The role of the time step and overshooting in the modelling of PMS evolution: the case of EK Cephei

EK Cephei (HD 206821) is a unique candidate to test predictions based on stellar evolutionary models. It is a double-lined detached eclipsing binary system with accurate absolute dimensions available and a precise determination of the metallicity. Most importantly for our work, its low mass (1.12 M⊙) component appears to be in the pre-main sequence (PMS) phase. We have produced detailed evolutionary models of the binary EK Cep using the CESAM stellar evolution code (Morel 1997). A χ2-minimisation was performed to derive the most reliable set of modelling parameters (age, αA, αB and Yi). We have found that an evolutionary age of about 26.8 Myrs fits both components in the same isochrone. The positions of EK Cep A and B in the HR diagram are consistent (within the observational uncertainties) with our results. Our revised calibration shows clearly that EK Cep A is in the beginning of the main sequence, while EK Cep B is indeed a PMS star. Such a combination allows for a precise age determination of the binary, and provides a strict test of the modelling. In particular we have found that the definition of the time step in calculating the PMS evolution is crucial to reproduce the observations. A discussion of the optimal time step for calculating PMS evolution is presented. The fitting to the radii of both components is a more difficult task; although we managed to do it for EK Cep B, EK Cep A has a lower radius than our best models. We further studied the effect of the inclusion of a moderate convective overshooting; the calibration of the binary is not significantly altered, but the effect of the inclusion of overshooting can be dramatic in the approach to the main sequence of stars with masses high enough to burn hydrogen through the CNO cycle on the main sequence.