A method for modelling high-order, g-mode pulsators: The case of γ Doradus stars.

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

2. 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. Brief introduction C C Radiative rb rt Smeyers & Moya, 2007 Tassoul, 1980 • No Rotation • No magnetic field • Adiabatic approximation

4. The problem of mode identification 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 Ylm(θ,φ) Observed frequency (n,ℓ,m) ¿(n,ℓ,m)?

5. 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. The problem of mode identification Possible tool: Asymptotic equidistance in period This give information about ℓ and the Brunt-Väisälä integral

7. The problem of mode identification 9 Aurigae HD12901

8. Frequency Ratio Method (FRM) Moya et al., 2005, A&A 432, 189 • 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.

9. FRM Observations: Physical parameters ≥ 3 frequencies Frequency ratio method Small set of possible theoretical models describing this star Several sets of (n1,n2,n3,ℓ,Iobs) (ν1,ν2,ν3)

10. The star HD12901

11. The star HD12901 ±0.005 ±0.005 ±0.005 β1,2=0.871 β2,3=0.639 β1,3=0.556

12. The star HD12901

15. The star HD12901

16. The star HD12901

17. The star HD12901

18. FRM with rotation Suárez et al., 2005, A&A, 443, 271 Two main conclusions: The FRM still works for m=0 modes There are not possible confusion between modes with different m

19. Multicolor photometry Non-adiabatic computations Influence of the local effective temperature variation Surface distortion Equilibrium atmosphere models (Kurucz 1993) Influence of the local effective gravity variation

20. Multicolor photometry As a result of the numerical computations we can obtain And the grow rate Where

21. Multicolor photometry Current most evolved tool: Time dependent convection

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

23. GDMS (9 Aurigae) =0.966 ±0.010 =0.447 ±0.010 =0.431 ±0.010

24. GDMS (9 Aurigae) And lower Iobs

25. GDMS (9 Aurigae) Model fulfilling FRM constraints

26. GDMS (9 Aurigae) Multicolor analysis with TDC (Dupret et al. and Grigahcene et al.) for the model coming from FRM Different αMLT and atmospheric models Strömgren filters ℓ=2

27. GDMS (9 Aurigae) 1.6 αMLT 2.0 1.4 1.8 Stability analysis with TDC for different αMLT αMLT=1.6

28. GDMS (9 Aurigae) Physical parameters Theoretical parameters Modal identification

29. Rotational coupling δmλ(coup)= β·δmλ(1)+(1-β) δmλ(2)

30. Rotational coupling

31. Rotational coupling

32. Rotational coupling How to obtain information in this case

33. GDMS 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 + Physical source of information

34. 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. Future prospects Extent to other g-mode pulsators as SPB, some SdB, etc. Through a statistical extension of the asymptotic expression

36. Future prospects Fully radiative star Convective core- radiative envelope Convective core- radiative envelope –convective envelope

37. Future prospects A is obtained by fitting this expression with the numerical spectrum of the differential equations for different stars

38. THANK YOU MERCI GRACIAS OBRIGADO DANKE GRAZIE DEKUJI DZIĘKUJĘ

39. The star HD12901

40. Photometry d Scuti g Doradus Mode identification White and/or multi-colour photometric Observations Equilibrium models (evolution code) Stellar parameters Mixing length ( a ) Convection Overshooting Frequencies and/or amplitude ratios & Phase differences Hydrodynamic Adiabatic and/or non-adiabatic computations Atmosphere models - Limb darkening b Cephei Chemical Composition (Z) , ... SPB Improving the fit

41. 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)