Contents
1 Introduction 1
References 7
2 Theory of MW Emissions of Solar Flaring Loops 13
2.1 Observational Characteristics of Solar Microwave Emissions 14
2.1.1 Intensity, Polarization, and Spectrum of MW Emission 14
2.1.2 Radiation Transfer 16
2.1.3 Thermal and Nonthermal (NT) Emission 17
2.2 Gyrosynchrotron (GS) Emission 17
2.2.1 Emissivity and Self-absorption Coefficient 18
2.2.2 Formation of GS Spectrum. 20
2.2.3 Influence of Magnetic Field Strength 21
2.2.4 Influence of Self-Absorption 22
2.2.5 Influence of High Plasma Density: Razin Effect 24
2.2.6 Razin Effect and Electron Power-Law Index 26
2.2.7 Plasma Density Increase on the Late Decay Phase 29
2.2.8 Influence of Plasma Inhomogeneity on GS Spectrum 29
2.3 Effects of Electron Pitch-Angle Anisotropy 32
2.3.1 Parameters of Numerical Simulation 33
2.3.2 Pitch-Angle Distributions of SinN Type 33
2.3.3 Effect of Pitch-Angle Distribution Shape: Gaussian Loss-Cone 40
2.3.4 Effect of Pitch-Angle Distribution Shape: Beam-like Distribution 43
2.3.5 Discussion 48
2.4 Trapping and Transport Effects 50
2.4.1 Dependence on the Position of Acceleration/Injection Site 50
2.4.2 Spectral an Polarization Responses to Specific Electron Distributions 52
2.4.3 Diagnostic Potential 54
2.5 Effects of Other Parameters on GS Emission 55
2.5.1 Spectral Shape 55
2.5.2 Radio Flux Density 56
2.5.3 Spectral Index 58
2.5.4 Turnover Frequency 59
2.6 Numerical Codes for Fast GS Emission Calculations 59
References 60
3 Observations and Explanations of MW Emissions in Solar Flaring Loops 65
3.1 Studies on Spatially Unresolvable Observations 65
3.1.1 Flattened Spectra in Solar Radio Bursts at Cm and Mm Bands and Dynamics of Energetic Electrons in Flaring Loops 65
3.1.2 Dynamics of Peak Frequency in Solar MW Bursts:Self-absorption and Razin Effect 75
3.1.3 Optically Thin Emission, Power-Law Distribution of Flares, and Occurrence Rate of Flares 95
3.2 Spatial Distribution of Microwave Brightness 100
3.2.1 Nonthermal MW Source at the Top of Extended Flaring Loops 101
3.2.2 Time Delays Between MW Emissions from Different Parts of Flaring Loop 102
3.2.3 Time Delays of MW Emissions at Different Frequencies 103
3.2.4 Redistribution of MW Brightness in Flaring Loops 104
3.2.5 Comparison of Observations and Model Predictions 106
3.2.6 Spatial Distribution of Energetic Electrons in Flaring Loops 108
3.2.7 Dynamics of Electron Spatial Distribution 110
3.2.8 Constraints on Particle Acceleration, Projection,and Motion 112
3.3 Statistical Studies on MW Brightness Distributions 112
3.3.1 Data Selection 112
3.3.2 Comparison of MW Brightness in LT and FPs 114
3.3.3 Relation of MW Brightness and Other Parameters 114
3.3.4 Asymmetry of MW Brightness in Flaring Loop FPs 117
3.4 Spectral Properties of MW Emissions 126
3.4.1 Distribution of Spectral Slopes Along Flaring Loops 127
3.4.2 Statistics of Optically Thin Spectral Indices of MW Emissions in LT and FPs 132
3.4.3 Hard-Soft-Hard (HSH)—a New Pattern of MW Spectral Evolution 133
3.4.4 Dependence of Spectral Evolution on Frequencies 136
3.4.5 Evolution of MW Spectra in Different Parts of Flaring Loops 138
3.5 Distribution and Evolution of Radio Polarization 139
3.5.1 Comparison of Polarization of MW Emissions in LT and FPs 140
3.5.2 Relation of Polarization and Other Parameters in LT and FPs 141
3.5.3 Relation of Polarization and Magnetic Field in LT and FPs 141
3.5.4 Time Variation of Polarization in LT and FPs 143
3.5.5 Linear Mode Coupling and Reversal of Polarization 147
3.5.6 Determination of Intrinsic Mode 151
3.5.7 Modeling the MW Polarization Distribution Along Flaring Loops 152
References 156
4 Theory of X-Ray Emissions in Solar Flaring Loops 163
4.1 Thick-Target and Thin-Target Models 164
4.1.1 Overview 164
4.1.2 Thin-Target Model 165
4.1.3 Thick-Target Model 168
4.1.4 Relation of Two Models 171
4.1.5 Effect of Low-Energy Cutoff on Spectral Indices of Electrons and Photons 172
4.2 Propagation of Electrons and Its Effect on X-Ray Emission 174
4.2.1 Overview 174
4.2.2 Magnetic Mirror and Loss-Cone Distribution 174
4.2.3 Formation of Loss-Cone Distribution 176
4.3 Spatial Distribution of X-Ray and c-Ray Brightness 181
4.3.1 Numerical Simulations of Spatial Distribution of Energetic Electrons in Flaring Loops 182
4.3.2 Simulated Results of Spatial Distribution of X-Rays and c-Rays 183
4.3.3 Conclusions 186
4.4 Spatial Distribution of X-Ray Directivity and Polarization 186
4.4.1 Modeling 187
4.4.2 Directivity at Different Positions in Flaring Loops 188
4.4.3 Polarization at Different Positions in Flaring Loops 192
4.4.4 Conclusions 194
References 195
5 Observations and Explanations of X-Ray Emissions in Flaring Loops 197
5.1 Overview 197
5.2 Distribution of Hard X-Ray (HXR) Brightness: Loop Top and Feet 198
5.3 Spectral Index of HXR Emissions: Loop Top and Feet 199
5.4 A New Pattern of HXR Spectral Evolution 202
5.5 Evolution of HXR Spectra in Dependence of Energies 204
5.6 Evolution of HXR Spectra in Dependence of Locations 208
5.7 Asymmetry of HXR Brightness in Flaring Loop Feet 210
References 213
6 Diagnostics of Flaring Loop Parameters 217
6.1 Overview 217
6.2 Diagnosis of Coronal Magnetic Field and Non-thermal Electron Density 219
6.2.1 Diagnosis Method 219
6.2.2 Sudden Change of Transverse Coronal Magnetic Component Around Magnetic Neutral Line 222
6.2.3 Attenuation of Coronal Magnetic Field in Solar MW Bursts 225
6.2.4 Evolution of Turnover Frequency and Magnetic field with Flattened Optically Thin Spectra 229
6.2.5 Theoretical Scaling Laws of Coronal Magnetic Field and Electron Power-Law Index in Corona 233
6.2.6 Comparison of Radio Diagnosis with Extrapolation of Solar Photospheric Magnetogram 241
6.2.7 Summary and Prospective 243
6.3 Diagnosis of Low-Energy Cutoff and Spectral Index of NT Electrons 245
6.3.1 Meaning and Debate of Low-Energy Cutoff 245
6.3.2 Cross Point of Spectral Lines at Different Times 246
6.3.3 Relation of Low-Energy Cutoff and Ratio of Radiation Intensities or Spectral Index 249
6.3.4 Joint Effect of Low-Energy Cutoff and Compton Scattering on Flattened Spectra at Lower Energies 250
6.3.5 Low-Energy Cutoff and Spectral Index of MW and HXR with Two Methods 251
6.3.6 Low-Energy Cutoff and Spectral Index of MW and HXR with Strict Methods 255
6.3.7 Discussions and Conclusions 261
6.4 Diagnosis of Pitch-Angle of NT Electrons 262
6.4.1 Overview 262
6.4.2 Diagnosis of Mirror Ratio of Coronal Loops 263
6.4.3 Diagnosis of Initial Pitch-Angle 264
6.5 Evidence for Dynamic Evolution of Energetic Electron Spectrum 264
6.5.1 Overview 264
6.5.2 Theoretical Prediction of MW and HXR Spectral Evolution 265
6.5.3 Observational Data 266
6.5.4 Theoretical Simulation of Electron Spectral Evolution in MW Sources 268
6.5.5 Conclusions 269
6.6 Diagnosis of Acceleration Site and Pitch-Angle Distribution of Accelerated Electrons 271
6.6.1 Overview 271
6.6.2 Observations 272
6.6.3 Evolution of Brightness Distribution 275
6.6.4 Discussions 280
6.6.5 Conclusions 286
6.7 Inversion of NT Electron Spectral Index 288
6.7.1 Overview 288
6.7.2 Comparison of NT Spectral Indices of MW and X-Ray Emissions in Solar Flares 290
6.7.3 Summary 295
6.8 Radio Diagnostics of the Solar Flaring Loop Parameters 296
6.8.1 Method for Recovering Flaring Loop Parameters 296
6.8.2 Determination of Model Radio Source Parameters 297
6.8.3 Recovering Physical Parameters of Solar Flaring Loops 297
6.8.4 Conclusions 303
References 305
7 Global Behaviors for Dynamics of Flaring Loops 311
7.1 Global Behaviors Revealed by Observations at Multi-wavebands 311
7.1.1 Contraction of Flaring Loops prior to Their Expansion 311
7.1.2 The Relaxation of Sheared Magnetic Field 313
7.1.3 Possible Impact on the Lower Atmosphere 316
7.1.4 Sigmoid Magnetic Ropes 317
7.2 Failed Eruption of Filaments 320
7.3 Dynamics of MW and HXR Flaring Loop System 323
7.3.1 Introduction 323
7.3.2 Observations 323
7.3.3 Morphological Feature of AR10798 at H-Alpha and EUV in Pre-flare Phase 324
7.3.4 Radio, Optical, and X-Ray Images of Flaring Loops 325
7.3.5 Time Profiles 326
7.3.6 Evolution of Spatial Characteristic Parameters 327
7.3.7 Trajectories of Flaring Loop Top and Feet 329
7.3.8 Discussions 329
7.3.9 Conclusions 335
7.4 Quasi-periodic Pulsations (QPPs) in Microwave Band 336
7.4.1 Types of QPPs in Microwave Band 337
7.4.2 Theoretical Explanations of QPPs 341
7.4.3 Relation of Repetition Rate and Burst Flux in QPPs 354
7.5 Motion of X-Ray Sources Along Flaring Loops 359
7.5.1 Overview 359
7.5.2 Motion of X-Ray Sources Along Flaring Loops 359
7.5.3 Summary 361
7.6 Interaction of Flaring Loops 362
7.6.1 Typical Examples of Loop Interaction. 362
7.6.2 Statistical Evidence of Loop Interaction 368
7.6.3 Conclusions 368
7.7 Numerical Models and Observations of Chromosphere Evaporation 368
7.7.1 Introduction 368
7.7.2 Numerical Models 369
7.7.3 Observations of Chromospheric Evaporation 372
7.7.4 X-Ray and Radio Imaging Observations 380
7.7.5 Summary 382
References 383
Appendix: Color Figures 395
Index 423