11: Environment of the Radiation Field
- Page ID
- 141670
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 11.1: Introduction
- This page highlights the significance of grasping the gas composition critical for building stellar atmosphere models. It underscores the necessity for frequency-dependent opacity to accurately assess photon escape, as opposed to relying on mean opacity. The calculation of the stellar spectrum demands solving the equation of radiative transfer, which entails a comprehensive understanding of gas interactions.
- 11.2: Statistics of the Gas and the Equation of State
- This page covers the principles of temperature and pressure in stellar atmospheres under local thermodynamic equilibrium (LTE), focusing on the Maxwell-Boltzmann statistics governing particle distributions and gas pressure. It introduces the Boltzmann excitation formula and the Saha ionization equilibrium equation, detailing their derivations and significance.
- 11.3: Continuous Opacity
- This page covers opacity calculations in stellar atmospheres, highlighting continuous versus bound-bound sources and the significance of the Rosseland mean opacity in thermodynamic equilibrium. It details key contributions from hydrogen, helium, and hydrogen-like atoms, alongside quasi-atomic states like the H-minus ion.
- 11.4: Einstein Coefficients and Stimulated Emission
- This page explores the atomic absorption and emission processes through quantum mechanics, focusing on the Einstein coefficients that define emission and absorption probabilities. It details the correction of mass absorption coefficients to incorporate stimulated emission effects, crucial for accurate radiative transport equations.
- 11.5: Definitions and Origins of Mean Opacities
- This page explores mean opacities in stellar atmospheres, including Rosseland, Chandrasekhar, and Planck means. It highlights Rosseland's utility under local thermodynamic equilibrium and the limitations of simplifying nongray radiative transfer to gray form. The Chandrasekhar mean helps with high-temperature atmospheres, while the Planck mean is essential for radiative equilibrium at the surface.
- 11.6: Hydrostatic Equilibrium and the Stellar Atmosphere
- This page examines the effects of radiation on stellar atmospheres, focusing on hydrostatic equilibrium as a key modeling assumption. It touches on radiation-driven winds in hot stars but emphasizes hydrostatic equilibrium. The content includes the application of optical depth to enhance atmospheric structure equations and outlines important relationships between pressure, optical depth, and gravity, which are essential for developing a model atmosphere.
- 11.7: Problems
- This page covers the calculation of ionization ratios for hydrogen and silicon in astronomical objects, focusing on the Sun and certain stars. It examines the interplay of pressure, surface gravity, and temperature in hydrogen-dominated atmospheres, highlighting radiation pressure and opacity from H-minus ions.
- 11.8: References
- This page presents recommended readings on stellar atmospheric opacities, featuring key texts like L. H. Aller's "The Atmospheres of the Sun and Stars" and D. Mihalas's "Stellar Atmospheres." It highlights contributions from Ueno et al. and Stewart and Webb, focusing on continuous absorption coefficients and photo-ionization processes.