Foundations of High-Energy Astrophysics (Theoretical Astrophysics)

Contents......Page 8
Preface......Page 16
1 Hydrodynamics......Page 20
1.1 The Mass Conservation Equation......Page 21
1.2 The Momentum Conservation Equation......Page 22
1.3 The Energy Conservation Equation......Page 24
1.4 Bernoulli’s Theorem......Page 26
1.5 The Equations of Hydrodynamics in Conservative Form......Page 27
1.6 Viscous Fluids......Page 30
1.7 Small Perturbations......Page 34
1.8 Discontinuity......Page 37
1.8.1 Surfaces of Discontinuity......Page 38
1.8.2 ShockWaves......Page 41
1.8.3 Physical Interpretation of Shock Waves......Page 42
1.8.4 Collisional and Noncollisional Shocks......Page 44
1.8.5 Formation of a Shock......Page 45
1.9 Self-similar Solutions......Page 47
1.9.1 Self-similar Solutions of the Second Kind......Page 52
1.10 Relativistic Hydrodynamics......Page 57
1.10.1 Shock Waves in Relativistic Hydrodynamics......Page 60
1.10.2 The Strong Explosion......Page 62
1.11 The De Laval Nozzle......Page 66
1.12 Problems......Page 72
2 Magnetohydrodynamics and Magnetic Fields......Page 74
2.1 Equations of Motion......Page 75
2.1.1 The Limit of Ideal Magnetohydrodynamics......Page 79
2.1.2 Equations of Motion in a Conservative Form......Page 81
2.2 The Force Exerted by the Magnetic Field......Page 83
2.3 Magnetic Flux Freezing......Page 85
2.4 Small Perturbations in a Homogeneous Medium......Page 89
2.5 Stability of Tangential Discontinuities......Page 96
2.6 Two-Temperature Fluids......Page 100
2.7.1 Magnetic Buoyancy......Page 103
2.7.2 Reconnection......Page 107
2.8 ShockWaves......Page 111
2.9.1 Observations......Page 114
2.9.2 Origin of Magnetic Fields......Page 120
2.10 Problems......Page 132
3.1 Radiative Transport......Page 134
3.1.1 Radiation Transport......Page 139
3.2 Low-Temperature Thermal Emission......Page 143
3.3 Bremsstrahlung......Page 147
3.4.1 Power Radiated by a Single Particle......Page 150
3.4.2 The Spectrum of a Single Particle......Page 153
3.4.3 The Spectrum of a Group of Nonthermal Particles......Page 157
3.4.4 Quantum Corrections......Page 159
3.4.5 Self-absorption......Page 161
3.4.6 Cyclotron Lines......Page 163
3.4.7 Processes in an Intense Magnetic Field......Page 165
3.4.8 The Razin-Tsytovich Effect......Page 167
3.5 Compton Processes......Page 169
3.5.1 Physical Mechanism of the Inverse Compton......Page 171
3.5.2 The Spectrum of Inverse Compton Processes......Page 176
3.5.3 About the Compton Parameter......Page 186
3.5.4 Self-synchro-Compton and Compton Limit......Page 187
3.5.5 Compton Broadening......Page 190
3.6 Relativistic Effects......Page 191
3.6.1 Superluminal Motions......Page 192
3.6.2 Emission Properties of Relativistic Sources......Page 193
3.7 Pair Creation and Annihilation......Page 196
3.8.1 Protons......Page 200
3.8.2 Photons......Page 205
3.9 Problems......Page 207
4 Nonthermal Particles......Page 210
4.1 The Classic Theory of Acceleration......Page 211
4.1.1 Acceleration......Page 212
4.1.2 Injection......Page 225
4.2 Constraints on the Maximum Energy......Page 227
4.3 More Details in the Newtonian Limit......Page 232
4.3.1 From the Vlasov Equation to the Convection-Scattering Equation......Page 234
4.3.2 Scattering in the Angle of Motion in a Medium at Rest......Page 236
4.3.3 Scattering and Convection in a Medium in Motion......Page 238
4.4 General Discussion......Page 245
4.4.1 An Equation for f......Page 246
4.4.2 The Small Pitch Angle Scattering Limit......Page 251
4.4.3 Distributions of Probability Pu and Pd......Page 257
4.4.4 The Particles’ Spectrum......Page 260
4.4.5 The Equations for Pu and Pd......Page 262
4.4.6 Results......Page 266
4.5 The Unipolar Inductor......Page 269
4.6 Problems......Page 273
5 Spherical Flows: Accretion and Explosion......Page 274
5.1 Accretion from Cold Matter......Page 275
5.2 Accretion from Hot Matter......Page 279
5.2.1 The Critical Point......Page 284
5.3 The Intermediate Case......Page 286
5.4 Doubts about the Bondi Accretion Rate......Page 287
5.5 The Eddington Luminosity......Page 289
5.6 The Efficiency of Spherical Accretion......Page 294
5.7 Explosive Motions......Page 296
5.7.1 Supernovae......Page 297
5.7.2 Gamma Ray Bursts......Page 305
5.8 Problems......Page 319
6 Disk Accretion I......Page 322
6.1 Qualitative Introduction......Page 324
6.2 Fundamental Equations......Page 326
6.3 Special Relations......Page 329
6.4 The α Prescription......Page 334
6.5 Equations for the Structure of Disks......Page 337
6.6 The Standard Solution......Page 341
6.7 The Origin of Torque......Page 345
6.8.1 Time Scales......Page 350
6.8.2 Instability......Page 351
6.9 Lense-Thirring Precession......Page 356
6.10 Problems......Page 364
7.1 Other Disk Models......Page 366
7.1.1 The Origin of Particles......Page 368
7.1.2 Dynamic Peculiarities of Pair Plasmas......Page 370
7.1.3 The Pair Plasma without Input ofExternal Photons......Page 371
7.1.4 The Pair Plasma with Input of External Photons......Page 381
7.2 Thick Accretion Disks......Page 385
7.2.1 Some General Properties......Page 387
7.2.2 The Inapplicability of the Eddington Limit......Page 390
7.2.3 Polytropic Models......Page 393
7.2.4 Properties of Thick Disks......Page 395
7.3 Nondissipative Accretion Flows......Page 398
7.4 Further Developments of the Theory......Page 405
7.4.2 The Fate of Angular Momentum at Large Radii......Page 406
7.5 Accretion Disks on Magnetized Objects......Page 412
7.5.1 The Alfven Radius......Page 413
7.5.2 Interaction between the Disk and the Magnetosphere......Page 420
7.5.3 Accretion Columns......Page 422
7.6 Boundary Layers......Page 433
7.7 Problems......Page 436
8 Electrodynamics of Compact Objects......Page 438
8.1 The Gold-Pacini Mechanism......Page 439
8.2 The Magnetospheres Surrounding Pulsars......Page 441
8.2.1 Quasi-Neutral or Charge-Separated Plasma?......Page 446
8.2.2 The Goldreich and Julian Magnetosphere......Page 448
8.2.3 The Pulsar Equation......Page 451
8.2.4 The Solution......Page 462
8.2.5 The Transport of Angular Momentum......Page 463
8.2.6 Discussion......Page 467
8.3.1 The Magnetic Field of a Black Hole......Page 469
8.3.2 The Black Hole Equation......Page 475
8.3.3 The Transport of Energy and of Angular Momentum......Page 489
8.3.4 A Qualitative Discussion......Page 492
8.3.5 A Simplified Discussion of Total Energetics......Page 494
8.4 The Generation of Charges......Page 498
8.5 Disk-Jet Coupling......Page 501
8.5.1 The Lovelace-Blandford Model......Page 503
8.5.2 A Special Solution......Page 504
8.5.3 Discussion......Page 509
8.5.4 A Model Including Inertial Effects......Page 513
8.5.5 A Special Solution......Page 519
8.5.6 Results......Page 522
8.5.7 A Brief Summary......Page 527
8.6 Problems......Page 529
A Propagation of Electromagnetic Waves......Page 532
B Orbits Around Black Holes......Page 538
B.1 Problem......Page 546
C.2 Cylindrical Coordinates......Page 548
C.3 Spherical Coordinates......Page 549
Bibliography......Page 552
Index......Page 562