High Energy Radiation from Black Holes

Gamma Rays, Cosmic Rays, and Neutrinos

By: Charles D. Dermer, Govind Menon

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Paperback | 4 January 2010

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568 Pages

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Bright gamma-ray flares observed from sources far beyond our Milky Way Galaxy are best explained if enormous amounts of energy are liberated by black holes. The highest- energy particles in nature--the ultra-high-energy cosmic rays--cannot be confined by the Milky Way's magnetic field, and must originate from sources outside our Galaxy. Understanding these energetic radiations requires an extensive theoretical framework involving the radiation physics and strong-field gravity of black holes. In High Energy Radiation from Black Holes, Charles Dermer and Govind Menon present a systematic exposition of black-hole astrophysics and general relativity in order to understand how gamma rays, cosmic rays, and neutrinos are produced by black holes.

Beginning with Einstein's special and general theories of relativity, the authors give a detailed mathematical description of fundamental astrophysical radiation processes, including Compton scattering of electrons and photons, synchrotron radiation of particles in magnetic fields, photohadronic interactions of cosmic rays with photons, gamma-ray attenuation, Fermi acceleration, and the Blandford-Znajek mechanism for energy extraction from rotating black holes. The book provides a basis for graduate students and researchers in the field to interpret the latest results from high-energy observatories, and helps resolve whether energy released by rotating black holes powers the highest-energy radiations in nature. The wide range of detail will make High Energy Radiation from Black Holes a standard reference for black-hole research.

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"Filling an important gap in a topical and fast-evolving area, this interesting book will be a valuable addition to the astrophysics literature. The scientific content is of a high quality, and includes a notable level of rigor in the derivations."-Peter Meszaros, Pennsylvania State University
"There is definite need for a book on this topic. Dermer and Menon have gathered together a wide range of useful results and the book's rigorous and comprehensive coverage of high-energy processes will be valuable to the advanced researcher in the field. Astronomers working on black-hole processes, jets, AGN, and gamma-ray bursts will want to have this for reference."-Andrew Fabian, University of Cambridge

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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
Table of Contents provided by Ingram. All Rights Reserved.

High Energy Radiation from Black Holes

Gamma Rays, Cosmic Rays, and Neutrinos

At a Glance

Paperback

Industry Reviews

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How to return your order

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