CONSTRAINING MIXING PROCESSES IN 16CYGA USING KEPLER DATA AND SEISMIC INVERSION TECHNIQUES. Gaël Buldgen Pr. Marc-Antoine Dupret Dr. Daniel R.

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1 CONSTRAINING MIXING PROCESSES IN 16CYGA USING KEPLER DATA AND SEISMIC INVERSION TECHNIQUES Gaël Buldgen Pr. Marc-Antoine Dupret Dr. Daniel R. Reese University of Liège June 215

2 GENERAL STRUCTURE OF THE PRESENTATION 1 State of the art; 2 Forward modelling of 16CygA (Seismic, spectro, interfero); 3 Inversions to further constrain 16CygA? (Mass and age); 4 Conclusions and perspectives.

3 THE 16CYG BINARY SYSTEM (A & B (+C+Bb) - 16CYGA Frequency ν (µhz) Kepler s best in class! Solar-like binary system l = Modes l = 1 Modes l = 2 Modes l = 3 Modes Frequency modulo (µhz) 16CygA properties < ν > (µhz) T eff (K) 583 ± 5 Y f (dex).24 ±.1 Fe H (dex).96 ±.26 log g (dex) 4.33 ±.7 R (R ) 1.22 ±.2 Extensively studied: Metcalfe et al. 212, Ramirez et al. 29, Verma et al. 214, Tucci-Maia et al. 214, White et al. 213, Davies et al. 215,...

4 POSITION OF THE PROBLEM Chemical composition problem: Metcalfe et al. 212 (AMP): Y =.25 ±.1 (Y f.2); Verma et al. 214 (Glitches): Y f =.24 ±.1 Y We consider: Y f [.23,.25] (Verma et al. 214) ( ) Z X [.29,.235] f (AGSS9 with Ramirez et al. 29) Verma et al. 214, ApJ, 79, 138.

5 MODELLING STRATEGY Five-step process 1 Compute reference models (Levenberg-Marquardt algorithm); 2 Carry out inversions of acoustic radius and mean density; 3 Improve the models - compute new reference models; 4 Carry out inversions for core conditions; 5 Build models fitting this additional constraint. A few comments... Local minimization algorithm; Dependency on solar mixture (here AGSS9) for Z X ; Dependency of mass and age on the physical ingredients of the models. Local behaviour assessed by starting from various initial conditions...

6 MODELLING RESULTS - FITTING PROCESS 12 Small Separation δνn,l (µhz) δν Diff,2 δν Nodiff 4,2 δν,2 Obs δν Diff 1,3 Observation 2 δν Nodiff No diffusion 1,3 δν Diffusion 1,3 Obs Observed Frequency ν obs (µhz) Free parameters M, age, α MLT, X, Z. Diffusion treatment (Thoul et al. 1994) Constraints < ν >, δν ( ) n,l, T eff, Y f, Z X + check the values of R, log g and L after the fit. f.

7 MODELLING RESULTS - DIFFERENCES WITH PREVIOUS STUDIES Age (Gy) Y=.24, Z/X= Y=.25, Z/X=.222 Y=.24, Z/X= No diffusion Slow diffusion Full treatment of diffusion Mass (M ) Impact of mixing + chemical composition! Results: M between.97 and 1.7 M ; Age between 6.8 and 8.3 Gy; α MLT around (solar). Origin of the difference with Metcalfe et al. 212? Y f Metcalfe Us et al. 212 M (M ) Age (Gy) Impact of Y f on mass and age!

8 (Reese et al. 212) (Buldgen et al. 215) SEISMIC INVERSIONS - A BRIEF INTRODUCTION In helioseismology = Localized function (Gaussian) to obtain structural profiles Starting point: integral relations Structure - Frequency relations (Gough & Thompson 1991) Sola Method Fit of a target using linear combinations of kernels In asteroseismology = Related to corrections of an integrated quantity (Pijpers & Thompson1994)

9 INVERSION RESULTS - ACOUSTIC RADIUS AND MEAN DENSITY Reference Values Inverted results Inversion Inversion for the acoustic radius, τ and the mean density ρ Good kernel fit; Small Dispersion of the results; Unable to reduce the dispersion of mass and age. But: Can be used as supplementary constraints! Result: Improved reference models by also fitting τ and ρ.

10 INVERSION TECHNIQUE - CORE CONDITIONS INDICATOR ) 2 Weighted ( du dx Goal: probing the core by probing the u = P ρ Diffusion from Thoul et al. (1994) No diffusion X C =.32 X C =.38 X C = Position x=r/r Improving models Improving fundamental parameters! T µ gradient. Definition: t u = ( ) R 2 f (r) du dr dr Very sensitive to changes in core conditions. See Buldgen et al. (submitted).

11 INVERSION RESULTS - CORE CONDITIONS INDICATOR The sensitivity of the indicator allows us to constrain chemical composition and diffusion! (Z/X) f,a [ ] (Ramirez et al. 29) Y f,a [.23.25] (Verma et al. 214) Indicator tu (g 2 /cm 6 ) Inversion results Reference values Yf Mean density ρ (g/cm ) (Z/X) f

12 INVERSION RESULTS - CORE CONDITIONS INDICATOR Age (Gy) How does it constrain mass and age? Initial Models Subbox Models M (M ) Age (Gy) Y (dex).3.31 Z (dex) L (L ) R (R ) Mass (M ) Solar values: Y =.273, Z =.142 From 5% to 2% in mass and 8% to 3% in age! (Also 3% to 1% in radius, between 1.19 and 1.2 R ).

13 COMMENTS AND PERSPECTIVES In conclusion: Strong constraints on chemical mixing and composition; Reduction of mass and age dispersion crucial for PLATO; Importance of Y constraints and incompatibility with GN93; Consistent independent modelling of 16CygB. But let us not be mistaken: Age is model-dependent (3% Internal error!); We need additional indicators (Convection, Opacity,...). Philosophy: Inversions are a tool using seismic information that will, through synergies with stellar modellers, help us build more physically accurate descriptions of stellar structure.

14 Thank you for your attention!

15 APPENDICES KAvg,tu KCross,tu Position r/r Position r/r

16 APPENDICES With Y f =.24, (Z/X) f =.24 M =.96M Age = 7.23Gy Depending on the assumed chemical composition, always less massive than 16CygA. t u serves as a consistency check but no gain in accuracy. tu (g 2 /cm 6 ) Reference models Inverted Values ρ (g/cm 3 )

17 GN93 MIXTURE ( ) If one considers GN93, we obtain Z X simply around different Z/X values. f [.287,.316], the box is slightly higher masses (1.3M ), slightly higher radii; slightly lower ages (around 6.8Gy); Using t u : The models reach values of t u = 3.1g 2 /cm 6 if one considers the lowest metallicity with the higher helium content and diffusion.

18 APPENDICES 5 KAvg,τ KCross,τ Position r/r KAvg, ρ Position r/r KCross, ρ Position r/r Position r/r

19 APPENDICES Tρ Tt Position r/r T ρ = 4πx 2 ρ T τ = 1 c ρ = R 4πr2 ρdr ( ν) 2 5 τ = R dr ( ν) 1 t = R 1 dc r dr T t = 1 d c x dx dr νδν ν Ttu Tτ Position r/r 2 T tu = f(x) ( ) dũ 2 dx 1.5 t u = R f(r)( du 2dr dr) c Position r/r Position r/r

20 APPENDICES 7.5 x x 1 3 tu (g 2 ) t (s 1 ) Age (Gyr) x Age (Gyr) x 1 9