Solar and AstrophysicalMagnetohydrodynamic Flowsedited by

Kanaris C. TsinganosDepartment of Physics,University of Crete,Heraklion, Greece

Kluwer Academic Publishers

Dordrecht / Boston / London

Published in cooperation with NATO Scientific Affairs Division

Table of Contents

Preface xxiii

Participants xxix

PART I:

SOLAR MAGNETOHYDRODYNAMIC FLOWS

1. Questions and Conjectures on the Origin of Stellarand Galactic Magnetic Fields

Eugene Parker 1

1 Introduction 12 The Difficulty 53 The Sun 64 The Galaxy 85 References 13

2. Magnetic Flux Tubes and the Solar Dynamo

Manfred Schiissler 17

1 The Dynamo Problem 182 Storage of Magnetic Flux 18

2.1 The Buoyancy Dilemma 182.2 Flux Tubes in Mechanical Equilibrium 20

3 Instability and Eruption 233.1 Undulatory Instability 233.2 Nonlinear Evolution of the Instability 25

4 Generation of Super-equipartition Fields 304.1 Stretching by Differential Rotation 304.2 'Explosion' of Magnetic Flux Tubes 32

5 Strong Fields and Dynamo Theory 356 Conclusions 36

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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 Tsuneta 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

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4.1 Cusp Reconnection and Loop-Loop Reconnection 954.2 Temperature Structure and Time Variability 95

5 The Scaling Laws 975.1 Scaling Law Obtained with Yohkoh 995.2 Temperature Distribution Along Loops 1005.3 The Energy Scaling Law 101

6 Solar Flares and Magnetic Reconnection 1026.1 Physical Parameters of the Reconnection Site 1026.2 How is the Neutral Sheet Structure Created ? 103

7 Magnetic Reconnection and Transient Phenomena 1047.1 Time Scale of Reconnection 1047.2 Why Does Reconnection Occur in the Solar Corona ? 106

8 From Yohkoh to Solar-B 1069 References 107

6. The Spontaneous Formation of Current-Sheetsin Astrophysical Magnetic Fields

Boon Chye Low 109

1 Introduction 1092 The Parker Problem 1103 Current-Sheet Formation by Flux Expulsion 115

3.1 A Two-Step Evolutionary Process 1163.2 Current-Sheets at Magnetic Null Points 1173.3 Current-Sheet Formation Without a Null Point 1213.4 Current-Sheet Formation in a Sheared Magnetic Field 1233.5 Influence of Pressure and Gravity 128

4 Discussion and Conclusion 1295 References 131

7. Magnetohydrodynamic Processes in the Solar Corona :Flares, Coronal Mass Ejections and Magnetic Helicity

Boon Chye Low 133

1 Introduction 1332 The Solar Corona 1343 Helmet-Streamers, Mass Ejections and the Solar Wind 136

3.1 Large-Scale Equilibrium 136

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3.2 Internal Structures of the Coronal Helmet 1383.3 Disruptions into Coronal Mass Ejections 140

4 Magnetic Flux Ropes and Magnetic Helicity 1435 Summary and Conclusion 1466 References 148

8. Reconnection of Magnetic Lines of Force

Eric R. Priest 151

1 Introduction 1512 Sweet-Parker Reconnection 1533 Almost-Uniform Potential Reconnection 1584 Almost-Uniform Non-Potential Reconnection 1645 Non-Uniform Reconnection 165

5.1 Potential Reconnection 1655.2 Non-Potential Reconnection 166

6 Conclusions 1687 References 169

9. New Developments in Magnetic Reconnection Theory

Eric R. Priest 171

1 Introduction 1722 Two-Dimensional Magnetic Reconnection Theory 174

2.1 Linear Reconnection 1742.2 X-Point Collapse 177

3 Three-Dimensional Reconnection 1793.1 Reconnection at Null Points 180

4 Reconnection Without Null Points 1845 Reconnection in Solar Coronal Heating 190

5.1 Converging Flux Model 1925.2 Application to Specific Bright Points 192

6 Conclusions 1937 References 193

IX

10. Hydrodynamic and Magnetohydrodynamic Turbulence

Annick Pouquet 195

1 Introduction 1952 The One-dimensional Case 196

2.1 A Fluid Model 1962.2 A Numerical Model 1992.3 The Hada Equation and the Asymmetric Stability of

Proto-stellar Jets 2013 Diagnostics 202

3.1 Structure Functions 2023.2 The She-Leveque Model 203

4 The Two-dimensional Case 2054.1 Are Nonlinear Interactions Self-defeating in MHD ? 2054.2 Does Reconnection Occur at a Finite Rate for R —• oo ? 2064.3 A Plausible Model for Heating the Solar Corona 207

5 The Three-dimensional Case 2085.1 The Betchov Relation 2085.2 The Structuring of Vorticity into Filaments 2085.3 Transport Coefficients and the Excess of Magnetic Energy

in the Small Scales 2095.4 Transport Coefficients and the Dynamo Problem 2095.5 The Dynamical Development of Singularities 210

6 Turbulence in the Interstellar Medium 2116.1 Evidence of Turbulence through Line Widths 2116.2 A Model of the ISM at the Kiloparsec Scale 2116.3 An Effective Thermodynamical Law 2126.4 The MHD Case 213

7 Conclusion 2138 References 214

11. Numerical Simulations of Solarand Astrophysical MHD Flows

Kazunari Shibata 217

1 Introduction 2172 Difficulties in Simulating MHD Phenomena in the Solar Atmosphere

and Astrophysical Gas Layers 219

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3 Jets - Plasma Acceleration due to Nonlinear MHD Wavesand Centrifugal Force 2213.1 Solar Jets: Spicules and Surges 221

3.1.1 Slow Shock Acceleration 2213.1.2 Nonlinear Alfven Wave (or Magnetic Twist) Acceleration . . . . 224

3.2 Astrophysical Jets ejected from Accretion Disks 2253.2.1 Nonsteady MHD Jets from Thin Disks - TheSweeping Magnetic Twist Mechanism 2253.2.2 Relation to the Magneto-Rotational (Balbus-Hawley)Instability " 2273.2.3 Nonsteady MHD Jets from Thick Disks 2283.2.4 Relation between Nonsteady and Steady Jets 2293.2.5 Three Dimensional Propagation of MHD Jets 231

4 Loops - Nonlinear Evolution of the Parker Instability 2324.1 Magnetic Loops in Galactic and Accretion Disks 232

4.1.1 Typical Nonlinear Evolution of the Parker Instability:The Most Unstable Mode 2324.1.2 Condition of Shock Wave Formation and NonlinearOscillation 2344.1.3 Effect of Corona (Halo) 2354.1.4 Effect of Rotation and Shearing Motion 236

4.2 Emerging Solar Magnetic Loops 2384.2.1 Self-similar Expansion of Magnetic Loops 2384.2.2 Three Dimensional Effect: Coupling with the InterchangeModes 2414.2.3 Emergence of Twisted Flux Tube 242

5 Flares - Magnetic Reconnection 2425.1 Solar Compact Flares and X-ray Jets 2425.2 Protostellar Magnetosphere 244

6 Future Directions 2447 References 245

12. Further Thoughts on the Solar Coronaas a Minimum Energy System

Paul Charbonneau and Art J. Hundhansen 249

1 Introduction 2492 An Illustrative Model 253

XI

2.1 Overview of Model Construction 2532.2 The Total Energy 2542.3 Sample Results 256

3 Implications 2593.1 Coronal Mass Ejections 2593.2 Numerical Simulations 260

4 Applications 2615 References 263

13. ULYSSES Observations of the Solar WindOut of the Ecliptic PlaneW.C. Feldman, J.L. Phillips, B.L. Barraclough and CM. Hammond 265

1 Introduction 2652 Observations 267

2.1 Overview of Solar Wind Flow Structure 2672.2 Corotating Interaction Regions (CIR s) 2692.3 Coronal Mass Ejections (CME s) 2712.4 Flow Structure at High Latitudes 2742.5 Helium Abundance 2812.6 Internal State of the High-Latitude Wind; Protons 2852.7 Internal State of the High-Latitude Wind; Electrons 288

3 Summary and Discussion 2904 References 297

14. Stellar WindsKeith B. MacGregor 301

1 Introduction 3012 The Winds From the Sun and Solar-type Stars 303

2.1 The Solar Wind: Some Preliminary Physical Considerations 3032.2 Winds from Solar-type Stars: Observational Evidence 304

3 Magnetic Modifications to Thermally Driven Flow 3113.1 Magnetic Definition of Flow Geometry 3113.2 Magnetic/Centrifugal Acceleration 3153.3 Alfven Wave-Driven Winds 322

4 Discussion: Extension to Winds From Non-Solar-type Stars 3274.1 Winds From Early-type Stars 327

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4.2 The Force of Radiation in Spectral Lines 3284.3 Magnetic Modifications to Radiatively Driven Flow 329

5 References 334

15. Some Implications of Solar and Stellar Activity

Eugene Parker 337

1 Suprathemal Activity and Variability 3372 Energy Supply 3413 The X-ray Corona 3424 Dissipation of Magnetic Energy 3445 Energy Input and Reconnection Rates 3466 Observational Tests 3497 References 351

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PART II:

ASTROPHYSICAL MAGNETOHYDRODYNAMIC FLOWS

16. Hubble Space Telescope Observations ofGalactic and Extragalactic Jets

John A. Biretta 357

1 Introduction 3572 Galactic Jets 358

2.1 Jets from Young Stellar Objects 3582.2 Jets From Older, Symbiotic Stars 363

3 Extragalactic Jets 3653.1 The Jet in M87 3673.2 The Jet in 3C273 3733.3 Optical Synchrotron Jets Discovered by HST 3753.4 Summary of HST Observations of Extragalactic Jets 376

4 Problems Posed by Observations of Extragalactic Jets 3775 Future Prospects 3796 References 380

17. Exact MHD Solutions for Self-similar Outflows

Edoardo Trussoni, Christophe Sauty and Kanaris Tsinganos 383

1 Introduction 3842 MHD Equations for Axisymmetric Configurations 386

2.1 Poloidal Components 3872.2 Toroidal Components 3872.3 Alfven Singularity 388

3 Scaling Laws for Self-similar Solutions 3884 Equations of the Wind 3915 Solutions with Prescribed Pressure Distribution 392

5.1 Energetics of the Outflow 3935.2 Asymptotic Structure of the Outflow 3935.3 Oscillations in the Width of Collimated Outflows 3955.4 Alfven and X-type Singularity 3965.5 Numerical Results 398

6 Solutions with Prescribed Streamlines 4006.1 Prescription of the Streamlines 402

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6.2 Asymptotic Structure of the Outflow 4026.3 Numerical Solutions 404

7 Concluding Remarks 4088 References 410

18. Numerical Simulation of Plasma Flow in theMagnetosphere of an Axisymmetric Rotator

Sergei V. Bogovalov 411

1 Introduction 4112 Equations of Stationary MHD Flow 4123 Boundary Conditions and Critical Surfaces for Mixed-type Equations . .4134 Time Dependent Model 4185 Structure of the Stationary Solutions 4196 Centrifugal Acceleration of Plasma 4217 References 423

19. Critical Points and Separatrix Characteristics inSolar and Astrophysical MHD Flows

Kanans Tsinganos, Christophe Sauty, George Surlantzis, Edoardo Trussoniand John Contopoulos 427

1 Introduction 4282 Critical Points in Symmetric MHD Flows 430

2.1 Bernoulli k Transfield Equations in Symmetric Polytropic Flows .. .4302.2 Characteristics of Symmetric MHD Flows 4322.3 Separatrix Characteristics of Bernoulli and Transfield Equations

in Polytropic Flows 4322.4 Critical Points in Self-similar Flows 440

3 Examples of Critical Points and Separatrix Characteristics in Symmetricand Self-similar Polytropic MHD Flows 4433.1 Vertically Self-Similar Flows in Loops Embedded in a Planar

Atmosphere 4433.2 Radially Self-similar Polytropic Disc Winds and Jets 445

4 Examples of Critical Points and Separatrix Characteristics inAxisymmetric and Meridionally-Self-similar Nonpolytropic MHD Flows 450

5 Summary 4566 References 458

XV

20. Collimation of MHD OutflowsJean Heyvaerts and Colin A. Norman 459

1 Introduction 4592 Basics of Axisymmetric Stationary MHD Flows 460

2.1 The Focusing Hoop Stress 4602.2 The Axisymmetric Stationary Wind Model 4602.3 Surface Functions 4612.4 Alfven Radius and Density 463

3 Field-aligned Flows 4643.1 The Bernoulli Integral 4643.2 Critical Points and Criticality Relations 465

4 The Transfield Equation 4664.1 Force Balance Perpendicular to Field Lines 4664.2 Alfven Regularity Condition 467

5 General Results on the Asymptotic Behaviour of PolytropicRotating MHD Winds 4695.1 Rotating Polytropic MHD Winds Do Not Asymptotically Bend

Towards the Equator 4695.2 Winds Which Carry No Poynting Flux at Infinity also Carry

No Poloidal Current and Focus Parabolically 4705.3 Magnetic Surfaces which Diverge off Axis Enclose

No Poloidal Current Between them at Infinity 4715.4 Winds which Carry Non Vanishing Poynting Flux at Infinity

Contain a Cylindrically Collimated Core 4736 References 473

21 . The Parker Instability in the Interstellar MediumTelemachos Ch. Mouschovias 475

1 Introduction 4752 Basic Equations and Physics of the Instability 476

2.1 Cosmic Rays as a Fluid 4782.2 Magnetic Rayleigh-Taylor (or Parker) Instability 479

2.2.1 The Zeroth-Order State 4802.2.2 Two-Dimensional Stability Analysis 4802.2.3 Instability in Three Dimensions 484

3 Final Equilibrium States 4853.1 Why Final States Exist 486

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3.2 Self-Consistent Formulation of the Problem 4863.3 Determination of Equilibrium States 489

4 Energy Integral for Isothermal Plasma 4905 Nonlinear Evolution 492

5.1 Summary of Past Work 4925.2 New Numerical Simulations 494

5.2.1 Nonlinear Evolution of the Odd Linear Modes 4945.2.2 Nonlinear Evolution of the Even Linear Modes 4955.2.3 Effect of Cosmic Rays on the Instability and Vice Versa 501

6 Summary 5027 References 503

22. Multifluid Magnetohydrodynamics and Star FormationTelemachos Ch. Mouschovias 505

1 Introduction - A Modern Theory of Star Formation 5052 Five-Fluid MHD Description of Protostar Formation 508

2.1 Physical Origin of the Five-Fluid Equations 5082.2 Reduction of the Five-Fluid Equations: Flux-Freezing in the Plasma 5132.3 Grain Motion and Attachment to the Magnetic Field 514

3 Two-Fluid Description of Protostar Formation 5153.1 Basic Equations 5153.2 Ambipolar Diffusion: General Considerations and Timescales 5163.3 Magnetic Braking 518

4 Results of Two-Fluid Description of Protostar Formation 5194.1 Ambipolar Diffusion in Nonrotating Models 5204.2 Rotating Models: Ambipolar Diffusion and Magnetic Braking 523

5 Protostar Formation in the Four-Fluid Approximation 5275.1 Main Effects of Grains 5275.2 Comparison with Observations: The Barnard I Cloud 5315.3 Effect of Ultraviolet Radiation 531

6 Hydromagnetic Waves, Linewidths, Ambipolar Diffusion,and Star Formation 532

7 Conclusion 5348 Appendix 5369 References 536

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23. Jets Associated with Young Stars

Tom P. Ray .'. 539

1 Historical Introduction 5391.1 Herbig-Haro Objects 5391.2 The Discovery of Jets from Young Stars 540

2 Jet Properties 5422.1 Spectroscopy 5422.2 Morphology 5442.3 Physical Parameters 5442.4 Sources of YSO Jets 547

3 The Propagation of YSO Jets 5493.1 What is the Origin of the Knots ? 5493.2 Bow Shocks 550

4 The View from Space and at Non-optical Wavelengths 5524.1 HST Imaging 5524.2 Observing YSO Jets at Non-optical Wavelengths 555

5 The Wider Perspective 5585.1 The Connection between YSO Jets and Molecular Outflows 5585.2 The Disc-Jet Connection: A Case Study 561

6 References 563

24. Molecular Outflows from Protostars

R.N. Henriksen 567

1 Introduction 5672 Pertinent Theoretical Questions 567

2.1 What is the Energy and Momentum Source for the Outflow ? 5672.2 How are these Flows Collimated and Where ? 5682.3 How Many 'Independent' Parts of the Machine are There ? 5682.4 What Kinds of Time Dependence are There ? 5692.5 What Determines the Characteristic Scales of the Outflows ? 5692.6 Does the Phenomenon Occur also in a Pre-Protostar Phase ? 5702.7 How Contingent or Universal is the Phenomenon ? 5702.8 What are the 'Neighbourhood' Magnetic and Velocity Fields ? 5712.9 Are There Differences between the Magnetic and Rotation Axes ? 571

3 General Considerations 5714 Models; Classification and Critique 576

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4.1 Wind Driven Models 5764.2 Entrained Outflow 5774.3 Outflow Driven by Wandering and/or Intermittent Jets 5774.4 Magnetized Disc Driven Outflow 5784.5 Boundary Layer Models 5804.6 Heated Quadrupolar Advection Models 581

5 References 582

25. Jets and MHD Flows Associated with Symbiotic Stars

Menas Kafatos 585

1 Introduction 5862 Symbiotic Star System Components 5883 Overall Properties of Symbiotics .' 5904 R Aquarii 5945 CH Cygni 5996 MHD Flows in R Aquarii 6007 References 603

26. Phenomenology and Modelling of Large-scale Jets

Attilio Ferrari, Silvano Massaglia, Gianluigi Bodo and Paola Rossi 607

1 Historical Introduction 6072 Observations of Collimated Outflows 610

2.1 Radio Data 6102.2 Optical and X-ray Data 6112.3 Physical Parameters 6122.4 Luminosity - Linear Size Diagram 6142.5 Unified Models 614

3 Physics of Collimated Outflows 6153.1 Relativistic Plasmas and Magnetic Fields 6163.2 Age, Expansion Speed and Spectral Break 6173.3 The Minimum Energy Hypothesis 617

4 Parsec-scale Jets 6184.1 Accretion Disks 6184.2 Dynamics of Equilibrium Jets 6194.3 Relativistic Jets 6204.4 Collimation 621

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4.5 Mini-jets as Chocked Jets 6214.6 Free Jets 6214.7 Magnetohydrodynamical and Centrifugal Models 6214.8 Difficulties and Improvements 622

5 Large-scale Jets, Morphologies, Radiation 6225.1 Fluid Instabilities: Linear Analysis 622

5.1.1 Kelvin-Helmholtz Instability 6235.1.2 Filamentation Instability 6245.1.3 Resistive Instabilities, etc 624

5.2 Nonlinear Evolution of Hydrodynamic Instabilities 6245.3 Shocks 6265.4 Nonlinear MHD Instabilities 6285.5 Instabilities and Radiation 628

6 Jet Termination ' 6296.1 Hot Spots 6326.2 Cocoons 6326.3 Filaments 6346.4 Numerical Simulations of Jet's Head Evolution 635

6.4.1 Dynamics of the Jet's Head 6366.4.2 Dynamics of the Cocoon 638

7 References 640

27. MHD Accretion-ejection Flows in Active GalacticNuclei

Guy Pelletier, J. Ferreira, G. Henri and A. Marcowith 643

1 Introduction 6432 The MHD Engine 643

2.1 Angular Momentum Transfer 6452.2 Diffusion 6452.3 Current Profile 6462.4 Crossing the Slow Magnetosonic Surface 647

3 Motion and Confinement Coupled 6483.1 Crossing the Alfven Surface 6493.2 Global Energy Budget 6493.3 Turbulent Heating 650

4 The Issue of the Turbulent Transport 6515 A Magnetic Cauldron for AGNs and Microquasars 651

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5.1 Why an Electron Positron Component ? 6525.2 Heating and Boosting the Pair Plasma 6535.3 The Proton Backstream Instability 6545.4 Turbulent Cascade in the Relativistic Plasma 655

6 Synthesis 6567 References 657

28. Interaction of Turbulent Accretion Diskswith Embedded Magnetic Fields

Jean F. Heyvaerts, Ann Bardou and Eric R. Priest 659

1 Turbulence and Accretion 6592 What Determines the Level of Turbulence ? 660

2.1 Self-consistent Turbulence in General ' 6612.2 Self-consistent Kolmogoroff Turbulence 661

3 Turbulence from the Magnetic Shearing Instability 6643.1 Fully Developed Magnetic Shearing Instability 6643.2 Accounting for Turbulence Anisotropy 6643.3 Inhibition of the Magnetic Shearing Instability and Consequences . 666

4 Magnetic Field Dragging by Turbulent Accretion Disks 6665 Interaction Between a Thin Turbulent Accretion Disk

and the Magnetic Field of the Accreting Star 6685.1 Field Rejection by the Disk: Physical Mechanism 6685.2 Field Inflation: a More Formal Derivation 669

6 References 671

29. Magnetic Reconnection in Accretion Disc Coronae

Harald Lesch 673

1 Introduction 6732 Magnetic Reconnection and Particle Acceleration 6753 Observational Consequences of Unstable Relativistic

Electron Beams 6784 Coherent Emission of Relativistic Electron Beams 6795 Discussion 6806 References 681

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30. Relativistic Outflows in the Galaxy/. Felix Mirabel and L.F. Rodriguez 683

1 Introduction 6832 GRS 1915+105 683

2.1 Superluminal Motions in GRS 1915+105 6842.2 Time Variability in the Radio and X-rays 6882.3 Evidence for a Circumstellar Cocoon 6902.4 Energy and Power Considerations 6912.5 Search for Extended Lobes in GRS 1915+105 691

3 The Two Superluminal Sources and SS 433 6934 Search for "Moving" Emission Lines 6955 Other Sources of Relativistic Jets in the Galaxy 6966 References : 697

31. Stationary Relativistic MHD FlowsMax Camenzind 699

1 Introduction 7002 The Disk-Jet Connection in AGN and Young Stellar Objects 7013 MHD of Rapidly Rotating Objects 703

3.1 The Gravitational Field of Compact Objects 7033.1.1 Rotating Neutron Stars 7053.1.2 Rotating Black Holes 705

3.2 Rotational Energy of Compact Objects 7073.3 Stationary MHD Flows 7093.4 Polytropic Wind Equation 7143.5 Axisymmetric Magnetospheres 7183.6 Prospects for Time-Dependent MHD 719

4 Relativistic Jets as Self-Collimated Plasma Flows Driven byRapid Rotation 7194.1 The Jet-Plasma Confinement 7194.2 Self-Collimated Solutions of the GSS Equation 7214.3 Plasma Diagnostics for Parsec-scale Jets 722

5 Conclusions 7236 References 724

Index 727