Lecture Notes on Stellar Oscillations

Contents

Preface (PDF)

1. Introduction (PDF)

2. Analysis of oscillation data (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 (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 (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. (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 (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 (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 (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 (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 (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 (PDF)

Appendix B. Effects of a perturbation on acoustic-mode frequencies (PDF)

Appendix C. Problems (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


Last updated by Jørgen Christensen-Dalsgaard Wednesday, 29 January, 2014 at 08:59