Theoretical Astrophysics: Astrophysical Processes

Front cover......Page 1
Annotation......Page 2
Title page......Page 3
Date-line......Page 4
Dedication......Page 5
Volume 1-3 contents......Page 6
Contents......Page 7
Preface......Page 15
1.1 Introduction......Page 21
1.2 Energy Scales of Physical Phenomena......Page 22
1.2.2 Atomic Binding Energies......Page 23
1.2.3 Molecular Binding Energy......Page 24
1.2.5 Gravitational Binding Energy......Page 25
1.2.6 Thermal and Degeneracy Energies of Particles......Page 26
1.3 Classical Radiative Processes......Page 30
1.3.1 Thermal Bremsstrahlung......Page 31
1.3.2 Synchrotron Radiation......Page 32
1.4.1 Fine Structure and Hyperfine Structure......Page 33
1.4.2 Transition Rates and Cross Sections......Page 34
1.4.3 Thermal Radiation......Page 36
1.4.4 Photon Opacities in Matter......Page 38
1.5 Varieties of Astrophysical Structures......Page 41
1.5.1 $t_{cool}\\approx t_{grav}$: Existence of Galaxies......Page 44
1.5.2 $\\epsilon_{grav}\\approx\\epsilon_a$: Existence of Giant Planets......Page 46
1.5.3 $\\epsilon_{grav}\\simeq\\epsilon_{nucl}$: Existence of Stars......Page 48
1.5.4 Existence of H-R Diagram for Stars......Page 49
1.5.5 $\\epsilon_{grav}\\simeq\\epsilon_F$: Existence of Stellar Remnants......Page 50
1.6.1 Role of Earth\'s Atmosphere......Page 53
1.6.2 Radio......Page 55
1.6.3 Microwave and Submillimeter......Page 56
1.6.5 Optical and Ultraviolet......Page 57
1.6.6 X-ray and $\\gamma$ ray......Page 58
2.2 Time Evolution of Dynamical Systems......Page 62
2.3.1 Motion Under a Central Force......Page 67
2.3.2 Motion in a Rotating Frame......Page 68
2.3.3 The Reduced Three-Body Problem......Page 71
2.4 Canonical Transformations......Page 74
2.5 Integrable Systems......Page 80
2.6 Adiabatic Invariance......Page 90
2.7 Perturbation Theory for Nonintegrable Systems......Page 93
2.8 Surface of Section......Page 97
3.2 The Principles of Special Relativity......Page 103
3.3 Transformation of Coordinates and Velocities......Page 105
3.4 Four Vectors......Page 109
3.5 Particle Dynamics......Page 113
3.6 Distribution Functions and Moments......Page 115
3.7 External Fields of Force......Page 119
3.8.1 Motion in a Coulomb Field......Page 124
3.8.3 Motion in a Constant, Uniform, Magnetic Field......Page 127
3.8.4 Motion in a Slowly Varying Magnetic Field......Page 128
3.8.5 Drifts in Magnetic Fields......Page 129
3.9 Maxwell\'s Equations......Page 133
3.10 Energy and Momentum of the Electromagnetic Field......Page 136
3.11 Time-Independent Electromagnetic Fields......Page 138
3.11.1 Coulomb Field of a Charged Particle......Page 139
3.11.2 Dipole and Multipole Moments......Page 140
3.11.3 Magnetic Field of a Steady Current......Page 141
3.11.4 Maxwell\'s Equations in a Polarisable Medium......Page 142
3.12 Electromagnetic Waves......Page 143
3.12.1 Monochromatic Plane Waves......Page 144
3.12.2 Polarisation of Light......Page 146
3.13 Diffraction......Page 149
3.13.1 Fraunhofer Diffraction ($r\\gg D^2/\\lambda$)......Page 152
3.13.2 Fresnel Diffraction ($r\\ll D^2/\\lambda$)......Page 154
3.14 Interference and Coherence......Page 156
3.15 Linear Optical Systems......Page 160
3.16 Wave Propagation through a Random Medium......Page 164
4.2.1 Why Does an Accelerated Charge Radiate?......Page 170
4.2.2 Relativistically Invariant Derivation......Page 173
4.3.1 Radiation in the Nonrelativistic Case......Page 177
4.3.2 Radiation in the Relativistic Case......Page 180
4.3.3 Radiation During an Impulsive Motion......Page 182
4.3.4 Relativistic Formula for Radiated Four Momentum......Page 183
4.4 Radiation Reaction......Page 184
4.5 Quantum Theory of Radiation......Page 187
4.5.1 Quantisation of an Electromagnetic Field......Page 188
4.5.2 Interaction of Matter and Radiation......Page 193
4.5.3 Quantum Dipole Radiation......Page 197
5.2 Operational Basis of Statistical Mechanics......Page 203
5.3 The Density of States and Microcanonical Distribution......Page 207
5.4 Mean Values in Canonical Distribution......Page 214
5.5 Derivation of Classical Thermodynamics......Page 216
5.6 Description of Macroscopic Thermodynamics......Page 220
5.7 Quantum Statistical Mechanics......Page 227
5.8 Partition Function for Bosons and Fermions......Page 232
5.9 Fermions......Page 237
5.9.1 Classical Limit: $z\\ll 1$......Page 238
5.9.2 Quantum Limit: $z\\gg 1$......Page 240
5.10 Bosons......Page 245
5.11 Statistical Mechanics of the Electromagnetic Field......Page 248
5.12.1 Ionisation Equilibrium for Hydrogen......Page 253
5.12.2 Pair Creation......Page 259
5.12.3 Nuclear Statistical Equilibrium......Page 260
5.13 Time Evolution of Distribution Functions......Page 261
5.14 Evolution under Scattering......Page 265
6.2 Macroscopic Quantities for Radiation......Page 271
6.3 Absorption and Emission in the Continuum Case......Page 283
6.4 Scattering of Electromagnetic Radiation......Page 285
6.5 Radiation Drag on a Charged Particle......Page 291
6.6 Compton Scattering and Comptonisation......Page 293
6.7 Kompaneets Equation......Page 297
6.8 Equations of Radiative Transport......Page 305
6.9.1 Classical Bremsstrahlung......Page 315
6.9.2 Quantum Bremsstrahlung......Page 318
6.9.3 Thermal Bremsstrahlung......Page 320
6.9.4 Free-free Absorption......Page 322
6.10 Synchrotron Radiation: Basics......Page 324
6.11 Synchrotron Radiation: Rigorous Results......Page 327
6.11.1 Angular Distribution of Radiation......Page 328
6.11.2 Spectral Distribution of Radiation......Page 329
6.11.3 Radiation from a Power-Law Spectrum of Electrons......Page 332
6.11.4 Synchrotron Self-Absorption......Page 333
6.12 Photoionisation......Page 335
6.13 Collisional Ionisation......Page 344
7.2 Width of Spectral Lines......Page 346
7.2.1 Natural Width of Spectral Lines......Page 347
7.2.2 Doppler Width of Spectral Lines......Page 350
7.2.3 Collisional Broadening of Spectral Lines......Page 351
7.3 Curve of Growth......Page 355
7.4.1 Energy Levels in the Nonrelativistic Theory......Page 359
7.4.2 Fine Structure of Energy Levels......Page 363
7.4.3 Hyperfine Structure of Energy Levels......Page 365
7.4.4 X-ray Emission From Atoms......Page 368
7.5 Selection Rules......Page 369
7.6 Energy Levels of Diatomic Molecules......Page 371
7.7.1 Rotational Transitions......Page 376
7.7.2 Vibrational-Rotational Spectrum......Page 378
7.7.3 Electronic-Vibrational-Rotational Transitions......Page 379
8.2 Molecular Collisions and Evolution of the Distribution Function......Page 381
8.3 Stress Tensor for an Ideal Fluid......Page 387
8.4 Stress Tensor for a Viscous Fluid......Page 388
8.5 Equations of Motion for the Viscous Fluid......Page 392
8.6 Flow of Ideal Fluids......Page 398
8.6.2 Steady Flows of Ideal Fluids......Page 400
8.6.3 Irrotational, Isoentropic Flow of Ideal Fluids......Page 402
8.7.1 Incompressible Flow of Viscous Fluids......Page 403
8.7.2 Scaling Relations in Viscous Flows......Page 404
8.8 Soundwaves......Page 405
8.9 Supersonic Flows......Page 407
8.9.1 de Laval Nozzle......Page 408
8.9.2 Spherical Accretion......Page 411
8.10 Steepening of Sound Waves......Page 417
8.11 Shockwaves......Page 421
8.12 Sedov Solution for Strong Explosions......Page 427
8.13 Fluid Instabilities......Page 429
8.13.1 Rayleigh-Taylor Instability......Page 430
8.13.2 Kelvin-Helmholtz Instability......Page 433
8.13.3 Thermal Instability......Page 436
8.14 Conduction and Convection......Page 440
8.15 Turbulence......Page 445
9.2 The Mean Field and Collisions in Plasma......Page 448
9.3 Collisions in Plasmas......Page 453
9.4 Collisionless Plasmas......Page 460
9.5 Waves in Magnetised Cold Plasmas......Page 472
9.5.1 Propagation Along the Magnetic Field......Page 474
9.5.3 Propagation Along a General Direction......Page 476
9.6.1 The assumptions and Equations of Magnetohydrodynamics......Page 478
9.6.2 Batteries and Generation of the Magnetic Field......Page 482
9.6.3 Ambipolar Diffusion......Page 483
9.6.4 Magnetic Virial Theorem......Page 486
9.7 Hydromagnetic Waves......Page 487
9.7.1 Alfven waves......Page 488
9.7.2 Fast and Slow Magnetohydrodynamic Waves......Page 489
10.2 Gravitational Interaction in Astrophysical Systems......Page 494
10.3 Self-Gravitating Barotropic Fluids......Page 496
10.3.1 Polytropic Equation of State......Page 497
10.3.2 Degenerate Fermionic Systems......Page 499
10.3.3 Isothermal Sphere......Page 500
10.3.4 Time-Dependent Isothermal Sphere Solutions......Page 505
10.3.5 Fluid Spheroids......Page 506
10.4 Collisionless Gravitating Systems in Steady State......Page 509
10.5 Moment Equations for Collisionless Systems......Page 513
10.6 Approach of a Collisionless System to Steady State......Page 514
10.7 Collisional Evolution......Page 519
10.8 Dynamical Evolution of Gravitating Systems......Page 524
11.2 Inescapable Connection between Gravity and Geometry......Page 528
11.3 Metric Tensor and Gravity......Page 533
11.4 Particle Trajectories in a Gravitational Field......Page 537
11.5 Physics in Curved Space-Time......Page 542
11.6 Curvature......Page 544
11.7.1 Action for the Gravitational Field......Page 548
11.7.2 Field Equations for the Gravitational Field......Page 551
11.7.3 Properties of the Energy-Momentum Tensor......Page 553
11.7.4 General Properties of the Gravitational- Field Equations......Page 555
11.8 Schwarzschild Metric......Page 558
11.9 Orbits in the Schwarzschild Metric......Page 563
11.9.1 Precession of the Perihelion......Page 566
11.9.2 Deflection of an Ultrarelativistic Particle......Page 568
11.9.3 Post-Newtonian Precession......Page 570
11.10 Gravitational Collapse and Black Holes......Page 572
11.11 The Energy-Momentum Pseudotensor for Gravity......Page 573
11.12 Gravitational Waves......Page 574
12.2 Nuclear Structure......Page 583
12.3 Thermonuclear Reactions......Page 587
12.3.1 Nonresonant Reaction Rates......Page 590
12.3.2 Resonant Reaction Rates......Page 592
12.4.1 Hydrogen Burning: PP Chain......Page 597
12.4.2 Hydrogen Burning: CNO Cycle......Page 600
12.4.3 Helium Burning......Page 601
12.4.4 Burning of Heavier Elements......Page 603
12.4.5 Neutron Capture Reactions......Page 604
Notes and References......Page 607
Index......Page 613
Back cover......Page 622