of Sun, mean distance Surface area of sphere of unit radius In heliographic coordinates At mean distance A 14.1.3 8~'79418 = 4.263 54 x 10-5 rad 1 AU = 1.495 979 x 1013 cm 1.4710 x 1013 cm 1.5210 x 1013 cm 959~'63 0.004 652 4 rad 0~'0086 6.8000 x 10-5 sr AI R0 = 214.94 (AI R0)2 = 46200 (AI R0)1/2 = 14.661 47l' A2 = 2.8123 x 1027 cm2 1°= 12147km l' of arc = 4.352 x 104 km I" of arc = 725.3 km Total Solar Radiation Solar constant S (total solar irradiance) = flux of total radiation received outside the Earth's atmosphere per unit area at the mean Sun-Earth distance [5-9]: Radiation from whole Sun Radiation per unit mass S = 1.365-1.369 Wm- 2 = 1.365-1.369 x 106 ergcm- 2 s-1, L0 = 3.845 x 1026 W = 3.845 x 1033 erg s-1. L01 M0 = 1.933 X 10- 4 W kg- 1 = 1.933 erg s-1 g-1 . 14.2 INTERIOR MODEL I 341 Radiation emittance at Sun's surface Mean radiation intensity of Sun's disk F = FIn = 2.009 x = 2.009 x 107 Wm- 2 sr-l. 10 10 ergcm- 2 s-l. 14.1.4 SUD as a Star Magnitudes of the Sun in three wavelength bands and the bolometric magnitude are given in Table 14.1 [10-13]. Table 14.1. Solar magnitudes. Visual (mv) Blue Ultraviolet Bolometric Apparent Modulus Absolute = -26.75 = -26.10 = -25.91 mbol = -26.83 31.57 MV = +4.82 MB = +5.47 Mu = +5.66 mbal = +4.74 V B U Color indices [10-14]: B U U V - V B V R = +0.650, = +0.195, = +0.845, = +0.54, V - 1= +0.88, V - K = +1.49. Bolometric correction Spectral type Effective temperature Velocity relative to near stars Solar apex Age of Sun [15, 16] Mean magnetic field [17] Average Peak BC = -0.08. G2V. 5777 K. 19.7 kms- 1 A = 271°, D L n = 57°, Bn (4.5-4.7) x 109 yr. = 30°(1900), = 22°. OG, ±1 G. 14.2 INTERIOR MODEL by Pierre Demarque and David Guenther The tabulated data in Table 14.2 are for a standard model of the Sun (no rotation, no diffusion), from Table 3B in [18]. This model was constructed using opacities from [19] and the solar mixture from [20]. Other similar recent models can be found in [21] and [22]. 342 / 14 SUN Central values Temperature Density Pressure Central hydrogen content by mass = 15.7 x 106 K. Pc = 151 gcm- 3 . Pc = 2.33 X 10 17 dyn cm- 2 . Xc = 0.355. Tc Surface composition parameters X Z = 0.6937, = 0.0188. The fraction of the radius at the base of the surface convection (SCZ or surface convection zone) can be determined by helioseismology [23, 24], which is within 1% of model [18]: rsczl Ro = 0.71. Table 14.2. Model of solar interior. Mr (Mo) Lr (ergs-I) Lr (LO) P (dynem- 2) logP (dynem- 2) 150 146 95.73 0.00003 0.001 0.057 1.01 x 1030 3.97x 1031 1.39 x 1033 0.0002 0.010 0.361 2.33 x 10 17 2.27x 1017 1.50x 1017 17.369 17.355 17.177 8.77 6.42 4.89 28.72 9.77 3.22 0.399 0.656 0.817 3.72xI033 3.85x 1033 3.85x1033 0.966 1.000 1.000 3.35x 1016 5.29x 1015 2.lOx10 15 16.525 15.724 15.324 3.62xlO lO 4.18xlO lO 4.94 x 1010 3.77 3.15 2.23 1.05 0.500 0.177 0.908 0.945 0.977 3.85xl033 3.85x 1033 3.85x 1033 1.000 1.000 1.000 5.28x 1014 2.lOx 1014 5.26x10 13 14.722 14.322 13.721 0.81 0.91 0.96 5.64xlOlO 6.33 x 1010 6.68xlO lO 1.29 0.514 0.208 0.0766 0.0194 4.85xl0- 3 0.992 0.999 0.9999 3.85x 1033 3.85x 1033 3.85x 1033 1.000 1.000 1.000 1.32 x 1013 1.32 x 10 12 1.31 x 1011 13.119 12.119 lLl18 0.99 0.995 0.999 6.89xlO lO 6.93x 1010 6.95 x 1010 0.00441 0.00266 0.00135 2.56xlO-4 4.83xlO- 5 1.29 x 10-6 1.0000 1.0000 1.0000 3.85x 1033 3.85x 1033 3.85x1033 1.000 1.000 1.000 1.31 x 109 1.31 x 108 1.31 x 106 9.118 8.118 6.118 1.000 6.96xlO lO 0.00060 2.18xlO- 7 1.0000 3.85x1033 1.000 8.27x 104 4.918 r (Ro) r (em) 0.007 0.02 0.09 4.87x108 1.39 x 109 6.24x109 15.7 15.6 13.6 0.22 0.32 0.42 1.53 x 1010 2.23xlO lO 2.92xlO lO 0.52 0.60 0.71 14.3 T (106 K) p (gem- 3) SOLAR OSCILLATIONS by Frank Hill = solar radius. g = gravitational acceleration at solar surface. Ro e= spherical harmonic degree of mode of oscillation. m = spherical harmonic azimuthal degree of mode. 14.3 SOLAR OSCILLATIONS / 343 n = radial order of mode. v = frequency of mode. (J) kh Pi = angular frequency of mode, = 21l' v. = horizontal wave number of mode, kh = J i(i + 1) /,R0' (J) = Legendre polynomial of degree i. A(v, i) = amplitude of mode. r(v, i) = full width at half maximum of mode. Characteristic period of p (pressure) modes Characteristic photospheric amplitude of p modes Characteristic lifetime of p modes Estimated number of excited p modes 14.3.1 5 min. 10 ems-I. 7 days. 107 . Approximations for Frequencies Vn,t of Zonal (m = 0) p Modes (a) Tassoul first-order asymptotic approximation for low-degree modes with i :::: 3 and 11 :::: n :::: 33 [25]: v(n, i) = V() (n +~ + 8) with measured coefficients in Table 14.3 [26] and accuracy of 2.8-4.1 JLHz. Table 14.3. Fit values. e II() (ILHz) 135.4 135.7 135.4 135.7 0 1 2 3 8 1.43 1.36 1.36 1.24 (b) Tassoul second-order asymptotic approximation for low-degree modes with i :::: 3 and 11 < n :::: 33 [25]: v(n, i) = V() (n i + 2" + 8 - i(i n + l)a - f3) + i/2 + 8 ' with measured coefficients in Table 14.4 [26] and accuracy of 1.4-2.0 JLHz. Table 14.4. Second-order fit values. e 0 1 2 3 II() (ILHz) 137.0 137.9 137.4 137.0 a fJ 8 0.20 0.15 0.20 5.6 7.8 7.8 7.4 0.90 0.62 0.70 0.80 344 / 14 SUN (c) Polynomial approximation for low-degree modes with l v(n. l) = t::. Vi + Vi (n + ~ - no) + Yi ~ (n 3 and 11 ~ n ~ + ~ _ no) 2 33 [27]: • using no = 22 as a reference order. measured coefficients listed in Table 14.5 in JLHz [26] and accuracy of 1.0-1.2 JLHz. Thble 14.5. Polynomialjit values. i ~Vl Vi Ye 0 1 2 3 3169.4 3166.2 3160.5 3150.8 135.31 135.52 135.35 135.52 0.090 0.105 0.085 0.070 The quantities t::. Vi and Vi are linear functions of l(l + 1): + I)Do. Vi = vo + l(l + l)do. t::.Vi = t::.vo - l(l with fitted values [26] t::.vo vo Do do = 3169.4 JLHz. = 135.35 JLHz. = 1.54 JLHz. = 0.012 JLHz. (d) Parabolic fit for intermediate-degree modes with 4 1-10 JLHz [26]: ~ l ~ 100. 3 ~ n ~ 24. and accuracy of where coefficients aj are fitted to second-order polynomials in n expressed in matrix form as ( ao) = (6438.6 al a2 -0.025 101.3 2.9 -0.008 0.71) ( 1 ) -0.047 n. -0.0002 n2 (e) Empirical fit for low- and intermediate-degree modes with 1 5.0 mHz. 'R0 in kIn. and accuracy of 10 JLHz [28]: v(n. l) x ~ l < 200. 1.7 mHz ~ v < = 2354.2(n + 1.57)eO.2053[(lnx-14.523)2+4.1l75f/2 -lnx JLHz. = (n + 1.57)1l"'R0 [l(l + l)rl/2. The Duvall dispersion law [29] collapses all p-mode ridges in an kh-(J) diagram to a single ridge via a transformation of coordinates. This transformation is (n + a)1l" = f W (w) kh 14.3 SOLAR OSCILLATIONS / 345 with fitted value a = 1.67. The dependence of v on m for p modes is [30] v(t, m, n) = v(t, n) + Jt(t + 1) I: a; (v, t)P; ( j=1 -m ), Jt(t + 1) where the splitting coefficients aj depend on v(n, t), in mHz [31]: aj(v, t) = a7(t) + b7(t)[v(n, t) - 2.5]. Some of these coefficients are given in Table 14.6. Thble 14.6. Selected splitting coefficients [1]. All coefficients in nHz. l a*1 11 436.7 438.4 439.5 440.7 441.4 441.5 20 29 38 47 56 b*1 a*2 b*2 -1.0 -0.7 -0.5 0.3 0.1 0.7 -3.5 -0.9 -0.5 -0.1 -0.3 0.2 -1.7 0.2 -0.5 -0.8 -1.0 0.6 a*3 12.0 16.9 19.9 21.3 21.5 22.3 b*3 a*4 b*4 a*5 b*5 -2.1 0.3 -5.1 -2.0 -0.7 -0.5 1.3 0.8 1.2 0.9 0.4 0.4 6.8 1.3 -1.1 1.4 1.9 1.3 1.3 -3.1 -3.4 -2.5 -3.3 -3.5 3.2 2.2 1.0 -0.1 0.5 0.3 Reference 1. Libbrecht, K.G. 1989, ApJ, 336, 1092 The dependence of p-mode frequency change absolute magnetic field B in Gauss [32] is ~v ~v of v(t, n) on area-weighted average full-disk = a(B -7), with fitted value a = 0.027 JLHzjG. The approximate formulas for amplitude A(v, t) of p modes [33,34] A(v, t) = 1O(b+c)/2 cm/s, with fitted values b= = c= = 2.2v - 3.5, -0.9v + 5.6, -8.8 x 1O-4 t, -3.1 x 1O-3 t + 0.75, v< v> t < t > 2.9 mHz, 2.9 mHz, 340, 340. The observed estimate of absorption fraction a of p-mode power by sunspots is discussed in [35] and listed in Table 14.7. 346 I 14 SUN Table 14.7. Sunspot absorption. kh (Mrn-l) a 0.2 0.3 0.4 0.10 0.18 0.34 0.42 ~0.5 Approximate formulas for the full width at half maximum (FWHM) r(v, l) of p modes [33, 36, 37] are r(v, l) = 1.7 x 1O- 2 (l - 20) + lotI tLHz, with fitted values d = v -2.3, v < 2.4 mHz ~ v ~ 3.1 mHz ~ v ~ 4.3mHz < =0.1, = v -3.0, = O.4v - 0.6, The dispersion relation for f 2.4 mHz, 3.1 mHz, 4.3 mHz, v. (fundamental) mode is (J) or equivalently = ..jgkh, v = 99.8569[l(l + 1)]1/4 tLHz. The first-order asymptotic approximation for period P(n, l) of g (gravity) mode with n P(n, l) Po »l 2n+l+4> = "2 [l(l + 1)]1/2' Theoretical estimates of period spacing Po and phase 4> from standard solar models [38] are Po 4> = 33.9 to 38.0 min, = -0.42 to -0.25. Po 4> = 29.9 to 42.6 min, = -0.35 to +2. Observational estimates [38] are Properties of "160-min" oscillation [38] are period amplitude = 160.010 min, = 54 cm/s. Table 14.8 gives zonal p-mode frequencies for selected nand l values. [25] is 1823.60 2093.50 2362.50 2629.60 2899.30 3168.60 3439.80 3711.50 3984.90 4257.40 4532.30 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 1823.33 2098.45 2371.21 2641.07 2913.54 3186.12 3459.57 3734.52 4009.61 5 1443.40 1737.84 2021.53 2302.80 2578.64 2855.70 3132.88 3410.10 3688.24 3967.99 4247.68 10 1489.44 1847.91 2181.78 2494.35 2797.28 3096.17 3390.93 3684.81 3977.49 4270.76 25 1409.99 1833.33 2296.79 2676.98 3045.59 3402.83 3753.12 4095.93 4428.00 4753.20 50 1655.77 2181.39 2638.73 3067.43 3474.37 3868.91 4252.25 4628.75 4999.33 75 1844.12 2423.47 2928.67 3397.96 3844.40 4271.92 4688.09 100 2148.50 2811.51 3405.04 3954.48 4475.10 150 2395.6 3130.2 3800.2 4425.0 200 References I. Duvall, Jr., T.L., Harvey, J.W., Libbrecht, K.G., Popp, B.D., & Pomerantz, M.A. 1988, ApJ, 324, 1158 2. Libbrecht, K.G., Woodard, M.P., & Kaufman, I.M. 1990, ApJS, 74, 1129 £=0 n 1743.6 2780.3 3650.1 4458.8 300 1998.0 3089.6 4092.1 4974.2 400 2227.8 3359.1 4475.4 500 Table 14.8. Selected measured zonal p-mode frequencies [1, 2]. All values in fLHz. 2438 3622 4815 600 2632 3877 5124 700 2821 4120 800 2984 4374 900 3140 4601 1000 ~ .....J ~ w ........ (I) oz ~ t= t'"' n (I) o > :;;0 ot'"' CI'.l W .- 348 / 14 SUN 14.4 PHOTOSPHERIC-CHROMOSPHERIC MODEL by Eugene Avrett Table 14.9 gives a model of the average quiet solar atmosphere, from [39]. The height h is the distance above TSOO = 1, where TSOO is the radial optical depth in the continuum at 500 om. Hydrostatic equilibrium is assumed so that m = Prot! g, where m is the column mass, Prot is the total pressure, and g is the gravitational acceleration at the solar surface. In the photosphere (-100 < h < 525 kIn) and in the chromosphere (525 < h < 2100 kIn) the temperature T has been adjusted empirically so that the computed spectrum is in agreement with the spatially averaged spectrum from quiet areas (away from sunspots and active regions). The temperature distribution in the transition region above h ~ 2100 kIn (up to T = lOS K) has been determined theoretically by balancing the downftow of energy from the corona (due to thermal conduction and diffusion) with the radiative energy losses. The microvelocity Vt roughly accounts for the Doppler broadening that is observed to exceed the thermal broadening of lines formed at various heights (see [40,41)). The total pressure Prot is the sum of the gas pressure Pgas and the turbulent pressure pv; /2, where p is the gas density. The table also lists the total hydrogen density nH and the proton and electron densities np and ne. The number densities and other quantities are determined by solving the coupled radiative transfer and statistical equilibrium equations [without assuming local thermal equilibrium (LTE)], given the T and Vt distributions. The helium to hydrogen abundance ratio is assumed to be 0.1. The abundances of the other contributing elements are from [42]. See [43] and [44] for similar empirical models of the photosphere. Models for faint and bright components of the quiet Sun and for a plage region are given in [39]. See [45] for a theoretical lineblanketed LTE photospheric model, and [46] for theoretical non-LTE line-blanketed chromospheric models. Bifurcated chromospheric models based on a combination of hot and cool components are given in [47] and [48]. Papers in [49] and [50] discuss related studies and include references to earlier work. Other aspects of the chromosphere, such as infrared and radio data, are referred to in [51-53]. h 2218.20 2216.50 2214.89 2212.77 2210.64 2209.57 2208.48 2207.38 2206.27 2205.72 2205.21 2204.69 2204.17 2203.68 2203.21 2202.75 2202.27 2201.87 2201.60 2201.19 2200.85 2200.10 2199.00 2190.00 2168.00 2140.00 2110.00 2087.00 2075.00 2062.00 2043.00 2017.00 1980.00 1915.00 1860.00 1775.00 1670.00 1580.00 1475.00 1378.00 (km) 0.00 x 7.70 x 1.53 x 2.60 x 3.75 x 4.38 x 5.06 x 5.81 x 6.64 x 7.10 x 7.55 x 8.05 x 8.61 x 9.19 x 9.81 x 1.05 x 1.13 x 1.21 x 1.27 x 1.36 x 1.44 x 1.63 x 1.90 x 4.15 x 9.85 x 1.76 x 2.62 x 3.30 x 3.66 x 4.05 x 4.62 x 5.41 x 6.53 x 8.53 x 1.03 x 1.31 x 1.69 x 2.07 x 2.59 x 3.19 x 10- 10 10- 10 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10-9 10- 8 10- 8 10- 8 10- 8 10- 8 10- 8 10- 8 10- 8 10- 8 10- 8 10- 7 10-7 10-7 10- 7 10- 7 10- 7 10- 7 10- 7 10- 7 10- 6 10- 6 10- 6 10-6 10-6 10-6 '500 m 6.777 x 6.779 x 6.781 x 6.785 x 6.788 x 6.790 x 6.792 x 6.794 x 6.797 x 6.798 x 6.800 x 6.801 x 6.803 x 6.805 x 6.807 x 6.809 x 6.812 x 6.815 x 6.817 x 6.820 x 6.823 x 6.830 x 6.840 x 6.936 x 7.203 x 7.588 x 8.063 x 8.483 x 8.724 x 9.005 x 9.453 x 1.014 x 1.128 x 1.387 x 1.676 x 2.298 x 3.510 x 5.186 x 8.435 x 1.363 x 10- 6 10- 6 10-6 10-6 10-6 10-6 10-6 10- 6 10-6 10-6 10-6 10-6 10-6 10-6 10- 6 10-6 10- 6 10-6 10-6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 6 10- 5 10- 5 10- 5 10- 5 10- 5 10- 5 10-5 10-5 10-4 (gcm- 2) 100000 95600 90816 83891 75934 71336 66145 60 170 53284 49385 45416 41178 36594 32145 27972 24056 20416 17925 16500 15000 14250 13500 13000 12000 11150 10550 9900 9450 9200 8950 8700 8400 8050 7650 7450 7250 7050 6900 6720 6560 11.73 11.65 11.56 11.42 11.25 11.14 11.02 10.86 10.67 10.55 10.42 10.27 10.09 9.90 9.70 9.51 9.30 9.13 9.02 8.90 8.83 8.74 8.66 8.48 8.30 8.10 7.87 7.70 7.61 7.52 7.41 7.26 7.06 6.74 6.49 6.12 5.69 5.34 4.93 4.53 VI (km s-I) T (K) 5.575 x 5.838 x 6.151 x 6.668 x 7.381 x 7.864 x 8.488 x 9.334 x 1.053 x 1.135 x 1.233 x 1.356 x 1.521 x 1.724 x 1.971 x 2.276 x 2.658 x 3.008 x 3.255 x 3.570 x 3.762 x 4.013 x 4.244 x 4.854 x 5.500 x 6.252 x 7.314 x 8.287 x 8.882 x 9.569 x 1.055 x 1.203 x 1.446 x 1.971 x 2.547 x 3.788 x 6.292 x 9.900 x 1.726 x 2.970 x nH 109 109 109 109 109 109 109 109 1010 1010 1010 1010 10 10 1010 1010 1010 1010 1010 1010 10 10 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1011 1011 1011 1011 1011 1011 1011 1011 10 12 10 12 (cm- 3) 5.575 x 5.837 x 6.150 x 6.667 x 7.378 x 7.858 x 8.476 x 9.307 x 1.047 x 1.125 x 1.217 x 1.332 x 1.483 x 1.667 x 1.887 x 2.154 x 2.483 x 2.778 x 2.979 x 3.218 x 3.343 x 3.441 x 3.456 x 3.411 x 3.619 x 3.806 x 3.923 x 3.954 x 3.956 x 3.952 x 3.937 x 3.921 x 3.908 x 3.974 x 4.100 x 4.399 x 4.922 x 5.390 x 6.037 x 6.824 x np 109 109 109 109 109 109 109 109 1010 1010 1010 1010 1010 1010 1010 1010 10 10 1010 1010 1010 1010 1010 1010 1010 1010 1010 10 10 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 (cm- 3) Table 14.9. Solar atmospheric model. 6.665 6.947 7.284 7.834 8.576 9.076 9.718 1.059 1.182 1.266 1.365 1.491 1.657 1.858 2.098 2.389 2.743 3.049 3.256 3.498 3.619 3.699 3.695 3.663 3.889 4.095 4.238 4.291 4.305 4.314 4.314 4.313 4.310 4.351 4.423 4.630 5.085 5.535 6.191 7.007 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ne 109 109 109 109 109 109 109 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 10 10 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 1010 (cm- 3) 1.857 x 1.857 x 1.858 x 1.859 x 1.860 x 1.860 x 1.861 x 1.862 x 1.862 x 1.863 x 1.863 x 1.863 x 1.864 x 1.864 x 1.865 x 1.866 x 1.866 x 1.867 x 1.868 x 1.869 x 1.869 x 1.871 x 1.874 x 1.900 x 1.974 x 2.079 x 2.209 x 2.324 x 2.390 x 2.467 x 2.590 x 2.778 x 3.092 x 3.800 x 4.593 x 6.297 x 9.616 x 1.421 x 2.311 x 3.735 x 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 10 10- 10 10- 10 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 Ptot (dyncm- 2) 0.952 0.950 0.948 0.945 0.941 0.938 0.935 0.931 0.925 0.921 0.916 0.910 0.903 0.894 0.883 0.871 0.856 0.843 0.834 0.823 0.816 0.808 0.801 0.785 0.775 0.769 0.760 0.753 0.748 0.743 0.738 0.732 0.727 0.724 0.727 0.736 0.752 0.767 0.787 0.809 Pg.. /Ptot 1.31 x 1.37 x 1.44 x 1.56 x 1.73 x 1.84 x 1.99 x 2.19 x 2.47 x 2.66 x 2.89 x 3.18 x 3.56 x 4.04 x 4.62 x 5.33 x 6.23 x 7.05 x 7.63 x 8.36 x 8.81 x 9.40 x 9.94 x 1.14 x 1.29 x 1.46 x 1.71 x 1.94 x 2.08 x 2.24 x 2.47 x 2.82 x 3.39 x 4.62 x 5.97 x 8.87 x 1.47 x 2.32 x 4.05 x 6.96 x 10- 13 10- 13 10- 13 10- 13 10- 13 10- 13 10- 12 10- 12 10- 12 10- 12 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 14 10- 13 10- 13 10- 13 10- 13 10- 13 10- 13 10- 13 P (gcm- 3) \0 ~ UJ '- ttl t'"' 0 0 ~ (") :;:tj ttl ...... ::t '"'C til 0 s:: 0 :;:tj ::t I () (") ...... :;:tj ttl ::t '"'C til 0 o-l 0 ::t ""C ~ ~ - 50.00 35.00 20.00 10.00 0.00 -10.00 -20.00 -30.00 -40.00 -50.00 -60.00 -70.00 -80.00 -90.00 -100.00 600.00 560.00 525.00 490.00 450.00 400.00 350.00 300.00 250.00 200.00 175.00 150.00 125.00 100.00 75.00 1278.00 1180.00 1065.00 980.00 905.00 855.00 805.00 755.00 705.00 650.00 h (km) 1.00 1.25 1.61 2.14 2.95 4.13 5.86 8.36 1.20 1.70 2.36 X X X 10 1 10 1 10 1 4.02 x 10-6 5.19 x 10-6 7.43 x 10-6 1.03 x 10-5 1.44 x 10-5 1.85 x 10-5 2.39 x 10-5 3.09 x 10-5 4.00 x 10-5 5.55 x 10-5 8.53 x 10-5 1.40 x 10-4 2.39 x 10-4 4.29 x 10-4 8.51 x 10-4 1.98 x 10- 3 4.53 x 10- 3 1.01 x 10- 2 2.20 X 10- 2 4.73 x 10-2 6.87 x 10-2 9.92 x 10-2 1.42 X 10- 1 2.02 x 10- 1 2.87 x 10- 1 4.13 x 10- 1 5.22 X 10- 1 6.75 x 10- 1 8.14 x 10- 1 ~SOO x x x x x x x x 2.538 3.680 5.125 7.149 1.044 1.664 2.626 4.103 6.344 9.705 4.686 4.975 5.269 5.567 5.869 6.174 6.481 6.790 7.102 7.417 3.148 3.496 3.869 4.132 4.404 1.195 1.466 1.790 2.174 2.625 x x x x x 3.282 4.710 6.868 1.022 1.624 x X x x x x x 2.312 4.022 8.074 1.396 2.314 10-4 10-4 10-4 10-3 10-3 10-3 10-3 10- 3 10-2 10- 2 10-2 10-2 10-2 10-2 10- 1 10- 1 10- 1 10- 1 10- 1 10- 1 (gcm- 2) m 6720 6980 7280 7590 7900 8220 8540 8860 9140 9400 4550 4430 4400 4410 4460 4560 4660 4770 4880 4990 5060 5150 5270 5410 5580 5790 5980 6180 6340 6520 5650 5490 5280 5030 4750 6390 6230 6040 5900 5755 (K) T 1.64 1.67 1.70 1.73 1.75 1.77 1.79 1.80 1.82 1.83 1.00 0.89 0.80 0.72 0.65 0.55 0.52 0.55 0.63 0.79 0.90 1.00 1.10 1.20 1.30 1.40 1.46 1.52 1.55 1.60 4.04 3.53 2.94 2.52 2.19 1.99 1.77 1.54 1.38 1.18 (kms-I) VI 9.895 1.478 2.078 2.898 4.192 6.549 1.012 1.545 2.331 3.476 4.211 5.062 6.024 7.107 8.295 9.558 1.027 1.098 1.142 1.182 1.219 1.246 1.264 1.280 1.295 1.307 1.317 1.325 1.337 1.351 X X X X X X X x x X x X x x x x x x X x x x x x x x x x x x 5.393 x 1.002 x 2.164 x 3.931 x 6.806 x 9.931 x 1.481 x 2.268 x 3.560 x 6.033 x x x x x x x x x x x x 1011 X 1011 x 1011 x 10 12 x 10 12 10 12 10 13 1013 10 13 10 13 X 10 13 x 10 14 x 10 14 X 10 14 X 10 14 5.368 2.825 2.424 2.618 3.600 6.715 1.267 2.604 5.605 1.253 2.028 3.579 7.119 1.485 3.281 7.614 1.439 2.588 3.926 6.014 9.269 1.536 2.597 4.249 6.668 1.022 1.515 2.180 2.942 3.826 X X X X X x x x x x lOIS lOIS lOIS lOIS lOIS 109 109 109 109 109 109 1010 1010 1010 1011 1011 1010 1010 1010 10 10 10 14 lOIS 1015 1015 1015 1015 10 16 10 16 10 16 10 16 10 16 10 16 10 16 10 16 10 16 10 16 10 17 10 17 10 17 10 17 10 17 10 17 10 17 10 17 10 17 1017 10 17 10 17 10 17 10 17 x x x x x 1.051 9.014 6.493 3.637 1.375 1013 10 14 10 14 10 14 10 14 1010 1010 1010 1011 1011 7.768 8.783 9.992 1.068 1.078 x x x x x (cm- 3) np 10 12 1013 10 13 1013 10 13 (cm- 3) nH 1Bble 14.9. (Continued.) 7.994 x 9.083 x 1.047 x 1.142 x 1.192 x 1.208 x 1.122 x 9.690 x 8.387 x 9.000 x 1.255 x 1.767 x 2.413 x 3.300 x 4.714 x 7.344 x 1.134 x 1.737 x 2.645 X 4.004 x 4.945 x 6.153 x 7.770 x 1.003 x 1.353 x 1.980 x 2.779 x 4.064 x 5.501 x 7.697 x 1.107 x 1.730 x 2.807 x 4.480 X 6.923 X 1.050 X 1.546 X 2.215 X 2.979 X 3.867 X lOIS lOIS lOIS lOIS lOIS 1010 1010 1011 1011 1011 1011 1011 1010 1010 1010 1011 1011 1011 1011 1011 1011 10 12 10 12 10 12 10 12 10 12 10 12 10 12 10 13 10 13 10 13 1013 10 13 1013 10 13 10 14 10 14 10 14 10 14 10 14 (cm- 3) n. x x x x x 104 104 loS loS loS 102 103 103 103 103 103 103 104 104 104 104 104 104 104 104 102 102 102 102 1.284 x loS 1.363 x loS 1.444 X loS 1.525 X loS 1.608 X loS 1.691 X loS 1.776 X loS 1.860 X loS 1.946 X loS 2.032 X loS 8.624 9.578 1.060 1.132 1.207 6.954 x 1.008 x 1.404 x 1.959 x 2.860 x 4.558 x 7.194 x 1.124 X 1.738 x 2.659 x 3.274 x 4.017 x 4.905 x 5.957 x 7.192 x 6.335 x 1.102 x 2.212 x 3.824 x 6.341 x 8.993 x 1.290 x 1.882 x 2.799 x 4.451 x 10- 10 101 101 101 101 101 (dyncm- 2) Ptot 0.983 0.986 0.989 0.991 0.993 0.995 0.996 0.995 0.994 0.990 0.988 0.985 0.983 0.980 0.977 0.975 0.973 0.972 0.971 0.971 0.970 0.970 0.970 0.971 0.971 0.972 0.972 0.973 0.973 0.974 0.837 0.867 0.901 0.924 0.940 0.949 0.958 0.967 0.972 0.978 Pgas/Ptot x x X x x x x x x x x x x x x x x x x x x x x x x x x x x x 2.86 x 2.92 x 2.96 X 3.00 X 3.04 X 3.06 X 3.09 X 3.10 X 3.13 X 3.17 X 2.32 3.46 4.87 6.79 9.82 1.53 2.37 3.62 5.46 8.14 9.87 1.19 1.41 1.67 1.94 2.24 2.40 2.57 2.68 2.77 1.26 2.35 5.07 9.21 1.59 2.33 3.47 5.31 8.34 1.41 10-9 10-9 10-9 10-9 10-9 10- 8 10- 8 10- 8 10- 8 10- 8 10- 8 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10-7 10- 7 10-7 10-7 10-7 10- 7 10-7 10-7 10- 10 10- 10 10-9 IO~IO 10- 11 10- 11 10- 11 10- 11 10- 10 10- 10 (gcm- 3) p -Z c:: en .J:>. 0 VI W 14.5 SPECTRAL LINES I 351 14.5 SPECTRAL LINES by William Livingston and Oran R. White 14.5.1 Absorption Features Selected Fraunhofer absorption features are given in Table 14.10. Equivalent width refers to disk center. Cycle variability, where known, refers to solar irradiance, or Sun as a star [54-64]. Table 14.10. AbsorptionJeatures. Wavelength (nm) 279.54 280.23 388.36 393.36 396.85 430.79 517.27 518.36 525.02 537.96 538.03 557.61 587.56 589.00 589.59 612.22 630.25 656.28 676.78 769.89 777.42 854.21 868.86 1006.37 1083.03 1281.81 1564.85 1565.29 2231.06 4652.55 4666.24 12318.3 Name Species MglI MglI (CNband head) K H Gband ~ h] D3 D2 D] C(Ra) HPaschfJ HPfundfJ CN Call Call CH (Fe I, Ti II) MgI MgI Fel Fel CI Fel Equiv. width (om) Cyclevar. [% (p-to-p)] 2.2 10 UV emission, high chromosphere 0.03 (index) 3 Photosphere, magnetic field tracer 2.0 1.5 0.72 0.075 0.025 0.0070 0.0079 0.0025 15 10 Chromosphere 0.3 0.3 0.0 Photo. magnetic fields (g = 3) Medium photosphere Low photosphere Photo. velocity fields (g = 0) Chromo., flares, prominences Upper photo., low chrom., prom. (same except water blend free) Photo. magnetic fields (g - 1.5) Photo. magnetic fields (g = 2.5) Chromo., prom., flares Photo. oscillations Photo. oscillations High photo. (?) (NLTE?) Low chromo., prom. Photo. magnetic fields (g = 1.7) Umbra! (only) mag. fields (g = 1.22) High chromosphere Chromosphere Photo. magnetic fields (g = 3) Photo. magnetic fields (g = 1.8) Umbra! (only) mag. fields (g = 2.5) Chromo., electric fields High photo. thermal structure High photo., magnetic fields (g = 1) He! Nal Nal Cal Fel HI Nil KI 0.075 0.056 01 0.0066 0.37 0.014 -I 0.003 0.19 0.0035 0.003 200 Cal Fel FeH Hel HI Fe] Fel Til HI CO MgI Comment 0.0083 0.40 6 Magnetic field tracer Low chromosphere 14.5.2 Emission Features Table 14.11 gives absolute spectral irradiances at the Earth for the UV and EUY with estimates of solar cycle variability where known. Irradiances from both individual lines and integration over bands are given in the table. The irradiance for all entries identified as a "line" in column 3 (bandwidth) is the integral for the line, and is in units ofmWm-2. In contrast, irradiances for the "bands" are mean fluxes per nanometer wavelength interval for that band [65,66]. 352 / 14 SUN Table 14.11. Solar spectral irradiances: 0.5-300 nm. Band GOESa 4 5 6 7 8 9 10 II 12 14 15 17 18 19 20 21 22 24 25 27 28 29 33 34 35 36 37 Band center (nm) 0.50 22.50 25.63 28.42 27.50 30.33 30.38 32.50 36.81 37.50 46.52 47.50 55.44 58.43 57.50 60.98 62.97 62.50 70.33 72.50 77.04 78.94 77.50 97.70 97.50 102.57 103.19 102.50 121.50 150.00 Solar irradiance Bandwidth (nm) Solar max. Solar min. 0.6 5 1.9 x 10- 2 6.5 x 10- 2 line line 2.6 2.9 8.6 x 10- 3 1.6 7.4 6.9 x 10- 2 1.2 1.5 x 10- 2 7.1 x 10- 1 3.0 x 10- 3 1.7 3.5 x 10- 1 1.1 x 10- 2 9.8 x 10- 1 1.5 x 10- 1 9.3 x 10- 3 1.2 x 10- 1 3.9 x 10-3 4.1 x 10- 1 5.5 x 10- 1 2.2 x.IO- 3 9.0 x 10- 1 5.4 x 10- 2 1.8 1.7 5.1 x 10- 2 1.0 x 10 1 1.0 x 10- 1 0 1.6 7.7 5.9 3.9 1.6 3.9 1.1 1.1 7.8 1.3 1.5 5.7 1.6 5.5 4.9 5.5 2.9 4.8 2.1 2.0 2.2 1.0 3.6 2.4 6.2 7.0 1.7 5 line line 5 line 5 line 5 line line 5 line line 5 line 5 line line 5 line 5 line line 5 x x x x x 10-2 10-2 10- 1 10-3 10- 1 x x x x x x x x x x x x x x x x x x x x x 10-2 10- 1 10-3 10- 1 10-3 10- 1 10- 1 10-3 10- 1 10-2 10- 3 10- 2 10-3 10- 1 10- 1 10-3 10- 1 10-2 10- 1 10- 1 10-2 Solar cycle variability /max//min 4 34 5 2 10 2 6 10 2 5 2 3 2 2 2 3 3 3 2 2 3 2 2 2 3 2 3 1.5 1.15 Species Hell, Six Fe XV SixI Hell Mglx NeVIl OIV Hel Mgx Ov Om Nevm OIV em HI (LyP) OVI HI (Lya) Note a Geostationary Operational Environmental Satellite. 14.5.3 Line Widths and Heights See [67] for a detailed description of curve-of-growth analysis techniques. These yield the following results [68-74]: Atomic thermal velocity Microturbulence (~mi) Macroturbulence (~ma) Velocity for line breadth = (2kT /ma)I/2 = 1.4kms-l. = 1.1 kms- 1. = 1.6 kms- 1 (vertical) = 2.8 kms- 1 (horizontal). = (~~ + ~~ + ~im) 1/2 = 2.4 km s-1 at center of disk = 3.3 km s-1 at limb. 14.6 SPECTRAL DISTRIBUTION 1 353 Table 14.12 gives heights offormation of spectral lines [75,76]: Table 14.12. Spectral line heights ojjol7lUJtion. Line (run) Continuum (388.385) CN388.33 Continuum (500.0) FeI537.9 C1538.0 HI 656.0 FeII564.8 Fe I 1564.8 (spot) Optical depth t' (FWHM) Height(km) 3.2 to 0.32 0.003 to 0.000039 2.5 to 0.25 0.35 to 0.0025 1.6 to 0.16 -45 to 60 370 to 740 -35 to 90 60 to 400 -20 to 110 2000 to 3000 -20 to -30 20 to 80 (FWHM) 14.6 SPECTRAL DISTRIBUTION by Heinz Neckel F).. = intensity of the mean solar disk per unit wavelength with spectrum irregularities smoothed (±50 A). Thus F = J F).. d'J.... :F).. = 1r F).. = emittance of the solar surface per unit wavelength range. fA = :F).. (R0 1A)2 = 6.80 x 10-5 F)..solar flux outside the Earth's atmosphere per unit area and wavelength range. A = astronomical unit. F{ same as for F).. but referring to the continuum between the lines. The curve joining the most intense windows between the lines is regarded as the continuum. This may differ appreciably from the continuum in the entire absence of absorption lines. F{ does not have any sudden changes (e.g., at the Balmer limit). 1)..(0) = intensity at the center of the Sun's disk with spectral irregularities smoothed (±50 A). I{ (0) = intensity of the center of the Sun's disk between spectrum lines. This is obtained by interpolation from the most intense windows, as for F{. I)..(O)II{ (0) represents the observed line blanketing for the center of the Sun's disk. FA! 1)..(0) represents the broadband (loo-A) disk-to-center ratio. It is approximately equal to F{II{ (0). The solar spectrum is given in Table 14.13. Table 14.13. Solar spectral distribution, 0.2-5.0 j.tm [1-3]. A (j.tm) 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 F).. F').. h(O) I~ (0) (103 Wm- 2 sr- I A-I) 0.01 0.07 0.08 0.19 0.34 0.83 1.12 1.34 1.42 0.014 0.10 0.13 0.27 0.68 1.48 1.97 2.39 2.56 0.014 0.13 0.13 0.37 0.60 1.34 1.67 1.89 1.96 0.02 0.19 0.21 0.53 1.21 2.39 2.94 3.30 3.47 h (10- 3 Wm- 2 A-I) h(O)/I~(O) F)../h(O) 0.65 4.5 5.2 13 23 56 76 91 97 0.7 0.7 0.6 0.7 0.5 0.56 0.57 0.57 0.56 0.7 0.5 0.6 0.5 0.56 0.62 0.67 0.71 0.72 354 / 14 SUN Table 14.13. (Continued.) A (tt m ) F). F'). h(O) l{ (0) (103 Wm- 2 sr- I A-I) f). (10- 3 Wm- 2 A-I) h(O)/I{ (0) F)./h(O) 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 1.67 1.58 1.52 2.17 2.50 2.54 2.34 2.71 2.94 2.67 2.99 3.21 3.35 3.42 3.47 3.50 3.49 3.47 2.28 2.16 2.08 2.97 3.38 3.45 3.12 3.61 3.87 3.60 4.14 4.41 4.58 4.63 4.66 4.67 4.62 4.55 113 107 103 148 170 173 159 184 200 0.63 0.52 0.47 0.65 0.73 0.74 0.67 0.78 0.85 0.73 0.73 0.73 0.73 0.74 0.74 0.75 0.75 0.76 0.46 0.48 3.01 2.99 3.41 3.28 3.95 3.84 4.44 4.22 205 203 0.89 0.91 0.76 0.78 0.50 0.55 0.60 0.65 0.70 0.75 2.83 2.76 2.61 2.34 2.08 1.87 3.20 2.93 2.67 2.41 2.13 1.92 3.61 3.43 3.17 2.81 2.46 2.18 4.08 3.63 3.24 2.90 2.52 2.24 192 188 177 159 141 127 0.88 0.94 0.98 0.97 0.975 0.975 0.78 0.80 0.82 0.83 0.85 0.86 0.8 0.9 1.0 l.l 1.2 1.68 1.38 l.ll 0.90 0.76 1.71 1.39 1.12 0.90 0.76 1.94 1.57 1.25 1.01 0.84 1.97 1.58 1.26 1.01 0.84 114 94 75 61 52 0.983 0.993 0.995 1.0 1.0 0.87 0.88 0.89 0.89 0.90 1.4 1.6 1.8 0.51 0.37 0.25 0.56 0.40 0.27 35 25.5 16.9 1.0 1.0 1.0 0.91 0.92 0.92 2.0 2.5 3.0 4.0 5.0 0.17 0.076 0.039 0.0130 0.0055 0.18 0.081 0.041 0.0135 0.0057 11.6 5.2 2.6 0.9 0.4 1.0 1.0 1.0 1.0 1.0 0.93 0.94 0.95 0.96 0.% References 1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd 00. (Athlone Press, London), Sees. 81 &82 2. Labs, D., Neckel, H., Simon, P.C., & Thuiller, G. 1987, Solar Phys., 90, 25 3. Neekel, H., & Labs, D. 1984, Solar Phys., 90, 205 Brightness temperatures for two optical wavelengths are given in Table 14.14, and Table 14.15 gives them for the infrared. Table 14.14. Brightness temperatures. 4400 A 5500 A 5850K 6125 K 6165 K 6465K 5860K 5940K 6155 K 6240K 14.7 LIMB DARKENING / 355 Mean intensity and brightness temperature in mid- and far-infrared regions with heights from the Vemazza, Avrett, and Loeser (VAL-C) model [77-79]: Table 14.15. Infrared brightness temperatures. 14.7 J.. (j.Lm) h (kIn) 5 10 20 50 100 200 1000= 1 mm lem 70 160 240 340 410 450 logF.. (:::: h:::: F{:::: I{) (Wm- 2 sr- 1 /Lm) Tb (K) 4.77 3.57 2.36 0.76 -0.45 -1.67 -4.31 5730 5140 4820 4500 4340 4200 5920 10-23000 (temp min.) (transition) LIMB DARKENING by Keith Pierce I{ (0) = intensity of the solar continuum at an angle 0 from the center of the disk; 0 = angle between the Sun's radius vector and the line of sight. I{ (0) = continuum intensity at the center of the disk. The ratio I{ (0)/ I{ (0), which varies with the wavelength A, defines limb darkening. As far as possible, measurements are made in the continuum between the lines (hence the primes in the notation). The results may be fitted to the following expressions: I{(O)/I{(O) = 1- I{ (0)/ I{ (0) = A + B cos 0 + C[1 - or where A U2 - V2 + U2COS 0 + V2 cos2 0, + B + (1 - cos 0 In(1 In 2)C = + sec 0)], 1. The ratio of the mean to central intensity is or F{/I{(O) = A + C + ~B - 2C(~ In2 = A + 0.667 B + 0.409C. 1) The ratio of the limb-to-central intensity is I{(90 0 )/I{(0) = 1- U2 - V2 ~ 1- Ul =A+C. Table 14.16 presents limb darkening details, and the fit constants are given in Table 14.17. 356 I 14 SUN Table 14.16. If (8)/ If (0) [1-16]. A (Jl,m) 0.20 0.22 0.245 0.265 0.28 0.30 0.32 0.35 0.37 0.38 0.40 0.45 0.50 0.55 0.60 0.80 1.0 1.5 2.0 3.0 5.0 10 20 Total cos 8 sin 8 1.0 0.000 0.8 0.600 0.6 0.800 0.5 0.866 0.4 0.916 0.3 0.954 0.2 0.980 0.1 0.995 0.05 0.9987 [7] [7] [7] [7] [7] [7] [9] [9] [9] [9] [9] [9] [9] [9] [9] [9] [9] [9] [9] [9] [8] [8] [8] 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.85 0.58 0.71 0.68 0.72 0.77 0.809 0.837 0.851 0.83 0.835 0.860 0.877 0.890 0.900 0.924 0.941 0.957 0.966 0.976 0.986 0.992 0.994 0.898 0.74 0.33 0.49 0.42 0.47 0.57 0.623 0.665 0.687 0.66 0.663 0.714 0.744 0.769 0.788 0.843 0.870 0.902 0.922 0.944 0.963 0.981 0.983 0.787 0.69 0.26 0.42 0.32 0.38 0.48 0.532 0.579 0.603 0.58 0.585 0.637 0.675 0.703 0.727 0.793 0.828 0.873 0.896 0.922 0.949 0.973 0.975 0.731 0.65 0.21 0.36 0.24 0.29 0.39 0.438 0.487 0.513 0.48 0.490 0.556 0.599 0.633 0.664 0.744 0.783 0.831 0.865 0.902 0.937 0.964 0.970 0.669 0.61 0.16 0.31 0.19 0.22 0.30 0.347 0.397 0.421 0.39 0.403 0.468 0.513 0.556 0.587 0.681 0.731 0.789 0.826 0.873 0.916 0.956 0.964 0.602 0.58 0.12 0.25 0.14 0.16 0.22 0.262 0.306 0.332 0.30 0.308 0.378 0.425 0.468 0.508 0.615 0.675 0.735 0.780 0.835 0.890 0.937 0.957 0.525 0.14 0.17 0.21 0.23 0.22 0.222 0.278 0.323 0.371 0.412 0.533 0.59 0.65 0.70 0.78 0.84 0.90 0.95 0.448 0.19 0.18 0.18 0.21 0.26 0.31 0.35 0.47 0.54 0.58 0.61 0.67 0.76 0.87 0.93 0.39 References 1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sec. 81 2. Pierce, A.K., McMath, R.R., Goldberg, L., & Mohler, O.C. 1950, ApJ, 112, 289 3. Pierce, A.K., & Waddell, J.H. 1961, MNRAS, 68, 89 4. Gaustad, J.E., & Rogerson, J.R. 1961, ApJ, 134, 323 5. Mouradian, Z. 1965, Ann. d'Astrophys., 28, 805 6. Heintz, J.R.W. 1965, Rech. Astron. Obs. Utrecht, 1712 7. Bonnet, R. 1968, Ann. d'Astrophys., 31, 597 8. Lena, P. 1970, A&AS, 4, 202 9. Pierce, A.K., & Slaughter, C.D. 1977, Solar Phys., 51, 25 10. Neckel, H., & Labs, D. 1987, Solar Phys., 110, 139 11. Neckel, H., & Labs, D. 1994, Solar Phys., 153,91 12. Neckel, H. 1996, Solar Phys., 167,9 13. Neckel, H. 1997, Solar Phys., 171, 257 14. Pierce, AK., Slaughter, C.D., & Weinberger, D. 1977, Solar Phys., 52,179 15. Petro, C.D., Foukal, P.V., Rosen, W.A., Kurucz, R.L., & Pierce, AK. 1984, ApJ, 283, 462 16. Elste, G.H. 1990, Solar Phys., 126,37 Table 14.17. Limb darkening constants. A u2 112 A 0.20 0.22 0.245 0.265 0.28 0.30 +0.12 -1.3 -0.1 -0.1 +0.38 +0.74 +0.33 +1.6 +0.85 +0.90 +0.57 +0.20 -0.2 -3.4 -1.9 -1.9 -1.3 -0.4 B C 0.9 2.9 2.0 2.1 1.8 1.2 +0.9 +5 +3 +2.7 +1.8 +0.5 :F'J,. If (0) If (90°) If (0) 0.79 0.51 0.61 0.540 0.588 0.648 0.54 0.06 0.20 0.08 0.10 0.06 0.02 0.9998 0.14 0.19 0.24 0.28 0.32 14.8 CORONA / 357 Table 14.17. (Continueti) A u2 v2 A B C 0.32 0.35 0.37 0.38 0.40 0.45 0.50 0.55 0.60 0.80 1.0 1.5 2.0 3.0 5.0 10.0 +0.88 +0.98 +1.03 +0.92 +0.91 +0.99 +0.97 +0.93 +0.88 +0.73 +0.64 +0.57 +0.48 +0.35 +0.22 +0.15 +0.84 +0.03 -0.10 -0.16 -0.05 -0.05 -0.17 -0.22 -0.23 -0.23 -0.22 -0.20 -0.21 -0.18 -0.12 -0.07 -0.07 -0.20 -0.02 +0.25 +0.42 +0.26 +0.20 +0.54 +0.68 +0.74 +0.78 +0.92 +0.97 +1.11 +1.09 +1.04 +1.02 +1.04 +0.72 0.97 0.79 0.68 0.78 0.81 0.60 0.49 0.43 0.39 0.25 0.18 0.08 0.07 0.06 0.05 0.00 +0.42 +0.1 -0.3 -0.4 -0.2 -0.1 -0.44 -0.56 -0.56 -0.57 -0.56 -0.53 -0.61 -0.49 -0.34 -0.18 -0.22 -0.45 Total 14.8 .rr l{ (0) l{ (90°) l{ (0) 0.685 0.705 0.71 0.71 0.718 0.755 0.782 0.803 0.817 0.862 0.886 0.916 0.932 0.948 0.964 0.982 0.82 0.08 0.11 0.13 0.13 0.13 0.11 0.16 0.20 0.24 0.39 0.48 0.56 0.60 0.72 0.81 0.87 0.32 CORONA by Serge Koutchmy Optical radiation from the corona contains three components: K F L = continuous spectrum due to Thomson scattering by electrons of the coronal plasma, = Fraunhofer spectrum diffracted and/or scattered by interplanetary dust particles [81], = coronal emission of forbidden lines; L is negligible for coronal photometry (about 1%). The total coronal light beyond 1.03R0 (for typical lunar disk at eclipse) [82-84] is at sunspot maximum = 1.5 x = 0.6 x Total F corona = 0.3 x at sunspot minimum 10-6 solar flux:::::: 0.66 full Moon, 10-6 solar flux:::::: 0.26 full Moon. 10-6 solar flux. Earthshine on Moon at total eclipse [85] = 2.5 x 10- 10 mean Sun brightness. The brightness of the sky near the Sun during a total eclipse [82, 84, 86] is 6 x 10- 10 < S < 10-8 x [mean Sun brightness (80 )], The spectral distribution of K components is similar to the solar spectrum, with B - V = 0.65. The F component is slightly redder in the outer corona [87], with B - V :::::: 0.75. The base of corona may be taken as the transition region at r = 1.0025R0 from the visible limb. Chromospheric extensions are seen up to r = 1.015R0 . The coronal ellipticity from isophotes € [83, 88, 89] is 358 / 14 SUN where Al and PI are equatorial and polar diameters, and for A3,P3 the corresponding diameters are averaged with those oriented 22.5° on either side. E at sunspot max. ~ 0.06, E at sunspot min. ~ 0.26 near r Values are tabulated against r(R 0 ). The polarization of coronal light (K = 2R0 (extrapolated values; the a + b index). + F) [82,90,91] is Ptot = (It - Ir)/(lt + Ir ), where It and Ir are intensities polarized in the tangential and radial direction. Pmax = 50%. Other values tabulated against rl R0 are listed in Tables 14.18 and 14.19. A most relevant parameter to describe the distribution of electron densities in the plasma corona is Pk = (It - Ir)/K with K = (It + Ir) - F; see [90]. Density irregularities in the corona may be specified approximately by an irregularity factor x = N;/(Ne)2, where Ne is the electron density. Then rms Ne = N e x l / 2 . In the striated outer corona one might write x ~ 1If.f. , where f.f. is the filling factor, which could be very small indeed. Only approximate data exist (see Table 14.18). x varies with r I R0' Temperature of corona: Loops Quiet corona Tmax at r Coronal condensation Coronal hole Table 14.18. Radial variations o/p, E, ~ 2R0 (1.0-3.0) x 106 K. 1.6 x 106 K. 3 x 106 K. lx106 K. and x/or homogeneous and minimum cycle corona at 0.55/Lm [1-3]. r/R0 1.0 1.2 1.5 2 3 Polarization in % Plot at equator Plot at pole Ellipticity E, minimum corona Irregularity x 20 20 0.06 35 25 0.10 41 17 0.16 38 10 0.13 > 2.5 21 3 0.11 4 References 1. Saito, K. 1972, Ann. Tokyo Astron. Obs. XlI, 53, 120 2. Koutchmy, S., Picat, J.P.• & Dantel, M. 1977, A&A, 59, 349 3. Allen, C.W. 1961, Solar Corona IAU Symp.• 16, I 5 10 10 < 1 0.12 8 4 0.18 17 20 25 2.6 0.25 21 25 14.8 CORONA / 359 Table 14.19. Smoothed coronal brightness and electron density in average models [1-5]. log (surface brightness) K Max. F Min. Eq. p = r/R0 Eq.fPole Max. Eq. Pole Pole (cm- 3) 10- 10 B0 log(p - 1) logNe Min. 9.0 8.8 8.7 8.6 8.4 8.25 -8.20 3.10 9.0 8.8 8.7 8.6 8.4 8.25 3.06 2.5 1.95 1.24 2.90 2.50 2.25 1.9111.82 7.90 7.44 7.05 6.52 7.8 7.35 7.05 6.50 7.10 6.25 5.95 5.0 1.63 1.25 0.7 0.25 1.6611.56 1048/1.33 6.00 5.60 5.95 5.50 4.75 4.50 0.61 0.2 -0.75 -0.35 -0.75 1.23/1.03 1.010.80 0.3110.06 -0.33/-0.72 5.1 4.8 4.10 3.2 5.05 4.75 4.05 4.20 4.0 1.003 1.005 1.01 1.03 1.06 1.10 -2.5 -2.3 -2.0 -1.5 -1.2 -1.0 4.9 4.65 4.45 4.3 4.8 4.6 4.35 4.20 4.25 4.10 3.85 3.60 1.2 104 1.6 2.0 -0.7 -0.4 -0.2 0.0 3.9 3.34 2.92 2.23 3.75 3.26 2.88 2.25 2.5 3.0 +0.2 +0.3 1.63 1.23 4.0 5.0 10.0 20.0 +0.5 +0.6 1.0 1.3 0.70 0.3 -0.5 8.0 7.50 References 1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sees. 73,84, and 85 2. Newkirk, G., Dupree, R.G., & Schmahl, E.J. 1970, Solar Phys., 15, 15 3. Koutchmy, S., Zirker, J.B., Steinolfson, R.S., & Zhugzda, J.D. 1991, in Solar Interior and Atmosphere, edited by A.N. Cox, W.e. Livingston, and M.S. Matthews (University of Arizona Press, Tucson) 4. Blackwell, D.E., & Petford, A.D. 1966, MNRAS, 131,383 5. Saito, K. 1972, Ann. Tokyo Astron. Obs. xn,53, 120 14.8.1 Coronal Photometry and Electron Density N e Assuming spherical symmetry, the distribution of coronal intensity 10 as a function of the projected radial distance p may be used to determine the distribution of Ne as a function of radial distance r in Table 14.20. The classical Baumbach expressions [92] are 106/0110 = 0.0532p-2.5 + 1.425p-7 + 2.565p-17, leading to The temperature in the inner corona is well described by the approximation of hydrostatic equilibrium [89] with Thyd = 6.08 x 106 [d (log N e)ld(r- 1)r 1 in K, assuming HIHe = 10. 360 / 14 SUN Table 14.20. Electron densities (log Ne (cm- 3» in coronal structures. r/R0 Coronal streamer Coronal hole (Void) 1.0 1.1 1.3 1.5 2.0 2.5 3.0 4.0 5.0 10.0 8.75 8.25 7.90 7.30 7.0 6.75 6.3 6.1 5.45 7.0 6.6 6.2 5.25 4.80 Thread Loop 10.0 9.5 9.0 8.25 10.0 9.0 Coronal line spectrum quantities are: Tm = temperature (K) at which spectrum reaches greatest intensity, f = energy flux (10- 6 W cm- 2 ) from the coronal line seen outside the Earth's atmosphere, W = equivalent width of coronal line in terms of K continuum, A = transition probability (s-I). Tables 14.21, 14.22, 14.23, and 14.24 give some permitted, forbidden, and infrared coronal lines. Table 14.21. Selected permitted lines, 1-61 nm [1-4]. A (nm) 0.92 1.21 1.36 1.51 1.69 Ion Transition f logTm MgXI Nex, Fe XVII NeIX Fe XVII Fe XVII Is2_1s2p 6.4 Is 2-1s2p 2p6_2p 53d 2p6_2p 53s 2 1 2 8 9 6.20 6.58 6.58 8 6 6 4 85 6.36 5.9 6.14 6.27 5.85 1.90 2.16 5.06 6.97 17.10 Six Fe XIV Fe IX Is-2p Is 2-1s2p 2p-3d 3p-4s 3p6_3p 53d 17.48 17.72 18.04 18.83 19.50 Fex Fex Fe XI Fe XI Fe XII 3p5_3p4 3d 3p5_3p4 3d 3p4-3p 33d 3p4-3p 33d 3p3_3p 23d 90 33 75 40 60 6.00 6.00 6.11 6.11 6.16 20.20 21.13 28.41 30.34 33.54 Fexm Fe XIV Fe xv SiXI Fe XVI 3p2-3p3d 3p-3d 3s 2-3s3p 2s 2-2s2p 3s-3p 25 15 40 30 20 6.21 6.27 6.31 6.22 6.40 Ovm o VII 14.8 CORONA / Table 14.21. (Continued) A (nrn) Ion Transition f 36.81 49.9 61.0 MgIX SiXII Mgx 2s 2-2s2p 2s-2p 2s-2p 15 10 12 logTm 5.97 6.27 6.04 References 1. Batstone, R.M., Evans, K., Parkinson, J.H., & Pounds, K.A. 1970, Solar Phys., 13, 389 2. Walker, A.B.C., & Rugge, R.H. 1970, A&A, S, 4 3. Jordan, C. 1965, Commun. Univ. London Obs., 68 4. Freeman, F.F., & Jones, B.B. 1970, Solar Phys., IS, 288 Table 14.22. Selectedforbidden lines, 100-300 nrn [1, 2]. Ion Transition logTm 124.22 Fe XII 6.16 134.96 Fe XII 144.60 Si VIII 146.70 Fe XI pHS J-2 P J 1'7 1'7 pHS J-2 p\ 1'7 '7 2p3 4 S J-2 D \ 1'7 1 '7 212.60 214.95 216.97 NixIII SiIX Fe XII ADm 6.16 5.93 3p43pI_ l So 6.11 3p43~_ID2 2p23~_ID2 3p3p 4 S J-2 D \ 1'7 2'7 6.27 6.04 6.16 References 1. Jordan, C. 1971, Eclipse of 1970, COSPAR Symp. 2. Gabriel, A.H. et a1. 1971, ApJ, 434,807 Table 14.23. Selectedforbidden lines, 300-700 Dm [1-3]. A (nrn) Ion Transition A (s-I) W (10- 10 DmxB0) 3.72 488 0.07 6.19 5.96 3.44 87 193 1.0 0.13 6.19 6.37 2.93 237 0.11 6.17 Upper E.P. (eV) logTm 332.9 CaxII 2 p 52p \_2pJ 338.82 360.09 Fe XIII NixVI 3p2 31'2_1 D2 3p2p\_2p \ 423.20 NixII 3p5 2 p \ 530.281 Fe XIV 3p2PJ_2 p \ 2.34 60 2.0 6.27 569.44 637.45 Caxv Fex 2p 23J>o_3 PI 3 p 52p \_2p\ 2.18 1.94 95 69 0.03 0.5 6.00 670.19 Nixv 3p23J>o_3 PI 1.85 57 0.12 6.32 1'7 '7 '7 1'7 1'7 '7 1'7 1 '7 '7 References 1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sees. 73, 84, and 85 2. Livingston, W., & Harvey, J. 1982, Proc. lnd NatL Sci. Acad., 48, Suppl. 3, 18 3. Jefferies, J.T., Orrall, F.Q., & Zirker, J.B. 1971, Solar Phys., 16, 103 361 362 / 14 SUN Table 14.24. Near IR lines [I, 2].a f (10- 2 Wm- 2 sr- I ) A- Ion 789.19 1074.617 1079.783 1083.0 1252.0 [Fe XI] [Fe XIII] [Fe XIII] Hel [SIX] 1.5 3p4 3l'7._3 PI 3 p 23J>o_3PI 3p 23PI_3 P2 2p 3 p_2s 3 S }s22s 22p4 3 PI_3 P2 1283.0 1431.0 HI [Six] 3.00 1.55 Paschen (5-3) }s22s 22p 2 P3 _2 P I 1523.0 1856.0 1876.0 [CrxI] [CrxI] HI 0.47 0.4 13.0 1922.0 2167.0 2747.0 3019.0 [SiXI] HI [Alx] [MgvIII] <0.7 <0.5 < 1 <I Transition l l 3s 23p2 3 P2-3 PI 3s 23 p2 3 PI-3 Po Paschen (4-3) }s22s2p 3l'7._3 PI Brackett (7-4) Is 22s2p 3l'7._3 PI }s22s 22p 2 P3 _2 PI l l Note aKuhn [3] points out that many of the IR lines in this table were not observed at the eclipse of 3 Nov. 1994 and questions their reality. References I. Olsen, K.H., Anderson, C.R., & Stewart, J.N. 1971, Solar Phys., 21, 360 2. Penn, M.J., & Kuhn, J.R. 1994, ApJ, 434,807 3. Kuhn, J. 1995, private communication 14.9 SOLAR ROTATION by Robert Howard The inclination of the solar equator to the ecliptic [93-96] is 7°15' . The longitude of the ascending node is 75°46' +84' T, where T is epoch in centuries from 2000.00. The sidereal differential rotation coefficients from the formulas w = A + B sin2 cp deg/day, where cp is the latitude, and w = A + B sin2 cp + C sin4 <I> deg/day, are often used for features that extend to higher latitudes. These are given in Table 14.25. See also [97]. 14.9 SOLAR ROTATION I 363 Table 14.25. Empirical rotation coefficients. B c 14.522 14.39 14.06 14.37 14.71 -2.84 -2.95 -1.83 -2.30 -2.39 -1.62 -1.78 14.48 13.46 14.42 -2.16 -2.99 -2.00 -2.09 A From tracers Individual sunspots [1] SUDSpot groups [I, 2] Plages [3] Magnetic field pattern [4] Supergranular pattern [5, 6] (Doppler features) Filaments, prominences [7] Coronal features [8, 9] Small magnetic features [10] From the Doppler effect in solar lines Surface plasma [11] Ha line [12] 14.11 14.1 -1.70 -2.35 References 1. Howard, R., Gilman, P.A., & Gilman, P.I. 1984, ApJ, 283, 373 2. Balthasar, H., Vazquez, M., & Woehl, H. 1986, A&A, 155, 87 3. Howard, R.F. 1990, Solar Phys., 126,299 4. Snodgrass, H.B. 1983, ApJ, 270, 288 5. Duvall, Jr., T.L. 1980, Solar Phys., 66, 213 6. Snodgrass, H.B., & Ulrich, R. 1990, ApJ, 351, 309 7. d' Azambuja, M., & d' Azambuja, L. 1948, Ann. Observ. Paris, 6, 1 8. Dupree, A.K., & Henze, Jr., W. 1972, Solar Phys., 27, 271 9. Henze, Jr., W., & Dupree, A.K. 1973, Solar Phys., 33, 425 10. Komm, R.W., Howard, R.F., & Harvey, I.W. 1993, Solar Phys., 145, 1 11. Snodgrass, H.B., Howard, R., & Webster, L. 1984, Solar Phys., 90, 199 12. Uvingston, W.C. 1969a, Solar Phys., 7,144; 1969b, 9, 448 Rotation of solar plasma as a function of depth from oscillation measurements increases from the surface rate by about 0.8 deglday at a depth from 0.01R0 to 0.08R0 , then decreases slowly with depth [98,99]. The period of sidereal rotation adopted for heliographic longitudes is 25.38 days. The corresponding synodic period is 27.2753 days. Conversion factors between different units are given in Table 14.26. Table 14.26. Conversion/actors. To convert from Multiply by deglday to p.rads- 1 deglday to ms- 1 degldaytooHz 0.20201 140.596 cos 1/1 32.150 Sidereal-synodic rotation = Earth's orbital motion = 0.9856 deglday (averaged over a year). 364 I 14.10 14 SUN GRANULATION by Richard Muller The solar surface is covered by a hierarchy of patterns that are convective in origin: granulation, mesogranulation, and supergranulation [98-109]: Granules Diameter of granules Range about 0~'25 to 3~'5 Intergranular distance Number of granules on whole photospheric surface Corresponding area occupied by a cell Granule intensity contrast Brighter granule/intergranule Corresponding temperature difference Root-mean-square variations Intensity at 550 nm observed Corrected Temperature Mean lifetime of granules Upward velocity of brighter granules 14.11 1~'4 = 1000 km t'o 5 x 106 1.5 x 106 km2 1.3 300K 0.09 0.15 IIOK 10 min 1 km s-1 Mesogranulation Diameter Lifetime Vertical velocity Proper motion 5000km 3h 0.06 km s-1 0.4kms- 1 Supergranulation Diameter Lifetime Horizontal velocity to edge 32000km 20h 0.4 kms- l SURFACE MAGNETISM AND ITS TRACERS by Peter Foukal, Sami Solanki, and Jack Zirker Buoyancy lofts magnetic fields from the solar interior into the photosphere where they emerge as active regions to be dispersed laterally under the influence of convection (various scales) and other largescale horizontal flows. White light tracers of magnetism are sunspots and faculae. Monochromatic tracers (line weakening) are plage, filigree, the network, internetwork, coronal holes, and prominences. The network and plages are presumed to be composed of aggregates of flux tubes. Prominences are found along magnetic neutral lines or above active regions. Magnetic field details for various surface structures are given in Table 14.27. 14.11 SURFACE MAGNETISM AND ITS TRACERS / 365 Table 14.27. Magneticfields. a Field strength Sunspot umbrae Sunspot penumbrae Pores Plage or facular magnetic elements B (z Network magnetic elements B (z = 0) Internetwork = 0) 2-4 kG 0.8-2 kG 1.7-2.5 kG 1.4-1.7 kG 1.3-1.5 kG :::: 600 G (probably) Aux [1] 3 x 1019 Mx 3 x 1020 Mx 3 x 102 1 Mx ::: 1022 Mx (20-50) x 1022 Mx Ephemeral region Small active region Moderate active region Large active region Giant active region = Magnetic elements Diameter [2, 3] Lifetime [4] 200-300km 18 min Global aspects [1] = (15-20) x 1022 Mx = (100-120) x 1022 Mx Total flux at solar min Total flux at solar max Note aThe field strength is strongly height dependent. See Sec. 14.12 on sunspots for more information on sunspot field gradients. For magnetic elements the field drops from the tabulated values at z 0 (i.e., the quiet Sun continuum forming layer) to roughly 200-500 G (in plage) near the temperature minimum (e.g., [6] and [7]). The magnetic element lifetime [5] is probably only a lower limit, being a lifetime measurement of the brightness structure that probably lives less long than the underlying magnetic structure. There is no permanent dipole field but one develops over solar cycle due to evolution of polar fields; at other times there is a dipole component to lower-latitude extended active-region fields [8,9]. Mx means maxwell (Gcm2). = References 1. Harvey, K. 1992, in Proceedings of the Workshop on Solar Electromagnetic Radiation Study for SOLAR CYCLE 22, edited by R.F. Donnelly (Nat!. Info. Tech. Service, Springfield, VA), p. 113 2. Keller, C.U. 1992, Nature, 359, 307 3. Grossmann-Doerth, U., Knolker, M., Schiissler, M., & Solanki, S.K. 1994, A&A, 285,648 4. Muller, R. 1985, Solar Phys., 100,237 5. Deming D., Boyle, R.J., Jennings D.E., & Wiedemann, G. 1988, ApJ, 333, 978 6. Zirin, H., & Popp, B. 1989, ApJ, 340, 571 7. Sheeley, Jr., N.R., & Boris, J.P. 1985, Solar Phys., 98, 219 8. Wang, Y.M., & Sheeley Jr., N.R. 1989, Solar Phys., 124, 81 14.11.1 Faculae Faculae are cospatial with photospheric magnetic fields. They become visible in white light near the limb (i.e., as p, = cos (J .... 0). While fragmented and irregular, they do tend to outline the circular boundaries of supergranular cells [112, 113]. The center-to-limb dependence of wide-band facular contrast (integrated over the spectral range 0.35-1.0 p,m) can be expressed as C(p,) - 1 = 0.115(1 - p,), 366 / 14 SUN where C(/L) = Iracula/ [photosphere [114]. At the highest spatial resolution values of C(/L) increase by a factor of 3-4 [115]. The wavelength dependence of facular contrast is approximately given by where C5300(/L) is the intensity of the faculae relative to the photosphere at 5300 A [116]. Life of average faculae Life of large faculae (dominating solar variations) 15 days 2.7 months The excess temperature of magnetic elements [117, 118] is given in Table 14.28. Table 14.28. Excess temperatures. iog1"5000 Piage: TMagel - Tphot (K) Network: TMagel - Tphot (K) -5 -4 -3 -2 -1 1400 1400 1500 1500 650 700 500 700 560 770 0 -130 460 14.11.2 Plages Plages or bright flocculi are readily visible in Hex and in the H and K lines of Ca II. The locations agree well with faculae but plages are visible over the whole disk. Measurements of area and eye estimates of intensity (scale 1 ~ 5) are made regularly [119]. Table 14.29 shows the approximate relation between plage area and sunspot area (both in 10-6 hemisphere). Table 14.29. Plage and sunspot areas. Piage area Sunspot area 500 0 1000 30 2000 100 3000 180 4000 280 6000 500 8000 900 10000 2000 Since the duration of the plage is longer than that of the spot, the spot area may be much less than the value given. Normally sunspots are present when the plage intensity is 2: 3. The exponential decay time of a plage observed area is 1.6 rotations (43 days). The actual area of a plage expands continuously but the fainter parts are below measurement threshold. Values for a typical large active region [115] are: Sunspot area Plage area Plage area at disk center Plage diameter 600 x 10-6 hemisphere. 6000 x 10-6 hemisphere. 12000 x 10-6 disk. 3.5 arcmin. 14.12 SUNSPOTS / 14.11.3 367 Prominences Table 14.30 shows the physical conditions in quiescent prominences. Table 14.30. Quiescent prominences. log [electron density (cm- 3)] Temperature (K) 10.48-11.02 [1] 9-10 5000-7000 20000-600000 [2] References 1. Hirayama, T. 1986, Coronal and Prominence Plasmas, edited by A.l. Poland (NASA, Washington, DC), p. 2442 2. Orrall, F.Q., & Schmahl, EJ. 1980, ApJ, 240, 908 The temperature varies considerably within a prominence. The proton-to-hydrogen density ratio is 0.05 < N p / NH < 1 [120]. Sizes Threads [121] Height Length Thickness Magnetic field (horizontal) Velocity 300-1800 km (diameter). 2000 kIn (active), 10000-50000 kIn (quiescent). 50000-200 000 kIn. 3000-5000 km. 2-20 G (quiescent) [122], 10-40 G (active). 15-35 kIn s-1 (threads, apparent) [123], 1-3 kIns- 1 (Doppler, horizontal) [124], 2-10 kIns- 1 (turbulent). The angle of the field with the axis of the prominence'" 20° [122]. Lifetimes are approximately 1 week to 3 months; the average is 2 months. 14.12 SUNSPOTS by Sami Solanki The formula for the center-to-limb variation of umbra! brightness (1 2: f.L > 0.3) is iu = Iu/1q, where Iq is the quiet Sun brightness, and ip given in Table 14.31. = Ip/lq. Brightness data for sunspots are 14 368 I SUN Table 14.31. Center-to-limb variation and A dependence of umbra I and penumbral brightness [1-4]. A (IAom) iu (lAo iu (lAo iu (lAo = I, A)early = I, A)middle = I, A)late bu (A) ip (lAo = l,A) 0.387 0.579 0.669 0.876 1.215 1.54 1.67 1.73 2.09 2.35 0.008 0.022 0.066 0.110 0.061 0.090 0.119 0.191 0.215 0.239 0.327 0.345 0.358 0.451 0.495 0.534 0.507 0.548 0.590 0.543 0.577 0.612 0.567 0.589 0.611 0.565 0.581 0.597 -0.010 0.012 0.009 0.019 0.031 0.087 0.087 0.094 0.090 0.058 0.64 0.768 0.794 0.827 0.876 0.914 0.928 References 1. Albregtsen, F., & Matby, P. 1978, MaJ., 274, 41 2. Albregtsen, F., JorAs, P.B., & Matby, P. 1984, Solar Phys., 90, 17 3. Maltby, P. 1972, Solar Phys., 26, 76 4. Matby, P., Avrett, B.B., Carlsson, M., Kje1dseth-Moe, 0., Kurucz, R.L., & Loeser, R. 1986, ApI, 306, 284 A model for the sunspot umbral core is given in Table 14.32. Table 14.32. Model of the dark umbral core [1-4]. log 1" T (K) log Pg (egs) log Pe (egs) z (kIn) 6140 5.78 2.01 -94 0 -1 -2 -3 -4 -5 -6 4040 3540 4.91 -0.28 95 3420 4.28 -0.80 220 3400 3.64 -1.28 380 3450 2.95 -1.75 600 6400 0.99 -1.96 1115 8700 -0.61 -1.04 1850 5.43 0.52 0 References 1. Maltby, P., Avrett, B.A., Carlsson, M., Kje1dseth-Moe, 0., Kuruez, R.L., & Loeser, R. 1986,ApJ,306,284 2. Avrett, E.B. 1981, in The Physics of Sunspots, edited by L.E. Cram and J.B. Thomas (Sacramento Peak Obs., Sunspot, NM), p.235 3. Van Bal1egooijen 1984,A&A, 91,195 4. Obridko, V.N., & Staude, J. 1988, A&A, 189,232 Magnetic field data for sunspots are given in Tables 14.33 and 14.34. Table 14.33. Maximum magneticjield BO as afunction ofumbral radius ru [1,2]. ru (kIn) BO (G) 500 2000 1000 2000 2000 2000 4000 2300 6000 2700 References 1. Brants, J.J., & Zwaan, C. 1982, Solar Phys., 80, 251 2. Kopp, G., & Rabin, D. 1992, Solar Phys., 81, 231 8000 3100 10000 3500 3.8 0.936 14.12SUNSPOTS / 369 Table 14.34. Relative magnetic field B / BO and its inclination y' relative to the vertical versus position in spot r Jor a large symmetric sunspot [I-51. r/rp 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 B/ BO y' (deg) 1 0 0.99 7 0.96 15 0.92 24 0.84 35 0.74 48 0.62 58 0.50 66 0.41 73 0.35 77 0.30 80 References 1. Solanki, S.K., Riiedi, I., & Livingston, W. 1992, A&A, 263, 339 2. McPherson, M.R., Lin, H., & Kuhn, J.R. 1992, Solar Phys., 139, 255 3. Lites, B.W., & Skumanich, A. 1990, ApJ, 348, 747 4. Kawakami, H. 1983, PASJ, 35, 459 5. Adam, M.G. 1990, Solar Phys., 125,37 The azimuthal angle of the field is ljJ ~ 20° for symmetric sunspots. In the penumbra y' is an average value, with bright and dark filaments inclined relative to each other by 20°-40° [125-127]. In the outer penumbra the inclination depends on the size of the sunspot, with smaller sunspots having more vertical fields [128]. Table 14.35 gives structure details of the outer parts of sunspots. Table 14.35. Superpenumbral canopy: Base height Zc as a function oj distanceJrom center oJ spot r/rp normalized by the spot radius rp [1,21. r/rp 1.0 1.2 1.4 1.6 Base height Zc (km) B/BO y' (deg) o 200 0.21 86 300 0.15 89-90 350 0.11 89-90 0.30 80 References 1. Giovanelli, R.G. 1980, Solar Phys., 68, 49 2. Giovanelli, R.G., & Jones, H.P. 1982, Solar Phys., 79, 267 Table 14.36 gives the magnetic field gradients in sunspots. Table 14.36. Vertical gradient oj the field [1-7]. r/rp 0.0 0.6 1.0 dB/dz in photosphere (GIkm) dB/dz in photosphere and chromosphere (GIkm) 2 0.5 2 0.4 0.2 1 References 1. Bruls, J.H.M.J., Solanki, S.K., Carlsson, M., & Rutten, R.J. 1993, A&A, 293, 225 2. Abdussamator, HJ. 1971, Solar Phys., 16, 384 3. Henze, N., Jr., Tandberg-Hanssen, E., Hagyard, M.J., Woodgate, B.E., Shine, R.A., Beckers, J.M., Bruner, M., Gurman, J.B., Hyder, L.L., & West, E.A. 1982, Solar Phys., 81, 231 4. Lee, J.W., Gary, E.E., & Hurford, GJ. 1993, Solar Phys., 144,45 and 349 5. Riiedi, I., Solanki, S.K., & Livingston, W. 1994, A&A, 293, 252 6. Whittman, A.D. 1974, Solar Phys., 36, 29 7. Pahlke, K.-D. 1988, Ph.D. thesis, University of Gottingen, Gottingen, Germany 370 / 14 SUN Wilson depression. The apparent depression of '[' and derived from MHS equilibrium [133, 134] is ZW = 1 of the umbra seen near the limb [129-132] = 600 ± 200 kIn. The relative magnetic flux in umbra and penumbra [135], with <l>t the total magnetic flux of spot, <l>u the magnetic flux of the umbra, and <I> p the magnetic flux of the penumbra, is = 1/3 <l>p/<I>t = 1/2 - 1/2, <l>u/<I>t 2/3. The variation of the umbral-to-photosphere intensity ratio rp with solar cycle (at A = 1.67 /Lm) is rp = 0.44 + 0.15t/to, where t is the time elapsed from the starting epoch and to is the length of the solar half-cycle [136]. The average East-West inclination of field lines in spots is all spots leading following spots -3?4, -2?8, -3?8. The negative angle indicates that the field lines trail the rotation [137]. Sunspot axial tilt angles (individual sunspots) are the angles between the line joining the leading and following spots of a group and the local parallel of latitude. The leading spots on average are closer to the equator than the following spots as a function of latitude with the value of about 2° at the equator to about 12° at ±35° latitude [138-141]. The area distribution of individual sunspots can be described as a two-parameter log-normal distribution [142]: In = _ (In + In dA 2lnua dA max (dN) A-In{A})2 (dN) in terms of sunspot umbral area A (in units of 1O-6 2rr R~). Values of the three other quantities in the above equation (Table 14.37) depend somewhat on the range ofumbral areas used to derive them: Table 14.37. Sunspot area distribution. Range (A) 1.5-141 5.5-116 0.62 0.34 (dN/dA)max 3.8 4.8 9.2 16.4 14.13 SUNSPOT STATISTICS by Karen Harvey and Robert M. Wilson The sunspot number is defined as R = k(10g + s), where k is an observatory reduction constant of order unity, g is the number of sunspot groups, and s is the total number of individual spots [143-145]. Prior to January 1981, R was referred to as the Zurich sunspot number. From January 1981 on, R has been referred to as the International sunspot number. 14.13 SUNSPOT STATISTICS / 371 Monthly values of R are combined to yield the 12-month moving average of R (denoted Ro), which is also known as the smoothed sunspot number [146]. For a cycle, the minimum value of Ro denotes the sunspot minimum (Rm), while the maximum value denotes the sunspot maximum (RM). Conventionally, the length of a sunspot cycle is determined from minimum to minimum (m ~ m) and is comprised of two parts: the ascent interval, the time from minimum to maximum (m ~ M), and the descent interval, the time from maximum to succeeding cycle minimum (M ~ m). Occasionally, the time between maxima is also of interest (M ~ M). Each sunspot cycle is numbered with the most recent sunspot cycle being cycle 22 (Rm occurred in September 1986 and RM occurred in July 1989). The sunspot record is of uneven quality [144]. The most reliable sunspot data extend from the present back to about 1850 and 1818 (covering cycles 7-9), while data of poor quality occur for earlier times (cycles before cycle 7). Some evidence exists suggesting that there was an extensive period of time when sunspots were few in number [147]. This interval of time (ca. 1645-1715; cycles -9 to -4) is often referred to as the Maunder minimum. Other information from the sunspot record follows: Waldmeier effect. The sunspot amplitude (RM) varies inversely with the ascent duration (m ~ M). Hale cycle. The magnetic polarity changes in alternate cycles (even-numbered cycles have leading spots of southern polarity in the northern hemisphere, and vice versa). Sporer law. The latitude of sunspots progresses equatorward with the phase of the solar cycle (yielding the so-called butterfly diagram). Odd-even effect. The odd-following cycle tends to be of larger amplitude than the even-preceding cycle. Gleissberg effect. Sunspot cycles vary according to an 8-cycle variation (the so-called 80--100 year variation). Tables 14.38 and 14.39 list the sunspot number variations over the solar cycle. Table 14.38. Variation of the annual sunspot number over the solar cycle (based on the reliable data of cycles [10-21 J). a Elapsed time (yr) from sunspot minimum occurrence year Parameter 0 Mean Standard deviation High Low 6.2 5.9 2804 0.0 18.9 16.7 89.2 0.0 2 3 4 5 6 7 8 9 10 60.2 38.6 201.3 9904 50.0 253.8 24.5 107.0 41.1 202.5 39.3 98.5 36.6 21704 17.8 79.1 27.6 153.8 3404 5204 19.7 108.5 14.8 36.5 19.6 8804 0.3 21.2 1304 60.7 1.6 12.0 lOA lOA 55.8 0.2 Note aYalues listed are monthly mean values based on cycles 10-21 only. Table 14.39. Variation of the smoothed sunspot number over the solar cycle (based on the reliable data of cycles [10-21]).a Elapsed time (month) from Rm Parameter 0 12 24 36 48 60 72 84 96 108 120 132 Mean Standard deviation High Low 5.1 3.2 12.2 1.5 18.6 6.1 26.3 9.3 61.6 23.9 118.7 35.5 98.0 41.2 181.0 52.5 109.2 41.3 196.8 54.5 99.3 33.9 169.2 56.9 79.9 25.9 119.6 48.0 5204 14.9 70.5 31.2 34.7 13.9 60.6 13.8 2004 9.8 41.3 11.5 11.7 8.3 30.3 3.2 11.7 704 1504 2.6 Note aYalues listed are smoothed sunspot number values based on cycles 10-21 only. Characteristics of all the known sunspot cycles are listed in Table 14.40. Mean values are listed in Table 14.41. 372 I 14 SUN 1Bble 14.40. Characteristics of sunspot cycles [1]. a Data quality p MaximumM epoch RM Cycle -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1615.5 1626.0 1639.5 1649.0 1660.0 1675.0 1685.0 1693.0 1705.5 1718.2 1727.5 1738.7 1750.3 1761.5 1769.8 1778.4 1788.2 1805.2 1816.3 F 7 8 9 R 10 11 12 13 14 15 16 17 18 19 20 21 22 Minimumm epochRM Intervals (yr) m_m m_M M_m 4.7 7.0 5.5 4.0 5.0 9.0 5.5 3.5 7.5 6.2 4.0 4.7 5.3 6.2 3.3 2.9 3.4 6.8 5.6 3.5 8.0 5.5 6.0 6.0 4.5 4.5 5.0 6.5 5.3 6.5 6.3 4.9 5.0 5.7 6.4 10.2 5.5 7.1 M_M 92.6 86.5 115.8 158.5 141.2 49.2 48.7 1610.8 1619.0 1634.0 1645.0 1655.0 1666.0 1679.5 1689.5 1698.0 1712.0 1723.5 1734.0 1745.0 1755.3 1766.5 1775.5 1784.8 1798.4 1810.7 8.4 11.2 7.2 9.5 3.2 0.0 8.2 15.0 11.0 10.0 11.0 13.5 10.0 8.5 14.0 11.5 10.5 11.0 10.3 11.2 9.0 9.3 13.6 12.3 12.7 1829.9 1837.3 1848.2 71.7 146.9 131.6 1823.4 1833.9 1843.6 0.1 7.3 10.5 10.5 9.7 12.4 6.5 3.4 4.6 4.0 6.3 7.8 13.6 7.4 10.9 1860.2 1870.7 1840.0 1894.1 1906.2 1917.7 1928.3 1937.3 1947.4 1958.3 1968.9 1980.0 1989.6 97.9 140.5 74.6 87.9 64.2 105.4 78.1 119.2 151.8 201.3 110.6 164.5 158.5 1856.0 1867.3 1879.0 1990.3 1902.1 1913.7 1923.7 1933.8 1944.2 1954.3 1964.8 1976.5 1986.8 3.2 5.2 2.2 5.0 2.6 1.5 5.6 3.4 7.7 3.4 9.6 12.2 12.3 11.3 11.7 10.7 11.8 11.6 10.0 10.1 10.4 10.1 10.5 11.7 10.3 4.2 3.4 5.0 3.8 4.1 4.0 4.6 3.5 3.2 4.0 4.1 3.5 2.8 7.1 8.3 6.3 8.0 7.5 6.0 5.5 6.9 6.9 6.5 7.6 6.8 12.0 10.5 13.3 10.1 12.1 11.5 10.6 9.0 10.1 10.9 10.6 10.5 13.5 9.5 11.0 15.0 10.0 8.0 12.5 12.7 9.3 11.2 11.6 ILl 8.3 8.6 9.8 17.0 ILl ILl 9.6 Note aR denotes a "reliable" data interval, F denotes a ''fair'' interval, and P denotes a "poor" interval. Reference 1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd cd. (Athlone Press, London), Sec. 87 1Bble 14Al. Mean values for selected sunspot cycle parameters. Mean value Parameter R R+F All (R+F+ P) m _ M _ m _ M _ RM Rm 10.9 10.9 3.9 7.0 119.6 5.7 10.9 10.8 4.0 6.8 119.0 5.7 11.0 11.0 4.7 6.3 112.9 6.0 m period (yr) M period (yr) M ascent interval (yr) m descent interval (yr) 14.14 FLARES AND CORONAL MASS EJECTIONS / 373 Table 14.42 shows how certain solar activity characteristics vary throughout the sunspot cycle. Table 14.42. Solar activity. 0 Year Minimum 1 2 3 5 4 Maximum 6 7 8 9 10 11 Sunspot regions R new cycle R old cycle Spot latitude 68 9 24 237 7 22 488 3 19 547 561 510 360 269 168 99 38 13 17 14 13 12 10 9 8 7 6 Low To high 16 42 7 39 3 1 42 0 33 0 28 0 24 0 20 1 16 1 9 Latitude range 40 0 38 0 37 Characteristics of an average size sunspot group: Sunspot number Number of individual spots Spot area (umbra + penumbra) = 12. 10. 200 millionths of hemisphere, 260 millionths of disk. Spot radius (if a single spot) Ca II plage area O.020R 0 · R 1800 millionths of hemisphere. 14.14 FLARES AND CORONAL MASS EJECTIONS by Steve Kahler 14.14.1 Flares Chromospheric (Cool) Component of Flares [148, 149] The Hex line importance classes are detailed in Table 14.43. Table 14.43. Classes of optical importance in the Ha line. Ha importance Area (10- 6 hemisphere) Mean duration S 1 2 A < 200 200 < A < 500 500 < A < 1200 1200 < A < 2400 A> 2400 few minutes 25 min 55 min 2hr 2hr 3 4 Ha brilliance: f = faint. n = nonnal. b = bright Temperature - 15000 K Density - 3 x 1013 cm- 3 374 / 14 SUN Frequency of observed importance ~ 1 flares: Frequency near solar maximum Frequency near solar minimum 1000-2000 flares per year. 20--60 flares per year. White-light flares [150, 151]: Frequency near solar maximum Luminosity '" 15 per year. 1027 _1028 erg s-1 . Coronal (Hot) Component [152] Classes of soft X-ray (1-8 A) peak fluxes measured at 1 AU: Bn Mn =n x = 10-7 Wm- 2 , n x 10-5 Wm- 2 , en Xn =n x = 10-6 Wm- 2 , n x 10-4 Wm- 2 • Frequency of 1-8 A flares [153]: Frequency of ~ Ml flares near solar maximum Frequency of ~ Ml flares near solar minimum Peak temperatures Peak emission measures (n;V) Density '" 500 per year. '" 15 per year. (8-22) x 106 K. 1048-1050 cm- 3 . 1010_10 12 cm- 3 . Impulsive Component The duration is from < 1 min to > 30 min; the median duration'" 100 s. The y-ray fluence [154] from < 10 to 104 y cm- 2 at > 300 keY; from < 0.3 to 3 x 102 y cm-2 for 4-8 MeV lines. For hard X-rays [155, 156]: Peak flux at E > 20 keY from < 10-6 to > 10-3 ergcm- 2 s-l. Spectra: 3 < y < 9, where N(E) = AE-Y photons cm- 2 s-l keV- 1• Thermal fits yield T ~ 108 K. For EUV (10--1030 A) [157]: Peak fluxes from < 3 x 10-2 to 10 ergcm- 2 S-l. Temporal profiles match those of E > 10 keY X-rays. For microwaves (1000-35000 MHz) [156]: Peak fluxes from < 10 to ~ 104 solar flux units (s.f.u.) (10- 22 W m- 2 Hz-I). Temporal profiles match those of E > 20 keY X-rays, and flux (E > 20 keY) (ergcm- 2 s- 1) '" 10-7 x flux (3 cm) (s.f.u.). 14.14.2 Coronal Mass Ejections Most coronal mass ejection (CME) quantities range over about two orders of magnitude. Average values follow [158-161]: Mass Kinetic energy 3 x 1015 g. 2 x 1030 erg. 14.15 SOLAR RADIO EMISSION / 375 Speeds (of leading edges) at solar maximum at solar minimum Angular width (plane of sky, subtended to solar disk) Frequency [162] at solar maximum at solar minimum 450 kms- I . 160kms- l . 47°. 2-3 CMEs per day. 0.1--0.3 CMEs per day. 14.15 SOLAR RADIO EMISSION by Timothy Bastian Solar radio emission is expressed quantitatively in terms of the flux density Sv, usually in solar flux units (s.f.u.), where 1 s.f.u. = 10- 22 W m- 2 Hz-I. For observations that spatially resolve the source of radio emission, the intensity of the radiation is often expressed in terms of its brightness temperature TB, where Sv = 7.22 x 1O- 51 TBV 2 Wm- 2 arcsec- 2 Hz-I. Tc refers to the brightness temperature at the center of the solar disk. The degree of polarization, Pc, is defined by the ratio of the Stokes polarization parameters V and I. Expressed in terms of brightness temperature in the orthogonal (right- and left-hand) senses of circular polarization, Pc = (TRCP - hcp)/(TRCP + hcp), where the RCP sense corresponds to a counterclockwise rotation for radiation propagating toward the observer. 14.15.1 Properties of Radio Emission from the Quiet Sun The brightness temperature of the quiet Sun at disk center may be calculated approximately from the following expressions for millimeter and centimeter wavelengths (Tc in K, U = loglo A, A in cm): log Tc = 3.9609 + 0.1856u + 0.0523u 2 + 0.13415u 3 + 0.0834u 4 , valid between 0.1 and 20 cm; log Tc = 0.7392 + 4.3185u - 0.9049u 2 , valid for A = 20--2000 cm. The fits are based on [163-165]. 14.15.2 Properties of Radio Emission from Solar Active Regions Meter and Decameter Wavelengths Storm continua and type I bursts (see below and [166]) are often associated with solar active regions. Type I storm durations range from hours to days and are distinguished by high values of pc, bandwidths of a few times 10 MHz, and apparent brightness temperatures < 10 10 K. Decimeter and Centimeter Wavelengths Decimetric and microwave emission associated with active regions is characterized by [167,168] a diffuse morphology for A i2: 10 cm and a low to moderate degree of circular polarization PC ;S 15%. Its brightness is typical of coronal temperatures [TB '" (1-2) x 106 K]. For A ;S 10 cm, the diffuse morphology gives way to one or more compact components associated with sunspot umbrae 376 I 14 SUN and penumbrae that possess a degree of polarization that ranges from low (pc "" few %) to high (pc ;::: 90%) values. The brightness of compact components is again near coronal values. Radio emission associated with solar active regions typically possesses a spectral maximum in flux density between 8 and 10 em [169]. 14.15.3 Properties of Solar Radio Bursts (Flares) Meter Wavelengths (i) 'JYpe I [166, 170]: Frequency· range Bandwidth Duration Brightness Polarization Fine structure (ii) 'JYpe IT [171]: Frequency range Bandwidth Frequency drift rate Duration Brightness Polarization Fine structures (iii) 'JYpe m [172]: Frequency range Frequency drift rate Duration Brightness Polarization Variants (iv) 'JYpe IV [173, 174]: Frequency range Bandwidth Duration Brightness Polarization Variants 150-350 MHz. 2.5-7 MHz (...... 0.025v MHz; v in MHz). 0.2-0.7 s (...... 80/v s). As high as 107_10 10 K. Up to 100% circularly polarized. Chains, periodic variations. < 20-150 MHz; harmonic structure in 60%. ...... IOOMHz. ...... 1 MHzs- l . 5-15 min. 107_10 13 K. Unpolarized or weakly circularly polarized; herringbone structure sometimes displays ...... 50% circular polarization. Band splitting, multiple lanes, herringbone structure. Full range; harmonic structure common, 1-100 MHz. -O.Olvl.84 MHzs- l . ...... 220v- 1 s. 108_10 12 K. Pc ;S 15% (harmonic); Pc ;S 50% (fundamental). 'JYpe J and type U bursts. 20-200 MHz. Broadband continuum. 3-45 min. < 108_10 10 K. Pc ;S 20% (early), often increasing to high values for events with durations longer than 20 min. Moving type IV, slow-drift continuum, type IT-associated, pulsations. 14.15 SOLAR RADIO EMISSION / 377 (v) Type V [172]: Frequency range Bandwidth Duration Brightness Polarization < 10-120 MHz. Broadband continuum. '" 500v- I / 2 s. 107 _10 12 K. Pc ;S 10%, decreasing from disk center-tolimb, sense of polarization usually opposite to that of preceding type III bursts. Decimeter Wavelengths [175] (i) Type III-like or fast-drift bursts: Bandwidth Variable. Duration 0.5-1.0 s. Drift rate > 100 MHz s-I. Variants Classical type III and type U bursts, dm extensions to type 111m bursts, narrowband type III bursts (blips), long duration type III bursts. (ii) Pulsations: Bandwidth Few x 100 MHz. Periods Pulses recur periodically or quasiperiodically with separations of 0.1-1.0 s. Duration Groups of pulses (10-100 s) last from seconds to minutes. Quasiperiodic pulsations (regular, long period), Variants dm pulsations (irregular, short period). (iii) Diffuse continua or type IV-like bursts: Bandwidth Duration Variants (iv) Spikes: Bandwidth Duration Variants Few x 100 MHz. 10 s of seconds to minutes. Smooth continua, modulated continua, ridges. Few MHz. < 0.1 s individually, with groups (10-104 ) occurring in broadband clusters during some seconds to minutes. Type III-associated spikes, type IV-associated spikes. 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'!ypical subscripts: V = visual, B = blue, U = ultraviolet, pg = photographic, pv = photovisual, bol = bolometric (total radiation); in general, mA. = apparent magnitude of spectral region A. mu, mB, mv = apparent magnitudes in the UBV system. absolute magnitude = apparent magnitude standardized to 10 pc without interstellar absorption. color index; (B - V)o = intrinsic color index (i.e., no interstellar absorption); or, in general a color index is the difference in the apparent magnitude as measured at two different wavelengths. bolometric correction = mbol - V (always negative). space absorption in magnitudes (usually visual). = = 381 382 I 15 mo EB- V m- M mo - M NORMAL STARS = magnitude corrected for absorption = m = color excess = (B - V) - (B - V)o. = distance modulus = Slog d - S + A. A. = distance modulus corrected for absorption = Slog d - S, where d is distance in parsecs (pc). F = total radiant flux at stellar surface. f = radiant flux for a star outside the Earth's atmosphere. Teff = stellar effective temperature (from F = (7 Te where (7 is Stefan's constant. Vrot = equatorial rotational velocity. g = surface gravity (cm s-2). d = distance, usually in parsecs (pc). 7r = parallax in seconds of arc (") = lid, with d in pc. 1r), All the logarithms in this chapter are common logs with a base of 10. 15.1.1 Numerical Relations = m + S + Slog 7r - A = m + MhoJ = -2.5 log LI L0 + 4.74, M S - Slog d - A, where L0 = 3.84S x 1033 ergs s-J, and +4.74 is the absolute bolometric magnitude of the Sun. The bolometric correction is the difference between the absolute visual and absolute bolometric magnitude: Be = MboJ- Mv. Bolometric luminosities, radii, and effective temperatures are related by MhoJ = 42.36 - Slog RI R0 - 10 log Teff, where solar values of MhoJ0 = 4.74 and Teff0 = S777 K have been adopted. = -3.147 + 2 log R + 4 log Teff, (mhoJ = == 2.48 x 10-5 erg cm- 2 s-l outside the Earth's atmosphere, (MboJ = 0) star == 2.97 x 1028 watts emitted radiation, (Mv = 0) star == 2.4S x 1029 candela. log L 0) star The zero age main sequence (ZAMS) is represented by [1] logRIR0 = 0.640 log M/M0 +0.011 log R/ R0 = 0.917 log M/ M0 - 0.020 (0.12 < logM/M0 < 1.3), (-1.0 < logM/M0 < 0.12). The mass-luminosity relation may be written [2,3]: logM/M0 = 0.48 - O.1OSMboJ for -8::; MhoJ < 1O.S, or logL/L0 = 3.81ogM/M 0 + 0.08 for M > 0.2M0. 15.2 SPECTRAL CLASSIFICATION / 383 Another representation is [4] logM/M0 logM/M0 = 0.46 = 0.75 - O.lOMboJ. Mbol < 7.5, 0.145Mbol, Mbol > 7.5. The most reliable stellar masses are summarized in [5] and [6]; also, see the discussion in [2]. 15.2 SPECTRAL CLASSIFICATION We define normal stars to be those which can be classified on the MK system (specifically, [7,8], and more generally [9]), or which are classified as white dwarfs according to the system described in [10]. Table 15.1 gives these classes. Table 15.1. MK spectral classes. MK spectral class o B A F G K M Class characteristics Hot stars with He II absorption He I absorption; H developing later Very strong H, decreasing later; Ca II increasing Ca II stronger; H weaker; metals developing Ca II strong; Fe and other metals strong; H weaker Strong metallic lines; CH and CN bands developing Very red; no bands developing strongly The spectral classes are further subdivided into decimal subclasses (e.g., BO, Bl, B2, etc.), although not all subdivisions are used, and some classes are further subdivided (e.g., 09.5). Table 15.2 lists the MK luminosity classes. Table 15.2. MK luminosity classes. MK luminosity class Examples I supergiants II bright giants mgiants IV subgiants V dwarfs (main sequence) BOI B5 II GOm G5IV GOV The luminosity classes are further subdivided (e.g., la, lab, Ib, etc.). The MK classification is based on the appearance of pairs of spectral lines in the blue spectral region at a spectral resolution of approximately 2 A, as compared to standard stars [7,8]. The main line pairs are as shown in Table 15.3 and are illustrated in [11], [12], and [13]. Table 15.3. Line pairs for spectral classes and luminosity. Class Line pairs for class Class Line pairs for luminosity 05<:>09 BO<:>BI B2<:>B8 4471 He I14541 He II 4552 Si nIl4089 Si IV 4128-30 Si 1114121 He I 09~B3 4116-21 (Si IV, He 1)/4144 He I 3995 N III4009 He II Balmer line wings BO~B3 Bl ~A5 384 I 15 NORMAL STARS Table 15.3. (Continued.) Class Line pairs for class Class Line pairs for luminosity B8~A2 4471 He 114481 Mg II 4026 He 113934 Ca II 4030-34 Mn I14l28-32 4300 CHl4385 4300 (G band)/4340 Hy 4045 Fe 114101 H8 4226 Ca I14340 Hy 4144 Fe 114101 H8 4226 Ca I14325 429014300 A3~FO 4416/4481 Mg II FO~F8 417214226 Ca I F2~K5 4045-63 Fe 114077 Sr II 4226 Ca I14077 Sr II Discontinuity near 4215 421514260, Ca I increasing A2~F5 F2~K F5~G5 G5~KO KO~K5 G5~M K3~M Other characteristics sometimes included with MK types: e f p n s k m = emission lines, e.g., Be; = certain 0 type emission line stars; = peculiar spectrum; = broad lines; = sharp lines; = interstellar lines present; = metallic line star. Additional classes [2] are shown in Table 15.4. Table 15A. Additional spectral classes Spectral class S R(orC) N (orC) IS.2.1 Class characteristics Strong bands of ZrO and YO, LaO, TiO Strong bands of CN and CO instead of TiO in class M Swan bands of C2, Na I (D), Ca I 4227, for the rest similartoR White Dwarf Spectral Classification The following information on white dwarf spectral classification was provided by J. Liebert and E. Sion ([10] and illustrated examples in [14]). The system consists of: (1) first symbol: an uppercase D for a degenerate star spectrum; (2) second symbol: an uppercase letter designating the primary or dominant ion or type of element in the optical spectrum; (3) third and possible subsequent symbols: (optional) uppercase letters designating any secondary ions or types of elements appearing in the optical spectrum, usually due to species with trace abundances (special secondary symbols are also provided for spectra showing polarized light and magnetic fields, and others with peculiar spectra); and (4) a temperature index defined by l08eff, which is equal to 50400ITeff. Originally, this index was specified to be a single digit from 0 to 9. This index can be estimated only from at least a rough analysis of spectrophotometric data, using colors, an energy distribution or the strengths of absorption features. In this way, the system differs from traditional, purely spectroscopic methodology. If such information is unavailable or ambiguous, the temperature subtype is omitted. 15.3 PHOTOMETRIC SYSTEMS I 385 Definition of Primary Symbols DA DB DO DZ DQ DX, DXP Hydrogen Balmer lines dominate optical spectrum. Neutral helium (He I) lines dominate. Ionized helium lines strongest, He I and/or H may be visible. Metal lines dominate, usually with Ca II strongest. Carbon features, either molecular or atomic, in any part of the electromagnetic spectrum (often strongest in the ultraviolet). Star with unidentified features, presumably due to a strong magnetic field. If light polarized, the secondary symbol "P" is also appropriate. Secondary Symbols: All of the Above. Plus ... P H V PEC Star showing polarized light. Star known to be magnetic from optical Zeeman features, but not known to be polarized. Star known to be photometrically variable (optional). Star with spectral peculiarities. Examples DAI DAOI DOZI DBAQ4 DXP5 DZA7 DC9 A white dwarf showing only hydrogen lines with 37 500 < Teff < 100000 K. Star in same temperature range showing hydrogen and weak He II. A star showing strong He II, weak He I, H, and N v features at Teff = 70000 K. A star showing He I, H, and C features in that order of decreasing strengths, near Teff = 12000 K. A polarized, magnetic white dwarf with unidentified spectral features, Teff '" 10 000 K. A metallic line white dwarf also showing weak hydrogen lines, Teff = 8500 K. A featureless, continuous spectrum with an estimated Teff = 5500 K. 15.3 PHOTOMETRIC SYSTEMS Various photometric systems are used to supplement or replace the spectral classifications referred to in the last section. Optical filters are used to isolate specific spectral features or wavelength ranges, and the fluxes received through these filters are usually expressed in magnitudes, m = -2.5 log(f/fo) , where f is the measured flux (corrected for atmospheric effects), and fo is the corresponding flux for a star with m = O. The system is defined by the magnitudes and color indices (magnitude differences) for a set of standard stars, which have been detennined using a particular instrumental setup. The standard stars are used to transform measurements made with other instrumental setups to the standard system. Also important for theoretical studies are the sensitivity functions (response of the original instrumental setup to a source that emits the same flux at all wavelengths) for the various filters as a function of wavelength. The effective wavelengths (peak sensitivity) and widths at half maximum of the sensitivity functions for selected photometric systems in common use at the present time are given in Table 15.5. References containing lists of standard stars, sensitivity functions, and calibrations, are indicatd in the last column. 386 / 15 NORMAL STARS Thble 15.5. Modem photometric systems. System Stromgren four-color system Geneva seven-color system Vilnius seven-color system Walraven system Washington system DDO five-color system RGV UBVRI and (RI)KC Characteristic wavelength passbands (effective wavelengths and half-widths) (A) 3500 (380), 4100 (200), 4700 (200), 5550 (200), plus HfJ (150/30) UBV system plus 4020 (170), 4480 (165), 5400 (200), 5810 (210) 3450 (400), 3740 (260), 4050 (220), 4660 (260),5160 (210), 5440 (260), 6550 (200) 5400 (710), 4300 (540), 3820 (430), 3620 (230),3250 (140) 3910 (1100), 5085 (1050), 6330 (800), 8050 (1500) 4886 (186), 4517 (76),4257 (73), 4166 (83), additional: 3815 (330),3460 (383) 3593 (530), 4658 (495), 6407 (430) 3600 (700), 4400 (1000), 5500 (900), 7000 (2200),8800 (2400), 6400 (1750), 7900 (1400) Designations References uvbyfJ [1-6] UBVBIB2VIG [1,7-9] [10--13] [I, 14-16] UPXfZVS VBLUW CMTIT2 C(41--42) C(42--45) C(45--48) RGU UBVRI [1,7,17,18] [19,20] [21-26] [1,7,27,28] [1,7,9,29-33] [1,34-38] References 1. Schmidt-Kaler, Th. 1982, Landolt-Bomstein: Numerical Data and Functional Relationships in Science and Technology, edited by K. Schaifers and H.H. Voigt (Springer-Verlag, Berlin), VIl2b 2. Crawford, D.L. 1975, AJ, 80, 955 3. Crawford, D.L. 1978, Ai, 83, 48 4. Crawford, D.L. 1979, AJ, 84, 1858 5. Olson, E.C. 1974, PASP, 86, 80 6. Stromgren, B. 1966, ARA&A, 4, 433 7. Golay, M. 1974,lntroduction to Astronomical Photometry (Reidel, Dordrecht) 8. Rufener, E, & Maeder, A. 1971, A&AS, 4, 43 9. Philip, A.G.D., editor, 1979, Problems of Calibration of Multicolor Photometric Systems (Davis, Schenectady) 10. Hauck, B. 1985, in Calibration of Fundamental Stellar Quantities, edited by D.S. Hayes, L.E. Pasinetti, and A.G.D. Philip (Kluwer Academic), p. 271 11. North, P., & Nicolet, B. 199O,A&A, 228, 78 12. Rufener, E, & Nicolet, B. 1988, A&A, 206, 357 13. Meynet, G., & Hauck, B. 1985, A&A, ISO, 163 14. Straizys, V., & Zdanavicius, K. 1970, Bull. Vilnius Astron. Obs. No. 29, 15 15. Straizys, V., 1977, Multicolor Stellar Photometry, Photometric Systems and Methods (Mokslos, Vilnius) 16. Straizys, V., & Jodinskiene, E. 1981, Bull. Vilnius Astron. Obs. No. 56 17. Lub, J., & Pel, J.W. 1977,A&A, 54,137 18. Pel, J.W. 1976, A&AS, 24, 413 19. De Ruiter, H.R., & Lub, J. 1986, A&AS, 63,59 20. Brand, J., & Wouterloot, J.G.A. 1988, A&AS, 75, 117 21. Cantema, R. 1976, Ai, 81, 228 22. Cantema, R., & Harris, H.C. 1979, Dudley Obs. Rep. No. 14; op. cit. [9], p. 199 23. Harris, H.C., & Cantema, R. 1979, Ai, 84,1750 24. Geisler, D. 1984, PASP, 96, 723 25. Geisler, D. 1990, PASP, 102, 344 26. Geisler, D., Claria, 1.1., & Minniti, D. 1991, Ai, 102, 1836 27. McClure, R.D. 1976, AJ, 81, 182 28. McClure, R.D., & van den Bergh, S. 1968, Ai, 73, 313 29. Steinlin, V.W. 1968, Z Astrophys., 69, 276 30. Smith, L.L., & Steinlin, V.w. 1964, Z Astrophys., 58, 253 31. Bell, R.A. 1972, MNRAS, 159, 34; 1972, A&A, 62, 411 32. Buser, R. 1978, A&A, 62, 411 33. Buser, R. 1978, A&A, 62, 425 34. Cousins, A.W.J. 1976, MemRAS, 81, 25 35. Landolt, A.V. 1992, AJ, 104, 340 36. Bessell, M.S. 1979, PASP, 91, 589 15.3 PHOTOMETRIC SYSTEMS / 387 37. Bessell, M.S. 1976, PASP, 88, 557 38. Menzies, l.W. et aI. 1991, MNRAS, 248, 642 Absolute calibration of a star of the spectral type AO V with the magnitude V system is shown in Table 15.6. = 0 [2] on the Johnson Table 15.6. Flux calibration for an AO V star. Symbol Flux(ergcm- 2 s- 1 A-I) U 4.22 6.40 3.75 1.75 8.4 B V R I x 10- 9 x 10-9 x 10-9 x 10-9 x 10- 10 AO(/Lm) 0.36 0.44 0.55 0.71 0.97 Useful relations for the UBV system [2]: = 0.08 + 3.85(B - V)o unreddened main sequence, (B - V)o < 0 and (U Q = (U - B) - O.72(B - V) independent of reddening for early-type stars, EU-B = {0.65 - 0.05(U - B)o + 0.05EB-V, (U - B)o < 0, EB-V 0.64 + 0.26(B - V)o + 0.05EB-V, (B - V)o > 0, (U - B)o Av - - = 3.30 + 0.28(B EB-V V)o - B)o < 0, + O.D4EB-v, where EU-B = (U - B) - (U - B)o, Av = V - Vo, EB-V = (B - V) - (B - V)o; and Vo, (B - V)o, and (U - B)o are the magnitude and color indices stars would have if space were transparent. Useful relations for the uvbyf3 system [15-20]: CI ml f3 = (u = (v - v) - (v - b), b) - (b - y), = 2.510g(W / N), where W and N are the fluxes measured through interference filters centered on Hf3 with half-widths of about 150 and 30 A, respectively. E(Cl) E(ml) E(u - b) = 0.20E(b - y), } = -0.32E(b - y), = 1.50E(b - color excesses according to standard reddening law, y), [cd = Cl - 0.20(b - y), } [md = ml + 0.32(b - y), reddening independent quantities, [u - b] = (u - b) - 1.50(b - y), 388 / 15 NORMAL STARS (b - y)o = -0.116 + 0.097C! for an unreddened main-sequence B star, (b - y)o = 2.946 - 1.0,8 - O.lekl (-0.2Sc5ml if ml < 0) for A stars with 2.870 > ,8 > 2.720 and c5C! < 0.28, (b - y)o = 0.222 + 1.11t::..{J + 2.7(t::..{J)2 - O.OSc5C! - (0.1 + 3.6t::..,8)c5ml for F stars with 2.630 < ,8 < 2.720 and c5C! < 0.28, or 2.S90 < ,8 < 2.630 and c5Cl < 0.20, where t::..,8 = 2.720 -,8, IS.3.1 Calibration of MK Spectral Types [2,21,22] c5C! = C! - Cstd, c5ml = mstd - ml; See Section lS.3.2 for Cstd and mstd· Table lS.7 presents the absolute magnitude, color, effective surface temperature, and bolometric correction calibrations for the MK spectral classes. Table lS.8 gives the calibrated physical parameters for stars of the various spectral classes. Table 15.7. Calibration of MK spectral types. Sp M(V) B-V U-B V-R R-J TeIJ BC MAIN SEQUENCE, V -5.7 -0.33 05 -4.5 -0.31 09 -4.0 -0.30 BO -2.45 B2 -0.24 -1.2 B5 -0.17 -0.25 -0.11 B8 AO +0.65 -0.02 +0.05 A2 +1.3 AS +1.95 +0.15 FO +2.7 +0.30 F2 +3.6 +0.35 +0.44 F5 +3.5 F8 +4.0 +0.52 GO +4.4 +0.58 02 +4.7 +0.63 05 +5.1 +0.68 +0.74 08 +5.5 +0.81 KO +5.9 +0.91 K2 +6.4 K5 +7.35 +1.15 MO +8.8 +1.40 M2 +1.49 +9.9 M5 +12.3 +1.64 -1.19 -1.12 -1.08 -0.84 -0.58 -0.34 -0.02 +0.05 +0.10 +0.03 0.00 -0.02 +0.02 +0.06 +0.12 +0.20 +0.30 +0.45 +0.64 +1.08 +1.22 +1.18 +1.24 -0.15 -0.15 -0.13 -0.10 -0.06 -0.02 0.02 0.08 0.16 0.30 0.35 0.40 0.47 0.50 0.53 0.54 0.58 0.64 0.74 0.99 1.28 1.50 1.80 -0.32 -0.32 -0.29 -0.22 -0.16 -0.10 -0.02 0.Ql 0.06 0.17 0.20 0.24 0.29 0.31 0.33 0.35 0.38 0.42 0.48 0.63 0.91 1.19 1.67 42000 34000 30000 20900 15200 11400 9790 9000 8180 7300 7000 6650 6250 5940 5790 5560 5310 5150 4830 4410 3840 3520 3170 -4.40 -3.33 -3.16 -2.35 -1.46 -0.80 -0.30 -0.20 -0.15 -0.09 -0.11 -0.14 -0.16 -0.18 -0.20 -0.21 -0.40 -0.31 -0.42 -0.72 -1.38 -1.89 -2.73 OIANTS,m 05 +0.9 08 +0.8 KO +0.7 K2 +0.5 -0.2 K5 MO -0.4 M2 -0.6 M5 -0.3 +0.56 +0.70 +0.84 +1.16 +1.81 +1.87 +1.89 +1.58 0.69 0.70 0.77 0.84 1.20 1.23 1.34 2.18 0.48 0.48 0.53 0.58 0.90 0.94 1.10 1.96 5050 4800 4660 4390 4050 3690 3540 3380 -0.34 -0.42 -0.50 -0.61 -1.02 -1.25 -1.62 -2.48 +0.86 +0.94 +1.00 +1.16 +1.50 +1.56 +1.60 +1.63 15.3 PHOTOMETRIC SYSTEMS I 389 Table 15.7. (Continued.) Sp B-V M(V) SUPERGIANTS, I 09 -6.5 -0.27 -0.17 B2 -6.4 B5 -6.2 -0.10 -6.2 -0.03 B8 -6.3 -0.01 AO -6.5 A2 +0.03 -6.6 A5 +0.09 -6.6 FO +0.17 -6.6 F2 +0.23 -6.6 F5 +0.32 -6.5 F8 +0.56 -6.4 GO +0.76 -6.3 G2 +0.87 -6.2 G5 +1.02 -6.1 G8 +1.14 -6.0 KO +1.25 -5.9 K2 +1.36 -5.S K5 +1.60 -5.6 MO +1.67 M2 -5.6 +1.71 -5.6 M5 +1.80 U-B V-R R-J Teff BC -1.13 -0.93 -0.72 -0.55 -0.38 -0.25 -0.08 +0.15 +0.18 +0.27 +0.41 +0.52 +0.63 +0.83 +1.07 +1.17 +1.32 +1.80 +1.90 +1.95 +1.60: -0.15 -0.05 0.02 0.02 0.03 0.07 0.12 0.21 0.26 0.35 0.45 0.51 0.58 0.67 0.69 0.76 0.85 1.20 1.23 1.34 2.18 -0.32 -0.15 -0.07 0.00 0.05 0.07 0.13 0.20 0.21 0.23 0.27 0.33 0.40 0.44 0.46 0.48 0.55 0.90 0.94 1.10 1.96 32000 17600 13600 11100 9980 9380 8610 7460 7030 6370 5750 5370 5190 4930 4700 4550 4310 3990 3620 3370 2880 -3.18 -1.58 -0.95 -0.66 -0.41 -0.28 -0.13 -0.01 -0.00 -0.03 -0.09 -0.15 -0.21 -0.33 -0.42 -0.50 -0.61 -1.01 -1.29 -1.62 -3.47 Table 15.8. Calibration of MK spectral types. a Sp M/M0 R/R0 MAIN SEQUENCE, V 03 120 15 05 12 60 37 06 10 08 23 8.5 BO 17.5 7.4 7.6 B3 4.8 B5 5.9 3.9 BS 3.8 3.0 AO 2.9 2.4 A5 2.0 1.7 1.6 FO 1.5 F5 1.4 1.3 1.05 GO 1.1 G5 0.92 0.92 KO 0.79 0.85 K5 0.67 0.72 MO 0.51 0.60 M2 0.40 0.50 M5 0.21 0.27 MS 0.06 0.10 ]og(g/g0) log (PI P0) -0.3 -0.4 -0.45 -0.5 -0.5 -0.5 -0.4 -0.4 -0.3 -0.15 -0.1 -0.1 -0.05 +0.05 +0.05 +0.1 +0.15 +0.2 +0.5 +0.5 -1.5 -1.5 -1.45 -1.4 -1.4 -1.15 -1.00 -0.85 -0.7 -0.4 -0.3 -0.2 -0.1 -0.1 +0.1 +0.25 +0.35 +0.8 +1.0 +1.2 Vrot (kms-l) 200 170 190 240 220 180 170 100 30 10 <10 <10 <10 390 / 15 NORMAL STARS Table 15.8. (Continueti) R/R0 log(g/g0) log(P/P0) Vrot GIANTS. ill 20 BO B5 7 AO 4 1.0 GO 1.1 G5 KO 1.1 1.2 K5 MO 1.2 15 8 5 6 10 15 25 40 -1.1 -0.95 -1.5 -1.9 -2.3 -2.7 -3.1 -2.2 -1.8 -1.5 -2.4 -3.0 -3.5 -4.1 -4.7 120 130 100 30 <20 <20 <20 SUPERGIANTS. I 70 05 06 40 08 28 BO 25 B5 20 AO 16 AS 13 FO 12 F5 10 10 GO G5 12 KO 13 K5 13 13 MO M2 19 30: 25: 20 30 50 60 60 80 100 120 150 200 400 500 800 -1.1 -1.2 -1.2 -1.6 -2.0 -2.3 -2.4 -2.7 -3.0 -3.1 -3.3 -3.5 -4.1 -4.3 -4.5 -2.6 -2.6 -2.5 -3.0 -3.8 -4.1 -4.2 -4.6 -5.0 -5.2 -5.3 -5.8 -6.7 -7.0 -7.4 Sp M/M0 (kms- 1) 125 102 40 40 38 30 <25 <25 < 25 < 25 < 25 Note a A colon indicates an uncertain value. Also see [23]. An independent absolute magnitude calibration is given in graphical form in [8]. Plots of (B - V) and (U - V) versus Mv for the various white dwarf subclasses are in [24]. Intrinsic colors and absolute magnitudes of the zero-age main sequence (ZAMS) (locus of young stars just starting hydrogen burning) follow [2]. See [25] for an alternative, and plots in Chapter 20. Table 15.9 gives the zero-age main sequence colors and absolute magnitudes. Table 15.9. Zero-age main sequence. (B - V)o (U - B)o -0!'l33 -0.305 -0.30 -0.28 -0.25 -0.22 -0.20 -0.15 -0.10 -0.05 0.00 +0.05 +0.10 -1!'l20 -1.10 -1.08 -1.00 -0.90 -0.80 -0.69 -0.50 -0.30 -0.10 +0.01 +0.05 +0.08 Mv -5!'l2 -3.6 -3.25 -2.6 -2.1 -1.5 -1.1 -0.2 +0.6 +1.1 +1.5 +1.7 +1.9 (B - V)o (U - B)o +0.40 +0.50 +0.60 +0.70 +0.80 +0.90 +1.00 +1.10 +1.20 +1.30 +1.40 +1.50 +1.60 -0.01 0.00 +0.08 +0.23 +0.42 +0.63 +0.86 +1.03 +1.13 +1.20 +1.22 +1.17 +1.20 Mv + 3.4 + 4.1 + 4.7 + 5.2 + 5.8 + 6.3 + 6.7 + 7.1 + 7.5 + 8.0 + 8.8 +10.3 +12.0 15.3 PHOTOMETRIC SYSTEMS / 391 Table 15.9. (Continued) 15.3.2 (8 - V)o (U - 8)0 +0.15 +0.20 +0.25 +0.30 +0.35 +0.09 +0.10 +0.07 +0.03 0.00 Mv +2.1 +2.4 +2.55 +2.8 +3.1 (B - V)o (U - 8)0 +1.70 +1.80 +1.90 +2.00 +1.32 +1.43 +1.53 +1.64 Mv +13.2 +14.2 +15.5 +16.7 uvbyfJ Standard Relations For the early-type stars, Table 15.10 gives the standard relation between the fJ index, colors, and the absolute magnitudes. Table 15.10. uvbyfJ standard relations. fJ b-y m, 2.590 2.600 2.620 2.640 2.660 2.680 2.700 2.720 2.740 2.760 2.780 2.800 2.820 2.840 2.860 2.880 2.900 2.910 -0.134 -0.126 -0.118 -0.109 -0.100 -0.091 -0.080 -0.070 -0.061 -0.050 -0.044 -0.041 -0.039 -0.037 -0.034 -0.029 -0.023 -0.020 0.045 0.055 0.075 0.080 0.085 0.093 0.100 0.100 0.109 0.110 0.116 0.120 0.120 0.123 0.128 0.132 0.138 0.140 2.880 2.870 2.860 2.850 2.840 2.830 2.820 2.810 2.800 2.790 2.780 2.710 2.760 2.750 2.740 2.730 2.720 0.066 0.076 0.086 0.096 0.106 0.116 0.126 0.136 0.146 0.156 0.166 0.176 0.186 0.196 0.206 0.216 0.226 0.200 0.202 0.205 0.206 0.208 0.207 0.206 0.204 0.203 0.200 0.196 0.192 0.188 0.185 0.182 O.ISO 0.177 q MV [mil [q] -4.65 -4.12 -3.17 -2.36 -1.69 -1.12 -0.65 -0.27 0.04 0.30 0.51 0.68 0.83 0.97 1.10 1.24 1.39 1.46 0.005 0.017 0.040 0.047 0.055 0.066 0.076 0.079 0.091 0.095 0.103 0.108 0.108 0.112 0.118 0.123 0.131 0.134 -0.223 -0.103 -0.001 0.087 0.170 0.253 0.337 0.418 0.503 0.588 0.665 0.732 0.793 0.840 0.885 0.931 0.980 1.004 2.30 2.40 2.50 2.57 2.64 2.67 2.70 2.73 2.76 2.79 2.82 2.85 2.88 2.92 2.96 3.03 3.10 0.220 0.225 0.231 0.235 0.240 0.242 0.244 0.245 0.247 0.247 0.246 0.245 0.244 0.244 0.244 0.245 0.245 0.917 0.895 0.873 0.851 0.829 0.812 0.795 0.713 0.751 0.729 0.707 0.685 0.663 0.641 0.619 0.587 0.555 B Stars -0.250 -0.128 -0.025 0.065 0.150 0.235 0.321 0.404 0.491 0.578 0.656 0.724 0.785 0.833 0.878 0.925 0.975 1.000 A Stars 0.930 0.910 0.890 0.870 0.850 0.835 0.820 0.800 0.7SO 0.760 0.740 0.720 0.700 0.680 0.660 0.630 0.600 392 I 15 NORMAL STARS Table 1S.10. (Continued.) b-y {3 ml Cl Mv [mil [cil 0.244 0.244 0.246 0.248 0.251 0.256 0.263 0.272 0.281 0.292 0.304 0.317 0.332 0.350 0.536 0.513 0.481 0.443 0.411 0.383 0.355 0.327 0.304 0.281 0.258 0.235 0.211 0.188 FStars 2.720 2.710 2.700 2.690 2.680 2.670 2.660 2.650 2.640 2.630 2.620 2.610 2.600 2.590 0.222 0.233 0.245 0.258 0.271 0.284 0.298 0.313 0.328 0.344 0.360 0.377 0.394 0.412 0.177 0.174 0.172 0.171 0.170 0.171 0.174 0.178 0.183 0.189 0.196 0.204 0.214 0.226 0.580 0.560 0.530 0.495 0.465 0.440 0.415 0.390 0.370 0.350 0.330 0.310 0.290 0.270 3.14 3.21 3.29 3.38 3.48 3.60 3.74 3.88 4.04 4.20 4.36 4.52 4.70 4.90 See [15-17] and [26]. See also [27] and [28] for grids for determining effective temperatures and surface gravities. Other calibrations may be found in [29-38]. 15.3.3 Empirical U BV(RI)KC Calibrations [39] The colors and spectral classes are given as a function of the surface effective temperature for dwarf and giant stars in Table 15.11. Table 1S.11. Empirical U BV(RI)KC calibrations. TetT b-y B-V 13000 12000 11000 10000 9500 9000 8500 8000 7500 7000 6500 6000 5500 5000 4500 4000 3500 3000 2750 -0.054 -0.041 -0.027 -0.010 +0.007 +0.035 +0.072 +0.118 +0.165 +0.220 +0.286 +0.360 +0.445 +0.535 +0.60 +0.80 +1.01 +1.22 +1.37 -0.14 -0.10 -0.065 -0.025 +0.005 +0.055 +0.14 +0.22 +0.275 +0.35 +0.45 +0.57 +0.70 +0.88 +1.02 +1.32 +1.53 +1.74 +2.0 (V - R)KC (R - I)KC (V - I)KC -0.070 -0.050 -0.032 -0.012 +0.008 +0.040 +0.084 +0.132 +0.168 +0.207 +0.250 +0.303 +0.364 +0.43 +0.51 +0.74 +1.18 +1.77 +2.18 -0.120 -0.085 -0.055 -0.020 +0.015 +0.072 +0.155 +0.250 +0.330 +0.415 +0.515 +0.625 +0.760 +0.93 +1.11 +1.53 +2.19 +3.03 +3.58 MK Dwarfs (V) -0.050 -0.035 -0.023 -0.008 +0.007 +0.032 +0.071 +0.118 +0.162 +0.208 +0.265 +0.322 +0.396 +0.50 +0.60 +0.79 +1.01 +1.26 +1.40 B7 B8 B9 AO Al A2 AS A7 PO F2 F5 GO G6 K2 K4 K7 M2 M4.5 M6 15.4 STELLAR ATMOSPHERES I 393 Table 15.11. (Continued.) Teff b-y 5 ()()() 4750 4500 4250 4 ()()() 3750 3500 3250 +0.55 +0.60 +0.68 +0.80 +0.90 +1.00 8-V (V - R)KC (R - I)KC (V - I)KC MK Giants (ill) 15.4 +0.89 +0.98 +1.11 +1.26 +1.43 +1.62 +0.497 +0.539 +0.60 +0.68 +0.795 +0.945 +1.19 +0.433 +0.461 +0.510 +0.600 +0.735 +1.025 +1.57 +0.93 +1.00 +1.11 +1.28 +1.53 +1.97 +2.76 +3.80 G7 KO K2 K3 K5 M2 M4.5 M6 STELLAR ATMOSPHERES 15.4.1 Model Atmospheres for Normal Stars (Solar Composition) [40] Table 15.12 lists stellar atmosphere parameters depending on the surface effective temperature and gravity of a star. Table 15.12. Model atmospheres Jar normal stars. Teff Feonv logg log 'fa 5500 4 -3.0 -2.0 -1.0 0.0 1.0 5500 log x F T logP logne logna logp log Pr 6.79 7.65 7.92 8.08 8.14 4282 4487 4846 6130 8176 3.23 3.84 4.41 4.92 5.10 11.35 11.91 12.49 13.50 14.94 15.47 16.05 16.59 16.99 17.04 -8.19 -7.61 -7.07 -6.66 -6.62 0.09 0.10 0.17 0.54 1.05 0.00 0.00 0.00 0.01 0.85 -3.0 -2.0 -1.0 0.0 1.0 10.65 10.98 11.14 11.22 11.24 4104 4444 4846 6145 8431 1.28 2.09 2.73 3.13 3.18 9.53 10.35 11.08 12.55 14.06 13.52 14.30 14.91 15.20 15.07 -10.13 -9.36 -8.75 -8.46 -8.58 0.09 0.10 0.17 0.56 1.10 0.00 0.00 0.00 0.00 0.91 6 ()()() 4 -3.0 -2.0 -1.0 0.0 1.0 7.60 7.90 8.08 8.18 8.22 4667 4891 5293 6789 8709 3.29 3.87 4.42 4.82 4.95 11.48 12.04 12.62 13.94 15.12 15.49 16.04 16.55 16.85 16.86 -8.17 -7.61 -7.10 -6.81 -6.79 0.24 0.25 0.32 0.70 1.16 0.00 0.00 0.00 0.05 0.88 6000 1 -3.0 -2.0 -1.0 0.0 1.0 10.75 11.03 11.17 11.24 11.25 4489 4869 5318 6861 8981 1.26 2.02 2.59 2.89 2.92 9.72 10.62 11.44 13.01 14.11 13.47 14.19 14.72 14.90 14.73 -10.19 -9.47 -8.94 -8.75 -8.93 0.24 0.25 0.33 0.75 1.21 0.00 0.00 0.00 0.00 0.91 7000 4 -3.0 -2.0 -1.0 0.0 1.0 7.63 7.95 8.12 8.20 8.24 5458 5726 6190 8217 9911 3.10 3.67 4.17 4.45 4.55 11.87 12.45 13.13 14.63 15.37 15.22 15.77 16.23 16.39 16.37 -8.44 -7.89 -7.42 -7.26 -7.28 0.51 0.52 0.60 1.02 1.38 0.00 0.00 0.00 0.20 0.92 I 394 / 15 NORMAL STARS Table 15.12. (Continued.) Teff logP logne logna logp logPr Fconv F 7586 8030 8982 11655 16287 1.71 2.36 2.86 3.17 3.75 12.84 13.42 14.08 14.62 15.08 13.63 14.26 14.67 14.71 15.12 -10.03 -9.40 -8.99 -8.95 -8.54 1.13 1.15 1.28 1.68 2.25 0.00 0.00 0.00 0.00 0.00 8.70 8.90 9.02 9.15 9.28 13060 14067 15560 19521 27451 1.38 2.09 2.71 3.33 4.03 12.81 13.49 14.07 14.60 15.15 12.84 13.52 14.08 14.60 15.15 -10.82 -10.14 -9.57 -9.05 -8.50 2.34 2.35 2.40 2.63 3.15 0.00 0.00 0.00 0.00 0.00 9.48 9.66 9.77 9.87 9.97 28059 31336 34855 40920 53682 1.19 2.16 2.93 3.55 4.21 12.31 13.24 13.96 14.52 15.06 12.29 13.21 13.93 14.48 15.02 -11.37 -10.45 -9.72 -9.18 -8.64 3.54 3.55 3.62 3.85 4.32 0.00 0.00 0.00 0.00 0.00 logg IOgT a 10 000 4 -3.0 -2.0 -1.0 0.0 1.0 8.34 8.48 8.58 8.65 8.83 20000 4 -3.0 -2.0 -1.0 0.0 1.0 40000 4 -3.0 -2.0 -1.0 0.0 1.0 log x T Note aT = continuum optical depth (5000 A); x = geometric depth; T = temperature (K); P = pressure; ne = electron number density; na = atom number density; p = mass density; Pr = radiation pressure; Fconv / F = fraction of flux carried by convection. All units are cgs. Model atmospheres for metal-deficient stars are given in [40] and [41]. 15.4.2 Theoretical Physical Continuum Fluxes [40] Logarithms of theoretical physical continuum fluxes (ergs cm- 2 s-1 A-I) for normal stars (solar composition) with logg 4 [40] are given in Table 15.13. = Table 15.13. Continuum fluxes for normal stars. A. (A) 506 890 920 1482 2012 2506 3012 3636 3661 4012 4512 5025 5525 6025 7075 8152 8252 10050 14594 = 5500 6000 7000 -00 -00 -00 -00 -00 -00 -5.80 0.05 4.14 5.91 6.80 6.86 6.94 6.94 6.92 6.89 6.86 6.81 6.72 6.62 6.61 6.45 6.13 -4.49 1.63 5.41 6.55 7.00 7.04 7.16 7.15 7.12 7.08 7.03 6.97 6.86 6.75 6.74 6.56 6.19 -2.07 3.83 6.88 7.19 7.29 7.27 7.56 7.52 7.46 7.38 7.31 7.24 7.09 6.95 6.95 6.74 6.29 Teff (K) 10000 -6.26 1.11 3.73 8.28 8.12 7.98 7.89 7.79 8.33 8.21 8.06 7.92 7.79 7.68 7.46 7.26 7.33 7.03 6.47 20000 40000 4.81 7.34 10.28 9.84 9.48 9.22 8.99 8.76 8.93 8.80 8.63 8.46 8.32 8.19 7.94 7.71 7.73 7.41 6.80 11.19 10.93 11.28 10.75 10.35 10.05 9.78 9.49 9.49 9.35 9.17 8.99 8.84 8.70 8.44 8.20 8.19 7.86 7.23 15.5 STELLAR STRUCTURE / 395 Table 15.13. (Continued.) A (A) Teff (K) 27000 50000 100000 200000 5.22 4.20 3.03 1.83 = 5500 6000 7000 10000 5.27 4.24 3.06 1.87 5.34 4.31 3.13 1.94 5.48 4.45 3.27 2.07 20000 40000 5.77 4.72 3.52 2.32 6.17 5.10 3.89 2.67 15.5 STELLAR STRUCTURE Age-zero models for X = 0.70, Z = 0.02, l/Hp = 1.7 [1]. I = mixing length; Pc = central pressure (dyn cm- 2 ); Tc = central temperature (K); Pc = central density (g cm- 3 ); Hp = pressure scale height; qcc = fraction of stellar mass within convective core; qce = fraction of stellar mass at bottom of convective envelope are given in Table 15.14. Table 15.14. Age-zero models [I]. M/M0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.5 2.0 1.8 1.6 1.4 1.2 1.0 0.8 logL/L0 3.7600 3.6118 3.4433 3.2480 3.0184 2.7381 2.3815 1.9087 1.6002 1.2157 1.0298 0.8186 0.5562 0.2325 -0.1523 -0.5742 log Teff logg R/R0 log Pc logTc log Pc qcc qce 4.4096 4.3855 4.3576 4.3251 4.2865 4.2380 4.1766 4.0928 4.0376 3.9658 3.9297 3.8855 3.8355 3.7964 3.7514 3.7016 4.269 4.275 4.280 4.287 4.296 4.303 4.317 4.330 4.338 4.339 4.334 4.317 4.322 4.422 4.548 4.674 3.8434 3.6213 3.3916 3.1472 2.8860 2.6122 2.2992 1.9620 1.7737 1.5858 1.5120 1.4532 1.3526 1.1157 0.8813 0.6820 16.6331 16.6688 16.7116 16.7617 16.8243 16.8995 16.9982 17.1280 17.2085 17.2943 17.3260 17.3476 17.3274 17.2645 17.1851 17.0651 7.5051 7.4959 7.4853 7.4729 7.4583 7.4400 7.4163 7.3844 7.3631 7.3333 7.3151 7.2913 7.2500 7.1936 7.1306 7.0603 0.974 1.024 1.081 1.148 1.229 1.326 1.450 1.614 1.716 1.834 1.883 1.930 1.948 1.941 1.924 1.882 0.3193 0.3088 0.2877 0.2772 0.2666 0.2455 0.2350 0.1928 0.1717 0.1401 0.1190 0.0874 0.0386 0.0129 0.0073 0.0875 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 ;:: 0.9999 0.9965 0.9720 0.8725 Reference 1. SchOnbemer, D., BlOCker, T., Herwig, F., & Driebe, T. 1996, private communication. REFERENCES I. Lacy, C.H. 1977, ApiS, 34, 479 2. Schmidt-Kaler, Th. 1982, Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, edited by K. Schaifers and H.H. Voigt (Springer-Verlag, Berlin), VII2b 3. McCluskey, G.E., Jr., & Kondo, Y. 1972,A&SS, 17,134 4. Harris, D.L., ill, Strand, K.Aa., & Worley, C.E. 1963, in Stars and Stellar Systems, ill (University of Chicago Press, Chicago), p. 273. 5. Popper,D.M. 1980, ARA&A, 18, 115 6. Andersen, J. 1991, A&AR, 3, 91 7. Morgan, W.w., & Keenan, P.C. 1973,ARA&A,l1, 29 8. Keenan, P.C. 1985, in Calibration of Fundamental Stellar Quantities, edited by D.S. Hayes, L.E. Pasinetti and A.G.D. Philip (Kluwer Academic), p. 121 9. Garrison, R.F., editor, 1984, The MK Process and Stellar Classification (David Dunlap Observatory, Toronto) 10. Sion, E.M., Greenstein, J.L., Landstreet, J.D., Liebert, J., Shipman, H.L., & Wegner, G.A. 1983, Api, 269, 253 II. Morgan, w.w., Abt, H.A., & Tapscott, J.w. 1978, Revised MK Spectral Atlas for Stars Earlier than the Sun (Yerkes Observatory) 12. Keenan, P.e., & McNeil, R.e. 1976, An Atlas of the Spectra of the Cooler Stars: Types G, K, M, S, & C (Ohio State University Press, Columbus) 13. Yamashita, Y., Nariai, K., & Morimoto, Y. 1977, An Atlas of Representative Stellar Spectra (University of Tokyo Press, Tokyo) 396 I 15 NORMAL STARS 14. Wesemael, F., Greenstein, J.L., Liebert, J., Lamontagne, R., Fontaine, G., Bergeron, P., & Glaspey, J.W. 1993, PASP, lOS, 761 15. Crawford, D.L. 1975, AJ, 80, 955 16. Crawford,D.L.I978,AJ,83,48 17. Crawford, D.L. 1979,AJ, 84,1858 18. Stromgren, B. 1966, ARA&A, 4, 433 19. Crawford, D.L., Glaspey, J.W., & Perry, C.L. 1970,AJ, 75,822 20. Crawford, D.L. 1975, PASP, 87, 481 21. Johnson,H.L. 1966,ARA&A,4,193 22. De Jager, C., & Nieuwenhuijzen, H. 1987, A&A, 177, 217 23. Habets, G.M.H.J., & Heintze, J.R.W. 1981, A&AS, 46, 193 24. Greenstein, J.L. 1988, PASP, 100, 82 25. VandenBerg, D.A., & Poll, H.E. 1989,AJ, 98,1451 26. Perry, C.L., Olsen, E.H., & Crawford, DL. 1987, PASP, 99,1184 27. Moon, T.T., & Dworetsky, M.M. 1985, MNRAS, 217, 305 28. Napiwotzki, R., SchOnbemer, D., & Wenslte, V. 1992, in The Atmospheres of Early-Type Stars, edited by U. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. Heber and C.S. Jeffery (Springer-Verlag, Berlin and New York), p. 18 Philip, A.G.D., & Egret, D. 1980, A&AS, 40, 199 Balona, L.A. 1984, MNRAS, 211, 973 Crawford, D.L. 1984, in The MK Process and Stellar Classification, edited by R.F. Garrison (David Dunlap Observatory, Toronto), p. 191 Balona, L.A., & Shobbrook, R.R. 1984, MNRAS, 211, 375 Kilkenny, D., &. Whittet, D.C.B. 1985, MNRAS, 21(;, 127 Greenstein, J.L. 1984, PASP, 96,62 Olsen, E.H. 1988, A&A, 189, 173 McNamara, D.H., & Powell,J.M. 1985,PASP,97, 1101 Olsen, E.H. 1984, A&AS, 57, 443. Hayes, D.S., Passinetti, L.E., & Philip, A.G.D. 1985, in Calibration of FundDmental Stellar Quantities, edited by D.S. Hayes, L.E. Pasinetti, and A.G.D. Philip (Reidel, Dordrecht) Bessell, M.S. 1979, PASP, 91, 589 Kurucz, Robert L. 1979, ApJS, 40, 1 Bell, R.A., Eriksson, K., Gustafsson, B., & Nordlund, A. 1976, A&AS, 23, 37 Chapter 16 Stars with Special Characteristics J. Donald Fernie 16.1 Variable Stars.. 16.2 Cepheid and Cepheid-Like Variables. 16.3 Variable White Dwarf Tables 400 16.4 Long-Period Variables ... 406 16.5 Other Variables ........ ... . . . . 406 16.6 Rotating Variables. . . . . . .. ... . . . . . 407 16.7 T Tauri Stars .. .... ... 408 16.8 Flare Stars . . . . . . . . . . . . . . . 16.9 Wolf-Rayet and Luminous Blue Variable Stars. 410 16.10 Be Stars. . . . . . . . . . . . . . . . 413 16.11 Characteristics of Carbon-Rich Stars . . . .. 16.12 Barium, CH, and Subgiant CH Stars 16.13 Hydrogen-Deficient Carbon Stars . . . . . . . . . 417 16.14 Blue Stragglers. 418 16.15 Peculiar A and Magnetic Stars 16.16 Pulsars......................... 420 16.17 Galactic Black Hole Candidate X-Ray Binaries 422 16.18 Double Stars 397 ........ ........ ... ...... . . 399 . . . 409 .. 415 . . . . . 416 ............ . . . . . . . . . . . 398 . . . . .. . . . . . 419 424 398 I 16.1 16 STARS WITH SPECIAL CHARACTERISTICS VARIABLE STARS by Douglas S. Hall All types of variables are collected in the General Catalogue of Variable Stars [1]. Except for the eclipsing variables, all are considered intrinsic variables, with the physical mechanism responsible for the variability being of four main classes. The approximate numbers of the principal types, as of 1990, are given in the following: Abbreviation Description Number Pulsating (periodic, multiperiodic, quasiperiodic, or nonperiodic) DCEP/CEP CW RR DSCT SXPHE BCEP ZZ RV SR L M RCB Classical Cepheids + those of uncertain type W Vrrginis stars + BL Herculis stars RR Lyrae stars 8 Scuti stars (some called dwarf Cepheids) SX Phe variables, pop. II 8 Sct variables f3 Cephei stars = f3 Canis Majoris stars ZZ Ceti variables RV Tauri stars Semiregular (sometimes called LPV) variables Slow irregular (sometimes called LPV) variables Mira stars (sometimes called LPV) R Coronae Borealis stars 638 172 6180 100 15 89 28 120 3377 2389 5827 37 Rotating (periodic or quasiperiodic) ELL ACV SXARI PSR BY RS FKCOM INT Ellipsoidal variables a 2 Canum Venaticorum variables SX Ari variables Optically variable pulsars BY Draconis variables RS Canum Venaticorum binaries FK Comae Berenices stars Orion variables of the T Tauri type 45 163 15 2 34 67 4 59 16.2 CEPHEID AND CEPHEID-LIKE VARIABLES / 399 Eruptive (all nonperiodic) Orion variables, including T Tauri stars and RW Aurigae stars FU Orionis variables y Cassiopeiae variables R Coronae Borealis variables UV Ceti variables or flare stars S Doradus variables or P Cygni stars IN FU GCAS RCB UV SDOR 898 3 108 37 746 15 Explosive or Cataclysmic (quasiperiodic or nonperiodic) N NL NR SN UG ZAND Novae Novalike variables Recurrent novae Supernovae U Geminorum variables or dwarf novae Symbiotic variables of the Z Andromedae type Eclipsing (periodic) all types 16.2 61 30 8 7 182 46 5074 CEPHEID AND CEPHEID-LIKE VARIABLES Descriptions of Cepheid families are given below [2-13]: IAU designation Name DCEP CW RR DSCT BCEP Classical Cepheids W Vir + BL Her stars RR Lyrae stars 8 Scuti fJ Cephei stars Population I II II I I Period (days) 1.5-60 1-50 0.4-1 0.04--0.2 0.15--0.25 Cepheid mean characteristics as a function of period P are given below. The period is that of the fundamental mode. In the K band MK = -2.97 log P - 1.08. The Cepheid ratio of radial velocity amplitude to V -light amplitude is 50 ± 5 lans- I mag. -I. 16 400 / logP STARS WITH SPECIAL CHARACTERISTICS Mv B-V logL/L0 logR/R0 logg Qa 0.54 0.61 0.68 0.75 0.82 0.89 0.97 1.04 2.2 1.9 1.7 1.5 1.3 1.0 0.8 0.6 0.036 0.037 0.039 0.040 0.041 0.042 0.044 0.045 0.21 0.25 0.31 4.5 3.9 3.6 0.039 0.037 0.037 -0.22 -0.22 -0.22 -0.22 2.5 2.1 1.5 1.2 0.049 0.059 0.076 0.080 3.86 3.82 3.78 -0.26 -0.26 -0.26 3.1 2.8 2.7 0.036 0.037 0.043 4.34 4.38 4.42 1.02 1.15 1.22 3.8 3.7 3.6 0.020 0.030 0.037 log Teff logM/M0 Classical Cepbeids 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 -2.4 -2.9 -3.5 -4.1 -4.7 -5.3 -5.8 -6.4 0.49 0.57 0.66 0.75 0.84 0.93 1.01 1.10 2.81 3.05 3.30 3.55 3.80 4.06 4.32 4.58 1.41 1.55 1.70 1.85 2.00 2.15 2.29 2.44 3.76 3.75 3.74 3.72 3.71 3.70 3.70 3.69 8 SctlDwarf Cepbeidsb -1.4 -1.0 -0.7 +2.7 +1.7 +0.8 0.1 0.5 1.0 1.3 -0.1 -0.9 -1.8 -2.4 0.20 0.25 0.29 0.90 1.22 1.58 0.07 0.37 0.59 3.91 3.88 3.86 Population II Cepbeids 0.30 0.44 0.60 0.70 1.95 2.27 2.63 2.87 0.86 1.08 1.34 1.52 3.82 3.79 3.75 3.72 RR Lyrae starsc -0.5 -0.3 -0.1 0.7 0.7 0.7 0.20 0.25 0.38 1.47 1.57 1.59 0.54 0.67 0.76 f3 Cepbei stars -1.0 -0.8 -0.6 -2.5 -3.1 -3.8 -0.23 -0.25 -0.27 3.99 4.33 4.69 0.84 0.93 1.03 Notes a Q == P(p/ P0)O.S is the pulsation constant expressed in days. bMany of these stars show higher-order and/or nonradial modes as well. C Mv depends on metallicity: Mv = 0.20[FeIH] + 1.0. 16.3 VARIABLE WHITE DWARF TABLES by Paul A. Bradley Tables 16.1, 16.2, and 16.3 give data for the DAV, DBV, and DOV variable white dwarfs, respectively. BPM 30551 [1.2] R548 [3-5] BPM 31594 [6--8] HL Thu 76 [9-11] G 38-29 [12] G 191-16 [13, 14] HS0507+0434B [15] GD 66 [16,17] KUV 08368+4026 [18] GD99 [19] G117-B15A [~22] KUV 11370+4222 [18] G255-2 [23] BPM 37093 [24] GD 154 [25, 26] G 238-53 [27] EC 14012-1446 [28] GD 165 [29-31] L 19-2 [32-34] R 808 [19] G 226-29 [35, 36] BPM 24754 [37] G 207-9 [38] G 185-32 [13] GD 385 [7,39] PG 2303+242 [40,41] G 29-38 [12,42-44] EC 23487-2424 [45] 0104 -464 0133 -116 0341 -459 0416 +272 0417 +361 0455 +553 0507 +0435 0517 +307 0837 +403 0858 +363 0921 +354 1137 +422 1159 +803 1236 -495 1307 +354 1350+656 1401 -1454 1422 +095 1425 -811 1559 +369 1647 +591 1714 -547 1855 +338 1935 +276 1950 +250 2303 +242 2326 +049 2349 -244 z:z V470Lyr PYVul PTVul KRPeg Psc HWAqr BTCam V886Cen BGCVn DUDra IUVir CXBoo MYAps TYCrB DNDra VWLyn RYLMi V361 Aur VYHor V411 Tau V468 Per BRCam AXPhe z:z Cet Variable star name 010656 013610 034325 04 1859 042018 045928 051013 052038 084008 090149 09 2417 11 3941 120148 123848 13 09 58 135212 140357 142440 143218 1601 21 164826 17 1854 185730 1937 13 195228 230616 232849 235122 a (2000.0) 1. 2. 3. 4. 5. (2000.0) -4610.2 -1120.7 -4548.7 +2718.4 +3616.6 +5525.3 +0438.6 +3048.5 +4015.1 +3607.2 +3516.9 +4205.3 +8005.0 -4949.0 +3509.5 +6524.9 -1501.1 +0917.3 -8120.1 +3647.0 +5903.5 -5447.1 +3357.2 +2743.3 +2509.3 +2432.0 +0515.0 -2408.2 ~ 12.0 [46, 49] 12.1 [46.48-51] 11.2 [46, 48] 12.5 [46--51] 12.9 12.0 [46--48, 51] 12.1 [46--48,50, 51] 11.7 [46, 47] 11.5 [46, 47] 11.8 [46--50] 11.4 [46,47] 11.7 [46.48,50,51] 11.2 [46,48-51] 11.9 [46, 49] 11.8 [46--49,51] 11.6 [46--51] 11.3 [46,47] 12.0 [46--50] 11.5 [46,47] 11.4 [46,47] 11.2 [46,47] 11.4 [46, 47] 11.8 12.0 [46, 49, 50] Teff (103 K) Hesser,I.E., Lasker, B.M., & Neupert, H.E. 1976, ApJ, 209, 853 McGraw,I.T. 1977, ApJ, 214, LI23 Lasker, B.M., & Hesser, I.E. 1971, ApJ, 163, L89 Stover, R.I., Hesser,I.E., Lasker, B.M., Nather, R.E., & Robinson, E.L. 1980, ApJ, 240, 865 Kepler, S.D. et aJ. 1995, Baltic Astr., 4,238 References bPhotographic (blue) magnitude. Notes aC means combination of frequencies and H means harmonics. Name WDNo. 15.26 14.16 15.03 15.20 15.59 15.98 15.36 15.56 15.55 14.55 15.50 16.56 16.04 13.96 15.33 15.51 15.67 14.32 13.75 14.36 12.24 15.60 14.62 12.97 15.12 15.50 13.03 15.33 (mag.) V 14.14 15.51 15.7 15.50 14.46 14.00 14.53 12.40 15.87 14.81 13.15 15.32 15.58b 13.17 15.52 15.43 14.33 15.24 15.40 15.79 16.1 15.6 15.78 15.77 14.74 15.72 16.78 (mag.) B Table 16.1. Names. positions. and magnitudes of the ZZ eeti (DAV) stars. 0.22 0.012 0.28 0.28 0.22 0.3 0.2 0.02 0.03 0.07 0.05 0.006 0.04 0.004 0.10 0.02 0.30 0.10 0.03 0.15 0.006 0.07 0.06 0.02 0.05 0.2 0.27 0.24 Amp. (mag.) 610, 724 + others 114, 120 192,250, C 113, 118, 143, 192,350 833, complex, C, H 109 ~ 1100 259,292,557,739,C 141,215, C, H 256,C 394,483,54O,611,936,C,H 284,615, 820, C, H ~ 800-1000, complex ~206 403, 1089, 1186, C, H ~6OO 823 + others 213,274 402,618, C, Ha 393, 625, 746, C, H ~ lOOO,C,H 510,6OO,710893,C,H 355,445, 560, CH 197,272,302,819,C,H 495,618 350,481,592 215,271,304, C, H 257 + others 685,830 + others Periods (seconds) 0 ~ - ....... til t""' ttl t;x:j ~ '"I1 ~:;g 0 >-l ttl ::I: ~ - t""' trJ > t:I:1 :;g - ~ 0'1 UJ - 6. McGraw,I.T. 1976,ApJ, 210, L35 7.0'Donoghue,D. 1986,AlN~S,220, 19P 8. O'Donoghue, D., Warner, B., & Cropper, M. 1992, AlN~S,158, 415 9.Page,C.G. 1972,AlN~S,159,25P 10. Fitch, W.S. 1973,ApJ, 181, L95 11. Dolez, N., & Kleinman, SJ. 1997 in White Dwarfs, edited by I.lsern, M. Hemanz, and E. Garcia-Berro (Kluwer Academic, Dordrecht), p. 437 12. McGraw,I.T., & Robinson, E.L. 1975, ApJ, 200, L89 13. McGraw,I.T., Fontaine, G., Dearborn, D.S.P., Gustafson,I., Lacombe, P., & Starrfield, S.G. 1981, ApJ, 250, 349 14. Vauclair,G.etal.I991,A&A,215,Ll7 15. Iordan, S., Koester, D., Vauclair, G., Dolez, N., Heber, U., Hager, H.I., Reimers, D., Chevreton, M., & Dreizler, S. 1998, A&A, 330, 277 16. Dolez, N., Vauclair, G., & Chevreton, M. 1983, A&A, 121, L23 17. Fontaine, G., Wesemael, F., Bergeron. P., Lacombe, P., Lamontagne, R., & Saumon. D. 1985,ApJ, 294, 339 18. Vauclair, G. et al. 1996, A&A, 322, 155 19. McGraw,I.T., & Robinson, E.L. 1976, ApJ, 205, Ll55 20. Kepler, S.O., Robinson. E.L., Nather, R.E., & McGraw,I.T. 1982, ApJ, 254, 676 21. Kepler, s.o. et al. 1991, ApJ, 378, L45 22. Kepler, S.O. et al. 1995, Baltic Astr., 4, 221 23. Vauclair, G., Dolez, N., & Chevreton, M. 1983, A&A, 103, Ll7 24. Kanaan, A.N. et al. 1992, ApJ, 390, L89 25. Robinson, E.L., Stover, R.I., Nather, R.E., & McGraw,I.T. 1978, ApJ, 220, 614 26. Pfeiffer, B. et al. 1996, A&A, 314, 182 27. Fontaine, G., & Wesemael, F. 1984,AJ, 89,1728 28. Stobie, R.S. et al. 1995, AlN~, 272, L21 29. Becldin, E.E., & Zuckerman, B. 1988, Nature, 336, 656 30. Bergeron, P., & McGraw,I.T. 1990, ApJ, 352, L45 31. Bergeron, P. et al. 1993, AJ, 106, 1987 32. O'Donoghue, D., & Warner, B. 1982, AlN~S, 200, 573 33. O'Donoghue, D., & Warner, B. 1987, AlN~S, 228, 949 34. Sullivan, DJ. 1995, Baltic Astr., 4, 261 35. Kepler, S.O., Robinson, E.R., & Nather, R.E. 1983, ApJ, 271, 744 36. Kepler, S.O. et al. 1995, ApJ, 447, 874 37. Giovannini, O. et al. 1998, A&A, 329, Ll3 38. Robinson, E.L., & McGraw,I.T. 1976, ApJ, 207, L37 39. Kepler, s.o. 1984, ApJ, 278, 754 40. Vauc1air, G., Chevreton, M., & Dolez, N. 1987, A&A, 175, Ll3 41. Vauclair, G. et al. 1992, A&A, 264, 547 42. Winget, D.E. et al. 1990, ApJ, 357, 630 43. Patterson,I.etal. 1991,ApJ,374,330 44. Kleinman, S.I. 1997 in White Dwarfs, edited by 1. !sern, M. Hemanz, and E. Garcia-Berro (Kluwer Academic, Dordrecht), p. 437 45. Stobie, R.S., Chen, A., O'Donoghue, D., & Kilkenny, D. 1993, AlN~S, 263, L13 46. Bergeron, P. Wesemael, F., Lamontagne, R. Fontaine, G., Saffer, R.A. & Allard, N.F. 1995, ApJ, 449, 258 47. Weidemann, V., & Koester, D. 1984, A&A, 132, 195 () CIl CIl o-j tt1 iiIC o-j -- n ::z:: > iiIC > () t""' () tt1 ~ -> til ::z:: o-j ~ CIl - iiIC ~ til 0'1 s -- 48. 49. 50. 51. VI063 Tau SWLMi DTLeo EMUMa CWBoo V777 Her V824 Her QUTel KUV 0513+2605 [1] CBS 114 [2] PG 1115+ 158 [3,4] PG 1351+489 [5] PG 1456+ 103 [6] GD 358 [7-10] PG 1654+160 [11] EC 20058-5234 [11] 0513 +261 0954 +342 1115 +158 1351 +489 1456 +103 1645 +325 1654 +160 2006 -523 (2000.0) 051628 09 57 50 111823 13 5310 145833 1647 19 165658 200940 IX (2000.0) +2608.6 +3359.7 +1533.5 +4840.4 +1008.3 +3228.5 +1556.4 -5225.4 ~ T:ff 22.5: [13, 14] 22.0: [13, 14] 22.5: [13, 14] 25.3 ± 0.3 [13, 14] 21.5: [13, 14] (103 K) 15.54 13.65 16.3 V (mag.) 17b 16.12b 16.38b 15.8gb 13.54 16.15b B (mag.) 0.10 0.30 0.06 0.05 0.10 0.10 0.10 0.07 Amp. (mag.) 400, complex 650, complex 1000, complex 489+harmonics 420-860, complex 700, -complex 150-850, complex 134,195,204,257,281 Period (seconds) References 1. Grauer, A.D., Wegner, G., & Liebert, J. 1989, Ai, 98, 2221 2. Winget, D.E., & Claver, C.F. 1989, in White Dwarfs, edited by G. Wegner (Springer-Verlag, Berlin), IAU Colloq. 114, p. 290 3. Winget, D.E., Nather, R.E., & Hill, J.A. 1987, Api, 316, 305 4. Clemens, J.C., et aI. 1993, in White Dwarfs: Advances in Observation and Theory, edited by M.A. Barstow (Kluwer Academic, Dordrecht), p. 515 5. Grauer, A.D., Bond, H.E., Green R.F., & Liebert, J. 1988,AJ, 95, 879 6. Winget, D.E., Robinson, E.R., Nather, R.E., & Fontaine, G. 1982, Api, 262, Lli 7. Winget, D.E. et aI. 1994, Api, 430, 839 8. Bradley, P.A., & Winget, D.E. 1994, Api, 430,850 9. Provencal, J.L. et aI. 1996, Api, 466, lOll 10. Winget, D.E., Robinson, E.L., Nather, R.E., & Balachandran, S. 1984, Api, 279, Ll5 II. O'Donoghue D. 1995, 9th European Workshop on White Dwarf Stars, edited by D. Koester & K. Werner (Springer-Verlag, Berlin), p. 297 12. Liebert, J. et al. 1986,Api, 309,241 13. Thejll, P., Vennes, S., & Shipman, H.L. 1991, Api, 370, 355 Notes aUncertain temperatures are marked by a colon. bPhotographic (blue) magnitude. Variable star name Name WDNo. Table 16.2. Names, positions, and magnitudes of the DBV sUlrs. Kepler. S.O., & Nelan, E.P. 1993, AJ, lOS, 608 Daou, D., Wesemael, F., Bergeron, P., Fontaine, G., & Holberg, J.B. 1990, Api, 364, 242 Wesemael, F., Lamontagne, R., & Fontaine, G. 1986, Ai, 91, 1376 Koester, D., Allard, N., & Vauc1air, G. 1994,A&A, 291, L9 W ~ ...... CI.l tr1 r I:I:l ;;2 'Tl ~~ o tr1 ~ ::z:: ..... ~ tr1 r I:I:l :; ~ ~ W 0\ - RXJ 0122.9-7521 0123 -754 0130 -196 0444+045 0704 +615 VV47 1144 +005 1151 -029 1424 +535 1504 +652 1517 +740 1520+525 NGC246 NGC 1501 [6] NGC 2371-2 [7] NGC2S67 Lo-4 [S] NGC51S9 Sanduleak 3 [15] K 1-16 NGC6905 2117 +341 PG 0122+200 [1-3] PG 1159-035 [4, 5,] PG 1707+427 [6-8] PG 2131+066 [6, 9] HS 2324+3944 [10-12] 0122 +200 1159 -035 1707 +427 2131 +066 2324 +3944 V2027Cyg DSDra LV Vel KNMus IS9+19°1 [13, 15] 27S-5° 1 [13] 274+9°1 [16, 17] 307-3°1 [13] 94+27°1 [IS, 19] 61-9°1 [13, 15] RXJ 2117+3412 [20-22] CHCam 8 (2000.0) +2017.S -0345.6 +4241.0 +0650.9 +4001.4 012255 013240 044704 0709 32 075750 114636 11 54 15 142555 1502 OS 15 1646 152147 -7521.2 -1921.7 +04 5S.7 +614S.3 +5325.0 +00 12.5 -03 12.1 +5315.4 +6612.5 +7352.1 +5222.0 Nonpulsating PG 1159 stars 0125 22 120146 17 OS 4S 2134 OS 232716 Pulsating PG 1159 (DOV) stars a (2000.0) ISO 95 100 65 130 150 140 100 170 95 150 75 140 100 SO 130 (103 K) Teff 004703 040659 072535 09 2125 100545 133333 1603 OS IS 2152 202223 211707 -1152.3 +6055.2 +2929.4 -5S IS.7 -4421.5 -655S.4 -3537.3 +6421.9 +2006.3 +3412.4 150 ND ND ND 120 ND 130 -140 ND 170 Pulsating planetary nebula nuclei (PNNVs) BBPsc GWVir VS17 Her IRPeg 144+6°1 [13, 14] lIS-74° 1 [13] PG 1144+005 PG 1151-029 PG 1424+535 H 1504+65 HS 1517+7403 PG 1520+525 164+31°1 HS 0444+0453 HS 0704+6153 MeT 0130-1937 Name WDNo. Variable star name 15.0S 15.7 13.16 16.6 11.96 14.20 14.S5 15.52 16.2 16.24 16.S3 15.45 15.84 14.S4 16.69 16.63 14.S V (mag.) 14.66 14.gb 13b 16.45 16.62b 14.91 15.9 15.56 15.12 15.55 15.9 16.S 16.53 15.04 16.07 15.S6 16.13 14.21 16.0S 16.24 B (mag.) Table 16.3. Names, positions, and magnitudes of the PG 1159 and PNNV stars. -0.002 -0.15 -0.01 -0.02 -0.06 -0.003 -0.01 -0.05 - 0.01 0.05 0.10 0.10 0.10 0.10 0.02 Amp. (mag.) -1500 - 1500, complex - 1000, complex -770 IS00-2000, complex -690 -1000 1500-1700, complex 710, S75, + others - SOO, complex - 500, complex - 450, complex 400--600, complex - 2100 400--600, complex Period (seconds) til n ..... til ~ :;c ..... trl ~ > :;c > n ::z:: t'"' (') > n ..... trl 'tI en ::z:: ~ ~ ..... til ~ :;c en 0'\ - ..... § p.491 16. Longmore, AJ., 1977, MNRAS,I7B, 251 17. Bond, H.E., &; Meakes, M.G. 1990,AJ, 100, 788 18. Grauer, A.D., & Bond, H.E. 1984, ApI, 277, 211 19. Grauer, A.D., Bond, H.E., Green, R.F., &; Liebert, J. 1987, in The Second Conference on Faint Blue Stars, edited by A.G.D. Philip, D.S. Hayes, and J.W. Liebert (Davis, Schenectady), IAU Colloq. 95, p. 231 20. Watson, T.K. 1992, IAU Cire. 5603 21. Vauclair, G. et aI. 1993, A&A, 267, L35 22. Motch, C., Werner, K., & Pakull, M.W. 1993, A&A, 268, 561 References I. Bond, H.E., &; Grauer, A.D. 1987, ApI, 321, LI23 2. Vauclair, G. et aI. 1995, A&A, m, 707 3. O'Brien, M.S. et aI. 1996, ApI, 467, 397 4. Wmget, D.E. et aI. 1991, ApI, 378, 326 5. Kawaler, S.D., & Bradley, P.A. 1994,ApJ, 427, 415 6. Bond, H.E., Grauer, A.D., Green, R.F., & Liebert, J. 1984, Api, 279,751 7. Fontaine, G. et aI. 1991, ApI, 378, L49 8. Grauer, A.D., Green, R.F., &; Liebert, J. 1992, ApJ, 399, 686 9. Kawaler, S.D. et aI. 1995, ApI, 450, 350 10. Silvotti, R. 1996, A&A, 309, L23 11. Dreizler, S. et aI. 1996, A&A, 309, 820 12. Handler, G. et aI. 1997,A&A,326, 692 13. Ciardullo, R., & Bond, H.E. 1996, AJ, 111, 2332 14. Bond, H.E. et aI. 1996,AJ,I12, 2699 15. Bond, H.E., & Ciardullo, R. 1993, in The 8th European Workshop on White Dwarf Stars, edited by M.A. Barstow (Kluwer Academic, Dordrecht), NATO ASI Ser., Notes aThmperatures for the DOV stars taken from Sion, E.M., & Downes, R.A. 1992, ApJ, 3%, L79; Werner, K., 1992, A&A,lSl, 147; Werner, K., & Heber, U. 1991, A&A,147, 476; Werner, K., Heber, U., & Hunger K. 1991, A&A,144, 437; and estimated by me from comparisons of optical and UV spectra given in Wesemael, F., Green, R.F., &; Liebert, J. 1985, ApIS, 58, 379. bPhotographic (blue) magnitude. ~ CIl t11 - = t'"" ~ "!1 ~:;g o t11 ~ :z: ~ - t'"" t11 :;g ->= ~ w 0'1 - 406 / 16 STARS WITH SPECIAL CHARACTERISTICS 16.4 LONG-PERIOD VARIABLES [14-19] Long-period variables (LPVs) including Mira stars are mostly M-type giant and supergiant stars, usually with emission lines in their spectra. Many carbon stars (C-type) and zirconium (S-type) stars also show this type of variability. OHIIR stars are probably dust-enshrouded Miras having periods ~ 600 to 2000 days and are not visible optically. 16.4.1 Properties of Mira Variables The visual magnitude variation range is 2.5-10 mag. The galactic scale height is 240 pc. The mass is '" 1 M0 log Teff ~ 4.255 - 0.35 log P (100 < P < 500). Luminosity: Mv at maximum light ~ O.OO4OP - 2.6 (200 < P < 500). = -3,47 log P + 1.0, (Mbol) = - 2.34 log P + 1.3. (MK) 1Ypes of variables are given below: Designation Type Pop P (days) Sp Mv AV (gal. lat.) Periodicity M SR a, b,c,d Mira, oxygen-rich; Long period, serniregular I&n I&n 200-600 100-500 M,e,S F-M,e,S in text -1 in text ::: 2.5 in text 22° regular serniregular L Slow irregular I&n 100-500 M,e,S -1 ::: 2.5 22° not regular 16.5 OTHER VARIABLES [19-22] Details of the classes and subclasses are given in [20]. Types of other kinds of variables are given below: Designation 1Ype and features Pop P RV RV Tau. Alternating depth of minimum R CrB. Deep fades + pulsation n 40--150 days '" years 40--70 days 40--70 days RCB UUHer UUHer I? I&n ~v G-K Mv -2 Average galactic latitude 1.3 23° F-G -4 5 0.2 14° FI ? 0.3 20° Sp 16.6 ROTATING VARIABLES I 407 16.6 ROTATING VARIABLES by Douglas S. Hall These stars vary in brightness periodically as the star rotates about its axis. Except for the ellipsoidal variables, the star is essentially spherical, and it is a longitudinally asymmetric distribution of surface brightness that causes the variability. Four basic mechanisms apply here: 1. The ellipticity effect results when one or both stars in a binary is ellipsoidal in shape. 2. The reflection effect in a close binary causes the facing hemisphere of one star to be brighter than its opposite hemisphere. 3. The oblique rotator model explains the ACV, SXARI, and PSR variables, where a strong dipolar magnetic field is not parallel to the rotation axis. 4. Starspots explain the BY, RS, and FKCOM variables and one component of the variability in some INT variables. The spots are magnetic in origin, like sunspots and sunspot groups, but a hundredfold larger in area. The temperature difference, photosphere minus spot, is 1000--2000 K [23]. Variability is periodic with the star's rotation but periods differ by a few percent due to solar-type differential rotation [24]. Physical mechanism for the large spots is strong dynamo action due to rapid rotation and deep convection [24]. Size of spots can be predicted by rotation period, B - V, and luminosity class [24]. Full amplitude can be up to 0.5 magnitude [24]. 16.6.1 Types of Rotating Variables ELL. No formal prototype, though b Persei is often considered so. Tidal forces in a close binary make one or both stars ellipsoidal (prolate) in shape. The difference in projected surface area between end-on and broad-side views causes the brightness to vary, with gravity darkening enhancing the effect [25]. There are two maxima and two minima per rotation, but limb-darkening effects can make the two minima unequal in depth [26]. Full amplitude, maximum to deeper minimum, can be up to 0.35 magnitude in V. Reflection variables. These are not defined formally in the GCVS. There is no formal prototype. The sole source of the variability is the reflection effect. Only a few cases are known. Examples are BH Canum Venaticorum [27] and HZ Herculis [28]. ACV. The prototype is a 2 Canum Venaticorum. Signatures of a strong (several kilogauss) magnetic field and an anomalous strengthening of absorption lines of certain elements both vary, along with the brightness, with the star's rotation period. These include the so-called Ap or peculiar A stars. The full amplitude can be up to around 0.1 magnitude in V [28]. SXARI. The prototype is SX Arietis. These are high-temperature, spectral type B, analogs of the ACV variables and are sometimes called the helium variables. The full amplitude is up to around 0.1 magnitude in V [28]. PSR. There is no formal prototype. These are optically variable pulsars like CM Tauri, the supernova remnant in the Crab Nebula: rapidly rotating neutron stars with very strong (several megagauss) magnetic fields emitting narrow beams of radiation in the radio, optical, and X-ray bands. The rotation periods are between milliseconds and seconds. The amplitude of light pulses can be up to about 1 magnitude in V [28]. More details can be found in Section 16.16. BY. The prototype is BY Draconis. These are defined by [29] and are K Ve or M Ve stars, where e means Ha emission. These can be single or binary. Rapid rotation is a consequence of the star's youth, i.e., recent arrival upon the main sequence, or by tidally enforced synchronism in a binary of short orbital period. There is considerable overlap with the UV variables, i.e., flare stars. 408 / 16 STARS WITH SPECIAL CHARACTERISTICS RS. The prototype is RS Canum Venaticorum. These are defined by [24, 30] and are G or K stars, always in binaries, by definition. Rapid rotation is caused by tidally enforced synchronism in a relatively short-period binary orbit, where "short" means days, weeks, or months for luminosity class V, IV, or III [24]. A spotted star typically is post-main-sequence but before Roche lobe overflow. FKCOM. The prototype is FK Comae Berenices. These stars are defined by [31] and are single, rapidly rotating G or K giants. They may be coalesced W UMa-type binaries [31] or A-type mainsequence stars after evolution into the Hertzsprung gap [32]. INT. Starspots cause one component of the complex variability in some T Tauri stars, Le., INT variables of spectral type G, K, M. Variability is periodic with the star's rotation [33]. 16.7 T TAURI STARS [34-37] by Gibor Basri The T Tauri stars are systems containing solar-type pre-main sequence stars. As such, they provide the opportunity to learn something about our own early solar system. Indeed, many of them are now thought to contain circumstellar disks analogous to the solar nebula. Signs of youth include their position in the HR diagram, association with molecular clouds, and undepleted lithium in their spectra. They fall into two basic categories: the so-called "classical" TIS, and the weak-lined TIS. These are roughly distinguished observationally by the strength of their Ha emission. Physically, the distinction is probably between systems containing an active accretion disk or disk extending almost to the stellar surface (the CTIS), and those that have no disk or only an outer disk (the WITS). The eTIS show many phenomena associated with accretion disks and (apparently related) strong mass loss, including infrared excesses (from 2 to 100 JLm), strong Balmer line (and continuum) emission, other emission lines (including forbidden-line emission in many systems), and an optical and ultraviolet excess thought to be generated by the accretion onto the star. When the accretion is strong, the photospheric absorption lines can be "veiled" by dilution from the accretion-related continuum. In extreme cases the light from the accretion disk can completely mask the stellar light (FU Ori systems). The WITS show none of these effects, displaying only the effects of very strong magnetic activity (chromospheres, coronae, starspots). Their properties generally lie along the activity sequence that extends down to old main-sequence stars, but they are among the most active examples known. The underlying stars in the eTIS are probably very similar. The eTIS and WITS are commingled both spatially and on the HR diagram, except that CTIS much older than 10 Myr are not found. There are generally more WITS than CTTS in well-surveyed clouds (and the WITS are more likely to be incompletely sampled). See Table 16.4 for characteristics of T Tauri stars. Table 16.4. TTauri Star Characteristics. Namea V (V range)b EW(Ha)(A)C v sinje f L star HBC No.; Sp.T. Av Veiling (5500 A)d P:"t L~ystem Remarks TTau 35; KOIV,V 9.9 (9.3-13.5) 1.3 50-70 0-0.2 20 2.8 12: 18.9+4.4 Prototype, but somewhat atypical; IR companion BPTau 32;K7V 12.1 (10.7-13.6) 0.5 30-50 0.5-1 <10 7.6 0.9 1.6 A fairly typical case, bright spots seen DFTau 36; MO,I V 11.5 (11.5-15) 0.45 30-90 1-1.5 22 8.5 2.0 5.1 Also typical; speckle binary 16.8 FLARE STARS / 409 Table 16.4. (Continued.) f Namei' V (V range)b EW(HaXA)C v sini e HBCNo.; Sp.T. AV Yeiling (5500 A)d pe rot L: Remarks DR Tau 74;c(M0) 11.2 (10.5-16) 17 40-90 3-8 < 10 137 0.9 5.3 Extremely variable, many emission lines RWAur 80; c(KS) 10.1 (9.6-13.6) 1.2 70-90 0.5-3 15 5.47 2.5 4.4 Very broad lines, variable veiling DGTau 37;c(K7MO) 12.0 (10.5-14.5) 17 70-100 3-5 20 7 0.9 10.1 Optical jet source, many emission lines FUOri 186; G: I,ll 9.6: (9.2-16.5) 1.85 27 Yerybigh 110: 7 47 490 Prototype of extreme outburst sources; light is declining slowly; pure disk spectrum Y410Tau 29;K3Y 10.8 (10.8-12.4) 0.03 3 0 73 1.88 2 2 Large spots, 1 solar mass, 1 Myrold Y830Tau 405;K7-MOY 12.2 (12.1-12.4) 0.4 3 0 29 2.75 1.2 1.2 Typical "weak" or "naked" T Tauri star Lsw: ystem Notes aHerbig and Bell catalog: compendium of 742 pre-main-sequence stars. For spectral types, c indicates a heavily veiled or "continuum" star. bYisuai magnitude and range; extinction is not very accurate, somewhat model-dependent (in classical T Tauri stars). cEstimated range of Ha equivalent width (A) (Iow-dispersion spectra). dExcess continuum veiling at 5500 A (in units of photospheric continuum). eProjected rotation velocity in kmls; period (from photometric modulation) in days. f Stellar luminosity (bolometric, in solar luminosities); estimated from flux near 1 ILm; not very accurate due to extinction and accretion disk effects, except on weak-lined stars. gSystemic bolometric luminosity (in solar luminosities, from 0.3-100 ILm); dominated by IR excess when well above stellar value. 16.8 FLARE STARS [38-42] by Douglas S. Hall Flares are observed on K Ve and M Ve (classical UV Cet stars), on spectral classes G and K, with luminosity classes V and IV (RS CVn, W UMa, and Algol binaries, FK Com stars). Flare amplitudes are up to :::::: 5 mag. in U. The energy output of any flare in the spectral windows are Ex :::::: Eeuv :::::: E opt » Eradio, Ebol :::::: 6Eopt; Eopt :::::: 4Eu, Eu : EB : Ev = 1.8: 1.5 : 1.0. The largest flare yet observed is represented by Eu = 1037 erg, Ebol = 2 x 1038 erg. The time-averaged bolometric luminosity of flares on a given star is (Lflare) = 0.OO3Lstar for active stars at saturation level, (Lflare) < 0.OO3Lstar for less active stars. 410 / 16 STARS WITH SPECIAL CHARACTERISTICS The flare duration (rise time and half-life of decay time) in sis log trise log t1/2 = 0.25 log Eu = 0.30 log Eu - 6.0, 7.5. Flare colors and temperatures are (B - V) T = +0.34 ± 0.44, = (U - B) = -0.88 ± 0.31, {3 X 107 K for dMe stars, 108 K for RS CVn stars. The flaring frequency, for a given star, depends on flare energy: vex E-f3, For UV Cet itself, v 16.9 = 1 flare/day at EB 0.4 < {J < 1.4. = 1031 erg. WOLF-RAYET AND LUMINOUS BLUE VARIABLE STARS by Kenneth R. Brownsberger and Peter S. Conti Wolf-Rayet (WR) stars are highly evolved descendants of massive stars, stars whose initial masses are larger than about 40M 0 . WR stars are characterized by strong, broad emission lines in their spectra, due to their intense stellar winds. The strengths of the emission lines serve as the basis for the classification of these stars. There are two main WR spectra types, WN and WC, and a third, less numerous type, WOo The WN types have spectra dominated by helium and nitrogen emission lines (see Table 16.5); in WC types, the predominant lines are from helium, carbon, and oxygen. The WO types have very strong oxygen lines (see Table 16.6). Because the underlying stars are shrouded behind their dense stellar winds, the intrinsic stellar parameters of WR stars are difficult to ascertain. Furthermore, comparisons with non-LTE (local thermodynamic equilibrium) wind models yield a spread of values of the stellar parameters for different stars of the same spectral subtype: Radii of WR stars range from 2 to 20 R0, temperatures from 30000 to 70000 K, wind velocities from 1000 to 3000 kms- I , and mass loss rates from 10-5 to 10-4 M0 yr- 1 [43,44]. (See Tables 16.7-16.11.) Luminous blue variables (LBVs) are hot, massive stars that show strong photometric and spectroscopic variations. LBVs include Hubble-Sandage variables, P Cygni stars, and S Doradus stars and can vary by 1 to 2 magnitudes on time scales of a few decades. Occasionally, they can erupt and increase their brightness by more than 3 mag. During their quiescent phases of minimum brightness, LBVs appear to be blue, B-type supergiants. During periods of maximum brightness they resemble late-type (A-F) supergiants [45,46]. (See Table 16.12.) Table 16.5. Classification criteria/or WN spectra [I, 2]. WN SUbtypes Nitrogen ions Other criteria WN2 WN2.5 WN3 N v weak or absent N v present, N IV absent N IV « N v. N II weak or absent Hell strong 16.9 WOLF-RAYET AND LUMINOUS BLUE VARIABLE STARS I 411 Table 16.5. (Continued.) WNsubtypes Nitrogen ions Other criteria WN4 WN4.5 WN5 WN6 WN7 WN8 WN9 N IV ~ N V, N III weak or absent N IV > N v, N III weak or absent Nm ~NlV ~Nv N m ~ N IV, N V present but weak N m > N IV, N III A4640 < He II A4686 N III » N IV, N m A4640 ~ He II A4686 N III present, N IV weak or absent He I weak P Cyg He I strong P Cyg He I, lower Balmer series P Cyg References l. van der Hucht, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981, SSRv, 28, 227 2. Conti, P.S., Massey, P., & Vreux, I.M. 1990, ApJ, 354, 359 Table 16.6. Classification criteria/or WC, WO spectra [1, 2, 3]. SUbtypes Carbon ions Other criteria WC4 WC5 WC6 WC7 WC8 WC9 C IV strong, C III weak or absent Cm« CIV Cm« CIV Cm < CIV Cm > CIV Cm > CIV OVmoderate Cm<Ov Cm>Ov Cm»Ov C II absent, 0 V weak or absent C II present, 0 V weak or absent Subtypes Oxygen ions Other criteria WOl OVI strong OVI strong OV<CIV W02 OV~CIV References 1. van der Huchl, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981, SSRv, 28, 227 2. Conti, P.S .• Massey, P., & Vreux, I.M. 1990, ApJ. 354,359 3. Barlow, 1.1., & Hummer, O.G. 1982, in Wolf-Rayet Stars: Observations, Physics, Evolution (Reidel, Dordrecht), IAU Symp. 99, p. 387 Table 16.7. Observed numbers o/Wolf-Rayet subtypes [1-7]. Galaxy LMC SMC WNE (WN2-WN5) WNL (WN&-WN9) WCE (WC4-WC7) WCL (WC8-WC9) 30 61 5 50 25 2 40 19 27 WNIWC WO 7 1 2 1 1 References 1. van der Huchl, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981. SSRv, 28, 227 2. Breysacher,I. 1981, A&A, 43,203 3. Azzopardi, M., & Breysacher, 1. 1979,A&A, 75,120 4. Lundstrom, 1., & Stenholm, B. 1984, A&A, 58, 163 5. Vacca, W.O., & Torres-Dodgen, A.V. 1990, ApJS, 73, 685 6. Conti, P.S., & Vacca, W.O. 1990, AJ, 100(2),431 7. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca, W.O. 1993, ApJ, 412, 324 412 / 16 STARS WITH SPECIAL CHARACTERISTICS Table 16.8. Observed numbers of single Wolf-Rayet stars and those with companions and/or absorption lines [1-7]. Galaxy LMC SMC WN WN+abs WC WC+abs WO 64 64 1 22 16 51 15 12 2 6 7 WO+abs 1 References 1. van der Hucht, K.A., Conti, P.S. Lundstrom, I., & Stenholm, B. 1981, SSRv,28,227 2. Breysacher, J. 1981, A&A, 43, 203 3. Azzopardi, M., & Breysacher, J. 1979, A&A, 75, 120 4. Lundstrom, I., & Stenholm, B. 1984, A&A, 58, 163 5. Vacca, W.O., & Torres-Dodgen, A.V. 199O,ApJS, 73, 685 6. Conti, P.S., & Vacca, W.O. 1990, AJ, 100(2), 431 7. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca, W.O. 1993, ApJ, 412, 324 Table 16.9. Average intrinsic colors and absolute magnitudes [1-3]. Mv (b - v)o WNE WNL WCE WCL -3.8 -0.2 -5.5 -0.2 -4.5 -0.3 -4.8 -0.3 References 1. Vacca, W.O., & Torres-Dodgen, A.V. 1990, ApJS, 73, 685 2. Conti, P.S., & Vacca, W.O. 199O,AJ,I00(2), 431 3. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca, W.O. 1993, ApJ, 412, 324 Table 16.10. Selected Wolf-Rayet stars [1-4]. ID Star Other AB5 Br08 Br26 WROO6 WR011 WR048 WR 111 WR 136 HD5980 HD32257 HD36063 HD50896 HD68273 HD 113904 HD 165763 HD 192163 AzV229 Sk-69°42 Sk-71°21 EZCMa y2 Vel (J Mus MR84 MR 102 III bll 302.07 280.81 282.64 234.76 262.80 304.67 9.24 75.48 -44.95 -35.29 -32.63 -10.08 -7.69 -2.49 -0.61 +2.43 Sp. Class v WN4+07I: WC4 WN7 WN5+(cc?) WC8+09I WC6+09.5I WC5 WN6(SBl) 11.88 14.89 12.68 7.26 1.74 5.58 8.25 7.79 E(b - v) [5,6] (m-M) 0.05 0.08 0.07 0.05 0.03 0.17 0.32 0.45 19.2 18.5 18.5 11.3 8.3 11.9 11.0 11.6 References 1. van der Hucht, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981, SSRv, 28, 227 2. Breysacher, J. 1981, A&AS, 43, 203 3. Azzopardi, M., & Breysacher, J. 1979,A&A, 75,120 4. Conti, P.S., & Vacca, W.O. 1990, AJ, 100(2),431 5. Vacca, W.O., & Torres-Dodgen, A.V. 1990, ApJS, 73, 685 6. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca, W.O. 1993,ApJ, 412, 324 7. Lundstrom, I., & Stenholm, B. 1984, A&AS, 58, 163 [7] 16.10 BE STARS / 413 Thble 16.11. Representative UV·NIR (0.1-1.1 JLm) emission lines in Wolf-Rayet stars. WN stars contain He. N. and C; WC stars contain He. C. and O. Ion IF (eV) A (A) Ion IF (eV) Hel Hell 24.6 54.4 Nm NIV 47.4 77.4 1751.4634.4641 1486.3480.4058.6383. 7115 CII 24.4 Nv 97.9 1240.1718.4604.4620 Cm 47.9 om 54.9 3265.3708.3760.3962 CIV 64.5 5876.6678.7065.10830 1640.2511.2734.3203. 4686.4860.5412.6560. 6683.6891.8237.10124 1335.4267.7236.9234. 9891 1176. 1247. 19091.2297. 4650.5696.6742.8500. 8665.9711 1549.2405.2530.4441. 4787.5017.5470.5805. 7061.7726.8859 OIV 77.4 3411.3730 Ov OVI 113.9 138.1 A (A) 2788.3140.4933.5592 3811.3834 Thble 16.12. Observed properties of luminous blue variables (LEV) [1. 21. LBV Star Galaxy 1/Car AGCar HRCar [31 WRA 751 [41 PCyg T (K) Minimum brightness Maximum brightness 27000: 25000: 14000: < 30000: 19000 9000 Mbol Mass loss yr- I ) (M0 -11.3 -10.1 -9.4 -9.5 -9.9 10- 3 to 10- 1 3 x 10-5 2 x 10-6 2 x 10-6 2 x 10-5 LMC SOor R 71 R 127 R 143 [51 20000--25 000 13600 30000 19000 8000 9000 8500 6500 -9.8 -8.8 -10.5 -10.0 5 x 10-5 5 x 10-5 6 x 10- 5 M33 VarC VarA 20000--25 000 35000 7500-8000 8000 -9.8 -9.5 4 x 10- 5 2 x 10-4 References 1. Humphreys. R.M. 1989. in Physics of Luminous Blue Variables (Kluwer Academic. Oordrecht). IAU Symp. 157. p. 3 2. Conti. P.S. 1984. in Observational Tests of Stellar Evolution Theory (Reidel. Dordrecht). IAU Symp. 157. p. 233 3. Hutsemekers. D .• & van Drom. E. 1991. A&A. 248. 141 4. van Genderen. A.M .• The. P.S .• & de Winter. D. 1992. A&A. 258. 316 5. Parker. I.W.. Clayton. G.C .• Winge. C.• & Conti. P.S. 1993. ApJ. 409. 770 16.10 Be STARS by Arne Slettebakt and Myron Smith Be stars may be defined as nonsupergiant B-type stars whose spectra have or had at one time Balmer lines in emission; the "Be phenomenon" is the episodic occurrence of rapid mass loss in these stars, resulting in Balmer emission. As a group, Be stars are characterized by rapid rotation, v sin i up to 400 km/s, but below the critical velocity. tDeceased. 414 / 16 STARS WITH SPECIAL CHARACTERISTICS Statistical studies show that Be stars are not exotic objects. They comprise nearly 20% of the BOB7 stars in a volume-limited sample of field stars, with a maximum incidence at B2 and considerably lower frequencies among late B-types. Studies of Be stars in clusters show that Be stars may exist anywhere from the main sequence to giant regions in the H-R Diagram, with an average of to 1 magnitudes above the ZAMS. These positions are consistent with core hydrogen-burning rapid rotators. Balmer (and occasionally He I) emission lines arise from equatorially confined disks of (typically) 5-20 stellar radii, 10000 K temperature, and 1010_1013 cm- 3 electron density. These disks are expelled from the star on a timescale from days to years. Be stars are variable on a continuum of timescales from several decades to minutes. Periodic variations in radial velocities and/or flux are often observed. The optical spectra of some Be stars can exhibit continual low-level absorptions and/or emission components which alter the line profile. Disks are fonned, sometimes quasi-periodically, on a variety of timescales from days to years and their dispersal from weeks to decades; the fractional amount returning to the star is unknown. It is generally assumed that the disk material is in Keplerian orbit. Departures from axisymmetry and/or inhomogeneous density particle distributions can cause cyclic variations in the Violet and Red emission components in the Balmer lines. Ultraviolet studies show that another side of the Be phenomenon is the appearance of strong, highvelocity absorption components in the UV resonance lines of C IV, Si IV (and occasionally Al III, N V, 0 VI) which can be attributed to the acceleration of a radiatively driven wind. The strengthening features are well, but imperfectly, correlated with Balmer emission episodes. Mass loss rates from the UV data are 10- 11 _10- 9 M0 ye 1; these are typically 10-50x lower than rates estimated from the slow expansion of the equatorial disks from infrared and radio data. 1\vo hypotheses are current explanations of the Be phenomenon: surface magnetic activity and nonlinearities in nonradial pulsations. Historically, rapid rotation, stellar winds, nonlinear pulsations, magnetic fields, and binary interactions, singly and in combination, have been invoked to explain this activity. Because there are a few subclasses of Be stars, various combinations of different mechanisms could be responsible in particular cases. Be-star catalogs (see [47]) list thousands of these objects. We list in Table 16.13 several of the brightest, recently well-studied stars which are not in interacting binaries (significant numbers are also Algol-type). ! Table 16.13. Best-known Be stars [1-8]. Be star name lID" Sp. type v sini (km/s) y Casb 5394 22192 23862 24534 33328 37202 45542 45725 56139 58715 105435 109387 120324 138749 142926 BO.5 IVe B5ille B8Ve 09.5ille B2ille Bl IVe B6IVe B4Ve B2.5 Ve B8Ve B2IVe B5ille B2IV-Ve B6ille B7IVe 230 280 320 200 220 220 170 300 80 245 220 200 155 320 300 '" Pet' 28 Taub X Per A Eri ~ Taub v Gem fJMonAb wCMa fJ CMi 8 Cen K Ora Jl,Cen OCrB 4 Her 16.11 CHARACTERISTICS OF CARBON-RICH STARS / 415 Table 16.13. (Continued.) Be star name lID" Sp. type v sini (km/s) 48 Lilf' X Oph 660ph 59 Cyg> 1C Aqr EWLacb 142983 148184 164284 200120 212571 217050 217 891 B3Ne B1.5 Ve B2N-Ve Bl Ve Blm-Ne B3Ne B5Ve 400 140 240 260 300 300 100 fJPsc Notes "Henry Draper Catalogue number. bIn addition to the Balmer emission and rotationally broadened lines of neutral helium, these stars' spectra may show hydrogen lines with sharp absorption cores as well as narrow absorption lines of ionized metals during the stars' shell phases. References 1. Doazan, V. 1982, in B Stars with and without Emission Lines, edited by A. Underhill and V. Doazan, Monograph Series on Nonthermal Phenomena in Stellar Atmospheres, NASA-CNRS, NASA SP-456, p. 277 2. Physics of Be Stars, 1987, IAU Colloq. 92, edited by A. Slettebak and T.P. Snow (Cambridge University Press, Cambridge) 3. Landolt-Bomstein, Vol. 2,1982, Part I, Peculiar Stars; 5.2.1.4, 4. Slettebak, A. 1988, PASP, 100,770 5. Slettebak, A. 1992, in The Astronomy and Astrophysics Encyclopedia, edited by S.P. Maran (Van Nostrand Reinhold, New York), p. 710 6. Balona, L.A., Henrichs, H.F., & Lecontel, 1.M. 1994, Pulsation, Rotation, and Mass Loss in Early-Type Stars, IAU Symp. No. 162 (Kluwer Academic, Dordrecht) 7.1aschek, M., & Egret, D. 1981, A Catalogue of Be Stars, Centre de Donnees Stellaires (CDS) Microfiche #3067 8. 1aschek, M. & Egret, D. 1982, Catalogue of Special Groups, Part 1: The Earlier Groups, CDS Pub. Spec. No.4 16.11 CHARACTERISTICS OF CARBON-RICH STARS by Cecilia Bambaum Carbon-rich stars (defined as having atmospheric C/O> 1 and C/O = 1 for C and S stars, respectively) make up an odd assortment of peculiar abundance stars. Atmospheric enhancement of carbon is caused either by internal dredge-up of processed material during the late stages of stellar evolution, or by environmental interactions such as mass transfer from an evolved, close companion. Carbon stars (C designation, also classified as spectral types R, N, or J [48,49]) on the asymptotic giant branch (AGB) have acquired their enriched carbon and s(slow)-process elements through convective dredge-up of the interior processed layers due to thermal pulsing [50]. s-Process elements result from slow neutron capture (and subsequent fJ decay) due to the low neutron flux in the stellar interior; the s-process produces different elements than the rapid (r-process) neutron capture that takes place in high neutron flux environments, such as in supernova events. An evolutionary sequence M-S-C is possible, but not verified [51]. Some stars with carbon-rich atmospheres have been shown to be the result of mass transfer in a binary system, e.g., the CH and Ba II stars [52,53], and a number of C and S stars that lack the s-process element 99Tc, a signature of the ABG phase [54]. A few C stars have a great overabundance of l3C; these are known as the J types. For most carbon stars, 12C1l3C is '" 30-50, whereas for J types it is '" 3 [55]. Most of these I-type stars are not enriched in s-process elements, although there are a few exceptions (e.g., WX Cyg). Finally, there are the dwarf C stars [56]. These faint 416 I 16 STARS WITH SPECIAL CHARACTERISTICS carbon-rich stars have a large proper motion, indicating that they are nearby and are therefore underluminous for the AGB (asymptotic giant branch). They are thought to be main sequence stars that have acquired their carbon-richness by mass transfer from a giant companion that has since evolved into a white dwarf. Table 16.14 gives characteristics of C-rich stars. Thble 16.14. Characteristics of carbon-rich stars. Type Evol. Pop. Chemistry Variability Lum. Special characte,o References C (Nand late R) AGB I. II C/O > I; CN. C2. s-pr. enhanced. often Tc LPV: Lb.M.SR 6 x 1037 x 10".c0 CSE: CO. dust; .oM - 10-7 to 10- 5 M0/yr [1-3] C (J and early R) ? preAGB I. II C/O> I; CN. C2. I3c isotopic species. not s-pr. enhanced Lb.M.SR < 103.c0 CSE: CO. dust; .oM - 10-7 M0/yr [4] S AGB+? I. II C/O I; ZrO; CN; s-pr. enhanced. often Tc Lb.M.SR 10" .c0 CSE: CO. dust; .oM 6 x 10- 8 [5-7] Ball Giant s-process enhanced. esp. Ba, Sr; no Tc Var. My < Oto-3 Binaries. C-rich by mass transfer [8.9] CH Giant II Stronger eN. CH than Ba II stars; s-pr. enhanced but weaker metals than Ba II stars Var. My Oto-3 Binaries. C-rich by mass transfer [9.10] sgCH Subgiant I. II CN. CH. s-pr. enhanced esp. Sr and Ba Var. Fainter than CH stars Progenitors ofCH stars? [9. II] dC Main Sequence? 11 CN; some I3C enhanced My -10 Binaries? Mass transfer? [3.12] Note a CSE = = circumstellar envelope. References 1. Claussen, M.J. et al. 1987, ApJS, 65, 385 2. Dean, C.A. 1976,AJ, 81, 364 3. Kastner, J.H. et al. 1993, A&A, 275, 163 4. Lambert, D.L. et al. 1986, ApJS, 62, 373 5. Jura, M. 1988, ApJS, 66, 33 6. Smith, V.V., & Lambert, D.L. 1988, ApJ, 333, 219 7. Johnson, H.R., Ake, T.B., & Ameen, M.M. 1993, ApJ, 402, 667 8. Jorrison A., & Mayor M. 1988, A&A, 198, 187 9. McClure, R.D. 1989, in Evolution ofPeculiar Red Giant Stars, edited by H.R. Johnson and B. Zuckerman (Cambridge University Press, Cambridge), p. 196 10. McClure, R.D. 1984, ApJ, 280, L31 II. Luck, R.E., & Bond, H.E. 1982, ApJ, 259, 792 12. Green, P.J., Margon, B., & MacConnell, D.J. 1991, ApJ, 380, L31 16.12 BARIUM, CD, AND SUB GIANT CD STARS by William Dean Pesnell Barium stars show absorption at Ball A4554, Srll A4077 and A4215, and bands of CH, CN, and C2. The enrichment of material is due to mass exchange from an evolved companion [57]. The subgiant 16.13 HYDROGEN-DEFICIENT CARBON STARS / 417 CH stars may be the main-sequence progenitors of the barium stars. CH stars have strong bands of CH, CN, and C2, but less metal enrichment than the Ba stars. See Tables 16.15 and 16.16. Table 16.15. The brighter barium stars [1, 2]. HR ex (2000.0) 8 (2000.0) my Sp. 774 2392 3123 3842 4474 4862 5058 5802 8204 24747.6 63246.9 75905.6 93801.4 113752.9 124944.9 13 2607.7 153629.5 21 2639.9 +812655 -11 09 59 -231838 -431127 +503704 -715911 -394519 +10 00 36 -222441 5.9 6.3 5.1 5.5 6.1 5.5 5.1 5.3 3.7 G8p KOm K2 G8II KOp G8Ib-II KO.5m KOm G4lb References 1. McClure, R.D. 1989, in Evolution of Peculiar Red Giant Stars, edited by H.R. lohnson and B. Zuckerman (Cambridge University Press, Cambridge), p. 196 2. MacConnell, D.l., Frye, R.L., & Upgren, A.R. 1972, AJ,77,384 Table 16.16. Subgiant CH stars [1, 2]. No. ex (2000.0) 8 (2000.0) HD89948 BD +17°2537 HD 123585 HD 127392 BD -10°4311 CPD -62°6195 HD207585 HD224621 102221.9 124722.8 140935.9 143153.5 162413.2 210602.8 215034.8 235917.3 -293321.1 +164935.0 -442201.7 -311201.1 -1113 07.5 -613345.3 -2411 11.4 -360237.0 my Sp. 7.50 8.82 9.28 9.89 10.1 10.1 10.0 9.59 G8m GO F7Vwp Gp GO G5 Gwp GOIIIIIV References 1. Hipparcos Input Catalogue (ESA), 1990 2. Luck, R.E., & Bond, H.E. 1991, ApJS, 77, 515 16.13 HYDROGEN-DEFICIENT CARBON STARS by Warrick Lawson Hydrogen-deficient carbon stars are luminous, probable born-again post-AGB stars consisting of the cool R Coronae Borealis (RCB) and hydrogen-deficient Carbon (HdC) stars (Teff :=:::; 5000 to 7000 K [58]) and extreme helium (eHe) stars (Teff :=:::; 8400 to 55000 K [59]). Three hot RCB-like stars may be unrelated [60]. Typically CIH > HP although at least two stars are relatively H-rich [61]. RCBIHdC and cooler eHe stars are unstable to radial pulsations [58-62], whereas higher-temperature eHe stars are nonradial pulsators. RCB stars have pulsation-related declines in light of up to 8 magnitudes due to dust formation [63,64] and have bright IR excesses [65,66]. See Table 16.17. 418 / 16 STARS WITH SPECIAL CHARACTERISTICS Table 16.17. Selected hydrogen-dejicient carbon stars. V Star Type a (2000.0) (2000.0) HV5637 WMen HV 12842 SUTau xx Cam HdC? RCB RCB RCB RCB 040839 051132 052624 054503 054906 +532139 -675600 -711118 -642424 +190400 7.3 14.8 13.9 13.7 9.7 BO+371977 UWCen OYCen HD 124448 V854Cen eHe RCB RCB? eHe RCB 092424 124317 132534 141459 143448 +364254 -543141 -541447 -461719 -393319 RCrB BO-94395 HD 148839 V20760ph PVTeI RCB eHe HdC eHe eHe 154834 162835 163546 174150 182315 V348Sgr MVSgr LS IV -14109 RYSgr UAqr RCB? RCB? eHe RCB RCB 184020 184432 185939 191633 220320 & B-V - Teff (K) Notes 0.87 1.23 0.42 0.51 1.10 7000 5000 7000 7000 7000 LMC LMC LMC 10.2 9.1 12.5 10.0 7.1 0.67 0.35 -0.10 0.50 55000 6800 14000 15500 7000 +280924 -091934 -670737 -175408 -563743 5.8 10.5 8.3 9.8 9.3 0.59 0.06 0.93 0.14 0.00 7000 28000 6500 31900 12400 -225429 -205716 -142611 -333118 -163740 11.8 12.7 11.1 6.2 11.2 0.30 0.26 0.33 0.62 1.00 20000 15400 8400 7000 5500 (at maximum) sdO? Nonvariable? Balmer lines present Nonradial pulsator? C/H-0.05 Nonradial pulsator Sr-. V-rich 16.14 BLUE STRAGGLERS by Peter J. T. Leonard Blue stragglers are main-sequence or slightly evolved stars in a stellar system that are apparently much younger than the majority of the stars in the system. Consequently, these stars pose a problem for standard stellar evolutionary theory. Blue stragglers have been discovered everywhere that they could have possibly been discovered, which includes OB associations, open clusters of all ages, globular clusters, the population II field, and dwarf spheroidal galaxies. Theories for these objects include stellar mergers due to physical stellar collisions, stellar mergers due to the slow coalescence of contact binaries, mass transfer in close binary systems, extended main-sequence lifetimes due to internal mixing (which may be induced by rapid rotation, strong magnetic fields, or pulsation), recent star formation, and several others. Table 16.18 provides a sample of blue stragglers found in various stellar systems. Table 16.18. Selected blue stragglers. Name Type of the parent stellar system HD93843 [1] HD 152233 [1] HD60855 [2] HD 162586 [2] HD27962 [3] HD73666 [3] F 81 [4] F 184 [4] S I. IT, 21 [5] Car OBI. OB association Sco OB 1. OB association NGC 2422. young open cluster NGC 6475. young open cluster Hyades. intermediate-age open cluster Praesepe. intermediate-age open cluster M67. old open cluster M67. old open cluster M3. globular cluster Characteristics = -9.5. 05m(f)var. v sini = 90 kms- l = -9.7. 06m:(f)p. vsini = 140kms- l Mv = -2.86. B2IVe. vsini = 320lmlS- l Mv = -1.08. B6V. vsini < 4Okms- l Am(KJHIM=A2JA3:/AS). v sini = 18 kms- l AIVP(Si). v sini = 40 kms- l V = 10.04. B8V V = 12.22. FO. vsini = 80kms- l mpv = 17.39. Cl = 0.06 MOOl MOOl 16.15 PECULIAR A AND MAGNETIC STARS / 419 Thble 16.18. (Continued.) Name Type of the parent stellar system Characteristics E 39 [6] NC 6 [7] AOL I [8] NH 19 [9] HST-I [10] BD +25°1981 BD -12°2669 MA 308 [12] D 227 [13] SI267 [14] BSS-19 [15] w Cen, globular cluster NGC 5053, globular cluster NGC 6397, globular cluster NGC 5466, globular cluster 47 Tuc, globular cluster Population 11 field Population 11 field Carina dwarf spheroidal galaxy Sculptor dwarf spheroidal galaxy M67, old open cluster 47 Tuc, globular cluster 0.056-day dwarf cepheid, V = 17.03, B - V = 0.31 g = 18.33, g - r = -0.47 V = 14.42, B - V = 0.16 0.34-day contact binary, V = 18.54, B - V = 0.15 m220 = 16.0, ml40 = 16.7 V = 9.29, B - V = 0.30, v sini = 9 krns- I V = 10.22, B - V = 0.30, v sini = 31 kms- I V = 20.54, B - V = -0.07 V = 21.67, B - V = 0.14 Porb = 846 days, eorb = 0.475 ± 0.125 M = 1.7 ± 0.4M0' v sini = 155 ± 55 km s-I [11] [11] References I. Mathys, G. 1987, A&AS, 71, 201 2. Mermilliod, I.-C. 1982,A&A, 109, 37 3. Abt, H.A. 1985, ApJ, 294, LI03 4. Mathys, G. 1991, A&A, 245, 467 5. Sandage, A.R 1953, AJ, 58, 61 6. IlIIrgensen, H.E., & Hansen, L. 1984, A&A, 133, 165 7. Nemec, I.M., & Cohen, I.G. 1989, ApJ, 336, 780 8. Auriere, M., Ortolani, S., & Lauzeral, C. 1990, Nature, 344, 638 9. Mateo, M., Harris, H.C., Nemec, I., & Olszewski, E.W. 1990, AJ, 100,469 10. Paresce, F. et al. 1991, Nature, 352, 297 11. Carney, B.w., & Peterson, RC. 1981, ApJ, 251, 190 12. Mould, I., & Aaronson, M. 1983, ApJ, 273, 530 13. Da Costa, G.S. 1984, ApJ, 285, 483 14. Latham, D.W., & Milone, A.R.R 1996, ASP ConfSer., 90, 385 15. Shara, M.M., Saffer, R.A., & Livia, M. 1997, ApJ, 489, L59 16.15 PECULIAR A AND MAGNETIC STARS [67-70] The peculiar A stars comprise the following: 1. Ap stars, which extend into B and earlier F types as well. The hotter (but not hottest) ones have unusually strong lines of Mn, Si, and Hg; the cooler ones have similarly strong lines of Si, Cr, Sr, and Eu, and other rare earth elements. 2. Am stars, for which the spectral type varies with the criterion used: the type based on the K-line is earlier than that from the Balmer lines and that, in tum, is earlier than the type from metallic lines. Differences are ~ 5 subclasses. Table 16.19 lists some other properties. Thble 16.19. Other properties. Ap(Mn,Hg) Temperature: Luminosity and mass: v sin i (krn/s): Magnetic field (gauss): Close binary frequency Ap (Sr, Eu) Am 10000-15000 K 8000-12000 K 7000-9000 K At or near main sequence values 30 30 40 o orlow 103 -104 Oorlow Normal Low High 420 / 16 STARS WITH SPECIAL CHARACTERISTICS Ap stars show spectrum, light, and magnetic variability due to rotational modulation on time scales of days to years. Magnetic Ap stars can also show rapid oscillations (roAp stars) on time-scales of 4 to 15 minutes due to high-overtone, low-degree, nonradial p modes [69]. 16.16 PULSARS by Kaiyou Chen and John Middleditch Pulsars are believed to be strongly magnetized rotating neutron stars. The radiated spectrum of a pulsar can extend over many decades in wavelength. So far, more than 500 radio pulsars have been discovered. Among these are about 50 so-called millisecond pulsars, the majority of which have spin periods less than 10 ms, and all of which are thought to have fields significantly weaker than the so-called pulsars with a canonical magnetic field strength near 1011 _1012 G, typical of the vast majority of known radio pulsars. A disproportionately large number of millisecond pulsars have been found to belong to the Galactic globular cluster population (about 30 so far). The suggestion that. the millisecond pulsar population is the result of recycling of old (radio-dead) neutron stars through accretion from an orbital companion in a low-mass X-ray binary phase has gained a wide acceptance. However, alternative production mechanisms have also been proposed, some of which do not suffer from the vast overpopUlation of the millisecond pulsars with respect to that of the low mass X-ray binaries. There are only about a few dozen accretion-powered X-ray pulsars known to date, with all of these thought to be strongly magnetized. Only two (Her X-I and 4UI626-67) are known to produce optical pulsations through reprocessing of the pulsed X-ray flux. There is only one rotation-powered pulsar (Geminga) with strong y-ray emission, which is not yet known as a radio source. The existence of non-(or slowly)-varying high-energy y-ray sources discovered by EGRET on the Compton Gamma-Ray Observatory satellite may indicate a larger population of y-ray pulsars yet undiscovered. So far there are three neutron star-neutron star binary systems known, two of which belong to the galactic disk population and one in the globular cluster MIS. Such binaries provide the best-known tests of general relativity theory in addition to the accurate measurement of the mass of the component neutron stars. At least one millisecond pulsar (1257+12) is thought to have at least two (few Earth mass) planetary companions in orbits apparently synchronized with a 2:3 period ratio. Further study of such systems may eventually be able to exclude pulsar precession as an alternative explanation to the timing irregularities. Neutron stars are thought to be the compact remnants of supernova explosions. The pulsar in the Crab nebula is almost certainly such a remnant. The most rapidly spinning pulsar associated with a supernova remnant, the 16 ms pulsar in N157B, may have had an initial spin period of only seven milliseconds. The detection of neutrinos from SN1987A indicated that a neutron star was indeed formed in the original core collapse. However, no evidence for a strong pulsar has yet been detected in this remnant. See Table 16.20 for characteristics of a few important pulsars and Figure 16.1 for a radio pulsar diagram. 16.16PULSARS / 421 -12. .:0. ~ '(i)' 0 :.: > ....... ~ > ....... -14. "Cl "Cl -16. ~ Q.) ~. -: •• ° • 0 ...... ~ Q.) & .' -18. ~ 0 ...... . .. ......... ~ -20. ~ '. -3. -2. -1. o. log [Period (s)] Figure 16.1. The "RR diagram" of 645 pulsars showing the period and the period derivative (seconds per second). Thble 16.20. Some important pulsars. Period (s) Comments 0021-72c 0.0058 Nine more pulsars with P < 6 ms in the same globular cluster, 47 Thc [I] 0531+21 (Crab pulsar) 0.033 Pulsed emission from radio to y-ray; obvious supernova association [2] 0538-69 (N157B pulsar) 0.016 In the Large Magellanic Cloud (LMC); fastest known pulsar associated with a supernova remnant 0540-69 (LMC pulsar) 0.050 Also in the LMC and supernova association; pulsed radio, optical, and X-ray emission [5] Geminga (lE0630+ 17) 0.237 Strong y-ray pulsar; no radio detection [6] 0833-45 (Vela pulsar) 0.089 Supernova association; strong y-ray source [7] 1257+12 0.0062 Having two companion planets [8] 1534+12 0.0379 Having a companion neutron star [9] Her X-I 1.24 Accretion-powered X-ray pulsar [10] 1821-24 0.003 First (millisecond) pulsar discovered; in a globular cluster, M28 [11] 1845-19 4.3082 Slowest known pulsar [12] Name Reference [3,4] 422 / 16 STARS WITH SPECIAL CHARACTERISTICS Table 16.20. (Continued.) Name Period (s) Comments 0.059 First binary pulsar discovered; evidence of gravitational radiation [13] 1919+21 1.337 First pulsar discovered; [14] 1937+21 0.0015 First millisecond pulsar discovered; fastest known pulsar [15] 1957+20 0.0016 Eclipsed by the evaporating companion every 9.2 hours [16] 1913+16 (Hulse-Taylor pulsar) Reference References 1. Manchester, R.N. et aI. 1991, Nature, 352, 219 2. Staelin, D.H., & Reifenstein, E.C. 1968, Science, 162, 1481 3. Marshall, F.E. et aI. 1998, IAU Circ. No 6810 4. Wang, D.Q., & Gotthelf, E.V. 1998,ApJ, 494, 623 5. Seward, F.D. et aI. 1984, ApJ, 287, Ll9 6. Halpern, J.P., & Holt, S.S. 1992, Nature, 357, 222 7. Large, M.I. et aI. 1968, Nature, 220, 340 8. Wolszczan, A., & Frail, D.A. 1992, Nature, 355,145 9. Wolszczan,A.I991,Nature,350,688 10. Tananbaum, H. et aI. 1972, ApI, 174, Ll43 11. Lyne, A.G. et aI. 1987, Nature, 328, 399 12. Newton, L.M. et aI. MNRAS, 194, 841 13. Hulse, R.A., & Taylor, J.H. 1975, ApI, 195, L51 14. Hewish, A. et aI. 1968, Nature, 217, 709 15. Backer, D.C. et aI. 1982, Nature, 300, 615 16. Fruchter, A.S. et aI. 1988, Nature, 333, 237 16.17 GALACTIC BLACK HOLE CANDIDATE X-RAY BINARIES by Jonathan E. Grindlay Black hole candidates in the Galaxy are best defined as X-ray binaries in which the accreting compact object has a probable mass Mx ;::: 3M 0 , or above the limit for neutron stars, as determined from spectroscopic measurements of the semiamplitude velocity, K, of the companion star with mass Me. Together with the orbital period P, this defines the mass function of the system: f(Mx) = P K3 /2rrG = M~ sin3 i/(Mx + Me)2. The mass function thus gives a firm lower limit for M x, although with additional constraints on system inclination, sin i, and spectral type and thus mass Me, the black hole candidate mass Mx can be measured [71,72]. The measurement [73] of Mx = 7.02 ± 0.22M0 obtained for the galactic "micro-quasar" source, with relativistic jets, GR0J1655-40 = Nova Sco 94 provides the currently (1998) most accurate determination of the mass of a probable black hole in the Galaxy. Secondary indicators for galactic black hole candidates are their similar hard X-ray spectra, with power law form typically extending out beyond 100 keY and containing a significant fraction of the total luminosity [74] and (in high luminosity states) accompanying ultra-soft X-ray spectral components [75]. The black hole binaries are most often found as transient X-ray sources which are often particularly luminous in their soft X-ray emission at their peak and are thus frequently called soft X-ray transients (despite their nearly universal accompanying hard X-ray emission which dominates the emission during the decay phase). In comparison with transients known to contain neutron stars from their X-ray bursts, the black hole transients show significantly larger increase from their quiescent low states to outburst, consistent with their having an event horizon and advection-dominated accretion flow at the low accretion rates found in quiescence [76]. 16.17 GALACTIC BLACK HOLE CANDIDATE X-RAY BINARIES / 423 The most reliable black hole candidates are the eight systems listed in Table 16.21 with lower mass companions for which radial velocities and mass functions were derived when these transient type X-ray sources faded to quiescent optical levels. The 7-8 mag. optical brightening of some of these recurrent (~ 50 year) transients resemble novae leading to the tenn X-ray novae for these systems. The three high mass (;G lOM 0 ) companion systems included in Table 16.22 are less well determined (with LMC X-I particularly questionable), although the prototype system Cyg X-I is most secure [72]. A general summary of the properties of X-ray transients of all types provides constraints on the galactic population of black holes in binary systems [77], and a statistical analysis of the quiescent transients suggests [78] the black hole masses may be clustered near 7 M0 for all but V404 Cyg. Table 16.21. Galactic black hole candidates with low mass companions [1-5]. Object Opt. ID GROI0422+32 Nova Per 92 A0620-00 NovaMon 75 GS1124-68 Nova Mus 91 4U1543-47 ILLup GROJl655-40 Nova Sco 94 H1705-25 NovaOph 77 OS2000+25 Nova Vu188 OS2023+33 V404Cyg ex (2000.0) 13 (2000.0) 04 2146.9 325436 06 2244.5 -00 2045 11 2626.7 -684033 154708.6 -474009 165400.2 -395045 17 0814.2 -250532 200249.6 25 1411 202403.8 335204 mv Sp. Type 22 MOV 18 f(Mx/Mo} Mx/Mo 5.1 1.21 ± 0.06 3.5-14 K5V 7.8 2.91 ± 0.08 2.8-25 20 K5V 10.4 3.01 ±0.15 4.5-6.2 17 AOV 27.0 0.22±0.02 2.7-7.5 21 F4IV 62.9 3.24±0.09 6.5-7.8 21 K3V 12.5 4.86±0.13 4.7-8.0 21 K5V 8.3 4.97 ±0.1O 5.8-18 19 G9V 155.3 6.08 ± 0.06 10.3-14 P (hours) References 1. McClintock, I.E. 1998, in Accretion Processes in Astrophysical Systems, AlP Conf. Proc., p. 431. 2. Van Paradijs, I., & McClintock, I.E. 1995, in X-ray Binaries, edited by W.H.G. Lewin, I. van Paradijs, and E.P.I. van den Heuval (Cambridge University Press, Cambridge), p. 58. 3. Orosz, I.A., & Bailyn, C.D. 1997, ApJ, 477, 876. 4. Tanaka, Y., & Shibazaki, N. 1996, ARA&A, 34, 607. 5. Bailyn, C.D., lain, R.K., Coppi, P., & Orosz, I.A. 1998, ApJ, 499,367. Table 16.22. Galactic black hole candidates with high mass companions [1, 2]. Object Opt. ID LMCX-l star R148 LMCX-3 starWP Cyg X-I HDE226868 ex (2000.0) 13 (2000.0) 053938.7 -694436 053856.4 -64 05 01 195821.7 35 1206 mv Sp. Type P (hours) f(Mx/Mo} 14 OB 4.2 0.14 ± 0.05 17 B3V 1.7 2.3 ±0.3 >7 9 09.71ab 5.6 0.24± 0.01 >7 Mx/Mo References 1. Van Paradijs, I., & McClintock. I.E. 1995, in X-ray Binaries, edited by W.H.G. Lewin, I. van Paradijs and E.P.I. van den Heuval, (Cambridge University Press, Cambridge), p. 58. 2. Tanaka, Y., & Shibazaki, N. 1996, ARA&A, 34, 607. 424 / 16 STARS WITH SPECIAL CHARACTERISTICS 16.18 DOUBLE STARS Indications are that some 40%-60% of all stars are members of double or multiple systems [79], with some estimates running as high as 85% [80]. As far as selection effects allow, there seems no significant dependence on stellar type. Such effects preclude any reliable determination of the percentage of duplicity as a function of semimajor axis size. The eccentricity of binary orbits and the orbital period are given below: log P (P in days) Mean eccentricity o 0.03 1 2 0.17 0.31 345 0.42 0.47 0.45 6 7 0.64 0.8 For further statistics of binary stars, see [79-82]. 16.18.1 Visual binaries Dawes's rule is the limit of resolution = 11.6/ D arcsec (D is objective diameter in centimeters). The limit of largest refractors under best conditions""" 0.1 arcsec. The angular separation beyond which it is unlikely that pairs are physical binaries log p = 2.8 - 0.2V, where p is in arcsec and V is the combined magnitude. Reference [83] suggests that a pair is likely not physical if the projected linear separation exceeds 0.01 pc. A catalogue of orbital elements for""" 850 visual binaries is given in [84]. See Table 16.23. Table 16.23. Selected visual binaries. a" Name Component T w (deg) e Sirius A B A B A B A B A B 50.1 1894.1 40.4 1967.9 79.9 1955.6 88.1 1984.0 44.6 1925.6 7.50 0.59 4.50 0.36 17.52 0.52 4.54 0.50 2.41 0.41 Procyon ct Cen 700ph Kriiger60 i (deg) Q (deg) P (yr) Equinox 147.3 44.6 268.8 284.8 231.6 204.9 13.2 301.7 217.8 161.1 136.5 1950 31.9 2000 79.2 2000 121.2 2000 164.5 2000 nil 0.379 0.290 0.760 0.199 0.253 Sp. Mho) M/M0 AIV DA F5IV-V WD G2V KOV KOV K4V dM4 dM6 0.8 11.2 2.6 12.6 4.4 5.6 5.6 6.8 9.6 10.6 2.28 0.98 1.69 0.60 1.08 0.88 0.90 0.65 0.27 0.16 16.18.2 Spectroscopic Binaries The formula relating the observed radial velocity maximum and period to the eccentricity, semimajor axis, and orbital inclination is for al in units of 106 km, K I in km s-l , and P in days, similarly for a2 and K2. 16.18 DOUBLE STARS / 425 If only one velocity curve is available, the mass function is If both velocity curves are available, then MI sin3 i = 1.036 x 1O-7(KI + K2)2 K2P (1 - e 2 )1.5, and similarly for M2 and K I. The mass is expressed in solar masses. The catalogue of orbital elements for'" 1470 spectroscopic binaries is given in [85]. Table 16.24. See Table 16.24. Selected spectroscopic binaries. Name w (deg) e (days) T (2400000+) Phea 1.6698 41643.689 0.0 f3 Aur 3.9600 31075.759 .0 a Vir 4.0145 40284.78 142 0.18 f3 Lyr 31 Cyg 12.9349 3784.3 42260.922 37169.73 201.1 0.0 0.22 ~ 16.18.3 P K (kms- l ) 131.5 202.6 111.5 107.5 120 189 184 14.0 20.8 Vy (kms- l ) f(M) (M0) 17.2 11.6 -17.1 0 -2 -17.8 -7.7 -12.3 M sin3 i (M0) a sini 006 km) Sp. 3.9 2.5 2.1 2.2 7.2 4.5 3.02 4.65 6.07 5.85 6.52 10.3 32.7 711 1060 B6V B8V A2IY A21V BIV B3V B8pe K41b B4V 8.4 9.2 6.2 Eclipsing binaries Classification schemes are as follows: 1. By ellipticity: EA EB EW Algol type f3 Lyr type W UMa type near spherical. P> 1 day P < 1 day ellipsoidal, unequal brightness. ellipsoidal, equal brightness. 2. By stability within critical equipotential surfaces (Roche lobes). Mass loss occurs when Roche lobes are filled: o SO C OC Detached Semidetached Contact Overcontact Both components are well within Roche lobes. One component reaches Roche lobes. Both components reach Roche lobes. Both components overfill Roche lobes. The inter-relations EA.= 0, SO, EB.= SD(D), EW.= C. No comprehensive catalogue of reliable elements for eclipsing binaries is presently available, but see [86] for a selection of 323 eclipsing systems. See Table 16.25. 426 I 16 STARS WITH SPECIAL CHARACTERISTICS Table 16.25. Selected eclipsing binaries (from [1 J). Name P (days) aa (RO) EROri 0.423 RYAqr e (deg) 2.12 0.00 80.9 1.967 7.61 0.00 82.1 RWMon 1.906 9.97 0.00 88.0 V889Aql 11.121 34.3 0.37 88.4 AIPhe 24.592 47.75 0.19 88.5 (r)b (unit = a) (K) qC 0.31 0.43 0.17 0.27 0.20 0.32 0.054 0.053 0.037 0.061 5800 5650 7605 4520 10650 5055 10200 10500 6310 5160 1.99 T 0.20 0.37 1.0 1.03 Fd 1.00 1.00 1.00 1.00 4.99 1.00 2.34 2.34 1.49 1.49 Sp. F8V A3 B9V B9 FlV KOIV Notes aa (= at + a2) is the semimajor axis of the relative orbit. b (r) is the approximate mean stellar radius. Cq is the mass ratio of secondary to primary. d F is the ratio of spin angular speed to mean orbital angular speed. 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Webbink 17.1 Types of Cataclysmic Variables . . . . . . . . . . . .. 429 17.2 Types of Symbiotic Variables . . . . . . . . . . . . .. 447 17.1 TYPES OF CATACLYSMIC VARIABLES A cataclysmic variable (CV) [1,2] is a binary star system in which a white dwarf primary accretes hydrogen-rich material usually through an accretion disk from a Roche lobe filling secondary that is on or near the main sequence. The CVs consist of several classes such as classical novae, recurrent novae, nova-likes, dwarf novae, helium CVs, and magnetic CVs. The distributions of their orbital periods are shown in Figure 17.1. Catalogues ofCVs are found in [3,4]. Proceedings ofCV conferences [5-9] are bountiful sources of information. A classical nova [10-12] is a CV that has undergone an outburst (9-15 mag. increase) which ejects a shell of gas at high velocity. Tables 17.1 and 17.2 contain the brightest and best-observed classical novae in our Galaxy. More extensive lists are found in [13] and [3]. Table 17.3 lists the brightest novae from 1991 to 1995. Well-observed novae in the Large Magellanic Cloud are given in Table 17.4. Classical novae are commonly assumed to be caused by a thermonuclear runaway in the accreted material on the white dwarf. The classical novae are also designated as CNO and ONeMg novae according to the composition of the ejecta (see Table 17.5). It is inferred that these novae occur on CO and ONeMg white dwarfs, respectively, and their ejecta include white dwarf material. As their name implies, recurrent novae have been observed to undergo more than one outburst. Although there are currently only nine members listed in this class (see Tables 17.6 and 17.7), it may be necessary to subdivide them according to their type of outburst or their type of secondary when they are better understood. In some systems the outbursts are probably caused by thermonuclear runaways, but in tDeceased. 429 430 I 17 CATACLYSMIC AND SYMBIOTIC VARIABLES CJ AM Her ~ SUUMa ~UGern 30 El Zearn li3 VV Sci J:!) UX UMa ~ Recurrent Novae ImJ Novae 25 ~ 20 g z 15 10 -1.2 -1.0 -O.B -0.6 -0.4 -0.2 0.0 log P (d) 0.2 0.4 0.6 O.B 1.0 Figure 17.1. The orbital period distributions of the cataclysmic variables. other systems the outburst may result from an episodic mass transfer accompanied by the release of gravitational energy onto the primary which could be a white dwarf or a main-sequence star [14, 15]. In addition, for some recurrent novae, the secondary is a late-type giant. The dwarf novae (Table 17.8) [16] undergo a periodic brightening (2-5 mag.) on a time scale of weeks to years with little or no mass ejection aside from the wind outflow during the outburst in most of the systems. Most dwarf novae change from having an emission line spectrum to having an absorption line spectrum during outburst. This phenomenon is normally assumed to be caused by an instability in the accretion disk surrounding the white dwarf. The SU UMa stars are a subclass of dwarf novae that also show semiperiodic outbursts of unusually large amplitude (superoutburst), distinguished by the appearance at outburst maximum of periodic modulations (superhumps) in the light curve with periods a few percent larger than the orbital period. Dwarf novae that show occasional standstills (episodes of intermediate brightness lasting days to years) during decline from maximum are termed Z Cam stars. The remainder of the dwarf novae are called U Gem systems after the original prototype. The nova-likes [16] are CVs that have the appearance of quiescent classical novae, i.e., they are probably classical novae that have not had a recorded outburst. Table 17.9 contains the best observed nova-likes. Additional listings are found in Ritter [3]. There are two subclasses of nova-likes: UX UMa and VY ScI. The UX UMa systems look like dwarf novae in a permanent outburst state while the VY Scl systems (or antidwarf novae) are normally in a high state but have slow, short excursions to a low state. These variations of luminosity are probably due to changes in the accretion rate. The helium CVs (or AM CVn systems) are transferring helium-rich material instead of hydrogen-rich material. Otherwise they appear to be nova-likes. The white dwarf in a magnetic CV has a sufficiently strong magnetic field to channel the flow of accreting material at least near the white dwarf's surface [17]. The magnetic CVs may be divided into two subclasses depending on whether the white dwarf is rotating synchronously (Table 17.10) with its binary companion, as in the AM Her binaries or polars, or asynchronously (Table 17.11) as in the DQ Her binaries or intermediate polars. In the AM Her binaries, the magnetic field is sufficiently strong so that the accretion flows via an accretion column and no accretion disk is formed. In the DQ Her 17.1 TYPES OF CATACLYSMIC VARIABLES / 431 binaries, the magnetic field is probably weaker and an accretion disk may form but is disrupted close to the white dwarf's surface. Being a member of one class of CVs does not prevent a system from being a member of another. For example, OK Per, an old classical nova, also shows dwarf nova outbursts. Nova V1500 Cyg is also an AM Her system. The space density of CVs, Pcv, is a subject of much controversy. Assuming that the novae, dwarf novae, and nova-likes found in a galactic plane survey [18] represent all the CVs, their space density, Pcv, is (5.3-8.2) x 10-7 pc-3. However, if novae fade considerably between outbursts, then a higher space density like that of Pcv 2:: 3 x 10-5 pc-3 found in a deep but narrow survey [19] may be more realistic. Many of the following tables make use of the SIMBAD database, operated at CDS (Centre de Donnees Stellaires), Strasbourg, France. Uncertain numbers are followed by a colon. Table 17.1. Selected list of classical novae. Name (alternate name) aD (2000) aD (2000) hrminsec degmin sec GKPer (N Per 1901) TAur (N Aur 1891) RRPic (N Pic 1925) CPPup (NPup 1942) GQMus (NMus 1983) DQHer (NHer 1934) FHSer (N Ser 1970) V693CrA (NCrA 1981) V603Aql (N Aq11918) V1370Aql (N Aq11982) PWVul (NVulI984No.l) HRDeI (NDell967) VlSOOCyg (N Cyg 1975) VI668Cyg (NCyg 1978) OS And (N And 1986) 0331 11.82 435416.8 150.55 -10.60 053159.06 302645.2 176.79 -2.30 06 35 36.05 -623823.4 272.30 -25.71 08 1145.96 -352105.7 252.59 -1.08 115202.35 -671220.2 296.92 -4.78 180730.17 455131.9 73.09 26.68 183046.92 023651.5 32.59 6.33 184157.63 -373113.1 357.51 1848 54.50 003502.9 32.82 1.37 192321.10 022926.1 38.43 -5.43 192605.03 272158.3 60.80 5.55 204220.18 190940.3 62.96 -13.64 2111 36.61 480901.9 89.48 -0.00 214235.22 440154.9 90.42 -6.70 231205.76 472819.7 105.69 -11.97 eb (deg) Ii' (deg) -13.79 mC max mC. t 3d (days) Light curve Refs. Secondary spectral typee 0.2v 13.Ov 4.1B 14.9B 1.2v 12.3v 0.2v 15.Ov 7.2v 17.5v 1.3v 14.7v 4.4v 16.1v 6.5v > 19v -1.4v 11.6v 7.5p 20.Op 6.4v 17.Ov 3.3v 12.1v 2.0B 16.3B 6.Ov 20: 6.2v 17.8v 13 [1] K2IV-V [2] 100 [3] 150 [4,5] 8 [4,6] 45 [8] 94 [4,9] 62 [11] 12 [12] 8 [4,13] 13: [14, 15] 97 [16] 230 [17] 3.6 [19,20] 23 [21,22] 22 [23] mm >M6 [7] M3V [10] K8 [18] Notes °Adapted from Duerbeck [24] and precessed to equinox 2000. bGalactic coordinates. cMaximum and minimum magnitudes from Warner [25]. and the light curve references B, v, and p are the blue, visual, and photographic magnitudes. dThe time for the visual light curve to fall three magnitudes after maximum, t3, was taken from Duerbeck [24]. eThe secondary spectral types are from spectroscopic or infrared photometric observations and do not include estimates from mass determinations. 432 / 17 CATACLYSMIC AND SYMBIOTIC VARIABLES References 1. Sabbadin, F., & Bianchini, A. 1983, A&AS, 54, 393 2. 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(days) 490n -9.20 1.996 803 [3] -8.4n 0.204 378 29 [11] -7.3n 0.1450255 [18] -9.7n 0.06143 [24] 0.068 34 [25] -7.4 0.0594 [29] -350QPO[4] [12] 20-40 QPO [19] 1200 [5] 655 [13] 475 [13] 710 [13] [6,7] [14] [20,21] [26,27) 800 [28] [28,30] 5600 -7.8n 0.1936206 [33,34,35] 71.074514 [36,37] 384 [38] [39,40] [41] [43] Name E(B - V)" shell studiesi' GKPer TAur RRPic CPPup 0.3 [1] 0.6 [9] 0.07 [16] 0.08 [23] [2) [9,10] [17) [23] GQMus 0.45 [28] DQHer 0.11 [31] FHSer 0.4[42] 850n -6.5n 560 [13] [43] V693CrA 0.56 [44] 5030 -8.8 2200 [44] [44,45] V603Aql 0.07 [16] 370n 1700 [5] [50] V1370Aql 0.6[52] -9.5n 0.138 15 [47] 0.144854 [48, 49] 2800 [53] [52,53) BOOn 460n 835n 4280 [10,32] [10,46) Quiescent spectra.! [8] [15] [22) [24] Descrip- tiong VF MF S VF MF [51] CNO no dust MF CNO dust MF Cdust VF ONeMg VF VF ONeMg C,SiC, Si~ PWVul 0.45 [54] HRDel 0.29 [58] V1500Cyg 0.5 [66] 2050 -6.6 [59,60] 850n [67] I080n -7.3n 0.214165 [61] 0.1775 [62] -9.8n 0.139613 [68,69] 0.2137 [55] [12] dust MF 285 [56] [57] 520 [13) [58,63] [64,65] 1180 [13] [70,71] [68] Solar Cdust VS VF CNO 17.1 TYPES OF CATACLYSMIC VARIABLES / 433 Thble 17.2. (Continued.) Name E(B - V)a VI66S Cyg 0.4 (72) OS And 0.25 (76) Nebular shell studiesb Distancec (pc) Max. abs. mag. Periood (days) 3660 -S.I 0.1384 (73) 7200 -S.2 Rapid optical oscillation period' (s) Expansion velocity (kmIs) Outburst spectra.! 700 (72) [74.75) 1000 (77) [7S) Quiescent spectra.! Descrip- tion' F CNO Cdust F CNO Notes aThe color excess. E(B - V). is assumed to be related to the visual interstellar extinction. Av. by Av = 3.2E(B - V). bIn addition to these nebular shell studies. a short spectroscopic description of the nova remnant is given by Duerbeck and Seitter [79]. cThe distances and absolute maximum magnitudes that are followed by an "n" have been determined by the nebular expansion parallax method. The angular shell sizes are from Cohen and Rosenthal [13]. except for V1500 Cyg [80]. DQ Her [38]. and FH Ser [42]. The other distances and absolute magnitudes are found from the maximum magnitude -t2 relationship derived by Cohen [80] and assuming t2 - t3/2 [81]. The time for the visual light curve to fall after maximum by n magnitudes is denoted by tn. d The spectroscopic period is the first entry while the photometric period is the second if it is different. Orbital parameters can usually be found in the reference for the spectroscopic period. elf only a reference is given in this column. it means an unsuccessful search. f Only optical references are given. 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(kmls) V351 Pup (N Pup 91) 8 1138.38 -350730.4 27 Dec 1991 5422 6.4v 3000 V4160 Sgr (N Sgr 91) V838 Her (NHer91) 18 14 13.83 -321228.5 29 July 1991 5313 7v 8000 184631.48 +121401.8 24 Mar 1991 5222 5.3v 2.8 0.6 6000 VI974Cyg (NCyg 92) 203031.66 +523750.8 20 Feb 1992 5454 4.9B 43 0.35 ±0.05 2000 V705 Cas (NCas 93) V1425 Aql (N Aq195) 234147.25 +573059.7 7 Dec 1993 5902 5.3v 190526.64 -014203.3 7 Feb 1995 6133 6.2:v 22: 2: 0.56 1600 Notes QThe time for the visual light curve to fall three magnitudes after maximum. bThe color excess. cThe full width half maximum velocity of the emission lines in IUE spectra measured by S. Shore. dThe description is the same as in Table 17.2 for classical novae. Desc.d ONeMg no dust VF ONeMg ONeMg Dust VF ONeMg No dust MF CO Dust ONeMg Dust F 436 / 17 CATACLYSMIC AND SYMBIOTIC VARIABLES 'Dlble 17.4. Recent novae in the Large Magellanic Cloud [1, 2]. a (2000) Nova hrminsec ~ (2000) deg min sec IAU Cire. No. LMCV3479 LMCV1161 LMCV2361 LMCV1341 LMCV0850 LMCI992 LMCI995 53529.33 50801.10 52321.82 50958.40 50344.99 51919.84 52650.33 -702129.4 -683737.7 -692948.5 -713951.6 -701813.7 -685435.1 -700123.8 4569 4663 4946 4964 5244 5651 6143 Outburst Vmax 1YPe Remarks 21 Mar 1988 12 Oct 1988 16 Jan 1990 15 Feb 1990 18 Apr 1991 11 Nov 1992 2 Mar 1995 11.0 10.4 10.6 11.9 8.9 10.2 11.3 Dust,CNO ONeMg ONeMg Recurrent CNO? CNO CNO a b c d e / Notes aUV versus optical analysis: Austin, S., Starrfield, S., Saizar, P., Shore, S.N., & Sonneborn, G. 1990, in Evolution in Astrophysics: lUE in the Era o/New Space Missions, edited by E. Rolfs (ESA SP 310), p. 367. Possible dust-forming nova. buy description: IAU Cire. No. 4669. First extragalactic ONeMg nova. C t3(optical) 5.8 days. Sonneborn, G., Shore, S.N., & Starrfield, S.G. 1990, in Evolution in Astrophysics: lUE in the Era 0/ New Space Missions, edited by E. Rolfs (ESA SP 310), p. 439; see also, Starrfield, S., Shore, S.N., Sparks, W.M., Sonneborn, G., Truran, J.W., & Politano, M. 1992, ApJ, 391, L71. dRecurrence of Nova LMC 1968. Dynamics, abundances: Shore, S.N., Starrfield, S., Sonneborn, G., Williams, R.E., Haumy, M., Cassatella, A., & Drechsel, H. 1991, ApJ, 370,193. First spectroscopically confirmed, extragalactic recurrent nova; U Sco analog (low mass companion, helium rich). e FUV.max 1.64 x 10-£0 erg s-1 cm- 2 ; t3(UV) 140 days; delay: optical versus UV peak Rl 10 days. This was the intrinsically brightest nova yet observed in the Local Group. Probable CNO nova. I Star is a match to the Galactic nova OS And 1986. = = = References 1. General reference for LMC novae: van den Bergh, S. 1988, PASP, 100, 1486. 2. General reference for M31 novae: Tomaney, A.B. & Shafter, A.W. 1992, ApJS, 81,683 3. General reference for extragalactic novae: Artiukhina, N.M. et al. 1995, General Catalogue o/Variable Stars, Vol. V. Extragalactic Variable Stars (Kosmosinform, Moscow) 'Dlble 175. Element abundances in novae (mass fraction). Object Year X Y TAur RRPic DQHer DQHer HRDeI V1500Cyg V1500Cyg V1668 Cyg V693CrA V693CrA V1370Aql GQMus PWVul PWVul QUVul QUVul V842Cen V827 Her QVVul V22140ph V977 Sco V433 Sct LMC 1990 No.1 V351 Pup 1891 1925 1934 1934 1967 1975 1975 1978 1981 1981 1982 1983 1984 1984 1984 1984 1986 1987 1987 1988 1989 1989 1990 1991 0.47 0.53 0.34 0.27 0.45 0.49 0.57 0.45 0.29 0.40 0.053 0.37 0.69 0.62 0.30 0.36 0.41 0.36 0.68 0.34 0.51 0.49 0.53 0.37 0.40 0.43 0.095 0.16 0.48 0.21 0.27 0.23 0.32 0.21 0.088 0.39 0.25 0.25 0.60 0.19 0.23 0.29 0.27 0.26 0.39 0.45 0.21 0.25 C 0.0039 0.045 0.058 0.070 0.058 0.047 0.046 0.0040 0.035 0.0080 0.0033 0.Q18 0.0013 0.12 0.087 0.014 0.0056 N 0 0.079 0.022 0.23 0.29 0.027 0.075 0.041 0.14 0.080 0.069 0.14 0.125 0.049 0.068 0.Q18 0.071 0.21 0.24 0.010 0.31 0.042 0.053 0.069 0.064 0.051 0.0058 0.29 0.22 0.047 0.13 0.050 0.13 0.12 0.067 0.051 0.095 0.014 0.044 0.039 0.19 0.030 0.016 0.041 0.060 0.030 0.0070 0.10 0.19 Ne 0.Q11 0.0030 0.023 0.0099 0.0068 0.17 0.23 0.52 0.0023 0.00066 0.00014 0.040 0.18 0.00090 0.00066 0.00099 0.017 0.026 0.00014 0.049 0.11 Z Ref. 0.13 0.043 0.57 0.57 0.077 0.30 0.16 0.32 0.39 0.39 0.86 0.24 0.067 0.13 0.10 0.44 0.36 0.35 0.053 0.40 0.10 0.062 0.26 0.38 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [17] [17] [17] [17] [17] [18] [19] 17.1 TYPES OF CATACLYSMIC VARIABLES / 437 Table 17.5. (ContinuetL) Object Year X Y C N 0 V838 Her V838 Her V1974Cyg V1974Cyg Solar 1991 1991 1992 1992 0.80 0.60 0.30 0.19 0.705 0.093 0.31 0.52 0.32 0.275 0.018 0.010 0.015 0.019 0.012 0.023 0.085 0.001 0.0032 0.0021 0.10 0.29 0.010 0.003 Ne 0.068 0.056 0.037 0.11 0.002 Z Ref. 0.11 0.09 0.18 0.49 0.020 [20] [10] [21] [16] [22] References 1. Gallagher, J.S. et al. 1980, ApJ, 237, 55 2. Wtlliams, R.E., & Gallagher, J.S. 1979, ApJ, 228, 482 3. Wtlliams, R.E. et al. 1978, ApJ, 224, 171 4. Petitjean, P., Boisson, C., & Pequignot, D. 1990, A&A, 240, 433 5. lYlenda, R. 1978, AcA, 28, 333 6. Ferland, G.J., & Shields, G.A. 1978,ApJ, 226,172 7. Lance, C.M., McCall, M.L., & Uomoto, A.K. 1988, ApJS, 66, 151 8. Stickland, D.J. et al. 1981, MNRAS, 197, 107 9. Williams, R.E., Ney, E.P., Sparks, W.M., Stanfield, S., Wyckoff, S., & Truran, J.W. 1985, MNRAS, 212, 753 10. Vanlandingham, K., Stanfield, S., & Shore, S.N. 1997, MNRAS, 290, 87 11. Snijders, M.AJ. et al. 1987, MNRAS, 228, 329 12. 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RecuTTf!nt novae. a ab /jb (2000) (2000) Name hr min sec LMC 1990#2 TPyx TCrB USco RSOph V745 Sea V394CrA V3890Sgr V1017 Sgr 05 09 15 16 17 17 18 18 18 09 04 59 22 50 55 00 30 32 58.40 41.47 30.09 30.68 13.08 22.13 25.97 43.32 04.30 min sec -71 39 22 55 52 42 14 00 01 23 -32 +25 -17 -06 -33 -39 -24 -29 (deg) bC (deg) Years of recorded outbursts 283.04 256.76 42.43 357.29 19.48 357.02 352.50 8.85 4.15 -33.49 +9.51 +48.66 +22.47 +10.96 -3.40 -7.13 -5.84 -8.50 1968,1990 1890, 1902, 1920, 1944, 1966 1866,1946 1863, 1906, 1936, 1979, 1987 1898, 1933, 1958, 1967, 1985 1937, 1989 1949, 1987 1962, 1990 1901, 1919, 1973 IC deg 51.6 47.0 11.4 42.1 28.4 58.3 35.1 08.6 12.8 Notes aThree possible recurrent novae have been found in M31. 1\vo are recorded by Rosino, L. 1973, A&AS, 9, 347, and all three (M31 V0609, M31 V0665, and M31 V(979) by Artiukhina, N.M. et al. 1995, General Catalogue o/Variable Stars, Vol. V. Extragalactic Variable Stars (Kosmosinfonn, Moscow). b Adapted from Duerbeck, H.W., 1987, Sp. Sci. Rev., 45, I, and precessed to equinox 2000. cGalactic coordinates. 438 / 17 CATACLYSMIC AND SYMBIOTIC VARIABLES Table 17.7. Recurrent novae data. Name t3a (days) Vrnax Vrnin Av (mag.) LMC 1990#2 TPyx TCrB USco RSOph V745 Sco V394CrA V3890 Sgr VI017 Sgr <7 88 6.8 5 9.5 14.9 5.0 17 130 11.7 7.0 2.0 8.9 4.6 9.6 7.0 8.2 7.0 > 20 ~ 15.2 10.2 17.9 1l.5 19.0 18.0 17.0 13.6 ~ 0.45 1.0 ~0.35 0.6 2.3 ~3 ~3 1.5 1.2 Distance (kpc) Spectral type secondary 55 ? ? M4.1 ±0.1 ill G3 K5.7 ± 0.4 I-ill M4/5ill K M5ill G5ill > 1 1 15: <1.3 4.6 > 10: ~ ~5 2 Periodb (days) ~0.1 227.5 1.23 460 ? 0.7577 ? 5.7 Refs. [1.2] [3-6] [3,5,7-9] [3-5] [3,5,10--13] [5, 14, 15] [4,5,16] [5, 14, 17] [3,5,18] Notes a The time for the visual light curve to fall three magnitudes after maximum. bOrbital period. References 1. Shore, S.N. et a1. 1991, ApJ, 370,193 2. Sekiguchi, K. et a1. 1990, MNRAS. 245, 28P 3. Webbink, R.F. et a1. 1987, ApJ, 314. 653 4. Schaefer, B.E. 1990, ApJ, 355, L39 5. Duerbeck, H.A. 1987, A Reference Catalog and Atlas of Galactic Novae (Reidel, Dordrecht) 6. Schaefer, B.E. et al. 1992, ApJS, 81, 321 7. Kenyon, S.J., & Garcia, M. 1986,AJ. 91,125 8. Selvelli, P.L., Cassatella, A., & Gilmozzi, R. 1992, ApJ, 393. 289 9. Shore, S.N., & Aufdenberg, J.P. 1993, ApJ, 416, 355 10. Bode, M. 1987, RS Oph (1985) and the Recurrent Nova Phenomenon (VNU Science, Utrecht) 11. Garcia, M.R. 1986, AJ, 91, 1400 12. Dobrzycka, D., & Kenyon, S.l. 1994. AJ, 108. 2259 13. Shore, S. et a1. 1996, ApJ, 456,717 14. Harrison, T.E. et a1. 1993. AJ, 105.320 15. Sekiguchi, K. et al. 1990, MNRAS. 246,78 16. Sekiguchi, K. et a1. 1989, MNRAS. 236, 611 17. Gonzalez-Riestra, R. 1992. A&A, 265, 71 18. Sekiguchi, K. 1992, Nature, 358, 563 Table 17.8. Dwaifnovae. (I) Name a •b (aIt. name) WWCet RXAnd HTCas FOAnd WXCet (N Cet 1963) TYPsc ARAnd WXHyi UVPer (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) Coord. c (2000.0) ON POrb Vrnin Vmax tree Incl. MWD XRS EC QP 0.85 0.11 1.14 0.33 0.62 0.04 1.62d 1.41' N N N Y 3.od N Y Y Y 0.7d 1.64' N Y Y Y N N N N N 450 N N N N N 12.2 11-35 370 11.0 25 N N N N N N N N N N O.3od N N N Y N N N N 01124.77 -112842.7 10435.55 41 1758.0 I 10 12.98 6004 35.9 I 1532.14 373735.5 1 17 04.17 -17 56 23.0 1 2539.35 322309.7 14503.27 375633.3 20950.65 -631839.9 21008.25 571120.6 Z 0.1765 15.0 9.3 31 Z 0.209893 12.6 10.9 5-20 SU 0.073647 16.4 SU 0.071 17.5 10.8 30-35 430 13.5 0.052: 17.5 SU 0.068: 15.3 U 0.19: 16.9 SU 0.074813 14.7 SU 0.0622: 17.5 9.5 12.5 11.7 14 140 360 54 4 51 9 81 40 0.9 10 0.3 0.82' N (14) WO SP Wind (15) Spect. type sec. 17.1 TYPES OF CATACLYSMIC VARIABLES I 439 1Bb1e 17.8. (ContinUild.) (I) Name"·b (all. name) CPEri OK Per (NPer 1901) AFCam VWHyi AHEri TUMen AQEri FSAur CNOri SSAur CWMon HLCMa (lE0643-1648) IRGem AWGem BVPup UGem ZCha YZCnc SUUMa ZCam ATCnc (Ton 323) SWUMa EIUMa (PG0834+488) BZUMa CUVel (2) (3) (4) (6) (7) (8) (9) (10) Coord.C (2000.0) ON Porb 31032.76 U 0.01995 -094505.3 33111.82 ON 1.996803 435416.8 33215.59 ON 0.23: 584722.1 4 09 11.34 SU 0.074271 -71 1741.1 42238_10 U -13 2130.2 44140.71 SU 0.1176 -763646.3 50613.04 SU 0.06094 -040807.0 54748.34 U 0.059: 2835 ILl 55207.77 U 0.163199 -052500.7 61322.44 U 0.1828 474425.7 63654.53 U 0.1762 000216.3 645 17.21 Z 0.2145 -165135.4 647 34.58 SU 0.0684 280622.7 7 22 40.83 SU 0.0762 283016.1 74905.26 U 0.225: -233400.7 7550S.29 U 0.176906 220005.7 8 07 28.30 SU 0.074499 -763201.3 81056.62 SU 0.0868 280833.6 81228.20 SU 0.07635 623622.6 82513.20 Z 0.289840 730639.4 82836.92 Z 0.238691 252002.6 83642.80 SU 0.056815 532838.2 83821.98 U 0.26810 48 38 01.7 85344.14 ON 0.0679 5748 41.1 85832.87 SU 0.0773 -4147 SO.8 90103.35 Z 0.380 175356.1 92207.48 U? 0.2146 ARCnc 310314.6 94636.67 SU? 0.08597 OVUMa (US 943) 444645.1 95101.51 U 0.1644 X Leo 11 5231.1 10 06 22.43 SU 0.063121 OYCar -701404.9 CHUMa 10 07 00.57 U 0.3448: (PGl0030+678) 673246.5 DO Leo 10 40 51.21 0.234515 (PO 1038+ 155) IS 11 33.7 SYCnc (5) Vrnin Vrnax tree 19.7 16.5 10.2 0.2 17.0 13.4 75 13.4 9.5 27 179 18.4 13.5 > 16 11.6 17.7 12.5 16.2 14.4 14.2 11.9 14.5 IO.S 40-75 16.3 11.9 122 13.2 11.7 17 16.3 11.7 22-48 150 13.8 98 410 13.1 19 18.8 15.6 Inc!. < 73 37 194 40: 8-22 (II) (12) (13) QP N N WD Wind Y N N N Y N N N N N N N Y Y N N Y N N N N N N Y N N N N N N N N N N < 0.32Ft N Y N N M4-5 N N N N Y MI-5 N Y N N N M3-S - 1.2od N N N Y N N N N N N N N N N 0.55' N N N N 1.12 0.13 0.84 0.09 - o.lsd Y Y Y N M4.5 0.87Ft 1.97F' Y Y Y N MS.5 O.24d 0.95e N Y N Y N N N N 0.90 0.20 EC N 60 0.63 65 0.6 10 67 3 38 16 0.74 0.10 1.08 0.40 45: 1.0: 118 15.3 12.4 82 287 14.1 11.9 38 0.82 3 0.05 14.2 12.2 6-16 134 5-33 13.6 IO.S 19-28 Y N Y 14 2.1Ft 18.7e N N 12.7B 57 0.99 11 0.15 Y N N N 45 0.71 18 0.22 0.32e Y Y N N N N N N 10.6 14.9B 69.7 0.7 81.8 0.1 1.5IY 9.1 16.5 160 459 sec. K0-4 10 0.15 14.0 15.0B (15) Spect. type SP MWO XRS (14) 0.4IY O.08e -3.l d Ll3' 1.01 e K7 M5.5 17.8 IO.S N N N N N 15.5 10.7 N N N N N < O.SlFt N Y N Y 08-9 N Y N N N M4-5 N N N N N M4.5 < 0.21Ft N Y N N M2 0.11' Y N Y N M6 N N N N N N N N N N 13.5 113 386 ILl 22-35 26 0.89 6 0.28 18.7 15.3 18.6 15.4 15.8 12.4 15.3 12.4 25-50 82.6 0.90 300 0.1 0.04 10.7 204 21.0 1.9S 4.0 0.30 15.9 16.0B 8-38 440 I 17 CATACLYSMIC AND SYMBIOTIC VARIABLES Table 17.8. (Continued.) (1) Name",b (all. name) CYUMa V436Cen V442Cen RZLco TLco DO Ora (PG1140+719) lWVll" ALCorn BVCen LYHya (1329-294) UZBoo TTBoo EKTrA DMOra BRLup SSUMi (PG1551+719) AHHer V20510pb V4260ph UZSer BDPav AYLyr EMCyg ABOra EYCyg UUAql V4140Sgr (NSV 12615) RZSge WZSge CMDel V503Cyg VWVul (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) Coonl,C (2000.0) DN Pori> Vrnin Vmax tree locI. Mwo XRS EC QP SU 0.0583 17.0 11.9 N N N N N SU 0.062501 15.3 12.4 N Y N N U 0.46: N N Y N N 0.41" N N N N 65 0.16 19 0.04 42 0.83 N N N N N N N Y N N M3-S 43 0.91 13 0.25 0.3sd N N N Y M2-4 N N Y N N N N N N N N N N N 105657.05 494118.7 111400.10 -374048.6 112451.92 -355437.7 113722.30 014857.8 113826.96 032208.1 114338.34 714120.4 114521.13 -042605.9 123225.90 142042.5 13 31 19.55 -545833.6 133153.84 -294059.1 144401.30 220056.0 145744.74 404342.2 15 1401.47 -650531.3 153412.13 594831.9 153553.15 -403405.5 1551 22.24 714511.9 164409.99 25 1502.1 170819.09 -254830.8 180751.71 055148.5 18 1124.90 -145533.9 1843 11.90 -573044.2 18 44 26.73 375951.8 193840.10 303028.0 194906.50 77 4423.5 195436.77 322154.7 195718.68 -091920.8 195849.71 -385612.3 20 03 18.49 170252.6 2007 36.40 174215.4 202456.92 17 1754.3 20 2717.44 434123.1 20 57 45.08 253026.0 16.5 22 335 11.9 14-39 19.0 11.5 0.058819 15.2 11.0 SU? 0.0708 SU U U 115: 297: 450 0.165 15.6B 1O.6B 0.18267 15.8 12.1 15-44 0.061: 20.8 12.8 225: 0.610116 12.6 10.5 150 65: 0.7: 5 0.1 5 0.18 62 0.83 5 0.10 8.3F! (14) WD SP Wind 0.13695 14.4 0.125: 19.B 1l.5 360: N N N N N SU 0.077: < 15.6 12.7 45 N N Y N N SU 0.0636 > 17 12.1 Y N N N N U 0.087: 20.8 15.5 231 487 N N N N N SU 0.0793 > 17.5 13.1 N N N N N U 0.088: 16.9 12.6 30-48 N N N N N Z 0.258116 13.9 11.3 N Y N Y U? 0.062428 15.0 13.0 O.48F! 2.38" Y y N N 1.07" N N N N N N N N N N Y N N N N N N N Y y N N N N N Y N N N N N N N N N 7-27 Z 0.2853 11.5 17-5S U 0.1730 15.5 11.9 10-40 U 0.17930 15.4 12.4 SU 0.07340 18.4B 13.2 8-43 205 46 0.95 3 0.10 80.5 0.44 2.0 O.OS S7 0.9 11 0.15 > 5S N Z 0.290909 13.3 12.5 1~ Z 0.15198 14.5 12.3 8-22 U 0.18123: 15.5 1l.4 96 U 0.14049: 16.1 11.0 71 SU? 0.061430 17.5 15.5 N Y N N N SU 0.0686 N N N N N SU 0.056688 14.9 y y N N N N N SU 0.07599 13.4 15.3 17.4 -0.30" 0.21" y 0.162 72 0.8: 2 0.3 73: 0.48 47 O.lS Y U 12.8 62-93 266 7.0: 11876 N N N N N U? 0.0731 13.6 44 0.24 12 0.06 N N N N N 16.9 13.4 28 14-29 63 0.S7 10 0.08 1.6" 3.62" N (15) Spect. type sec. OS-8 K2-MO K2-4 KS KO 17.1 TYPES OF CATACLYSMIC VARIABLES / 441 Table 17.8. (Continued.) (I) Name"·b (alt. name) VY Aqr SSCyg RUPeg TYPsA (PS 74) GD552 IP Peg (2) (3) (4) (5) (6) (7) (8) (9) (10) (II) (12) (13) Coord.c (2000.0) DN Porb Vmin Vrnax tree Incl. MWO XRS EC QP SU 0.06312 3.96' N N N N 86Ft 1.12' 18.2d 7.90' N N Y Y Y K5 N Y N Y K2-3 N Y N N 21 1209.20 -084936.5 214242.66 433509.5 221402.58 1242 11.4 224939.86 -270654.2 225039.64 632839.3 232308.60 182459.4 17.1 8.0B U 0.275130 11.4 8.2 24-63 U 0.3746 12.7 9.0 75--85 SU 0.08400 16.0 0.07134 16.5 U 0.158206 14.0 18.5B 12.0 12.B 95 37 1.19 5 0.02 33 1.21 5 0.19 (14) WD SP Wind 20: 1.4: N N N N N 68 1.15 0.10 N Y N N N (15) Spect. type sec. M4 Key definitions of columns (I) System name. (2) Right ascension, declination (Equinox 2000.0). (3) Dwarf nova sub-type, U Gem, Z Cam (standstills), SU UMa (superoutbursts), DN (undetermined subtype). (4) Orbital period in days (spectroscopic period), colon indicates uncertain value as adapted from [I]. (5) Vrnin: minimum visual brightness in quiescence, B denotes a B magnitude measurement (adapted from [1, 2]). (6) Maximum visual brightness peak at dwarf nova outburst (adapted from [1, 2]). (7) Recurrence time of dwarf nova outbursts in days; the second entry is the approximate recurrence time of super outbursts in the case of SU UMa systems (adapted from [I]). (8) Orbital inclination in degrees; second entry is the ± error estimate in degrees (adapted from [1]). (9) Mass determination for the white dwarf in solar masses; the second entry is ± error estimate (adapted from [3] and [1]). (10) X-ray data. If the system is a detected hard-X-ray source (0.1-4 keY) with the Einstein Observatory (HEAO-B) imaging proportional counter (!PC) [4-7] or has an upper limit detection, then an X-ray luminosity is given in units of 1031 ergs/s when a distance estimate is available, otherwise a count rate. If the system is a detected X -ray source with the EXOSAT (2-20 keY) medium energy (ME) experiment [8] or is an upper limit detection, then an X-ray luminosity is given in units of 1031 ergs/so If the system is a detected Einstein !PC source but with no distance estimate, then a count rate is given followed by an F. If the entry is N, then the system has not been observed with either Einstein or EXOSAT, but ROSAT data may exist. (11) Does the system undergo eclipses, yes (Y) or no (N)? (12) Does the system exhibit quasiperiodic oscillations (QPO), yes or no? (13) Is the underlying white dwarf detected spectroscopically during dwarf nova quiescence (Le., dominates the light in the far UV, EUV (IUE, HST, HUT, EUVE) andlor in the optical), yes or no [9-13] and references therein? (14) Does the system exhibit direct spectroscopic evidence of wind outflow (e.g., P Cygni line structurelshortward-shifted absorption or broad wind emission, during dwarf nova outburst), yes or no [14] and references therein? (15) Spectral type of the cool, normally main sequence, lower mass, secondary star, if known. Notes aFinding charts for dwarf nova systems are given in [2]. Other references to finding charts are in [I] and [15]. bReferences to the key ground-based and space-based spectroscopic studies of dwarf novae are given in [1,2, 15, 16] and references therein. cCoordinates for equinox 2000.0 adapted from [1, 2]. Coordinates for 2000.0 measured off the Space Telescope Guide Star plates are given in [2]. d Einstein !PC X-ray luminosity. e EXOSAT ME data. I Einstein IPC observed flux. Informative and stimulating reviews of virtually all aspects of dwarf novae can be found in [13, 14, 17-22]. References to original spectroscopy can be found in [1, 14-18, 21]. References 1. Ritter, H. 1990, A&AS, 85, 1179 2. Downes, R.A., Webbink, R.F., & Shara, M.M. 1997, PASP, 109,345 3. Webbink. R.E. 1990, in Accretion-Powered Compact Binaries, edited by C. Mauche (Cambridge University Press, Cambridge), p. 177 4. C6rdova, F.M., & Mason, KO. 1984, MNRAS, 206, 879 5. Eracelous, M., Halpern, J., & Patterson, J., 1991, ApJ, 370, 330 6. Eracelous, M., Halpern, J., & Patterson, J., 1991, ApJ, 382, 290 7. Patterson, J., & Raymond, J. 1985, ApJ, 292, 535 8. Mukai, K, & Shiokawa, K 1993, ApJ, 418,803 9. Panek, R., & Holm, A. 1984, ApJ, 277, 700 442 / 17 CATACLYSMIC AND SYMBIOTIC VARIABLES 10. Sion, E.M. 1987, in The 2nd Conference on Faint Blue Stars, IAU Coll. No. 95, edited by A.G.D. Philip, D. Hayes, and J. Liebert (Davis, Schenectady), p. 413 11. Smak, J. 1992, AcA, 42, 323 12. Long, K. et al. 1993, ApJ, 405, 327 13. La Dous, C. 1991, A&AS, 252, 100 14. Pattemon,J. 1984,ApJS,S4,443 15. Williams, G. 1983, ApJS, 53, 523 16. Szkody, P. 1987, ApJS, 63, 685 17. Robinson, E.L. 1980, ARA&A, 14, 119 18. C6rdova, F.M. 1995, X-Ray Binaries, edited by W.H.G. Lewin, J. van Paradijs, and E.P.J. van den Heuvel (Cambridge Univemity Press, Cambridge) 19. Verbunt, F. 1986, in The Physics ofAccretion onto Compact Objects, edited by M.G. Watson and N.E. White (SpringerVerlag, Berlin), p. 59 20. Wade, R. 1985,Interacting Binaries, edited by P.P. Eggleton and J.E. Pringle (Reidel, Dordrecht) 21. Warner, B. 1995, Cataclysmic Variable Stars (Cambridge Univemity Press, Cambridge) 22. Szkody, P. 1985, in Cataclysmic and Low Mass X-Ray Binaries, edited by D.Q. Lamb and J. Pattemon (Reidel, Dordrecht), p.385 Table 17.9. Selected listofnova-1Uces. Name (alt. names) IT Ari (BD+14°341) RWTri Coord.a (2000) Galactic Vrnax b coord. B-V Vrnin E(B - V)C 020653.09 +151743.0 02 25 36.14 +28 05 51.4 081518.90 -4913 18.3 10 1956.63 -084156.0 110542.80 -683758.0 147.69 -44.05 146.34 -30.59 264.80 -8.09 251.32 38.28 293.35 -7.79 9.5 16.3 12.6 15.6 9.1 10.0 10.4 10.8 11.1 11.5 -0.04 [I] 0.02 [I] 0.10 [2] 133640.97 +515450.3 MVLyr 190716.30 (MacRAE+43° 1) +440108.4 V3885 Sgr 194740.54 (CD-42°14462) -420025.5 107.67 63.91 74.61 16.08 357.32 -27.14 12.7 14.1 12.1 18.0 9.6 10.3 0.07 [I] 0.0 [2] -0.13 [I] -0.35 [I] 0.0 [I] 0.0 [2] V794Aql 39.38 -20.22 19.84 -71.14 13.7 20.2 12.9 18.5 IX Vel (CPD-48°1577) RWSex (BD-7°3007) QUCar (HOE 310376) (CD-67° 1010) UXUMa VYScl (pS 141) (SPC Var4) 201733.97 -033951.0 232900.45 -294646.0 Second. spectral classd 0.0 [2] 0.15 [I] 0.25 [9] 0.1 [2] -0.03 [13] 0.03 [13] K5V [10] Period' (d) 0.137551 [3.4] 0.1329 [5. 6] 0.231 883 297 [11, 12] 0.193929 [14, 15] 0.245 07 [25] Rapid oscillation period (s) Spec.! Refs. 1000-1600 [3,8] QPO [7] [11] 'JYpe VY UX [16-22] [14,23] UX 620.1280 QPO [26] [24.25] UX 28-30 QPO[32] 2800 QPO [36] 29-30 [38,41] [33,34] UX 0.32 [19] 0.0 [2] 0.19667126 [30,31] 0.1336 [35] 0.1379 [36] 0.206-0.259 [38.39] 0.2163 [40] 0.237 [20] -0.10 [16] 0.06 [16] 0.1662 [17] -500 QPO [18] -0.04 [24] 0.0 [2] 0.0 [2] 0.454 [27] 0.113471 [28] K8VM6V[29] M5V [35] [27] [35.37] VY [39] UX [21,42] VY [17,19] VY Notes a Adapted from [43]. bThe range in magnitudes is taken from [44]. cThe color excess, E(B - V), is assumed to be related to the visual intemtellar extinction, Av. by Av = 3.2 E(B - V). dThe secondary spectral types are from spectroscopic or photometric observations and do not include estimates from mass determinations. eThe spectroscopic period is the fimt entry while the photometric period is the second if it is different. Orbital parameters can usually be found in the reference for the spectroscopic period. f Only optical references are given. 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Synchronously rotating magnetic CVs (AM Her binaries).a Mag. fieldc •e Name (alt. name) BLHyi (H0139-68) WWHor (EXOO234.5-5232) EFEri (2A0311-227) VYFor (EXOO32957-2606.9) UZFor (EXOO33319-2554.2) BY Cam (H0538+608) VVPup EKUMa (lEI048+524l) ANUMa STLMi (CWI103+254) DPLeo (lE1114+ 182) EUUMaf (REI 149+28) V834Cen (lEI405-45l) MRSer (PGI550+191) AMHer8 (3Ul809+50) EPDra (HI907+690) QSTel (RE 1938-461) QQVul (lE2003+225) V1500Cyg (Nova Cyg 1975) CEGru (Grus VI) Coord. b (2000) 14100.25 -675327.7 23611.45 -521913.5 31413.03 -223541.4 33104.58 -255655.5 33528.61 -254422.6 54248.90 60 5131.8 81506.73 -190316.8 105135.23 540436.0 110425.71 450315.0 11 05 39.75 250628.9 11 17 16.00 17 57 41.1 11 4955.70 284507.5 140907.46 -451717.1 155247.23 185627.6 18 16 13.33 495204.2 1907 06.13 690842.4 193835.73 -461256.5 200541.93 223959.1 21 11 36.61 480901.9 21 3756.38 -434213.1 Dist.c (PC) pd om (min) mv c .d 128 113.6 14-18.5 500 114.6 19-21 > 89 81.0 13.5-17.5B 228 17.5 250 126.5 18-20.5 200 201.9 14.5->17B 145 100.4 14.5-18 114.5 18-20 > 270 114.8 14.5-19B 128 113.9 15.~17 >380 89.8 17.5-19.5B 16.5B 86 90: 103: 101.5 112 113.6 15-17 75 185.6 12-15.5 600: 104.6 18 140.0 15.5 >400 222.5 14.5-15.5 10001400 201.0 197.5i 108.6 17-18 199.3h 14.~17 18-218 Polarization BI> B2 Bd Lsx Cire. (MG) (MG) (ergs s-l) (%) (%) Refs. 30 I x loJ l 17 12 [1.2] 4 x loJ 3 30 > I x loJ 2 20 33 P 25: P Z 15 Z Lin. [3] 9 [6] 1~50: P 53.75: C 41: C 31.5.56 C 47: C 36 C 7 x loJ 3 6 3 5 x loJ 2 30.5.59 C.Z 15 [7.8] [9-12] 10 18 Z [4.5] 15 [13-15] 20 [16. 17] >3xlO32 35 [18-20] 2 x loJ2 20 12 [21-24] > I x loJ3 35 9 [25.26] [27] 23 Z.C 24 C 14.28 C 1~50: P 25-50: P 20:.20: P 10 Z 22 Z 1 x 1032 30 10 [28-31] 5 x loJ° 12 5 [32.33] 9 x 1032 10 8 [34-37] [38] 10 > 4 x 1034 6 10 [39] 8 2 [40] 10 [41] 15 [42.43] Notes aThese binaries contain accreting white dwarfs that are strongly magnetized and rotate essentially synchronously, i.e., rotation period within 2% of the orbital period Porb [44, 45]. They are more commonly known as AM Herculis binaries, or polars, and are characterized by the strong optically polarized radiation they emit. mv: Visual magnitude. B indicates blue magnitude. Nova outburst magnitude not given. BI, B2 are the dominant and less dominant accretion poles, respectively. 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Asynchronously rotating magnetic CVs (DQ Her binaries).a Name (alt. name) XY Arif (1 H0253+ 193) Coord. b (2000) 25608.1 192634. Dist. c Prot Porb (pc) (min) (h) 200 3.42 6.06 Lhx c •e mud 12-13.5K (erg s-l) 2 x 1032 Refs. [1.2] 446 / 17 CATACLYSMIC AND SYMBIOTIC VARIABLES Table 17.11. (Continued.) Name (alt. name) Coord. b GKPer8 (Nova Per 1901) V471 Tau 33111.82 435416.8 35024.79 171447.8 52925.44 -324904.5 53450.67 -580140.9 54320.22 -410155.2 73128.98 95622.6 TV Col (2A0526-328) TWPic (H0534-581) TXCoI (1H0542-407) BGCMih (3A0729+ 103) PQGemi (RE0751+14) EXHya V795Herf (PO 1711+336) DQHer (Nova Her 1934) V533Herf (Nova Her 1963) V1223 Sgr AEAqr8 FOAqr (82215-086) AOPsc (H2252-035) (2000) 75117.39 144424.6 125224.40 -291456.7 171256.09 333121.4 180730.17 455131.9 181420.34 415121.3 185502.24 -310948.5 204009.02 -05215.5 22 1755.43 -82104.6 225517.97 -31040.4 Dist. c (PC) Prot (min) (h) mv d Lhxc,e (erg s-l) Refs. 525 5.86 47.9 10-14.0 7.4 x 1032 [3-5] 49 9.24 12.51 9-10 >500 31.9 5.49 13.5-14 650: 126: 6.5: 14-16 >500 31.9: 5.72 15.5 700-1000 14.1: 15.2: 28.2: 13.9: 3.24 14-14.5 -6: 14.5 76-90 67.0 1.64 10-14 2.60 12.5-13B 300-500 93.8: 106.4: 1.18 4.65 14-17.5 < (1.1-3.0) x 1030 1000: 1.06 5.04 14.5-16 < 2 x 103 1 540-660 12.4 3.37 12-> 17 28-78 0.55: 9.88 10-11.5 200-640 20.9 4.85 13-14 100-750 13.4 3.59 13.5-15 Porn [6-8] > 6.1 x 1032 [9.10] [11] > 2.8 x 1032 [12. 13] (0.7-1.4) x 1033 [14-19] [20.21] (0.3-1.8) x 1032 [22.23] [24.25] [26-28] [26.27.29] (0.9-1.3) x 1033 [30-33] < (0.5-3.6) x 1030 [34-37] (0.8-8.3) x 1032 [38-41] (0.02-1.3) x 1033 [33,42-44] Notes aThese binaries are believed to contain accreting magnetized white dwarfs that rotate asynchronously with the rotation period Prot differing by more than 2% from the orbital period Porb. 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