"Each chapter ends with up to six student problems. There is full set of worked answers at the end of the book but modern students might not be enlightened by the samples of Fortran code, probably meant to illustrate how realistic calculations might be made."
Contemporary Physics
On a clear and moonless night, especially in remote areas such as deserts, myriads of points of light cover the sky. The great majority of them are stars, many like the Sun, but so far away that they can only be seen as point sources of light. The problem faced by astronomers is to find their properties and distances, just from the light they emit. This is done by using the knowledge of science, mainly physics, acquired from small-scale experiments carried out on Earth. However, the stars themselves are laboratories in which matter behaves in ways that cannot be reproduced on Earth so, in finding out about stars, we complement scientific knowledge gained from earthbound experimentation.
This book describes the means - some very ingenious - by which to explore the properties, locations and planetary companions of stars, and provides a sound foundation for further study.

About the Author v

Introduction xvii

Part 1 Creating Material for the First Stars 1

Chapter 1 The Creation of the First Matter 3

1.1 The Nature of Matter 3

1.2 The Components of Atoms 6

      1.2.1 The Discovery and Properties of the Electron 6

      1.2.2 The Discovery of Protons and Neutrons 10

      1.2.3 The Elusive Neutrino 13

1.3 Other Particles 15

1.4 Even More Particles 19

      1.4.1 Leptons 19

      1.4.2 Quarks 19

1.5 How the Universe Began 21

      1.5.1 The Expanding Universe 21

      1.5.2 The Big Bang Hypothesis 23

      1.5.3 The Creation of Particles and Atoms 25

1.6 Dark Matter and Dark Energy 29

Problems 1 31

Part 2 Making Stars 33

Chapter 2 Some Useful Physical Theory 35

2.1 The Gravitational Potential Energy of a Spherically-Symmetric Sphere 35

2.2 The Virial Theorem 37

2.3 The Jeans Critical Mass 39

2.4 Free-Fall Collapse 42

      2.4.1 The Relationship of the Virial Theorem to Free Fall 45

2.5 Gravitational Instability 47

2.6 The Equipartition Theorem 49

2.7 Cooling Processes 50

2.8 Opacity 52

2.9 The Light from Stars 54

2.10 The Doppler Effect 57

Problems 2 59

Chapter 3 The Evolution of the Universe 61

3.1 The Structure of the Universe 61

3.2 The First Condensations 63

3.3 The Development of Galaxies and Larger Structures 66

3.4 Forming the First Stars 68

Problem 3 71

Chapter 4 The Formation and Evolution of Stars 73

4.1 From Protostar to Main-Sequence Star 73

4.2 Types of Pressure Within a Star 78

4.3 Evolution from the Main Sequence for Moderate and Low-Mass Stars 79

4.4 Evolution from the Main Sequence for High-Mass Stars 83

4.5 The Ages of Globular Clusters 86

4.6 The Interstellar Medium 88

4.7 The Formation of Dark Cool Clouds 88

4.8 The Formation of Protostars 90

4.9 Types of Clusters and Their Locations 91

Problems 4 93

Part 3 The Structure and Composition of Stars 95

Chapter 5 The Equilibrium of Main-Sequence Stars 97

5.1 Conditions for Modelling a Main-Sequence Star 97

5.2 The Pressure Gradient 98

5.3 The Gradient of Included Mass 99

5.4 The Luminosity Gradient 100

5.5 The Temperature Gradient 100

5.6 Modelling Stars 102

Problem 5 103

Chapter 6 Finding the Compositions of Stars 105

6.1 Atoms, Isotopes, Molecules, Ions and Energy Levels 105

6.2 The Nature of Light 107

6.3 Fraunhofer Lines: The Interaction of Light with Atoms 109

6.4 The Composition of Stars 111

6.5 Metallicity 113

Problems 6 115

Part 4 The Distances of Stars 117

Chapter 7 Finding the Distances of Nearby Stationary Stars 119

7.1 How Far Away is That Church Steeple? 120

7.2 Radians and Small Angles 123

7.3 How Far Away is That Stationary Star? 124

7.4 Space-based Measurements 127

Problem 7 128

Chapter 8 Finding the Distances and Velocities of Nearby Moving Stars 129

8.1 Speed and Velocity 129

8.2 The Components of a Star's Velocity 130

8.3 Finding the Distance and Transverse Velocity of a Nearby Star 130

8.4 Determining the Radial Velocity of a Star 132

Problem 8 133

Chapter 9 Finding Distances to Faraway Stars 135

9.1 Finding the Temperatures of Stars 135

9.2 Luminosity, Magnitude and Brightness 138

9.3 Distance Measurement Out to 10,000 pc Using Main-Sequence Stars 140

9.4 Distance Measurement Using Cepheid Variables 142

9.5 Distance Measurement Using Rotating Galaxies 144

9.6 Distance Estimation from Type la Supernovae 145

Problems 9 147

Part 5 The General Properties of Stars 149

Chapter 10 Determining the Radii of Stars 151

10.1 The Radii of Main-Sequence Stars 151

10.2 The Radii of Giant Stars 153

10.3 The Radii of White Dwarfs 155

      10.3.1 The Nature of White Dwarf Material 155

      10.3.2 Fermions 156

10.4 Basis of a Theoretical Approach to White Dwarf Structure 156

      10.4.1 Degeneracy Kinetic Energy 156

10.5 An Approximate Treatment of White Dwarf Structure 157

10.6 A Relativistic Treatment 158

10.7 Neutron Stars and Black Holes 160

Problems 10 161

Chapter 11 Determining the Masses of Stars 163

11.1 General Comments 163

11.2 Kepler's Laws 163

11.3 The Characteristics of an Ellipse 165

11.4 The Centre of Mass and the Orbits of Binary Stars 166

11.5 The Mathematics of Binary Star Orbits 168

11.6 Determining the Masses of Stars in Binary Systems 169

      11.6.1 Wide Binaries 169

      11.6.2 Spectroscopic and Eclipsing Binaries 170

      11.6.3 Astrometric Binary System 174

Problems 11 176

Chapter 12 Other Stars and Star-like Objects 179

12.1 Pulsars 179

12.2 Quasars 181

12.3 Wolf-Rayet Stars 182

Problem 12 183

Part 6 Exoplanets 185

Chapter 13 Planets About Other Stars 187

13.1 Planets Around Pulsars 187

13.2 Detecting Exoplanets Around Main-Sequence Stars 189

13.3 Transiting Exoplanets 193

13.4 The Orbits of Exoplanets 194

      13.4.1 Semi-Major Axis and Eccentricity 194

      13.4.2 Inclination (Spin-Orbit Misalignment) 195

13.5 Other Observations 198

13.6 Other Features Associated with Planets 198

13.7 Requirements for a Plausible Theory of Planet Formation 199

Problems 13 200

Chapter 14 The Nebula Theory 203

14.1 The Laplace Nebula Theory 203

14.2 Revisiting Nebula Ideas and the Angular Momentum Problem 205

      14.2.1 Angular Momentum Transfer by a Magnetic Field 207

      14.2.2 The Armitage and Clarke Mechanism 208

      14.2.3 A Mechanical Process for Transferring Angular Momentum 209

      14.2.4 Angular Momentum Distribution in a Newly Formed Star 211

      14.2.5 Magnetic Braking of Stellar Spin 211

14.3 The Formation of Planets 217

      14.3.1 Converting a Dusty Disk into Planets 218

      14.3.2 Forming Planetesimals 218

      14.3.3 From Planetesimals to Planets 221

14.4 Migration Mechanisms 225

      14.4.1 Type I Migration 225

      14.4.2 Type II Migration 225

      14.4.3 The Interaction of a Planet with Planetesimals 226

      14.4.4 The Nice Model 227

14.5 The Proportion of Stars with Planets 230

14.6 Smaller Bodies of the Solar System 231

      14.6.1 Asteroids 231

      14.6.2 The Kuiper Belt 232

      14.6.3 Dwarf Planets 232

      14.6.4 The Oort Cloud 233

14.7 The Inclinations of Exoplanet Orbits 234

14.8 Exoplanets Around Binary Stars 234

14.9 Satellite Formation 235

14.10 An Overview of the Nebula Theory 235

Problems 14 236

Chapter 15 The Capture Theory 237

15.1 Introduction 237

15.2 Observations Relating to Star Formation 237

15.3 Interactions in a Star-Forming Cloud 239

15.4 Capture-Theory Simulations 240

15.5 The Proportion of Stars with Planets 244

15.6 Angular Momentum in the Solar System 248

15.7 The Capture Theory and Circumstellar Disks 249

15.8 The Evolution of Planetary Orbits 251

15.9 Exoplanets Around Binary Stars 254

15.10 Commensurabilities of Planetary Orbits 255

15.11 The Inclinations of Exoplanet Orbits 257

15.12 Satellites and Angular Momentum 259

15.13 A Mechanism for Satellite Formation 260

      15.13.1 Dust Settling 261

      15.13.2 Formation of Satellitesimals 262

      15.13.3 From Satellitesimals to Satellites 263

15.14 The Problem of the Terrestrial Planets 264

15.15 Deuterium in the Colliding Planets 265

15.16 The Planetary Collision; Earth and Venus 266

15.17 The Moon 269

15.18 Mars and Mercury 271

15.19 The Neptune-Pluto-Triton System 273

15.20 Asteroids and Comets 275

15.21 Dwarf Planets 279

15.22 The Ice Giants 280

15.23 Isotopic Anomalies in Meteorites 284

15.24 An Overview of the Capture Theory 288

Problems 15 290

Appendices 291

Appendix A Planck's Radiation Law and Quantum Physics 293

A.1 The Rayleigh-Jeans Radiation Law 294

A.2 The Planck Radiation Law 295

Problem A 298

Appendix B The Relativistic Doppler Effect 299

B.1 A Non-Relativistic Moving Clock 300

B.2 A Relativistic Moving Clock 301

B.3 The Relativistic Doppler Effect Equation 303

Problem B 304

Appendix C Energy Production in Stars 305

C.1 Proton-Proton Reactions from a Classical Viewpoint 306

C.2 An Approximate Quantum-Mechanical Approach 307

C.3 A More Precise Quantum-Mechanical Approach 308

      C.3.1 The Distribution of the Relative Energies of Protons 308

      C.3.2 The Rate of Making Close Approaches 309

      C.3.3 The Tunnelling Probability 310

      C.3.4 The Cross-Section Factor 311

      C.3.5 The Energy Generation Function 312

C.4 Nuclear Reaction Chains in the Sun 313

Problems C 316

Appendix D Radiation Pressure 317

D.1 A Photon Model for Finding Radiation Pressure 317

D.2 The Energy Density from the Planck Radiation Equation 318

Problem D 319

Appendix E Electron Degeneracy Pressure 321

E.1 Position-Momentum Space 321

E.2 The Energy Density in Degenerate Material 322

Appendix F The Eddington Accretion Mechanism 325

F.1 The Accretion Cross Section 325

Problems F 327

Solutions to Problems 329

References 355

Name Index 359

Subject Index 363

Michael M. Woolfson is Professor Emeritus in Theoretical Physics at the University of York. His main fields of research are the development of methods of solving crystal structures, particularly proteins and in the study of star and planet formation. He has published 25 books on various scientific topics.

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