Overshooting calibration and age determination from evolved binary system

We evaluated the bias and variability on the fitted age and convective core overshooting parameter for evolved binary stars accounting for observational and internal uncertainties. We considered a binary system composed of a 2.50 $M_{\sun}$ primary star coupled with a 2.38 $M_{\sun}$ secondary in three evolutionary stages (primary at the end of the central helium burning; at the bottom of the RGB; and in the helium core burning). The simulations have been carried out for two values of accuracy on the mass determination (1% and 0.1%). We found that the fitted age and overshooting efficiency are always biased towards low values. The underestimation is relevant for a primary in the central helium burning stage, reaching -8.5% in age and -0.04 (-25% relative error) in the overshooting parameter $\beta$. In the other scenarios, an undervaluation of the age by about 4% occurs. A large variability in the fitted values between simulations was found: for an individual system calibration, the value of $\beta$ can vary from 0.0 to 0.26. For an error of 0.1% on the masses the global variability is suppressed by a factor of two. We accounted for a systematic offset in the effective temperature of the stars by $\pm 150$ K. For a mass error of 1% $\beta$ is largely biased towards the edges of the explored range, while for the lower mass uncertainty it is basically unconstrained from 0.0 to 0.2. We evaluated the possibility of individually recovering the $\beta$ value for both stars. We found that this is impossible for a primary near to central hydrogen exhaustion, while in the other cases the fitted $\beta$ are consistent, but always biased. Finally, the possibility to distinguish between models computed with mild overshooting from models with no overshooting resulted in a reassuring power of 80%. However, the scenario with a primary in the central helium burning showed a power lower than 5%.