What is the metallicity of our reference star, the Sun?

What is the metallicity of our reference star, theSun?

Gaël Buldgen

University of Geneva

September 2019

1

Introduction

The Sun as a benchmark star

The role of the Sun:

Well-studied, helioseismic constraints, neutrino �uxes, testbed forphysical ingredients. The Sun is used as a reference:

Metallicity scale,

Enrichment laws,

SSM framework,

Paved the way for asteroseismology using solar-like oscillations.

Most of our models will include some ingredients that have beencalibrated on the Sun. Thus, if you change the way you modelthe Sun, you impact stellar physics as a whole.

But how well do we know the Sun?

2

Solar abundances

1D Models of the 20th century

1D solar atmosphere models

Theoretical models: MARCS,Kurucz, ...

1 Hydrostatic,2 MLT type convection,3 LTE.

Usually, semi-empirical modelswere used e.g. Holweger-Müllermodel (1974).Led to high abundances of C,Nand O (AG89, GN93, GS98).

Pereira et al. (2009)3

Solar abundances

Advent of 3D Models and abundance revisions

Asplund et al. (2009)

Revision of theabundances:Hydrodynamicalmodel,

Non-LTE corrections,

improved atomicdata,

Careful selection oflines,

Use of all indicators.

⇒ 30% reduction ofZ�!

4

Solar abundances

The solar modelling problem

A brief history of Standard Solar Models

Before 2004, high metallicity solar models (Z = 0.0182):1 Correct position of the BCZ,2 Correct Helium abundance in the CZ,3 Sound Speed pro�le relative di�erences of up to 0.006.

(From Kosovichev & Fedorova 1991, 1993, Vorontsov et al. 1991)But: slow degradatation as physical ingredients were updated.

From 2004, downward revision of the solar Z:

1 Wrong position of the BCZ,

2 Wrong Helium abundance in the CZ,

3 Sound Speed pro�le relative di�erences of up to 0.02.

5

Solar abundances

Discussions of the revised abundances

Study by Ca�au et al. 2011: Higher C,N,O abundances, closer to the “oldvalues”.Subsequent analyses by Scott et al. 2015a, Scott et al. 2015b, Grevesse et al.2015, Lind et al. 2017, Bergemann et al. 2017, Amarsi and Asplund 2017,Nordlander and Lind 2017, Amarsi et al. 2018, Amarsi et al. 2019: con�rmlow C,N,O abundances.

What causes the discrepancies?

3D Models? No! Stagger and Co5bold agree (Beeck et al. 2012).

Selection of lines, blends, molecular lines.

If the same inputs are used, the same results are obtained.

What about meteorites? Di�erentiation, they are not substitutes tophotospheric abundances! (N.Grevesse, private communication)

6

Solar abundances

Neon revision and latest changes

The problem of Neon: No photospheric lines.⇒ Inferences from coronal lines, solar wind, ... Variations with activity!

Landi & Testa (2015)

Di�cultmeasurements,Ne/H unacessible,Ne/O measured,

Antia & Basu(2004): increase of400% to solve the“solar problem”.

Landi & Testa2015 + Young2018: increase of40% of Ne/O. 7

Helioseismology

The solar modelling problem as seen in seismology:

Current state of the issue, for various abundance and opacity tables...

8

Helioseismology

Inferring Z from helioseismic data I

Constraints from seismic inversions:

Inversions can only constrain variables from the acoustic structure :

ρ , c2 or Γ1 =(

∂ lnP∂ lnρ

)Sfor example.

However, assuming an E.O.S, one has:

δΓ1

Γ1=

(∂ lnΓ1

∂ lnP

)ρ,Y,Z

δPP

+

(∂ lnΓ1

∂ lnρ

)P,Y,Z

δρ

ρ+

(∂ lnΓ1

∂Y

)P,ρ,Z

δY

+

(∂ lnΓ1

∂Z

)P,ρ,Y

δZ,

thus allowing for inversions of Y , the helium abundance, or Z, themetallicity.

Previous studies by Takata & Shibahashi (2001), Antia & Basu (2006) and Vorontsov etal. (2013). 9

Helioseismology

Inferring Z from helioseismic data II

Initial attempts in Takata and Shibahashi (2001) using density and Γ1 kernels.

Impossibility to conclude because of the errors bars.However, the conclusion mentions that the three last point are consistentwith a 30% reduction of the solar metallicity.

10

Helioseismology

Inferring Z from helioseismic data III

This inversion (Buldgen et al. 2017c) favours a low metallicity (as inVorontsov et al. 2013).

0 1 2 3 4 5 60.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Z

Reference Models

Suboptimal parameters set

Optimal parameters set

GN93

AGSS09

Outliers

GN93

FreeEOSOPLIB x1.05

.

GN93GN93OPLIB

FreeEOS FreeEOS

GN93 GN93OPALOPAL

Diff x0.75

OPLIBCEFF FreeEOS

11

Helioseismology

Potential solutions to the solar modelling problem I (Buldgen et al. 2019, in prep.)

Combination of: Neon increase from Landi & Testa (2015) and Young et al.(2018), extra-mixing and opacity modi�cation (from A. Pradhan)

12

Helioseismology

Impact on stellar physics

A few illustration of the potential impact of the solar problem1 Solar reference for the chemical abundances,2 Revision of key ingredients: opacity, EOS, screening factor

(Mussack & Däppen 2011, Bailey et al. 2015),3 Transport of chemicals (see talk by R. Hirschi),4 Angular momentum transport processes (see talk by P.

Eggenberger),5 Impact on asteroseismic modelling and characterization of stellar

populations in the Galaxy (see talk by C. Chiappini).

The role of calibrator of the Sun implies that changing its ingredientsimpacts a wide range of stellar models.

13

Conclusions and prospects

Conclusion and perspectives

In conclusion

Still a problem: Will new opacity computations do it? Maybe.(Pradhan 2017, Zhao 2017, Pain 2019).What about the BCZ: Extensively studied (see e.g. Hughes 2007 andreferences therein)Is that it? No: Microscopic di�usion, EOS improvements, convection,instabilities, early history (see also Zhang et al. 2019)...

What is clear? Stop using GN93 and GS98. (listen to NicolasGrevesse)

The solar problem is not purely an issue of abundances, ratheran issue of other modelling ingredients. No signi�cant variationsfound in 2015 by AGSS. Its impact reaches beyond the range ofsolar models.

14


Thank you for your attention!

15


Potential solutions to the solar modelling problem II

Other approach: build a seismic model and try to see what itsproperties may be (Buldgen et al. In prep).

Help li� some degeneracies and drive revisions of physical ingredients. 16


Opacity kernels

Vinyoles et al. (2017)Allow for a static analysis of the required changes inopacity to match helioseismic constraints.

Based onTripathy &Christensen-Dalsgaard(1998).

Assumes linearbehaviour withrespect to smallκ perturbation.

17


The current state of the issue

18



19



20


Combining seismic information I

Combining: A, S5/3, c2, Y , position of BCZ, mCZ ... (Buldgen et al. submitted to A&A)

Similar to Christensen-Dalsgaard & Houdek (2010), Ayukov et al. (2011),Christensen-Dalsgaard et al. (2018). 21


Combining seismic information II

Combination of: Neon increase from Landi & Testa (2015) and Young et al.(2018), extra-mixing and opacity modi�cation (from A. Pradhan)

22


Combining seismic information III

It seems: Opacity increase too high and perhaps too steep + wrong ∇Ttransition in overshooting region (improve on Christensen-Dalsgaard 2011)(Work by Rempel et al. 2004, Zhang et al. 2012) 23


Inferring Z from helioseismic data - Tests

Tests on arti�cial data (same ν , same σν ) to ensure accuracy.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.013

0.014

0.015

0.016

0.017

0.018

0.019

0.02

0.021

0.022

Model Number

Z

Reference modelsInverted resultsTarget value

24


Extended solar calibration

Add additional free parameters and constraints to the solar models to expandthe calibration procedure. (Ayukov & Baturin 2013, 2017)

25


Considered opacity modi�cation

6.2 6.4 6.6 6.8 7 7.2

0

0.05

0.1

0.15

26


Other classical diagnostics

rConv/R� YConv

Helioseismic measurements 0.713±0.001 0.2485±0.0035SSM (AGSS09, Free, OPAL) 0.720 0.236SSM (AGSS09, Free, OPLIB) 0.718 0.230SSM (AGSS09, Free, OPAS) 0.717 0.232SSM (GN93, Free, OPAL) 0.711 0.245SSM (GN93, Free, OPLIB) 0.708 0.240

27


Standard Models with new opacities - Frequency ratios

1500 2000 2500 3000 35000.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

ν (µHz)

r02

ObsGN93−OPAL

AGSS09−OPAL

GN93−OPLIB

AGSS09−OPLIB

1500 2000 2500 3000 35000.1

0.11

0.12

0.13

0.14

0.15

0.16

ν (µHz)

r13

ObsGN93−OPAL

AGSS09−OPAL

GN93−OPLIB

AGSS09−OPLIB r02, r13 ⇒ AGSS09favoured!

c2 inversions stillfavour GN93.

BCZ wrong for bothAGSS09 and GN93.

YS very low forAGSS09.

⇒ Need new diagnostics.

28


Inversions of the convective parameter for Standard Solar Models

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1

Position r/R

ASun−A

Model

Base of the solarconvective zone

AGSS09−OPLIB − ZXGNGN93−OPLIB

The compensation is related to the heavy-element mixture. 29



0.5 0.55 0.6 0.65 0.7

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Position r/R

AX Y

(

r R

)

ATotAGSS09

ATAGSS09

Aµ

AGSS09

ATotGN93

ATGN93

Aµ

GN93

30



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Position r/R

ASun−A

Model


AGSS09−ATOMIC −DOBGN93−ATOMICAGSS09−ATOMICGN93−ATOMIC +DOB

The compensation is also related to the temperature gradient. 31


Relative di�erences OPLIB-OPAL

3.5 4 4.5 5 5.5 6 6.5 7 7.5−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

log T

κO

PLIB

− κ

OP

AL /

κO

PA

L

32


Metallicity Inversions for the Solar Envelope

Metallicity kernels can thus be derived to estimate Z in the envelope.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−2

−1

0

1

2

3

Position r/R

Kn,l

Z,A

,Y

K20,0Z,A,Y

K30,0Z,A,Y

K20,1Z,A,Y

K25,2Z,A,Y

33


Appendices Helioseismology - Hare-and-Hounds exercises

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01

r/R

STarget−SReference

SReference

Real DifferencesSOLA ResultsSOLA Results (Less regularized)

34


Appendices Helioseismology - Kernel �ts

0 0.2 0.4 0.6 0.8 1

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

r/R

SSun−SM

odel

SM

odel Base of the solar

convective zone

AGSS09-OPLIB (SOLA)

0 0.2 0.4 0.6 0.8 1−5

0

5

10

15

20

25

30

Position r/R

K(r)

Averaging KernelTarget Function

35


Links with opacity and chemical composition

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.03

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

r/R

SSun−SM

odel

SM

odel


GS98

AGSS09

AGSS09− Free−OPLIBAGSS09− Free−OPLIB + TurbDiffAGSS09− Free−OPLIB + 10% Iron at BCZGS98− Free−OPLIB

Entropy inversions hint directly at inaccuracies in the radiative zone.36


Parameters of the solar models with modi�ed opacities and additional mixing

used in this study

(r/R)BCZ (m/M)CZ YCZ ZCZ Y0 Z0 Opacity Abundances Di�usion0.7122 0.9757 0.2416 0.01385 0.2692 0.01494 OPAL+Poly AGSS09Ne Thoul0.7129 0.9761 0.2427 0.01383 0.2678 0.01483 OPAL+Poly AGSS09Ne Paquette0.7106 0.9762 0.2425 0.01383 0.2685 0.01466 OPAL+Poly AGSS09Ne Thoul+DTurb0.7106 0.9762 0.2374 0.01359 0.2645 0.01490 OPAS+Poly AGSS09 Thoul+DTurb0.7121 0.9756 0.2460 0.01376 0.2696 0.01500 OPAL+Poly AGSS09Ne Thoul+DTurb−Prof0.7118 0.9757 0.2437 0.01381 0.2692 0.01495 OPAL+Poly AGSS09Ne Thoul+Ov−Rad

0.71056 0.9751 0.2438 0.01381 0.2700 0.01506 OPAL+Poly AGSS09Ne Thoul+Ov−Ad

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What is the metallicity of our reference star, the Sun?

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