G. Contopoulos D. Kotsakis

Cosmology The Structure and Evolution of the Universe

Translated by M. Petrou and P. L. Palmer

With 54 Figures

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

Professor Dr. Georgios Contopoulos Astronomy Department, University of Athens, Panepistimiopolis GR-15783 Zografos, Athens, Greece

Professor Dr. Dimitrios Kotsakis t

Translators:

Dr. M. Petrou NERC Unit for Thematic Information Systems, Department of Geography, White Knights P.O. Box 227, IV. Reading, Berks, RG6 2BA, England

Dr. P. L. Palmer Queen Mary College, University of London, Mile End Road London E1 4NS, England

Cover picture: The supernova remnant in Vela (Photograph: European Southern Observatory)

Title of the original Greek edition:

Kosmologia - I Domi Kai I Exelixi Tu Sympantos, 2nd updated and expanded edition © G. Contopoulos and D. Kotsakis, Athens 1984

ISBN-13: 978-3-540-16922-2 DOl: 10.1007/978-3-642-71464-1

e-ISBN-13: 978-3-642-71464-1

Library of Congress Cataloging-in-Publication Data. Kontopoulos, Georgios Ioannou, 1928 - Cos­mology : the structure and evolution of the universe, with 54 figures. Translation of: Kosmologia. 1. Cosmology. I. Kotsakis, D. (Dimitrios). II. Title. III. Title: Structure and evolution of the universe. QB981.K69513 1987 523.1 86-21920 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesell­schaft Wort", Munich.

© Springer-Verlag Berlin Heidelberg 1987

The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

2153/3150-543210

Preface

This is a translation from the second Greek edition (1984). We have added a few more sections and increased the bibliography to keep up with the developments in cosmology over recent years. In this edition, the parts containing mathematical supplements and various digressions are indi­cated by a vertical grey line in the margin and may be skipped if desired.

We wish to thank Drs. M. Petrou and P. Palmer for the translation of the book. We also thank Dr. D. Kazanas for his remarks.

May 1986 G. Contopouios . D. Kotsakis

Preface to the First Greek Edition

This book has been written in close collaboration between the two au­thors. However, D. K. is mainly responsible for the first part, while G. C. is mainly resonsible for the 2nd and 3rd parts. The bibliography has been updated up to the beginning of 1982.

We thank our colleague Dr. B. Barbanis for many useful comments on the book, Drs. P. Mihailidis and A. Pinotsis for drawing the figures and Dr. M. Zikidis for preparing the cover page.

May 1982 G. Contopou/os . D. Kotsakis

Obituary

In May 1986 Professor D. Kotsakis passed away. Dimitrios Kotsakis was born in Filiatra, Greece, in 1903. He gradu­

ated from the University of Athens in 1931 and became Professor of Astronomy in 1965. His scientific work was both observational and theo­retical. Among other things he studied the dispersion of the fragments of a hypothetical exploding planet. He also studied pure mathematical prob­lems in the field of differential equations etc., and the history of science in Greece. He published more than 20 books in Greek, for students and the general public, which had considerable success.

His most important contribution to Greek astronomy was the estab­lishment of the new observatory in Kryonerion, near Corinth. The Kryo­nerion Observatory, which contains a 120-cm telescope, the largest in Greece, belongs to the National Observatory and has been in operation since 1975. D. Kotsakis also encouraged and supported several students to study astronomy abroad. Thus D. Kotsakis will be remembered as one of the main individuals who brought about the modernisation of Greek astronomy.

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . .. 1

Part I Observations

1. Our Galaxy . . . . . . . . . . . . 6 1.1 Observing Our Galaxy . . . . . 6 1.2 The Hertzsprung-Russell Diagram 9 1.3 Globular Clusters 11 1.4 Open Clusters. . . 12 1. 5 0 B Associations. . 15 1.6 Interstellar Medium 15 1.7 Interstellar Clouds . 16

1.7.1 Bright Nebulae 16 1. 7.2 Dark Nebulae. 17 1.7.3 Neutral Hydrogen Nebulae 19

1.8 Radio Waves from Our Galaxy . 19 1.8.1 Radio Sources .. . . . 19 1.8.2 The 21 em-Line and the Distribution of

Hydrogen in the Galaxy . . . . . . 20 1.8.3 Recombination Lines ....... 22 1.8.4 Microwave Radiation from Molecules 22 1.8.5 Continuous Radio Emission .... 22

1.9 x-Ray, y-Ray, Ultraviolet and Infrared Astronomy. 23 1.10 Pulsars (Neutron Stars) .... 24 1.11 Magnetic Fields and Cosmic Rays 25

1.11.1 Magnetic Fields 25 1.11.2 Cosmic Rays . . . . . . 25

1.12 Stellar Populations ...... 26 1.13 The Spiral Shape of Our Galaxy . 26 1.14 Kinematics of the Galaxy. . . . 27

1.14.1 Motion of the Sun. . . . 27 1.14.2 Distribution of Stellar Velocities 28 1.14.3 Rotation of the Galaxy. . . . 28

X Contents

1.15 Dynamics of the Galaxy . . . . 1.16 A General Picture of the Galaxy .

2. Galaxies and Clusters of Galaxies 2.1 Classification of Galaxies 2.2 Observations of Galaxies 2.3 Magellanic Clouds. . . 2.4 The Andromeda Galaxy 2.5 Spiral Galaxies . 2.6 Elliptical Galaxies . . . 2.7 The Local Group . . . 2.8 Multiple Galaxies and Clusters of Galaxies 2.9 Collisions of Galaxies . . . . . . . . . 2.10 Distances of Galaxies and Clusters of Galaxies 2.11 Masses of Galaxies and Clusters of Galaxies 2.12 The Virial Theorem 2.13 Peculiar Galaxies 2.14 Quasars . . . . .

3. Distribution of Matter in the Universe 3.1 Intergalactic Matter 3.2 Superclusters . . . . . . . . 3.3 Voids .......... . 3.4 Isotropy and Homogeneity of the Universe 3.5 Counts of Galaxies . . . . . . 3.6 Microwave Background Radiation 3.7 Expansion of the Universe . . .

Part II Theory

29 30

32 32 34 35 37 39 44 46 47 52 53 54 56 56 59

62 62 64 65 66 69 70 72

4. Introduction to the Study of the Universe. . . . . . . . . . . 78 4.1 Olbers' Paradox . . . . . . . . . . . . . . . . . . . 78 4.2 Calculation of the Energy Which Comes from all the Stars 80

5. General Theory of Relativity . . . . . . . . . . 5.1 The Concept of Curved Spacetime . . . . . 5.2 Tensors and the General Theory of Relativity 5.3 Einstein's Field Equations . . . . . . . . 5.4 Experimental Verification of the General Theory

of Relativity 5.5 Gravitational Waves . . . . . . 5.6 Black Holes ........ . 5.7 Formulae Related to Black Holes

82 82 85 86

87 91 93 94

Contents XI

5.8 Schwarzschild Black Holes . 95 5.9 Observations of Black Holes 100 5.10 Rotating Black Holes 101 5.11 Thermodynamics and Quantum Mechanics

of Black Holes ........... 104

6. Relativistic Cosmology . . . . . . . . . . . . . 107 6.1 Cosmological Solutions of Einstein's Equations 107 6.2 The Geometry of the Universe .... 110 6.3 Spherical Space of Three Dimensions 114 6.4 The Theory of the Expanding Universe. . 115 6.5 Theoretical Interpretation of Hubble's Law 117 6.6 Is the Universe Finite or Not? . 119

6.6.1 Intergalactic Gas and Dust 121 6.6.2 Intergalactic Stars . . . 121 6.6.3 Photons and Gravitons. . 121 6.6.4 Neutrinos . . . . . . . 122 6.6.5 Magnetic Monopoles and Other Exotic

Particles . . . . . . . . . . . . . . 123 6.6.6 Limits Imposed by Cosmic Nucleosynthesis 124

6.7 The Big Bang Theory . . . . . 125 6.8 The Distribution of Radiogalaxies . . 129 6.9 The Age of the Universe . . . . . . 130

6.9.1 The Expansion of the Universe 130 6.9.2 The Ages of the Radioactive Elements 131 6.9.3 The Ages of the Globular Clusters. . 133

6.10 The Ages of the Chemical Elements . . . . 134 6.11 Different Models Derived from the General Theory

of Relativity . . . . . . . . . . . . . . . . . 136

7. Other Cosmological Theories. 137 7.1 Newtonian Cosmology . 137 7.2 Kinematic Relativity . . 137 7.3 The Theory of Continuous Creation 138 7.4 The Brans-Dicke Theory 140 7.5 Dirac's Theory . 141 7.6 Jordan's Theory. 143 7.7 Conclusions 144

8. The Beginning of the Universe . . . . 147 8.1 The First Stages of the Expansion 147

8.1.1 Temperature 1011 K (Age of the Universe t = 0.01 sec) 151

XII Contents

8.1.2 Temperature 1010 K (Age of the Universe t = 1.1 sec) 151

8.1.3 Temperature 109 K (Age of the Universe t = 3 min) 151

8.2 Energy of Radiation and Matter . . . 152 8.3 The Formation of Galaxies and Clusters of Galaxies 153

8.3.1 Theories of the Formation of Proto galaxies and Protoclusters. . . . . . . . . . . .. 154

8.3.2 Theories of Galaxy Formation from the Collapse of Protogalaxies . . . . . . 158

8.4 Jeans'Instability . . . . . . . . . 161 8.5 Cosmology and Elementary Particles 162 8.6 Matter and Antimatter . 169 8.7 Quantum Gravity 173 8.8 The Inflationary Universe 176

9. The Evolution of the Universe . 9.1 The Arrow of Time. . .

9.1.1 The Increase of Entropy. 9.1.2 Psychological Time ... 9.1.3 The Expansion of the Universe 9.1.4 The Decay of KO Particles

9.2 The Future of the Universe . . . . 9.2.1 Pulsating Universe ..... 9.2.2 Continuously Expanding Universe

Part III Fundamental Problems

180 180 181 182 183 185 186 186 188

10. The Physics of the Universe. . 192 10.1 The Unity of Nature . . 192 10.2 The Laws of the Universe 194 10.3 The Uncertainty of the Physical Laws 196

10.3.1 The Uncertainty in the Knowledge of the Physical Laws . . . . . 196

10.3.2 Instabilities . . . . . . . . . . . . . 197 10.3.3 The Finite Speed of Light . . . . . . . 199 10.3.4 Heisenberg's Principle of Uncertainty and

the Uncertainty of Human Actions 200 10.4 How Certain Are Our Conclusions? . 201

11. Cosmological Problems. . . . . . . . . 205 11.1 Inflation and Causality . . . . . . 205 11.2 Space and Time at the Beginning of the Expansion 206

Contents XIII

11.3 Is the Universe Cyclic? . . . . . . . . . 210 11.4 Is There an "Ultimate" Theory of the Universe? 212 11.5 Causality and Teleology. . 215 11.6 Cosmology and Metaphysics 221

References . . . . . . . . . . . 225

Further References for the Figures . 229

Name Index . 231

Subject Index 233