1. Excitation and damping of oscillation modes in red-giant stars Marc-Antoine Dupret, Université de Liège, Belgium Workshop Red giants as probes of the structure and evolution of the milky way Academia Belgica Roma 15-17 November 2010 K. Belkacem, J. De Ridder, J. Montalban, A.Miglio, R. Samadi, P. Ventura, H-G. Ludwig, A.Grigahcène, A. Noels

2. - Mode physics in red giant stars - Predictions for specific models - Conclusions Plan of the presentation Subgiants Intermediate High luminosity

3. How red giants differ from the Sun from an acoustic point of view ? Simple p-modes (  2 > N 2, L 1 2 ) Sun

4. How red giants differ from the Sun ? = 0 = 1 = 2 Regular frequency pattern ~ Asymptotic Small separation Large separation Sun

5. Helium burning Red Giant Mode physics in Red Giants 3 M ⊙, 12.6 R ⊙ T eff = 5025 K, log(L/L ⊙ ) = 1.96 Huge restoring force by buoyancy Non-radial modes are mixed modes

6. Mode trapping Mode physics in Red Giants Trapped in the core Trapped in the envelope See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004) ENERGY density M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning

7. Mode trapping Mode physics in Red Giants Trapped in the envelope Trapped in the core See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004) M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning

8. Stochastic excitation (top of the convective envelope) Mode physics in Red Giants Stochastic power Damping rate Inertia Stochastic excitation model Amplitude (velocity) Reynolds stress Entropy Samadi et al. (2003, …) Belkacem et al. (2006, …) Two types of terms : Outermost part of the convective envelope Main uncertainties : Injection length scale, kinetic energy spectrum Houdek et al.

9. Mode physics in Red Giants Coherent interaction convection-oscillations Convective damping in the envelope Very complex because : Convective time-scale ~ thermal time-scale ~ oscillation periods Damping of the modes See e.g. Gabriel (1996), Grigahcène et al. (2005), Balmforth et al. (1992) Large uncertainties but … only depend on mode physics in the outermost part of the convective envelope Not affected by mode trapping

10. Radiative damping in the core Mode physics in Red Giants  T > 0  T <0 q q Large variations of the temperature gradient Large radiative damping In a cavity with short wavelength oscillations : Significant for models with huge N 2 in the core huge core-envelope density contrast Affected by mode trapping

11. Similar heights for radial and resolved non-radial modes If  / I -1 : If the modes are resolved : Mode profiles in the power spectrum Mode physics in Red Giants Amplitude = area !  Mode profile Height in the power spectrum If the modes are not resolved : If  / I -1 : Smaller heights for very long lifetime unresolved modes !

12. Models considered 3 M ¯ 2 M ¯ Stellar evolution code : ATON (Mazzitelli, Ventura et al.)

13. A : Model at the bottom of red giant branch M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Lifetimes Lifetime = Oscillatory behaviour due to mode trapping No radiative damping Dupret et al. (2009)

14. Model at the bottom of red giant branch M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Resolved modes: same H Height in power spectrum Unresolved: Complex spectrum for l=1 modes ! A : Model at the bottom of red giant branch Dupret et al. (2009)

15. Model at the bottom of red giant branch Predicted power spectrum A : Model at the bottom of red giant branch Complex spectrum for l=1 modes ! l = 0 l = 2 l = 1

16. 3 M ¯ 2 M ¯ B : Intermediate model in the red giant branch

17. Intermediate model in the red giant branch Mode life-times M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Lifetimes Lifetime = B : Intermediate model in the red giant branch Dupret et al. (2009)

18. Intermediate model in the red giant branch Trapped in the envelope Trapped in the core M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Work integrals Convective damping near the surface Radiative damping in the core B : Intermediate model in the red giant branch

19. Intermediate model in the red giant branch The detectable modes have p-modes asymptotic pattern M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Height in PS B : Intermediate model in the red giant branch

20. Model at the bottom of red giant branchB : Intermediate model in the red giant branch Predicted power spectrum Regular for l=0 and 2 « Fine structures » of l=1 mixed modes l = 0 l = 2 l = 1

21. 3 M ¯ 2 M ¯ An Helium burning model

22. Predicted power spectrum An Helium burning model Regular for l = 0 and 2 « Fine structures » of l=1 mixed modes l = 0 l = 2 l = 1

23. 3 M ¯ 2 M ¯ C : High luminosity model in the red giant branch

24. High luminosity model in the red giant branch Mode life-times M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning Lifetimes C : High luminosity model in the red giant branch

25. High luminosity model in the red giant branch Height in the power spectrum Negligible height for non-radial modes Not detectable M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning Height in PS Huge radiative damping of most non-radial modes C : High luminosity model in the red giant branch

26. Predicted power spectrum Regular spectrum similar to main sequence stars C : High luminosity model in the red giant branch l = 0 l = 2 l = 1

27. 2 M ¯ A. Model at the bottom of red giant branch 3 M ¯ Conclusions: Complex spectrum (for l=1 modes)

28. 3 M ¯ 2 M ¯ B. Intermediate model in the giant branch Regular for l=0 and 2, « Fine structure » for l=1 Conclusions:

29. 3 M ¯ 2 M ¯ Regular spectrum ~ main sequence stars C. Intermediate model in the giant branch Conclusions:

30. Very high potential of asteroseismology to probe the deep layers of red giants Conclusions of the conclusions Depending on the evolutionary status, very different kinds of spectra are predicted

31. Interpretation Damping rate = 1 / Kelvin- Helmholtz time Radiative damping as star evolves Most radiative damping occurs at the top of the pure Helium core

32. Mode physics in Red Giants Kinetic energy :  |  r| 2 Huge number of nodes in the core Gravity EVANEEVANE Acoustic SCENTSCENT KINETIC ENERGY M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Very dense spectrum of non-radial modes

33. Intermediate model in the red giant branch Mode life-times M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Inertia

34. 3 M ¯ 2 M ¯ Pre-Helium versus Helium burning

35. M=3 M ¯, Log(L/L ¯ )=2, pre-He burning Mode life-times Pre-Helium

36. M=3 M ¯, Log(L/L ¯ )=2, He burning Helium burning Mode life-times

37. Pre-Helium M=3 M ¯, Log(L/L ¯ )=2, pre-He burning Life-times/Inertia / Height 1/2

38. Helium burning M=3 M ¯, Log(L/L ¯ )=2, He burning Life-times/Inertia / Height 1/2

39. Asymptotic treatment Final numerically improved version of MAD : Full numerical results close to asymptotic-numerical Numerical improvements Numerator in the core Denominator in the core Damping rate

40. Model at the bottom of red giant branch Resolved Not resolved M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Decreasing artificially the frequency resolution could be a tool allowing to filter the radial modes

41. Intermediate model in the red giant branch Height in power spectrum The detectable modes follow p-modes asymptotic relations M=3 M ¯, Log(L/L ¯ )=2, Helium burning

42. Model at the bottom of red giant branch M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Mode trapped in the core, = 201.3  Hz Mode trapped in the envelope, = 208.5  Hz d E K /d log T

43. Eigenfunctions with many nodes in the g-mode cavity Very dense spectrum of non-radial modes !! Huge ! Solar-type modes : n g ~ 100 – 1000 !!! in the g-cavity Mode physics in Red Giants

44. Trapping and radiative damping Life-time = Envelope : Convective damping independent of Core : Radiative damping depends on and mode trapping Inertia : depends on and mode trapping

45. Radiative damping Life-time ~ Huge radiative damping: Life-time depends on Independent of trapping

46. Mode trapping Mode physics in Red Giants See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004)

47. Intermediate model in the red giant branch Life-times/Inertia / Height 1/2 M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning  I Lifetimes/Inertia

48. Intermediate model in the red giant branch M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Amplitude

49. Kinetic energy :  |  r| 2 Mode physics in Red Giants Huge number of nodes in the core Dense spectrum of non-radial modes G R A V I T Y EVANESCENTEVANESCENT A C O U S T I C

50. Work integral Huge radiative damping of most non-radial modes Mode nearly trapped in the envelope = 22.8  Hz High luminosity model in the red giant branch M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning

51. Model at the bottom of red giant branch Amplitude M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Amplitudes

52. How red giants differ from the Sun ? Sun Mode lifetimes do not depend on Pure acoustic modes, (radial component of displacement dominates everywhere) (for small )

53. High luminosity model in the red giant branch Only radial modes could be observed !  I Lifetimes/Inertia M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning

54. Model at the bottom of red giant branch M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Lifetimes/Inertia / Height 1/2 (if resolved) Lifetime =  I A : Model at the bottom of red giant branch

55. Model at the bottom of red giant branch M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Lifetimes/Inertia / Height 1/2 (if resolved) Lifetime =  I A : Model at the bottom of red giant branch

56. Model at the bottom of red giant branch M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning Life-times/Inertia / Height 1/2 Work integral No radiative damping Mode trapped in the core, = 201.3  Hz M=2 M ¯, Log(L/L ¯ )=1.32, pre-He burning A : Model at the bottom of red giant branch

57. High luminosity model in the red giant branch Mode life-times M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning Lifetimes C : High luminosity model in the red giant branch

58. High luminosity model in the red giant branch Amplitude Very small amplitudes for non-radial modes Huge radiative damping of most non-radial modes M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning C : High luminosity model in the red giant branch

59. Very dense spectrum of non-radial modes !! = 0 = 1 = 2 Pre-Helium burning Red Giant Mode physics in Red Giants