Turbulence and Magnetic Fields in Astrophysics (Lecture Notes in Physics, 614)

✍ Scribed by Edith Falgarone (editor), Thierry Passot (editor)

• Publisher: Springer
• Year: 2003
• Tongue: English
• Leaves: 454
• Edition: 2003
• Category: Library

✦ Synopsis

This book contains review articles of most of the topics addressed at the conf- ence on Simulations of Magnetohydrodynamic turbulence in astrophysics: recent achievements and perspectives which took place from July 2 to 6, 2001 at the Institut Henri Poincar´e in Paris. We made the choice to publish these lectures in a tutorial form so that they can be read by a broad audience. As a result, this book does not give an exhaustive view of all the subjects addressed during the conference. The main objective of this workshop which gathered about 90 scientists from di?erent ?elds, was to present and confront recent results on the topic of t- bulence in magnetized astrophysical environments. A second objective was to discuss the latest generation of numerical codes, such as those using adaptive mesh re?nement (AMR) techniques. During a plenary discussion at the end of the workshop discussions were held on several topics, often at the heart of vivid controversies. Topics included the timescale for the dissipation of magneto-hydrodynamical (MHD) turbulence, the role of boundary conditions, the characteristics of imbalanced turbulence, the validity of the polytropic approach to Alfv´en waves support within interst- lar clouds, the source of turbulence inside clouds devoid of stellar activity, the timescale for star formation, the Alfv´en Mach number of interstellar gas motions, the formation process for helical ?elds in the interstellar medium. The impact of small upon large scales was also discussed.

✦ Table of Contents

Chapter 1
1 Introduction
2 Properties of Magnetohydrodynamics
2.1 The Ideal Invariants
2.2 Elsasser Variables
3 Phenomenologies of MHD Turbulence
3.1 Kolmogorov Picture (K41)
3.2 Iroshnikov-Kraichnan Picture (IK)
3.3 Goldreich-Sridhar Picture (GS)
4 Intermittency
4.1 She-Leveque Model (SL)
5 Energy Decay
6 Experimental and Numerical Evidence
6.1 Numerics
6.2 Energy Decay
6.3 Energy Spectra
6.4 Intermittency
6.5 Local Anisotropy
7 Summary
References
Chapter 2
1 Introduction
2 Reduced MHD
2.1 Equations and Timescale Conditions
2.2 Anisotropy and Cascades
2.3 Relevance in the Corona
3 Coronal Heating Models
3.1 Coronal Holes
3.2 Coronal Loops
4 Conclusions
Appendix A: Alternative Derivations of RMHD
Appendix B: Self-consistency of RMHD Simulations
Acknowledgments
References
Chapter 3
1 Introduction
2 Observational Data
2.1 Solar Wind
2.2 Electron Density Statistics
2.3 Velocity and Density Statistics from Spectral Lines
2.4 Magnetic Field Statistics
3 Theoretical Approaches to MHD Turbulence
3.1 Iroshnikov-Kraichnan Theory
3.2 Anisotropy
3.3 Goldreich-Sridhar Theory
3.4 Weak/Intermediate Turbulence
4 Testing and Extending Incompressible Theory
4.1 Scaling Laws
4.2 Intermittency
5 Damping of Turbulence
5.1 Imbalanced Cascade
5.2 Ion-Neutral Damping: A New Regime of Turbulence
6 Compressible Turbulence
6.1 Alfven, Slow, and Fast Modes
6.2 Theoretical Considerations
6.3 Coupling of MHD Modes and Scaling of Alfven Modes
6.4 Scaling of the Slow Modes
6.5 Scaling of the Fast Modes
7 Astrophysical Implications
7.1 Cosmic Ray Propagation
7.2 Grain Dynamics
7.3 Turbulence in HII Regions
7.4 Tiny-Scale Atomic Structures
7.5 Magnetic Reconnection
7.6 Support and Compression of Molecular Clouds
7.7 Heating of Diffuse Ionized Gas
8 Observational Tests
8.1 Is the Big Power Law Real?
8.2 Does Turbulence Reveal Magnetic Field Direction?
8.3 How Else Can We Compare Observations and Simulations?
9 Summary
Acknowledgments
References
Chapter 4
1 Introduction
2 The Magnetic Induction Equation: Theory and Tests
2.1 Induction Equation and Consequences
2.2 Helicity Conservation in the ZEUS Code
3 Parameter Space
3.1 Macroscopic Parameters
3.2 Microscopic Parameters
3.3 Implications for Numerical Techniques
4 Results from Theories and Simulations
4.1 Turbulent Amplification ofa Weak Field
4.2 Magnetic Fluctuations
4.3 Intermittency: Current Sheets and Flux Tubes
4.4 Dynamical Effects of Turbulence
5 Ambipolar Drift
6 Summary and Future Agenda
Acknowledgements
References
Chapter 5
1 Introduction
2 Numerical Principles
3 Adaptive Mesh Refinement
4 Code Tests and Application
4.1 AMR-MHD Test Problems
4.2 Application: Rise of Isolated Flux Tubes in Disks
References
Chapter 6
1 Introduction
2 Observational Techniques
2.1 Polarization
2.2 Tracers of B_{||}
2.3 Tracers of B_{perp}
3 Large-Scale Magnetic Fields
3.1 Starlight Polarization
3.2 Synchrotron Emission
3.3 Pulsars
3.4 H I Zeeman
3.5 Galactic Center
3.6 Other Galaxies
3.7 Recent Developments
4 Magnetic Fields and Star Formation
4.1 Theoretical Framework
4.2 Zeeman Results
4.3 Field Morphology
5 Conclusions
Acknowledgments
References
Chapter 7
1 Introduction
2 Decaying Turbulence
3 Driven Turbulence
4 Self-gravitating Turbulence
5 Characterization ofT urbulence
5.1 Wavelet Transforms
5.2 Clump Characterization
6 Supernova-Driven Turbulence
7 Conclusions
Acknowledgements
References
Chapter 8
1 Introduction
2 Review of the Linear Theory and the Role of the Ratio of Cooling Time to Crossing Time
2.1 Entropy Perturbations
2.2 Adiabatic Perturbations
2.3 Entropy vs. Adiabatic Fluctuations
2.4 The Magnetic Case
3 Nonlinear Evolution of Entropy Perturbations
4 The Case of Velocity Fluctuations
5 The Magnetic Pressure in Turbulent Media
6 TI in Models of the ISM
6.1 Numerical Considerations
6.2 Results
6.3 Discussion and Caveats
7 Summary and Conclusions
Acknowledgements
References
Chapter 9
1 Introduction
2 Density and Column Density Statistics
3 Clumps in Turbulent Clouds
4 Linewidth-Size Relationships
5 Polarization as a Magnetic Field Diagnostic
6 Summary
Acknowledgements
References
Chapter 10
1 Introduction
2 Supernova Driving of the Interstellar Medium
3 Turbulent Cascade of the Interstellar Medium
3.1 Molecular Clouds as Part of a Turbulent Cascade
3.2 Supersonic Turbulent Cascades
3.3 Super-Alfvenic Conditions
3.4 The Magnetic Flux Problem
3.5 Gravitationally Bound and Unbound Clouds
3.6 Power Laws and Equipartition
4 A New Analytical Theory of Supersonic Turbulence
5 Star Formation and the Initial Mass Function
5.1 The Initial Mass Function
5.2 Mass Distribution of Prestellar Cores in Numerical Simulations
6 Conclusions
Acknowledgments
References
Chapter 11
1 Introduction
2 Self-gravity in Pressure-Truncated Isothermal Molecular Clouds
3 Turbulence Simulations
4 The Ostriker Model and Pressure-Truncated Hydrostatic Filaments
5 Virial Analysis of Magnetized Filamentary Molecular Clouds
5.1 The Virial Equation Applied to Magnetized Filaments
5.2 Observational Considerations
6 The Radial Structure of Filaments Threaded by Helical Magnetic Fields
6.1 Basic Equations
6.2 Scaling Arguments and the Bonnor-Ebert Stability of Magnetized Filaments
6.3 Solutions
6.4 The r^{-2} Density Profile: An Analytical Limit
7 The Dynamics and Radial Stability of Filamentary Molecular Clouds
7.1 Radial Equation of Motion
7.2 The Radial Stability of Filamentary Molecular Clouds
8 The Global Topology of the Magnetic Field in Filamentary Clouds
8.1 Isolated Filaments
8.2 Current Networks and Open Circuits
9 Fragmentation of Filaments
9.1 Equations and Boundary Conditions
9.2 Results of the Stability Analysis
9.3 Dynamical Consequences of Fragmentation
10 The Shapes of Cores and Bok Globules
10.1 Prolate, Oblate, or Triaxial?
10.2 Theoretical Models
11 Sub-millimetre Polarimetry
11.1 What Can We Learn from Polarimetry?
11.2 Polarization Maps of the Fiege & Pudritz Model
12 Discussion
Acknowledgements
References
Chapter 12
1 Introduction
2 The Magnetorotational Instability
2.1 Formal Calculation
2.2 Qualitative Description
2.3 General Stability Criteria
3 Local Nonlinear Simulations
3.1 Governing Equations
3.2 Local Axisymmetric Flow
3.3 Local Three-Dimensional Simulations
3.4 Radiative Effects
3.5 Low Ionization Disks
4 Global Disk Simulations
4.1 Two-Dimensional Simulations
4.2 “Cylindrical Disks”
4.3 Three-Dimensional Simulations
5 Summary
Acknowldgements
References
Chapter 13
1 Introduction
2 Trigger for Sawtooth Collapse in High-Temperature Tokamaks
3 Sudden Enhancement of Thin Current Sheets in the Earth’s Magnetotail Prior to Substorm Onset
4 Quasi-steady Reconnection
4.1 Dispersion Relations
4.2 Nonlinear Estimates of the Reconnection Rate
4.3 Comparison with Numerical Simulations
5 Fast Trigger for Flare Dynamics in the Solar Corona
6 Summary
Acknowledgements
References
Chapter 14
1 Introduction
2 Rates of Magnetic Reconnection
2.1 The Sweet-Parker Scheme and Its Modifications
2.2 X-point Reconnection
2.3 Stochastic Reconnection
2.4 Reconnection in Partially Ionized Gas
3 The Dynamo Process
3.1 Conventional Theory and Its Problems
3.2 Magnetic Helicity Conservation Constraint
4 Applying and Testing the Theory
5 Discussion and Summary
Acknowledgements
References
Chapter 15
1 Introduction
2 Magnetic Helicity Production

3.1 Linear Behavior
3.2 Nonlinear Behavior
3.3 The Final Saturation Value
3.4 Sensitivity to Using Hyperdiffusivity
3.5 The Magnetic Helicity Constraint

3.7 Implications
4 Open Boundaries: Good or Bad?
4.1 Enhancement through Losses at Small Scales
4.2 The Modified Magnetic Helicity Constraint
4.3 Simulations with Open Boundaries
5 How Long Is Long? – Or What the Skin Depth Has to Do with the Solar Cycle

6.1 The Lorentzian Quenching Formula
6.2 Other QuenchingF ormulae
6.3 Non-universality of the Lorentzian Quenching Formula
7 Dynamical Quenching
7.1 Adiabatic Approximation and Force-Free Degeneracy

7.3 aOmega-Dynamos
7.4 Open Boundaries

8 Conclusions
References
Chapter 16
1 Small-Scale vs. Large-Scale Field Amplification
1.1 Small-Scale Dynamo
1.2 Large-Scale Dynamo
2 Magnetic Helicity Conservation and Dynamo Quenching
2.1 Case 1: Homogeneous, Stationary Turbulence in Periodic Box
2.2 Case 2: Inhomogeneous Turbulence, Finite Boundary Terms and Implications for Coronal Activity in Steady State
2.3 Case 3: Time-Dependent Dynamo Action and Dynamical Quenching in a Periodic Box

3 Conclusions and Open Questions
3.1 Small-Scale Dynamo

3.3 Coronal Activity and Open Boundary Dynamos (OBD)
3.4 New Diagram of MFD Operation Is Needed
3.5 What Is the Role of Magnetic Reconnection?
Acknowledgments
References