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
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.
THE 16CYG BINARY SYSTEM (A & B (+C+Bb) - 16CYGA Frequency ν (µhz) Kepler s best in class! Solar-like binary system. 3 28 26 24 22 2 18 16 14 l = Modes l = 1 Modes l = 2 Modes l = 3 Modes 2 4 6 8 1 Frequency modulo 13.75 (µhz) 16CygA properties < ν > (µhz) 13.78 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,...
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.28.3. 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.
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...
MODELLING RESULTS - FITTING PROCESS 12 Small Separation δνn,l (µhz) 1 8 6 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 15 2 25 3 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.
MODELLING RESULTS - DIFFERENCES WITH PREVIOUS STUDIES Age (Gy) Y=.24, Z/X=.222 8.2 Y=.25, Z/X=.222 Y=.24, Z/X=.29 8 7.8 7.6 7.4 7.2 7 6.8 6.6 No diffusion Slow diffusion Full treatment of diffusion.98 1 1.2 1.4 1.6 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 1.6 1.7 (solar). Origin of the difference with Metcalfe et al. 212? Y f Metcalfe Us et al. 212 M (M ) 1.11 1.9 Age (Gy) 6.9 7.1 Impact of Y f on mass and age!
(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)
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.
INVERSION TECHNIQUE - CORE CONDITIONS INDICATOR ) 2 Weighted ( du dx Goal: probing the core by probing the u = P ρ 3.5 3 2.5 2 1.5 1.5 Diffusion from Thoul et al. (1994) No diffusion X C =.32 X C =.38 X C =.41.5.1.2.3.4.5 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).
INVERSION RESULTS - CORE CONDITIONS INDICATOR The sensitivity of the indicator allows us to constrain chemical composition and diffusion! 4.4 4.2.25 (Z/X) f,a [.29.235] (Ramirez et al. 29) Y f,a [.23.25] (Verma et al. 214) Indicator tu (g 2 /cm 6 ) 4 3.8 3.6 3.4 3.2 3 Inversion results Reference values Yf.245.24.235 2.8.23.81.82.83 Mean density ρ (g/cm 3.21.215.22.225.23.235 ) (Z/X) f
INVERSION RESULTS - CORE CONDITIONS INDICATOR Age (Gy) How does it constrain mass and age? 8.5 8 7.5 Initial Models Subbox Models M (M ).96 1. Age (Gy) 7. 7.4 Y (dex).3.31 Z (dex).194.199 L (L ) 1.49 1.56 R (R ) 1.19 1.2 7.96.98 1 1.2 1.4 1.6 1.8 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 ).
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.
Thank you for your attention!
APPENDICES 1 1.5 1.5 5 KAvg,tu KCross,tu.5 1 1.5 2 2.5 5.2.4.6.8 1 Position r/r 3.2.4.6.8 1 Position r/r
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 ) 4 3.5 3 2.5 Reference models Inverted Values 2 1 1.2 1.4 1.6 1.8 ρ (g/cm 3 )
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.
APPENDICES 5 KAvg,τ KCross,τ 1 5.2.4.6 Position r/r.8 1 1 KAvg, ρ 5 5 1.2.4.6.8 1 Position r/r KCross, ρ 2 4 2.2.4.6.8 1 Position r/r.2.4.6.8 1 Position r/r
APPENDICES Tρ Tt 3.5 3 2.5 2 1.5 1.5.2.4.6.8 1 Position r/r 4 3 2 1 1 6 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 4 3 2 1.2.4.6.8 1 Position r/r 2 T tu = f(x) ( ) dũ 2 dx 1.5 t u = R f(r)( du 2dr dr) 1.5 1 c 2.2.4.6.8 1 Position r/r.5.2.4.6.8 1 Position r/r
APPENDICES 7.5 x 165 1 x 1 3 tu (g 2 ) 7 6.5 6 5.5 t (s 1 ) 1.5 2 2.5 5 1 2 3 4 5 6 Age (Gyr) x 1 9 3 1 2 3 4 5 6 Age (Gyr) x 1 9