Quantitative estimates of the constraints on solar-like models imposed by observables

Abstract

Context. Seismic parameters such as the large Δ 0 and small δ 02 frequency separations are now being measured in a very large number of stars and begin to be used to test the physics of stellar models. Aims. We estimate the influence of different observed quantities (oscillation frequencies, interferometry, etc.) and the impact of their accuracy in constraining stellar model parameters. Methods. To relate the errors in observed quantities to the precision of the theoretical model parameters, we analyse the behaviour of the χ 2 fitting function around its minimum using the singular value decomposition (SVD) formalism. A new indicator called "weighting" quantifies the relative importance of observational constraints on the determination of each physical parameter individually. These tools are applied to a grid of evolutionary sequences for solar-like stellar models with varying age and mass, and to a real case: HD 49933 -a typical case for which seismic observations are available from space using CoRoT. Results. The mass M is always the best determined parameter. The new indicator "weighting" allows us to rank the importance of the different constraints: the mean large separation Δ 0 , the radius R/R , the mean small separation δ 02 , the luminosity L/L , the effective temperature T eff . If the metallicity and age parameters are known, for example in an open cluster, using either individual or mean frequency separations yields the same uncertainties for masses less than 1.1 M . For HD 49933 the combination of M and Y 0 : M 2 Y 0 is well determined because of their correlation. However, they are poorly constrained individually. The frequency difference δ 01 , if known with an error of about 0.3%, can determine the size of the convective core overshooting with about 3% accuracy.

Differential asteroseismic study of seismic twins observed by CoRoT

“…Table 6 gives their parameters for the two chemical mixtures. To determine the uncertainty of the model parameters of HD 181420, we used the singular value decomposition method (SVD; for a detailed description, see e.g., Ozel et al 2011, and references therein).…”

Fundamental properties of fiveKeplerstars using global asteroseismic quantities and ground-based observations

“…We also include case (case 1d) to eliminate the M-Y i correlation e.g. Metcalfe et al (2009); Ozel et al (2011). We repeat the same exercise while also including He diffusion as described by Michaud & Proffit (1993).…”

TheCoRoTtarget HD 49933: a possible seismic signature of heavy elements ionization in the deep convective zone

“…The star HD 49933 has been modelled a few times by different authors (e.g. Piau et al 2009;Ozel et al 2009;Bigot et al 2011;Creevey & Bazot 2011;Liu et al 2014;Roxburgh 2015). We use the stellar evolution code CESAM 2k to generate a grid of models with different values for the mass, metallicity and mixing length parameter.…”

“…We computed four theoretical models, fully compatible to the other models of this star described in literature (Bruntt 2009;Bigot et al 2011;Ozel et al 2009;Piau et al 2009;Kallinger et al 2010;Creevey & Bazot 2011;Liu et al 2014;Roxburgh 2015). Our goal is to probe, from a seismological point of view, the outer layers of the star HD 49933.…”