15: Breakdown of Local Thermodynamic Equilibrium
- Page ID
- 141702
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 15.1: Introduction
- This page explores local thermodynamic equilibrium (LTE) in stellar interiors and atmospheres, highlighting how LTE is maintained in dense interiors through gas and photon interactions, but fails in the upper atmosphere due to lower density and insufficient collisions. This breakdown affects the energy level populations of excited atoms, notably hydrogen and helium, complicating the calculation of non-LTE effects on stellar spectra and atmospheric structure.
- 15.2: Phenomena Which Produce Departures from Local Thermodynamic Equilibrium
- This page explains detailed balancing in local thermodynamic equilibrium, emphasizing equal particle flows into and out of energy levels. It addresses deviations caused by atmospheric interactions and interlocking transitions. Additionally, it contrasts photoionization, which dominates in star atmospheres, with collisional ionization, influencing atomic population dynamics and resulting in non-LTE behavior.
- 15.3: Rate Equations for Statistical Equilibrium
- This page explores key concepts in statistical equilibrium and radiative transfer within atomic systems, focusing on two-level atoms. It discusses the establishment of rate equations, the significance of the source function, and non-LTE effects on level populations, emphasizing the departure coefficient and its relevance to atomic transitions.
- 15.4: Non-LTE Transfer of Radiation and the Redistribution Function
- This page covers the impact of non-LTE effects on spectral line profiles, detailing alterations in photon absorption and emission due to atomic motion and Doppler shifts. It discusses key concepts such as scattering and absorption probabilities, and the complexities of redistribution functions in different scenarios, especially with strong lines.
- 15.5: Line Blanketing and Its Inclusion in the Construction of Model Stellar Atmospheres and Its Inclusion in the Construction of Model Stellar Atmospheres
- This page covers Chapter 10, which focuses on the impact of weak spectral lines on the opacity of stellar atmospheres, particularly in early-type stars, affecting photon flow. It introduces two key modeling techniques: Opacity Sampling, which simplifies opacity calculations using discrete frequency points, and Opacity Distribution Functions (ODFs), which represent absorption over wider spectral areas.
- 15.6: Problems
- This page covers methods in atomic and astrophysics, detailing ionization processes, line profiles, and redistribution functions. It estimates collisional versus photoionization in hydrogen, examines the Lyα profile mechanisms in the sun, and derives integral equations related to radiative transfer. The significance of physical constants and analytical techniques for solving these equations and understanding line radiation characteristics is also highlighted.
- 15.7: References and Supplemental Reading
- This page provides a curated list of key references on stellar atmospheres and line formation, recommending texts by Mihalas and Böhm, and emphasizing the significance of understanding deviations from Local Thermodynamic Equilibrium (LTE). It suggests specific chapters for in-depth study and points out Jefferies’ alternative perspective on atomic interactions.