MHD Flows in Compact Astrophysical Objects (eBook)

Preface 7
Acknowledgments 11
Contents 13
Acronyms 17
Introduction 19
1 Hydrodynamical Limit---Classical Problems of Accretion and Ejection 23
Astrophysical Introduction---Accretion onto Compact Objects 24
Accretion Disks 24
Standard Model 28
ADAF, ADIOS, etc. 31
Main Properties of Transonic Hydrodynamical Flows 33
Basic Equations 33
Spherically Symmetric Flow 35
Potential Plane Flow 39
Nonrelativistic Axisymmetric Stationary Flows 46
Basic Equations 46
Mathematical Intermezzo---the Covariant Approach 48
Two-Dimensional Flow Structure 49
Bondi--Hoyle Accretion 58
Outflow from a Slowly Rotating Star 62
Axisymmetric Stationary Flows in the Vicinity of a Black Hole 71
Physical Intermezzo---(3+1)-Splitting in the Kerr Metric 71
Basic Equations 75
Exact Solutions 81
Bondi--Hoyle Accretion---The Relativistic Regime 84
Accretion onto a Slowly Rotating Black Hole 87
Accretion of Matter with Small Angular Momentum 89
Thin Transonic Disk 95
Conclusion 106
2 Force-Free Approximation---The Magnetosphere of Radio Pulsars 107
Astrophysical Introduction 107
Basic Physical Processes 111
Vacuum Approximation 111
Particle Generation in the Strong Magnetic Field 116
Magnetosphere Structure 119
Secondary Plasma Generation 123
``Inner Gap'' 123
Neutron Star Surface 128
Propagation of -Quanta in the Superstrong Magnetic Field 129
General Relativity Effects 130
Particle Generation in the Magnetosphere 132
``Hollow Cone'' Model 134
Secondary Plasma Generation---``Outer Gap'' 138
Pulsar Equation 138
Force-Free Approximation. The Magnetization Parameter 138
Integrals of Motion 140
Grad--Shafranov Equation 143
Mathematical Intermezzo---Quasistationary Formalism 146
Energy Losses of Radio Pulsars 149
Current Loss Mechanism 149
Slowing Down of Inclined and Orthogonal Rotators 153
Magnetosphere Structure 161
Exact Solutions 161
Magnetosphere Structure with Longitudinal Currents 180
Magnetosphere Models 187
Conclusion 193
3 Force-Free Approximation---The Black Hole Magnetosphere 194
Astrophysical Introduction---The Central Engine in Active Galactic Nuclei 194
Possible Mechanisms of Black Hole Formation 194
Nature of Activity and Variability 1
Magnetized Accretion Disk 198
Regular Magnetic Field Generation 200
Basic Equations 203
(3+1)-Splitting for the Electromagnetic Field 203
``No Hair'' Theorem 205
Vacuum Approximation 208
Force-Free Grad--Shafranov Equation in the Kerr Metric 213
Particle Generation 218
Energy Release Mechanism 220
Blandford--Znajek Process 220
Physical Intermezzo---Black Hole Thermodynamics 224
Black Hole Magnetosphere Structure 227
General Properties 227
Exact Solutions 228
Magnetosphere Models 236
Conclusion 241
4 Full MHD Version---General Properties 243
Physical Introduction---Magnetohydrodynamic Waves 243
Relativistic Flows in the Kerr Metric 248
Integrals of Motion 248
Singular Surfaces 253
Grad--Shafranov Equation 257
Special Cases 260
Nonrelativistic Flows 260
Anisotropic Pressure 264
General Properties 268
Some Useful Relations 268
Alfvén Surface 272
Fast Magnetosonic Surface---Relativistic Flows 274
Fast Magnetosonic Surface---Nonrelativistic Flows 282
Behavior of the Solution at Large Distances 288
Behavior of the Solution in the Vicinity of the Horizon 295
5 Full MHD Version---Particle Acceleration and Collimation 301
Astrophysical Introduction 301
Radio Pulsars 301
Active Galactic Nuclei 305
Young Stellar Objects 309
Microquasars, Cosmological Gamma-Bursters, etc. 312
Cylindrical Flows 314
Cylindrical Jets---The Force-Free Approximation 314
Relativistic Jets 319
Nonrelativistic Jets 335
General Properties and Application 341
Cold Quasimonopole Outflows 343
Relativistic Slowly Rotating Outflows 343
Relativistic Outflows with Differential Rotation 347
Nonrelativistic Slowly Rotating Outflows 350
Relativistic Fast-Rotating Outflow 352
Relativistic Outflow in the Parabolic Magnetic Field 358
General Properties 362
Black Hole Magnetosphere 363
Slowly Rotating Black Hole Surrounded by a Thin Disk 363
Slowly Rotating Black Hole Surrounded by a Rotating Shell 371
Other Methods 376
Analysis of the Algebraic Relations 376
Self-Similar Solutions 380
Computational Results 387
Conclusion 395
6 Conclusion 397
A From Euler to Grad--Shafranov---The Simplest Way 400
B Nonrelativistic Force-Free Grad--Shafranov Equation 402
C Part-Time Job Pulsars 404
D Special Functions 406
Legendre Polynomials 406
Bessel Functions 407
Hypergeometric Function 408
E List of Symbols 410
References 416
Index 438