1. Modelling high-order g-mode pulsators Nice 27/05/2008 A method for modelling high-order, g-mode pulsators: The case of γ Doradus stars. A. Moya Instituto de Astrofísica de Andalucía – CSIC, Granada, Spain Brief introduction The problem of mode identification Photometry (FRM and multicolour) Gamma Doradus Modelling Scheme Future prospects Rotational coupling J.C. Suárez S. Martín-Ruíz P.J. Amado R. Garrido A. Grigacehene M.A. Dupret

2. Modelling high-order g-mode pulsators Nice 27/05/2008 Brief introduction γ Doradus stars High n Low ℓ Very low photometric amplitude Period close to 1 day Space missions essential for improving our observational knowledge of these stars

3. Modelling high-order g-mode pulsators Nice 27/05/2008 Brief introduction C C Radiative rbrb rtrt Tassoul, 1980 No Rotation No magnetic field Adiabatic approximation Smeyers & Moya, 2007

4. Modelling high-order g-mode pulsators Nice 27/05/2008 What is the meaning of mode identification? In the approximation of the star to have spherical symetry, each mode can be asociated to a spherical armonic Y l m (θ,φ) Observed frequency (n,ℓ,m) ¿(n,ℓ,m)? The problem of mode identification

5. Modelling high-order g-mode pulsators Nice 27/05/2008 The problem of mode identification There are two different observational techniques of modal identification: 1) Spectroscopy : This gives us part of the identification of the mode, that is (ℓ,m) 2) Photometry : We just have the periods of each mode and we have to connect with theoretical models to identify (n,ℓ,m)

6. Modelling high-order g-mode pulsators Nice 27/05/2008 The problem of mode identification Possible tool: Asymptotic equidistance in period This give information about ℓ and the Brunt- Väisälä integral

7. Modelling high-order g-mode pulsators Nice 27/05/2008 The problem of mode identification HD129019 Aurigae

8. Modelling high-order g-mode pulsators Nice 27/05/2008 Frequency Ratio Method (FRM) Assumptions: Some knowledge of the spherical order ℓ (assume all modes having the same ℓ or we know each individual ℓ). No rotation, no magnetic field and adiabatic behaviour. The integral is almost constant for the different modes within a given model. Moya et al., 2005, A&A 432, 189

9. Modelling high-order g-mode pulsators Nice 27/05/2008 Observations: Physical parameters ≥ 3 frequencies Frequency ratio method Several sets of (n 1,n 2,n 3,ℓ,I obs ) Small set of possible theoretical models describing this star FRM (ν1, ν2,ν3)(ν1, ν2,ν3)

10. Modelling high-order g-mode pulsators Nice 27/05/2008 The star HD12901

11. Modelling high-order g-mode pulsators Nice 27/05/2008 The star HD12901 T eff Log g[Fe/H]Km/s 69964.04-0.37 70794.47-0.40 53 66 Freqc/dμHz fIfI 1.21614.069 f II 1.39616.157 f III 2.18625.305 β 1,2 =0.871β 2,3 =0.639β 1,3 =0.556 ±0.005

12. Modelling high-order g-mode pulsators Nice 27/05/2008 The star HD12901 Namen1n1 n2n2 n3n3 ℓI obs t1t1 1727311987.0 t2t2 21333811202.4 t3t3 2133382694.2 t4t4 2641472860.0 t5t5 3047542984.3 t6t6 33526021087.9

13. Modelling high-order g-mode pulsators Nice 27/05/2008

15. The star HD12901

16. Modelling high-order g-mode pulsators Nice 27/05/2008 The star HD12901

17. Modelling high-order g-mode pulsators Nice 27/05/2008 The star HD12901

18. Modelling high-order g-mode pulsators Nice 27/05/2008 FRM with rotation Suárez et al., 2005, A&A, 443, 271 The FRM still works for m=0 modes There are not possible confusion between modes with different m Two main conclusions:

19. Modelling high-order g-mode pulsators Nice 27/05/2008 Non-adiabatic computations Surface distortion Influence of the local effective temperature variation Influence of the local effective gravity variation Equilibrium atmosphere models (Kurucz 1993) Multicolor photometry

20. Modelling high-order g-mode pulsators Nice 27/05/2008 As a result of the numerical computations we can obtain And the grow rate Where Multicolor photometry

21. Modelling high-order g-mode pulsators Nice 27/05/2008 Multicolor photometry Current most evolved tool: Time dependent convection

22. Modelling high-order g-mode pulsators Nice 27/05/2008 Observations giving physical parameters and three frequencies Frequency ratio method Set of possible mode identifications and equilibrium models Fix α in MLT and ℓ Instability and non- adiabatic multicolor study with TDC (or spectroscopy) Photometric multicolour predictions (models, modes and free parameters fixed) Multicolour photometric observations Gamma Doradus Modeling Scheme

23. Modelling high-order g-mode pulsators Nice 27/05/2008 T eff Log g[Fe/H]Km/s 69904.17-0.1818 Freqc/d f1f1 0.7948 f2f2 0.7679 f3f3 0.3429 =0.966 ±0.010 =0.447 ±0.010 =0.431 ±0.010 GDMS (9 Aurigae)

24. Modelling high-order g-mode pulsators Nice 27/05/2008 Namen1n1 n2n2 n3n3 ℓ I obs t1t1 3334771681.14 t2t2 57591332678.24 And lower I obs GDMS (9 Aurigae)

25. Modelling high-order g-mode pulsators Nice 27/05/2008 MassT eff Log gLog L/L Θ R/R Θ AgeI th [Fe/H]α ov 1.470064.280.631.41600681.5-0.10.3 Model fulfilling FRM constraints GDMS (9 Aurigae)

26. Modelling high-order g-mode pulsators Nice 27/05/2008 Multicolor analysis with TDC (Dupret et al. and Grigahcene et al.) for the model coming from FRM Different α MLT and atmospheric models Strömgren filters ℓ =2 GDMS (9 Aurigae)

27. Modelling high-order g-mode pulsators Nice 27/05/2008 Stability analysis with TDC for different α MLT α MLT 1.6 2.0 1.4 1.8 α MLT =1.6 GDMS (9 Aurigae)

28. Modelling high-order g-mode pulsators Nice 27/05/2008 Physical parameters MassT eff Log gLog L/L Θ R/R Θ Age[Fe/H] 1.470064.280.631.41600-0.1 Theoretical parameters α MLT I th α ov 1.6681.50.3 Modal identification n1n1 n2n2 n3n3 ℓ 57591332 Freqc/d f1f1 0.7948 f2f2 0.7679 f3f3 0.3429 GDMS (9 Aurigae)

29. Modelling high-order g-mode pulsators Nice 27/05/2008 Rotational coupling δm λ (coup)= β·δm λ (1)+(1-β) δm λ (2)

30. Modelling high-order g-mode pulsators Nice 27/05/2008 Rotational coupling

31. Modelling high-order g-mode pulsators Nice 27/05/2008 Rotational coupling

32. Modelling high-order g-mode pulsators Nice 27/05/2008 Rotational coupling How to obtain information in this case

33. Modelling high-order g-mode pulsators Nice 27/05/2008 Frequency ratio method gives a set of possible models fitting the physical parameters and the observed frequencies, fixing the parameters directly related with the Brunt- Väisälä frequency as metallicity, overshooting, etc. + Time dependent convection-pulsation interaction can give a range for α by studying the instability regions, estimating also the multicolour photometric observables for those theoretical models GDMS Physical source of information

34. Modelling high-order g-mode pulsators Nice 27/05/2008 Future prospects Test these methods with different γ Doradus stars a) With more than 3 frequencies b) Belonging a cluster c) Include most evolved tools with rotation and develop the rest.

35. Modelling high-order g-mode pulsators Nice 27/05/2008 Future prospects Extent to other g-mode pulsators as SPB, some SdB, etc. Through a statistical extension of the asymptotic expression

36. Modelling high-order g-mode pulsators Nice 27/05/2008 Future prospects Fully radiative star Convective core- radiative envelope Convective core- radiative envelope – convective envelope

37. Modelling high-order g-mode pulsators Nice 27/05/2008 Future prospects A is obtained by fitting this expression with the numerical spectrum of the differential equations for different stars

38. Modelling high-order g-mode pulsators Nice 27/05/2008 THANK YOU MERCI GRACIAS OBRIGADO DANKE GRAZIE DEKUJI DZIĘKUJĘ

39. Modelling high-order g-mode pulsators Nice 27/05/2008 The star HD12901 Name[Fe/H]M/M  T eff L/L  Log gXcXc Ageρ/ρρ/ρ L A1A1 -0.41.23.830.524.280.5019909.192 A2A2 -0.41.33.850.724.170.4021006.102 A3A3 -0.41.43.840.904.020.2620903.472 B 1,C 1 -0.61.23.830.674.120.2731205.361,2 B 2,C 2 -0.61.33.830.843.980.1727203.201,2 B 3,C 3 -0.61.43.830.983.880.1022902.201,2

40. Modelling high-order g-mode pulsators Nice 27/05/2008 White and/or multi-colour photometric Observations Frequencies and/or amplitude ratios & Phase differences Equilibrium models (evolution code) Adiabatic and/or non-adiabatic computations Mode identification Mixing length (  Improving the fit Stellar parameters  Scuti  Doradus  Cephei SPB Convection Chemical Composition (Z) Atmosphere models - Limb darkening Hydrodynamic Overshooting,... Photometry

41. Modelling high-order g-mode pulsators Nice 27/05/2008 Brief introduction What is the astroseismology? Is to infer properties of the stellar interiors by observing, identifying and fitting the proper modes some stars pulse with the equilibrium and pulsating stellar models One of the main problems is the modal identification, that is, to label each observed mode with its frequency and the numbers (n,l,m)