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 2015
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);
THE 16CYG BINARY SYSTEM (A & B (+C+Bb) - 16CYGA
Kepler’s best in class! Solar-like binary system. 20 40 60 80 100 1400 1600 1800 2000 2200 2400 2600 2800 3000 F re q u en cy ν (µ H z) Frequency modulo 103.75 (µH z) ℓ= 0 Modes ℓ= 1 Modes ℓ= 2 Modes ℓ= 3 Modes 16CygA properties < ∆ν > (µHz) 103.78 Teff (K ) 5830 ± 50 Yf (dex) 0.24 ± 0.01 Fe H (dex) 0.096 ± 0.026 log g (dex) 4.33 ± 0.07 R (R ) 1.22 ± 0.02
Extensively studied: Metcalfe et al. 2012, Ramirez et al. 2009, Verma et al. 2014, Tucci-Maia et al. 2014, White et al. 2013, Davies et al. 2015, ...
POSITION OF THE PROBLEM
Chemical composition problem:
Metcalfe et al. 2012(AMP):Y0 = 0.25 ± 0.01 (Yf ≈ 0.20); Verma et al. 2014 (Glitches): Yf = 0.24 ± 0.01
⇒Y0≈ 0.28 − 0.30.
Verma et al. 2014, ApJ, 790, 138.
We consider: Yf ∈ [0.23, 0.25](Verma et al. 2014) Z X f ∈ [0.0209, 0.0235] (AGSS09 with Ramirez et al. 2009)
MODELLING STRATEGY
Five-step process
1 Compute reference models (Levenberg-Marquardt algorithm); 2 Carry outinversionsof acoustic radiusand mean density; 3 Improve the models - computenew reference models; 4 Carry outinversionsforcore conditions;
5 Buildmodels fitting this additional constraint.
A few comments...
Localminimization algorithm;
Dependency on solar mixture(here AGSS09) for XZ;
Dependencyof mass and age on thephysical ingredients of the models. Local behaviour assessed by starting from various initial conditions...
MODELLING RESULTS - FITTING PROCESS 1500 2000 2500 3000 0 2 4 6 8 10 12 S m a ll S ep a ra ti o n ˜ δν n ,l (µ H z )
Observed Frequency νobs(µHz) No diffusion Diffusion Observation ˜ δν0,2Dif f ˜ δν0,2N odif f ˜ δνObs 0,2 ˜ δν1,3Dif f ˜ δν1,3N odif f ˜ δνObs 1,3 Free parameters M , age, αMLT, X0, Z0. Diffusion treatment (Thoul et al. 1994) Constraints < ∆ν >, ˜δνn,l, Teff, Yf, Z X f. + check the values of R, log g and L after the fit.
MODELLING RESULTS - DIFFERENCES WITH PREVIOUS STUDIES 0.98 1 1.02 1.04 1.06 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2 Mass (M⊙) A ge (G y ) Y=0.25, Z/X=0.0222 Y=0.24, Z/X=0.0209 Y=0.24, Z/X=0.0222 No diffusion Slow diffusion
Full treatment of diffusion
Impact of mixing + chemical composition!
Results:
M between0.97 and 1.07 M ;
Age between6.8 and 8.3 Gy; αMLT around 1.6 ≈ 1.7 (solar). Origin of the difference with
Metcalfe et al. 2012? ⇒ Yf Metcalfe Us et al. 2012 M (M ) 1.11 1.09 Age (Gy) 6.9 7.1
SEISMIC INVERSIONS - A BRIEF INTRODUCTION
In helioseismology
In asteroseismology
Sola Method Starting point: integral relations
Structure - Frequency relations (Gough & Thompson 1991)
Fit of a target using linear combinations of kernels Localized function (Gaussian) to obtain structural profiles
=
=
Related to corrections of an integrated quantity (Pijpers & Thompson1994) (Reese et al. 2012) (Buldgen et al. 2015)INVERSION RESULTS - ACOUSTIC RADIUS AND MEAN DENSITY
Inversion
Reference Values
Inverted results
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 Goal: probing the core by probing the u0 = Pρ00 ∝ Tµ gradient.
0 0.1 0.2 0.3 0.4 0.5 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 Position x=r/R W ei g h te d ! d u d x " 2
Diffusion from Thoul et al. (1994) No diffusion
XC= 0.32
XC= 0.38
XC= 0.41
Improving models ⇒ Improving fundamental parameters! Definition: tu =R0Rf (r ) du 0 dr 2 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!
0.81 0.82 0.83 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 Mean density ¯ρ(g/cm3) In d ic at or tu (g 2/c m 6) Inversion results Reference values 0.021 0.0215 0.022 0.0225 0.023 0.0235 0.23 0.235 0.24 0.245 0.25 Yf (Z/X)f
(Z/X)f,A∈[0.0209 0.0235] (Ramirez et al. 2009)
INVERSION RESULTS - CORE CONDITIONS INDICATOR
How does it constrain mass and age?
0.967 0.98 1 1.02 1.04 1.06 1.08 7.5 8 8.5 Mass (M⊙) A ge (G y ) Initial Models Subbox Models M (M ) 0.96 − 1.0 Age (Gy) 7.0 − 7.4 Y0 (dex) 0.30 − 0.31 Z0 (dex) 0.0194 − 0.0199 L (L ) 1.49 − 1.56 R (R ) 1.19 − 1.20 Solar values: Y0= 0.2703, Z0= 0.0142
From 5% to 2% in mass and 8% to 3% in age! (Also 3% to 1% in radius, between 1.19 and 1.20 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.
APPENDICES 0 0.2 0.4 0.6 0.8 1 −50 0 50 100 Position r/R KA v g ,tu 0 0.2 0.4 0.6 0.8 1 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 Position r/R KC r o s s ,tu
APPENDICES
With Yf = 0.24, (Z /X )f = 0.0204
M = 0.96M Age = 7.23Gy
Depending on the assumed chemical composition, always less massive than 16CygA. tu serves as a consistency check but no gain in accuracy. 1 1.02 1.04 1.06 1.08 2 2.5 3 3.5 4 ¯ ρ(g/cm3) tu (g 2/c m 6) Reference models Inverted Values
GN93 MIXTURE
If one considers GN93, we obtainXZ
f ∈ [0.0287, 0.0316], the box is simply around different Z /X values.
slightly higher masses (1.03M ), slightly higher radii; slightly lower ages (around 6.8Gy);
Using tu :
The models reach values of tu = 3.01g2/cm6 if one considers the lowest metallicity with the higher helium content and diffusion.
APPENDICES 0 0.2 0.4 0.6 0.8 1 −10 −5 0 5 10 Position r/R KA v g ,¯ρ 0 0.2 0.4 0.6 0.8 1 0 20 40 Position r/R KC r o s s ,¯ρ 0 0.2 0.4 0.6 0.8 1 −5 0 5 Position r/R KA v g ,τ 0 0.2 0.4 0.6 0.8 1 −20 −10 0 Position r/R KC r o s s ,τ
APPENDICES 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 Position r/R Tρ Tρ= 4πx2ρ˜ 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 Position r/R Tτ Tτ=1 ˜ c 0 0.2 0.4 0.6 0.8 1 −20 −10 0 10 20 30 40 Position r/R Tt Tt=1 xd˜dxc 0 0.2 0.4 0.6 0.8 1 −0.5 0 0.5 1 1.5 2 Position r/R Ttu Ttu= f (x)!d˜u dx "2 ¯ ρ=R0R4πr2ρdr ∝ (∆ν)2 τ=RR 0 1cdr ∝ (∆ν)−1 tu=R0Rf (r) !du dr "2 dr t =R0R1 rdrdcdr ∝νδν∆ν
APPENDICES 0 1 2 3 4 5 6 x 109 5 5.5 6 6.5 7 7.5x 10 65 Age (Gyr) tu (g 2) 0 1 2 3 4 5 6 x 109 −3 −2.5 −2 −1.5 −1x 10 −3 Age (Gyr) t (s − 1)
