## Quantitative estimates of the constraints on solar-like models imposed by observables^{⋆}

^{1}
Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France

e-mail: Nesibe.Ozel@obspm.fr
^{2}
Institut d’Astrophysique et de Géophysique de l’Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium

e-mail: MA.Dupret@ulg.ac.be

Received: 17 June 2009

Accepted: 3 May 2011

*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.

Key words: methods: numerical / stars: fundamental parameters / stars: interiors / stars: oscillations

*© ESO, 2011*