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

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 from the main sequence to the zero age horizontal branch (ZAHB). 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: 1H(p,nu e+)2H, 14N(p,gamma)15O, and triple-alpha reaction rates, radiative and conductive opacities, neutrino energy losses, and microscopic diffusion velocities. We performed 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 (RGB) tip luminosity, the helium core mass, and the ZAHB luminosity in the RR Lyrae region are statistically analyzed. For a 0.9 Msun model, the cumulative uncertainty on the turn-off, the RGB tip, and the ZAHB luminosities accounts for $\pm$ 0.02 dex, $\pm$ 0.03 dex, and $\pm$ 0.045 dex respectively, while the central hydrogen exhaustion time varies of about $\pm$ 0.7 Gyr. 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 $\pm$ 0.013 dex, the mass at the isochrone turn-off varies of $\pm$ 0.015 Msun, and the difference between ZAHB and turn-off log-luminosity varies of $\pm$ 0.05 dex. The effect of the physical uncertainty affecting the age inferred from turn-off luminosity and from the vertical method are of $\pm$ 0.375 Gyr and $\pm$ 1.25 Gyr respectively.