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Selected (two) topical problems in solar/stellar modelling
Stellar Astrophysics Centre

Improving solar physics by studying other stars
GЭnter Houdek

The effect of the surface layers on the oscillation frequencies

Asteroseismic ages and heavy-element abundances of the Sun & solar-like stars

Courtesy of J. Christensen-Dalsgaard

IAU-GA-SP13 ­ Beijing ­ August 2012

Observed solar frequencies
m-averaged frequencies from MDI instrument on SOHO

Observed solar frequencies
in distant stars typically only low-degree (l = 0,1,2,3) modes available

1000 error bars

Frequency

n=1 n = 0 (f mode)

spherical degree
Courtesy of J. Christensen-Dalsgaard (C-D)

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Observed solar frequencies (power spectrum)
in distant stars typically only low-degree (l = 0,1,2,3) modes available

Examples of Kepler solar-like pulsators
(three-month time series)

16 Cyg A
VIRGO on SOHO (whole-disk):

16 Cyg B

Metcalfe et al. (2012)

Solar-like pulsators: surface effects
Solar observations ­ adiabatic calculations
Christensen-Dalsgaard et al. (1996) observations ­ Model S

Solar-like pulsators: surface effects
C-D & Gough (1980): surface contribution from a plane-parallel polytropic layer supporting an isothermal atmosphere:

Kjeldsen et al. (2008):

GONG data

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Solar-like pulsators: surface effects
C-D & Gough (1980): surface contribution from a plane-parallel polytropic layer supporting an isothermal atmosphere:

Solar-like Kepler pulsators: surface effects
Empirical power law:

KIC 3632418
Kjeldsen et al. (2008): Mathur et al. (2012)

Observations ­ solar model

BiSON data: b = 4.82 radial modes dipole modes

Kepler data

b = 4.82 Metcalfe et al. (2010)

Solar-like Kepler pulsators: surface effects
Empirical power law:

Solar-like Kepler pulsators: surface effects
Empirical power law:

KIC 6106415
Mathur et al. (2012)

Kepler data

b = 4.82

Mathur et al. (2012)

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Solar-like pulsators: surface effects
Solar observations ­ adiabatic calculations
Christensen-Dalsgaard et al. (1996) observations ­ Model S Rosenthal et al. (1995)

Solar-like pulsators: surface effects
Momentum equation of stellar (envelope) structure:

(mean) turbulent momentum flux (turbulent pressure):
3D num. simulations ­ Model S Sun

GONG data

GH (2006)

Solar-like pulsators: surface effects
Momentum equation of stellar (envelope) structure:
Nonadiabaticity:

Solar-like pulsators: surface effects
Convection dynamics: ;

observations ­ Model S

adiabatic model with pt ­ adiabatic model without pt

GONG data

GH (1997, 2010)

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Solar-like pulsators: surface effects
Nonadiabaticity: ; Convection dynamics: Nonadiabaticity:

Solar-like pulsators: surface effects
Convection dynamics: ;

(i)

contribution in the overshoot region

(ii) opacity effect: "back warming"

Asteroseismic (,) diagram
Christensen-Dalsgaard (1994)

Asteroseismic solar/stellar ages
Cen A

Cen B Sun

= Xcore

age

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Asteroseismic (,) diagram
Monteiro et al. (2002)
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Modelling global stellar parameters (R, M, age)
Non-seismic observational constraints (input from spectroscopy): (input from parallaxes & galactic extinction):

Teff, log g, [Fe/H]
L

Method - Grid modelling:

median seismic input (statistical) uncertainties (%) max i R M age

<> (Hz)

15

10

(a) RADIUS (Stello et al. 2009) (b) Yale-Birmingham (Gai et al. 2011) (c) SEEK (Quirion et al. 2010)

1.4 3.0 4.9

4-6 4-6 4-6

15-21 15-21 15-21

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- fitting all observed frequencies: AMP (Asteroseismic Modeling Portal) (Metcalfe et al. 2010) 100 120 140 160 180 200 0.8 1.2 2.5

0

Mathur et al. 2012

<> (Hz)

Age-sensitive diagnostics of the stellar structure
-asymptotic p-mode frequency behaviour ( ):

Age-sensitive diagnostics of the stellar structure
-asymptotic p-mode frequency behaviour ( ):

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Age-sensitive diagnostics of the stellar structure
-asymptotic p-mode frequency behaviour ( ):

Age-sensitive diagnostics of the stellar structure
-asymptotic p-mode frequency behaviour ( ):

- evolutionary computations depend on 3 initial parameters: e.g., Y0, Z0 and c - Calibrated (L, R) models: Z0(Y0,c) @ any t 2-parameter set of models (Z0,t )

- evolutionary computations depend on 3 initial parameters: e.g., Y0, Z0 and c - Calibrated (L, R) models: Z0(Y0,c) @ any t 2-parameter set of models (Z0,t )

4.15 Gy 4.60 Gy 5.10 Gy

at constant Z0

Gough & Novotny (1990)

Age-sensitive diagnostics of the stellar structure
-asymptotic p-mode frequency behaviour ( ):

Age-sensitive diagnostics of the stellar structure
-asymptotic p-mode frequency behaviour ( ):

- evolutionary computations depend on 3 initial parameters: e.g., Y0, Z0 and c - Calibrated (L, R) models: Z0(Y0,c) @ any t 2-parameter set of models (Z0,t )

integrand:

Z0 = 0.016 Z0 = 0.020 Z0 = 0.022

at constant t

Houdek & Gough (2011)

=r/R

Houdek & Gough (2007)

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Age-sensitive diagnostics of the stellar structure

Age-sensitive diagnostics of the stellar structure

- calibration using combinations of the seismically determined parameters ? age Xi

- calibration using combinations of the seismically determined parameters

age helium abundance

we need a seismic diagnostics to estimate

Seismic diagnostic
Adiabatic exponent

Applying the seismic diagnostic to low-degree p modes: Sun

Seismic diagnostic (GH & Gough 2007) no He ( ) He (solar value )
surface contrib.
BiSON data: (Chaplin et al.)

glitch contributions

surface contribution

He I He II

HeI HeII

...helium abundance
For BiSON data: For Model S:

Solar model

produces oscillatory glitch contribution
seismic diagnostic models:

Base of convection zone

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KIC 6933899

KIC 10963065

KIC 8006161

Solar/stellar age calibration Kepler stars
KIC 1124118 KIC 6603624

Solar/stellar age calibration

Solar/stellar age calibration
Results after five iterations using BiSON data &

calibration using combinations of the seismically determined parameters

age

- approximate solar value

by a two-term expansion about reference value

:

- and the solution is:

from reference model

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Age calibration Summary
GH & Gough (2009) Simulated SONG data

Summary/Conclusions
Observed surface effects in Kepler stars can contribute to improve our understanding of the near-surface physics in the Sun & solar-type stars.

Mean turbulent pressure dominating surface effect; nonadiabaticity and convection dynamics must also not be neglected.

Including the seismic signatures of the two stages of helium ionization substantially improve the calibration of stellar ages and abundances.

improvement by 2 of age accuracy

This seismic calibration procedure can be applied to data from CoRoT, Kepler and planned observing campaigns (SONG).

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