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Driving mechanism and energetic aspects of pulsations in g Doradus stars

Driving mechanism and energetic aspects of pulsations in g Doradus stars. M.-A. Dupret. LESIA, Paris Observatory, France. Grigahcène. Miglio J. Montalban. Algiers, Algeria. Liège, Belgium. Driving mechanism and energetic aspects in g Doradus stars. Amplitude and phases.

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Driving mechanism and energetic aspects of pulsations in g Doradus stars

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  1. Driving mechanism and energetic aspects of pulsations in g Doradus stars M.-A. Dupret LESIA, Paris Observatory, France • Grigahcène • Miglio J. Montalban Algiers, Algeria Liège, Belgium

  2. Driving mechanism and energetic aspects in g Doradus stars Amplitude and phases Excitation Mode identification

  3. g Doradus stars Internal physics: Convection and partial ionization zones • 1 convective core • 1 convective envelope Fc/F k He an H partial ionization zones are inside the convective envelope rad = (Γ3-1) / 1

  4. dS0 Coupling between • the dynamical equations and • the thermal equations g Doradus stars Driving mechanism Main driving occurs in the transition region where the thermal relaxation time is of the same order as the pulsation periods For a solar calibrated mixing-length, the transition region for the g-modes is near the convective envelope bottom. Non-adiabatic region Quasi-adiabatic region Log(tth) g50

  5. g Doradus Driving mechanism Flux blocking at the base of the convective envelope Motor thermodynamical cycle

  6. g Doradus Driving mechanism Flux blocking at the base of the convective envelope Motor thermodynamical cycle Luminosity variation Work integral M = 1.6 M0 , Teff = 7000 K , a = 2 , Mode l=1, g50

  7. M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism Role of time-dependent convection Fc / F tc : Life-time of convective elements s : Angular frequency Log (stc )

  8. 3-D hydrodynamic simulations Analytical approach All motions are convective ones Separation between convection and pulsation in the Fourier space of turbulence In particular the p-modes (present in the solution) Convective motions: short wave-lengths Oscillations: long wave-lengths Nordlund & Stein Samadi, Belkacem (Meudon) 1. Static solution without oscillations 2. Stability study of this solution Oscillations Perturbation MLT Gough´s theory Gabriel´s theory Convection – pulsation interaction Gabriel´s theory

  9. Convection – pulsation interaction: Gabriel´s theory Hydrodynamic equations Convective fluctuations equations Mean equations Perturbation Perturbation Equations of linear non-radial non-adiabatic oscillations Correlation terms • Convective flux • Reynolds stress Perturbation of • Turbulent kinetic • energy dissipation

  10. Radiative luminosity Convective luminosity Turbulent pressure Turbulent kinetic energy dissipation Convection – pulsation interaction: Work integral

  11. M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism WFRr: Radial radiative flux term

  12. M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism WFRr: Radial radiative flux term WFcr: Radial convective flux term

  13. M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism WFRr: Radial radiative flux term WFcr: Radial convective flux term Wpt: Turbulent pressure We2: Turbulent kinetic energy dissipation

  14. M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism WFRr: Radial radiative flux term WFcr: Radial convective flux term WFh: Transversal convective and radiative flux

  15. M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism WFRr: Radial radiative flux term WFcr: Radial convective flux term Wtot: Total work

  16. l = 1 Instability strips g Doradus

  17. Instability strips g Doradus l = 1

  18. g Dor g-modes • Sct p-g modes Unstable modes g Doradus

  19. Unstable modes g Doradus

  20. Unstable modes g Doradus Period range decreases with l

  21. Unstable modes g Doradus

  22. Key point: Location of the convective envelope bottom Instability region very sensitive to the effective temperature and the description of convection (a, …) Unstable modes g Doradus

  23. HD 209295 Handler et al. (2002) Tidally excited ? HD 8801 Henry et al. (2005) Am star HD 49434 Hybrid d Sct – g Dor Comparison : d Sct red edge (l=0, p1) g Dor instability strip (l=1)

  24. g Dor g-modes • Sct p-g modes Hybrid d Sct – g Dor Unstable modes

  25. Hybrid d Sct – g Dor Unstable modes Stable regions

  26. Hybrid d Sct – g Dor HD 49434 HD 49434

  27. Hybrid d Sct – g Dor Unstable modes (HD 49434) 2 4 0.5 20 40

  28. Hybrid d Sct – g Dor Work integral : l = 1 p2

  29. Hybrid d Sct – g Dor Work integral Work integral : l = 1 p2 p1

  30. Hybrid d Sct – g Dor Work integral Work integral : l = 1 p2 p1 g1

  31. Hybrid d Sct – g Dor Work integral Work integral : l = 1 p2 p1 g1 g2

  32. Hybrid d Sct – g Dor Work integral Work integral : l = 1 p2 p1 g1 g2 g3

  33. Hybrid d Sct – g Dor Work integral Work integral : l = 1 p2 p1 g1 g2 g3 g4

  34. Hybrid d Sct – g Dor Work integral Work integral : l = 1 p2 p1 g1 g2 g3 g4 g6

  35. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g6

  36. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g8 g6

  37. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g10 g8 g6

  38. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g12 g10 g8 g6

  39. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g15 g12 g10 g8 g6

  40. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g21 g15 g12 g10 g8 g6

  41. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g21

  42. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g21

  43. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g21 g30

  44. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g21 g30 g35

  45. Hybrid d Sct – g Dor Work integral Work integral : l = 1 g21 g30 g35 g40

  46. Hybrid d Sct – g Dor Work integral Work integral l = 1 , g25 l = 1 , g6

  47. Hybrid d Sct – g Dor Radiative damping mechanism Growth-rate

  48. Hybrid d Sct – g Dor Radiative damping mechanism Growth-rate < 0

  49. Hybrid d Sct – g Dor Work integral Propagation diagrams

  50. Hybrid d Sct – g Dor Work integral Propagation diagrams g-mode p-mode g-mode cavity Evanescent g-mode cavity

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