Magnetohydrodynamics in binary stars

Title......Page 1
Preface......Page 2
Table of Contents ......Page 4
1.1 Close Binaries ......Page 9
1.2 Magnetic Fields in Binaries ......Page 12
1.3 Magnetohydrodynamics ......Page 13
1.4 Types of Problems ......Page 14
2.1 Introduction ......Page 17
2.2.1 Plasma fluids ......Page 18
2.2.2 Maxwell's equations ......Page 23
2.2.3 The induction equation ......Page 25
2.2.4 Magnetic force ......Page 31
2.2.5 The magneto-fluid equations ......Page 33
2.2.6 Hydromagnetic waves ......Page 40
2.2.7 The free-fall Alfven radius ......Page 45
2.2.8 Poloidal and toroidal representation of B ......Page 46
2.2.9 Decay modes of B in a conductor ......Page 48
2.2.10 Magnetic diffusivity ......Page 50
2.3.1 Field generation ......Page 53
2.3.2 Types of mean-field dynamos ......Page 57
2.4.1 The Roche model ......Page 58
2.4.2 Mass transfer ......Page 64
2.4.3 Accretion discs ......Page 68
2.5 Spin Dynamics ......Page 81
3.1 The Discovery of AM Herculis ......Page 87
3.2 Other Systems ......Page 89
3.3 Synchronous Rotation of the Primary ......Page 92
3.4 MHD Problems ......Page 93
4.1 Induction of Currents in the Secondary ......Page 95
4.2 Solution of the Diffusion Equation ......Page 97
4.3 The Dissipation Torque ......Page 103
4.4 Asymptotic Synchronization Times ......Page 109
4.5 Discussion ......Page 111
5.1 The Effect of Magnetic Force ......Page 113
5.2 Angular Momentum Transfer ......Page 115
5.3.1 The synchronous case ......Page 123
5.3.2 The asynchronous case ......Page 129
5.4 Partial Field Channelling ......Page 131
5.5 Discussion ......Page 133
6.1 Non-Dissipative Torques ......Page 135
6.2 Accretion Versus Magnetism in Two-Dimensions ......Page 136
6.3.1 Orientations with zero torque ......Page 140
6.3.2 Stability of the synchronous state ......Page 142
6.3.3 Stable synchronous orientations ......Page 147
6.4 Quadrupolar Magnetic Fields ......Page 148
6.5.1 The synchronous state ......Page 149
6.5.2 Stability of the synchronous state ......Page 153
6.5.3 Distribution of synchronous states ......Page 157
6.6 Orbital Torques ......Page 159
6.7 Conclusions ......Page 161
7.1 The Combined Effect of Torques ......Page 163
7.2 The Effect of a Locking Mechanism ......Page 167
7.3 Conclusions ......Page 169
8.2.1 Discovery and classification ......Page 171
8.3.1 Discovery and classification ......Page 173
8.3.2 Systems with accretion discs ......Page 174
8.3.3 Neutron star spin evolution ......Page 175
8.4 MHD Problems ......Page 176
9.1 Introduction ......Page 179
9.2.1 The magnetic disc equations ......Page 180
9.2.2 Vertical equilibrium and angular momentum advection ......Page 187
9.2.3 Dissipation and radiative transfer ......Page 189
9.2.4 Disc solution with unspecified /etha ......Page 191
9.2.5 Disc structure with specified /etha ......Page 193
9.2.6 Discussion ......Page 195
9.3.1 The magneto-viscous equations ......Page 196
9.3.2 Solutions and viscous instability ......Page 197
9.4 Conclusions ......Page 199
10.1 Introduction ......Page 201
10.2.1 The kinematic condition ......Page 202
10.2.2 Magnetic buoyancy diffusivity ......Page 203
10.2.3 Turbulent diffusivity ......Page 204
10.3.1 Constant diffusivity ......Page 205
10.3.2 Variable diffusivity ......Page 208
10.4.1 Magnetic and accretion torques ......Page 210
10.4.2 Magnetic buoyancy ......Page 211
10.4.3 Turbulent diffusion ......Page 212
10.5.1 Magnetic buoyancy ......Page 213
10.5.2 Turbulent diffusion ......Page 214
10.6 Conclusions ......Page 216
11.1 Introduction ......Page 219
11.2.1 Turbulent /alpha/omega-dynamos in thin discs ......Page 221
11.2.2 Dynamo action by internal waves ......Page 229
11.2.3 Shear instabilities in weakly magnetized discs ......Page 230
11.2.4 Disc dynamos with hydromagnetic turbulence ......Page 235
11.3.1 Magnetic disc equations ......Page 239
11.3.2 Vertical integrals ......Page 246
11.3.3 Thermal energy transport ......Page 248
11.3.4 The dynamo ......Page 249
11.3.5 Magnetic disc structure ......Page 252
11.3.6 Conclusions ......Page 253
11.4.1 Vertical integrals ......Page 254
11.4.2 Disc solutions ......Page 255
11.5 Discussion ......Page 256
12.1 Introduction ......Page 259
12.2.1 Angular momentum transport ......Page 260
12.2.2 The wind flow ......Page 264
12.2.3 The braking torque ......Page 266
12.2.4 A simple field model ......Page 267
12.3.1 Orbital angular momentum loss and mass transfer ......Page 276
12.3.2 The wind mass loss rate and the thermal time-scale ......Page 281
12.3.3 Linear dynamo law ......Page 282
12.3.4 Inverse Rossby number law ......Page 284
12.3.5 A non-linear law ......Page 285
12.3.6 The period gap ......Page 287
12.3.7 AM Herculis systems ......Page 291
12.4.1 The wind source ......Page 292
12.4.2 Wind flow stability ......Page 295
12.5 Discussion ......Page 301
C Operators in Orthogonal Coordinates ......Page 303
C.2 Cylindrical coordinates ......Page 304
D.2 Rate of strain tensor in cylindrical coordinates ......Page 305
E.2 Associated Legendre functions ......Page 306
G Gravitational Torque on a Spheroid ......Page 308