Punsly Black Hole Gravitohydromagnetics

2. Auflage 2009
ISBN: 978-3-540-76957-6
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 355, 399 Seiten

Reihe: Astrophysics and Space Science Library

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. This second edition of the book is updated throughout and contains a completely new chapter discussing state of the art and results of numerical simulations of ergospheric disk jets occurring in magnetohydrodynamic accretion flows.

Autoren/Hrsg.

Punsly, Brian

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Introduction;14
3.1;1.1 Introductory Physical Perspective;14
3.2;1.2 Evidence for Astrophysical Black Holes;15
3.3;1.3 Extragalactic Radio Sources;19
3.4;1.3.1 Unified Scheme for Radio Loud AGN;21
3.5;1.3.2 Quantifying the Power of Extragalactic Radio Sources;28
3.6;1.3.3 Summary of Evidence of a Black Hole Central Engine in Radio Loud AGN;36
3.7;1.4 Extracting Energy from a Black Hole;38
3.8;1.5 Historical Perspective;44
3.9;1.6 Black Hole GHM;45
4;Relativistic Plasma Physics;47
4.1;2.1 Introduction;47
4.2;2.2 The Equations of Perfect MHD Plasmas;48
4.3;2.3 Perfect MHDWave Speeds in aWarm Plasma;50
4.4;2.4 Covariant Formulation of the PlasmaWave Speeds;56
4.5;2.5 The Perfect MHD Alfv • en Mode;57
4.6;2.6 The Magneto-Acoustic Waves in a Perfect MHD Plasma;59
4.7;2.7 MHD Waves in a Resistive Medium;60
4.8;2.8 High FrequencyWaves in a Perfect MHD Plasma;62
4.9;2.9 The Cylindrical Plasma-FilledWaveguide;63
4.9.1;2.9.1 Plasma Waves in a Cylindrical Waveguide;63
4.9.2;2.9.2 Fast Waves;65
4.9.3;2.9.3 Alfv • en Waves;66
4.9.4;2.9.4 The Faraday Wheel;67
4.10;2.10 Anisotropic Electrical Conductivity in Strong Magnetic Fields;77
4.11;2.11 High FrequencyWaves in Protonic Plasmas;82
4.12;2.12 Longitudinal Polarized MHD Discontinuities;84
4.13;2.13 What is Important About This Chapter?;86
4.14;2.14 Appendix. The Role of the Alfv • enWave in the Plasma-Filled Waveguide;87
4.15;2.14.1 Constructing Wave Packets;87
4.16;2.14.2 Physical Discussion;90
5;Particle Trajectories in the Ergosphere;91
5.1;3.1 Motivation;91
5.2;3.2 Coordinate Systems and Frames;91
5.3;3.3 Geodesic Motion;94
5.4;3.4 The Momentum Equations of a Magneto-Fluid;96
5.5;3.5 Frame Dragging and Negative Energy States;102
5.6;3.6 MaxwellÌs Equations;104
5.7;3.7 Inviscid Hydromagnetic Horizon Boundary Conditions;106
5.7.1;3.7.1 Electromagnetic Forces;108
5.7.2;3.7.2 Radiative Forces;113
5.7.3;3.7.3 Other Possible Forces in the Equation of Motion;113
6;Vacuum Electrodynamics;115
6.1;4.1 Motivation;115
6.2;4.2 Maxwell’s Equations in the Newman–Penrose Formalism;116
6.3;4.3 PoissonÌs Equations in the Kerr SpaceÒTime;124
6.4;4.4 LaplaceÌs Equations in the Kerr SpaceÒTime;126
6.5;4.5 The Electrodynamics of the Event Horizon;130
6.5.1;4.5.1 Electromagnetic Sources of PoissonÌs Equations Near the Horizon;130
6.5.2;4.5.2 External Fields From Electromagnetic Sources Near the Horizon;134
6.6;4.6 Simple Solutions to LaplaceÌs Equations;140
6.7;4.7 The Horizon Electromagnetic Boundary Conditionont;146
6.8;4.8 The Charge of a Rotating Black Hole;158
6.9;4.9 The Example of Axisymmetric Current Loops;160
6.9.1;4.9.1 Magnetic Flux Exclusion From Rapid Rotators;160
6.9.2;4.9.2 The No Hair Theorem;160
6.9.3;4.9.3 Magnetic Field Line Reconnection Near the Event Horizon;162
6.9.4;4.9.4 The Physical Interpretation of the Results;163
6.10;4.10 The Implications of Vacuum Electrodynamics to GHM;164
7;Magnetically Dominated Time Stationary Perfect MHDWinds;165
7.1;5.1 The Perfect MHD Wind Equations;166
7.2;5.2 Constants of Motion within a Flux Tube;167
7.3;5.3 TheWind Equations;170
7.4;5.4 The Critical Surfaces;171
7.5;5.5 The Topology of the Outgoing MHD Wind Solution Space;175
7.6;5.6 The Minimum Torque Solution;177
7.7;5.7 The GradÒShafranov Equation;179
8;Perfect MHDWinds andWaves in the Ergosphere;184
8.1;6.1 Paired MHD Winds;185
8.2;6.2 Ingoing Perfect MHD ErgosphericWinds;188
8.3;6.3 The Horizon is an Asymptotic Infinity to MHD Winds;189
8.4;6.4 Outgoing FastWaves Near the Horizon;193
8.4.1;6.4.1 The Vacuum Electrodyanmic Equations;194
8.4.2;6.4.2 Current Sources Near the Horizon;196
8.4.3;6.4.3 Solutions of the Inhomogeneous MaxwellÌs Equations Near the Horizon;198
8.4.4;6.4.4 Outgoing Fast Waves Near the Fast Point;198
8.4.5;6.4.5 The Singular Set of Long Wavelength Solutions;200
8.4.6;6.4.6 The Linearized Perturbation Equations for Short Wavelength Modes;204
8.4.7;6.4.7 Outgoing Magnetic Stresses Carried Fast Waves Near the Horizon;212
8.4.8;6.4.8 The Singular Point Structure of the Wave Equation Near the Fast Critical Surface;213
8.4.9;6.4.9 Comparison to the Locally Covariant Calculation of Chapter 2;216
8.4.10;6.4.10 Summary of Results;218
8.5;6.5 Causality and the BlandfordÒZnajek Horizon Boundary Condition;219
9;Ergosphere Driven Winds;223
9.1;7.1 Analogy to the Physics of the Faraday Wheel;223
9.2;7.2 Causal Determination of the Constants of Motion;224
9.2.1;7.2.1 Axisymmetric Vacuum Electromagnetic Fields;224
9.2.2;7.2.2 The Gravitational Field;225
9.2.3;7.2.3 Light Waves and Waves in a Highly Dissipative Medium;225
9.2.4;7.2.4 Perfect MHD Waves and Mildly Dissipative MHD Waves;226
9.3;7.3 The Causal Structure of the Dynamo;227
9.3.1;7.3.1 Radial Gravity;228
9.3.2;7.3.2 The Dragging of Inertial Frames;228
9.4;7.4 The Torsional Tug of War;229
10;Ergospheric Disk Dynamos;233
10.1;8.1 Fate of Accreted Magnetic Flux;233
10.2;8.2 The Global Structure of the Flow;240
10.2.1;8.2.1 Poynting Flux and Disk Formation;240
10.2.2;8.2.2 The Slow Shock and Disk Atmosphere;241
10.2.3;8.2.3 Some General Disk Structure;243
10.3;8.3 The RankineÒHugoniot Relations;243
10.3.1;8.3.1 The Field Line Angular Velocity;244
10.3.2;8.3.2 The Specific Enthalpy of the Post Shock Gas;245
10.3.3;8.3.3 The Density of the Post Shock Gas;247
10.3.4;8.3.4 The Downstream Poloidal Velocity;248
10.4;8.4 A Parametric Realization of Shock Parameters;249
10.5;8.5 The Dynamics and Structure of the Disk;249
10.6;8.6 The Global Energetics of the Disk;253
10.7;8.7 Near the Stationary Limit;255
10.8;8.8 The Inner Edge of the Disk;255
10.9;8.9 Summary;256
11;Winds From Event Horizon Magnetospheres;258
11.1;9.1 Time Dependent Dissipative Winds;258
11.2;9.2 The Causal Determination of O;261
11.3;9.3 The Ergospheric Dynamo in Free Floating Flux Tubes;265
11.4;9.4 Perfect MHD Paired Outgoing Minimum TorqueWinds:;270
11.4.1;9.4.1 Mathematical Formulation of Paired Wind as a Boundary Value Problem;271
11.4.2;9.4.2 The Outgoing Minimum Torque Wind;272
11.4.3;9.4.3 Initial Data for the Ingoing Wind;273
11.4.4;9.4.4 The Force Free Limit of the Ingoing Wind;274
11.4.5;9.4.5 The Poloidal Equation of Motion of the Ingoing Wind;277
11.4.6;9.4.6 Numerically Quantifying the Wind Near the Inner Light Cylinder;279
11.4.7;9.4.7 Accessibility of the Inner Alfv • en Point;281
11.4.8;9.4.8 Accessibility of the Inner Fast Point;284
11.4.9;9.4.9 The Terminus of the Perfect MHD Wind;290
11.4.10;9.4.10 The Ingoing Extension of the Subcritical Solution;292
11.5;9.5 The Radiative Instability Near the Light Cylinder;293
11.5.1;9.5.1 The Initial Unperturbed State;295
11.5.2;9.5.2 The Radiation Resistance Perturbation;295
11.5.3;9.5.3 The Perturbed Four Velocity;296
11.5.4;9.5.4 The Perturbed Field Strengths;297
11.5.5;9.5.5 The Perturbed Proper Electric Field;299
11.5.6;9.5.6 Stationary Point Analysis;301
11.6;9.6 The Dynamo Region;304
11.6.1;9.6.1 Resistivity and the Saturation of the Instability;304
11.6.2;9.6.2 The Anchor Point;306
11.6.3;9.6.3 Causal Structure of the Dynamo;309
11.6.4;9.6.4 The Global Energetics of the Dynamo;310
11.7;9.7 The Deflagration Wind;313
11.7.1;9.7.1 The Near Zone;313
11.7.2;9.7.2 The Breakdown of Near Zone Physics;315
11.7.3;9.7.3 The Asymptotic Wind Zone;317
11.8;9.8 The Unique Physical Solution;318
12;Applications to the Theory of Extragalactic Radio Sources;320
12.1;10.1 Spectral Diagnostics of Blazar Central Engines;320
12.1.1;10.1.1 BL Lacs and Quasars;324
12.1.2;10.1.2 Other Correlations;325
12.2;10.2 The Black Hole GHM Theory of the Central Engine;327
12.2.1;10.2.1 The Distribution of Poloidal Magnetic Flux;329
12.2.2;10.2.2 The Structure of the Ergospheric Disk;333
12.3;10.3 The Electromagnetic Power From the Three Component Central Engine;334
12.4;10.4 Applications of the Theory;339
12.4.1;10.4.1 Interpreting the Unified Scheme;339
12.4.2;10.4.2 Correlations with Blazar Spectra;347
12.4.3;10.4.3 Radio Source Evolution;349
12.5;10.5 The GHM Theory of Extragalactic Radio Sources;352
13;Numerical Results;355
13.1;11.1 The Current State of Numerical Simulations;356
13.2;11.2 Simulations of Relativistic Strings;361
13.3;11.3 Ergospheric Disk Jets in 3-D MHD Accretion Flow Simulations;367
13.3.1;11.3.1 The Equatorial Poynting Flux Source in KDJ;369
13.3.2;11.3.2 The Vertical Flux in the Equatorial Dynamo;371
13.3.3;11.3.3 The Field Line Angular Velocity;373
13.3.4;11.3.4 The Creation of Negative Energy Plasma;374
13.3.5;11.3.5 The Simulation KDE;377
13.4;11.4 Source of Poynting Flux in Event Horizon Magnetospheres;379
13.4.1;11.4.1 The Propagation of the Ergospheric Disk Jet;382
13.4.2;11.4.2 The MHD Coronal Piston;384
13.5;11.5 Discussion;390
13.5.1;11.5.1 The Ergospheric Disk Jet;390
13.5.2;11.5.2 The Truncated Ergospheric Disk Jet;390
13.5.3;11.5.3 The BlandfordÒZnajek Jet;391
13.5.4;11.5.4 The KDJ Ergospheric Disk Data Point;391
13.5.5;11.5.5 The KDE Ergospheric Disk Data Point;392
13.5.6;11.5.6 The KDH Ergospheric Disk Data Point;392
13.5.7;11.5.7 Constraints Imposed by Observations;393
14;References;395
15;Index;400