Beskin MHD Flows in Compact Astrophysical Objects

Accretion, Winds and Jets
2010
ISBN: 978-3-642-01290-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 425 Seiten

Reihe: Astronomy and Astrophysics Library

Accretion flows, winds and jets of compact astrophysical objects and stars are generally described within the framework of hydrodynamical and magnetohydrodynamical (MHD) flows. Analytical analysis of the problem provides profound physical insights, which are essential for interpreting and understanding the results of numerical simulations. Providing such a physical understanding of MHD Flows in Compact Astrophysical Objects is the main goal of this book, which is an updated translation of a successful Russian graduate textbook. The book provides the first detailed introduction into the method of the Grad-Shafranov equation, describing analytically the very broad class of hydrodynamical and MHD flows. It starts with the classical examples of hydrodynamical accretion onto relativistic and nonrelativistic objects. The force-free limit of the Grad-Shafranov equation allows us to analyze in detail the physics of the magnetospheres of radio pulsars and black holes, including the Blandford-Znajek process of energy extraction from a rotating black hole immersed in an external magnetic field. Finally, on the basis of the full MHD version of the Grad-Shafranov equation the author discusses the problems of jet collimation and particle acceleration in Active Galactic Nuclei, radio pulsars, and Young Stellar Objects. The comparison of the analytical results with numerical simulations demonstrates their good agreement. Assuming that the reader is familiar with the basic physical and mathematical concepts of General Relativity, the author uses the 3+1 split approach which allows the formulation of all results in terms of physically clear language of three dimensional vectors. The book contains detailed derivations of equations, numerous exercises, and an extensive bibliography. It therefore serves as both an introductory text for graduate students and a valuable reference work for researchers in the field.

Autoren/Hrsg.

Beskin, Vasily S.

Beskin, V.S.

Inhaltsverzeichnis

1;Preface;7
2;Acknowledgments;11
3;Contents;13
4;Acronyms;17
5;Introduction;19
6;1 Hydrodynamical Limit---Classical Problems of Accretion and Ejection;23
6.1; Astrophysical Introduction---Accretion onto Compact Objects;24
6.1.1; Accretion Disks;24
6.1.2; Standard Model;28
6.1.3; ADAF, ADIOS, etc.;31
6.2; Main Properties of Transonic Hydrodynamical Flows;33
6.2.1; Basic Equations;33
6.2.2; Spherically Symmetric Flow;35
6.2.3; Potential Plane Flow;39
6.3; Nonrelativistic Axisymmetric Stationary Flows;46
6.3.1; Basic Equations;46
6.3.2; Mathematical Intermezzo---the Covariant Approach;48
6.3.3; Two-Dimensional Flow Structure;49
6.3.4; Bondi--Hoyle Accretion;58
6.3.5; Outflow from a Slowly Rotating Star;62
6.4; Axisymmetric Stationary Flows in the Vicinity of a Black Hole;71
6.4.1; Physical Intermezzo---(3+1)-Splitting in the Kerr Metric;71
6.4.2; Basic Equations;75
6.4.3; Exact Solutions;81
6.4.4; Bondi--Hoyle Accretion---The Relativistic Regime;84
6.4.5; Accretion onto a Slowly Rotating Black Hole;87
6.4.6; Accretion of Matter with Small Angular Momentum;89
6.4.7; Thin Transonic Disk;95
6.5; Conclusion;106
7;2 Force-Free Approximation---The Magnetosphere of Radio Pulsars;107
7.1; Astrophysical Introduction;107
7.2; Basic Physical Processes;111
7.2.1; Vacuum Approximation;111
7.2.2; Particle Generation in the Strong Magnetic Field;116
7.2.3; Magnetosphere Structure;119
7.3; Secondary Plasma Generation;123
7.3.1; ``Inner Gap'';123
7.3.2; Neutron Star Surface;128
7.3.3; Propagation of -Quanta in the Superstrong Magnetic Field;129
7.3.4; General Relativity Effects;130
7.3.5; Particle Generation in the Magnetosphere;132
7.3.6; ``Hollow Cone'' Model;134
7.3.7; Secondary Plasma Generation---``Outer Gap'';138
7.4; Pulsar Equation;138
7.4.1; Force-Free Approximation. The Magnetization Parameter;138
7.4.2; Integrals of Motion;140
7.4.3; Grad--Shafranov Equation;143
7.4.4; Mathematical Intermezzo---Quasistationary Formalism;146
7.5; Energy Losses of Radio Pulsars;149
7.5.1; Current Loss Mechanism;149
7.5.2; Slowing Down of Inclined and Orthogonal Rotators;153
7.6; Magnetosphere Structure;161
7.6.1; Exact Solutions;161
7.6.2; Magnetosphere Structure with Longitudinal Currents;180
7.6.3; Magnetosphere Models;187
7.7; Conclusion;193
8;3 Force-Free Approximation---The Black Hole Magnetosphere ;194
8.1; Astrophysical Introduction---The Central Engine in Active Galactic Nuclei;194
8.1.1; Possible Mechanisms of Black Hole Formation;194
8.1.2; Nature of Activity and Variability;1
8.1.3; Magnetized Accretion Disk;198
8.1.4; Regular Magnetic Field Generation;200
8.2; Basic Equations;203
8.2.1; (3+1)-Splitting for the Electromagnetic Field;203
8.2.2; ``No Hair'' Theorem;205
8.2.3; Vacuum Approximation;208
8.2.4; Force-Free Grad--Shafranov Equation in the Kerr Metric;213
8.2.5; Particle Generation;218
8.3; Energy Release Mechanism;220
8.3.1; Blandford--Znajek Process;220
8.3.2; Physical Intermezzo---Black Hole Thermodynamics;224
8.4; Black Hole Magnetosphere Structure;227
8.4.1; General Properties;227
8.4.2; Exact Solutions;228
8.4.3; Magnetosphere Models;236
8.5; Conclusion;241
9;4 Full MHD Version---General Properties ;243
9.1; Physical Introduction---Magnetohydrodynamic Waves;243
9.2; Relativistic Flows in the Kerr Metric;248
9.2.1; Integrals of Motion;248
9.2.2; Singular Surfaces;253
9.2.3; Grad--Shafranov Equation;257
9.3; Special Cases;260
9.3.1; Nonrelativistic Flows;260
9.3.2; Anisotropic Pressure;264
9.4; General Properties;268
9.4.1; Some Useful Relations;268
9.4.2; Alfvén Surface;272
9.4.3; Fast Magnetosonic Surface---Relativistic Flows;274
9.4.4; Fast Magnetosonic Surface---Nonrelativistic Flows;282
9.4.5; Behavior of the Solution at Large Distances;288
9.4.6; Behavior of the Solution in the Vicinity of the Horizon;295
10;5 Full MHD Version---Particle Acceleration and Collimation;301
10.1; Astrophysical Introduction;301
10.1.1; Radio Pulsars;301
10.1.2; Active Galactic Nuclei;305
10.1.3; Young Stellar Objects;309
10.1.4; Microquasars, Cosmological Gamma-Bursters, etc.;312
10.2; Cylindrical Flows;314
10.2.1; Cylindrical Jets---The Force-Free Approximation;314
10.2.2; Relativistic Jets;319
10.2.3; Nonrelativistic Jets;335
10.2.4; General Properties and Application;341
10.3; Cold Quasimonopole Outflows;343
10.3.1; Relativistic Slowly Rotating Outflows;343
10.3.2; Relativistic Outflows with Differential Rotation;347
10.3.3; Nonrelativistic Slowly Rotating Outflows;350
10.3.4; Relativistic Fast-Rotating Outflow;352
10.3.5; Relativistic Outflow in the Parabolic Magnetic Field;358
10.3.6; General Properties;362
10.4; Black Hole Magnetosphere;363
10.4.1; Slowly Rotating Black Hole Surrounded by a Thin Disk;363
10.4.2; Slowly Rotating Black Hole Surrounded by a Rotating Shell;371
10.5; Other Methods;376
10.5.1; Analysis of the Algebraic Relations;376
10.5.2; Self-Similar Solutions;380
10.5.3; Computational Results;387
10.6; Conclusion;395
11;6 Conclusion ;397
12;A From Euler to Grad--Shafranov---The Simplest Way;400
13;B Nonrelativistic Force-Free Grad--Shafranov Equation;402
14;C Part-Time Job Pulsars;404
15;D Special Functions;406
15.1; Legendre Polynomials;406
15.2; Bessel Functions;407
15.3; Hypergeometric Function;408
16;E List of Symbols;410
17;References;416
18;Index;438