Convective overshooting in low mass stars.

The evolution of horizontal branch stars up to the starting of the thermally pulsing regime of the He-burning shell is investigated with the aid of a non local treatment of the core convection. The formalism follows the overshooting model by Bressan et al. (1981) which opposes to the classical, local schemes for overshooting and semiconvection currently in use. Evolutionary models based on these latter prescriptions at the end of central He-burning meet with the problem of breathing convection. The authors find that those instabilities are merely due to the local approach and they disappear when a non-local, more physical description of convection is adopted. Furthermore, that breathing convection is likely not to occur in real stars is also supported. The comparison of theoretical predictions with the observational ratio shows that only a non-local treatment of convection leads to the correct amount of core mixing during the He-burning phase.