Calibrating convective-core overshooting with eclipsing binary systems The case of low-mass main-sequence stars

Context. Double-lined eclipsing binaries have often been adopted in literature to calibrate the extension of the convective-core overshooting beyond the border defined by the Schwarzschild criterion. Aims. In a robust statistical way, we quantify the magnitude of the uncertainty that affects the calibration of the overshooting efficiency parameter beta that is owing to the uncertainty on the observational data. We also quantify the biases on the beta determination that is caused by the lack of constraints on the initial helium content and on the efficiencies of the superadiabatic convection and microscopic diffusion. Methods. We adopted a modified grid-based SCEPtER pipeline to recover the beta parameter from synthetic stellar data. Our grid spans the mass range [1.1; 1.6] M-circle dot and evolutionary stages from the zero-age main sequence (MS) to the central hydrogen depletion. The beta estimates were obtained by generalising the maximum likelihood technique described in our previous works. As observational constraint, we adopted the effective temperatures, [Fe/H], masses, and radii of the two stars. Results. By means of Monte Carlo simulations, adopting a reference scenario of mild overshooting beta = 0.2 for the synthetic data, and taking typical observational errors into account, we found both large statistical uncertainties and biases on the estimated values of beta. For the first 80% of the MS evolution, beta is biased by about -0.04, with the 1 sigma error practically unconstrained in the whole explored range [0.0; 0.4]. In the last 5% of the evolution the bias vanishes and the 1 sigma error is about 0.05. The 1 sigma errors are similar when adopting different reference values of beta. Interestingly, for synthetic data computed without convective-core overshooting, the estimated beta is biased by about 0.12 in the first 80% of the MS evolution, and by 0.05 afterwards. Assuming an uncertainty of +/- 1 in the helium-to-metal enrichment ratio Delta Y/Delta Z, we found a large systematic uncertainty in the recovered beta value, reaching 0.2 at the 60% of the MS evolution. Taking into account both the helium abundance indetermination and 1 sigma statistical uncertainty, we found that in the terminal part of the MS evolution the error on the estimated beta values ranges from -0.05 to +0.10, while beta is basically unconstrained throughout the explored range at earlier evolutionary stages. We quantified the impact of a uniform variation of +/- 0.24 in the mixing-length parameter alpha(ml) around the solar-calibrated value. The largest bias occurs in the last 5% of the evolution with an error on the estimated median beta from -0.03 to +0.07. In this last part, the 1 sigma uncertainty that addresses statistical and systematic error sources ranges from -0.09 to +0.15. Finally, we quantified the impact of a complete neglect of diffusion in the stellar evolution computations. In this case, the 1 sigma uncertainty that addresses statistical and systematic error sources ranges from -0.08 to +0.08 in the terminal 5% of the MS, while beta is practically unconstrained in the first 80% of the MS. Conclusions. The calibration of the convective core overshooting with double-lined eclipsing binaries-in the explored mass range and with both components still in their MS phase-appears to be poorly reliable, at least until further stellar observables, such as asteroseismic ones, and more accurate models are available.