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.

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Presentation transcript:

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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 

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Instability strips  Doradus = 1

Workshop: «  Doradus stars in the COROT fields » Nice, May, Instability strips  Doradus = 1

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes  Doradus

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes  Doradus Period range decreases with

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes  Doradus

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes Stable regions Hybrid  Sct –  Dor

Workshop: «  Doradus stars in the COROT fields » Nice, May, HD Hybrid  Sct –  Dor

Workshop: «  Doradus stars in the COROT fields » Nice, May, Hybrid  Sct –  Dor Unstable modes (HD 49434)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Hybrid  Sct –  Dor Work integralPropagation diagrams

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Hybrid  Sct –  Dor Unstable modes (HD 49434)

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Doradus 3 frequencies: f 1 = c/d, f 2 = c/d, f 3 = c/d Balona et al. 1994Strömgren photometry Balona et al 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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Doradus Balona et al 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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes  Doradus

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes  Doradus

Workshop: «  Doradus stars in the COROT fields » Nice, May, Unstable modes  Doradus

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  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  = M 0 -  = 1.5

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Scuti Instability strips Radial modes

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Scuti Instability strips  = 2 modes

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May,

Workshop: «  Doradus stars in the COROT fields » Nice, May, Oscillations de type solaire Taux de dámortissement confrontables aux observations (largeurs de raie) Mécanisme déxcitation : Excitation stochastique Oscillateur vibrationellement stable forcé stochastiquement par la convection Contrainte sur les modèles non-adiabatiques díntéraction convection-oscillations

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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)

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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 :

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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)

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Scuti Bandes d´instabilité p7p7 p1p1 1.4 M 0 2 M M M M 0  = 1 - = 0

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Scuti Bandes d´instabilité p7p7 p1p1 1.4 M M M 0 2 M M 0  = = 0

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Scuti Bandes d´instabilité p6p6 fBfB g7g7 fRfR 1.4 M 0 2 M M M M 0  = = 2

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Excitation mechanism M = 4 M 0 T eff = 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Identification photométrique des modes HD  = 1  = 2  = 3 Slowly Pulsating B stars

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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 )

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Modes stables et instables  Scuti  = 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, M 0 - = 1 -  = 1.5 Modes instables  Doradus

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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:

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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:

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

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

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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Work integral Influence of turbulent Reynolds stress perturbation

Workshop: «  Doradus stars in the COROT fields » Nice, May, 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

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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Influence of Reynolds stress: Work integral

Workshop: «  Doradus stars in the COROT fields » Nice, May,  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

Workshop: «  Doradus stars in the COROT fields » Nice, May, Aurigae 3 frequencies: f 1 =0.795 c/d, f 2 =0.768 c/d, f 3 =0.343 c/d Zerbi et al 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

Workshop: «  Doradus stars in the COROT fields » Nice, May,  Aurigae Balona et al 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