- ISBN: 9780691144085 | 0691144087
- Cover: Paperback
- Copyright: 9/21/2009
Preface | p. xix |
Introduction | p. 1 |
Black Holes in Nature | p. 1 |
Energy Fluxes | p. 8 |
Timing Studies and Black-Hole Mass Estimates | p. 10 |
Flux Distribution | p. 11 |
The Nighttime Sky | p. 12 |
Relativistic Kinematics | p. 14 |
Lorentz Transformation Equations | p. 14 |
Four-Vectors and Momentum | p. 16 |
Relativistic Doppler Factor | p. 18 |
Three Useful Invariants | p. 19 |
Relativistic Reaction Rate | p. 21 |
Secondary Production Spectra | p. 23 |
Introduction to Curved Spacetime | p. 25 |
Special Relativity | p. 25 |
Curved Space/Spacetime | p. 29 |
The Schwarzschild Metric | p. 33 |
Physical Cosmology | p. 36 |
Robertson-Walker Metric | p. 36 |
Friedmann Models | p. 39 |
Hubble Relation from the Cosmological Principle | p. 39 |
Expansion of the Universe | p. 40 |
Einstein-de Sitter Universe | p. 43 |
Universe with Zero Cosmological Constant | p. 43 |
Flat Universe | p. 43 |
Luminosity and Angular-Diameter Distances | p. 44 |
Event Rate of Bursting Sources | p. 45 |
Flux and Intensity from Distributed Sources | p. 47 |
Radiation Physics of Relativistic Flows | p. 50 |
Radiation Preliminaries | p. 50 |
Invariant Quantities | p. 53 |
Blackbody Radiation Field | p. 53 |
Transformed Quantities | p. 56 |
Transformation of Total Distribution and Energy | p. 56 |
Transformation of Differential Distributions | p. 56 |
Fluxes of Relativistic Cosmological Sources | p. 59 |
Blob Geometry | p. 60 |
Spherical Shell Geometry | p. 63 |
Equivalence of Blob and Blast Wave Geometries | p. 68 |
Compton Scattering | p. 70 |
Compton Effect | p. 70 |
The Compton Cross Section | p. 71 |
Transforming the Compton Cross Section | p. 73 |
Differential Thomson Cross Section | p. 75 |
Head-on Approximation | p. 77 |
Differential Compton Cross Section | p. 77 |
Moments of the Compton Cross Section | p. 79 |
Compton Scattering in the ¿-Function Approximation | p. 80 |
Energy-Loss Rates in Compton Scattering | p. 81 |
Thomson Energy-Loss Rate | p. 81 |
Klein-Nishina Energy-Loss Rate | p. 82 |
Differential Compton Cross Sections and Spectra | p. 83 |
Comparison of Scattered Spectra for Different ERF Photon Energies | p. 83 |
Spectral Comparisons for Isotropic Monochromatic Photons and Power-Law Electrons | p. 84 |
Thomson Scattering: Isotropic Photons and Electrons | p. 92 |
Thomson-Scattered Radiation Spectrum in the ¿-Function Approximation | p. 92 |
Spectral Comparisons for Isotropic Power-Law Photons and Electrons | p. 93 |
External Photon Fields Compton-Scattered by Jet Electrons | p. 94 |
Thomson-Scattered Spectrum for an External Point Source of Radiation from Behind | p. 96 |
Thomson-Scattered Spectrum for External Isotropic Radiation in the ?-Function Approximation | p. 97 |
External Isotropic Photons Compton-Scattered by let Electrons | p. 99 |
Cosmic Microwave Background Radiation Compton-Scattered by Jet Electrons | p. 103 |
Accretion-Disk Field Compton-Scattered by Jet Electrons | p. 105 |
Optically Thick Shakura-Sunyaev Disk Spectrum | p. 106 |
Integrated Emission Spectrum from Shakura-Sunyaev Disk | p. 107 |
Transformed Accretion-Disk Radiation Field | p. 108 |
Thomson-Scattered Shakura-Sunyaev Disk Spectrum in the Near Field | p. 112 |
Thomson-Scattered Shakura-Sunyaev Disk Spectrum in the Far Field | p. 113 |
Beaming Patterns | p. 113 |
Broad-Line Region Scattered Radiation | p. 114 |
Synchrotron Radiation | p. 117 |
Covariant Electrodynamics | p. 118 |
Synchrotron Power and Peak Frequency | p. 119 |
Elementary Synchrotron Radiation Formulae | p. 121 |
Relations between Emitted, Received, and 90° Pitch-Angle Powers | p. 123 |
Particle Synchrotron Radiation | p. 126 |
Synchrotron Spectrum from a Power-Law Electron Distribution | p. 127 |
¿-Function Approximation for Synchrotron Radiation | p. 129 |
Equipartition Magnetic Field | p. 131 |
Equipartition Magnetic Field: Qualitative Estimate | p. 132 |
Equipartition Magnetic Field: Quantitative Treatment | p. 133 |
Energelics and Minimum Jet Powers | p. 135 |
Synchrotron Self-Compton Radiation | p. 138 |
SSC in the Thomson Regime | p. 138 |
SSC in the Thomson Regime for Broken Power-Law Electron Distribution | p. 140 |
Accurate SSC for General Electron Distribution | p. 141 |
Synchrotion/SSC Model | p. 142 |
SSC Electron Energy-Loss Rate | p. 143 |
Synchrotron Self-Absorption | p. 143 |
Einstein Coefficients | p. 145 |
Brightness Temperature and Self-Absorbed Flux: Qualitative Discussion | p. 146 |
Derivation of the Synchrotron Self-Absorption Coefficient | p. 148 |
¿-Function Approximation for Synchrotron Self-Absorption | p. 148 |
Synchrotron Self-Absorption Coefficient for Power-Law Electrons | p. 149 |
Maximum Brightness Temperature | p. 150 |
Compton Limits on the Doppler Factor | p. 153 |
Self-Absorbed Synchrotron Spectrum | p. 154 |
Hyper-Relativistic Electrons | p. 156 |
Jitter Radiation | p. 158 |
Binary Particle Collision Processes | p. 160 |
Coulomb Energy Losses | p. 161 |
Stopping Power of Cold Plasma | p. 161 |
Thermal Relaxation | p. 163 |
Stopping Power of Thermal Plasma | p. 164 |
Knock-On Electrons | p. 165 |
Bremsstrahlung | p. 166 |
Electron Bremsstrahlung Energy-Loss Rate | p. 167 |
Electron Bremsstrahlung Production Spectra | p. 167 |
Secondary Nuclear Production | p. 169 |
¿ Rays from ¿0 Decay | p. 171 |
Cross Section for p + p &leftarrrow; ¿ + X Production | p. 172 |
Electron-Positron Annihilation Radiation | p. 180 |
Annihilation in a Thermal Medium | p. 181 |
Thermal Annihilation Line and Continuum Spectra | p. 182 |
Nuclear ¿-Ray Line Production | p. 185 |
Photohadronic Processes | p. 187 |
Scattering and Energy-Loss Timescales | p. 189 |
Photopion Process | p. 190 |
Photopion Cross Section | p. 191 |
Analytic Expression for Photopion Cross Section | p. 192 |
Numerical Calculation of Photopion Cross Section | p. 194 |
Photopion Energy-Loss Rate | p. 194 |
GZK Energy | p. 196 |
Stochastic and Continuous Energy Losses | p. 197 |
Photopair Process | p. 197 |
Photopair Cross Section | p. 198 |
Photopair Energy-Loss Timescale | p. 198 |
Accurate Expression for Photopair Energy-Loss Rates of Ions in an Isotropic Radiation Field | p. 201 |
Relative Importance of Photopion and Photopair Losses | p. 203 |
Expansion Losses | p. 203 |
Cosmogenic Neutrino Flux | p. 204 |
Ultrahigh-Enetgy Cosmic-Ray Evolution | p. 208 |
Normalization to Local Luminosity Density | p. 209 |
Energy Evolution of Cosmic-Ray Protons | p. 210 |
Rate Density Evolution and the Star Formation Rate | p. 211 |
Waxman-Bahcail Bound | p. 213 |
UHECR and GZK Neutrino Intensities | p. 215 |
Photonuclear Reactions | p. 219 |
Photodisintegration Reaction Rate | p. 222 |
Effective Photodisintegration Energy-Loss Rate | p. 224 |
Neutrinos from Photodisintegration | p. 225 |
¿¿ Pair Production | p. 227 |
¿¿Pair Production Cross Section | p. 228 |
Absorption by a Blackbody and a Modified Blackbody Photon Gas | p. 231 |
Absorption by a Power-Law Photon Gas in a Relativistic Jet | p. 233 |
¿¿ Attenuation in Anisotropic Radiation Fields | p. 235 |
?-Function Approximation for ¿¿¿ | p. 236 |
Opacity of the Universe to ¿¿ Attenuation | p. 237 |
¿¿ Optical Depth of the Universe | p. 238 |
Measurements of the EBL | p. 240 |
¿¿ Attenuation at Low Redshifts | p. 241 |
¿¿ Attenuation at All Redshifts | p. 244 |
The ¿-Ray Horizon | p. 244 |
Compactness Parameter | p. 245 |
Minimum Doppler Factor from ¿¿ Constraint | p. 247 |
Correlated ¿-Ray and Neutrino Fluxes | p. 249 |
Electromagnetic Cascades | p. 253 |
Cascades in Jets | p. 254 |
Cascades in the Intergalactic Medium | p. 256 |
¿¿ &leftarrrow; ¿ | p. 257 |
Blast-Wave Physics | p. 258 |
Fireballs and Relativistic Blast Waves | p. 258 |
Blast-Wave Deceleration | p. 260 |
Blast-Wave Equation of Motion | p. 261 |
Dissipated Internal Energy | p. 270 |
Elementary Blast-Wave Theory | p. 270 |
Characteristic Electron Energies | p. 271 |
Characteristic Synchrotron Frequencies | p. 274 |
Afterglow Theory | p. 278 |
Relativistic Shock Hydrodynamics | p. 282 |
Relativistic Shock Thermodynamics | p. 282 |
Synchrotron Radiation from a Relativistic Reverse Shock | p. 288 |
Beaming Breaks and Jets | p. 290 |
Synchrotron Self-Compton Radiation | p. 292 |
Theory of the Prompt Phase | p. 294 |
X-Ray Flares and ¿-Ray Pulses from External Shocks | p. 295 |
Colliding Shells and Internal Shocks | p. 301 |
Thermal Photospheres | p. 303 |
The Amati and Ghirlanda Relations | p. 303 |
Thermodynamics of a Steady Relativistic Wind | p. 304 |
Photospheric Radius | p. 306 |
Pair Photosphere | p. 308 |
Thermal Neutrons | p. 310 |
GRB Cosmology | p. 312 |
Introduction to Fermi Acceleration | p. 314 |
Stochastic and Shock Fermi Acceleration | p. 316 |
Wave Turbulence Spectrum | p. 317 |
The Hillas Condition | p. 320 |
Energy Gain per Cycle from Fermi Acceleration | p. 321 |
Diffusion in Physical Space | p. 322 |
Maximum Particle Energy | p. 324 |
First-Order Fermi Acceleration | p. 327 |
Nonrelativistic Shock Hydrodynamics | p. 328 |
Convection-Diffusion Equation | p. 330 |
Nonrelativistic Shock Acceleration | p. 332 |
Spectral Index from Convection-Diffusion Equation | p. 332 |
Spectral Index from Probability Arguments | p. 334 |
Finite Shell Width | p. 335 |
Cosmic-Ray Pressure and Shock Width | p. 337 |
Maximum Particle Energy in Nonrelativistic Shock Acceleration | p. 339 |
Maximum Particle Energy in Nonrelativistic Shocks | p. 343 |
Amplification of Upstream Medium Magnetic Field | p. 344 |
Relativistic Shock Acceleration | p. 346 |
Fokker-Planck Equation for a Stationary, Parallel Shock | p. 347 |
Spectral Index in Relativistic Shock Acceleration | p. 348 |
Maximum Particle Energies in Relativistic Shock Acceleration | p. 349 |
Second-Order Fermi Acceleration | p. 351 |
Power-Law Particle Spectra from Second-Order Fermi Acceleration | p. 353 |
The Resonance Condition | p. 353 |
Plasma Waves | p. 355 |
Diffusive Particle Acceleration | p. 359 |
Approximate Derivation of Diffusion Coefficients | p. 362 |
Pitch-Angle Diffusion Coefficient | p. 362 |
Momentum Diffusion Coefficient | p. 363 |
Energy Gain and Diffusive Escape Rates | p. 364 |
Momentum Diffusion Equation | p. 367 |
Ramaty-Lee Spectrum for Hard-Sphere Scattering | p. 368 |
Green's Function Solution | p. 370 |
Maximum Particle Energy in Second-Order Fermi Acceleration | p. 372 |
Gyroresonant Stochastic Acceleration | p. 373 |
Stochastic Energization in Nonrelativistic Shocks | p. 374 |
Stochastic Energization in Relativistic Flows | p. 376 |
The Geometry of Spacetime | p. 379 |
Introduction | p. 379 |
Splitting Spacetime into Space and Time | p. 380 |
The Kerr Metric | p. 384 |
The Geodesic Equation and Its Integrability in Kerr Geometry | p. 386 |
The Kerr Metric in Kerr-Schild Coordinates | p. 391 |
The Ergosphere | p. 394 |
The Event Horizon | p. 396 |
The Penrose Process | p. 397 |
Hawking Radiation | p. 402 |
Scalar Fields in Curved Spacetime | p. 402 |
The Quantum Field for a Scalar Particle in a Flat Spacetime | p. 404 |
Particle Creation in Curved Spacetime | p. 405 |
Particle Creation in Rindler Spacetime | p. 408 |
Particle Creation in Schwarzschild Geometry | p. 415 |
Black-Hole Electrodynamics | p. 417 |
3+1 Electrodynamics | p. 417 |
The Energy-Momentum Tensor | p. 424 |
The Blandford-Znajek Process | p. 427 |
Explicit Expressions for the Fields and Currents | p. 431 |
The Force-Free Constraint Equation | p. 432 |
The Znajek Regularity Condition | p. 433 |
Energy and Angular-Mom en turn Extraction from the Force-Free Magnetosphere | p. 435 |
Geodesic Currents in the Magnetosphere | p. 436 |
An Exact Solution | p. 439 |
Fields and Energy Extraction for the ¿- Solution | p. 441 |
An Approximate Solution | p. 442 |
Uniqueness of the ¿_ Solution | p. 447 |
Energy Extraction for the ¿+ Solution | p. 448 |
Blandford-Znajek Process in Astrophysical Sources | p. 450 |
High-Energy Radiations from Black Holes | p. 452 |
¿ Rays | p. 453 |
Modeling ¿ Rays from Black Holes | p. 454 |
Statistics of Black-Hole Sources | p. 456 |
Blazar Physics | p. 457 |
GRB Classes | p. 458 |
Unresolved and Diffuse ?-Ray Background | p. 458 |
Cosmic Rays | p. 459 |
Acceleration of Cosmic Rays at Supernova Remnant Shocks | p. 461 |
Acceleration of UHECRs at Relativistic Blast Waves | p. 462 |
Charged-Particle Astronomy | p. 463 |
UHECR Propagation | p. 466 |
UHECR Source Power Requirements | p. 466 |
Neutrinos | p. 468 |
Concluding Remarks | p. 471 |
Essential Tensor Calculus | p. 473 |
Introduction | p. 473 |
The Tangent Vector | p. 473 |
Dual Vectors | p. 476 |
The Space T**(M) | p. 477 |
Tensors | p. 478 |
The Metric Tensor | p. 480 |
The Volume Element and the Levi-Civita Tensor | p. 481 |
The Covariant Derivative | p. 483 |
The Divergence Theorem | p. 485 |
The Einstein Equation | p. 486 |
Mathematical Functions | p. 488 |
The Gamma Function and Error Function | p. 488 |
Modified Bessel Functions of the Second Kind | p. 488 |
Exponential Integral Function | p. 489 |
Planck's Function | p. 490 |
Bernoulli Numbers and Riemann ? Function | p. 490 |
Whittaker Functions | p. 491 |
Lambert W Function | p. 491 |
Solutions of the Continuity Equation | p. 492 |
Basics of Monte Carlo Calculations | p. 497 |
Supplementary Information | p. 499 |
Glossary and Acronym List | p. 505 |
Bibliography | p. 509 |
Index | p. 531 |
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