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

Context. Seismic parameters such as the large Δ[SUB]0[/SUB] and small δ[SUB]02[/SUB] 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. <BR /> Aims: We estimate the influence of different observed quantities (oscillation frequencies, interferometry, etc.) and the impact of their accuracy in constraining stellar model parameters. <BR /> Methods: To relate the errors in observed quantities to the precision of the theoretical model parameters, we analyse the behaviour of the χ[SUP]2[/SUP] 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. <BR /> 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[SUB]0[/SUB], the radius R/R[SUB]&sun;[/SUB], the mean small separation δ[SUB]02[/SUB], the luminosity L/L[SUB]&sun;[/SUB], the effective temperature T[SUB]eff[/SUB]. 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[SUB]&sun;[/SUB]. For HD 49933 the combination of ℳ and Y[SUB]0[/SUB]: ℳ[SUP]2[/SUP]Y[SUB]0[/SUB] is well determined because of their correlation. However, they are poorly constrained individually. The frequency difference δ[SUB]01[/SUB], if known with an error of about 0.3%, can determine the size of the convective core overshooting with about 3% accuracy. Appendices A and B are available in electronic form at <A href="http://www.aanda.org">http://www.aanda.org</A>