Black Hole Gravitohydromagnetics / Edition 2

Black Hole Gravitohydromagnetics / Edition 2

by Brian Punsly
ISBN-10:
3540769552
ISBN-13:
9783540769552
Pub. Date:
11/28/2008
Publisher:
Springer Berlin Heidelberg
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Overview

Black Hole Gravitohydromagnetics / Edition 2

Black hole gravitohydromagnetics (GHM) is developed from the rudiments to the frontiers of research in this book. GHM describes plasma interactions that combine the effects of gravity and a strong magnetic field, in the vicinity (ergosphere) of a rapidly rotating black hole. This topic was created in response to the astrophysical quest to understand the central engines of radio loud extragalactic radio sources. The theory describes a "torsional tug of war" between rotating ergospheric plasma and the distant asymptotic plasma that extracts the rotational inertia of the black hole. The recoil from the struggle between electromagnetic and gravitational forces near the event horizon is manifested as a powerful pair of magnetized particle beams (jets) that are ejected at nearly the speed of light. These bipolar jets feed large-scale magnetized plasmoids on scales as large as millions of light years (the radio lobes of extragalactic radio sources). This interaction can initiate jets that transport energy fluxes exceeding 10[superscript 47] ergs/s.

Product Details

ISBN-13: 9783540769552
Publisher: Springer Berlin Heidelberg
Publication date: 11/28/2008
Series: Astrophysics and Space Science Library Series , #355
Edition description: 2nd ed. 2009
Pages: 399
Product dimensions: 6.30(w) x 9.40(h) x 0.80(d)

Table of Contents

1 Introduction 1

1.1 Introductory Physical Perspective 1

1.2 Evidence for Astrophysical Black Holes 2

1.3 Extragalactic Radio Sources 6

1.3.1 Unified Scheme for Radio Loud AGN 8

1.3.2 Quantifying the Power of Extragalactic Radio Sources 15

1.3.3 Summary of Evidence of a Black Hole Central Engine in Radio Loud AGN 23

1.4 Extracting Energy from a Black Hole 25

1.5 Historical Perspective 31

1.6 Black Hole GHM 32

2 Relativistic Plasma Physics 35

2.1 Introduction 35

2.2 The Equations of Perfect MHD Plasmas 36

2.3 Perfect MHD Wave Speeds in a Warm Plasma 38

2.4 Covariant Formulation of the Plasma Wave Speeds 44

2.5 The Perfect MHD Alfven Mode 45

2.6 The Magneto-Acoustic Waves in a Perfect MHD Plasma 47

2.7 MHD Waves in a Resistive Medium 48

2.8 High Frequency Waves in a Perfect MHD Plasma 50

2.9 The Cylindrical Plasma-Filled Waveguide 51

2.9.1 Plasma Waves in a Cylindrical Waveguide 51

2.9.2 Fast Waves 53

2.9.3 Alfven Waves 54

2.9.4 The Faraday Wheel 55

2.10 Anisotropic Electrical Conductivity in Strong Magnetic Fields 65

2.11 High Frequency Waves in Protonic Plasmas 70

2.12 Longitudinal Polarized MHD Discontinuities 72

2.13 What is Important About This Chapter? 74

2.14 Appendix. The Role of the Alfven Wave in the Plasma-Filled Waveguide 75

2.14.1 Constructing Wave Packets 75

2.14.2 Physical Discussion 78

3 Particle Trajectories in the Ergosphere 79

3.1 Motivation 79

3.2 Coordinate Systems and Frames 79

3.3 Geodesic Motion 82

3.4 The Momentum Equations of a Magneto-Fluid 84

3.5 Frame Dragging and Negative Energy States 90

3.6 Maxwell's Equations 92

3.7 Inviscid Hydromagnetic Horizon Boundary Conditions 94

3.7.1Electromagnetic Forces 96

3.7.2 Radiative Forces 101

3.7.3 Other Possible Forces in the Equation of Motion 101

4 Vacuum Electrodynamics 103

4.1 Motivation 103

4.2 Maxwell's Equations in the Newman-Penrose Formalism 104

4.3 Poisson's Equations in the Kerr Space-Time 112

4.4 Laplace's Equations in the Kerr Space-Time 114

4.5 The Electrodynamics of the Event Horizon 118

4.5.1 Electromagnetic Sources of Poisson's Equations Near the Horizon 118

4.5.2 External Fields From Electromagnetic Sources Near the Horizon 122

4.6 Simple Solutions to Laplace's Equations 128

4.6.1 The Kerr Newman Solution 128

4.6.2 The Wald Solution 129

4.6.3 Axisymmetric Time Stationary Fields 133

4.7 The Horizon Electromagnetic Boundary Condition 134

4.7.1 Displacement Currents at the Ingoing Flow Front 134

4.7.2 The Horizon as a Circuit Element 136

4.7.3 The Horizon is not a Conductor 137

4.7.4 The Absence of Unipolar Induction Near the Horizon 138

4.7.5 The Horizon is an Electrodynamic Infinity 146

4.8 The Charge of a Rotating Black Hole 146

4.9 The Example of Axisymmetric Current Loops 148

4.9.1 Magnetic Flux Exclusion From Rapid Rotators 148

4.9.2 The No Hair Theorem 148

4.9.3 Magnetic Field Line Reconnection Near the Event Horizon 150

4.9.4 The Physical Interpretation of the Results 151

4.10 The Implications of Vacuum Electrodynamics to GHM 152

5 Magnetically Dominated Time Stationary Perfect MHD Winds 153

5.1 The Perfect MHD Wind Equations 154

5.2 Constants of Motion within a Flux Tube 155

5.3 The Wind Equations 158

5.4 The Critical Surfaces 159

5.5 The Topology of the Outgoing MHD Wind Solution Space 163

5.6 The Minimum Torque Solution 165

5.7 The Grad-Shafranov Equation 167

6 Perfect MHD Winds and Waves in the Ergosphere 173

6.1 Paired MHD Winds 174

6.2 Ingoing Perfect MHD Ergospheric Winds 177

6.3 The Horizon is an Asymptotic Infinity to MHD Winds 178

6.4 Outgoing Fast Waves Near the Horizon 182

6.4.1 The Vacuum Electrodyanmic Equations 183

6.4.2 Current Sources Near the Horizon 185

6.4.3 Solutions of the Inhomogeneous Maxwell's Equations Near the Horizon 187

6.4.4 Outgoing Fast Waves Near the Fast Point 187

6.4.5 The Singular Set of Long Wavelength Solutions 189

6.4.6 The Linearized Perturbation Equations for Short Wavelength Modes 193

6.4.7 Outgoing Magnetic Stresses Carried Fast Waves Near the Horizon 201

6.4.8 The Singular Point Structure of the Wave Equation Near the Fast Critical Surface 202

6.4.9 Comparison to the Locally Covariant Calculation of Chapter 2 205

6.4.10 Summary of Results 207

6.5 Causality and the Blandford-Znajek Horizon Boundary Condition 208

7 Ergosphere Driven Winds 213

7.1 Analogy to the Physics of the Faraday Wheel 213

7.2 Causal Determination of the Constants of Motion 214

7.2.1 Axisymmetric Vacuum Electromagnetic Fields 214

7.2.2 The Gravitational Field 215

7.2.3 Light Waves and Waves in a Highly Dissipative Medium 215

7.2.4 Perfect MHD Waves and Mildly Dissipative MHD Waves 216

7.3 The Causal Structure of the Dynamo 217

7.3.1 Radial Gravity 218

7.3.2 The Dragging of Inertial Frames 218

7.4 The Torsional Tug of War 219

8 Ergospheric Disk Dynamos 223

8.1 Fate of Accreted Magnetic Flux 223

8.2 The Global Structure of the Flow 230

8.2.1 Poynting Flux and Disk Formation 230

8.2.2 The Slow Shock and Disk Atmosphere 231

8.2.3 Some General Disk Structure 233

8.3 The Rankine-Hugoniot Relations 233

8.3.1 The Field Line Angular Velocity 234

8.3.2 The Specific Enthalpy of the Post Shock Gas 235

8.3.3 The Density of the Post Shock Gas 237

8.3.4 The Downstream Poloidal Velocity 238

8.4 A Parametric Realization of Shock Parameters 239

8.5 The Dynamics and Structure of the Disk 239

8.6 The Global Energetics of the Disk 243

8.7 Near the Stationary Limit 245

8.8 The Inner Edge of the Disk 245

8.9 Summary 246

9 Winds From Event Horizon Magnetospheres 249

9.1 Time Dependent Dissipative Winds 249

9.2 The Causal Determination of [Omega subscript F] 252

9.3 The Ergospheric Dynamo in Free Floating Flux Tubes 256

9.4 Perfect MHD Paired Outgoing Minimum Torque Winds: [Omega subscript F] [double less-than sign] [Omega subscript H] 261

9.4.1 Mathematical Formulation of Paired Wind as a Boundary Value Problem 262

9.4.2 The Outgoing Minimum Torque Wind 263

9.4.3 Initial Data for the Ingoing Wind 264

9.4.4 The Force Free Limit of the Ingoing Wind 265

9.4.5 The Poloidal Equation of Motion of the Ingoing Wind 268

9.4.6 Numerically Quantifying the Wind Near the Inner Light Cylinder 270

9.4.7 Accessibility of the Inner Alfven Point 272

9.4.8 Accessibility of the Inner Fast Point 275

9.4.9 The Terminus of the Perfect MHD Wind 281

9.4.10 The Ingoing Extension of the Subcritical Solution 283

9.5 The Radiative Instability Near the Light Cylinder 284

9.5.1 The Initial Unperturbed State 286

9.5.2 The Radiation Resistance Perturbation 286

9.5.3 The Perturbed Four Velocity 287

9.5.4 The Perturbed Field Strengths 288

9.5.5 The Perturbed Proper Electric Field 290

9.5.6 Stationary Point Analysis 292

9.6 The Dynamo Region 295

9.6.1 Resistivity and the Saturation of the Instability 295

9.6.2 The Anchor Point 297

9.6.3 Causal Structure of the Dynamo 300

9.6.4 The Global Energetics of the Dynamo 301

9.7 The Deflagration Wind 304

9.7.1 The Near Zone 304

9.7.2 The Breakdown of Near Zone Physics 306

9.7.3 The Asymptotic Wind Zone 308

9.8 The Unique Physical Solution 309

10 Applications to the Theory of Extragalactic Radio Sources 311

10.1 Spectral Diagnostics of Blazar Central Engines 311

10.1.1 BL Lacs and Quasars 315

10.1.2 Other Correlations 316

10.2 The Black Hole GHM Theory of the Central Engine 318

10.2.1 The Distribution of Poloidal Magnetic Flux 320

10.2.2 The Structure of the Ergospheric Disk 324

10.3 The Electromagnetic Power From the Three Component Central Engine 325

10.4 Applications of the Theory 330

10.4.1 Interpreting the Unified Scheme 330

10.4.2 Correlations with Blazar Spectra 338

10.4.3 Radio Source Evolution 340

10.5 The GHM Theory of Extragalactic Radio Sources 343

11 Numerical Results 347

11.1 The Current State of Numerical Simulations 348

11.2 Simulations of Relativistic Strings 353

11.3 Ergospheric Disk Jets in 3-D MHD Accretion Flow Simulations 359

11.3.1 The Equatorial Poynting Flux Source in KDJ 361

11.3.2 The Vertical Flux in the Equatorial Dynamo 363

11.3.3 The Field Line Angular Velocity 365

11.3.4 The Creation of Negative Energy Plasma 366

11.3.5 The Simulation KDE 369

11.4 Source of Poynting Flux in Event Horizon Magnetospheres 371

11.4.1 The Propagation of the Ergospheric Disk Jet 374

11.4.2 The MHD Coronal Piston 376

11.5 Discussion 382

11.5.1 The Ergospheric Disk Jet 382

11.5.2 The Truncated Ergospheric Disk Jet 382

11.5.3 The Blandford-Znajek Jet 383

11.5.4 The KDJ Ergospheric Disk Data Point 383

11.5.5 The KDE Ergospheric Disk Data Point 384

11.5.6 The KDH Ergospheric Disk Data Point 384

11.5.7 Constraints Imposed by Observations 385

References 387

Index 393

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