The Evolution of He-burning Stars: Horizontal and Asymptotic Branches in Galactic Globulars

A grid of theoretical evolutionary models covering the horizontal-branch (HB) and the asymptotic-giant-branch (AGB) phases of globular cluster stars is presented. The computations were performed for a fixed amount of the original He and for metallicity values. For each value of the assumed metallicity, the evolutionary structure at the He flash was used to construct an initial set of He-burning models with the same mass of the central He core but with decreasing masses of the H-rich envelopes. Results are presented of the evolution of these models through the exhaustion of central He up to the minimum in luminosity marking the reignition of the H shell. The luminosity of the AGB clump and the number ratio of AGB to HB stars was found to remain fairly constant with the cluster metallicity. The parameter R is recalibrated, and it is suggested that there is a small increase in the adopted value of the original He in Galactic globulars and a correlation of helium and metals in 47 Tuc.