14: Shape of Spectral Lines
- Page ID
- 141692
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 14.1: Introduction
- This page explains the formation and broadening of spectral lines in stellar spectra, noting discrepancies between classical atomic models and observed results. It details how broadening occurs due to quantum mechanics, thermal motions, and gas dynamics, with the atmospheric conditions of stars impacting spectral profiles.
- 14.2: Relation between the Einstein, Mass Absorption, and Atomic Absorption Coefficients
- This page explores the connection between the Einstein coefficient for atomic transitions and the mass absorption coefficient, detailing how atomic state changes relate to photon absorption. It presents essential equations for upward transitions and mass absorption along a spectral line, with a focus on understanding the frequency dependence of atomic line absorption. This indicates a progression towards a deeper analysis of spectral characteristics in the context of atomic phenomena.
- 14.3: Natural or Radiation Broadening
- This page covers the frequency dependence of atomic line absorption coefficients, detailing atomic properties influencing photon behavior and introducing classical radiation damping concepts. It elaborates on quantum mechanical perspectives, emphasizing energy level broadening due to the Heisenberg uncertainty principle and employs the Lorentzian power spectrum. The Ladenburg f-value bridges quantum and classical models, illustrating transition strengths.
- 14.4: Doppler Broadening of Spectral Lines
- This page explores the effects of atomic motions on spectral line broadening in stellar atmospheres, categorizing them into microscopic and macroscopic factors. It discusses thermal and turbulent broadening, their mathematical treatment through convolution integrals, and the use of the Voigt function for simplifying absorption coefficient calculations.
- 14.5: Collisional Broadening
- This page covers various aspects of spectral line broadening due to atomic interactions, emphasizing collisional broadening from neighboring particles. It details theoretical approaches such as impact phase-shift theory and static broadening theory, focusing on their distinct methods and limitations.
- 14.6: Curve of Growth of the Equivalent Width
- This page examines the relationship between atomic abundance and spectral line equivalent width, illustrating that greater abundance results in stronger lines. It covers the classical "curve of growth," the roles of optical depth and various models (e.g., Schuster-Schwarzschild, Milne-Eddington), and their applications in estimating stellar parameters like abundances and temperatures.
- 14.7: Problems
- This page analyzes atomic line profiles in stellar atmospheres, covering aspects like Doppler broadening, natural line widths, and absorption coefficients. It details methods for computing line profiles for elements, estimating transition times, and examining collision rates.
- 14.8: References and Supplemental Reading
- This page provides an extensive list of references on line broadening theory related to stellar atmospheres and electromagnetism, covering topics like pressure broadening and the Voigt function. It includes notable works and guidance for students towards comprehensive texts by Böhm, Jefferies, Mihalas, and Griem for deeper insights into line formation and plasma spectroscopy.