Bridging the gap between physics and astronomy textbooks, this book provides step-by-step physical and mathematical development of fundamental astrophysical processes underlying a wide range of phenomena in stellar, galactic, and extragalactic astronomy. The book has been written for upper-level undergraduates and beginning graduate students, and its strong pedagogy ensures solid mastery of each process and application. It contains over 150 tutorial figures, numerous examples of astronomical measurements, and 201 exercises. Topics covered include the Kepler–Newton problem, stellar structure, binary evolution, radiation processes, special relativity in astronomy, radio propagation in the interstellar medium, and gravitational lensing. Applications presented include Jeans length, Eddington luminosity, the cooling of the cosmic microwave background (CMB), the Sunyaev–Zeldovich effect, Doppler boosting in jets, and determinations of the Hubble constant. This text is a stepping stone to more specialized books and primary literature. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521846561.

List of figures page xv

List of tables xx

Preface xxi

Also by the author xxv

Acknowledgments xxvii

1 Kepler, Newton, and the mass function 1

1.1 Introduction 2

1.2 Binary star systems 2

1.3 Kepler and Newton 9

1.4 Newtonian solutions M m 15

1.5 Arbitrary masses 22

1.6 Mass determinations 28

1.7 Exoplanets and the galactic center 39

2 Equilibrium in stars 49

2.1 Introduction 50

2.2 Jeans length 50

2.3 Hydrostatic equilibrium 52

2.4 Virial theorem 54

2.5 Time scales 59

2.6 Nuclear burning 65

2.7 Eddington luminosity 73

2.8 Pulsations 78

2-D phase space – Fermi momentum – Compression and cooling – Temperature

3 Equations of state 87

3.1 Introduction 88

3.2 Maxwell–Boltzmann distribution 89

3.3 Phase-space distribution function 92

3.4 Ideal gas 97

3.5 Photon gas 101

3.6 Degenerate electron gas 102

4 Stellar structure and evolution 117

4.1 Introduction 118

4.2 Equations of stellar structure 118

4.3 Modeling and evolution 124

4.4 Compact stars 142

4.5 Binary evolution 157

5 Thermal bremsstrahlung radiation 181

5.1 Introduction 182

5.2 Hot plasma 183

5.3 Single electron-ion collision 185

5.4 Thermal electrons and a single ion 190

5.5 Spectrum of emitted photons 193

5.6 Measurable quantities 199

6 Blackbody radiation 205

6.1 Introduction 205

6.2 Characteristics of the radiation 208

6.3 Cosmological expansion 222

6.4 Mathematical notes 230

7 Special theory of relativity in astronomy 233

7.1 Introduction 234

7.2 Postulates of special relativity 234

7.3 Lorentz transformations 235

7.4 Doppler shift 249

7.5 Aberration 255

7.6 Astrophysical jets 258

7.7 Magnetic force and collisions 275

7.8 Addendum: Lorentz invariance of distribution function 281

8 Synchrotron radiation 290

8.1 Introduction 291

8.2 Discovery of celestial synchrotron radiation 291

8.3 Frequency of the emitted radiation 295

8.4 Power radiated by the electron 309

8.5 Ensemble of radiating particles 311

8.6 Coherent curvature radiation 318

9 Compton scattering 329

9.1 Introduction 329

9.2 Classic Compton scattering 330

9.3 Inverse Compton scattering 332

9.4 Synchrotron self-Compton (SSC) emission 338

9.5 Sunyaev–Zeldovich effect 342

10 Hydrogen spin-flip radiation 355

10.1 Introduction 355

10.2 The Galaxy 356

10.3 Hyperfine transition at 1420 MHz 362

10.4 Rotation of the Galaxy 374

10.5 Zeeman absorption at 1420 MHz 389

11 Dispersion and Faraday rotation 400

11.1 Introduction 401

11.2 Maxwell’s equations 401

11.3 Dispersion 409

11.4 Faraday rotation 419

11.5 Galactic magnetic field 432

12 Gravitational lensing 437

12.1 Introduction 438

12.2 Discovery 438

12.3 Point-mass lens 442

12.4 Extended-mass lens 460

12.5 Fermat approach 465

12.6 Strong and weak lensing 477

Credits, further reading, and references 483

Glossary 487

Appendix – Units, symbols, and values 489

Index 493

Hale Bradt is Professor Emeritus of Physics at the Massachusetts Institute of Technology. During his forty years on the faculty, he carried out research in cosmic ray physics and X-ray astronomy and taught courses in physics and astrophysics. Bradt founded the MIT sounding rocket program in x-ray astronomy, and was a senior or principal investigator on three missions for x-ray astronomy. He was awarded the NASA Exceptional Science Medal for his contributions to HEAO-1 (High Energy Astronomical Observatory), the 1990 Buechner Teaching Prize of the MIT Physics Department, and shared the 1999 Bruno Rossi prize of the American Astronomical Society for his contributions to the RXTE (Rossi X-ray Timing Explorer) program. His previous book, Astronomy Methods: A Physical Approach to Astronomical Observations, was published by Cambridge University Press in 2004.

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