1. Helioseismology Jørgen Christensen-Dalsgaard
Institut for Fysik og Astronomi, Aarhus Universitet
Dansk AsteroSeismologisk Center

2. The Sun

3. Five-min oscillations: A local phenomenon in the solar atmosphere?
Musman & Rust
(1970; Solar Phys. 13, 261)

4. Oscillation modes of the Sun
Ando & Osaki (1975):
Models:
Ulrich (1970):
Wolff (1972):
Deubner (1975; Astron. Astrophys. 44, 371)

5. The start of global helioseismology
Grec et al. (1980; Nature 288, 541)

6. Crucial advantages Access to modes of degree up to 1000+
Observations over very extended period (more than 10 years nearly continuously)
Well-determined global parameters

7. Frequencies of solar model
Observed solar modes
n = w / 2 p

8. Asymptotics of frequencies
Acoustic-wave dispersion relation
Hence

9. Rays

10. Inversion with rays

11. Observing a Doppler image

12. Data on solar oscillations
Observations:
MDI on SOHO
VIRGO on SOHO (whole-disk):

13. Observed frequencies
m-averaged frequencies from MDI instrument on SOHO
1000 s error bars

14. Frequency dependence on solar 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

15. Frequency differences, Sun - model

16. The solar internal sound speed
Sun - model
No settling
No settling
Including settling

17. The solar internal sound speed
Sun - model
Basu et al. (1997; MNRAS 292, 243)

18. Changes in composition
The evolution of stars is controlled by the changes in their interior composition:
Nuclear reactions
Convective mixing
Molecular diffusion and settling
Circulation and other mixing processes outside convection zones
Nuclear burning
Settling

19. Relativistic electrons in the Sun
Including relativistic effects
No relativistic effects
Elliot & Kosovichev (1998; ApJ 500, L199)

20. Neon discovery solves mystery of sun's interior NASA's Chandra X-ray Observatory survey of nearby sun-like stars suggests there is nearly three times more neon in the sun and local universe than previously believed. If true, this would solve a critical problem with understanding how the sun works.        FULL STORY                                                                                               
               
(Spaceflight Now – 14 Aug 2005)

21. Revision of solar surface abundances
Pijpers, Houdek et al.
Model S
Z = 0.015
Asplund et al. (2004; A&A 417, ; astro-ph/ v2):
Improvements:
Non-LTE analysis
3D atmosphere models
Consistent abundance determinations for a variety of indicators

22. How do we correct the models?
Basu & Antia (2004; ApJ 606 L85): an opacity increase to compensate for lower Z is required
Seaton & Badnell (2004; MNRAS 354, 457): recent Opacity Project results do indicate some increase over the OPAL values, but hardly enough
Antia & Basu (2005; ApJ 620, L129): could the neon abundance be wrong?

23. The neon story
Ne x 2.5
Bahcall et al. (2005; ApJ, in the press [astro-ph/ ])
Drake & Testa (2005; Nature 436, 525): X-ray observations of nearby stars indicate such a neon increase

24. Spherical harmonics

25. Rotational splitting

26. Simple rotational splitting

27. Kernels for rotational splitting

28. Kernels for rotational splitting
(5,2)
(20,8)
(20,17)
(20,20)

29. Inferred solar internal rotation
Base of convection zone
Tachocline
Near solid-body rotation of interior
Schou et al. (1998; ApJ 505, 390)

30. Rotation of the solar interior
BiSON and LOWL data; Chaplin et al. (1999; MNRAS 308, 405)

31. Tachocline oscillations
● GONG-RLS
▲MDI-RLS
∆ MDI-OLA
See Howe et al. (2000; Science 287, 2456)

32. Zonal flows Rotation rate - average value at solar minimum
Vorontsov et al. (2002; Science 296, 101)

33. Radial development of zonal flows
Howe et al., (ApJ, in the press)

34. Observed and modelled dynamics
6 1/2 year MDI inversion, enforcing 11-yr periodicity
Vorontsov et al. (2002; Science 296, 101)
Non-linear mean-field solar dynamo models
Covas, Tavakol and Moss (2001; Astron. Astrophys 371, 718)