Physics of the Solar Corona an Introduction with Problems and Solutions Markus J Aschwanden Physics of the Solar Corona an Introduction with Problems and Solutions

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Physics of the Solar Corona An Introduction with Problems and Solutions Markus J Aschwanden Physics of the Solar Corona An Introduction with Problems and Solutions

Published in association with Praxis Publishing Chichester, UK Dr Markus J Aschwanden Lockheed Martin Advanced Technology Center Solar and Astrophysics Laboratory Palo Alto California USA

SPRINGER–PRAXIS BOOKS IN ASTRONOMY AND PLANETARY SCIENCES SUBJECT ADVISORY EDITOR: Dr. Philippe Blondel, C.Geol., F.G.S., Ph.D., M.Sc., Senior Scientist, Department of Physics, University of Bath, Bath, UK; John Mason B.Sc., M.Sc., Ph.D. ISBN 3-540-30765-6 Springer-Verlag Berlin Heidelberg New York

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# Praxis Publishing Ltd, Chichester, UK, 2005 Printed in Germany Reprinted with corrections, problems and solutions and issued in paperback 2006

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Cover design: Jim Wilkie Completed in LaTex: EDV-Beratung, Germany

Printed on acid-free paper To Susanna Contents

Preface xix

Preface to 2nd Edition xxii

1 Introduction 1 1.1HistoryofSolarCoronaObservations...... 1 1.2NomenclatureofCoronalPhenomena...... 8 1.3TheSolarMagneticCycle...... 14 1.4MagneticFieldoftheSolarCorona...... 17 1.5GeometricConceptsoftheSolarCorona ...... 20 1.6DensityStructureoftheSolarCorona...... 23 1.7TemperatureStructureoftheSolarCorona ...... 26 1.8 Plasma-β ParameteroftheSolarCorona ...... 28 1.9 Chemical Composition of the Solar Corona ...... 30 1.10RadiationSpectrumoftheSolarCorona...... 32 1.11Summary...... 36

2 Thermal Radiation 37 2.1RadiationTransferandObservedBrightness ...... 37 2.2Black-BodyThermalEmission...... 39 2.3 Thermal Bremsstrahlung (Free−FreeEmission)...... 42 2.4AtomicEnergyLevels...... 47 2.5 Atomic Transition Probabilities ...... 50 2.6IonizationandRecombinationProcesses ...... 52 2.7 Ionization Equilibrium and Saha Equation ...... 55 2.8EmissionLineSpectroscopy...... 57 2.9RadiativeLossFunction...... 61 2.10FirstIonizationPotential(FIP)Effect...... 63 2.11Summary...... 66

3 Hydrostatics 67 3.1HydrostaticScaleHeight...... 67 3.2HydrostaticWeightingBias ...... 71 3.3 Multi-Hydrostatic Corona ...... 76 viii CONTENTS

3.4LoopGeometryandInclination...... 83 3.4.1 Vertical Semi-Circular Loops ...... 83 3.4.2 Inclined Semi-Circular Loops ...... 84 3.4.3 Diverging Semi-Circular Loops ...... 85 3.4.4 CoordinateTransformations...... 86 Image(orObserver’s)CoordinateSystem...... 87 HeliographicCoordinateSystem...... 88 LoopPlaneCoordinateSystem...... 88 Column Depth of Loops with Constant Cross Section . . . . . 89 3.5LoopLine-of-SightIntegration...... 89 3.5.1 BrightSingleLoop...... 90 3.5.2 FaintSingleLoop...... 92 3.5.3 Statistical Distribution of Loops ...... 92 3.6HydrostaticSolutionsandScalingLaws...... 93 3.6.1 UniformHeatingandRTVScalingLaws...... 94 3.6.2 Nonuniform Heating and Gravity ...... 96 3.6.3 Analytical Approximations of Hydrostatic Solutions . . . . . 96 3.7HeatingFunction...... 99 3.8 Instrumental Response Functions ...... 108 3.9 Observations of Hydrostatic Loops ...... 109 3.10HydrostaticDEMDistributions ...... 113 3.11Summary...... 116

4 Hydrodynamics 117 4.1 Hydrodynamic Equations ...... 117 4.2 Steady-Flow and Siphon-Flow Solutions ...... 122 4.3 Thermal Stability of Loops ...... 127 4.3.1 Radiative Loss Instability ...... 128 4.3.2 Heating Scale Instability ...... 133 4.4 Observations of Flows in Coronal Loops ...... 135 4.5 Observations of Cooling Loops ...... 139 4.5.1 CoolingDelays...... 141 4.5.2 Iron Abundance and Filling Factors ...... 142 4.5.3 Scaling Law of Cooling Loops ...... 145 4.5.4 Catastrophic Cooling Phase ...... 145 4.6 Observations of Non-Hydrostatic Loops ...... 148 4.6.1 TRACEObservations...... 150 4.6.2 TheoreticalModels...... 153 4.7 Hydrodynamic Numerical Simulations of Loops ...... 155 4.8 Hydrodynamics of the Transition Region ...... 159 4.9 Hydrodynamics of Coronal Holes ...... 167 4.10 Hydrodynamics of the Solar Wind ...... 172 4.11Summary...... 173 CONTENTS ix

5 Magnetic Fields 175 5.1ElectromagneticEquations...... 176 5.1.1 Maxwell’sEquations...... 176 5.1.2 Ampère’sLaw...... 176 5.1.3 Ohm’sLaw...... 177 5.1.4 Induction Equation ...... 177 5.2PotentialFields...... 178 5.2.1 UnipolarField...... 179 5.2.2 DipoleField...... 180 5.2.3 Potential-Field Calculation Methods ...... 182 Green’s Function Methods ...... 182 Eigenfunction Expansion Methods ...... 184 5.3Force-FreeFields...... 186 5.3.1 LinearForce-FreeFields...... 187 5.3.2 ShearedArcade...... 188 5.3.3 Nonlinear Force-Free Field Calculation Methods ...... 190 TheVerticalIntegrationMethod...... 190 The Boundary Integral Method ...... 192 TheEulerPotentialMethod...... 193 FullMHDMethod...... 194 Potential Vector Grad−RubinMethod...... 195 Evolutionary Methods ...... 195 5.4MagneticFieldinActiveRegionCorona ...... 196 5.4.1 3D Stereoscopy of Active Region Loops ...... 196 5.4.2 AlfvénVelocityinActiveRegions...... 202 5.4.3 Non-Potentiality of Soft X-Ray Loops ...... 205 5.4.4 The Width Variation of Coronal Loops ...... 209 5.5MagneticHelicity...... 213 5.5.1 UniformlyTwistedCylindricalForce-FreeFluxtubes..... 215 5.5.2 Observations of Sigmoid Loops ...... 217 5.5.3 ConservationofHelicity...... 218 5.6MagneticNullpointsandSeparators...... 220 5.6.1 Topological Definitions ...... 220 5.6.2 ObservationsofCoronalNullpoints...... 222 5.7 Magnetic Field Measurements in Radio ...... 224 5.7.1 Magnetic Fields Measured from Free-Free Emission . .... 224 5.7.2 GyroresonanceEmission...... 227 5.7.3 GyroresonanceStereoscopy...... 230 5.7.4 Non-Potential Field Modeling of Gyroresonance Emission . . 233 5.8 Magnetic Field in the Transition Region ...... 234 5.8.1 TheMagneticCanopyStructure...... 235 5.8.2 Force-FreenessoftheChromosphericMagneticField..... 237 5.9Summary...... 239 x CONTENTS

6 Magneto-Hydrodynamics (MHD) 241 6.1MHDEquations...... 241 6.1.1 ParticleConservation...... 242 6.1.2 MomentumorForceEquation...... 243 6.1.3 IdealMHD...... 244 6.1.4 EnergyEquation...... 245 6.1.5 ResistiveMHD...... 246 6.2 MHD of Coronal Loops ...... 247 6.2.1 Magneto-StaticsinVerticalFluxtubes...... 247 6.2.2 LorentzForcenearMagneticNullpoints...... 249 6.2.3 LorentzForceinCurvedFluxtubes...... 252 6.2.4 DynamicsofTwistedFluxtubes...... 253 6.2.5 MHDSimulationsofEmergingFluxtubes...... 257 6.2.6 MHD Simulations of Coronal Loops ...... 259 6.3 MHD Instabilities in Coronal Loops ...... 263 6.3.1 Rayleigh−Taylor Instability ...... 264 6.3.2 Kruskal−Schwarzschild Instability ...... 265 6.3.3 Kelvin−Helmholtz Instability ...... 265 6.3.4 Ballooning Instability ...... 266 6.3.5 Convective Thermal Instability ...... 266 6.3.6 Radiatively-Driven Thermal Instability ...... 266 6.3.7 Heating Scale-Height Instability ...... 268 6.3.8 Resistive Instabilities ...... 268 6.3.9 Kink Instability (m=1) ...... 269 6.3.10 Sausage Instability (m=0) ...... 270 6.4MHDofQuiescentFilamentsandProminences...... 270 6.4.1 MagneticFieldConﬁguration...... 272 6.4.2 Equilibrium Models ...... 275 6.4.3 FormationandEvolution...... 278 Coronal Condensation ...... 278 ChromosphericInjection...... 280 FootpointHeating...... 281 DisappearanceofFilaments/Prominences...... 281 6.5 Summary...... 282

7 MHD Oscillations 283 7.1DispersionRelationofMHDWaves...... 284 7.1.1 Unbounded Homogeneous Medium ...... 285 7.1.2 SingleMagneticInterface...... 289 7.1.3 SlenderSlabGeometry...... 291 7.1.4 CylindricalGeometry...... 291 7.2 Fast Kink-Mode Oscillations ...... 293 7.2.1 Kink-ModePeriod...... 293 7.2.2 Magnetic Field Strength and Coronal Seismology ...... 294 7.2.3 Observations of Kink-Mode Oscillations ...... 295 7.2.4 Prominence Oscillations ...... 301 CONTENTS xi

7.3 Fast Sausage-Mode Oscillations ...... 304 7.3.1 TheWaveNumberCutoff...... 304 7.3.2 Sausage-ModePeriod...... 306 7.3.3 Imaging Observations of Sausage-Mode Oscillations . .... 307 7.3.4 Non-Imaging Observations of Sausage-Mode Oscillations . . 311 7.4 Slow-Mode (Acoustic) Oscillations ...... 316 7.4.1 Slow-Mode Oscillation Period ...... 316 7.4.2 Observations of Slow-Mode Oscillations ...... 317 7.5 Damping of MHD Oscillations ...... 320 7.5.1 Non-IdealMHDEffects...... 321 7.5.2 LateralWaveLeakage...... 322 7.5.3 FootpointWaveLeakage...... 323 7.5.4 PhaseMixing...... 324 7.5.5 ResonantAbsorption...... 325 7.5.6 ObservationalTests...... 326 7.6Summary...... 329

8 Propagating MHD Waves 331 8.1 Propagating MHD Waves in Coronal Loops ...... 332 8.1.1 EvolutionaryEquationforSlow-ModeMHDWaves..... 332 8.1.2 Observations of Acoustic Waves in Coronal Loops ...... 334 8.1.3 Propagating Fast-Mode Waves in Coronal Loops ...... 336 8.2PropagatingMHDWavesintheOpenCorona...... 341 8.2.1 Evolutionary Equation of MHD Waves in Radial Geometry . . 341 8.2.2 ObservationsofAcousticWavesinOpenCorona...... 344 8.2.3 Spectral Observations of Alfv´en Waves in the Open Corona . 346 8.3GlobalWaves...... 348 8.3.1 MoretonWaves,EITWaves,andCMEDimming...... 348 8.3.2 ModelingandSimulationsofGlobalWaves...... 352 8.4Summary...... 354

9 Coronal Heating 355 9.1HeatingEnergyRequirement...... 356 9.2OverviewofCoronalHeatingModels...... 359 9.3DCHeatingModels...... 364 9.3.1 Stress-InducedReconnection...... 364 9.3.2 Stress-InducedCurrentCascade...... 366 9.3.3 Stress-InducedTurbulence...... 368 9.4ACHeatingModels...... 371 9.4.1 Alfv´enicResonance...... 371 9.4.2 ResonantAbsorption...... 372 9.4.3 PhaseMixing...... 374 9.4.4 CurrentLayers...... 374 9.4.5 MHDTurbulence...... 375 9.4.6 CyclotronResonance...... 376 9.5OtherCoronalHeatingScenarios...... 377 xii CONTENTS

9.5.1 AcousticHeating...... 377 9.5.2 ChromosphericReconnection...... 377 9.5.3 Velocity Filtration ...... 378 9.6ObservationsofHeatingEvents...... 380 9.6.1 Microﬂares − Soft X-ray Transient Brightenings ...... 382 9.6.2 Nanoﬂares − EUVTransientBrightenings...... 387 9.6.3 Transition Region Transients − Explosive Events, Blinkers . . 388 9.7ScalingLawsofHeatingEvents...... 390 9.7.1 GeometricScaling...... 391 9.7.2 Density,Temperature,andEnergyScaling...... 393 9.7.3 MagneticScaling...... 396 9.8StatisticsofHeatingEvents...... 398 9.8.1 TheoryofFrequencyDistributions...... 398 9.8.2 FrequencyDistributionsofFlareParameters...... 400 9.8.3 Energy Budget of Flare-like Events ...... 402 9.8.4 Measurements of Frequency Distributions ...... 403 9.9Summary...... 406

10 Magnetic Reconnection 407 10.1Steady2DMagneticReconnection...... 408 10.1.1 Sweet−ParkerReconnectionModel...... 409 10.1.2PetschekReconnectionModel...... 410 10.1.3 Generalizations of Steady 2D Reconnection Models . . . . . 412 10.1.4 Numerical Simulations of Steady 2D Reconnection ...... 413 10.2Unsteady/Bursty2DReconnection...... 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 10.33DMagneticReconnection...... 421 10.3.13DX-TypeReconnection...... 421 10.3.2 Topology of 3D Nullpoints ...... 422 10.3.33DSpine,Fan,andSeparatorReconnection...... 424 10.4MagneticReconnectionintheChromosphere...... 426 10.4.1MagneticFluxEmergence...... 426 10.4.2MagneticFluxCancellation...... 428 10.4.3ChromosphericReconnectionJets...... 435 10.5Flare/CMEModels...... 436 10.5.1TheStandard2DFlareModel...... 436 10.5.2TheEmergingFluxModel...... 439 10.5.3 The Equilibrium Loss Model ...... 441 10.5.4 2D Quadrupolar Flare Model ...... 443 10.5.5TheMagneticBreakoutModel...... 445 10.5.6 3D Quadrupolar Flare Models ...... 447 10.5.7UniﬁcationofFlareModels...... 449 10.6Flare/CMEObservations...... 452 10.6.1EvidenceforReconnectionGeometry...... 452 CONTENTS xiii

X-PointGeometry...... 452 Quadrupolar Geometry ...... 455 3DNullpointGeometry...... 459 10.6.2EvidenceforReconnectionFlowsandJets...... 460 10.6.3Large-ScaleMagneticRestructuring...... 462 10.6.4OpenIssuesonMagneticReconnection...... 462 10.7Summary...... 463

11 Particle Acceleration 465 11.1BasicParticleMotion...... 466 11.1.1ParticleOrbitsinMagneticFields...... 466 11.1.2ParticleDriftsinForceFields...... 467 11.1.3RelativisticParticleEnergies...... 468 11.2 Overview of Particle Acceleration Mechanisms ...... 469 11.3 Electric DC-Field Acceleration ...... 471 11.3.1Sub-DreicerDCElectricFields...... 472 11.3.2Super-DreicerDCElectricFields...... 474 11.3.3 Acceleration near Magnetic X-Points ...... 476 11.3.4 Acceleration near Magnetic O-Points ...... 478 11.3.5 Acceleration in Time-Varying Electromagnetic Fields . .... 481 Betatron Acceleration ...... 481 Field-AlignedElectricPotentialDrops...... 482 CoalescenceandX-PointCollapse...... 483 11.4 Stochastic Acceleration ...... 486 11.4.1GyroresonantWave-ParticleInteractions...... 487 11.4.2 Stochastic Acceleration of Electrons ...... 493 11.4.3 Stochastic Acceleration of Ions ...... 497 11.4.4 Acceleration by Electrostatic Wave-Particle Interactions . . . 499 11.4.5 General Evaluation of Stochastic Acceleration Models .... 500 11.5 Shock Acceleration ...... 500 11.5.1 Fermi Acceleration ...... 501 11.5.2 Shock-Drift (or First-Order Fermi) Acceleration ...... 502 11.5.3 Diffusive Shock Acceleration ...... 505 11.5.4 Shock Acceleration in Coronal Flare Sites ...... 509 11.5.5 Shock Acceleration in CMEs and Type II Bursts ...... 512 11.6Summary...... 515

12 Particle Kinematics 517 12.1OverviewonParticleKinematics...... 518 12.2KinematicsofFree-StreamingParticles...... 520 12.2.1 Deﬁnition of Time-of-Flight Distance ...... 520 12.2.2 Time-of-Flight Measurements ...... 522 12.3 Kinematics of Particle Acceleration ...... 524 12.3.1 Stochastic Acceleration ...... 525 12.3.2 Electric DC Field Acceleration ...... 526 12.4KinematicsofParticleInjection...... 529 xiv CONTENTS

12.4.1ScenariosofSynchronizedInjection...... 529 12.4.2 Model of Particle Injection During Magnetic Reconnection . . 531 12.5KinematicsofParticleTrapping...... 537 12.5.1MagneticMirroring...... 537 12.5.2BifurcationofTrappingandPrecipitation...... 539 12.5.3TrappingTimes...... 541 12.6KinematicsofParticlePrecipitation...... 543 12.6.1SymmetricTraps...... 543 12.6.2AsymmetricTraps...... 544 12.6.3 Collisional Limit ...... 548 12.7Summary...... 549

13 Hard X-Rays 551 13.1HardX-rayInstruments...... 552 13.1.1 SMM − HXRBS,GRS,HXIS...... 552 13.1.2 Yohkoh − HXT...... 553 13.1.3 CGRO − BATSE...... 554 13.1.4RHESSI...... 555 13.2Bremsstrahlung...... 556 13.2.1BremsstrahlungCrossSections...... 556 13.2.2Thick-TargetBremsstrahlung...... 558 13.2.3Thin-TargetBremsstrahlung...... 561 13.3HardX-raySpectra...... 562 13.3.1Thermal-NonthermalSpectra...... 562 13.3.2Soft-Hard-SoftSpectralEvolution...... 565 13.3.3Low-EnergyandHigh-EnergyCutoffs...... 566 13.3.4SpectralInversion...... 567 13.4HardX-rayTimeStructures...... 568 13.4.1PulseObservations...... 568 13.4.2DistributionofPulseDurations...... 569 13.4.3ScalingofPulseDurationwithLoopSize...... 571 13.5HardX-RayTimeDelays...... 574 13.5.1Time-of-FlightDelays...... 574 13.5.2ScalingofTOFDistancewithLoopSize...... 578 13.5.3ConjugateFootpointDelays...... 583 13.5.4TrappingTimeDelays...... 585 13.5.5Thermal-NonthermalDelays(NeupertEffect)...... 587 13.6HardX-raySpatialStructures...... 589 13.6.1FootpointandLoopSources...... 590 13.6.2 Footpoint Ribbons ...... 596 13.6.3 Above-the-Looptop (Masuda) Sources ...... 600 13.6.4OccultedFlares...... 602 13.7HardX-RayStatistics...... 603 13.7.1FlareStatisticsofNonthermalEnergies...... 603 13.7.2FlareStatisticsDuringSolarCycles...... 604 13.8Summary...... 606 CONTENTS xv

14 Gamma-Rays 607 14.1 Overview on Gamma-Ray Emission Mechanisms ...... 608 14.2 Electron Bremsstrahlung Continuum ...... 611 14.2.1Electron-DominatedFlares...... 613 14.2.2 Maximum Acceleration Energy ...... 613 14.2.3 Long-Term Trapping Sources ...... 614 14.3NuclearDe-excitationLines...... 618 14.3.1Gamma-RayLineSpectroscopy...... 618 14.3.2Ion-ElectronRatios...... 620 14.3.3Ion-ElectronTiming...... 622 14.3.4DirectivityandPitchAngleDistributions...... 624 14.3.5Gamma-RayLineEmissioninOccultedFlares...... 627 14.3.6 Abundances of Accelerated Ions ...... 628 14.4NeutronCaptureLine...... 629 14.5PositronAnnihilationLine...... 631 14.6 Pion Decay Radiation ...... 634 14.7Summary...... 635

15 Radio Emission 637 15.1 Overview on Radio Emission Mechanisms ...... 638 15.2 Free-Free Emission (Bremsstrahlung) ...... 640 15.2.1TheoryofBremsstrahlunginMicrowaves...... 640 15.2.2RadioObservationsofFree-FreeEmission...... 642 15.3IncoherentGyroemission...... 644 15.3.1TheoryofGyrosynchrotronEmission...... 644 15.3.2RadioObservationsofGyrosynchrotronEmission...... 645 15.4PlasmaEmission...... 651 15.4.1ElectronBeams...... 651 15.4.2LangmuirWaves...... 655 15.4.3ObservationsofPlasmaEmission...... 657 Metric Type III, J, U, and RS Bursts ...... 657 OtherMetricandDecimetricBursts...... 661 15.5LossconeEmission...... 664 15.5.1ElectronCyclotronMaserEmission...... 664 15.5.2DecimetricObservations...... 667 15.6Summary...... 669

16 Flare Plasma Dynamics 671 16.1CoronalFlarePlasmaHeating...... 672 16.1.1ResistiveorJouleHeating...... 672 16.1.2AnomalousResistivity...... 673 16.1.3ShockHeating...... 674 16.1.4ElectronBeamHeating...... 675 16.1.5ProtonBeamHeating...... 675 16.1.6 Inductive Current Heating ...... 676 16.2ChromosphericFlarePlasmaHeating...... 676 xvi CONTENTS

16.2.1 Electron and Proton Precipitation−DrivenHeating...... 676 16.2.2 Heat Conduction-Driven Heating ...... 679 16.2.3 Hα Emission...... 681 16.2.4White-LightEmission...... 683 16.2.5UVEmission...... 683 16.3ChromosphericEvaporation...... 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 16.4PostﬂareLoopCooling...... 695 16.4.1CoolingDelaysofFluxPeaks...... 695 16.4.2 Differential Emission Measure Evolution ...... 697 16.4.3 Conductive Cooling ...... 699 16.4.4RadiativeCooling...... 700 16.5Summary...... 702

17 Coronal Mass Ejections (CMEs) 703 17.1TheoreticalConceptsofCMEs...... 704 17.1.1ThermalBlastModel...... 704 17.1.2DynamoModel...... 704 17.1.3MassLoadingModel...... 706 17.1.4TetherReleaseModel...... 706 17.1.5TetherStrainingModel...... 707 17.2NumericalMHDSimulationsofCMEs...... 707 17.2.1AnalyticalModelsofCMEs...... 708 17.2.2NumericalMHDSimulationsofCMEs...... 708 17.3Pre-CMEConditions...... 711 17.3.1PhotosphericShearMotion...... 711 17.3.2 Kink Instability of Twisted Structures ...... 713 17.4GeometryofCMEs...... 714 17.5DensityandTemperatureofCMEs...... 718 17.5.1 Density Measurements of CMEs ...... 718 17.5.2TemperatureRangeofCMEs...... 720 17.6 Velocities and Acceleration of CMEs ...... 721 17.7EnergeticsofCMEs...... 724 17.8CoronalDimming...... 727 17.9InterplanetaryCMEPropagation...... 731 17.9.1InterplanetaryMagneticField(IMF)...... 731 17.9.2SolarWind...... 733 17.9.3InterplanetaryShocks...... 734 17.9.4SolarEnergeticParticles(SEP)...... 735 17.9.5InterplanetaryRadioBursts...... 736 17.10Summary...... 737

Problems 739 CONTENTS xvii

Solutions 759

Appendices 789 AppendixA:PhysicalConstants...... 789 AppendixB:ConversionofPhysicalUnits...... 790 Appendix C: Maxwell’s Equations in Different Physical Unit Systems 790 AppendixD:PlasmaParameters...... 791 Appendix E: Conversion Table of Electron Temperatures into Rela- tivisticParameters...... 792 AppendixF:EUVSpectralLines...... 793 Appendix G: Vector Identities ...... 794 Appendix H: Integral Identities ...... 795 Appendix I: Components of Vector Operators ...... 796

Notation 797 PhysicalUnitsSymbols...... 797 LatinSymbols...... 797 GreekSymbols...... 802

Acronyms 805

References 807 Proceedings List ...... 807 Book/Monograph List ...... 815 PhDThesisList...... 818 ReferenceList...... 818 JournalAbbreviations...... 819

Index 869 Preface

In this book we provide a comprehensive introduction into the basic physics of phenomena in the solar corona. Solar physics has evolved over three distinctly different phases using progressively more sophisticated observing tools. The first phase of naked-eye observations that dates back over several thousands of years has been mainly concerned with observations and reports of solar eclipses and the role of the Sun in celestial mechanics. In the second phase that lasted about a century before the beginning of the space age, ground-based solar-dedicated telescopes, spectrometers, coronagraphs, and radio telescopes were built and quantitative measurements of solar phenomena developed, which probed the basic geometric and physical parameters of the solar corona. During the third phase, that started with the beginning of the space age around 1950, we launched solar-dedicated spacecraft that explored the Sun in all possible wavelengths, conveying to us high-resolution images and spectral measurements that permitted us to conduct quantitative physical modeling of solar phenomena, supported by numerical simulations using the theories of magneto-hydrodynamics and plasma particle physics. This book focuses on these new physical insights that have mostly been obtained from the last two decades of space missions, such as from soft X-ray observations with Yohkoh, extreme-ultraviolet (EUV) observations with SoHO and TRACE, and hard X-ray observations with Compton and the recently launched RHESSI. The last decade (1992−2002) has been the most exciting era in the explo- ration of the solar corona in all wavelengths, producing unprecedented stunning pic- tures, movies, and high-precision spectral and temporal data. There are a lot of new insights into the detailed structure of the solar corona, mass flows, magnetic field interactions, coronal heating processes, and magnetic instabilities that lead to flares, accelerated particles, and coronal mass ejections, which have not been covered in previous textbooks. The philosophy and approach of this textbook is to convey a physics introduction course to a selected topic of astrophysics, rather than to provide a review of observational material. The material is therefore not described in historical, phenomenological, or morphological order, but rather structured by physical principles. In each chapter we outline the basic physics of relevant physical models that explain coronal structures, flare processes, and coronal mass ejections. We include in each chapter analytical and numerical model calculations that have been applied to these solar phenomena, and we show comprehensive data material that illustrate the models and physical interpretations. This textbook is aimed to be an up-to-date introduction into the physics of the solar corona, suitable for graduate students and researchers. The 17 chapters build up the physical concepts in a systematic way, starting xx PREFACE

Table 1: Selection of textbooks and monographs on solar physics.

Author Year Book title Sun: general Bruzek & Durrant 1977 Illustrated Glossary for Solar and Solar-Terrestrial Physics Zirin 1988 Astrophysics of the Sun Foukal 1990 Solar Astrophysics Phillips 1992 Guide to the Sun Lang 1995 Sun, Earth, and Sky Lang 2000 The Sun from Space Murdin 2000 Encyclopedia of Astronomy and Astrophysics Lang 2001 The Cambridge Encyclopedia of the Sun Golub & Pasachoff 2001 Nearest Star: The Surprising Science of Our Sun Stix 2002 The Sun Zirker 2002 Journey from the Center of the Sun

Photosphere Stenﬂo 1994 Solar Magnetic Fields: Polarized Radiation Diagnostics Sch¨ussler & Schmidt 1994 Solar Magnetic Fields

Transition region Mariska 1992 The Solar Transitions Region

Corona, ﬂares, plasma physics Kundu 1965 Solar Radio Astronomy Zheleznyakov 1970 Radio Emission of the Sun and Planets Svestka 1976 Solar Flares Krueger 1979 Introduction to Solar Radio Astronomy and Radio Physics Melrose 1980 Plasma Astrophysics (Vol. 1 & 2): Nonthermal Processes in Diffuse Magnetized Plasmas. Priest 1982 Solar Magnetohyrdodynamics McLean & Labrum 1985 Solar Radiophysics Melrose 1986 Instabilities in Space and Laboratory Plasmas Bray et al. 1991 Plasma Loops in the Solar Corona Benz 1993 Plasma Astrophysics. Kinetic Processes in Solar and Stellar Coronae Sturrock 1994 Plasma Physics. An Introduction to the Theory of Astrophysical, Geophysical and Laboratory Plasmas Kirk, Melrose, & Priest 1994 Plasma Astrophysics Tandberg−Hanssen 1995 The Nature of Solar Prominences Golub & Pasachoff 1997 The Solar Corona Strong et al. 1999 The Many Faces of the Sun: A Summary of the Results from NASA’s Solar Maximum Mission Schrijver & Zwaan 2000 Solar and Stellar Magnetic Activity Priest & Forbes 2000 Magnetic Reconnection (MHD Theory and Applications) Tajima & Shibata 2002 Plasma Astrophysics Aschwanden 2002 Particle Acceleraion and Kinematics in Solar Flares

Heliosphere and interplanetary Russell, Priest, Lee 1990 Physics of Magnetic Flux Ropes Schwenn & Marsch 1991 Physics of the Inner Heliosphere: Vol. 1: Large-Scale Phenomena Vol. 2: Particles, Waves and Turbulence Kivelson & Russell 1995 Introduction to Space Physics Crooker et al. 1997 CMEs Song et al. 2001 Space Weather Balogh, Marsden, & Smith 2001 The Heliosphere near Solar Minimum − The Ulysses Perspective Carlowicz & Lopez 2002 Storms from the Sun − The Emerging Science of Space Weather PREFACE xxi with introductions into the basic concepts (§1−2), magneto-hydrodynamics (MHD) of the coronal plasma (§3−6), MHD of oscillations and waves (§7−8), coronal heating (§9), magnetic reconnection processes (§10), particle acceleration and kinematics (§11−12), flare dynamics and emission in various wavelengths (§13−16), and coronal mass ejection (CME) phenomena (§17). So the first-half of the book is concerned with phenomena of the quiet Sun (§1−9), while the second-half focuses on eruptive phenomena such as flares and CMEs (§10−17). The scope of the book is restricted to the solar corona, while other parts of the Sun, such as the solar interior, the photosphere, the chromosphere, or the heliosphere, are referred to in other textbooks, of which a selection is given in Table 1. Extensive literature (reviews and theoretical or modeling studies) are referenced preferentially at the beginning or end of the chapters and subsections. The material of this textbook is based on some 10,000 original papers published in solar physics, which grows at a current rate of about 700 papers per year. The physical units used in this textbook are the cgs units, as they are most frequently used in the original publications in solar physics literature. Conversion into SI units can be done easily by using the conversion factors given in Appendix B. The author is most indebted to invaluable discussions, comments, reviews, and graphics provisions from colleagues and friends, which are listed in alphabetical order: Loren Acton, Spiro Antiochos, Tim Bastian, Arnold Benz, John Brown, In- eke DeMoortel, Brian Dennis, Marc DeRosa, George Doschek, Robertus (von Fay- Siebenburgen) Erdélyi, Terry Forbes, Allen Gary, Costis Gontikakis, Marcel Goossens, Joe Gurman, Iain Hannah, Jack Harvey, Eberhard Haug, Jean Heyvaerts, Gordon Hol- man, Joe Huba, Marion Karlický, Jim Klimchuk, Boon Chye Low, John Mariska, Eckart Marsch, Don Melrose, Zoran Mikić, Jim Miller, Valery Nakariakov, Aake Nord- lund, Leon Ofman, Eugene Parker, Spyridon Patsourakos, Alex Pevtsov, Ken Phillips, Eric Priest, Reza Rezaei, Bernie Roberts, Jim Ryan, Salvatore Serio, Karel Schrijver, Gerry Share, Kazunari Shibata, Daniele Spadaro, Barbara Thompson, Alan Title, Ka- naris Tsinganos, Tong-Jiang Wang, Harry Warren, Stephen White, Thomas Wiegel- mann, David Williams, Amy Winebarger, Takaaki Yokoyama, and Paolo Zlobec. The author wishes to acknowledge the efficient and most helpful support provided by PRAXIS Publishing Ltd., in particular for reviewing by John Mason, copy-editing by Neil Shuttlewood (Originator), and cover design by Jim Wilkie. LATEX support was kindly provided by Stephen Webb, image scanning by David Schiff (Lockheed Martin), SolarSoft software by Sam Freeland (Lockheed Martin), and archive support by the NASA Astrophysics Data System (ADS). Most gratefully I wish to thank the publisher Clive Horwood, who had the vision to produce this textbook, and who invited me to undertake this project, provided untiring encouragement and patience during the 3-year production period. Special thanks goes to my entire family, my late wife Susanna to whom this book is dedicated with eternal love, my children Pascal Dominique and Alexander Julian, and to my friend Carol J. Kersten, who all supported this work with an enthusiastic spirit.

Palo Alto, California, June 2004 Markus J. Aschwanden xxii PREFACE

Preface to 2nd Edition

The second edition (in paperback) reproduces the entire body of the first edition (with hardbound cover) with identical text, except for minor corrections of typographical misprints, but contains in addition a section with some 170 Problems and Solutions at the end of the main text body (p. 739−788), suitable as exercises for students and researchers to obtain a deeper understanding of the text. The analytical and numerical solutions provided for these specific problems allows the reader to verify whether he/she understands practical applications to solar observations, which are not always exemplified in detail in the main body of the text. The author is most indebted to the following friends and colleagues who double-checked and proof-read the sections of the Problems and Solutions, as well as parts or the first edition text: Henry Aurass, Mitchell Berger, Jeff Brosius, Amir Caspi, Steven Christe, Ineke DeMoortel, Robertus Erdélyi, Gregory Fleishman, Andre Fludra, Dale Gary, Sarah Gibson, Holly Gilbert, Costis Gontikakis, Iain Hannah, Leon Kocharov, Bernhard Kliem, Eduard Kontar, Enrico Landi, Yuri Litvinenko, Scott McIntosh, Thomas Metcalf, Thomas Neukirch, Hardi Peter, Gordon Petrie, John Raymond, Pete Riley, Julia Saba, David Smith, Youra Taroyan, David Tsiklauri, Aad VanBallegooijen, Gary Verth, Angelos Vourlidas, Harry Warren, Thomas Wiegelmann, and Jie Zhang. Due to the short interval between the first and second edition we refrained from updating the text and references. However, we are happy to report that significant new science results have been produced as a consequence of the flawless continued performance of the major solar space missions, such as SoHO, TRACE, and RHESSI. The reader may consult the official NASA mission websites or the author’s website on solar literature: http://www.lmsal.com/∼aschwand/publications/index.html for recent updates of SoHO, TRACE, and RHESSI publications. New solar missions such as STEREO, Solar-B, and SDO are planned for launch shortly after this second edition comes out in print. We are looking forward to another exciting decade of vibrant solar research.

Palo Alto, California, December 2005 Markus J. Aschwanden