1. Inversion of rotation profile for solar-like stars Jérémie Lochard IAS 19/11/04

2. Rotational splitting: rotation lifts the degeneracy

3. Rotational splitting:

4. what we observe

5. Rotational splitting: what we observe what we search

6. Rotational splitting: what we observe what we compute from models what we search

7. Structure and rotation inversion gave strong constraints on solar models Helioseismology

8. Structure and rotation inversion gave strong constraints on solar models Helioseismology Asteroseismology Restricted mode set: l=0,1,2(,3) (up to a few 1000 for the Sun)

9. Our aim: is rotational inversion possible for some specific solar-like stars ? give selection constraints Structure and rotation inversion gave strong constraints on solar models Helioseismology Asteroseismology

10. Structure and rotation inversion gave strong constraints on solar models Helioseismology Asteroseismology Other stars may show modes with different nature from those observed on the Sun Our aim: is rotational inversion possible for some specific solar-like stars ? give selection constraints Restricted mode set: l=0,1,2(,3) (up to a few 1000 for the Sun)

11. With evolution g-mode cavity appears at the edge of the convective core

12. With evolution g-mode cavity appears at the edge of the convective core look for evolved stars (but still on the main sequence)

13. Eigen-functions and rotational kernels P modes Mixed modes

14. Mode set selection: Amplitude computation: from the excitation and damping rates Selection threshold: from the COROT specifications mixed modes

15. Mode set selection: Amplitude computation: from the excitation and damping rates Selection threshold: from the COROT specifications mixed modes Mode amplitudes increase with mass look for massive stars with outer convective zone

16. Building a trial model to compute the rotational kernels HR diagram constraints: Effective temperature and luminosity

17. Building a trial model to compute the rotational kernels Seismic constraints: large separation:global constraint (mean density) HR diagram constraints: Effective temperature and luminosity

18. HR diagram constraints: Effective temperature and luminosity Building a trial model to compute the rotational kernels Seismic constraints: large separation:global constraint: mean density small separation: constraint on the deep interior (evolution stage …)

19. Kernels from the initial model Inversion forward inversion

20. Kernels from the initial model Kernels from the trial model Inversion

21. Kernels from the initial model Kernels from the trial model and random errors added Inversion

22. Forward check computing the splittings from the recovered rotation profile

23. Constraints on the rotational inversion for solar-like stars: Mass (modes amplitude) Evolution (mixed modes) Surface velocity (relative precision)

24. Constraints on the rotational inversion for solar-like stars: Mass (modes amplitude) Evolution (mixed modes) Surface velocity (relative precision) Needs: stellar parameters (Teff, luminosity, surface chemical composition…) long observation periods and low noise level (Corot, Eddington…)