A statistical test on the reliability of the non-coevality of stars in binary systems

Aims. We develop a statistical test on the expected difference in age estimates of two coeval stars in detached double-lined eclipsing binary systems that are only caused by observational uncertainties. We focus on stars in the mass range [0.8; 1.6] M-circle dot, with an initial metallicity [Fe/H] from -0.55 to 0.55 dex, and on stars in the main-sequence phase. Methods. The ages were obtained by means of the SCEPtER technique, a maximum-likelihood procedure relying on a pre-computed grid of stellar models. The observational constraints used in the recovery procedure are stellar mass, radius, effective temperature, and metallicity [Fe/H]. To check the effect of the uncertainties affecting observations on the (non-)coevality assessment, the chosen observational constraints were subjected to a Gaussian perturbation before applying the SCEPtER code. We defined the statistic W computed as the ratio of the absolute difference of estimated ages for the two stars over the age of the older one. We determined the critical values of this statistics above which coevality can be rejected in dependence on the mass of the two stars, on the initial metallicity [Fe/H], and on the evolutionary stage of the primary star. Results. The median expected difference in the reconstructed age between the coeval stars of a binary system - caused alone by the observational uncertainties - shows a strong dependence on the evolutionary stage. This ranges from about 20% for an evolved primary star to about 75% for a near ZAMS primary. The median difference also shows an increase with the mass of the primary star from 20% for 0.8 M-circle dot stars to about 50% for 1.6 M-circle dot stars. The reliability of these results was checked by repeating the process with a grid of stellar models computed by a different evolutionary code; the median difference in the critical values was only 0.01. We show that the W test is much more sensible to age differences in the binary system components than the alternative approach of comparing the confidence interval of the age of the two stars. We also found that the distribution of W is, for almost all the examined cases, well approximated by beta distributions. Conclusions. The proposed method improves upon the techniques that are commonly adopted for judging the coevality of an observed system. It also provides a result founded on reliable statistics that simultaneously accounts for all the observational uncertainties.