The horizontal-branch stars in globular clusters. II. The second parameter phenomenon

Using synthetic horizontal-branch models, we have investigated the origin of the systematic variation in horizontal-branch (HB) morphology with galactocentric distance (R_G) among globular clusters. The variations in He abundance, CNO abundance, and core mass required separately to explain this effect are inconsistent with either the observed properties of the RR Lyrae variables or the observed main-sequence turnoffs in the clusters. There is also no clear evidence that the trend with R_G is related to the central concentrations, central densities, or absolute magnitudes of the clusters. The variations in cluster age required to explain this effect are not in conflict with any observations. A detailed comparison of our synthetic HB calculations with pairs of clusters of very different HB morphology but similar [Fe/H] reveals reasonably good agreement between the age differences inferred from HB morphology and the main-sequence turnoff. The major source of uncertainty is the need for ad hoc hypotheses in the modeling of the HB morphologies of a few peculiar clusters (e.g., NGC 6752). Nonetheless, there is firm evidence for age variations of several gigayears (as much as ∼5 Gyr) among the halo globular dusters. Our results support the hypothesis of Searle & Zinn that the inner halo is more uniform in age and is older in the mean than the outer halo, and we estimate this difference to be ∼2 Gyr.