WhoSGlAd : A precise characterisation of the Kepler Legacy sample

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WhoSGlAd : A precise characterisation of

the Kepler Legacy sample

Martin Farnir Université de Liège Prof. Marc-Antoine Dupret

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Introduction

• Aims:

→ Constrain solar-like models taking advantage of

Kepler data precision:

→ Ex: Helium - mass degeneracy, extra mixing

• Outline:

→ Solar-like spectrum and glitches

→ Method

→ Results: Kepler Legacy Sample, 16 Cyg A

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Introduction Solar-like spectrum

Solar-like spectrum and Acoustic glitches

Solar-like oscillations spectra exhibit:

¬

regular pattern,smooth

oscillation,glitch, caused

by a sharp variation (Γ1, c), provide localised info:

→ Surface helium content, Ys

→ Nature/amount of convective extra mixing

→ Glitches can help lift model

degeneracies 0.4 0.6 0.8 ν/∆ν modulo 1 1500 2000 2500 ν (µ Hz) νo,s νo 1500 2000 2500 ν (µHz) −2 −1 0 1 δν (µ Hz) δνofit δνowith σ τHe AHe

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Solar-like spectrum and Acoustic glitches

Solar-like oscillations spectra exhibit:

¬

regular pattern,smooth

oscillation,glitch, caused

by a sharp variation (Γ1, c), provide localised info:

→ Surface helium content, Ys

→ Nature/amount of convective extra mixing

→ Glitches can help lift model

degeneracies 0.4 0.6 0.8 ν/∆ν modulo 1 1500 2000 2500 ν (µ Hz) νo,s νo,s+ δνo νo 1500 2000 2500 ν (µHz) −2 −1 0 1 δν (µ Hz) δνofit δνowith σ τHe AHe

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Why improve methods?

Several glitches analysis, for solar-like, have been realised :

Basu et al. 2004,Verma et al. 2014,Monteiro et al. 2014,... However,

• Separatetreatment of glitch and smooth components,

• Use ofcorrelatedindicators,

• Seismic and non-seismic constraints not combined in

a statistically relevant way.

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WhoSGlAd

• Whole Spectrum and Glitches Adjustment

(Farnir et al. 2019)

→ Coherentadjustment ofboth smoothandglitches

component of the oscillation spectrum

→ Propercovariancesretrieved

⇒ Precise seismic measurements_{⇒ better constraints on} stellar modelling

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WhoSGlAd Principle

Principle

Represent νn,l∼(n + l)∆l+p2,l(n)+δνHe+δνCZas: 2nd_{order polynomial} 13 15 17 19 21 23 1500 2000 2500 ν (µ H z) 13 15 17 19 21 23 n −2 0 2 4 6 δν (µ H z) (n + l)∆l p2,l(n) + oscillatory function 12.5 15.0 17.5 20.0 22.5 −0.5 0.0 0.5 1.0 δνH e (µ H z) 12.5 15.0 17.5 20.0 22.5 n + l/2 −1 0 1 δνC Z (µ H z) δνHe δνCZ

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WhoSGlAd Indicators

Indicators

Combineindependentcoefficients into indicators:

ˆ

r0l(∼Roxburgh & Vorontsov 2003) Mean distance

between 2 ridges → Info about:

• ˆr01: Composition

• rˆ02: Evolution σ 4 times smallerthan

usual indicators 0.4 0.6 0.8 ν/∆ modulo 1 1500 2000 2500 ν (µ Hz) νo ˆ r01 ˆ r02 ˆr03

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WhoSGlAd Indicators

ˆ

r01

- ∆01

diagram

Evolution on MS of models of given mass and composition:

0.2 0.4 0.6 0.8 1.0 ∆01(µHz) ×10−2 0.02 0.04 0.06 0.08 ˆr01 αov=0.005 αov=0.10 αov=0.15 αov=0.20 αov=0.25 αov=0.30

Credits:Farnir et al. 2019

αov = 0.00 αov = 0.10 αov = 0.15 αov = 0.20 αov = 0.25 αov = 0.30

Credits:Deheuvels et al. 2016

Relative slope differences: ∆0l= ∆∆0l − 1 →∆01: central extra mixing

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WhoSGlAd Indicators

Helium glitch amplitude

Models at fixed ∆: 0.16 0.18 0.20 0.22 0.24 Ysurf 10 20 30 40 AHe 1M 1.025M 1.052M 1.052MSurf. eff. σ 0.006 0.008 0.010 0.012 0.014 Zsurf 10 15 20 25 30 AHe 1M 1.025M 1.052M

Credits:Farnir et al. 2019

→ Very good indicator of Ys

→ ButYs− Zsdegeneracy (see alsoBasu et al. 2004)

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Results Kepler Legacy

WhoSGlAd and Kepler Legacy Sample

66 solar-like stars_{→ best quality data}

Credits:Silva Aguirre et al. 2016

Application: • Free parameters: → M , t, αov, (Z/X)0, Y0 • Constraints: → ∆, ˆr01, ˆr02, ∆01, AHe, [F e/H]

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Results Kepler Legacy

WhoSGlAd and Kepler Legacy Sample

• No αovand M correlation observed (to be confirmed) • Y0and (Z/X)0correlated ⇒ Galactic enrichment? Typical precision: • σ(M )_{∈ [0.02, 0.05]M} • σ(t)_{∈ [0.1, 0.5] Gyrs} • σ(Y )_{∈ [0.01, 0.05]} • σ(αov)∈ [0.01, 0.05]

Only one set of input physics tested

⇒ σ relative to the method

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Results 16 Cygni A

In depth modelling: 16 Cygni A

1.02 1.04 1.06 1.08 M (M) 6.50 6.75 7.00 7.25 Age (Gyr) 3.755 3.760 3.765 3.770 log(Teff) 0.14 0.16 0.18 0.20 0.22 log( L/L ) Obs AGSS09 GN93 OP LANL CEFF OPAL05 Dturb αMLT=1.7 0.030 0.035 0.040 0.68 0.70 0.72 X0 1.02 1.04 1.06 1.08 M (M) 6.50 6.75 7.00 7.25 Age (Gyr) 3.755 3.760 3.765 3.770 log(Teff) 0.14 0.16 0.18 0.20 0.22 log( L/L ) Obs AGSS09 GN93 OP LANL CEFF OPAL05 Dturb αMLT=1.7 0.030 0.035 0.040 (Z/X)0 0.68 0.70 0.72 X0 Physics tested: • Solar ref. • Opacity • EOS • αMLT • Diffusion

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Conclusion

• Method:

→ σ4 timeslower_{⇒ better models}

• 16 Cyg A: (Farnir et al. 2019b in prep.)

→ Possibility to discriminate choices of physics

• Kepler Legacy: (Farnir et al. 2019c in prep.)

→ Both [ Fe/H ] and AHenecessary

→ Correlation between Y0and (Z/X)0

⇒ Galactic enrichment?

→ No correlation between αov and M observed

• Future perspectives:

→ Adaptation to subgiants and mixed modes

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Appendices Principle

Principle

Observed spectrum νobs Independent coefficients νf =P j ajqj Projection over basis aj =hνobs|qji

• Gram-Schmidt_{→ discrete}orthonormalbasis functions

→ glitchcompletely independentof smooth part

• Combine coefficients aj → seismic indicators as

uncorrelatedas possible

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Appendices Gram-Schmidt

Gram-Schmidt

Construction of orthonormal basis elements

¬

Subtract from current element its projection on the

previous orthonormal elements,

Normalise it. uj0 = pj0 − j0−1 X j=1 p_j₀_|q_j q_j, (1) q_j₀ = uj0 kuj0k . (2)

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Appendices An Illustrative Example

An Illustrative Example : Smooth

At a given degree,

projection of the frequencies on the successive basis elements.

→ 0 order : mean value;

→ 1st order : straight line approximation;

→ 2nd order : parabola

approximation.

Follow the properorderingto

define seismic indicators

13 15 17 19 21 23 1500 2000 2500 ν (µ H z) 13 15 17 19 21 23 n −2 0 2 4 6 δν (µ H z)

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Appendices An Illustrative Example

An Illustrative Example : Glitch

Simultaneous projection of the frequencies for every spherical degree on the successive basis elements.

→ First for the helium;

→ Then for the convection

zone. 12.5 15.0 17.5 20.0 22.5 −0.5 0.0 0.5 1.0 δνH e (µ H z) 12.5 15.0 17.5 20.0 22.5 n + l/2 −1 0 1 δνC Z (µ H z)

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Appendices Formulation

Formulation

f (n, l) = Smooth z }| { 2 X k=0 ak,lnk + He Glitch z }| { 4 X k=5 sk,Hesin(4πTHeen) + ck,Hecos(4πTHeen) e n−k (3)

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Appendices Y-Z Degeneracy

Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 1.052M⊙ Y0= 0.24

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 1.052M⊙ Y0= 0.24 Y0= 0.25

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 1.052M⊙ Y0= 0.24 Y0= 0.25 Y0= 0.26

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 1.052M⊙ Y0= 0.24 Y0= 0.25 Y0= 0.26 Y0= 0.27

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 Y0= 0.24 1.052M⊙ Y0= 0.24 Y0= 0.25 Y0= 0.26 Y0= 0.27 Z0= 0.008

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 Y0= 0.24 1.052M⊙ Y0= 0.24 Y0= 0.25 Y0= 0.26 Y0= 0.27 Z0= 0.008 Z0= 0.011

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 Y0= 0.24 1.052M⊙ Y0= 0.24 Y0= 0.25 Y0= 0.26 Y0= 0.27 Z0= 0.008 Z0= 0.011 Z0= 0.014

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Degeneracy

• Correlated with Ysurf; • Anti-correlated with Zsurf; → Γ1 toy model provides an explanation. 0.95 0.96 0.97 0.98 0.99 r/R_∗ 1.4 1.5 1.6 1.7 Γ1 (Z/X)0= 0.022 Y0= 0.24 1.052M⊙ Y0= 0.24 Y0= 0.25 Y0= 0.26 Y0= 0.27 Z0= 0.008 Z0= 0.011 Z0= 0.014 Z0= 0.017

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Appendices Γ1Toy Model

Γ1

Toy Model

4.8 4.9 5.0 5.1 5.2 5.3 log(T ) 1.58 1.60 1.62 1.64 1.66 Γ1 Y0 Y > Y0 Y < Y0 Y > Y0, ref. T ,ρ profiles Y < Y0, ref. T ,ρ profiles 4.95 5.00 5.05 5.10 log(T ) 1.59 1.60 1.61 Γ1 Z0 Z > Z0 Z < Z0 Z > Z0, ref. T ,ρ profiles Z < Z0, ref. T ,ρ profiles

WhoSGlAd : A precise characterisation of the Kepler Legacy sample