Introduction to Advanced Astrophysics

486 Pages·1979·34.056 MB·English

by  V. Kourganoff (auth.)

INTRODUCTION TO ADVANCED ASTROPHYSICS
GEOPHYSICS AND
ASTROPHYSICS MONOGRAPHS
AN INTERNATIONAL SERIES OF FUNDAMENTAL TEXTBOOKS
Editor
B. M. MCCORMAC, Lockheed Palo Alto Research Laboratory. Palo Alto. Calif.. U.S.A.
Editorial Board
R. GRANT ATHAY, High Altitude Observatory. Boulder. Colo .. U.S.A.
W. S. BROECKER, Lamont-Doherty Geological Observatory. Palisades. New York. U.S.A.
P. J. COLEMAN, JR., University of California. Los Angeles. Calif.. U.S.A.
G. T. CSANADY, Woods Hole Oceanographic Institution. Woods Hole. Mass .. U.S.A.
D. M. HUNTEN, University of Arizona. Tucson. Ariz .. U.S.A.
C. DE JAGER, The Astronomical Institute. Utrecht. The Netherlands
J. KLECZEK, Czechoslovak Academy o.lSciences. Ondrejov. Czechoslovakia
R. LOST, President Max-Planck Gesellschaftfur Forderullg del' Wissenschafien. Munchen. F.R.G.
R. E. MUNN, University o.lToronto. Toronto. Ont .. Canada
Z. SVESTKA, The Astronomical Institute. Utrecht. The Netherlands
G. WEILL, Institute d·Astrophysique. Paris. France
VOLUME 17
INTRODUCTION TO
ADVANCED
ASTROPHYSICS
by
V.KOURGANOFF
Professor Emeritus, University of Paris
D. REIDEL PUBLISHING COMPANY
DORDRECHT: HOLLAND / BO STON: U.S.A.
LONDON:ENGLAND
Library of Congress Cataloging in Publication Data
Kourganoff, Vladimir, 1912-
Introduction to advanced astrophysics.
(Geophysics and astrophysics monographs; v. 17)
Includes bibliographical references and index.
1. Astrophysics. I. Title. II. Series.
QB461.K69 523.01 79-20463
ISBN-13:978-90-277-1003-1 e-ISBN-13:978-94-009-9468-3
DOl: 10.1007/978-94-009-9468-3
Published by D. Reidel Publishing Company,
P.O. Box 17, Dordrecht, Holland
Sold and distributed in the U.S.A., Canada and Mexico
by D. Reidel Publishing Company, Inc.
Lincoln Building, 160 Old Derby Street, Hingham,
Mass. 02043, U.S.A.
All Rights Reserved
Copyright © 1980 -by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover 1st edition 1980
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any informational storage and
retrieval system, without written permission from the copyright owner
T ABLE OF CONTENTS
PREFACE xi
Part 1. Radiative Transfer and Internal Structure of Normal Stars
CHAPTER 1. INTRODUCTION TO THE THEORY OF RADIATIVE
TRANSFER
1. Basic Concepts in the Description of a Radiation Field 3
2. Relations between Macroscopic and Microscopic Parameters Describing the
Interactions between Matter and Radiation 8
3. Equation of Transfer and the Corresponding Equation of Continuity 20
4. Applications to the Physics of Stellar Interiors 31
Appendix: The Relations between Einstein's Coefficients 44
CHAPTER 2. ELEMENTARY INTRODUCTION TO THE PHYSICS OF
STELLAR INTERIORS
1. General Conditions of Mechanical Equilibrium 46
2. The Equilibrium between the Gradient of the Total Pressure and the Gravi-
tational Force per Unit Volume 47
3. The Relation between Mr and the Density p at a Distance r from the Center 53
4. The Expression for div g as a Function of the Local Density p. Poisson's
Equation 54
5. The Calculation of the Gas Pressure Pgas. The Concept of the Mean Mass /J.
of a Particle of the Mixture, in Units of mB (where mB is the Mass in Grams
of a Baryon) 55
6. A Model of the Sun at Constant Density p = P 59
CHAPTER 3. THE PHYSICS OF INTERIORS OF THE MAIN
SEQUENCE STARS
1. Introduction 61
2. The Equation of Energy Equilibrium 62
3. The Expression for e(r) in the Case when Energy is Produced by the p-p
Chain or the C-N Cycle 63
4. The System of Differential Equations and of Boundary Conditions which
Determine the Internal Structure of a Normal Star 65
5. Evolutionary Models and Solution of the Problem Concerning the Func-
tion X(r) 67
vi TABLE OF CONTENTS
6. Utilization of Boundary Conditions in the Study of Initial Models 71
7. From Initial Models to Models Corresponding to the Present State. Deter-
mination of the Age of a Star 73
8. The Present Internal Structure of the Sun 74
9. Comparison between the Present Structure of the Sun and its Structure at
Age Zero 78
10. The Superficial Convective Zone of the Sun 79
Part ll. White Dwarfs, Neutron Stars and Pulsars
CHAPTER 4. ELEMENTARY PROPERTIES OF A DEGENERATE
FERMI GAS
1. Different 'Energy Parameters' of an Isolated Particle. Energy Groups (NR),
(UR) and (RR) 91
2. The Number of Independent Identical Particles (Confined in a Macroscopic
Unit of Volume) whose Momentum lies between p and (p + dp) 94
3. The General Trend of the Fermi-Dirac Distribution Function. Definition of
the Complete Degeneracy. The Fermi Level 98
4. Relations between the Number Density of a System of Fermions in a State
of Complete Degeneracy and Energy Parameters of the Fermi Level 101
5. Energy Density (for Total and for Kinetic Energy) of a Completely Degener-
ate System of Independent Identical Fermions 106
6. The Mean (Total) Energy and the Mean Kinetic Energy of One Particle of a
Completely Degenerate System of Independent Identical Fermions.
Relations with the Fermi Level 109
7. Expressions for Partial Number Densities of Different Components of a
Stellar Mixture as a Function of the Mass Density of the Mixture. Parameters
/l, J.le and ~ 111
8. The Pressure Produced by a System of Independent Identical Fermions in a
State of Complete Degeneracy 117
9. The Domain of Separation between the State of a Perfect Gas and the State
of Complete Degeneracy. Application to the Sun 122
Appendix: Establishment of the Rigorous (RR) Expressions for u(n, m) and
uk(n,m) 126
CHAPTER 5. WHITE DWARFS
1. A Few Historical Remarks 129
2. Poly tropes and the Virial Theorem. Application to an Elementary Theory
of White Dwarfs 130
3. Polytropic White Dwarfs Studied by Means of the Emden-Lane Equation 141
4. Chandrasekhar's 'Rigorous' Theory of White Dwarfs 146
Appendix: The Gravitational Binding Energy of a Star 151
TABLE OF CONTENTS vii
CHAPTER 6. NEUTRON STARS
1. Introduction: (Rz) Reactions (Electron Captures and (3-Disintegrations) 154
2. Neutronization by a Degenerate Gas of Free Electrons 159
3. (RA) Reactions Leading to an Increase of Atomic Weight of Nuclei 162
4. The Different Domains of Mass Density 163
5. Different Forms of Equilibrium Equations for (Rz) Reactions 166
6. Equilibrium Equations for (RA) Reactions 172
7. The Domain A: Determination of A and Z Corresponding to an Equilib-
rium with Respect to Reactions (Rz) and (RA) 174
8. The Domain B: A Mixture of Free Electrons, Free Neutrons and Nuclei
(A, Z) 176
9. The Domain C: A Mixture of Free Electrons, Free Protons and Free
Neutrons 178
10. The Structure of Neutron Stars. Their Radius as a Function of Their Mass
181
CHAPTER 7. PULSARS
1. The Discovery of Pulsars 187
2. The First Investigations and the First General Pro perties 191
3. Pulsar Distances 198
4. Pulsar Ages 222
5. Luminosity Problems and the Pacini Model 228
6. The Problem of Association of Pulsars with Supernovae 233
7. The 'Celibacy' of Radio Pulsars (and Binary Character of the 'X-ray' Pulsars) 234
Part HI. Newton's Law, Binary Systems and Galactic X-ray Sources
CHAPTER 8. THEOR Y OF SPECTROSCOPIC AND ECLIPSING
BINARIES. STELLAR MASSES
1. The Newtonian Form of Kepler's Third Law 241
2. Elementary Interpretation of Observations 243
3. The Values of Stellar Masses. Relations between Masses, Luminosities and
Spectral Classes 264
Appendix A. On Keplerian Motion 265
Appendix B. Inductions Leading from Kepler's Empirical Laws to Newton's Law
of Gravitation 272
CHAPTER 9. GALACTIC X-RA Y SOURCES
1. Introduction 282
2. The Classification Problem 301
3. A few Particularly Interesting Galactic X-ray Sources 302
Appendix: A Dictionary of Abbreviations in the Field of Galactic Sources.
Conversion of Names. Tables 308
viii TABLE OF CONTENTS
Part N. Cosmology: Elementary Theory and Basic Observational Data
CHAPTER 10. ELEMENTARY THEORETICAL COSMOLOGY:
THE NEWTONIAN APPROACH
l. Introduction 315
2. The Fundamental Principles 316
3. The Kinematics of a Model of Cosmic Fluid. Hubble's law 318
4. A few Observational Data 323
5. The Friedmann Model of Universe 324
6. The Ratio of the Age of the Friedmann Universe to the 'Hubble Time' as a
Function of Q 341
7. The Radiation Model of the Early Universe 342
CHAPTER 11. BASIC CONCEPTS OF RELATIVISTIC COSMOLOGY
1. Introduction 348
2. Some Elementary Relativistic Concepts 348
3. The Characteristic Properties of Non-Euclidean Spaces 356
4. The Geodesic Principle 375
CHAPTER 12. RELATIVISTIC EFFECTS IN OBSERVATIONAL
COSMOLOGY. THE COSMOLOGICAL REDSHIFT IN
EXPANDING UNIVERSE
1. A Bi-dimensional Model of an Expanding Universe. Fixity in Mobility: The
Comoving Coordinates 383
2. Tri-dimensional Friedmann Relativistic Models of Expanding Universe 384
3. The Cosmological Redshift 387
4. The Metric (Mathematical) Linear Distance of a Source 397
5. The Classical Distance of a Source as a Function of its Redshift 400
6. The Relativistic Variation of the Angular Diameter, for Sources of a given
Linear Diameter, as a Function of their Redshift 401
7. A Physical Interpretation of the Metric Distance 406
8. The Relativistic Variation of the Integrated (Bolo metric) Brightness, for
Point Sources of given Luminosity, as a Function of their Redshift 407
9. The Brightness of an Extended Source per Unit Solid Angle 414
10. The Source Counts 416
Appendix: Relations between the Magnitudes, the Luminosities and the Cosmo-
logical Redshift 430
CHAPTER 13. BASIC DAT A IN OB SER V ATION AL COSMO LOG Y:
ACTIVE GALACTIC NUCLEI AND CLUSTERS OF
GALAXIES
1. Introduction 434
2. Active Galactic Nuclei (Quasars and Similar Objects) 434
T ABLE OF CONTENTS ix
3. Clusters of Galaxies 453
4. Superc1usters of Galaxies? 454
5. General Comments on the Confrontation of Cosmological Theories with
Observational Data 456
Appendix: A Dictionary of Abbreviations in the Field of Extragalactic Objects 462
467
TABLE OF VALUES
INDEX 469
PREFACE
The purpose of this textbook is to provide a basic knowledge of the main parts of modern
astrophysics for all those starting their studies in this field at the undergraduate level. The
reader is supposed to have only a high school training in physics and mathematics. In many
respects this Introduction to Advanced Astrophysics could represent a volume of the
Berkeley Physics Course. Thus, the primary audience for this work is composed of students
in astronomy, physics, mathematics, physical chemistry and engineering. It also includes
high school teachers of physics and mathematics. Many amateur astronomers will fmd it
quite accessible.
In the frame of approximations proper to an introductory textbook, the treatment is
quite rigorous. Therefore, it is also expected to provide a firm background for a study of
advanced astrophysics on a postgraduate level.
A rather severe selection is made here among various aspects of the Universe accessible
to modern astronomy. This allows us to go beyond simple information on astronomical
phenomena - to be found in popular books - and to insist upon explanations based on
modern general physical theories.
More precisely, our selection of topics is determined by the following considerations:
The study of the solar system (the Moon and the planets) has recently progressed at a
tremendous rate. However, the very rich harvest of observations provided by space
research is mainly purely descriptive and is perfectly presented in review papers of Scien
tific American, Science, Physics Today and similar magazines.
A detailed description of our own galaxy, and of external galaxies, is given in dozens
of well known books, illustrated with excellent reproductions of photographs obtained
with giant telescopes.
On the other hand, a systematic use of electronic computers in stellar dynamics has
recently made it possible to attempt an explanation of the spiral structure of galaxies.
However, a clear account of this problem would oblige us to expand too much the scope
of our book.
The description of solar activity (sunspots, prominences, solar flares, etc.) and of geo
physical phenomena associated with this activity (aurorae, magnetic storms, etc.) can also
be found in many textbooks. Moreover, the corresponding explanations involve theories
(plasma physics, magneto-hydrodynamics, ...) probably too advanced for our prospective
readers.
Similarly, the study of interstellar medium relies more on advanced physics than on
advanced astrophysics.
Finally, Otto Struve's fundamental Elementary Astronomy can give all basic astro
physics omitted from our textbook.
After all these exclusions, we are left with several important and interesting problems:
xi