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] Msun, and on stars in the main-sequence phase. The ages were
obtained by means of the maximum-likelihood SCEPtER technique. The
observational constraints used in the recovery procedure are stellar mass,
radius, effective temperature, and metallicity [Fe/H]. 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. 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 Msun stars to about
50% for 1.6 Msun stars. The reliability of these results was checked by
repeating the process with a grid of stellar models computed by a different
evolutionary code. 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. 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.Comment: Abstract shortened. Accepted for publication in A&A. One reference
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