Solar Ast ro p h y s ics

Peter V. Foukal Solar Ast ro p h y s ics Second, Revised Edition WI LEY- VCH WILEY-VCH Verlag Co. KCaA

Contents Preface 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.1.1 2.1.2 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 2.4.1 2.4.2 2.4.3 2.4.4 Development of the Ideas and Instruments of Modern Solar Research Early Telescopic Discoveries on the Sun The Spectroscope and Photography Solar-Terrestial Research and the New Astronomy 8 Solar Chemical Composition and Energy Generation The Mt. Wilson Era of Large Telescopes 17 Advances in Coronal Physics and in the Theory of Solar Activity Observations at Radio, Ultraviolet, and X-Ray Wavelengths 26 The Solar Wind and Heliosphere 28 Future Directions in Solar Instrumentation 30 Radiative Transfer in the Sun s Atmosphere 36 Photometric Principles 36 The Radiative Intensity 36 The Net Outward Flux and the Solar Constant 38 The Radiative Transfer Equation 41 The Optical Depth and Source Function Solution for Constant Source Function Solution for a Linear Source Function: The Eddington-Barbier Relation Thermodynamic Equilibrium The Planck Function Kirchhoff Law 48 Local Thermodynamic Equilibrium (LTE) 49 The Brightness- and Effective Temperatures The Gray Atmosphere 50 Formulation of the Problem 50 Gray Limb Darkening in the Eddington Approximation 52 The Photospheric Level Identified with Radiation at Teff Radiative Diffusion 54 Solar Astrophysics. Peter V. Foukal Copyright 2004 WILEY-VCH Verlag Weinheim

Contents 2.5 Radiative Transfer in the Fraunhofer Lines 55 2.5.1 Formation of Fraunhofer Lines 55 2.5.2 The Transfer Equation for Lines 56 2.5.3 The Milne-Eddington Model 57 2.5.4 Comparison with Observations of Line Depth near Disk Center 58 Comparison with Observed Center-to-Limb Behavior 3 3.1 3.2 3.3 3.3.1 3.4 3.5 3.6 3.7 3.8 3.9 3.9.1 3.9.2 3.9.3 3.9.4 3.10 Solar Spectroscopy 65 A Survey of the Sun s Spectrum 65 Atomic Structure 74 Space Quantization and the Zeeman and Stark Effects The Zeeman Effect The Stark Effect 84 Multiplet Rules for Transitions 86 Atomic Transitions and their Excitation 88 Rates for Radiative Transitions 90 Boltzmann Equilibrium and the Saha Equation Rate Equations in Statistical Equilibrium 93 Line Broadening 95 Thermal and Turbulent Doppler Broadening 95 Radiation Damping and Pressure Broadening 97 Broadening by Self-Absorption 98 Analysis of the Observed Profile of a Spectral Line 98 Molecules on the Sun 78 4 4.1 4.1.1 4.1.2 4.1.3 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 Dynamics of Solar Plasmas 103 Hydrostatic Equilibrium 104 Equilibrium in a Homogeneous Gravitational Field 104 Self-Gravitating Atmospheres The Polytropic Approximation The Equations of Motion 107 Euler s Equation 107 Viscous Forces and the Navier-Stokes Equation 108 The Equation of Continuity The Heat-Balance Equation 111 Conservation of Total Energy 124 The Influence of Magnetic Fields in Solar Plasma Dynamics The Lorentz Force 115 The Importance of Self-induction The Diffusive and Frozen-in Approximations 117 Wave Motions in the Sun Types of Waves Expected and Observed Sound Waves Simple Waves and Shock Formation 115

Properties of Shock Waves Magnetohydrodynamic Waves Internal Gravity Waves Plasma Oscillations Charged Particle Dynamics Validity of the Continuum Approximation and of Thermal Equilibrium Charged Particle Motions Contents The Photosphere Observations of the Quiet Photosphere Limb Darkening Observed Properties of Granulation The Supergranulation and Photospheric Network Construction of a Photospheric Model Physical Assumptions Determination of the Temperature Profile from Continuum Limb Darkening Determination of the Photospheric Opacity The Empirical Technique The Sources of Photospheric Opacity Physical Structure and Energy Balance of the Photosphere Models of Photospheric Structure Comparison with Observations Energy Transport Mechanisms in the Photosphere The Photospheric Chemical Composition and the Curve of Growth The Theoretical Curve of Growth Comparison with the Empirical Curve The Sun s Chemical Composition The Sun s Internal Structure and Energy Generation Equations of Stellar Structure Mechanical Equilibrium Energy Transport Boundary Conditions Physical Parameters Required for the Solution Chemical Composition The Mean Molecular Weight The Ratio of Specific Heats The Radiative Opacity Energy Generation Processes Nuclear Reactions in the Sun s Interior Factors That Determine the Dominant Reactions The Proton-Proton Chain The Carbon-Nitrogen Cycle

Contents 6.3.4 6.4 6.5 6.5.1 6.5.2 6.5.3 6.5.4 6.5.5 Nuclear Energy Generation Rates 179 The Standard Model of Physical Conditions in the Solar Interior Observational Tests of the Standard Model 183 Solar Neutrino Observations 183 Lithium and Beryllium Abundances Stellar Structure and Evolution 187 Geological and Climatological Evidence 189 The Sun s Angular Momentum and Shape 190 Solar Oscillations 191 180 7 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.3 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.3.6 7.3.7 7.4 7.4.1 7.4.2 7.5 7.5.1 7.5.2 7.5.3 7.5.4 Rotation, Convection, and Oscillations in the Sun 195 Observations of Solar Rotation Photospheric Doppler Measurements 196 Helioseismic Measurements of Rotation in the Solar Interior Tracer Measurements 199 Measurements on Convection 201 Observations of Convection at the Photosphere Comparison with Laboratory Measurements Dynamics of Solar Convection and Rotation 203 Condition for Onset of Convection 203 Gravity Waves 205 Mixing Length Theory Dynamics of Convection in a Plane Layer 208 Models of Granulation 209 Dynamics of Supergranulation 212 Dynamics of the Solar Interior Observations of Solar Oscillations 215 The 5-min Oscillations 215 Oscillations of Longer and Shorter Periods 219 Interpretation of Solar Oscillations Resonances in the Sun Oscillation Modes of the Solar lnterior 223 Excitation and Damping Mechanisms 225 Comparison of the Observed and Calculated Properties of the p-modes 226 Oscillations as a Probe of the Solar Interior 228 198 8 8.1 8.1.1 8.1.2 8.1.3 8.1.4 8.2 8.2.1 Observations of Photospheric Activity and Magnetism Sunspot Observations 234 Structure of the Umbra and Penumbra 234 Birth and Evolution of Spot Groups 240 Photometry and Spectra of Umbrae 241 Mass Motions and Oscillations 244 Dynamics of Spots 247 Thermal Structure of the Umbra 247 233

8.2.2 8.2.3 8.2.4 8.3 8.3.1 8.3.2 8.3.3 8.4 8.4.1 8.4.2 8.4.3 8.4.4 Why Spots Are Cool 249 Why Spots Cause Dips in the Solar Luminosity 252 Dynamics of Sunspot Evolution 252 Faculae 254 Structure and Evolution 254 Physical Measurements 254 Why Faculae Are Bright 259 Observations of Solar Magnetism 262 The Sunspot Magnetic Field 262 Photospheric Fields in Faculae and Magnetic Network 263 Large-scale Structure and Evolution of the Photospheric Field Global Structure of the Sun s Magnetic Field 272 266 Contents 9 9.1 9.1.1 9.1.2 9.1.3 9.1.4 9.1.5 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 10 10.1 10.1.1 10.1.2 10.2 10.2.1 10.2.2 10.2.3 11 11.1 11.1.1 11.1.2 11.1.3 11.1.4 11.1.6 The Chromosphere and Corona 277 The Chromosphere 278 Observations of Structures and Motions at the Limb 278 Observations on the Disk 282 Physical Conditions 288 Energy Balance 293 Chromospheric Heating 293 Dynamics of Spicules and Fibrils 295 The Corona and Transition Region 297 Spectrum and Radiation Mechanisms 297 Structures of the Corona and Transition Region 298 Magnetic Fields and Plasma Motions 303 Physical Conditions in Closed and Open Magnetic Structures Heating and Dynamics of Coronal Loops and Holes 32 Prominences and Flares 329 Prominences and Filaments 320 Observations and Physical Conditions 320 Dynamics 324 Flares Observations and Physical Conditions 332 Energy Release and Dynamics Acceleration of Energetic Charged Particles 348 Dynamics of the Solar Magnetic Field 352 Dynamics of Solar Magnetic Flux Tubes 352 Dynamical Equilibrium and Geometry 352 Dynamical Stability 355 Thermal Instability Steady Flows 358 Oscillations and Waves 360 Magnetic Field Dissipation 363 306

11.2 11.2.1 11.2.2 1.1.2 11.3 11.3.1 11.3.2 Activity Behavior over the Solar Cycle 365 The Sunspot Number and Other Activity Indices Time Behavior of the Sun s Magnetic Field 367 Long-Term Behavior of Solar Activity 371 Dynamics of the Solar Magnetic Cycle 376 The Babcock Model of the Solar Cycle 376 Dynamical Dynamo Models 379 365 12 12.1 12.1.1 12.1.2 12.1.3 12.1.4 12.1.5 12.2 12.2.1 12.2.2 12.2.3 12.3 12.3.1 12.3.2 12.3.3 12.3.4 12.3.5 13 13.1 13.1.1 13.1.2 13.1.3 13.1.4 13.1.5 13.2 13.2.1 13.2.2 13.2.3 13.3 13.3.1 13.3.2 13.3.3 13.3.4 The Solar Wind and Heliosphere 387 Structure of the Solar Wind 388 In Situ Measurements of Particles and Fields 388 Observations Out of the Ecliptic Plane Cosmic Rays 394 Interplanetary Gas and Dust 398 Structure of the Heliosphere 400 Transient Features in the Solar Wind 402 High-speed Streams 402 Interplanetary Shock Waves 403 Coronal Mass Ejections (CME s) 405 Dynamics of the Solar Wind 407 Thermal Conductivity of the Corona 407 Expansion of the Corona 408 Geometry of the Interplanetary Magnetic Field 411 Energy and Angular Momentum Fluxes 412 Sources of the Wind 415 The Sun, Our Variable Star 421 The Sun Compared to other Stars 422 The Sun s Location and Proper Motion in the Galaxy 422 Mass, Chemical Composition and Spectrum 423 Luminosity, Radius, and Effective Temperature 424 Chromospheric and Coronal Radiations 425 Stellar Winds and Mass Loss 426 Angular Momentum and Magnetism 426 Evolution of the Sun 427 The H-R Diagram and Stellar Evolution 427 The Sun s Future Evolution 431 The Early Sun 433 Solar and Stellar Variability 438 Observations of Stellar Activity 438 Mechanisms of Stellar Activity 442 The Sun s Variable Outputs 446 Prediction of Solar Activity and Space Weather Index 459