THE MAGNETIC UNIVERSE - GEOPHYSICAL AND ASTROPHYSICAL DYNAMO THEORY

Magnetism is one of the most pervasive features of the Universe, with planets, stars and entire galaxies all having associated magnetic fields. All of these fields are generated by the motion of electrically conducting fluids, the so-called dynamo effect. The precise details of what drives the motion, and indeed what the fluid consists of, differ widely though. In this work the authors draw upon their expertise in geophysical and astrophysical MHD to explore some of these phenomena, and describe the similarities and differences between different magnetized objects. They also explain why magnetic fields are crucial in the formation of the stars, and discuss promising experiments currently being designed to study some of the relevant physics in the laboratory. This interdisciplinary approach makes the book appealing to a wide audience in physics, astrophysics and geophysics.

Güenther Ruediger received his PhD from the University of Jena, Germany. He is Professor at the Astrophysical Institute Potsdam, and lectures at the University of Potsdam. He worked at the University of Goettingen, and the High Altitude Observatory in Boulder, Colorado. He is also a former visiting professor at the University of Newcastle upon Tyne, England.

Rainer Hollerbach is Reader in Applied Mathematics at the University of Glasgow, Scotland. He has a PhD in Geophysics from the University of California, San Diego. He recently spent a year in Germany as a Research Fellow of the Alexander von Humboldt Foundation.

Preface.

1 Introduction.

2 Earth and Planets.

2.1 Observational Overview.

2.1.1 Reversals.

2.1.2 Other Time-Variability.

2.2 Basic Equations and Parameters.

2.2.1 Anelastic and Boussinesq Equations.

2.2.2 Nondimensionalization.

2.3 Magnetoconvection.

2.3.1 Rotationor Magnetism Alone.

2.3.2 Rotation and Magnetism Together.

2.3.3 Weakversus Strong Fields.

2.3.4 Oscillatory Convection Modes.

2.4 Taylor’s Constraint.

2.4.1 Taylor’s Original Analysis.

2.4.2 Relaxation of Ro=E=0.

2.4.3 Taylor States versus Ekman States.

2.4.4 From Ekman States to Taylor States.

2.4.5 Torsional Oscillations.

2.4.6 αΩ-Dynamos.

2.4.7 Taylor’s Constraint in the Anelastic Approximation.

2.5 Hydromagnetic Waves.

2.6 The Inner Core.

2.6.1 Stewartson Layers on C.

2.6.2 Nonaxisymmetric Shear Layers on C.

2.6.3 Finite Conductivity of the Inner Core.

2.6.4 Rotation of the Inner Core.

2.7 Numerical Simulations.

2.8 Magnetic Instabilities.

2.9 Other Planets.

2.9.1 Mercury, Venus and Mars.

2.9.2 Jupiter’s Moons.

2.9.3 Jupiter and Saturn.

2.9.4 Uranus and Neptune.

3 Differential Rotation Theory.

3.1 The Solar Rotation.

3.1.1 Torsional Oscillations.

3.1.2 Meridional Flow.

3.1.3 Ward’s Correlation.

3.1.4 Stellar Observations.

3.2 Angular Momentum Transport in Convection Zones.

3.2.1 The Taylor Number Puzzle.

3.2.2 The Λ-Effect.

3.2.3 The Eddy Viscosity Tensor.

3.2.4 Mean-Field Thermodynamics.

3.3 Differential Rotation and Meridional Circulation for Solar-Type Stars.

3.4 Kinetic Helicity and the DIV-CURL-Correlation.

3.5 Overshoot Region and the Tachocline.

3.5.1 The NIRVANA Code.

3.5.2 Penetration into the Stable Layer.

3.5.3 A Magnetic Theory of the Solar Tachocline.

4 The Stellar Dynamo.

4.1 The Solar-Stellar Connection.

4.1.1 The Phase Relation.

4.1.2 The Nonlinear Cycle.

4.1.3 Parity.

4.1.4 Dynamo-related Stellar Observations.

4.1.5 The Flip-Flop Phenomenon.

4.1.6 More Cyclicities.

4.2 The α-Tensor.

4.2.1 The Magnetic-Field Advection.

4.2.2 The Highly Anisotropic α-Effect.

4.2.3 The Magnetic Quenching of the α-Effect.

4.2.4 Weak-Compressible Turbulence.

4.3 Magnetic-Diffusivity Tensor and η-Quenching.

4.3.1 The Eddy Diffusivity Tensor.

4.3.2 Sunspot Decay.

4.4 Mean-Field Stellar Dynamo Models.

4.4.1 The α2-Dynamo.

4.4.2 The αΩ-Dynamo for Slow Rotation.

4.4.3 Meridional Flow Influence.

4.5 The Solar Dynamo.

4.5.1 The Overshoot Dynamo.

4.5.2 The Advection-Dominated Dynamo.

4.6 Dynamos with Random α.

4.6.1 Aturbulence Model.

4.6.2 Dynamo Models with Fluctuating α-Effect.

4.7 Nonlinear Dynamo Models.

4.7.1 Malkus-Proctor Mechanism.

4.7.2 α-Quenching.

4.7.3 Magnetic Saturation by Turbulent Pumping.

4.7.4 η-Quenching.

4.8 Λ-Quenching and Maunder Minimum.

5 The Magnetorotational Instability (MRI).

5.1 Star Formation.

5.1.1 Molecular Clouds.

5.1.2 The Angular Momentum Problem.

5.1.3 Turbulence and Planet Formation.

5.2 Stability of Differential Rotation in Hydrodynamics.

5.2.1 Combined Stability Conditions.

5.2.2 Sufficient Condition for Stability.

5.2.3 Numerical Simulations.

5.2.4 Vertical Shear.

5.3 Stability of Differential Rotation in Hydromagnetics.

5.3.1 Ideal MHD.

5.3.2 Baroclinic Instability.

5.4 Stability of Differential Rotation with Strong Hall Effect.

5.4.1 Criteria of Instability of Protostellar Disks.

5.4.2 Growth Rates.

5.5 Global Models.

5.5.1 A Spherical Model with Shear.

5.5.2 A Global Disk Model.

5.6 MRI of Differential Stellar Rotation.

5.6.1 T Tauri Stars (TTS).

5.6.2 The Ap-Star Magnetism.

5.6.3 Decay of Differential Rotation.

5.7 Circulation-Driven Stellar Dynamos.

5.7.1 The Gailitis Dynamo.

5.7.2 Meridional Circulation plus Shear.

5.8 MRI in Kepler Disks.

5.8.1 The Shearing Box Model.

5.8.2 A Global Disk Dynamo?

5.9 Accretion-Disk Dynamo and Jet-Launching Theory.

5.9.1 Accretion-Disk Dynamo Models.

5.9.2 Jet-Launching.

5.9.3 Accretion-Disk Outflows.

5.9.4 Disk-Dynamo Interaction.

6 The Galactic Dynamo.

6.1 Magnetic Fields of Galaxies.

6.1.1 Field Strength.

6.1.2 Pitch Angles.

6.1.3 Axisymmetry.

6.1.4 Two Exceptions: Magnetic Torus and Vertical Halo Fields.

6.1.5 The Disk Geometry.

6.2 Nonlinear Winding and the Seed Field Problem.

6.2.1 Uniform Initial Field.

6.2.2 Seed Field Amplitude and Geometry.

6.3 Interstellar Turbulence.

6.3.1 The Advection Problem.

6.3.2 Hydrostatic Equilibrium and Interstellar Turbulence.

6.4 From Spheres to Disks.

6.4.1 1DdynamoWaves.

6.4.2 Oscillatory vs. Steady Solutions.

6.5 Linear 3DModels.

6.6 The Nonlinear Galactic Dynamo with Uniform Density.

6.6.1 The Model.

6.6.2 The Influences of Geometry and Turbulence Field.

6.7 Density Wave Theory and Swing Excitation.

6.7.1 Density Wav Theory.

6.7.2 The Short-Wave Approximation.

6.7.3 Swing Excitation in Magnetic Spirals.

6.7.4 Nonlocal Density Wave Theory in Kepler Disks.

6.8 Mean-Field Dynamos with Strong Halo Turbulence.

6.8.1 Nonlinear 2D Dynamo Model with Magnetic Supported Vertical Stratification.

6.8.2 Nonlinear 3D Dynamo Models for Spiral Galaxies.

6.9 New Simulations: Macroscale and Microscale.

6.9.1 Particle-Hydrodynamics for the Macroscale.

6.9.2 MHD for the Microscale.

6.10 MRI in Galaxies.

7 Neutron Star Magnetism.

7.1 Introduction.

7.2 Equations.

7.3 Without Stratification.

7.4 With Stratification.

7.5 Magnetic-Dominated Heat Transport.

7.6 White Dwarfs.

8 The Magnetic Taylor–Couette Flow.

8.1 History.

8.2 The Equations.

8.3 Results without Hall Effect.

8.3.1 Subcritical Excitation for Large Pm.

8.3.2 The Rayleigh Line (a = 0) and Beyond.

8.3.3 Excitation of Nonaxisymmetric or Oscillatory Modes.

8.3.4 Wave Number and Drift Frequencies.

8.4 Results with Hall Effect.

8.4.1 Hall Effect with Positive Shear.

8.4.2 Hall Effect with Negative Shear.

8.4.3 A Hall-Driven Disk-Dynamo?

8.5 Endplate effects.

8.6 Water Experiments.

8.7 Taylor–Couette Flow as Kinematic Dynamo.

9 Bibliography.

Index.