Aims. The capability of grid-based techniques to estimate the age together with the convective core overshooting efficiency of stars in detached eclipsing binary systems for main sequence stars has previously been investigated. We have extended this investigation to later evolutionary stages and have evaluated the bias and variability on the recovered age and convective core overshooting parameter accounting for both observational and internal uncertainties.
Methods. We considered synthetic binary systems, whose age and overshooting efficiency should be recovered by applying the SCEPtER pipeline to the same grid of models used to build the mock stars. We focus our attention on a binary system composed of a 2.50 M⊙ primary star coupled with a 2.38 M⊙ secondary. To explore different evolutionary scenarios, we performed the estimation at three different times: when the primary is at the end of the central helium burning, when it is at the bottom of the RGB, and when it is in the helium core burning phase. The Monte Carlo simulations have been carried out for two typical values of accuracy on the mass determination, that is, 1% and 0.1%.
Results. Adopting typical observational uncertainties, we found that the recovered age and overshooting efficiency are biased towards low values in all three scenarios. For an uncertainty on the masses of 1%, the underestimation is particularly 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 β. In the other scenarios, an undervaluation of the age by about 4% occurs. A large variability in the fitted values between Monte Carlo simulations was found: for an individual system calibration, the value of the overshooting parameter can vary from β = 0.0 to β = 0.26. When adopting a 0.1% error on the masses, the biases remain nearly unchanged but the global variability is suppressed by a factor of about two. We also explored the effect of a systematic discrepancy between the artificial systems and the model grid by accounting for an offset in the effective temperature of the stars by ± 150 K. For a mass error of 1% the overshooting parameter 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 also evaluate the possibility of individually recovering the β value for both binary stars. We found that this is impossible for a primary near to central hydrogen exhaustion owing to huge biases for the primary star of + 0.14 (90% relative error), while in the other cases the fitted β are consistent, but always biased by about − 0.04 (− 25% relative error). Finally, the possibility to distinguish between models computed with mild overshooting from models with no overshooting was evaluated, resulting in a reassuring power of distinction greater than 80%. However, the scenario with a primary in the central helium burning was a notable exception, showing a power of distinction lower than 5%.
Implementation of Reed Solomon Code Over GF(9) and 9-Ary Symmetric Channel
