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Cambridge University Press 978-0-521-56632-2 - Course of Theoretical Astrophysics, Volume 1: Astrophysical Processes T. Padmanabhan Frontmatter More information

Course of Theoretical Astrophysics Volume I: Astrophysical Processes

Graduate students and researchers in astrophysics and cosmology need a solid understanding of a wide range of physical processes. This clear and authoritative textbook has been designed to help them to develop the necessary toolkit of theory. Assuming only an undergraduate background in physics and no detailed knowledge of astronomy, this book guides the reader step by step through a comprehensive collection of fundamental theoretical topics. The book is modular in design, allowing the reader to pick and choose a selection of chapters, if necessary. It can be used alone or in conjunction with the forth- coming accompanying two volumes (covering stars and stellar systems and galaxies and cosmology, respectively). After the basics of dynamics, electromagnetic theory, and statistical physics are re- viewed, a solid understanding of all the key concepts such as radiative processes, spectra, ﬂuid mechanics, plasma physics and magnetohydrodynamics, dynamics of gravitating systems, general relativity, and nuclear physics is developed. Each topic is developed methodically from undergraduate basic physics. Throughout, the reader’s understanding is developed and tested with carefully structured problems and helpful hints. This welcome volume provides graduate students with an indispensable introduction to and reference on all the physical processes they will need to tackle successfully cutting-edge research in astrophysics and cosmology.

THANU PADMANABHAN is a Professor at Inter-University Centre for Astronomy and Astrophysics in Pune, India. His research interests are Gravitation, Cosmology, and Quantum Theory. He has published over hundred technical papers in these areas and has written four books: Structure Formation in the Universe, Cosomology and Astrophysics Through Problems, After the First Three Minutes, and, together with J.V. Narlikar, Gravity, Gauge Theories and Quantum Cosmology. He is a member of the Indian Academy of Sciences, National Academy of Sciences, and International Astronomical Union. He has received numerous awards, including the Shanti Swarup Bhatnagar Prize in Physics (1996) and the Millenium Medal (2000) awarded by the Council of Scientiﬁc and Industrial Research, India. Professor Padmanabhan has also written more than 100 popular science articles, a comic strip serial, and several regular columns on astronomy, recreational mathematics, and history of science that have appeared in international journals and papers. He is married, has one daughter, and lives in Pune, India. His hobbies include chess, origami, and recreational mathematics.

© Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-56632-2 - Course of Theoretical Astrophysics, Volume 1: Astrophysical Processes T. Padmanabhan Frontmatter More information

COURSE OF THEORETICAL ASTROPHYSICS Volume I: Astrophysical Processes

T. PADMANABHAN

Inter-University Centre for Astronomy and Astrophysics Pune, India

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org Information on this title: www.cambridge.org/9780521562409

This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

First published 2000

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication data Padmanabhan, T. (Thanu), 1957– Theoretical astrophysics : astrophysical processes / T. Padmanabhan. p. cm. ISBN 0-521-56240-6 1. Astrophysics. I. Title. QB461.B33 2000 523.01 – dc21 00-025837

ISBN 978-0-521-56240-9 hardback ISBN 978-0-521-56632-2 paperback

Transferred to digital printing 2007

Dedicated to the memory of L.D. Landau, who understood the importance of pedagogy

COURSE OF THEORETICAL ASTROPHYSICS

– in three volumes –

VOLUME I: ASTROPHYSICAL PROCESSES

1: Order-of-magnitude astrophysics; 2: Dynamics; 3: Special Relativity, Electro- dynamics, and Optics; 4: Basics of Electromagnetic Radiation; 5: Statistical Mechanics; 6: Radiative Processes; 7: Spectra; 8: Neutral Fluids; 9: Plasma Physics; 10: Gravitational Dynamics; 11: General Theory of Relativity; 12: Basics of Nuclear Physics.

VOLUME II: STARS AND STELLAR SYSTEMS

1: Overview: Stars and Stellar Systems; 2: Stellar Structure; 3: Stellar Evolution; 4: Supernova; 5: White Dwarfs, Neutron Stars, and Black Holes; 6: Pulsars; 7: Binary Stars and Accretion; 8: Sun and Solar System; 9: Interstellar Medium; 10: Globular Clusters.

VOLUME III: GALAXIES AND COSMOLOGY

1: Observational Overview; 2: Galactic Structure; 3: Galactic Dynamics and Interactions; 4: Friedmann Model; 5: Active Galactic Nuclei–Structural Aspects; 6: Thermal History of the Universe; 7: Structure Formation; 8: Cosmic Microwave Background Radiation; 9: Formation of Baryonic Structures; 10: Active Galactic Nuclei–Cosmological Aspects; 11: Intergalactic Medium and Absorption Systems; 12: Cosmological Observations.

Contents

Preface xv

Chapter 1 Order-of-Magnitude Astrophysics 1 1.1 Introduction 1 1.2 Energy Scales of Physical Phenomena 2 1.2.1 Rest-Mass Energy 3 1.2.2 Atomic Binding Energies 3 1.2.3 Molecular Binding Energy 4 1.2.4 Nuclear Energy Scales 5 1.2.5 Gravitational Binding Energy 5 1.2.6 Thermal and Degeneracy Energies of Particles 6 1.3 Classical Radiative Processes 10 1.3.1 Thermal Bremsstrahlung 11 1.3.2 Synchrotron Radiation 12 1.4 Radiative Processes in Quantum Theory 13 1.4.1 Fine Structure and Hyperﬁne Structure 13 1.4.2 Transition Rates and Cross Sections 14 1.4.3 Thermal Radiation 16 1.4.4 Photon Opacities in Matter 18 1.5 Varieties of Astrophysical Structures 21 1.5.1 tcool ≈ tgrav: Existence of Galaxies 24 1.5.2 grav ≈ a: Existence of Giant Planets 26 1.5.3 grav nucl: Existence of Stars 28 1.5.4 Existence of H–R Diagram for Stars 29 1.5.5 grav F : Existence of Stellar Remnants 30 1.6 Detecting the Photons 33 1.6.1 Role of Earth’s Atmosphere 33 1.6.2 Radio 35 1.6.3 Microwave and Submillimeter 36 1.6.4 Infrared 37

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1.6.5 Optical and Ultraviolet 37 1.6.6 X-ray and γ ray 38

Chapter 2 Dynamics 42 2.1 Introduction 42 2.2 Time Evolution of Dynamical Systems 42 2.3 Examples of Dynamical Systems 47 2.3.1 Motion Under a Central Force 47 2.3.2 Motion in a Rotating Frame 48 2.3.3 The Reduced Three-Body Problem 51 2.4 Canonical Transformations 54 2.5 Integrable Systems 60 2.6 Adiabatic Invariance 70 2.7 Perturbation Theory for Nonintegrable Systems 73 2.8 Surface of Section 77

Chapter 3 Special Relativity, Electrodynamics, and Optics 83 3.1 Introduction 83 3.2 The Principles of Special Relativity 83 3.3 Transformation of Coordinates and Velocities 85 3.4 Four Vectors 89 3.5 Particle Dynamics 93 3.6 Distribution Functions and Moments 95 3.7 External Fields of Force 99 3.8 Motion of Charged Particles in External Fields 104 3.8.1 Motion in a Coulomb Field 104 3.8.2 Motion in a Constant, Uniform, Electric Field 107 3.8.3 Motion in a Constant, Uniform, Magnetic Field 107 3.8.4 Motion in a Slowly Varying Magnetic Field 108 3.8.5 Drifts in Magnetic Fields 109 3.9 Maxwell’s Equations 113 3.10 Energy and Momentum of the Electromagnetic Field 116 3.11 Time-Independent Electromagnetic Fields 118 3.11.1 Coulomb Field of a Charged Particle 119 3.11.2 Dipole and Multipole Moments 120 3.11.3 Magnetic Field of a Steady Current 121 3.11.4 Maxwell’s Equations in a Polarisable Medium 122 3.12 Electromagnetic Waves 123 3.12.1 Monochromatic Plane Waves 124 3.12.2 Polarisation of Light 126 3.13 Diffraction 129 3.13.1 Fraunhofer Diffraction (r D2/λ) 132 3.13.2 Fresnel Diffraction (r D2/λ) 134 3.14 Interference and Coherence 136

Contents ix

3.15 Linear Optical Systems 140 3.16 Wave Propagation through a Random Medium 144

Chapter 4 Basics of Electromagnetic Radiation 150 4.1 Introduction 150 4.2 Radiation from an Accelerated Charge 150 4.2.1 Why Does an Accelerated Charge Radiate? 150 4.2.2 Relativistically Invariant Derivation 153 4.3 General Properties of the Radiation Field 157 4.3.1 Radiation in the Nonrelativistic Case 157 4.3.2 Radiation in the Relativistic Case 160 4.3.3 Radiation During an Impulsive Motion 162 4.3.4 Relativistic Formula for Radiated Four Momentum 163 4.4 Radiation Reaction 164 4.5 Quantum Theory of Radiation 167 4.5.1 Quantisation of an Electromagnetic Field 168 4.5.2 Interaction of Matter and Radiation 173 4.5.3 Quantum Dipole Radiation 177

Chapter 5 Statistical Mechanics 183 5.1 Introduction 183 5.2 Operational Basis of Statistical Mechanics 183 5.3 The Density of States and Microcanonical Distribution 187 5.4 Mean Values in Canonical Distribution 194 5.5 Derivation of Classical Thermodynamics 196 5.6 Description of Macroscopic Thermodynamics 200 5.7 Quantum Statistical Mechanics 207 5.8 Partition Function for Bosons and Fermions 212 5.9 Fermions 217 5.9.1 Classical Limit: z 1 218 5.9.2 Quantum Limit: z 1 220 5.10 Bosons 225 5.11 Statistical Mechanics of the Electromagnetic Field 228 5.12 Ionisation and Pair-Creation Equilibria 233 5.12.1 Ionisation Equilibrium for Hydrogen 233 5.12.2 Pair Creation 239 5.12.3 Nuclear Statistical Equilibrium 240 5.13 Time Evolution of Distribution Functions 241 5.14 Evolution under Scattering 245

Chapter 6 Radiative Processes 251 6.1 Introduction 251 6.2 Macroscopic Quantities for Radiation 251 6.3 Absorption and Emission in the Continuum Case 263

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6.4 Scattering of Electromagnetic Radiation 265 6.5 Radiation Drag on a Charged Particle 271 6.6 Compton Scattering and Comptonisation 273 6.7 Kompaneets Equation 277 6.8 Equations of Radiative Transport 285 6.9 Bremsstrahlung 295 6.9.1 Classical Bremsstrahlung 295 6.9.2 Quantum Bremsstrahlung 298 6.9.3 Thermal Bremsstrahlung 300 6.9.4 Free–free Absorption 302 6.10 Synchrotron Radiation: Basics 304 6.11 Synchrotron Radiation: Rigorous Results 307 6.11.1 Angular Distribution of Radiation 308 6.11.2 Spectral Distribution of Radiation 309 6.11.3 Radiation from a Power-Law Spectrum of Electrons 312 6.11.4 Synchrotron Self-Absorption 313 6.12 Photoionisation 315 6.13 Collisional Ionisation 324

Chapter 7 Spectra 326 7.1 Introduction 326 7.2 Width of Spectral Lines 326 7.2.1 Natural Width of Spectral Lines 327 7.2.2 Doppler Width of Spectral Lines 330 7.2.3 Collisional Broadening of Spectral Lines 331 7.3 Curve of Growth 335 7.4 Atomic-Energy Levels 339 7.4.1 Energy Levels in the Nonrelativistic Theory 339 7.4.2 Fine Structure of Energy Levels 343 7.4.3 Hyperﬁne Structure of Energy Levels 345 7.4.4 X-ray Emission From Atoms 348 7.5 Selection Rules 349 7.6 Energy Levels of Diatomic Molecules 351 7.7 Aspects of Diatomic Spectra 356 7.7.1 Rotational Transitions 356 7.7.2 Vibrational–Rotational Spectrum 358 7.7.3 Electronic–Vibrational–Rotational Transitions 359

Chapter 8 Neutral Fluids 361 8.1 Introduction 361 8.2 Molecular Collisions and Evolution of the Distribution Function 361 8.3 Stress Tensor for an Ideal Fluid 367 8.4 Stress Tensor for a Viscous Fluid 368

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8.5 Equations of Motion for the Viscous Fluid 372 8.6 Flow of Ideal Fluids 378 8.6.1 Barotropic Fluids 380 8.6.2 Steady Flows of Ideal Fluids 380 8.6.3 Irrotational, Isoentropic Flow of Ideal Fluids 382 8.6.4 Incompressible, Irrotational Flow of Ideal Fluids 383 8.7 Flow of Viscous Fluids 383 8.7.1 Incompressible Flow of Viscous Fluids 383 8.7.2 Scaling Relations in Viscous Flows 384 8.8 Sound Waves 385 8.9 Supersonic Flows 387 8.9.1 de Laval Nozzle 388 8.9.2 Spherical Accretion 391 8.10 Steepening of Sound Waves 397 8.11 Shock Waves 401 8.12 Sedov Solution for Strong Explosions 407 8.13 Fluid Instabilities 409 8.13.1 Rayleigh–Taylor Instability 410 8.13.2 Kelvin–Helmholtz Instability 413 8.13.3 Thermal Instability 416 8.14 Conduction and Convection 420 8.15 Turbulence 425

Chapter 9 Plasma Physics 428 9.1 Introduction 428 9.2 The Mean Field and Collisions in Plasma 428 9.3 Collisions in Plasmas 433 9.4 Collisionless Plasmas 440 9.5 Waves in Magnetised Cold Plasmas 452 9.5.1 Propagation Along the Magnetic Field 454 9.5.2 Propagation Perpendicular to the Magnetic Field 456 9.5.3 Propagation Along a General Direction 456 9.6 Magnetohydrodynamics 458 9.6.1 The assumptions and Equations of Magnetohydrodynamics 458 9.6.2 Batteries and Generation of the Magnetic Field 462 9.6.3 Ambipolar Diffusion 463 9.6.4 Magnetic Virial Theorem 466 9.7 Hydromagnetic Waves 467 9.7.1 Alfven waves 468 9.7.2 Fast and Slow Magnetohydrodynamic Waves 469

Chapter 10 Gravitational Dynamics 474 10.1 Introduction 474 10.2 Gravitational Interaction in Astrophysical Systems 474

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10.3 Self-Gravitating Barotropic Fluids 476 10.3.1 Polytropic Equation of State 477 10.3.2 Degenerate Fermionic Systems 479 10.3.3 Isothermal Sphere 480 10.3.4 Time-Dependent Isothermal Sphere Solutions 485 10.3.5 Fluid Spheroids 486 10.4 Collisionless Gravitating Systems in Steady State 489 10.5 Moment Equations for Collisionless Systems 493 10.6 Approach of a Collisionless System to Steady State 494 10.7 Collisional Evolution 499 10.8 Dynamical Evolution of Gravitating Systems 504

Chapter 11 General Theory of Relativity 508 11.1 Introduction 508 11.2 Inescapable Connection between Gravity and Geometry 508 11.3 Metric Tensor and Gravity 513 11.4 Particle Trajectories in a Gravitational Field 517 11.5 Physics in Curved Space–Time 522 11.6 Curvature 524 11.7 Dynamics of Gravitational Field 528 11.7.1 Action for the Gravitational Field 528 11.7.2 Field Equations for the Gravitational Field 531 11.7.3 Properties of the Energy-Momentum Tensor 533 11.7.4 General Properties of the Gravitational- Field Equations 535 11.8 Schwarzschild Metric 538 11.9 Orbits in the Schwarzschild Metric 543 11.9.1 Precession of the Perihelion 546 11.9.2 Deﬂection of an Ultrarelativistic Particle 548 11.9.3 Post-Newtonian Precession 550 11.10 Gravitational Collapse and Black Holes 552 11.11 The Energy-Momentum Pseudotensor for Gravity 553 11.12 Gravitational Waves 554

Chapter 12 Basics of Nuclear Physics 563 12.1 Introduction 563 12.2 Nuclear Structure 563 12.3 Thermonuclear Reactions 567 12.3.1 Nonresonant Reaction Rates 570 12.3.2 Resonant Reaction Rates 572 12.4 Speciﬁc Thermonuclear Reactions 577 12.4.1 Hydrogen Burning: PP Chain 577

Contents xiii

12.4.2 Hydrogen Burning: CNO Cycle 580 12.4.3 Helium Burning 581 12.4.4 Burning of Heavier Elements 583 12.4.5 Neutron Capture Reactions 584

Notes and References 587 Index 593

Preface

“...yoyum varo gudham anupravisto, naanyam thasman Nachiketa vrinithe.” (“...Nachiketa does not choose any other boon but [learning about] that of which Knowledge is hidden.”)

Katho Upanishad, Verse 29.

During the past decade or so, theoretical astrophysics has emerged as one of the most active research areas in physics. This advance has also been reflected in the greater interdisciplinary nature of research that is being carried out in this area in the recent years. As a result, those who are learning theoretical astrophysics with the aim of making a research career in this subject need to assimilate considerable amount of concepts and techniques, in different areas of astrophysics, in a short period of time. Every area of theoretical astrophysics, of course, has excellent textbooks that allow the reader to master that particular area in a well-defined way. Most of these textbooks, however, are written in a traditional style, focussing on one area of astrophysics (say stellar evolution, galactic dynamics, radiative processes, cosmology etc.) Because different authors have different perspectives regarding their subject matter it is not very easy for a student to understand the key unifying principles behind several different astrophysical phenomena by studying a plethora of separate textbooks, as they do not link up together as a series of core books in theoretical astrophysics covering everything which a student would need. A few books, which do cover the whole of astrophysics, deal with the subject at a rather elementary (“first course”) level. What we require is clearly something analogous to the famous Landau– Lifshitz course in theoretical physics, but focussed to the subject of theoretical astrophysics at a fairly advanced level. In such a course, all the key physical concepts (e.g., radiative processes, fluid mechanics, plasma physics, etc.) can be

xvi Preface

presented from a unified perspective and then applied to different astrophysical situations. This book is the first of a set of three volumes that are intended to do exactly that. They form one single coherent unit of study through the use of which a student can acquire mastery over all the traditional astrophysical topics. What is more, these volumes emphasise the unity of concepts and techniques in different branches of astrophysics. The interrelationship among different areas and com- mon features in the analysis of different theoretical problems will be stressed throughout. Because many of the basic techniques need to be developed only once, it is possible to achieve a significant economy of presentation and crispness of style in these volumes. Needless to say, there are some basic “boundary conditions” one has to respect in such an attempt to cover the whole of Theoretical Astrophysics in approximately 3 × 580 pages. Not much space is available to describe the nuances in greater length or to fill in the details of algebra. For example, I have made con- scious choices as to which parts of the algebra can be left to the reader and which need to be worked out explicitly in the text, and I have omitted a detailed discussion of elementary concepts and derivations. However, I do not expect the reader to know anything about astrophysics. All astrophysical concepts are developed ab initio in these volumes. The approach used in these three volumes is similar to that used by Gengis Khan, namely, (1) cover as much area as possible, (2) capture the important points, and (3) be utterly ruthless! To cut out as much repetition as possible, the bulk of the physical principles are presented at one go in Vol. I and are applied in the other two volumes to different situations. This implies that there will be a lot of physics but very little of “concrete” astrophysics in Vol. I; that comes in Vol. II (Stars and Stellar Systems) and Vol. III (Extragalactic Astronomy and Cosmology). The criteria for the selection of material for Vol. I have been the following: (1) Any physical principle that finds application in more than one chapter of Vol. II or Vol. III (for example, bremsstrahlung, Voigt profile, etc.) is discussed in Vol. I. Certain topics that are used in only a specific chapter in Vol. II or Vol. III are discussed in situ rather than in Vol. I. (2) By and large, everything discussed in Vol. I will be utilized directly somewhere in Vols. II and III. On rare occasion, I do cover a topic in Vol. I even if it is not fully utilized in Vol. II or Vol. III because a reader who is going to work in theoretical astrophysics will eventually need an understanding of that particular topic. (3) These three volumes concentrate on theoretical aspects. Observation and phenomenology are, of course, discussed in Vols. II and III to the extent necessary to make the motivation clear. However, I do not have the space to discuss how these observations are made, the errors, reliability, etc., of the observations or the astronomical techniques. (Maybe there should be a fourth volume describing observational astrophysics!) The target audience for this three-volume work will be fairly large and is made up of (1) students in the first year of their Ph.D. Program in theoretical physics,

Preface xvii

astronomy, astrophysics, and cosmology; (2) research workers in various fields of theoretical astrophysics, cosmology, etc.; and (3) teachers of graduate courses in theoretical astrophysics, cosmology and related subjects. In fact, anyone working in or interested in some area of astronomy or astrophysics will find something useful in these volumes. They are also designed in such a way that parts of the material can be used in modular form to suit the requirements of different people and different courses. Let me briefly highlight the features which are specific to Vol. I. The reader of Vol.I is assumed to have done basic courses in classical mechanics, nonrelativistic quantum mechanics, and classical electromagnetic theory. Of the 12 chapters in Vol.I, the first one is a broad-brush overview of physical principles in an order- of-magnitude manner and is intended to set the stage. I expect the reader to survey this chapter rapidly but to come back to it periodically at later stages. This chapter is probably the easiest or the most difficult, depending on one’s background and aptitude. It is easy in the sense that very little sophisticated mathematics is used; difficult because it takes a high level of maturity to appreciate some of the physical arguments that are presented. Chapters 2 (Dynamics), 3 (Special Relativity, Electrodynamics, and Optics), and 5 (Statistical Mechanics) cover the ground the reader may already be familiar with – but from an advanced perspective. The aim is to introduce powerful techniques in familiar contexts so that the reader can learn and appreciate them. For example, no apologies are made for introducing four-vector notation up front or dealing with distribution functions right from the beginning, so as to get the main results as quickly as possible. The emphasis throughout is on topics relevant in astrophysics, such as the reduced three-body problem, action-angle variables, diffraction and interference, optical systems, propagation in random media, ionisation equilibria, etc. Chapter 4 deals with the basics of radiation theory – both classical and quantum – that is developed from scratch and the reader is not assumed to be familiar with quantum field theory. Chapters 6–12 develop the toolkit for astrophysics in a self-contained manner, virtually ab initio. Chapters 6 (Radiative Processes) and 8 (Fluid Mechanics) are fairly exhaustive and detailed. The short chapter on Spectra (Chap. 7) covers general material that is of astronomical relevance; more specific aspects will be dealt with in Vols. II and III within the appropriate contexts. In Chap. 9 (Plasma Physics) I had to make choices as to which topics are of sufficiently general nature to appear in Vol. I; some specific topics (e.g., instability of axisymmetric systems with magnetic fields, alpha effect, and dynamos) will appear in the relevant chapters of Vols. II and III. Chapter 10 (Gravitational Dynamics) covers the background needed for galactic dynamics, globular cluster evolution, etc. Chapter 11 is a compact introduction to general relativity and no previous fa- miliarity with tensor analysis is assumed. Finally, Chap. 12 deals with aspects of nuclear physics that are needed in the study of stellar evolution. Any one of these topics is fairly vast and often requires a full textbook to do justice to it, whereas I have devoted approximately 60 pages to each of them!

xviii Preface

I would like to emphasise that such a crisp, condensed discussion is not only possible but also constitutes a basic matter of policy in these volumes. After all, the idea is to provide the student with the essence of several textbooks in one place. It should be clear to lecturers that these material can be easily regrouped to serve different graduate courses at different levels, especially when complemented by other textbooks. Because of the highly pedagogical nature of the material covered in Vol. I, I have not given detailed references to original literature except on rare occasions when a particular derivation is not available in standard textbooks. The annotated list of references given at the end of the book cites several other textbooks that I found very useful. Some of these books, of course, contain extensive bibliographies and references to original literature. The selection of core books cited here clearly reﬂects the personal bias of the author and I apologise to anyone who feels that their work or contribution has been overlooked. Several people have contributed to the making of these volumes and especially to Vol. I. The idea for these volumes originated over a dinner with J.P.Ostriker in late 1994, while I was visiting Princeton. I was lamenting to Jerry about the lack of a comprehensive set of books covering all of theoretical astrophysics and Jerry said, “Why don’t you write them?” He was very enthusiastic and supportive of the idea and gave extensive comments and suggestions on the original outline I produced in the next one week. I am grateful to him for the comments and for the moral support that I needed to launch into such a project. I sincerely hope the volumes do not disappoint him. Adam Black of Cambridge University Press took up the proposal with his char- acteristic enthusiasm and initiative; this is the third project on which we worked together and I thoroughly enjoyed it. I should also thank him for choosing six excellent (anonymous) referees for this proposal whose support and comments helped to mould the proper framework. Many of my friends and colleagues carried out the job of reading the earlier drafts and providing comments. Of these, M. Vivekanand has gone through most of the book with meticulous care and has given extensive comments. Many other colleagues, especially Roger Blandford, George Djorgovsky, Peter Goldreich, John Huchra, Donald Lynden-Bell, J.V. Narlikar, R. Nityananda, Sterl Phinney, and Douglas Richstone looked at the whole draft and provided comments and suggestions at different levels of detail. J.S. Bagla, Sai Iyer, Nissim Kanekar, Ben Oppenheimer, K. Subramanian, S. Sankaranarayanan, and K. Srinivasan gave detailed comments on selected chapters; the last two took pains to check most of the derivations and algebraic expressions. I thank all of them for their help. I have been visiting the Astronomy Department of Caltech during the past several years and the work on this book has beneﬁtted tremendously through my discussions and interactions with the students and staff of the Caltech Astronomy Department. I especially thank Roger Blandford, Peter Goldreich, Shri Kulkarni,

Preface xix

Sterl Phinney, and Tony Readhead for several useful discussions and for sharing with me their insights and experience in physics teaching. This project would not have been possible but for the dedicated support from Vasanthi Padmanabhan, who not only did the entire TEXing and formatting but also produced most of the ﬁgures – often writing the necessary programs for the same. I thank her for the help and look forward to receiving the same for the next two volumes! I also thank Sunu Engineer who was resourceful in solving several computer-related problems that cropped up periodically. It is a pleasure to acknowledge the library and other research facilities available at the Inter- University Centre for Astronomy and Astrophysics, which were useful in this task.

T. Padmanabhan