Confronting stellar structure theory with asteroseismic data

1. Confronting stellar structure theory with asteroseismic data Sarbani Basu Yale University

2. Sir Arthur Eddington in “The internal constitution of stars” (1926) “At first sight it would seem that the deep interior of the Sun and stars is less accessible to scientific investigation than any other region of the universe. Our telescopes may probe farther and farther into the depths of space; but how can we ever obtain certain knowledge of that which is being hidden behind substantial barriers? What appliance can pierce through the outer layers of a star and test the conditions within?”

3. A Crash Course in Asteroseismology • Starsoscillates in millions of different modes. • These are normal modes of oscillations, and hence the oscillation frequencies depend on stellar structure and dynamics. • The oscillations are linear and adiabatic. • Each mode is characterized by three numbers: (1)n: the radial order, the number of nodes in the radial direction (2)l: the degree;no. of nodal planes (3)m: the azimuthal order. m goes from +l to -l;no. of node circles crossing a latitude If stars were spherically symmetric and did not rotate, all modes with the same l and n but different m would have the same frequency.

4. How can we use stellar oscillations to study stars? Different waves travel to different parts of the star.

5. A Sample of Solar Data

6. Solar-like oscillators have substantial outer convection zones that randomly excite pulsations. Image courtesy J. Christensen-Dalsgaard

7. Huber et al. 2011

8. The Biggest Difference w.r.t. Helioseismology? We cannot resolve stellar discs! One pixel observations. Cannot observe high-degree modes

9. One big problem: most data are photometric

11. Stellar data are more sparse. We represent them in “ECHELLE” diagrams

12. Solar Echelle Diagram: BiSON data l=2 l=0 l=3 l=1

13. Echelle diagram of A solar analogue

14. Modelling Stars • For most parts, stars are spherically symmetric, i.e., their internal structure is only a function of radius and not of latitude or longitude. • This means that we can express the properties of stars using a set of 1D equations, rather than a full set of 3D equations. The main equations concern the following physical principles: • Conservation of Mass • Conservation of momentum • Thermal equilibrium • Transport of energy • Nuclear reaction rates • Change of abundances by various processes • Equation of state

15. Why we need a test

16. Rcz,=0.713±0.001 Ycz,=0.249 ± 0.003

17. Helioseismology has taught us a lot Some equations of state are better than others

18. Our current obsession? OPACITIES! Trouble in Paradise! A problem with the solar heavy-element abundances. Grevesse & Sauval (1998)Z/X=0.023 Asplund et al (2004,2005)Z/X=0.0165O, C, N all reduced. Asplund et al. (2009) (met) Z/X=0.0178 Asplund et al. (2009), Grevesse et al. (2010) (ph)Z/X=0.0181

19. Caffau et al. (2011): Z/X=0.0209

20. Some stars can be modelled, some can’t!

21. Modelling average properties: a star that can be modelled

22. Modelling average properties: A star that cannot be modelled

23. What can we do: Global properties

24. Large frequency separation: Small frequency separation:

27. Do the scaling relations work? Silva Aguirre et al. (in prep)

28. Silva Aguirre et al. (in prep)

29. Chaplin et al. 2011

30. Mass observed synthetic Radius Chaplin et al. 2011

31. Examining one usually neglected model input: The mixing length parameterWhat happens if we use solar α for all stars?

32. If we use solar α most stars in our sample would need sub-primordial helium abundances! Bonaca et al. (submitted)

33. Bonaca et al. (submitted)

34. What can we learn using the full frequency spectrum?

35. Model of present Sun Describing the modes Eigenfunction oscillates as function of r when

36. P-modes: Equidistant in frequency G-modes: Equidistant in period

37. Modelling 16 Cyg A

38. Model Sun

39. Same interior physics could still give rise to different surface terms

40. 16 Cyg A: Corrected frequencies Mass= 1.11 M, Radius=1.244 R Age=6.9 Gyr, Zi=0.026, Yi=0.26

41. How do we know that the surface term correction is valid? Sun 16 Cyg A

42. things do not always work out Silva Aguirre et al. (in prep)

43. M=1.120    t=3.530 Gyr   log g=4.208 M=1.190    t=3.435 Gyr   log g=4.217 Silva Aguirre et al. (in prep)

44. Evolved stars

45. “Avoided crossings” in the echelle diagram Appourchaux et al. 2012 (in press)

46. Core rotation in subgiants: “Otto” Deheuvels et al., submitted.

47. Rotational splittings of Otto modes

48. Deheuvels et al. (submitted)

49. Schou et al. (1998) Howe et al. (2000)

50. Deheuvels et al. (submitted)