Uncertainties in grid-based estimates of stellar mass and radius: SCEPtER: Stellar CharactEristics Pisa Estimation gRid

Context. The availability of high-quality astero-seismological data provided by satellite missions stimulated the development of several grid-based estimation techniques to determine the stellar masses and radii. Some aspects of the systematic and statistical errors affecting these techniques have still not been investigated well. Aims: We study the impact on mass and radius determination of the uncertainty in the input physics, in the mixing-length value, in the initial helium abundance, and in the microscopic diffusion efficiency adopted in stellar model computations. Methods: We consider stars with mass in the range [0.8-1.1] M⊙ and evolutionary stages from the zero-age main sequence to the central hydrogen exhaustion. To recover the stellar parameters, a maximum-likelihood technique was employed by comparing the observations constraints to a precomputed grid of stellar models. Synthetic grids with perturbed input were adopted to estimate the systematic errors arising from the current uncertainty in model computations. Results: We found that the statistical error components, owing to the current typical uncertainty in the observations, are nearly constant in all cases at about 4.5% and 2.2% on mass and radius determination, respectively. The systematic bias on mass and radius determination due to a variation of ± 1 in ΔY/ΔZ is ±2.3% and ± 1.1%; the one due to a change of ± 0.24 in the value of the mixing-length αml is ± 2.1% and ± 1.0%; the one due to a variation of ± 5% in the radiative opacity is ∓ 1.0% and ∓ 0.45%. An important bias source is to neglect microscopic diffusion, which accounts for errors of about 3.7% and 1.5% on mass and radius. The cumulative effects of the considered uncertainty sources can produce biased estimates of stellar characteristics. Comparison of the results of our technique with other grid techniques shows that the systematic biases induced by the differences in the estimation grids are generally greater than the statistical errors involved.