1. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 1 Driving mechanism and energetic aspects of pulsations in  Doradus stars A.Miglio J. Montalban Liège, Belgium M.-A. Dupret LESIA, Paris Observatory, France A.Grigahcène Algiers, Algeria

2. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 2 Driving mechanism and energetic aspects in  Doradus stars Excitation Amplitude and phases Mode identification

3. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 3 Convection and partial ionization zones  Doradus stars Internal physics: 1 convective core 1 convective envelope He an H partial ionization zones are inside the convective envelope Fc/F r ad = (Γ 3 -1) /  1 

4. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 4 Driving mechanism  Doradus stars 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. Quasi-adiabatic region Non-adiabatic region g 50 Log(  th )  S  0 S  0 Coupling between the dynamical equations and the thermal equations

5. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 5 Driving mechanism  Doradus Flux blocking at the base of the convective envelope Motor thermodynamical cycle

6. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 6 Driving mechanism  Doradus M = 1.6 M 0, T eff = 7000 K,  = 2, Mode =1, g 50 Flux blocking at the base of the convective envelope Motor thermodynamical cycle Work integral Luminosity variation

7. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 7 Driving mechanism  Doradus M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50 Role of time-dependent convection  c : Life-time of convective elements  : Angular frequency Log (   c ) F c / F

8. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 8 Convection – pulsation interaction 3-D hydrodynamic simulations All motions are convective ones In particular the p-modes (present in the solution) Nordlund & Stein Samadi, Belkacem (Meudon) Analytical approach Separation between convection and pulsation in the Fourier space of turbulence Convective motions: short wave-lengths Oscillations: long wave-lengths 1. Static solution without oscillations 2. Stability study of this solution Perturbation Oscillations Gough´s theoryGabriel´s theory MLT Gabriel´s theory

9. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 9 Hydrodynamic equations Mean equations Convective fluctuations equations Equations of linear non-radial non-adiabatic oscillations Correlation terms Perturbation Convection – pulsation interaction: Gabriel´s theory Convective flux Reynolds stress Turbulent kinetic energy dissipation Perturbation of

10. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 10 Radiative luminosityConvective luminosityTurbulent pressure Turbulent kinetic energy dissipation Convection – pulsation interaction: Work integral

11. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 11 Driving mechanism  Doradus W FRr : Radial radiative flux term M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50

12. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 12 Driving mechanism  Doradus W FRr : Radial radiative flux term W Fcr : Radial convective flux term M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50

13. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 13 Driving mechanism  Doradus M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50 W FRr : Radial radiative flux term W Fcr : Radial convective flux term W pt : Turbulent pressure W  2 : Turbulent kinetic energy dissipation

14. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 14 Driving mechanism  Doradus M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50 W FRr : Radial radiative flux term W Fcr : Radial convective flux term W Fh : Transversal convective and radiative flux

15. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 15 Driving mechanism  Doradus M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50 W FRr : Radial radiative flux term W Fcr : Radial convective flux term W tot : Total work

16. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 16 Instability strips  Doradus = 1

17. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 17 Instability strips  Doradus = 1

18. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 18 Unstable modes  Doradus  Dor g-modes  Sct p-g modes

19. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 19 Unstable modes  Doradus

20. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 20 Unstable modes  Doradus Period range decreases with

21. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 21 Unstable modes  Doradus

22. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 22 Unstable modes  Doradus Key point: Location of the convective envelope bottom Instability region very sensitive to the effective temperature and the description of convection ( , …)

23. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 23 Hybrid  Sct –  Dor Comparison :  Sct red edge ( =0, p 1 )  Dor instability strip ( =1) HD 209295 Handler et al. (2002) Tidally excited ? HD 8801 Henry et al. (2005) Am star HD 49434

24. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 24  Dor g-modes  Sct p-g modes Unstable modes Hybrid  Sct –  Dor

25. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 25 Unstable modes Stable regions Hybrid  Sct –  Dor

26. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 26 HD 49434 Hybrid  Sct –  Dor

27. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 27 Hybrid  Sct –  Dor Unstable modes (HD 49434) 24 20400.5

28. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 28 Hybrid  Sct –  Dor Work integral : = 1 p2p2

29. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 29 Hybrid  Sct –  Dor Work integral p2p2 p1p1 Work integral : = 1

30. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 30 Hybrid  Sct –  Dor Work integral p2p2 p1p1 g1g1 Work integral : = 1

31. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 31 Hybrid  Sct –  Dor Work integral p2p2 p1p1 g1g1 g2g2 Work integral : = 1

32. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 32 Hybrid  Sct –  Dor Work integral p2p2 p1p1 g1g1 g2g2 g3g3 Work integral : = 1

33. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 33 Hybrid  Sct –  Dor Work integral p2p2 p1p1 g1g1 g2g2 g3g3 g4g4 Work integral : = 1

34. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 34 Hybrid  Sct –  Dor Work integral p2p2 p1p1 g1g1 g2g2 g3g3 g4g4 g6g6 Work integral : = 1

35. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 35 Hybrid  Sct –  Dor Work integral g6g6 Work integral : = 1

36. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 36 Hybrid  Sct –  Dor Work integral g6g6 g8g8 Work integral : = 1

37. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 37 Hybrid  Sct –  Dor Work integral g6g6 g8g8 g 10 Work integral : = 1

38. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 38 Hybrid  Sct –  Dor Work integral g6g6 g8g8 g 10 g 12 Work integral : = 1

39. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 39 Hybrid  Sct –  Dor Work integral g6g6 g8g8 g 10 g 12 g 15 Work integral : = 1

40. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 40 Hybrid  Sct –  Dor Work integral g6g6 g8g8 g 10 g 12 g 15 g 21 Work integral : = 1

41. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 41 Hybrid  Sct –  Dor Work integral g 21 Work integral : = 1

42. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 42 Hybrid  Sct –  Dor Work integral g 21 Work integral : = 1

43. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 43 Hybrid  Sct –  Dor Work integral g 21 g 30 Work integral : = 1

44. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 44 Hybrid  Sct –  Dor Work integral g 21 g 30 g 35 Work integral : = 1

45. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 45 Hybrid  Sct –  Dor Work integral g 21 g 30 g 35 g 40 Work integral : = 1

46. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 46 Hybrid  Sct –  Dor Work integral  = 1, g 6  = 1, g 25

47. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 47 Hybrid  Sct –  Dor Radiative damping mechanism Growth-rate

48. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 48 Hybrid  Sct –  Dor Radiative damping mechanism Growth-rate < 0

49. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 49 Hybrid  Sct –  Dor Work integralPropagation diagrams

50. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 50 Hybrid  Sct –  Dor Work integralPropagation diagrams g-mode cavity Evanescent g-modep-mode g-mode cavity

51. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 51 Hybrid  Sct –  Dor Work integralAsymptotic behaviour In propagation regions :  2 < N 2, L 2

52. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 52 Hybrid  Sct –  Dor Work integralAsymptotic behaviour In evanescent regions : L 2 <  2 < N 2

53. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 53 Hybrid  Sct –  Dor Work integralEigenfunctions behaviour  = 1, g 25 Small amplitude In the g-mode cavity Large amplitude at the bottom of the convective envelope

54. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 54 Hybrid  Sct –  Dor Work integralEigenfunctions behaviour  = 1, g 25 Radiative damping negligible Significant driving

55. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 55 Hybrid  Sct –  Dor Work integralEigenfunctions behaviour  = 1, g 6 Large amplitude in the g-mode cavity Smaller amplitude at the bottom of the convective envelope EVANESCENTEVANESCENT

56. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 56 Hybrid  Sct –  Dor  = 1, g 6 Eigenfunctions behaviour Significant radiative damping Driving negligible

57. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 57 Hybrid  Sct –  Dor Work integral  = 1, g 6  = 1, g 25

58. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 58 Hybrid  Sct –  Dor Unstable modes (HD 49434) 24 20400.5

59. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 59 Hybrid  Sct –  Dor Work integralPropagation diagrams  = 1  = 2

60. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 60 Hybrid  Sct –  Dor Work integralPropagation diagrams =2, g 25  = 1  = 2

61. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 61 Spectro-photometric amplitudes and phases and mode identification  Doradus Phase-lags Line-profile variations Moment method Amplitude ratios Very sensitive to the non-adiabatic treatment of convection Mode identification SpectroscopyPhotometry

62. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 62 Distortion of the stellar surface described by the lagrangian displacement of matter Temperature : Flux : Limb darkening : Thermal equilibrium in the local atmosphere Hypotheses Photometric amplitudes and phases and mode identification

63. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 63 Non - adiabatic computations Influence of the local effective temperature variations Influence of the local effective gravity variations Equilibrium atmosphere models Stellar surface variation FiltersIntegration on the pass-band Linear computationsAmplitude ratios and phase differences Dependence with the degree Identification of Monochromatic magnitude variation

64. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 64 Multi-colour photometric Observations Amplitude ratios & Phase lags Range of frequencies Mode identification Range of frequencies Non-adiabatic asteroseismology Improving the fit Stellar parameters  Scuti  Doradus  Cephei SPB Convection Chemical composition Atmosphere models - Limb darkening Time-dependence Mixing Length (  ) Full spectrum Non-adiabatic computations Equilibrium models, Stellar evolution code

65. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 65 Spectro-photometric amplitudes and phases and mode identification Very sensitive to the non-adiabatic treatment of convection Time-dependent convection Frozen convection Phase-lag

66. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 66 Frozen convectionTime-dependent convection  -mechanism Not allowed by time-dependent convection Spectro-photometric amplitudes and phases and mode identification Very sensitive to the non-adiabatic treatment of convection

67. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 67  Doradus 3 frequencies: f 1 =1.32098 c/d, f 2 =1.36354 c/d, f 3 =1.47447 c/d Balona et al. 1994Strömgren photometry Balona et al. 1996 Simultaneous photometry and spectroscopy Spectroscopic mode identification:( 1, m 1 ) = (3, 3), ( 2, m 2 ) = (1, 1), ( 3, m 3 ) = (1, 1) Spectro-photometric amplitudes and phases and mode identification

68. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 68  Doradus Balona et al. 1996 Simultaneous photometry and spectroscopy Phase-lag ( Vmagnitude – displacement ): Observations:  1 = - 65° ± 5°  3 = - 29° ± 8° Theory: Time-dependent convection Frozen convection (  = 2)  = - 30°  = - 165° Spectro-photometric phase differences

69. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 69 Photometric mode identification  Doradus Frozen  = 2 - MLT  = 1 - MLT Time-dependent Best models:Time-dependent convection = 1 modes

70. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 70 Influence of the effective temperature variations Influence of the effective gravity variations Importance of ultraviolet observations (bracketing the Balmer discontinuity) Gravity derivatives vary quickly in u-v Changes the weight of T eff and g e terms Helps for the mode identification and gives constraints on |  T eff /T eff | Stromgren, Geneva systems are perfects

71. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 71 Conclusions Driving mechanism: Main driving due to convective blocking at the base of the convective envelope Time-Dependent convection does not inhibits the mechanism Driving mechanism and energetic aspects in  Doradus stars The size of the convective envelope is the key point ) predictions very sensitive to the treatment of convection

72. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 72 Conclusions Mode identification, multi-color amplitudes and phases: Time-Dependent Convection required, gives constrain on : Convective envelope Interaction convection – oscillations Atmosphere models Mode identification and non-adiabatic asteroseismology of  Doradus stars Hybrid  Scuti -  Doradus Driving at the bottom of the convective envelope Radiative damping, deep in the g-mode cavity Instability ranges depend on: Location of convective envelope Spherical degree Local wave-length ) Brunt-Vaisala, Lamb frequencies

73. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 73  Doradus Stabilization mechanism Radiative damping in the g-modes cavity

74. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 74  Doradus Stabilization mechanism Radiative damping in the g-modes cavity

75. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 75 Comparison :  Sct red edge ( =0, p 1 )  Dor instability strip ( =1)  = 1.8

76. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 76 Stabilization mechanism  Doradus W FRr : Radial radiative flux term M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 50

77. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 77 Unstable modes  Doradus

78. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 78 Unstable modes  Doradus

79. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 79 Unstable modes  Doradus

80. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 80 Non-adiabatic stellar oscillations: utility Excitation mechanisms Mode identification Solar-like oscillations Unstable modes: growth rates Stable modes: damping rates Line-widths in the power spectrum Observations Stochastic excitation models Amplitudes Stable modes: damping rates

81. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 81 Radiative luminosityConvective luminosityTurbulent pressure Turbulent kinetic energy dissipation Convection – pulsation interaction: Work integral

82. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 82 Solar-type oscillations Difficulties :1. Treatment in the efficient part of convection Very short wave-length oscillations of the eigenfunctions Local treatment

83. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 83 Difficulties:1. Treatment in the efficient part of convection Origin of the problem: Wavelength much shorter than the mixing-length ! Solar-type oscillations

84. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 84 Difficulties:1. Treatment in the efficient part of convection Non-local (Balmforth 1992) Local (Gabriel 2003) Introduction of new free parameters Solutions Solar-type oscillations

85. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 85 Difficulties:1. Treatment in the efficient part of convection Solutions Local (Gabriel 2003) Solar-type oscillations

86. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 86 Difficulties: 2. Treatment of turbulent pressure perturbation Increases the order of the system Very stiff problem at the boundaries Numerical instabilities Solar-type oscillations

87. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 87 Models of stochastic excitation The Sun is a vibrationally stable oscillator. Excitation of the mode is due to stochastic forcing coming from turbulent convective motions. Non-adiabatic models Damping rate:  Stochastic models Acoustical noise generation rate: P Velocity Theory Observations Line-widths Observed amplitudes Solar-type oscillations: confrontation to observations

88. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 88 Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997) Solar-type oscillations: confrontation to observations

89. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 89 Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997) Solar-type oscillations: confrontation to observations

90. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 90 Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997) Solar-type oscillations: confrontation to observations

91. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 91 Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997) Solar-type oscillations: confrontation to observations

92. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 92  Scuti Stables and unstable modes Time-dependent convection p7p7 p6p6 p4p4 p5p5 p3p3 g1g1 f p1p1 p2p2 g2g2 g3g3 g4g4 g6g6 g8g8 Frozen convection p7p7 p6p6 p4p4 p5p5 p3p3 g1g1 f p1p1 p2p2 g2g2 g3g3 g4g4 g6g6 g8g8  = 2 - 1.8 M 0 -  = 1.5

93. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 93  Scuti Instability strips Radial modes

94. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 94  Scuti Instability strips  = 2 modes

95. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 95 Photometric amplitudes and phases =0 =1 =3 =2 =3 =0 =1 =2 =3 phase(b-y)-phase(y) (deg) Amplitude ratios vs. phase difference - Stroemgren photometry  = 0.5  = 1  Scuti

96. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 96 Conclusions Damping ratesLine-widths Convection-pulsation interaction in solar-like stars Efficient part of convective envelope Local treatment → Spatial oscillations of the eigenfunctions → Introduction of a free parameter  in the perturbation of the closure equations Perturbation of turbulent pressure → Numerical instabilities Amplitudes Stochastic excitation We found a model fitting the observed damping rates but … Theoretical difficulties Confrontation to observations

97. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 97

98. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 98 Oscillations de type solaire Taux de d´amortissement confrontables aux observations (largeurs de raie) Mécanisme d´excitation : Excitation stochastique Oscillateur vibrationellement stable forcé stochastiquement par la convection Contrainte sur les modèles non-adiabatiques d´intéraction convection-oscillations

99. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 99 Oscillations de type solaire Difficulté des modèles non-adiabatiques: intéraction convection-oscillations Grande enveloppe convective Convection efficace ( t c >> t p ) Oscillations spatiales non-physiques des fonctions propres

100. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 100 Oscillations de type solaire Difficulté des modèles non-adiabatiques: intéraction convection-oscillations Grande enveloppe convective Convection efficace ( t c >> t p ) Oscillations spatiales non-physiques des fonctions propres Solutions Non-locales (Balmforth 1992) Locales (Gabriel 2003) Introduction de paramètres libres supplémentaires

101. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 101 Oscillations de type solaire Difficulté des modèles non-adiabatiques: intéraction convection-oscillations Grande enveloppe convective Convection efficace ( t c >> t p ) Oscillations spatiales non-physiques des fonctions propres Solutions Locales (Gabriel 2003)

102. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 102 Conclusions Mécanismes d’excitation Bandes d’instabilité Amplitudes et phases photométriques Identification des modes Astérosismologie non-adiabatique Astérosismologie “classique” (fréquences)

103. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 103 Mécanismes d’excitation Conclusions Amplitudes et phases photométriques Bandes d’instabilité Astérosismologie non-adiabatique Identification des modes Mécanisme  (Fe) Contraintes sur la métallicité Marche très bien Idem OK mais effet de la rotation ?  Cephei Modes p SPB Modes g

104. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 104 Mécanismes d’excitation Conclusions Amplitudes et phases photométriques Bandes d’instabilité Astérosismologie non-adiabatique Identification des modes Frontière bleue: mécanisme  (HeII) Frontière rouge: convection Contraintes sur les modèles de convection et d’intéraction convection - pulsation Bon accord avec  solaire Idem Nettement mieux avec l’intéraction convection-pulsation OK mais reste difficile Effet de la rotation ?  Scuti Modes p  Dor Modes g

105. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 105 Conclusions Type solaire Modes p Mécanismes d’excitation Amplitudes et phases photométriques Excitation stochastique, modélisation difficile de l’intéraction convection – oscillations Amplitudes données par les modèles d’excitation stochastique. Grands espoirs futurs :

106. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 106 Oscillations de type solaire Difficulté des modèles non-adiabatiques: intéraction convection-oscillations : Solutions Non-locales (Balmforth 1992) Locales (Gabriel 2003)

107. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 107  Scuti Taille de l´enveloppe convective pour différentes températures effectives T eff =8345.5 K T eff =6119.5 K M=1.8 M 0, α=1.5

108. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 108  T eff / T eff |        Longueur de mélange - différents  - convection gelée Sensibilité à la structure de l´enveloppe convective  Scuti Amplitudes et phases photométriques

109. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 109 Photométrie multi-couleur et astérosismologie non - adiabatique Observations en photométrie multi-couleur Rapports d´amplitude & déphasages Modèles d´équilibre Code d´évolution stellaire Calculs non-adiabatiques Identification de mode Paramètres stellaires  Scuti  Doradus  Cephei SPB Convection Metallicité (Z) Modèles d´atmosphère - Limb darkening Mixing length (  ) Hydrodynamique FST

110. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 110 Full Spectrum of TurbulenceLongueur de mélange  T eff / T eff | Amplitudes et phases photométriques  Scuti Sensibilité à la structure de l´enveloppe convective

111. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 111 Amplitudes et phases photométriques  Scuti Full Spectrum of TurbulenceLongueur de mélange = 3 = 2 = 1 = 0 Q = 0.015 d Q = 0.033 d Rapport d´amplitude vs. Différences de phase - photométrie Stroemgren

112. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 112  Doradus Types spectraux F Masses +/- 1.5 M 0 Périodes 0.3 à 3 jours modes g

113. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 113  Doradus Amplitudes et phases photométriques Comparaison : convection gelée convection dépendant du temps M = 1.5 M 0 - T eff = 7000 K -  = 1.8

114. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 114 Type solaire Types spectraux F et G Masses 1 M 0 à 1.5 M 0 Périodes Quelques minutes Modes p élevés Faibles amplitudes

115. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 115 Excitation mechanisms Photometric amplitudes and phases in different filters Identification of the degree Non - adiabatic asteroseismology Non adiabatic oscillations at the photosphere Need of a non - adiabatic code for the confrontation between theory and observations Utility of our non - adiabatic code Multi-colour photometry

116. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 116 Introduction Stellar pulsations Pressure modes Acoustic waves Gravity modes Buoyancy force Asteroseismology

117. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 117 stellar oscillationsNon - radialnon - adiabatic Splitting in spherical harmonics Non - radial p - modesAcoustic waves g - modesBuoyancy force 1)

118. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 118 stellar oscillationsNon - radialnon - adiabatic  S  0 non - adiabatic Coupling between thedynamicalthermalandequations Equation of momentum conservation Equation of mass conservation Poisson equation dynamical Equations of transfer by radiation and convection thermal Equation of energy conservation 1)

119. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 119 Stellar surface distortion Influence of the local effective temperature variations Influence of the local effective gravity variations Equilibrium atmosphere models (Kurucz 1993) Monochromatic magnitude variation Non - adiabatic computations FiltersIntegration on the pass-band Linear computationsAmplitude ratios and phase differences Dependence with the degree Identification of

120. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 120 4.2  Scuti Time dependent convection - MLT Theory of M. Gabriel Red edge of the instability strip Time-dependent convectionFrozen convection Radial modes – 1.8 M 0,  = 1.5 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 p1p1 p8p8 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 p1p1 p8p8

121. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 121 4.2  Scuti Red edge of the instability strip Time-dependent convection = 2 modes – 1.8 M 0,  = 1.5 Frozen convection p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 p1p1 f g1g1 g2g2 g3g3 g4g4 g5g5 g6g6 g7g7 g8g8 g9g9 g 10 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 p1p1 f g1g1 g2g2 g3g3 g4g4 g5g5 g6g6 g7g7 g8g8 g9g9

122. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 122 p7p7 p2p2 p3p3 p4p4 p5p5 p6p6 g2g2 g1g1 f p1p1 g7g7 g8g8 g6g6 g4g4 g3g3 g5g5 Frozen Convection Time-dependent convection p7p7 p6p6 p4p4 p5p5 p3p3 g1g1 f p1p1 p2p2 g2g2 g3g3 g4g4 g5g5 g6g6 g7g7 g8g8 Figure 5Figure 6 III. Instability Strip III. 1. δ Scuti stars

123. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 123  Scuti Bandes d´instabilité p7p7 p1p1 1.4 M 0 2 M 0 1.8 M 0 1.6 M 0 2.2 M 0  = 1 - = 0

124. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 124  Scuti Bandes d´instabilité p7p7 p1p1 1.4 M 0 1.6 M 0 1.8 M 0 2 M 0 2.2 M 0  = 0.5 - = 0

125. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 125  Scuti Bandes d´instabilité p6p6 fBfB g7g7 fRfR 1.4 M 0 2 M 0 2.2 M 0 1.8 M 0 1.6 M 0  = 1.5 - = 2

126. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 126 Plan de l’exposé 1. Introduction 2. Oscillations stellaires non-adiabatiques : utilité 5. Conclusions 4. Applications  Cephei Slowly Pulsating B  Scuti  Doradus Type solaire 3. Modélisation du problème Atmosphère Convection

127. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 127 Z  T eff / T eff | Multi-colour photometry  Cephei 16 Lacertae High sensitivity of the non - adiabatic results to the metallicity  L / L| Z = 0.015 Z = 0.02 Z = 0.025 Z = 0.015 Z = 0.02 Z = 0.025 Johnson photometry

128. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 128 Modes excitation Z > 0.016 Non-adiabatic constraints on the metallicity 4.1  Cephei : HD 129929 Unstable Stable

129. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 129 Contraintes sismiques sur l´overshooting  ov = 0.1 ± 0.05  ov = 0.1  ov = 0.2  ov = 0 Instable Stable  Cephei : HD 129929

130. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 130 Excitation mechanism M = 4 M 0 T eff = 13 955 K Z = 0.02 Mode = 1 g 22 Work integral and luminosity variation from the center to the surface of the star Slowly Pulsating B stars

131. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 131 Identification photométrique des modes HD 74560  = 1  = 2  = 3 Slowly Pulsating B stars

132. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 132 Excitation mechanism Transition zone  mechanism of excitation Partial ionization zone of Helium II = Opacity and thermal relaxation time from the center to the surface  Scuti   PS log (  th )

133. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 133 M = 1.8 M 0 T eff = 7480 K Z = 0.02,  = 1 Radial fundamental mode Work integral and luminosity variation from the center to the surface of the star  Scuti Excitation mechanism

134. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 134 Modes stables et instables  Scuti  = 0 - 1.8 M 0 -  = 1.5 p1p1 p8p8 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2 Convection dépendant du tempsConvection gelée p1p1 p8p8 p7p7 p6p6 p5p5 p4p4 p3p3 p2p2

135. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 135 Mécanisme d´excitation :  Doradus ?? Bloquage convectif ?? (Guzik et al. 2000) Travail intégré M = 1.6 M 0 T eff = 7000 K  = 2 Mode =1, g 47

136. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 136 1.6 M 0 - = 1 -  = 1.5 Modes instables  Doradus

137. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 137 Convection – pulsation interaction: Gabriel´s theory P: Pressure tensor ; p : its diagonal component. Radiative Flux Hydrodynamic equations

138. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 138 Mean equations Dissipation of turbulent kinetic energy into heat Reynolds stress tensor Turbulent pressure Convection – pulsation interaction: Gabriel´s theory

139. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 139 Convective efficiency Life time of the convective elements Characteristic frequency of radiative energy lost by turbulent eddies In the static case, assuming constant coefficients (Hp>>l !), we have solutions which are plane waves identical to the ML solutions. Approximations of Gabriel’s Theory Convective fluctuations equations Convection – pulsation interaction: Gabriel´s theory

140. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 140 Linear pulsation equations Perturbation of the mean equations Equation of mass conservation Radial component of the equation of momentum conservation Transversal component of the equation of momentum conservation A : Anisotropy parameter A=1/2 for isotropic turbulence  : Angular pulsation frequency Convection – pulsation interaction: Gabriel´s theory

141. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 141 Convection – pulsation interaction: Gabriel´s theory Equation of Energy conservation FCH : Amplitude of the horizontal component of the convective flux

142. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 142 Convective Flux : Perturbation : Convective flux perturbation Convection – pulsation interaction: Gabriel´s theory

143. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 143 Turbulent pressure : Perturbation : Convection – pulsation interaction: Gabriel´s theory Turbulent pressure perturbation Perturbation of the mixing-length H p Pressure scale height

144. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 144 Convection – pulsation interaction: the Solar case Difficulties:2. Treatment of turbulent pressure perturbation Local analysis Movement Transfer Characteristic polynomial New terms  = 0 New root:  = 1/(b  ) ∞ at the convective boundaries The worse numerical case gives the best fits with observations Re(1/(b  )) < 0 at the left boundary Re(1/(b  )) > 0 at the right boundary

145. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 145 Convection – pulsation interaction: the Solar case Difficulties:2. Treatment of turbulent pressure perturbation The worse numerical case gives the best fits with observations Re(1/(b  )) < 0 at the left boundary Re(1/(b  )) > 0 at the right boundary Example:

146. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 146 Convection – pulsation interaction: the Solar case Difficulties:2. Treatment of turbulent pressure perturbation The worse numerical case gives the best fits with observations Re(1/(b  )) < 0 at the left boundary Re(1/(b  )) > 0 at the right boundary Example:

147. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 147 Plan de l’exposé 1. Introduction 2. Convection-pulsation interaction Plan of the presentation 1. Introduction 3. Confrontation to observations 2.1. The MLT theory of Gabriel 2.2. The case of solar-like oscillations 4. Conclusions 2. Convection-pulsation interaction 2.1. The MLT theory of Gabriel 2.2. The case of solar-like oscillations 3. Confrontation to observations 4. Conclusions

148. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 148 Non-adiabatic stellar oscillations Quasi-adiabatic region Non-adiabatic region  S  0 S  0 Coupling between the dynamical equations the thermal equations Introduction

149. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 149 Theoretical damping rates ↔ line-widths observed by GOLF Confrontation to observations

150. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 150 Problem: This solution fitting very well the observations is subject to numerical instabilities near the upper boundary of the convective envelope. They come from the turbulent pressure perturbation term. Confrontation to observations Theoretical damping rates ↔ line-widths observed by GOLF

151. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 151 Theoretical work integrals for different  (mode l=0, p 22 ) Confrontation to observations

152. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 152 Amplitudes et phases photométriques  Scuti Convection dépendant du temps M = 1.8 M 0 - T eff = 7150 K -  = 0.5  T eff / T eff | 

153. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 153 Amplitudes et phases photométriques  Scuti Convection dépendant du temps M = 1.8 M 0 - T eff = 7130 K -  = 1  T eff / T eff | 

154. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 154 Amplitudes et phases photométriques  Scuti Convection dépendant du temps M = 1.8 M 0 - T eff = 7150 K -  = 1.5  T eff / T eff | 

155. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 155 Propagation cavities  Doradus stars Internal physics: High inertia of the g-modes near the convective core top Main displacement is in the transversal direction Small radial displacement g 50

156. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 156 Radial component of the equation of momentum conservation Transversal component of the equation of momentum conservation A : Anisotropy parameter A=1/2 for isotropic turbulence  : Angular pulsation frequency Influence of turbulent Reynolds stress perturbation

157. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 157 Work integral Influence of turbulent Reynolds stress perturbation

158. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 158 P turb 0 and d P turb / dr discontinuous at the bottom of the convective envelope singularity of the equations unphysical discontinuity of the eigenfunctions Influence of turbulent Reynolds stress perturbation

159. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 159 Non-local treatments: Improves the things (continuity) but problem still present Influence of turbulent Reynolds stress perturbation

160. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 160 Influence of Reynolds stress: Work integral

161. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 161  Doradus - d W / d log T |  L / L| F R / F W For hot or small  models: very thin convective envelope the transition region is in the radiative zone Small  -driving (Fe, ~ SPBs) compensated by large radiative damping below and above

162. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 162 9 Aurigae 3 frequencies: f 1 =0.795 c/d, f 2 =0.768 c/d, f 3 =0.343 c/d Zerbi et al. 1994 Simultaneous photometry and spectroscopy Spectroscopic mode id. :( 1, |m 1 |) = (3, 1), Aerts & Krisciunas (1996) ( 3, |m 3 |) = (3, 1) Spectro-photometric amplitudes and phases

163. Workshop: «  Doradus stars in the COROT fields » Nice, 26-28 May, 2008 163  Aurigae Balona et al. 1996 Simultaneous photometry and spectroscopy Phase-lag ( Vmagnitude – displacement ): Observations:  1 = - 77° ± 12°  3 = - 41° ± 10° Theory (  = 2): TDC   = - 22°   = - 39° FC   = - 156°   = - 140° Spectro-photometric phase differences