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Physics of the Sun

A First Course

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## Book Description

With an emphasis on numerical modeling, **Physics of the Sun: A First Course** presents a quantitative examination of the physical structure of the Sun and the conditions of its extended atmosphere. It gives step-by-step instructions for calculating the numerical values of various physical quantities.

The text covers a wide range of topics on the Sun and stellar astrophysics, including the structure of the Sun, solar radiation, the solar atmosphere, and Sun-space interactions. It explores how the physical conditions in the visible surface of the Sun are determined by the opacity of the material in the atmosphere. It also presents the empirical properties of convection in the Sun and discusses how the physical parameters increase with depth through the convection zone. The author shows how certain types of "real stars" are actually polytropes and offers a simplified version of oscillation equations to highlight the properties of p- and g-modes in the Sun. He also focuses on the initial temperature rise into the chromosphere, why the temperature in the quiet corona has the value it does, and how the physics of magnetic fields help us to understand various striking phenomena that are observed on the Sun.

This text enables a practical appreciation of the physical models of solar processes. Through the included numerical modeling problems, it encourages a firm grasp of the numerical values of actual physical parameters as a function of radial location in the Sun.

## Table of Contents

**The Global Parameters of the Sun**

Orbital Motion of the Earth

Astronomical Unit (AU)

*GM *and the Mass of the Sun

Power Output of the Sun: The Solar Luminosity

Radius of the Sun: *R*

Surface Gravity of the Sun

Escape Speed from the Solar Surface

Effective Temperature of the Sun

Shape of the Sun

Critical Frequency for Solar Oscillations

Mean Density of the Sun

**Radiation Flow through the Solar Atmosphere**

Radiation Field in the Solar Atmosphere

Empirical Properties of the Radiant Energy from the Sun

RTE

Optical Depth and the Concept of "the Photosphere"

Special Solutions of the RTE

Eddington–Barbier Relationship

Is Limb Brightening Possible?

Is *S*(*tau*) = *a *+ *b tau *Realistic? The Gray Atmosphere

How Does Temperature Vary as a Function of *tau*?

Properties of the Eddington Relation

**Toward a Model of the Sun: Opacity**

Relationship between Optical Depth and Linear Absorption Coefficient

Two Approaches to Opacity: Atomic and Astrophysical

Atomic Physics: (i) Opacity due to Hydrogen Atoms

Atomic Physics: (ii) Opacity due to Negative Hydrogen Ions

Atomic Physics: (iii) Opacity due to Helium Atoms and Ions

Astrophysics: The Rosseland Mean Opacity

Power-Law Approximations to the Rosseland Mean Opacity

Narrow Band Opacity: Absorption Lines in the Spectrum

**Toward a Model of the Sun: Ionization**

Statistical Weights of Free Electrons

Saha Equation

Application of the Saha Equation to Hydrogen in the Sun

Application of the Saha Equation to Helium in the Sun

Contours of Constant Ionization: The Two Limits

Application of the Saha Equation to the Negative Hydrogen Ion

**Computing a Model of the Sun: The Photosphere**

Hydrostatic Equilibrium: The Scale Height

Sharp Edge of the Sun’s Disk

Preparing to Compute a Model of the Solar Photosphere

Computing a Model of the Photosphere: Step by Step

The Outcome of the Calculation

Overview of the Model of the Solar Photosphere

**Convection in the Sun: Empirical Properties**

Nonuniform Brightness

Granule Shapes

Upflow and Downflow Velocities

Linear Sizes of Granules

Circulation Time around a Granule

Temperature Differences between Bright and Dark Gas

Energy Flux Carried by Convection

Onset of Convection in the Sun: The Critical Gradient *g _{ad} *

Numerical Value of *g _{ad }*

Alternative Expression for *g _{ad}*

**Computing a Model of the Sun: The Convection Zone**

Quantifying the Physics of Convection: Vertical Acceleration

Velocities and Vertical Length Scales

Mixing Length Theory (MLT) of Convection

Temperature Excesses Associated with MLT Convection

MLT Convective Flux in the Photosphere

MLT Convective Flux below the Photosphere

Adiabatic and Nonadiabatic Processes

Computing a Model of the Convection Zone: Step by Step

Overview of Our Model of the Convection Zone

**Radiative Transfer in the Deep Interior of the Sun**

Thermal Conductivity for Photons

Flux of Radiant Energy at Radius *r*

Base of the Convection Zone

Temperature Gradient in Terms of Luminosity

Temperature Gradient in Terms of Pressure

Integrating the Temperature Equation

**Computing a Mechanical Model of the Sun: The Radiative Interior**

Computational Procedure: Step by Step

Overview of Our Model of the Sun’s Radiative Interior

Photons in the Sun: How Long before They Escape?

Global Property of the Solar Model

Does the Material in the Sun Obey the Perfect Gas Law?

Summary of Our Solar Model

**Polytropes**

Power-Law Behavior

Polytropic Gas Spheres

Lane–Emden Equation: Dimensional Form

Lane–Emden Equation: Dimensionless Form

Boundary Conditions for the Lane–Emden Equation

Analytic Solutions of the Lane–Emden Equation

Are Polytropes Relevant for "Real Stars"?

Calculating a Polytropic Model: Step by Step

Central Condensation of a Polytrope

**Energy Generation in the Sun**

pp-I Cycle of Nuclear Reactions

Reaction Rates in the Sun

Proton Collision Rates in the Sun

Conditions Required for Nuclear Reactions in the Sun

Rates of Thermonuclear Reactions: Two Contributing Factors

Temperature Dependence of Thermonuclear Reaction Rates

Rate of Reaction (c) in the pp-cycle

**Neutrinos from the Sun**

Generation and Propagation of Solar Neutrinos

Fluxes of Solar Neutrinos at the Earth’s Orbit

Neutrinos from Reactions other than pp-I

Detecting Solar Neutrinos on Earth

Solution of the Solar Neutrino Problem

**Oscillations in the Sun: The Observations**

Variability in *Time *Only

Variability in *Space *and *Time*

Radial Order of a Mode

Which p-Modes have the Largest Amplitudes?

Trapped and Untrapped Modes

Long-Period Oscillations in the Sun

**Oscillations in the Sun: Theory**

Small Oscillations: Deriving the Equations

Conversion to Dimensionless Variables

Overview of the Equations

The Simplest Exercise: Solutions for the Polytrope *n *= 1

What about g-Modes?

Asymptotic Behavior of the Oscillation Equations

Depth of Penetration of p-Modes beneath the Surface of the Sun

Why are Certain Modes Excited More than Others in the Sun?

Using Helioseismology to Test a Solar Model

**The Chromosphere**

Definition of the Chromosphere

Linear Thickness of the Chromosphere

Observing the Chromosphere on the Solar Disk

Appearance of the Chromosphere on the Disk

Properties of Supergranules in the CaK Line

Supergranules Observed in the Ha Line

The Two Principal Components of the Chromosphere

Temperature Increase into the Chromosphere: Empirical Results

Temperature Increase into the Chromosphere: Mechanical Work

Modeling the Chromosphere: The Input Energy Flux

Modeling the Chromosphere: Depositing the Energy

Modeling the Equilibrium Chromosphere: Radiating the Energy Away

**Magnetic Fields in the Sun**

Sunspots

Chromospheric Emission

Magnetic Fields: The Source of Solar Activity

Measurements of Solar Magnetic Fields

Empirical Properties of Solar Magnetic Fields

Interactions between Magnetic Fields and Ionized Gas

Understanding Magnetic Structures in the Sun

Amplification of Strong Solar Magnetic Fields

Why Does the Sun Have a Magnetic Cycle with P ˜ 10 Years?

Releases of Magnetic Energy

**The Corona**

Electron Densities

Spatial Structure in the White Light Corona

Electron Temperatures

Temperature of Line Formation

Pressure Scale Heights in the Corona

Ion Temperatures

X-Ray Line Strengths: The Emission Measure

Densities and Temperatures: Quiet Sun versus Active Regions

Gas Pressures in the Corona

Spatial Structure in the X-Ray Corona

Magnetic Structures: Loops in Active Regions

Magnetic Structures: Coronal Holes

Magnetic Structures: The Quiet Sun

Why Are Quiet Coronal Temperatures of Order 1–2MK?

Abrupt Transition from Chromosphere to Corona

Rate of Mechanical Energy Deposition in the Corona

What Heats the Corona?

Solar Flares

**The Solar Wind**

Global Breakdown of Hydrostatic Equilibrium in the Corona

Localized Applicability of HSE

Solar Wind Expansion: Steady State Flow

Observational Evidence for Solar Wind Acceleration

Energy Equation

Asymptotic Speed of the Solar Wind

Rate of Mass Outflow from the Sun

Coronal Mass Ejections

How Far Does the Sun’s Influence Extend in Space?

**Appendix**

**Index**

*Exercises and References appear at the end of most chapters.*

## Author(s)

### Biography

**Dermott J. Mullan** is a professor in the Bartol Research Institute, Department of Physics and Astronomy at the University of Delaware. He is also director of the NASA Space Grant Program and the NASA EPSCoR Program in Delaware.

## Reviews

Physics of the Sunindeed starts as a ‘first course’ with a discussion of the sun’s global properties which can be easily observed and quantified. Very skillfully this information is used for a phenomenological description of the sun as observed from the earth. … very clear and easy to read. It is full of interesting bits of information … The quality of the paper, the print, and the book as a whole is very good. As far as the scope is concerned, it is clearly written for undergraduate students, but also accessible for non-students with some understanding of physics and mathematics. Style-wise, however, the book is a nice read also for experts and can thus be recommended without constraint.

—Contemporary Physics, Volume 52, Issue 3, 2011… the scope of core physics that can be taught with the Sun as an illuminating vehicle is impressive … . For colleagues interested enough to think a bit more about this possibility or immediately keen to try, Mullan’s book is an excellent starting place. … this is a very useful book with lots of nice details supported by accessible calculations. … The idea of teaching general physics through the Sun, in both senses of the word, is surely a promising one.

—James L. Collett,Reviews, Volume 11, Issue 1, 2010