1 Introduction. 1. 1.1 History of Solar Corona Observations. 1. 1.2 Nomenclature of Coronal Phenomena. 8. 1.3 The Solar Magnetic Cycle. 14. 1.4 Magnetic Field ...
Markus J Aschwanden
Physics of the Solar Corona An Introduction with Problems and Solutions
Published ruDlisned in in association association with with
Springer
ids Publishing Publisl Praxis Chichester, UK
PR
Contents Preface
xix
Preface to 2nd Edition
xxii
1 Introduction 1.1 History of Solar Corona Observations 1.2 Nomenclature of Coronal Phenomena 1.3 The Solar Magnetic Cycle 1.4 Magnetic Field of the Solar Corona 1.5 Geometric Concepts of the Solar Corona 1.6 Density Structure of the Solar Corona 1.7 Temperature Structure of the Solar Corona 1.8 Plasma-/? Parameter of the Solar Corona 1.9 Chemical Composition of the Solar Corona 1.10 Radiation Spectrum of the Solar Corona 1.11 Summary
1 1 8 14 17 20 23 26 28 30 32 36
2
37 37 39 42 47 50 52 55 57 61 63 66
Thermal Radiation 2.1 Radiation Transfer and Observed Brightness 2.2 Black-Body Thermal Emission 2.3 Thermal Bremsstrahlung (Free—Free Emission) 2.4 Atomic Energy Levels 2.5 Atomic Transition Probabilities 2.6 Ionization and Recombination Processes . . 2.7 Ionization Equilibrium and Saha Equation 2.8 Emission Line Spectroscopy 2.9 Radiative Loss Function 2.10 First Ionization Potential (FIP) Effect 2.11 Summary
Hydrodynamics 4.1 Hydrodynamic Equations 4.2 Steady-Flow and Siphon-Flow Solutions 4.3 Thermal Stability of Loops 4.3.1 Radiative Loss Instability 4.3.2 Heating Scale Instability 4.4 Observations of Flows in Coronal Loops 4.5 Observations of Cooling Loops 4.5.1 Cooling Delays 4.5.2 Iron Abundance and Filling Factors 4.5.3 Scaling Law of Cooling Loops 4.5.4 Catastrophic Cooling Phase 4.6 Observations of Non-Hydrostatic Loops 4.6.1 TRACE Observations 4.6.2 Theoretical Models 4.7 Hydrodynamic Numerical Simulations of Loops 4.8 Hydrodynamics of the Transition Region 4.9 Hydrodynamics of Coronal Holes 4.10 Hydrodynamics of the Solar Wind 4.11 Summary
5 Magnetic Fields 175 5.1 Electromagnetic Equations 176 5.1.1 Maxwell's Equations 176 5.1.2 Ampere's Law 176 5.1.3 Ohm's Law 177 5.1.4 Induction Equation 177 5.2 Potential Fields 178 5.2.1 UnipolarField 179 5.2.2 Dipole Field 180 5.2.3 Potential-Field Calculation Methods 182 Green's Function Methods 182 Eigenfunction Expansion Methods 184 5.3 Force-Free Fields 186 5.3.1 Linear Force-Free Fields 187 5.3.2 Sheared Arcade 188 5.3.3 Nonlinear Force-Free Field Calculation Methods 190 The Vertical Integration Method 190 The Boundary Integral Method 192 The Euler Potential Method 193 Full MHD Method 194 Potential Vector Grad-Rubin Method 195 Evolutionary Methods 195 5.4 Magnetic Field in Active Region Corona 196 5.4.1 3D Stereoscopy of Active Region Loops 196 5.4.2 Alfven Velocity in Active Regions 202 5.4.3 Non-Potentiality of Soft X-Ray Loops 205 5.4.4 The Width Variation of Coronal Loops 209 5.5 Magnetic Helicity 213 5.5.1 Uniformly Twisted Cylindrical Force-Free Fluxtubes 215 5.5.2 Observations of Sigmoid Loops 217 5.5.3 Conservation of Helicity 218 5.6 Magnetic Nullpoints and Separators 220 5.6.1 Topological Definitions 220 5.6.2 Observations of Coronal Nullpoints . 222 5.7 Magnetic Field Measurements in Radio 224 5.7.1 Magnetic Fields Measured from Free-Free Emission 224 5.7.2 Gyroresonance Emission 227 5.7.3 Gyroresonance Stereoscopy 230 5.7.4 Non-Potential Field Modeling of Gyroresonance Emission . . 233 5.8 Magnetic Field in the Transition Region 234 5.8.1 The Magnetic Canopy Structure 235 5.8.2 Force-Freeness of the Chromospheric Magnetic Field 237 5.9 Summary 239
x
CONTENTS
6 Magneto-Hydrodynamics (MHD) 6.1 MHD Equations 6.1.1 Particle Conservation 6.1.2 Momentum or Force Equation 6.1.3 Ideal MHD 6.1.4 Energy Equation 6.1.5 Resistive MHD 6.2 MHD of Coronal Loops 6.2.1 Magneto-Statics in Vertical Fluxtubes 6.2.2 Lorentz Force near Magnetic Nullpoints 6.2.3 Lorentz Force in Curved Fluxtubes 6.2.4 Dynamics of Twisted Fluxtubes 6.2.5 MHD Simulations of Emerging Fluxtubes 6.2.6 MHD Simulations of Coronal Loops 6.3 MHD Instabilities in Coronal Loops 6.3.1 Rayleigh-Taylor Instability 6.3.2 Kruskal—Schwarzschild Instability 6.3.3 Kelvin-Helmholtz Instability 6.3.4 Ballooning Instability 6.3.5 Convective Thermal Instability 6.3.6 Radiatively-Driven Thermal Instability 6.3.7 Heating Scale-Height Instability 6.3.8 Resistive Instabilities 6.3.9 Kink Instability (m=l) 6.3.10 Sausage Instability (m=0) 6.4 MHD of Quiescent Filaments and Prominences 6.4.1 Magnetic Field Configuration 6.4.2 Equilibrium Models 6.4.3 Formation and Evolution Coronal Condensation Chromospheric Injection Footpoint Heating Disappearance of Filaments/Prominences 6.5 Summary
7 MHD Oscillations 7.1 Dispersion Relation of MHD Waves 7.1.1 Unbounded Homogeneous Medium 7.1.2 Single Magnetic Interface 7.1.3 Slender Slab Geometry 7.1.4 Cylindrical Geometry 7.2 Fast Kink-Mode Oscillations 7.2.1 Kink-Mode Period 7.2.2 Magnetic Field Strength and Coronal Seismology 7.2.3 Observations of Kink-Mode Oscillations 7.2.4 Prominence Oscillations
283 284 285 289 291 291 293 293 294 295 301
CONTENTS 7.3
7.4
7.5
7.6
xi
Fast Sausage-Mode Oscillations 304 7.3.1 The Wave Number Cutoff 304 7.3.2 Sausage-Mode Period 306 7.3.3 Imaging Observations of Sausage-Mode Oscillations 307 7.3.4 Non-Imaging Observations of Sausage-Mode Oscillations . . 311 Slow-Mode (Acoustic) Oscillations 316 7.4.1 Slow-Mode Oscillation Period 316 7.4.2 Observations of Slow-Mode Oscillations 317 Damping of MHD Oscillations 320 7.5.1 Non-Ideal MHD Effects 321 7.5.2 Lateral Wave Leakage 322 7.5.3 Footpoint Wave Leakage 323 7.5.4 Phase Mixing 324 7.5.5 Resonant Absorption 325 7.5.6 Observational Tests 326 Summary 329
8 Propagating MHD Waves 331 8.1 Propagating MHD Waves in Coronal Loops 332 8.1.1 Evolutionary Equation for Slow-Mode MHD Waves 332 8.1.2 Observations of Acoustic Waves in Coronal Loops 334 8.1.3 Propagating Fast-Mode Waves in Coronal Loops 336 8.2 Propagating MHD Waves in the Open Corona 341 8.2.1 Evolutionary Equation of MHD Waves in Radial Geometry . . 341 8.2.2 Observations of Acoustic Waves in Open Corona 344 8.2.3 Spectral Observations of Alfven Waves in the Open Corona . 346 8.3 Global Waves 348 8.3.1 Moreton Waves, EIT Waves, and CME Dimming 348 8.3.2 Modeling and Simulations of Global Waves 352 8.4 Summary 354 9 Coronal Heating 9.1 Heating Energy Requirement 9.2 Overview of Coronal Heating Models 9.3 DC Heating Models 9.3.1 Stress-Induced Reconnection 9.3.2 Stress-Induced Current Cascade 9.3.3 Stress-Induced Turbulence 9.4 AC Heating Models 9.4.1 Alfvenic Resonance 9.4.2 Resonant Absorption 9.4.3 Phase Mixing 9.4.4 Current Layers 9.4.5 MHD Turbulence 9.4.6 Cyclotron Resonance 9.5 Other Coronal Heating Scenarios
9.5.1 Acoustic Heating 377 9.5.2 Chromospheric Reconnection 377 9.5.3 Velocity Filtration 378 Observations of Heating Events 380 9.6.1 Microflares — Soft X-ray Transient Brightenings 382 9.6.2 Nanoflares - EUV Transient Brightenings 387 9.6.3 Transition Region Transients — Explosive Events, Blinkers . . 388 Scaling Laws of Heating Events 390 9.7.1 Geometric Scaling 391 9.7.2 Density, Temperature, and Energy Scaling 393 9.7.3 Magnetic Scaling 396 Statistics of Heating Events 398 9.8.1 Theory of Frequency Distributions 398 9.8.2 Frequency Distributions of Flare Parameters 400 9.8.3 Energy Budget of Flare-like Events 402 9.8.4 Measurements of Frequency Distributions 403 Summary 406
10 Magnetic Reconnection 407 10.1 Steady 2D Magnetic Reconnection 408 10.1.1 Sweet—Parker Reconnection Model 409 10.1.2 Petschek Reconnection Model 410 10.1.3 Generalizations of Steady 2D Reconnection Models 412 10.1.4 Numerical Simulations of Steady 2D Reconnection 413 10.2 Unsteady/Bursty 2D Reconnection 414 10.2.1 Tearing-Mode Instability and Magnetic Island Formation . . . 414 10.2.2 Coalescence Instability 416 10.2.3 Dynamic Current Sheet and Bursty Reconnection 417 10.3 3D Magnetic Reconnection 421 10.3.1 3D X-Type Reconnection 421 10.3.2 Topology of 3D Nullpoints 422 10.3.3 3D Spine, Fan, and Separator Reconnection 424 10.4 Magnetic Reconnection in the Chromosphere 426 10.4.1 Magnetic Flux Emergence 426 10.4.2 Magnetic Flux Cancellation 428 10.4.3 Chromospheric Reconnection Jets 435 10.5 Flare/CME Models 436 10.5.1 The Standard 2D Flare Model 436 10.5.2 The Emerging Flux Model 439 10.5.3 The Equilibrium Loss Model 441 10.5.4 2D Quadrupolar Flare Model 443 10.5.5 The Magnetic Breakout Model 445 10.5.6 3D Quadrupolar Flare Models 447 10.5.7 Unification of Flare Models 449 10.6 Flare/CME Observations 452 10.6.1 Evidence for Reconnection Geometry 452
CONTENTS X-Point Geometry Quadrupolar Geometry 3D Nullpoint Geometry 10.6.2 Evidence for Reconnection Flows and Jets 10.6.3 Large-Scale Magnetic Restructuring 10.6.4 Open Issues on Magnetic Reconnection 10.7 Summary
xiii 452 455 459 460 462 462 463
11 Particle Acceleration 11.1 Basic Particle Motion 11.1.1 Particle Orbits in Magnetic Fields 11.1.2 Particle Drifts in Force Fields 11.1.3 Relativistic Particle Energies 11.2 Overview of Particle Acceleration Mechanisms 11.3 Electric DC-Field Acceleration 11.3.1 Sub-Dreicer DC Electric Fields 11.3.2 Super-Dreicer DC Electric Fields 11.3.3 Acceleration near Magnetic X-Points 11.3.4 Acceleration near Magnetic O-Points 11.3.5 Acceleration in Time-Varying Electromagnetic Fields Betatron Acceleration Field-Aligned Electric Potential Drops Coalescence and X-Point Collapse 11.4 Stochastic Acceleration 11.4.1 Gyroresonant Wave-Particle Interactions 11.4.2 Stochastic Acceleration of Electrons 11.4.3 Stochastic Acceleration of Ions 11.4.4 Acceleration by Electrostatic Wave-Particle Interactions . . . 11.4.5 General Evaluation of Stochastic Acceleration Models . . . . 11.5 Shock Acceleration 11.5.1 Fermi Acceleration 11.5.2 Shock-Drift (or First-Order Fermi) Acceleration 11.5.3 Diffusive Shock Acceleration 11.5.4 Shock Acceleration in Coronal Flare Sites 11.5.5 Shock Acceleration in CMEs and Type II Bursts 11.6 Summary
12 Particle Kinematics 12.1 Overview on Particle Kinematics 12.2 Kinematics of Free-Streaming Particles 12.2.1 Definition of Time-of-Flight Distance 12.2.2 Time-of-Flight Measurements 12.3 Kinematics of Particle Acceleration 12.3.1 Stochastic Acceleration 12.3.2 Electric DC Field Acceleration 12.4 Kinematics of Particle Injection
517 518 520 520 522 524 525 526 529
xiv
CONTENTS 12.4.1 Scenarios of Synchronized Injection 529 12.4.2 Model of Particle Injection During Magnetic Reconnection . . 531 12.5 Kinematics of Particle Trapping 537 12.5.1 Magnetic Mirroring 537 12.5.2 Bifurcation of Trapping and Precipitation 539 12.5.3 Trapping Times 541 12.6 Kinematics of Particle Precipitation 543 12.6.1 Symmetric Traps 543 12.6.2 Asymmetric Traps 544 12.6.3 Collisional Limit 548 12.7 Summary 549
13 Hard X-Rays 13.1 Hard X-ray Instruments 13.1.1 SMM - HXRBS, GRS, HXIS 13.1.2 Yohkoh - HXT 13.1.3 CGRO - BATSE 13.1.4 RHESSI 13.2 Bremsstrahlung 13.2.1 Bremsstrahlung Cross Sections 13.2.2 Thick-Target Bremsstrahlung 13.2.3 Thin-Target Bremsstrahlung 13.3 Hard X-ray Spectra 13.3.1 Thermal-Nonthermal Spectra 13.3.2 Soft-Hard-Soft Spectral Evolution 13.3.3 Low-Energy and High-Energy Cutoffs 13.3.4 Spectral Inversion 13.4 Hard X-ray Time Structures 13.4.1 Pulse Observations 13.4.2 Distribution of Pulse Durations 13.4.3 Scaling of Pulse Duration with Loop Size 13.5 Hard X-Ray Time Delays 13.5.1 Time-of-Flight Delays 13.5.2 Scaling of TOF Distance with Loop Size 13.5.3 Conjugate Footpoint Delays 13.5.4 Trapping Time Delays 13.5.5 Thermal-Nonthermal Delays (Neupert Effect) 13.6 Hard X-ray Spatial Structures 13.6.1 Footpoint and Loop Sources 13.6.2 Footpoint Ribbons 13.6.3 Above-the-Looptop (Masuda) Sources 13.6.4 Occulted Flares 13.7 Hard X-Ray Statistics 13.7.1 Flare Statistics of Nonthermal Energies 13.7.2 Flare Statistics During Solar Cycles 13.8 Summary
15 Radio Emission 15.1 Overview on Radio Emission Mechanisms 15.2 Free-Free Emission (Bremsstrahlung) 15.2.1 Theory of Bremsstrahlung in Microwaves 15.2.2 Radio Observations of Free-Free Emission 15.3 Incoherent Gyroemission 15.3.1 Theory of Gyrosynchrotron Emission 15.3.2 Radio Observations of Gyrosynchrotron Emission 15.4 Plasma Emission 15.4.1 Electron Beams 15.4.2 Langmuir Waves 15.4.3 Observations of Plasma Emission Metric Type III, J, U, and RS Bursts Other Metric and Decimetric Bursts 15.5 Losscone Emission 15.5.1 Electron Cyclotron Maser Emission 15.5.2 Decimetric Observations 15.6 Summary
CONTENTS 16.2.1 Electron and Proton Precipitation—Driven Heating 676 16.2.2 Heat Conduction-Driven Heating 679 16.2.3 Ha Emission 681 16.2.4 White-Light Emission 683 16.2.5 UV Emission 683 16.3 Chromospheric Evaporation 685 16.3.1 Hydrodynamic Simulations of Chromospheric Evaporation . . 687 16.3.2 Line Observations of Chromospheric Evaporation 689 16.3.3 Imaging Observations of Chromospheric Evaporation 691 16.3.4 Radio Emission and Chromospheric Evaporation 693 16.4 Postflare Loop Cooling . 695 16.4.1 Cooling Delays of Flux Peaks 695 16.4.2 Differential Emission Measure Evolution 697 16.4.3 Conductive Cooling 699 16.4.4 Radiative Cooling 700 16.5 Summary 702
17 Coronal Mass Ejections (CMEs) 17.1 Theoretical Concepts of CMEs 17.1.1 Thermal Blast Model 17.1.2 Dynamo Model 17.1.3 Mass Loading Model 17.1.4 Tether Release Model 17.1.5 Tether Straining Model 17.2 Numerical MHD Simulations of CMEs 17.2.1 Analytical Models of CMEs 17.2.2 Numerical MHD Simulations of CMEs 17.3 Pre-CME Conditions 17.3.1 Photospheric Shear Motion 17.3.2 Kink Instability of Twisted Structures 17.4 Geometry of CMEs 17.5 Density and Temperature of CMEs 17.5.1 Density Measurements of CMEs 17.5.2 Temperature Range of CMEs 17.6 Velocities and Acceleration of CMEs 17.7 Energetics of CMEs 17.8 Coronal Dimming 17.9 Interplanetary CME Propagation 17.9.1 Interplanetary Magnetic Field (IMF) 17.9.2 Solar Wind 17.9.3 Interplanetary Shocks 17.9.4 Solar Energetic Particles (SEP) 17.9.5 Interplanetary Radio Bursts 17.10 Summary
Appendices Appendix A: Physical Constants Appendix B: Conversion of Physical Units Appendix C: Maxwell's Equations in Different Physical Unit Systems Appendix D: Plasma Parameters Appendix E: Conversion Table of Electron Temperatures into Relativistic Parameters Appendix F: EUV Spectral Lines Appendix G: Vector Identities Appendix H: Integral Identities Appendix I: Components of Vector Operators
789 789 790 790 791
Notation
797 797 797 802
Physical Units Symbols Latin Symbols Greek Symbols
792 793 794 795 796
Acronyms
805
References Proceedings List Book/Monograph List PhD Thesis List Reference List Journal Abbreviations
