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 zeroage 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 α ml 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.

Context. The last decade showed an impressive observational effort from the photometric and spectroscopic point of view for ancient stellar clusters in our Galaxy and beyond, leading to important and sometimes surprising results. Aims. The theoretical interpretation of these new observational results requires updated evolutionary models and isochrones spanning a wide range of chemical composition so that the possibility of multipopulations inside a stellar cluster is also taken also into account. Methods. With this aim we built the new "Pisa Stellar Evolution Database" of stellar models and isochrones by adopting a welltested evolutionary code (FRANEC) implemented with updated physical and chemical inputs. In particular, our code adopts realistic atmosphere models and an updated equation of state, nuclear reaction rates and opacities calculated with recent solar elements mixture. Results. A total of 32 646 models have been computed in the range of initial masses 0.30 ÷ 1.10 M for a grid of 216 chemical compositions with the fractional metal abundance in mass, Z, ranging from 0.0001 to 0.01, and the original helium content, Y, from 0.25 to 0.42. Models were computed for both solar-scaled and α-enhanced abundances with different external convection efficiencies. Correspondingly, 9720 isochrones were computed in the age range 8÷15 Gyr, in time steps of 0.5 Gyr. The whole database is available to the scientific community on the web. Models and isochrones were compared with recent calculations available in the literature and with the color-magnitude diagram of selected Galactic globular clusters. The dependence of relevant evolutionary quantities, namely turn-off and horizontal branch luminosities, on the chemical composition and convection efficiency were analyzed in a quantitative statistical way and analytical formulations were made available for reader's convenience. These relations can be useful in several fields of stellar evolution, e.g. evolutionary properties of binary systems, synthetic models for simple stellar populations and for star counts in galaxies, and chemical evolution models of galaxies.

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 mixinglength α ml 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.