Magnetic Processes in Astrophysics

In this work the authors draw upon their expertise in geophysical and astrophysical MHD to explore the motion of electrically conducting fluids, the so–called dynamo effect, and describe the similarities and differences between different magnetized objects. They also explain why magnetic fields are crucial to the formation of the stars, and discuss promising experiments currently being designed to investigate some of the relevant physics in the laboratory. This interdisciplinary approach will appeal to a wide audience in physics, astrophysics and geophysics. This second edition covers such additional topics as small–scale dynamos, while also presenting the latest results and experiments. INDICE: Preface IX 1 Differential Rotation of Stars 1 1.1 Solar Observations 2 1.1.1 The Rotation Law 2 1.1.2 Torsional Oscillations 5 1.1.3 Meridional Flow 6 1.2 Stellar Observations 9 1.2.1 Rotational Evolution 9 1.2.2 Differential Rotation 11 1.3 The Reynolds Stress 13 1.3.1 The Λ Effect 14 1.3.1.1 Numerical Simulations 15 1.3.1.2 Quasi–linear Theory of the Λ Effect 19 1.3.2 Eddy Viscosities 22 1.4 The Meridional Flow 24 1.4.1 Origin of the Meridional Flow 26 1.4.2 The Differential Temperature 28 1.4.3 Advection–Dominated Solar Dynamo 32 1.5 The Sun 35 1.5.1 Sun without Λ Effect 38 1.5.2 Sun without Baroclinic Flow 39 1.5.3 Global Simulations 40 1.6 Individual Stars 42 1.6.1 Two Most Stars 44 1.6.2 Young Stars 46 1.7 Dwarfs & Giants 50 1.7.1 M Dwarfs 50 1.7.2 F Stars 51 1.7.3 Giants 55 1.8 Differential Rotation along the Main Sequence 58 2 Radiation Zones: Magnetic Stability and Rotation 63 2.1 The Watson Problem 65 2.1.1 The Stability Equations 65 2.1.2 2D Approximation 67 2.1.3 Stability Maps 69 2.2 The Magnetic Tachocline 72 2.2.1 A Planar Model 72 2.2.2 Magnetic Field Confinement by Meridional Flow 75 2.2.3 Tachocline Model in Spherical Geometry 79 2.3 Stability of Toroidal Fields 82 2.3.1 Equations 82 2.3.2 Nonexistence of 2D Magnetic Instabilities 85 2.3.3 No Diffusion 86 2.3.4 Growth Rates, Drift Rates and Radial Mixing 88 2.4 Stability of Thin Toroidal Field Belts 91 2.4.1 Rigid Rotation 92 2.4.2 Differential Rotation 93 2.4.3 High Fourier Modes 94 2.5 Helicity and Dynamo Action 94 2.5.1 Helicity and Alpha Effect 95 2.5.2 Dynamo Action 100 2.6 Ap Star Magnetism 103 2.7 The Shear–Hall Instability (SHI) 109 3 Quasi–linear Theory of Driven Turbulence 115 3.1 The Turbulence Pressure 116 3.2 The η–Tensor 124 3.2.1 Rotating Turbulence 124 3.2.2 Nonrotating Turbulence but Helical Background Fields 128 3.3 Kinetic Helicity and DIV–CURL Correlation 131 3.4 Cross–Helicity 134 3.4.1 Theory 135 3.4.2 Simulations and Observations 136 3.5 Shear Flow Electrodynamics 138 3.5.1 Hydrodynamic Stability of Shear Flow 138 3.5.2 The Magnetic–Diffusivity Tensor 140 3.5.3 Dynamos without Stratification 141 3.6 The Alpha Effect 143 3.6.1 Helical–driven Turbulence 143 3.6.2 Shear Flow 145 3.6.3 Shear–Dynamos with Turbulence–Stratification 149 3.6.4 Alpha Effect by Density Stratification 150 3.7 The Current Helicity 153 4 The Galactic Dynamo 157 4.1 Magnetic Fields of Galaxies 157 4.2 Interstellar Turbulence 161 4.2.1 Hydrostatic Equilibrium and Interstellar Turbulence 162 4.2.2 Alpha Effect by Supernova Explosions 165 4.2.3 The Advection Problem 168 4.3 Dynamo Models 170 4.3.1 Linear Models 171 4.3.2 Nonlinear Dynamo Models 173 4.4 Magnetic Instabilities 175 4.4.1 The Seed Field Problem 175 4.4.2 Magnetorotational Instability 176 4.4.3 Tayler Instability 180 5 The Magnetorotational Instability (MRI) 185 5.1 Taylor–Couette Flows 185 5.2 The Stratorotational Instability (SRI) 188 5.2.1 The AngularMomentum Transport 192 5.2.2 Electromotive Force by Magnetized SRI 195 5.3 The Standard Magnetorotational Instability (SMRI) 198 5.3.1 The Equations 200 5.3.1.1 The Rayleigh Limit 202 5.3.1.2 Pseudo–Kepler Rotation 203 5.3.2 Nonaxisymmetric Modes 204 5.3.3 Wave Numbers 206 5.3.4 Nonlinear Simulations 208 5.3.5 The AngularMomentum Transport 211 5.4 Diffusive Kepler Disks 214 5.5 MRI with Hall Effect 216 5.6 The Azimuthal MRI (AMRI) 218 5.6.1 The Equations 219 5.6.2 The Instability Map 223 5.6.3 Different Scalings with Pm 224 5.6.4 Nonlinear Results 224 5.6.5 The AMRI Experiment 228 5.7 Helical Magnetorotational Instability (HMRI) 231 5.7.1 From AMRI to HMRI 231 5.7.2 Nonaxisymmetric Modes for small Pm 236 5.7.3 Pseudo–Kepler Rotation 236 5.7.4 The Frequencies 237 5.8 Laboratory Experiment Promise 238 5.8.1 Experimental Results 240 5.8.2 Endplate Effects 242 5.8.3 Promise 2 244 6 The Tayler Instability (TI) 247 6.1 Stationary Fluids 249 6.2 Experiment Gate 254 6.3 Rotating Fluids 256 6.3.1 Rigid Rotation 257 6.3.2 Differential Rotation 258 6.3.3 Eddy Viscosity and Turbulent Diffusivity 262 6.3.3.1 Eddy Viscosity 262 6.3.3.2 Turbulent Diffusivity 263 6.3.3.3 Mixing of Chemicals 265 6.4 The Tayler Generator 267 6.5 Helical Background Fields and Alpha Effect 272 6.5.1 Helical Fields with Weak Axial Current 272 6.5.2 Uniform Electric Current 275 6.5.3 Alpha Effect 278 6.5.3.1 The Helicities 278 6.5.3.2 The Alpha Effect 280 6.6 TI with Hall Effect 282 7 Magnetic Spherical Couette Flow 287 7.1 Stewartson Layers 287 7.2 Shercliff Layers 289 7.3 Finite Re in an Axial Field 296 7.3.1 Numerics 296 7.3.2 The Maryland Experiment 302 7.3.3 The Princeton Experiment 305 7.4 The Grenoble DTS Experiment 307 7.5 Other Waves and Instabilities 313 7.5.1 Inertial Oscillations 313 7.5.2 Torsional Oscillations 314 7.5.3 Alfvén Waves 316 7.5.4 The Magnetostrophic MRI 317 7.6 Linear Combinations of Axial and Dipolar Fields 318 7.7 Dynamo Action 321 References 327 Index 341

• ISBN: 978-3-527-41034-7
• Editorial: Wiley VCH
• Encuadernacion: Cartoné
• Páginas: 356
• Fecha Publicación: 04/09/2013
• Nº Volúmenes: 1
• Idioma: Inglés