16: Beyond the Normal Stellar Atmosphere
- Page ID
- 141710
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 16.1: Introduction
- This page critiques existing stellar models for their focus on spherical stars, revealing complexities in star atmospheres influenced by convection, turbulence, and instability. It also addresses the effects of stellar winds and external radiation in binary systems, highlighting gaps in current theories. The discussion emphasizes these topics as active research areas, encouraging further exploration.
- 16.2: Illuminated Stellar Atmospheres
- This page explores the effects of incident radiation from companion stars on the atmospheric structure of binary systems, detailing how it alters appearance and spectral energy distribution. It discusses the need for modified radiative transfer equations due to complexities in this context, particularly highlighting limitations of the Eddington approximation.
- 16.3: Transfer of Polarized Radiation
- This page covers the properties and behaviors of polarized light, focusing on Stokes parameters, their transformations, and applications in radiative transfer and scattering processes. It delves into how electrons scatter light under varying conditions, including magnetic fields, and the impact on polarization in stellar atmospheres. Mathematical formulations are provided for modeling radiation and source functions, emphasizing the role of polarization in understanding stellar characteristics.
- 16.4: Extended Atmospheres and the Formation of Stellar Winds
- This page explores the transition region between a star's atmosphere and the interstellar medium, detailing complex processes in low-density environments and the failure of standard astrophysical assumptions. It covers stellar winds, Doppler shifts, mass loss, and introduces P-Cygni profiles as mass loss indicators. The dynamics of radiation-driven winds in early-type stars are examined, discussing effective optical depth and radiation pressure.
- 16.5: Problems
- This page covers mathematical problems concerning radiation fields in illuminated stellar atmospheres, validating equations for diffuse field sources and the Avrett-Krook perturbation scheme. It derives an integral expression for radiative flux through a plane-parallel atmosphere influenced by a point source and examines polarization and rotation matrices. The discussion culminates with the derivation of expressions for radiative flux under specific atmospheric conditions.
- 16.6: References and Supplemental Reading
- This page provides a reference list focused on stellar atmospheres, radiative transfer, and light polarization in celestial bodies. It covers essential themes such as radiative equilibrium, light-matter interactions in binary systems, and stellar wind dynamics. Key contributions by authors like Chandrasekhar, Kuzma, and Castor are highlighted, along with a recommendation for Cassinelli's work for deeper insights into stellar winds.