Stellar Oscillations: Contents

Lecture Notes on Stellar Oscillations

Preface (PS) (PDF)
1. Introduction (PS) (PDF)
2. Analysis of oscillation data (PS) (PDF): 2.1 Spatial filtering; 2.2 Fourier analysis of time strings; 2.2.1 Analysis of a single oscillation; 2.2.2 Several simultaneous oscillations; 2.2.3 Data with gaps; 2.2.4 Further complications; 2.2.5 Large-amplitude oscillations; 2.3 Results on solar oscillations; 2.4 Other types of multi-periodic stars; 2.4.1 Solar-like oscillations in other stars; 2.4.2 Observations of delta Scuti oscillations; 2.4.3 Subdwarf B variables; 2.4.4 Pulsating white dwarfs
3. A little hydrodynamics (PS) (PDF): 3.1 Basic equations of hydrodynamics; 3.1.1 The equation of continuity; 3.1.2 Equations of motion; 3.1.3 Energy equation; 3.1.4 The adiabatic approximation; 3.2 Equilibrium states and perturbation analysis; 3.2.1 The equilibrium structure; 3.2.2 Perturbation analysis; 3.3 Simple waves; 3.3.1 Acoustic waves; 3.3.2 Internal gravity waves; 3.3.3 Surface gravity waves
4. Equations of linear stellar oscillations (PS) (PDF): 4.1 Mathematical preliminaries; 4.2 The Oscillation Equations; 4.2.1 Separation of variables; 4.2.2 Radial oscillations; 4.3 Linear, adiabatic oscillations; 4.3.1 Equations; 4.3.2 Boundary conditions
5. Properties of solar and stellar oscillations. (PS) (PDF): 5.1 The dependence of the frequencies on the equilibrium structure; 5.1.1 What do frequencies of adiabatic oscillations depend on?; 5.1.2 The dependence of oscillation frequencies on the physics of the stellar interiors; 5.1.3 The scaling with mass and radius; 5.2 The physical nature of the modes of oscillation; 5.2.1 The Cowling approximation; 5.2.2 Trapping of the modes; 5.2.3 p modes; 5.2.4 g modes; 5.3 Some numerical results; 5.3.1 Results for the present Sun; 5.3.2 Results for the models with convective cores; 5.3.3 Results for the subgiant eta Bootis; 5.4 Oscillations in stellar atmospheres; 5.5 The functional analysis of adiabatic oscillations; 5.5.1 The oscillation equations as linear eigenvalue problems in a Hilbert space; 5.5.2 The variational principle; 5.5.3 Effects on frequencies of a change in the model; 5.5.4 Effects of near-surface changes
6. Numerical techniques (PS) (PDF): 6.1 Difference equations; 6.2 Shooting techniques; 6.3 Relaxation techniques; 6.4 Formulation as a matrix eigenvalue problem; 6.5 Richardson extrapolation; 6.6 Variational frequencies; 6.7 The determination of the mesh
7. Asymptotic theory of stellar oscillations (PS) (PDF): 7.1 A second-order differential equation for xi_r; 7.2 The JWKB analysis; 7.3 Asymptotic theory for p modes; 7.4 Asymptotic theory for g modes; 7.5 A general asymptotic expression; 7.5.1 Derivation of the asymptotic expression; 7.5.2 The Duvall law for p-mode frequencies; 7.6 Asymptotic properties of eigenfunctions; 7.6.1 Asymptotic properties of the p-mode eigenfunctions; 7.6.2 Asymptotic properties of the g-mode eigenfunctions; 7.7 Analysis of the Duvall law; 7.7.1 The differential form of the Duvall law; 7.7.2 Inversion of the Duvall law; 7.7.3 The phase-function difference H_2(omega)
8. Rotation and stellar oscillations (PS) (PDF): 8.1 The effect of large-scale velocities on the oscillation frequencies; 8.2 The effect of pure rotation; 8.3 Splitting for spherically symmetric rotation; 8.4 General rotation laws
9. Helioseismic inversion (PS) (PDF): 9.1 Inversion of the rotational splitting; 9.1.1 One-dimensional rotational inversion; 9.1.2 Two-dimensional rotational inversion; 9.2 Inversion for solar structure; 9.3 Some results of helioseismic inversion
10. Excitation and damping of the oscillations (PS) (PDF): 10.1 A perturbation expression for the damping rate; 10.1.1 The quasi-adiabatic approximation; 10.1.2 A simple example: perturbations in the energy generation rate; 10.1.3 Radiative damping of acoustic modes; 10.2 The condition for instability; 10.3 Stochastic excitation of oscillations
Appendix A. Useful properties of Legendre functions (PS) (PDF)
Appendix B. Effects of a perturbation on acoustic-mode frequencies (PS) (PDF)
Appendix C. Problems (PS) (PDF): C.1 Analysis of oscillation data; C.2 A little hydrodynamics; C.3 Properties of solar and stellar oscillations; C.4 Asymptotic theory of stellar oscillations; C.5 Rotation and stellar oscillations; C.6 Excitation and damping of stellar oscillations

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Last updated by Jørgen Christensen-Dalsgaard Sunday, 1 June, 2003 at 20:01