Physics of the Sun

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Title
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Contents
Preface
Author
Chapter 1 The Global Parameters of the Sun
1.1 Orbital Motion of the Earth
1.2 The Astronomical Unit (AU)
1.3 GMʘ and the Mass of the Sun
1.4 Power Output of the Sun: The Solar Luminosity
1.5 The Radius of the Sun: Rʘ
1.6 Acceleration due to Gravity at the Surface of the Sun
1.7 The Mean Mass Density of the Sun
1.8 Escape Speed from the Solar Surface
1.9 Effective Temperature of the Sun
1.10 The Oblateness of the Sun
1.11 The Observed Rotation of the Sun’s Surface
1.12 A Characteristic Frequency for Solar Oscillations Due to Gravity
Exercises
References
Chapter 2 Radiation Flow through the Solar Atmosphere
2.1 Radiation Field in the Solar Atmosphere
2.2 Empirical Properties of the Radiant Energy from the Sun
2.3 The Radiative Transfer Equation (RTE)
2.4 Optical Depth and the Concept of “the Photosphere”
2.5 Special Solutions of the RTE
2.5.1 S = Constant at All Optical Depths
2.5.2 S = Constant in a Slab of Finite Thickness
2.5.3 Depth-Dependent S: Polynomial Form
2.5.4 Depth-Dependent S: Exponential Form
2.6 The “Eddington–Barbier” (or “Milne–Barbier–Unsöld”) Relationship
2.7 Is Limb Brightening Possible?
2.8 Is S(τ) = a + bτ Realistic? The Gray Atmosphere
2.9 How Does Temperature Vary as a Function of τ?
2.10 Properties of the Eddington (Milne) Relation
Exercises
References
Chapter 3 Toward a Model of the Sun: Opacity
3.1 Relationship between Optical Depth and Linear Absorption Coefficient
3.2 Two Approaches to Opacity: Atomic and Astrophysical
3.2.1 Energy Levels in Atomic Hydrogen
3.3 Atomic Physics: (i) Opacity due to Hydrogen Atoms
3.3.1 Absorption from the Ground State: Dependence on Wavelength
3.3.2 Absorption from Excited States: Dependence on Wavelength and T
3.4 Atomic Physics: (ii) Opacity due to Negative Hydrogen Ions
3.5 Atomic Physics: (iii) Opacity due to Helium Atoms and Ions
3.6 Astrophysics: The Rosseland Mean Opacity
3.6.1 Limit of Low Density and/or High T: Electron Scattering
3.6.2 Low T Limit
3.6.3 Higher Density: Free-Bound Absorptions
3.6.4 Magnitude of the Largest Opacity
3.7 Power-Law Approximations to the Rosseland Mean Opacity
3.8 Narrow Band Opacity: Absorption Lines in the Spectrum
3.8.1 Characterizing the Properties of Absorption Lines
3.8.2 Heights of Formation of Different Spectral Lines
3.8.3 Shape of an Absorption Line Profile: C-Shaped Bisectors
3.8.4 Shape of an Absorption Line: Magnetic Fields
Exercises
References
Chapter 4 Toward a Model of the Sun: Properties of Ionization
4.1 Statistical Weights of Free Electrons
4.2 Saha Equation
4.3 Application of the Saha Equation to Hydrogen in the Sun
4.4 Application of the Saha Equation to Helium in the Sun
4.5 Contours of Constant Ionization: The Two Limits
4.6 Application of the Saha Equation to the Negative Hydrogen Ion
Exercises
References
Chapter 5 Computing a Model of the Sun: The Photosphere
5.1 Hydrostatic Equilibrium: The Scale Height
5.2 Sharp Edge of the Sun’s Disk
5.3 Preparing to Compute a Model of the Solar Photosphere
5.4 Computing a Model of the Photosphere: Step by Step
5.5 The Outcome of the Calculation
5.6 Overview of the Model of the Solar Photosphere
Exercises
References
Chapter 6 Convection in the Sun: Empirical Properties
6.1 Nonuniform Brightness
6.2 Granule Shapes
6.3 Upflow and Downflow Velocities in Solar Convection
6.4 Linear Sizes of Granules
6.5 Circulation Time around a Granule
6.6 Temperature Differences between Bright and Dark Gas
6.7 Energy Flux Carried by Convection
6.7.1 Convective Energy Flux in the Photosphere
6.7.2 Convective Energy Flux above the Photosphere?
6.7.3 Convective Energy Flux in Gas That Lies below the Photosphere
6.8 Onset of Convection: The Schwarzschild Criterion
6.9 Onset of Convection: Beyond the Schwarzschild Criterion
6.10 Numerical Value of gad
6.11 Alternative Expression for gad
6.12 Supergranules
Exercises
References
Chapter 7 Computing a Model of the Sun: The Convection Zone
7.1 Quantifying the Physics of Convection: Vertical Acceleration
7.2 Vertical Velocities and Length-Scales
7.3 Mixing Length Theory (MLT) of Convection
7.4 Temperature Excesses Associated with MLT Convection
7.5 MLT Convective Flux in the Photosphere
7.6 MLT Convective Flux below the Photosphere
7.7 Adiabatic and Nonadiabatic Processes
7.8 Computing a Model of the Convection Zone: Step by Step
7.9 Overview of Our Model of the Convection Zone
Exercises
References
Chapter 8 Radiative Transfer in the Deep Interior of the Sun
8.1 Thermal Conductivity for Photons
8.2 Flux of Radiant Energy at Radius r
8.3 Base of the Convection Zone
8.4 Temperature Gradient in Terms of Luminosity
8.5 Temperature Gradient in Terms of Pressure
8.6 Integrating the Temperature Equation
Exercise
References
Chapter 9 Computing a Mechanical Model of the Sun: The Radiative Interior
9.1 Computational Procedure: Step by Step
9.2 Overview of Our Model of the Sun’s Radiative Interior
9.3 Photons in the Sun: How Long before They Escape?
9.4 A Particular Global Property of the Solar Model
9.5 Does the Material in the Sun Obey the Perfect Gas Law?
9.6 Summary of Our (Simplified) Solar Model
Exercises
References
Chapter 10 Polytropes
10.1 Power-Law Behavior
10.2 Polytropic Gas Spheres
10.3 Lane–Emden Equation: Dimensional Form
10.4 Lane–Emden Equation: Dimensionless Form
10.5 Boundary Conditions for the Lane–Emden Equation
10.6 Analytic Solutions of the Lane–Emden Equation
10.6.1 Polytrope n = 0
10.6.2 Polytrope n = 1
10.6.3 Polytrope n = 5
10.7 Are Polytropes in Any Way Relevant for “Real Stars”?
10.8 Calculating a Polytropic Model: Step by Step
10.9 Central Condensation of a Polytrope
Exercises
References
Chapter 11 Energy Generation in the Sun
11.1 The pp-I Cycle of Nuclear Reactions
11.2 Reaction Rates in the Sun
11.3 Proton Collision Rates in the Sun
11.4 Conditions Required for Nuclear Reactions in the Sun
11.4.1 Nuclear Forces: Short-Range
11.4.2 Classical Physics: The “Coulomb Gap”
11.4.3 Quantum Physics: Bridging the “Coulomb Gap”
11.4.4 Center of the Sun: Thermal Protons Bridge the Coulomb Gap
11.4.5 Other Stars: Bridging the Coulomb Gap
11.4.6 Inside the Nuclear Radius
11.5 Rates of Thermonuclear Reactions: Two Contributing Factors
11.5.1 Bridging the Coulomb Gap: “Quantum Tunneling”
11.5.2 Post-Tunneling Processes
11.5.3 Probability of pp-I Cycle in the Solar Core: Reactions (a) and (b)
11.6 Temperature Dependence of Thermonuclear Reaction Rates
11.7 Rate of Reaction (c) in the pp-I cycle
Exercises
References
Chapter 12 Neutrinos from the Sun
12.1 Generation and Propagation of Solar Neutrinos
12.2 Fluxes of pp-I Solar Neutrinos at the Earth’s Orbit
12.3 Neutrinos from Reactions Other than pp-I
12.3.1 pp-II and pp-III Chains
12.3.2 Other Reactions That Occur in the Sun
12.4 Detecting Solar Neutrinos on Earth
12.4.1 Chlorine Detector
12.4.2 Cherenkov Emission
12.4.3 Gallium Detectors
12.4.4 Heavy Water Detector
12.5 Solution of the Solar Neutrino Problem
Exercises
References
Chapter 13 Oscillations in the Sun: The Observations
13.1 Variability in Time Only
13.2 Variability in Space and Time
13.3 Radial Order of a Mode
13.4 Which p-Modes Have the Largest Amplitudes?
13.5 Trapped and Untrapped Modes
13.5.1 Vertically Propagating Waves in a Stratified Atmosphere
13.5.2 Simplest Case: The Isothermal Atmosphere
13.5.3 Critical Frequency and the “Cut-Off” Period
13.5.4 Physical Basis for a Cut-Off Period
13.5.5 Numerical Value of the Cut-Off Period
13.6 Waves Propagating in a Non-Vertical Direction
13.7 Long-Period Oscillations in the Sun
13.8 p-mode Frequencies and the Sunspot Cycle
Exercises
References
Chapter 14 Oscillations in the Sun: Theory
14.1 Small Oscillations: Deriving the Equations
14.2 Conversion to Dimensionless Variables
14.3 Overview of the Equations
14.4 The Simplest Exercise: p-Mode Solutions for the Polytrope n = 1
14.4.1 Procedure for Computation
14.4.2 Comments on the p-mode Results: Patterns in the Eigenfrequencies
14.4.3 Eigenfunctions
14.5 What About g-Modes?
14.6 Asymptotic Behavior of the Oscillation Equations
14.6.1 p-modes
14.6.2 g-modes
14.7 Depth of Penetration of p-modes beneath the Surface of the Sun
14.8 Why Are Certain p-Modes Excited More than Others in the Sun?
14.8.1 Depths Where p-Modes Are Excited
14.8.2 Properties of Convection at the Excitation Depth
14.9 Using p-Modes to Test a Solar Model
14.9.1 Global Sound Propagation
14.9.2 Radial Profile of the Sound Speed
14.9.3 The Sun’s Rotation
14.10 r-Modes in the Sun
Exercises
References
Chapter 15 The Chromosphere
15.1 Definition of the Chromosphere
15.2 Linear Thickness of the Chromosphere
15.3 Observing the Chromosphere on the Solar Disk
15.4 Supergranules Observed in the Hα Line
15.5 The Two Principal Components of the Chromosphere
15.6 Temperature Increase from Photosphere to Chromosphere: Empirical Results
15.7 Temperature Increase into the Chromosphere: Mechanical Work
15.8 Modeling the Chromosphere: The Input Energy Flux
15.9 Modeling the Chromosphere: The Energy Deposition Rate
15.10 Modeling the Equilibrium Chromosphere: Radiating the Energy Away
15.10.1 Radiative Cooling Time-Scale
15.10.2 Magnitude of the Temperature Increase: The Low Chromosphere
15.10.3 Magnitude of the Temperature Increase: The Middle Chromosphere
15.10.4 Magnitude of the Temperature Increase: The Upper Chromosphere
15.11 The IRIS Satellite
15.12 A Variety of Wave Modes in the Chromosphere?
15.12.1 The “Plasma Beta” Parameter and Conversions between Wave Modes
Exercise
References
Chapter 16 Magnetic Fields in the Sun
16.1 Sunspots
16.1.1 Spot Temperatures
16.1.2 Why Are Sunspots Cooler than the Rest of the Photosphere?
16.1.3 Areas of Spots and Plages
16.1.4 Spot Numbers: The “11-Year” Cycle
16.1.5 Spot Lifetimes
16.1.6 Energy Deficits and Excesses
16.2 Chromospheric Emission
16.3 Magnetic Fields: The Source of Solar Activity
16.4 Measurements of Solar Magnetic Fields
16.4.1 Measurement of Magnetic Fields on the Sun: Optical Data
16.4.1.1 Zeeman Splitting
16.4.1.2 Zeeman Polarization: The Longitudinal Case
16.4.1.3 Zeeman Polarization: The Transverse Case
16.4.1.4 Babcock Magnetograph: Longitudinal Fields
16.4.1.5 Vector Magnetograph
16.4.2 Magnetic Field Strengths in Sunspot Umbrae
16.4.3 Orderly Properties of Sunspot Fields
16.4.4 Remote Sensing of Solar Magnetic Fields: Radio Observations
16.4.5 How Are Coronal Fields Related to Fields in the Photosphere?
16.4.6 Direct Magnetic Measurements in Space: The Global Field of the Sun
16.5 Empirical Properties of Global and Local Solar Magnetic Fields
16.6 Interactions between Magnetic Fields and Ionized Gas
16.6.1 Motion of a Single Particle
16.6.2 Motion of a Conducting Fluid
16.6.2.1 Magnetic Pressure and Tension
16.6.2.2 The Equations of Magnetohydrodynamics (MHD)
16.6.2.3 Time-Scales for Magnetic Diffusion in the Sun
16.7 Understanding Magnetic Structures in the Sun
16.7.1 Sunspot Umbrae: Inhibition of Convection
16.7.2 Pores: The Smallest Sunspots
16.7.3 Sunspots: The Wilson Depression
16.7.4 Sunspots: What Determines Their Lifetimes?
16.7.5 Prominences
16.7.6 Faculae
16.7.7 Excess Chromospheric Heating: Network and Plages
16.7.8 Magnetic Field and Gas Motion: Which Is Dominant?
16.8 Amplification of Strong Solar Magnetic Fields
16.9 Why Does the Sun Have a Magnetic Cycle with P ≈ 10 Years?
16.10 Releases of Magnetic Energy
16.11 Magnetic Helicity
Exercises
References
Chapter 17 The Corona
17.1 Electron Densities
17.2 Electron Temperatures
17.2.1 Optical Photons
17.2.2 X-ray Photons
17.3 “The” Temperature of Line Formation
17.4 Emission Lines That Are Popular for Imaging the Corona
17.4.1 SOHO/EIT
17.4.2 SDO/AIA
17.4.3 Hinode/EIS
17.5 Quantitative Estimates of the “Emission Measure” of Coronal Gas
17.6 The Solar Cycle in X-rays
17.7 The Solar Cycle in Microwave Radio Emission
17.8 Ion Temperatures
17.9 Densities and Temperatures: Quiet Sun versus Active Regions
17.10 Gas Pressures in the Corona
17.11 Spatial Structure in the X-ray Corona
17.12 Magnetic Structures: Loops in Active Regions
17.13 Magnetic Structures: Coronal Holes
17.14 Magnetic Structures: The Quiet Sun
17.15 Why Are Quiet Coronal Temperatures of Order 1–2 MK?
17.15.1 Thermal Conduction by Electrons
17.15.2 Radiative Losses
17.15.3 Combination of Radiative and Conductive Losses
17.16 Abrupt Transition from Chromosphere to Corona
17.17 Rate of Mechanical Energy Deposition in the Corona
17.18 What Heats the Corona?
17.18.1 Wave Heating
17.18.1.1 Acoustic Waves?
17.18.1.2 Alfven Waves?
17.18.2 Non-Wave Heating: The Magnetic Carpet
17.19 Solar Flares
17.19.1 General
17.19.2 How Many Solar Flares Have Been Detected?
17.19.3 Flare Temperatures and Densities
17.19.4 Spatial Location and Extent
17.19.5 Energy in Nonthermal Electrons
17.19.6 Where Are Flare Electrons Accelerated?
17.19.7 Other Channels of Flare Energy
17.19.8 Do Flares Perturb Solar Structure Significantly?
17.19.9 Energy Densities in Flares
17.19.10 Physics of Flares (Simplified): Magnetic Reconnection in 2-D
17.19.11 Physics of Flares (More Realistic): Magnetic Reconnection in 3-D
17.19.12 Consequences of Magnetic Reconnection
17.19.13 Can Flares Be Predicted?
References
Chapter 18 The Solar Wind
18.1 Global Breakdown of Hydrostatic Equilibrium in the Corona
18.2 Localized Applicability of HSE
18.3 Solar Wind Expansion: Parker’s Model of a “Thermal Wind”
18.4 Conservation of Energy
18.5 Asymptotic Speed of the Solar Wind: The Magnetic Spiral
18.6 Magnetic Field Effects: “High-Speed” Wind and “Slow” Wind
18.7 Observations of Solar Wind Properties
18.7.1 In situ Measurements: ≈ 1 AU and Beyond
18.7.2 In situ Measurements in the Inner Wind: r < 1 AU
18.7.3 Remote Sensing of the Solar Wind
18.8 Rate of Mass Outflow from the Sun
18.9 Coronal Mass Ejections (CMEs)
18.9.1 Rates of CME Occurrence
18.9.2 Masses of CMEs
18.9.3 Speeds of CMEs
18.9.4 Kinetic and Potential Energies of CMEs
18.9.5 Comparison and Contrast between Flares and CMEs
18.9.6 CME Contributions to Solar Mass Loss Rates
18.9.7 CMEs and Magnetic Helicity
18.10 How Far Does the Sun’s Influence Extend in Space?
18.10.1 Where Does the “True” Corona End and the “True” Wind Begin?
18.10.2 The Outer Edge of the Heliosphere
Exercises
References
Appendix A: symbols used in the text
Appendix B: instruments used to observe the Sun
Index