Observed solar frequencies. Observed solar frequencies. Selected (two) topical problems in solar/stellar modelling
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1 Selected (two) topical problems in solar/stellar modelling Stellar Astrophysics Centre Improving solar physics by studying other stars Günter 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 1000 σ error bars Observed solar frequencies in distant stars typically only low-degree (l = 0,1,2,3) modes available Frequency n = 1 n = 0 (f mode) spherical degree Courtesy of J. Christensen-Dalsgaard (C-D) 1
2 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 16 Cyg B VIRGO on SOHO (whole-disk): Metcalfe et al. (2012) Solar observations adiabatic calculations C-D & Gough (1980): surface contribution δν from a plane-parallel polytropic layer supporting an isothermal atmosphere: Christensen-Dalsgaard et al. (1996) observations Model S Kjeldsen et al. (2008): GONG data 2
3 C-D & Gough (1980): surface contribution δν from a plane-parallel polytropic layer supporting an isothermal atmosphere: Solar-like Kepler pulsators: surface effects Empirical power law: Kjeldsen et al. (2008): KIC 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 Solar-like Kepler pulsators: surface effects Empirical power law: Empirical power law: KIC Mathur et al. (2012) Kepler data b = 4.82 Mathur et al. (2012) 3
4 Solar observations adiabatic calculations Momentum equation of stellar (envelope) structure: Christensen-Dalsgaard et al. (1996) observations Model S Rosenthal et al. (1995) 3D num. simulations Model S (mean) turbulent momentum flux (turbulent pressure): Sun GONG data GH (2006) Momentum equation of stellar (envelope) structure: Nonadiabaticity: ; Convection dynamics: observations Model S adiabatic model with p t adiabatic model without p t GONG data GH (1997, 2010) 4
5 Nonadiabaticity: Convection dynamics: Nonadiabaticity: Convection dynamics: ; ; (i) contribution in the overshoot region (ii) opacity effect: back warming Asteroseismic (Δν,δν) diagram Christensen-Dalsgaard (1994) Asteroseismic solar/stellar ages Sun α Cen B α Cen A = X core age 5
6 Monteiro et al. (2002) Asteroseismic (Δν,δν) diagram Modelling global stellar parameters (R, M, age) Non-seismic observational constraints (input from spectroscopy): T eff, log g, [Fe/H] (input from parallaxes & galactic extinction): L 20 Method median seismic input (statistical) uncertainties (%) ν max ν δν ν i R M age <δν> (μhz) Grid modelling: (a) RADIUS (Stello et al. 2009) (b) Yale-Birmingham (Gai et al. 2011) (c) SEEK (Quirion et al. 2010) <Δν> (μhz) - fitting all observed frequencies: AMP (Asteroseismic Modeling Portal) (Metcalfe et al. 2010) Mathur et al
7 - evolutionary computations depend on 3 initial parameters: e.g., Y 0, Z 0 and α c - Calibrated (L, R) models: Z 0 (Y 0,α c any t 2-parameter set of models (Z 0,t ) - evolutionary computations depend on 3 initial parameters: e.g., Y 0, Z 0 and α c - Calibrated (L, R) models: Z 0 (Y 0,α c any t 2-parameter set of models (Z 0,t ) 4.15 Gy 4.60 Gy 5.10 Gy at constant Z 0 Gough & Novotny (1990) - evolutionary computations depend on 3 initial parameters: e.g., Y 0, Z 0 and α c - Calibrated (L, R) models: Z 0 (Y 0,α c any t 2-parameter set of models (Z 0,t ) integrand: Z 0 = Z 0 = Z 0 = at constant t Houdek & Gough (2011) = r / R Houdek & Gough (2007) 7
8 - calibration using combinations of the seismically determined parameters? - calibration using combinations of the seismically determined parameters age X i age helium abundance we need a seismic diagnostics to estimate Seismic diagnostic Applying the seismic diagnostic to low-degree p modes: Sun Adiabatic exponent 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 Solar model For BiSON data: For Model S: produces oscillatory glitch contribution Base of convection zone seismic diagnostic models: 8
9 KIC KIC KIC Solar/stellar age calibration Kepler stars KIC KIC Solar/stellar age calibration Solar/stellar age calibration calibration using combinations of the seismically determined parameters Results after five iterations using BiSON data & age - approximate solar value by a two-term expansion about reference value : - and the solution is: from reference model 9
10 Age calibration Summary Summary/Conclusions GH & Gough (2009) Simulated SONG data 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). 10
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