High-energy radiation from black holes : gamma rays, cosmic rays, and neutrinos / Charles D. Dermer, Govind Menon.

Format:

Book

Author/Creator:

Dermer, Charles.

Contributor:

Govind Menon.

Series:

Princeton series in astrophysics

Language:

English

Subjects (All):

Black holes (Astronomy).

Cosmic rays.

Gamma ray astronomy.

Neutrinos.

Physical Description:

xx, 538 pages : illustrations ; 24 cm.

Place of Publication:

Princeton, N.J. ; Woodstock : Princeton University Press, 2009.

Summary:

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, includidng 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.

Contents:

Chapter 1 Introduction 1

1.1 Black Holes in Nature 1

1.2 Energy Fluxes 8

1.3 Timing Studies and Black-Hole Mass Estimates 10

1.4 Flux Distribution 11

1.5 The Nighttime Sky 12

Chapter 2 Relativistic Kinematics 14

2.1 Lorentz Transformation Equations 14

2.2 Four-Vectors and Momentum 16

2.3 Relativistic Doppler Factor 18

2.4 Three Useful Invariants 19

2.5 Relativistic Reaction Rate 21

2.6 Secondary Production Spectra 23

Chapter 3 Introduction to Curved Spacetime 25

3.1 Special Relativity 25

3.2 Curved Space/Spacetime 29

3.3 The Schwarzschild Metric 33

Chapter 4 Physical Cosmology 36

4.1 Robertson-Walker Metric 36

4.2 Friedmann Models 39

4.2.1 Hubble Relation from the Cosmological Principle 39

4.2.2 Expansion of the Universe 40

4.2.3 Einstein-de Sitter Universe 43

4.2.4 Universe with Zero Cosmological Constant 43

4.2.5 Flat Universe 43

4.3 Luminosity and Angular-Diameter Distances 44

4.4 Event Rate of Bursting Sources 45

4.5 Flux and Intensity from Distributed Sources 47

Chapter 5 Radiation Physics of Relativistic Flows 50

5.1 Radiation Preliminaries 50

5.2 Invariant Quantities 53

5.3 Blackbody Radiation Field 53

5.4 Transformed Quantities 56

5.4.1 Transformation of Total Distribution and Energy 56

5.4.2 Transformation of Differential Distributions 56

5.5 Fluxes of Relativistic Cosmological Sources 59

5.5.1 Blob Geometry 60

5.5.2 Spherical Shell Geometry 63

5.5.3 Equivalence of Blob and Blast Wave Geometries 68

Chapter 6 Compton Scattering 70

6.1 Compton Effect 70

6.2 The Compton Cross Section 71

6.3 Transforming the Compton Cross Section 73

6.3.1 Differential Thomson Cross Section 75

6.3.2 Head-on Approximation 77

6.3.3 Differential Compton Cross Section 77

6.3.4 Moments of the Compton Cross Section 79

6.3.5 Compton Scattering in the δ-Function Approximation 80

6.4 Energy-Loss Rates in Compton Scattering 81

6.4.1 Thomson Energy-Loss Rate 81

6.4.2 Klein-Nishina Energy-Loss Rate 82

6.5 Differential Compton Cross Sections and Spectra 83

6.5.1 Comparison of Scattered Spectra for Different ERF Photon Energies 83

6.5.2 Spectral Comparisons for Isotropic Monochromatic Photons and Power-Law Electrons 84

6.6 Thomson Scattering: Isotropic Photons and Electrons 92

6.6.1 Thomson-Scattered Radiation Spectrum in the δ-Function Approximation 92

6.6.2 Spectral Comparisons for Isotropic Power-Law Photons and Electrons 93

6.7 External Photon Fields Compton-Scattered by Jet Electrons 94

6.7.1 Thomson-Scattered Spectrum for an External Point Source of Radiation from Behind 96

6.7.2 Thomson-Scattered Spectrum for External Isotropic Radiation in the ?-Function Approximation 97

6.7.3 External Isotropic Photons Compton-Scattered by let Electrons 99

6.7.4 Cosmic Microwave Background Radiation Compton-Scattered by Jet Electrons 103

6.8 Accretion-Disk Field Compton-Scattered by Jet Electrons 105

6.8.1 Optically Thick Shakura-Sunyaev Disk Spectrum 106

6.8.2 Integrated Emission Spectrum from Shakura-Sunyaev Disk 107

6.8.3 Transformed Accretion-Disk Radiation Field 108

6.8.4 Thomson-Scattered Shakura-Sunyaev Disk Spectrum in the Near Field 112

6.8.5 Thomson-Scattered Shakura-Sunyaev Disk Spectrum in the Far Field 113

6.8.6 Beaming Patterns 113

6.9 Broad-Line Region Scattered Radiation 114

Chapter 7 Synchrotron Radiation 117

7.1 Covariant Electrodynamics 118

7.2 Synchrotron Power and Peak Frequency 119

7.3 Elementary Synchrotron Radiation Formulae 121

7.3.1 Relations between Emitted, Received, and 90ʻ Pitch-Angle Powers 123

7.3.2 Particle Synchrotron Radiation 126

7.3.3 Synchrotron Spectrum from a Power-Law Electron Distribution 127

7.4 δ-Function Approximation for Synchrotron Radiation 129

7.5 Equipartition Magnetic Field 131

7.5.1 Equipartition Magnetic Field: Qualitative Estimate 132

7.5.2 Equipartition Magnetic Field: Quantitative Treatment 133

7.6 Energelics and Minimum Jet Powers 135

7.7 Synchrotron Self-Compton Radiation 138

7.7.1 SSC in the Thomson Regime 138

7.7.2 SSC in the Thomson Regime for Broken Power-Law Electron Distribution 140

7.7.3 Accurate SSC for General Electron Distribution 141

7.7.4 Synchrotion/SSC Model 142

7.7.5 SSC Electron Energy-Loss Rate 143

7.8 Synchrotron Self-Absorption 143

7.8.1 Einstein Coefficients 145

7.8.2 Brightness Temperature and Self-Absorbed Flux: Qualitative Discussion 146

7.8.3 Derivation of the Synchrotron Self-Absorption Coefficient 148

7.8.4 δ-Function Approximation for Synchrotron Self-Absorption 148

7.8.5 Synchrotron Self-Absorption Coefficient for Power-Law Electrons 149

7.9 Maximum Brightness Temperature 150

7.10 Compton Limits on the Doppler Factor 153

7.11 Self-Absorbed Synchrotron Spectrum 154

7.12 Hyper-Relativistic Electrons 156

7.13 Jitter Radiation 158

Chapter 8 Binary Particle Collision Processes 160

8.1 Coulomb Energy Losses 161

8.1.1 Stopping Power of Cold Plasma 161

8.1.2 Thermal Relaxation 163

8.1.3 Stopping Power of Thermal Plasma 164

8.1.4 Knock-On Electrons 165

8.2 Bremsstrahlung 166

8.2.1 Electron Bremsstrahlung Energy-Loss Rate 167

8.2.2 Electron Bremsstrahlung Production Spectra 167

8.3 Secondary Nuclear Production 169

8.3.1 γ Rays from π0 Decay 171

8.3.2 Cross Section for p + p ← π + X Production 172

8.4 Electron-Positron Annihilation Radiation 180

8.4.1 Annihilation in a Thermal Medium 181

8.4.2 Thermal Annihilation Line and Continuum Spectra 182

8.5 Nuclear γ-Ray Line Production 185

Chapter 9 Photohadronic Processes 187

9.1 Scattering and Energy-Loss Timescales 189

9.2 Photopion Process 190

9.2.1 Photopion Cross Section 191

9.2.2 Analytic Expression for Photopion Cross Section 192

9.2.3 Numerical Calculation of Photopion Cross Section 194

9.2.4 Photopion Energy-Loss Rate 194

9.2.5 GZK Energy 196

9.2.6 Stochastic and Continuous Energy Losses 197

9.3 Photopair Process 197

9.3.1 Photopair Cross Section 198

9.3.2 Photopair Energy-Loss Timescale 198

9.3.3 Accurate Expression for Photopair Energy-Loss Rates of Ions in an Isotropic Radiation Field 201

9.3.4 Relative Importance of Photopion and Photopair Losses 203

9.4 Expansion Losses 203

9.5 Cosmogenic Neutrino Flux 204

9.6 Ultrahigh-Enetgy Cosmic-Ray Evolution 208

9.6.1 Normalization to Local Luminosity Density 209

9.6.2 Energy Evolution of Cosmic-Ray Protons 210

9.6.3 Rate Density Evolution and the Star Formation Rate 211

9.7 Waxman-Bahcail Bound 213

9.8 UHECR and GZK Neutrino Intensities 215

9.9 Photonuclear Reactions 219

9.9.1 Photodisintegration Reaction Rate 222

9.9.2 Effective Photodisintegration Energy-Loss Rate 224

9.9.3 Neutrinos from Photodisintegration 225

Chapter 10 γγ Pair Production 227

10.1 γγPair Production Cross Section 228

10.1.1 Absorption by a Blackbody and a Modified Blackbody Photon Gas 231

10.1.2 Absorption by a Power-Law Photon Gas in a Relativistic Jet 233

10.1.3 γγ Attenuation in Anisotropic Radiation Fields 235

10.2 ?-Function Approximation for σγγ 236

10.3 Opacity of the Universe to γγ Attenuation 237

10.3.1 γγ Optical Depth of the Universe 238

10.3.2 Measurements of the EBL 240

10.3.3 γγ Attenuation at Low Redshifts 241

10.3.4 γγ Attenuation at All Redshifts 244

10.4 The γ-Ray Horizon 244

10.5 Compactness Parameter 245

10.6 Minimum Doppler Factor from γγ Constraint 247

10.7 Correlated γ-Ray and Neutrino Fluxes 249

10.8 Electromagnetic Cascades 253

10.8.1 Cascades in Jets 254

10.8.2 Cascades in the Intergalactic Medium 256

10.9 γγ ← ν 257

Chapter 11 Blast-Wave Physics 258

11.1 Fireballs and Relativistic Blast Waves 258

11.1.1 Blast-Wave Deceleration 260

11.1.2 Blast-Wave Equation of Motion 261

11.1.3 Dissipated

Internal Energy 270

11.2 Elementary Blast-Wave Theory 270

11.2.1 Characteristic Electron Energies 271

11.2.2 Characteristic Synchrotron Frequencies 274

11.2.3 Afterglow Theory 278

11.3 Relativistic Shock Hydrodynamics 282

11.3.1 Relativistic Shock Thermodynamics 282

11.3.2 Synchrotron Radiation from a Relativistic Reverse Shock 288

11.4 Beaming Breaks and Jets 290

11.5 Synchrotron Self-Compton Radiation 292

11.6 Theory of the Prompt Phase 294

11.6.1 X-Ray Flares and γ-Ray Pulses from External Shocks 295

11.6.2 Colliding Shells and Internal Shocks 301

11.7 Thermal Photospheres 303

11.7.1 The Amati and Ghirlanda Relations 303

11.7.2 Thermodynamics of a Steady Relativistic Wind 304

11.7.3 Photospheric Radius 306

11.7.4 Pair Photosphere 308

11.8 Thermal Neutrons 310

11.9 GRB Cosmology 312

Chapter 12 Introduction to Fermi Acceleration 314

12.1 Stochastic and Shock Fermi Acceleration 316

12.2 Wave Turbulence Spectrum 317

12.3 The Hillas Condition 320

12.4 Energy Gain per Cycle from Fermi Acceleration 321

12.5 Diffusion in Physical Space 322

12.6 Maximum Particle Energy 324

Chapter 13 First-Order Fermi Acceleration 327

13.1 Nonrelativistic Shock Hydrodynamics 328

13.2 Convection-Diffusion Equation 330

13.3 Nonrelativistic Shock Acceleration 332

13.3.1 Spectral Index from Convection-Diffusion Equation 332

13.3.2 Spectral Index from Probability Arguments 334

13.3.3 Finite Shell Width 335

13.3.4 Cosmic-Ray Pressure and Shock Width 337

13.3.5 Maximum Particle Energy in Nonrelativistic Shock Acceleration 339

13.3.6 Maximum Particle Energy in Nonrelativistic Shocks 343

13.3.7 Amplification of Upstream Medium Magnetic Field 344

13.4 Relativistic Shock Acceleration 346

13.4.1 Fokker-Planck Equation for a Stationary, Parallel Shock 347

13.4.2 Spectral Index in Relativistic Shock Acceleration 348

13.4.3 Maximum Particle Energies in Relativistic Shock Acceleration 349

Chapter 14 Second-Order Fermi Acceleration 351

14.1 Power-Law Particle Spectra from Second-Order Fermi Acceleration 353

14.2 The Resonance Condition 353

14.3 Plasma Waves 355

14.4 Diffusive Particle Acceleration 359

14.5 Approximate Derivation of Diffusion Coefficients 362

14.5.1 Pitch-Angle Diffusion Coefficient 362

14.5.2 Momentum Diffusion Coefficient 363

14.6 Energy Gain and Diffusive Escape Rates 364

14.7 Momentum Diffusion Equation 367

14.7.1 Ramaty-Lee Spectrum for Hard-Sphere Scattering 368

14.7.2 Green's Function Solution 370

14.8 Maximum Particle Energy in Second-Order Fermi Acceleration 372

14.8.1 Gyroresonant Stochastic Acceleration 373

14.8.2 Stochastic Energization in Nonrelativistic Shocks 374

14.8.3 Stochastic Energization in Relativistic Flows 376

Chapter 15 The Geometry of Spacetime 379

15.1 Introduction 379

15.2 Splitting Spacetime into Space and Time 380

15.3 The Kerr Metric 384

15.3.1 The Geodesic Equation and Its Integrability in Kerr Geometry 386

15.3.2 The Kerr Metric in Kerr-Schild Coordinates 391

15.3.3 The Ergosphere 394

15.3.4 The Event Horizon 396

15.4 The Penrose Process 397

15.5 Hawking Radiation 402

15.5.1 Scalar Fields in Curved Spacetime 402

15.5.2 The Quantum Field for a Scalar Particle in a Flat Spacetime 404

15.5.3 Particle Creation in Curved Spacetime 405

15.5.4 Particle Creation in Rindler Spacetime 408

15.5.5 Particle Creation in Schwarzschild Geometry 415

Chapter 16 Black-Hole Electrodynamics 417

16.1 3+1 Electrodynamics 417

16.2 The Energy-Momentum Tensor 424

16.3 The Blandford-Znajek Process 427

16.3.1 Explicit Expressions for the Fields and Currents 431

16.3.2 The Force-Free Constraint Equation 432

16.3.3 The Znajek Regularity Condition 433

16.3.4 Energy and Angular-Mom en turn Extraction from the Force-Free Magnetosphere 435

16.4 Geodesic Currents in the Magnetosphere 436

16.5 An Exact Solution 439

16.6 Fields and Energy Extraction for the Ω- Solution 441

16.7 An Approximate Solution 442

16.8 Uniqueness of the Ω_ Solution 447

16.9 Energy Extraction for the Ω+ Solution 448

16.10 Blandford-Znajek Process in Astrophysical Sources 450

Chapter 17 High-Energy Radiations from Black Holes 452

17.1 γ Rays 453

17.1.1 Modeling γ Rays from Black Holes 454

17.1.2 Statistics of Black-Hole Sources 456

17.1.3 Blazar Physics 457

17.1.4 GRB Classes 458

17.1.5 Unresolved and Diffuse ?-Ray Background 458

17.2 Cosmic Rays 459

17.2.1 Acceleration of Cosmic Rays at Supernova Remnant Shocks 461

17.2.2 Acceleration of UHECRs at Relativistic Blast Waves 462

17.2.3 Charged-Particle Astronomy 463

17.2.4 UHECR Propagation 466

17.2.5 UHECR Source Power Requirements 466

17.3 Neutrinos 468

17.4 Concluding Remarks 471.

Notes:

Includes bibliographical references (pages [509]-530) and index.

ISBN:

9780691137957

0691137951

9780691144085

0691144087

OCLC:

318874701