8: Stellar Pulsation and Oscillation
- Page ID
- 141647
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 8.1: Introduction
- This page explains variable stars, focusing on Cepheid variables, whose brightness changes are intrinsic. It argues against the binary hypothesis by pointing out inconsistencies in orbital characteristics and radial velocity. The page highlights the important period-luminosity relationship that allows these stars to measure distances accurately, correcting previous errors in galaxy estimations.
- 8.2: Linear Adiabatic Radial Oscillations
- This page explores stellar pulsations, their relationship to star size, and the intricacies of predicting these phenomena. It compares various pulsating stars, detailing the energy-conserving adiabatic processes involved and the foundational theories by Eddington and Ledoux. The text examines the effects of angular momentum and magnetic fields on pulsation periods and stability, introducing key concepts like Jacobi's stability criterion and the linear adiabatic wave equation.
- 8.3: Linear Nonadiabatic Radial Oscillations
- This page covers the nonadiabatic processes impacting stellar pulsations, comparing them to adiabatic conditions and highlighting thermodynamic properties crucial for gas behavior during stellar evolution. It analyzes pulsational stability and energy transfer mechanisms akin to Carnot engines.
- 8.4: Nonradial Oscillations
- This page provides an overview of stellar oscillation modes, focusing on gravity modes and their characteristics. It explains the influence of gravity on oscillations, introduces the f mode, and discusses how rotation affects r modes and overall stellar dynamics. Additionally, it highlights uncertainties in internal stellar structures and emphasizes the crucial role of observational data in studying stellar evolution and interiors.
- 8.5: Problems
- This page discusses deriving astrophysical equations through the Virial theorem, focusing on the radial pulsation period of homogeneous stars with a specific equation of state. It calculates the lowest-order oscillation modes for polytropes of varying indices and stellar masses. The page also addresses torsional oscillations in white dwarfs near the Chandrasekhar limit, estimating their frequencies, and explains the wave equation derivation from the equations of motion.
- 8.6: References and Supplemental Reading
- This page provides an overview of important references in the study of pulsating stars, noting seminal works by Eddington, Ledoux, and Cox. It covers key investigations into both radial and non-radial pulsations, stability, and internal structures of stars. Resources on Cepheid variables and accessible texts on pulsation theories are mentioned, along with articles discussing the influence of nonadiabatic effects on pulsation, highlighting the development of astrophysical knowledge in this field.