Cumulative physical uncertainty in modern stellar models I. The case of low-mass stars

Context. Theoretical stellar evolutionary models are still affected by not negligible uncertainties due to the errors in the adopted physical inputs. Aims. In this paper, using our updated stellar evolutionary code, we quantitatively evaluate the effects of the uncertainties in the main physical inputs on the evolutionary characteristics of low mass stars, and thus of old stellar clusters, from the main sequence to the zero age horizontal branch (ZAHB). To this aim we calculated more than 3000 stellar tracks and isochrones, with updated solar mixture, by changing the following physical inputs within their current range of uncertainty: H-1(p, nu e(+))H-2, N-14(p, gamma)O-15, and triple-alpha reaction rates, radiative and conductive opacities, neutrino energy losses, and microscopic diffusion velocities. Methods. The analysis was conducted performing a systematic variation on a fixed grid, in a way to obtain a full crossing of the perturbed input values. The effect of the variations of the chosen physical inputs on relevant stellar evolutionary features, such as the turn-off luminosity, the central hydrogen exhaustion time, the red-giant branch tip luminosity, the helium core mass, and the ZAHB luminosity in the RR Lyrae region are analyzed in a statistical way. Results. We find that, for a 0.9 M-circle dot model, the cumulative uncertainty on the turn-off, the red-giant branch tip, and the ZAHB luminosities accounts for +/- 0.02 dex, +/- 0.03 dex, and +/- 0.045 dex respectively, while the central hydrogen exhaustion time varies of about +/- 0.7 Gyr. For all examined features the most relevant effect is due to the radiative opacities uncertainty; for the later evolutionary stages the second most important effect is due to the triple-alpha reaction rate uncertainty. For an isochrone of 12 Gyr, we find that the isochrone turn-off log luminosity varies of +/- 0.013 dex, the mass at the isochrone turn-off varies of +/- 0.015 M-circle dot, and the difference between ZAHB and turn-off log-luminosity varies of +/- 0.05 dex. The effect of the physical uncertainty affecting the age inferred from turn-off luminosity and from the vertical method are of +/- 0.375 Gyr and +/- 1.25 Gyr, respectively.