Convective Overshooting in Horizontal Branch Stars

Abstract

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. We 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 by observational determinations of the parameter R₂ (the number ratio of AGB to HB stars) in several galactic globular clusters. This parameter reflecting the ratio of lifetimes in the corresponding evolutionary phases, is particularly sensitive to the internal mixing during central He-burning, while it turns out to be almost independent from the adopted helium abundance. 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. In fact, in models which strictly obey the Schwarzschild condition, the amount of mixed material is too low and in turn R₂ is too high. On the contrary, in models which allow for local overshooting and semiconvection, the extension of the mixed region is too large and in turn R₂ gets much lower than observed. The occurrence of breathing convection makes the theoretical expectation even worse, in that only about half of the observed AGB stars can be accounted for.