Solar and Astrophysical Magnetohydrodynamic Flows

769 Pages·1996·56.186 MB·English

by  Eugene Parker (auth.), Kanaris C. Tsinganos (eds.)

Solar and Astrophysical Magnetohydrodynamic Flows
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Series C: Mathematical and Physical Sciences - Vol. 481
Solar and Astrophysical
Magnetohydrodynamic Flows
edited by
c.
Kanaris Tsinganos
Department of Physics,
University of Crete,
Heraklion, Greece
Kluwer Academic Publishers
Dordrecht / Boston / London
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on
Solar and Astrophysical Magnetohydrodynamic Flows
Heraklion, Crete, Greece
June 11-23, 1995
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-13 :978-94-0 10 -6603-7 e-ISBN-13: 978-94-009-0265-7
DOl: 10.1007/978-94-009-0265-7
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Table of Contents
Preface ........ , .......................................................... XX111
Participants .........................................•.................... XXIX
PART I:
SOLAR MAGNETOHYDRODYNAMIC FLOWS
1. Questions and Conjectures on the Origin of Stellar
and Galactic Magnetic Fields
Eugene Parker .............................................................. 1
1 Introduction ............................................................ 1
2 The Difficulty ........................................................... 5
3 The Sun ................................................................ 6
4 The Galaxy ............................................................. 8
5 References ............................................................. 13
2. Magnetic Flux Tubes and the Solar Dynamo
Manfred Schussler .......................................................... 17
1 The Dynamo Problem ................................................. 18
2 Storage of Magnetic Flux .............................................. 18
2.1 The Buoyancy Dilemma ........................................... 18
2.2 Flux Tubes in Mechanical Equilibrium ............................. 20
3 Instability and Eruption ............................................... 23
3.1 Undulatory Instability ............................................. 23
3.2 Nonlinear Evolution of the Instability .............................. 25
4 Generation of Super-equipartition Fields ............................... 30
4.1 Stretching by Differential Rotation ................................ 30
4.2 'Explosion' of Magnetic Flux Tubes ................................ 32
5 Strong Fields and Dynamo Theory ..................................... 35
6 Conclusions ............................................................ 36
vi
7 References ............................................................. 37
3. Siphon Flows in Solar Magnetic Flux Tubes and Sunspots
John H. Thomas ........................................................... 39
1 Introduction ........................................................... 39
2 Steady Siphon Flows in Isolated Magnetic Flux Tubes .................. 40
2.1 Basic Equations ................................................... 40
2.2 Isothermal Siphon Flows .......................................... 42
2.3 More Realistic Siphon Flows ....................................... 45
3 Tube Shocks in Supercritical Siphon Flows ............................. 48
4 Siphon Flows in Intense Photospheric Flux Tubes ...................... 53
5 Siphon Flows and the Evershed Effect in Sunspots ..................... 53
6 References ............................................................. 59
4. MHD Waves in Magnetic Flux Tubes
Marcel Goossens and Michael Ruderman .................................... 61
1 Introduction ........................................................... 61
2 Asymptotic State of Resonant Alfven Waves ........................... 65
3 Resonant Alfven Waves in Linear Ideal MHD ........................... 68
4 Resistive MHD Equations for Resonant Alfven Waves .................. 71
5 Resistive MHD Solutions for Resonant Alfven Waves Close to the Ideal
Resonance Position .................................................... 73
6 Conclusions ............................................................ 80
7 References ............................................................. 81
5. The Dynamic Solar Corona in X-rays with Yohkoh
Saku Tsuneia .............................................................. 85
1 Introduction ........................................................... 85
2 The X-ray Corona ..................................................... 87
2.1 The Overall X-ray Corona ......................................... 87
2.2 The Active Region Corona ........................................ 89
3 Transient and Steady Loops in the Solar Corona ....................... 90
3.1 Transient Loops in the Solar Corona ............................... 90
3.2 Can Transient Brightenings Explain Coronal Heating? .......... 91
4 Temperature Structure of Active Regions ............................... 94
vii
4.1 Cusp Reconnection and Loop-Loop Reconnection .................. 95
4.2 Temperature Structure and Time Variability ....................... 95
5 The Scaling Laws ...................................................... 97
5.1 Scaling Law Obtained with Yohkoh ................................ 99
5.2 Temperature Distribution Along Loops ........................... 100
5.3 The Energy Scaling Law ......................................... 101
6 Solar Flares and Magnetic Reconnection .............................. 102
6.1 Physical Parameters of the Reconnection Site ..................... 102
6.2 How is the Neutral Sheet Structure Created? .................... 103
7 Magnetic Reconnection and Transient Phenomena ..................... 104
7.1 Time Scale of Reconnection ...................................... 104
7.2 Why Does Reconnection Occur in the Solar Corona? ............. 106
8 From Yohkoh to Solar-B .............................................. 106
9 References ............................................................ 107
6. The Spontaneous Formation of Current-Sheets
in Astrophysical Magnetic Fields
Boon Chye Low ........................................................... 109
1 Introduction .......................................................... 109
2 The Parker Problem .................................................. 110
3 Current-Sheet Formation by Flux Expulsion ........................... 115
3.1 A Two-Step Evolutionary Process ................................ 116
3.2 Current-Sheets at Magnetic Null Points ........................... 117
3.3 Current-Sheet Formation Without a Null Point ................... 121
3.4 Current-Sheet Formation in a Sheared Magnetic Field ............ 123
3.5 Influence of Pressure and Gravity ................................. 128
4 Discussion and Conclusion ............................................ 129
5 References ............................................................ 131
7. Magnetohydrodynamic Processes in the Solar Corona:
Flares, Coronal Mass Ejections and Magnetic Helicity
Boon Chye Low .......................................................... 133
1 Introduction .......................................................... 133
2 The Solar Corona ..................................................... 134
3 Helmet-Streamers, Mass Ejections and the Solar Wind ................ 136
3.1 Large-Scale Equilibrium .......................................... 136
viii
3.2 Internal Structures of the Coronal Helmet ........................ 138
3.3 Disruptions into Coronal Mass Ejections .......................... 140
4 Magnetic Flux Ropes and Magnetic Helicity ........................... 143
5 Summary and Conclusion ............................................. 146
6 References ............................................................ 148
8. Reconnection of Magnetic Lines of Force
Eric R. Priest ............................................................. 151
1 Introduction .......................................................... 151
2 Sweet-Parker Reconnection ........................................... 153
3 Almost-Uniform Potential Reconnection ............................... 158
4 Almost-Uniform Non-Potential Reconnection .......................... 164
5 Non-Uniform Reconnection ........................................... 165
5.1 Potential Reconnection ........................................... 165
5.2 Non-Potential Reconnection ...................................... 166
6 Conclusions .......................................................... 168
7 References ............................................................ 169
9. New Developments in Magnetic Reconnection Theory
Eric R. Priest ............................................................. 171
1 Introduction .......................................................... 172
2 Two-Dimensional Magnetic Reconnection Theory ..................... 174
2.1 Linear Reconnection ............................................. 174
2.2 X-Point Collapse ................................................. 177
3 Three-Dimensional Reconnection ...................................... 179
3.1 Reconnection at Null Points ...................................... 180
4 Reconnection Without Null Points .................................... 184
5 Reconnection in Solar Coronal Heating ................................. 190
5.1 Converging Flux Model .......................................... 192
5.2 Application to Specific Bright Points ............................. 192
6 Conclusions .......................................................... 193
7 References ............................................................ 193
ix
10. Hydrodynamic and Magnetohydrodynamic Turbulence
Annick Pouquet ........................................................... 195
1 Introduction .......................................................... 195
2 The One-dimensional Case ........................................... 196
2.1 A Fluid Model ................................................... 196
2.2 A Numerical Model .............................................. 199
2.3 The Hada Equation and the Asymmetric Stability of
Proto-stellar Jets ... ; ............................................ 201
3 Diagnostics ........................................................... 202
3.1 Structure Functions .............................................. 202
3.2 The She-Leveque Model .......................................... 203
4 The Two-dimensional Case ........................................... 205
4.1 Are Nonlinear Interactions Self-defeating in MHD? .............. 205
4.2 Does Reconnection Occur at a Finite Rate for R --+ oo? .......... 206
4.3 A Plausible Model for Heating the Solar Corona .................. 207
5 The Three-dimensional Case .......................................... 208
5.1 The Betchov Relation ............................................ 208
5.2 The Structuring of Vorticity into Filaments ....................... 208
5.3 Transport Coefficients and the Excess of Magnetic Energy
in the Small Scales ............................................... 209
5.4 Transport Coefficients and the Dynamo Problem .................. 209
5.5 The Dynamical Development of Singularities ...................... 210
6 Turbulence in the Interstellar Medium ................................ 211
6.1 Evidence of Turbulence through Line Widths ..................... 211
6.2 A Model of the ISM at the Kiloparsec Scale ...................... 211
6.3 An Effective Thermodynamical Law .............................. 212
6.4 The MHD Case .................................................. 213
7 Conclusion ........................................................... 213
8 References ............................................................ 214
11. Numerical Simulations of Solar
and Astrophysical MHD Flows
J(a zunari Shibata .......................................................... 217
1 Introduction .......................................................... 217
2 Difficulties in Simulating MHD Phenomena in the Solar Atmosphere
and Astrophysical Gas Layers ......................................... 219
x
3 Jets - Plasma Acceleration due to Nonlinear MHD Waves
and Centrifugal Force ................................................ 221
3.1 Solar Jets: Spicules and Surges ................................... 221
3.1.1 Slow Shock Acceleration .................................... 221
3.1.2 Nonlinear Alfven Wave (or Magnetic Twist) Acceleration .... 224
3.2 Astrophysical Jets ejected from Accretion Disks ................... 225
3.2.1 Nonsteady MHD Jets from Thin Disks - The
Sweeping Magnetic Twist Mechanism ............................. 225
3.2.2 Relation to the Magneto-Rotational (Balbus-Hawley)
Instability ........................................................ 227
3.2.3 Nonsteady MHD Jets from Thick Disks ..................... 228
3.2.4 Relation between N onsteady and Steady Jets ................ 229
3.2.5 Three Dimensional Propagation of MHD Jets ............... 231
4 Loops - Nonlinear Evolution of the Parker Instability ................. 232
4.1 Magnetic Loops in Galactic and Accretion Disks .................. 232
4.1.1 Typical Nonlinear Evolution of the Parker Instability:
The Most Unstable Mode ........................................ 232
4.1.2 Condition of Shock Wave Formation and Nonlinear
Oscillation ...................................................... 234
4.1.3 Effect of Corona (Halo) ..................................... 235
4.1.4 Effect of Rotation and Shearing Motion ..................... 236
4.2 Emerging Solar Magnetic Loops .................................. 238
4.2.1 Self-similar Expansion of Magnetic Loops ................... 238
4.2.2 Three Dimensional Effect: Coupling with the Interchange
Modes ........................................................... 241
4.2.3 Emergence of Twisted Flux Tube .......................... 242
5 Flares - Magnetic Reconnection ....................................... 242
5.1 Solar Compact Flares and X-ray Jets ............................. 242
5.2 Protostellar Magnetosphere ...................................... 244
6 Future Directions ..................................................... 244
7 References ............................................................ 245
12. Further Thoughts on the Solar Corona
as a Minimum Energy System
Paul Charbonneau and Art J. Hundhausen ................................. 249
1 Introduction .......................................................... 249
2 An Illustrative Model ................................................. 253