Uncertainties in asteroseismic grid-based estimates of stellar ages: SCEPtER: Stellar CharactEristics Pisa Estimation gRid

Context. Stellar age determination by means of grid-based techniques that adopt asteroseismic constraints is a well established method nowadays. However some theoretical aspects of the systematic and statistical errors affecting these age estimates still have to be investigated. Aims. We study the impact on stellar age determination of the uncertainty in the radiative opacity, in the initial helium abundance, in the mixing-length value, in the convective core overshooting, and in the microscopic diffusion efficiency adopted in stellar model computations. Methods. We extended our SCEPtER grid to include stars with mass in the range [0.8; 1.6] M⊙ and evolutionary stages from the zero-age main sequence to the central hydrogen depletion. For the age estimation we adopted the same maximum likelihood technique as described in our previous work. To quantify the systematic errors arising from the current uncertainty in model computations, many synthetic grids of stellar models with perturbed input were adopted. Results. We found that the current typical uncertainty in the observations accounts for 1σ statistical relative error in age determination, which on average ranges from about -35% to +42%, depending on the mass. However, owing to the strong dependence on the evolutionary phase, the age's relative error can be higher than 120% for stars near the zero-age main sequence, while it is typically of the order of 20% or lower in the advanced main-sequence phase. The systematic bias on age determination due to a variation of ±1 in the helium-to-metal enrichment ratio ΔY/ΔZ is about one-fourth of the statistical error in the first 30% of the evolution, while it is negligible for more evolved stages. The maximum bias due to the presence of the convective core overshooting is -7% and -13% for mild and strong overshooting scenarios. For all the examined models, the impact of a variation of ±5% in the radiative opacity was found to be negligible. The most important source of bias is the uncertainty in the mixing-length value αml and the neglect of microscopic diffusion. Each of these effects accounts for a bias that is nearly equal to the random error uncertainty. Comparison of the results of our technique with other grid techniques on a set of common stars showed general agreement. However, the adoption of a different grid can account for a variation in the mean estimated age up to 1 Gyr.