1. From temporal spectra to stellar interiors (and back)
Jørgen Christensen-Dalsgaard
Institut for Fysik og Astronomi, Aarhus Universitet
Dansk AsteroSeismologisk Center

2. Overview

3. Pulsating stars in the HR diagram

4. Excitation mechanisms
Heat engine (k mechanism, etc)
Critical layer in the star is heated at compression
Mode is intrinsically unstable and grows exponentially
???Amplitude limitation mechanism, mode selection ???
Stochastic excitation
Mode is intrinsically damped
Excitation through stochastic driving by convection (compare church bell in sandstorm)
Resulting amplitudes from balance between forcing and damping

5. Pulsating stars in the HR diagram

6. Observational differences
1/(Observing time)
1/(Lifetime)
Heat engine mode
Stochastically excited mode

7. Separated equations
Separation of time as exp(- i  t)

8. Spherical harmonics

9. Frequency dependence on stellar structure
Frequencies depend on dynamical quantities:
However, from hydrostatic equilibrium and Poisson’s equation p and g can be determined from r
Hence adiabatic oscillations are fully characterized by
or, equivalently

10. Characteristic frequencies
Acoustic frequency
Buoyancy frequency:

11. Internal gravity waves
In reality increased inertia owing to horizontal motion

12. Boundary conditions At centre At surface
Equations and boundary conditions determine frequencies wnl

13. Approximated equations
High radial order
Cowling approximation

14. Mode trapping Eigenfunction oscillates as function of r when
Model of present Sun
Eigenfunction oscillates as function of r when

15. (Kawaler, Lecture 3)

16. Asymptotics of low-degree p modes
Large frequency separation:

17. Small frequency separations

18. Asteroseismic HR diagram

19. Echelle diagram

20. Structure of evolving star with convective core
2.2 M¯
(Scaling with tdyn to ZAMS)

21. Evolution of (scaled) frequencies

22. Evolution of frequencies and eigenfunctions