Quantitative estimates of the constraints on solar-like models imposed by observables⋆
Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France
2 Institut d’Astrophysique et de Géophysique de l’Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium
Received: 17 June 2009
Accepted: 3 May 2011
Context. Seismic parameters such as the large Δ0 and small δ02 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 χ2 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 Δ0, the radius R/R⊙, the mean small separation δ02, the luminosity L/L⊙, the effective temperature Teff. 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 Y0: ℳ 2Y0 is well determined because of their correlation. However, they are poorly constrained individually. The frequency difference δ01, if known with an error of about 0.3%, can determine the size of the convective core overshooting with about 3% accuracy.
Key words: methods: numerical / stars: fundamental parameters / stars: interiors / stars: oscillations
Appendices A and B are available in electronic form at http://www.aanda.org
© ESO, 2011