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Non-adiabatic non-radial models for δ Scuti and γ Dor stars

Non-adiabatic non-radial models for δ Scuti and γ Dor stars. R. Garrido M. A. Dupret A. Grigahcène A. Moya J. C. Suárez. Mode identification through colour information Non-adiabatic asteroseismology Rotation ( M. J. Goupil ) Interaction convection-pulsation. Theoretical developments.

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Non-adiabatic non-radial models for δ Scuti and γ Dor stars

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  1. Non-adiabatic non-radial models for δScuti and γDor stars R. Garrido M. A. Dupret A. Grigahcène A. Moya J. C. Suárez

  2. Mode identification through colour information Non-adiabatic asteroseismology Rotation (M. J. Goupil) Interaction convection-pulsation Theoretical developments

  3. Non-adiabatic computations Local effective temperature variation Surface distorsion New equilibrium atmosphere models Local effective gravity variation

  4. Temperature distribution: • Monochromatic Flux: • Limb darkening: Non-adiabatic models: Radiative equilibrium in the local atmosphere

  5. Colour predictions

  6. Colour predictions

  7. 3-D hydrodynamic simulations Perturbative 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 MLT Gough´s theory Gabriel´s theory Convection – pulsation interaction Gabriel´s theory

  8. 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

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

  10. Stables and unstable modes l = 2 - 1.8 M0 - a = 1.5 Frozen convection Time-dependent convection p7 p7 p6 p6 p5 p5 p4 p4 p3 p3 p2 p2 p1 p1 f f g1 g1 g2 g2 g3 g3 g4 g4 g6 g8 g6 g8 d Scuti

  11. Instability strips a = 1.8 Radial modes d Scuti

  12. a = 1.8 l = 2 modes d Scuti Instability strips

  13. Phase lags

  14. 28 And FC

  15. 28 And TDC

  16. Convective blocking ? (Guzik et al. 2000) W: Total work integral WFcr: Radial convective flux term WFch: Transversal convective flux term WFRr: Radial radiative flux term WFRh: Transversal radiative flux term M = 1.6 M0 Teff = 7000 K a = 2 Mode l=1, g50 g Doradus Driving mechanism

  17. Unstable modes g Doradus

  18. l = 1 a = 1, 1.5, 2 Instability strips g Doradus

  19. a = 1.8 Comparison : d Sct red edge (l=0, p1) g Dor instability strip (l=1)

  20. Star HD 164615, freq. = 1.233 cycles/day Amplitude ratios - Stroemgren photometry Kurucz atmosphere FST atmosphere Time-dependent convection Frozen convection g Doradus Photometric amplitudes and phases

  21. Convection-pulsation interaction Non-adiabatic rotating models Non-linear models Present and future work

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