Physics of the Solar Corona: An Introduction with Problems and Solutions

Contents......Page 6
Plate Section......Page 908
Preface......Page 17
Preface to 2nd Edition......Page 20
1.1 History of Solar Corona Observations......Page 21
1.2 Nomenclature of Coronal Phenomena......Page 28
1.3 The Solar Magnetic Cycle......Page 34
1.4 Magnetic Field of the Solar Corona......Page 37
1.5 Geometric Concepts of the Solar Corona......Page 40
1.6 Density Structure of the Solar Corona......Page 43
1.7 Temperature Structure of the Solar Corona......Page 46
1.8 Plasma-β Parameter of the Solar Corona......Page 48
1.9 Chemical Composition of the Solar Corona......Page 50
1.10 Radiation Spectrum of the Solar Corona......Page 52
1.11 Summary......Page 56
2.1 Radiation Transfer and Observed Brightness......Page 57
2.2 Black-Body Thermal Emission......Page 59
2.3 Thermal Bremsstrahlung (Free–Free Emission)......Page 62
2.4 Atomic Energy Levels......Page 67
2.5 Atomic Transition Probabilities......Page 70
2.6 Ionization and Recombination Processes......Page 72
2.7 Ionization Equilibrium and Saha Equation......Page 75
2.8 Emission Line Spectroscopy......Page 77
2.9 Radiative Loss Function......Page 81
2.10 First Ionization Potential (FIP) Effect......Page 83
2.11 Summary......Page 86
3.1 Hydrostatic Scale Height......Page 87
3.2 Hydrostatic Weighting Bias......Page 91
3.3 Multi-Hydrostatic Corona......Page 96
3.4.1 Vertical Semi-Circular Loops......Page 103
3.4.2 Inclined Semi-Circular Loops......Page 104
3.4.3 Diverging Semi-Circular Loops......Page 105
3.4.4 CoordinateTransformations......Page 106
3.5 Loop Line-of-Sight Integration......Page 109
3.5.1 Bright Single Loop......Page 110
3.5.3 Statistical Distribution of Loops......Page 112
3.6 Hydrostatic Solutions and Scaling Laws......Page 113
3.6.1 Uniform Heating and RTV Scaling Laws......Page 114
3.6.3 Analytical Approximations of Hydrostatic Solutions......Page 116
3.7 Heating Function......Page 119
3.8 Instrumental Response Functions......Page 128
3.9 Observations of Hydrostatic Loops......Page 129
3.10 Hydrostatic DEM Distributions......Page 133
3.11 Summary......Page 136
4.1 Hydrodynamic Equations......Page 137
4.2 Steady-Flow and Siphon-Flow Solutions......Page 142
4.3 Thermal Stability of Loops......Page 147
4.3.1 Radiative Loss Instability......Page 148
4.3.2 Heating Scale Instability......Page 153
4.4 Observations of Flows in Coronal Loops......Page 155
4.5 Observations of Cooling Loops......Page 159
4.5.1 Cooling Delays......Page 161
4.5.2 Iron Abundance and Filling Factors......Page 162
4.5.4 Catastrophic Cooling Phase......Page 165
4.6 Observations of Non-Hydrostatic Loops......Page 168
4.6.1 TRACE Observations......Page 170
4.6.2 Theoretical Models......Page 173
4.7 Hydrodynamic Numerical Simulations of Loops......Page 175
4.8 Hydrodynamics of the Transition Region......Page 179
4.9 Hydrodynamics of Coronal Holes......Page 187
4.10 Hydrodynamics of the Solar Wind......Page 192
4.11 Summary......Page 193
5 Magnetic Fields......Page 195
5.1.2 Ampère\'s Law......Page 196
5.1.4 Induction Equation......Page 197
5.2 Potential Fields......Page 198
5.2.1 Unipolar Field......Page 199
5.2.2 Dipole Field......Page 200
5.2.3 Potential-Field Calculation Methods......Page 202
5.3 Force-Free Fields......Page 206
5.3.1 Linear Force-Free Fields......Page 207
5.3.2 Sheared Arcade......Page 208
5.3.3 Nonlinear Force-Free Field Calculation Methods......Page 210
5.4.1 3D Stereoscopy of Active Region Loops......Page 216
5.4.2 Alfvén Velocity in Active Regions......Page 222
5.4.3 Non-Potentiality of Soft X-Ray Loops......Page 225
5.4.4 The Width Variation of Coronal Loops......Page 229
5.5 Magnetic Helicity......Page 233
5.5.1 Uniformly Twisted Cylindrical Force-Free Fluxtubes......Page 235
5.5.2 Observations of Sigmoid Loops......Page 237
5.5.3 Conservation of Helicity......Page 238
5.6.1 Topological Definitions......Page 240
5.6.2 Observations of Coronal Nullpoints......Page 242
5.7.1 Magnetic Fields Measured from Free-Free Emission......Page 244
5.7.2 Gyroresonance Emission......Page 247
5.7.3 Gyroresonance Stereoscopy......Page 250
5.7.4 Non-Potential Field Modeling of Gyroresonance Emission......Page 253
5.8 Magnetic Field in the Transition Region......Page 254
5.8.1 The Magnetic Canopy Structure......Page 255
5.8.2 Force-Freeness of the Chromospheric Magnetic Field......Page 257
5.9 Summary......Page 259
6.1 MHD Equations......Page 260
6.1.1 Particle Conservation......Page 261
6.1.2 Momentum or Force Equation......Page 262
6.1.3 Ideal MHD......Page 263
6.1.4 Energy Equation......Page 264
6.1.5 Resistive MHD......Page 265
6.2.1 Magneto-Statics in Vertical Fluxtubes......Page 266
6.2.2 Lorentz Force near Magnetic Nullpoints......Page 268
6.2.3 Lorentz Force in Curved Fluxtubes......Page 271
6.2.4 Dynamics of Twisted Fluxtubes......Page 272
6.2.5 MHD Simulations of Emerging Fluxtubes......Page 276
6.2.6 MHD Simulations of Coronal Loops......Page 278
6.3 MHD Instabilities in Coronal Loops......Page 282
6.3.1 Rayleigh–Taylor Instability......Page 283
6.3.3 Kelvin–Helmholtz Instability......Page 284
6.3.6 Radiatively-Driven Thermal Instability......Page 285
6.3.8 Resistive Instabilities......Page 287
6.3.9 Kink Instability (m=1)......Page 288
6.4 MHD of Quiescent Filaments and Prominences......Page 289
6.4.1 Magnetic Field Configuration......Page 291
6.4.2 Equilibrium Models......Page 294
6.4.3 Formation and Evolution......Page 297
6.5 Summary......Page 301
7 MHD Oscillations......Page 302
7.1 Dispersion Relation of MHD Waves......Page 303
7.1.1 Unbounded Homogeneous Medium......Page 304
7.1.2 Single Magnetic Interface......Page 308
7.1.4 Cylindrical Geometry......Page 310
7.2.1 Kink-Mode Period......Page 312
7.2.2 Magnetic Field Strength and Coronal Seismology......Page 313
7.2.3 Observations of Kink-Mode Oscillations......Page 314
7.2.4 Prominence Oscillations......Page 320
7.3.1 The Wave Number Cutoff......Page 323
7.3.2 Sausage-Mode Period......Page 325
7.3.3 Imaging Observations of Sausage-Mode Oscillations......Page 326
7.3.4 Non-Imaging Observations of Sausage-Mode Oscillations......Page 330
7.4.1 Slow-Mode Oscillation Period......Page 335
7.4.2 Observations of Slow-Mode Oscillations......Page 336
7.5 Damping of MHD Oscillations......Page 339
7.5.1 Non-Ideal MHD Effects......Page 340
7.5.2 Lateral Wave Leakage......Page 341
7.5.3 Footpoint Wave Leakage......Page 342
7.5.4 Phase Mixing......Page 343
7.5.5 Resonant Absorption......Page 344
7.5.6 Observational Tests......Page 345
7.6 Summary......Page 348
8 Propagating MHD Waves......Page 350
8.1.1 Evolutionary Equation for Slow-Mode MHD Waves......Page 351
8.1.2 Observations of Acoustic Waves in Coronal Loops......Page 353
8.1.3 Propagating Fast-Mode Waves in Coronal Loops......Page 355
8.2.1 Evolutionary Equation of MHD Waves in Radial Geometry......Page 360
8.2.2 Observations of Acoustic Waves in Open Corona......Page 363
8.2.3 Spectral Observations of Alfvén Waves in the Open Corona......Page 365
8.3.1 Moreton Waves, EIT Waves, and CME Dimming......Page 367
8.3.2 Modeling and Simulations of Global Waves......Page 371
8.4 Summary......Page 373
9 Coronal Heating......Page 374
9.1 Heating Energy Requirement......Page 375
9.2 Overview of Coronal Heating Models......Page 378
9.3.1 Stress-Induced Reconnection......Page 383
9.3.2 Stress-Induced Current Cascade......Page 385
9.3.3 Stress-Induced Turbulence......Page 387
9.4.1 Alfvénic Resonance......Page 390
9.4.2 Resonant Absorption......Page 391
9.4.4 Current Layers......Page 393
9.4.5 MHD Turbulence......Page 394
9.4.6 Cyclotron Resonance......Page 395
9.5.2 Chromospheric Reconnection......Page 396
9.5.3 Velocity Filtration......Page 397
9.6 Observations of Heating Events......Page 399
9.6.1 Microflares – Soft X-ray Transient Brightenings......Page 401
9.6.2 Nanoflares – EUV Transient Brightenings......Page 406
9.6.3 Transition Region Transients – Explosive Events, Blinkers......Page 407
9.7 Scaling Laws of Heating Events......Page 409
9.7.1 Geometric Scaling......Page 410
9.7.2 Density,Temperature,and Energy Scaling......Page 412
9.7.3 Magnetic Scaling......Page 415
9.8.1 Theory of Frequency Distributions......Page 417
9.8.2 Frequency Distributions of Flare Parameters......Page 419
9.8.3 Energy Budget of Flare-like Events......Page 421
9.8.4 Measurements of Frequency Distributions......Page 422
9.9 Summary......Page 425
10 Magnetic Reconnection......Page 426
10.1 Steady 2D Magnetic Reconnection......Page 427
10.1.1 Sweet–Parker Reconnection Model......Page 428
10.1.2 Petschek Reconnection Model......Page 429
10.1.3 Generalizations of Steady 2D Reconnection Models......Page 431
10.1.4 Numerical Simulations of Steady 2D Reconnection......Page 432
10.2.1 Tearing-Mode Instability and Magnetic Island Formation......Page 433
10.2.2 Coalescence Instability......Page 435
10.2.3 Dynamic Current Sheet and Bursty Reconnection......Page 436
10.3.1 3D X-Type Reconnection......Page 440
10.3.2 Topology of 3D Nullpoints......Page 441
10.3.3 3D Spine, Fan, and Separator Reconnection......Page 443
10.4.1 Magnetic Flux Emergence......Page 445
10.4.2 Magnetic Flux Cancellation......Page 447
10.4.3 Chromospheric Reconnection Jets......Page 454
10.5.1 The Standard 2D Flare Model......Page 455
10.5.2 The Emerging Flux Model......Page 458
10.5.3 The Equilibrium Loss Model......Page 460
10.5.4 2D Quadrupolar Flare Model......Page 462
10.5.5 The Magnetic Breakout Model......Page 464
10.5.6 3D Quadrupolar Flare Models......Page 466
10.5.7 Unification of Flare Models......Page 468
10.6.1 Evidence for Reconnection Geometry......Page 471
10.6.2 Evidence for Reconnection Flows and Jets......Page 479
10.6.4 Open Issues on Magnetic Reconnection......Page 481
10.7 Summary......Page 482
11 Particle Acceleration......Page 484
11.1.1 Particle Orbits in Magnetic Fields......Page 485
11.1.2 Particle Drifts in Force Fields......Page 486
11.1.3 Relativistic Particle Energies......Page 487
11.2 Overview of Particle Acceleration Mechanisms......Page 488
11.3 Electric DC-Field Acceleration......Page 490
11.3.1 Sub-Dreicer DC Electric Fields......Page 491
11.3.2 Super-Dreicer DC Electric Fields......Page 493
11.3.3 Acceleration near Magnetic X-Points......Page 495
11.3.4 Acceleration near Magnetic O-Points......Page 497
11.3.5 Acceleration in Time-Varying Electromagnetic Fields......Page 500
11.4 Stochastic Acceleration......Page 505
11.4.1 Gyroresonant Wave-Particle Interactions......Page 506
11.4.2 Stochastic Acceleration of Electrons......Page 512
11.4.3 Stochastic Acceleration of Ions......Page 516
11.4.4 Acceleration by Electrostatic Wave-Particle Interactions......Page 518
11.5 Shock Acceleration......Page 519
11.5.1 Fermi Acceleration......Page 520
11.5.2 Shock-Drift (or First-Order Fermi) Acceleration......Page 521
11.5.3 Diffusive Shock Acceleration......Page 524
11.5.4 Shock Acceleration in Coronal Flare Sites......Page 528
11.5.5 Shock Acceleration in CMEs and Type II Bursts......Page 531
11.6 Summary......Page 534
12 Particle Kinematics......Page 535
12.1 Overview on Particle Kinematics......Page 536
12.2.1 Definition of Time-of-Flight Distance......Page 538
12.2.2 Time-of-Flight Measurements......Page 540
12.3 Kinematics of Particle Acceleration......Page 542
12.3.1 Stochastic Acceleration......Page 543
12.3.2 Electric DC Field Acceleration......Page 544
12.4.1 Scenarios of Synchronized Injection......Page 547
12.4.2 Model of Particle Injection During Magnetic Reconnection......Page 549
12.5.1 Magnetic Mirroring......Page 555
12.5.2 Bifurcation of Trapping and Precipitation......Page 557
12.5.3 Trapping Times......Page 559
12.6.1 Symmetric Traps......Page 561
12.6.2 Asymmetric Traps......Page 562
12.6.3 Collisional Limit......Page 566
12.7 Summary......Page 567
13 Hard X-Rays......Page 569
13.1.1 SMM – HXRBS, GRS, HXIS......Page 570
13.1.2 Yohkoh – HXT......Page 571
13.1.3 CGRO – BATSE......Page 572
13.1.4 RHESSI......Page 573
13.2.1 Bremsstrahlung Cross Sections......Page 574
13.2.2 Thick-Target Bremsstrahlung......Page 576
13.2.3 Thin-Target Bremsstrahlung......Page 579
13.3.1 Thermal-Nonthermal Spectra......Page 580
13.3.2 Soft-Hard-Soft Spectral Evolution......Page 583
13.3.3 Low-Energy and High-Energy Cutoffs......Page 584
13.3.4 Spectral Inversion......Page 585
13.4.1 Pulse Observations......Page 586
13.4.2 Distribution of Pulse Durations......Page 587
13.4.3 Scaling of Pulse Duration with Loop Size......Page 589
13.5.1 Time-of-Flight Delays......Page 592
13.5.2 Scaling of TOF Distance with Loop Size......Page 596
13.5.3 Conjugate Footpoint Delays......Page 601
13.5.4 Trapping Time Delays......Page 603
13.5.5 Thermal-Nonthermal Delays (Neupert Effect)......Page 605
13.6 Hard X-ray Spatial Structures......Page 607
13.6.1 Footpoint and Loop Sources......Page 608
13.6.2 Footpoint Ribbons......Page 614
13.6.3 Above-the-Looptop (Masuda) Sources......Page 618
13.6.4 Occulted Flares......Page 620
13.7.1 Flare Statistics of Nonthermal Energies......Page 621
13.7.2 Flare Statistics During Solar Cycles......Page 622
13.8 Summary......Page 624
14 Gamma-Rays......Page 625
14.1 Overview on Gamma-Ray Emission Mechanisms......Page 626
14.2 Electron Bremsstrahlung Continuum......Page 629
14.2.2 Maximum Acceleration Energy......Page 631
14.2.3 Long-Term Trapping Sources......Page 632
14.3.1 Gamma-Ray Line Spectroscopy......Page 636
14.3.2 Ion-Electron Ratios......Page 638
14.3.3 Ion-Electron Timing......Page 640
14.3.4 Directivity and Pitch Angle Distributions......Page 642
14.3.5 Gamma-Ray Line Emission in Occulted Flares......Page 645
14.3.6 Abundances of Accelerated Ions......Page 646
14.4 Neutron Capture Line......Page 647
14.5 Positron Annihilation Line......Page 649
14.6 Pion Decay Radiation......Page 652
14.7 Summary......Page 653
15 Radio Emission......Page 655
15.1 Overview on Radio Emission Mechanisms......Page 656
15.2.1 Theory of Bremsstrahlung in Microwaves......Page 658
15.2.2 Radio Observations of Free-Free Emission......Page 660
15.3.1 Theory of Gyrosynchrotron Emission......Page 662
15.3.2 Radio Observations of Gyrosynchrotron Emission......Page 663
15.4.1 Electron Beams......Page 669
15.4.2 Langmuir Waves......Page 673
15.4.3 Observations of Plasma Emission......Page 675
15.5.1 Electron Cyclotron Maser Emission......Page 682
15.5.2 Decimetric Observations......Page 685
15.6 Summary......Page 687
16 Flare Plasma Dynamics......Page 689
16.1.1 Resistive or Joule Heating......Page 690
16.1.2 Anomalous Resistivity......Page 691
16.1.3 Shock Heating......Page 692
16.1.5 Proton Beam Heating......Page 693
16.2.1 Electron and Proton Precipitation–Driven Heating......Page 694
16.2.2 Heat Conduction-Driven Heating......Page 697
16.2.3 Hα Emission......Page 699
16.2.5 UV Emission......Page 701
16.3 Chromospheric Evaporation......Page 703
16.3.1 Hydrodynamic Simulations of Chromospheric Evaporation......Page 705
16.3.2 Line Observations of Chromospheric Evaporation......Page 707
16.3.3 Imaging Observations of Chromospheric Evaporation......Page 709
16.3.4 Radio Emission and Chromospheric Evaporation......Page 711
16.4.1 Cooling Delays of Flux Peaks......Page 713
16.4.2 Differential Emission Measure Evolution......Page 715
16.4.3 Conductive Cooling......Page 717
16.4.4 Radiative Cooling......Page 718
16.5 Summary......Page 720
17 Coronal Mass Ejections (CMEs)......Page 721
17.1.2 Dynamo Model......Page 722
17.1.4 Tether Release Model......Page 724
17.2 Numerical MHD Simulations of CMEs......Page 725
17.2.2 Numerical MHD Simulations of CMEs......Page 726
17.3.1 Photospheric Shear Motion......Page 729
17.3.2 Kink Instability of Twisted Structures......Page 731
17.4 Geometry of CMEs......Page 732
17.5.1 Density Measurements of CMEs......Page 736
17.5.2 Temperature Range of CMEs......Page 738
17.6 Velocities and Acceleration of CMEs......Page 739
17.7 Energetics of CMEs......Page 742
17.8 Coronal Dimming......Page 745
17.9.1 Interplanetary Magnetic Field (IMF)......Page 749
17.9.2 Solar Wind......Page 751
17.9.3 Interplanetary Shocks......Page 752
17.9.4 Solar Energetic Particles (SEP)......Page 753
17.9.5 Interplanetary Radio Bursts......Page 754
17.10 Summary......Page 755
Problems......Page 756
Solutions......Page 776
Appendix A: Physical Constants......Page 805
Appendix C: Maxwell\'s Equations in Different Physical Unit Systems......Page 806
Appendix D: Plasma Parameters......Page 807
Appendix E: Conversion Table of Electron Temperatures into Relativistic Parameters......Page 808
Appendix F: EUV Spectral Lines......Page 809
Appendix G: Vector Identities......Page 810
Appendix H: Integral Identities......Page 811
Appendix I: Components of Vector Operators......Page 812
Latin Symbols......Page 813
Greek Symbols......Page 818
Acronyms......Page 820
Proceedings List......Page 822
Book/Monograph List......Page 830
Journal Abbreviations......Page 833
A......Page 884
C......Page 885
D......Page 887
E......Page 888
F......Page 890
H......Page 892
I......Page 894
L......Page 895
O......Page 899
P......Page 900
R......Page 901
S......Page 902
T......Page 905
W......Page 906
Z......Page 907