THE STRUCTURE OF HORIZONTAL-BRANCH MODELS .1. THE ZERO-AGE HORIZONTAL BRANCH

We present a detailed study of the structure of zero-age horizontal-branch (HB) models. We first demonstrate explicitly the properties of composite polytropes on the homology-invariant (U,V)-plane and then use the discussion as a framework for understanding the results from more detailed stellar models. We have constructed a variety of test models and sequences to aid in the investigation of the underlying factors that give rise to the wide variation in HB model properties with composition. As part of the study, we reexamine the roles of the CNO elements as nuclear catalysts and of envelope opacity sources, as well as the envelope helium abundance. We are able to demonstrate general results concerning the equilibrium of HB envelopes which can predict qualitatively how structure and evolutionary calculations will vary with the input physics and assumptions regarding the realistic stellar abundances in globular clusters. In particular, we find that, for stars of a fixed range of mass arriving on the HB, the stellar distribution is determined mainly by CNO for low metallicities ([Fe/H less than or similar to -1), but mainly by opacity sources for high metallicities. The value of [Fe/H] where CNO ceases to dominate depends significantly on the adopted opacity and will decrease if and when opacity estimates are revised upward. These results have relevance to the perceived discrepancy between the masses derived for RR Lyrae stars from stellar evolution and pulsation calculations, for the observed relationship between HB luminosity and metallicity, and for the HB morphology of globular clusters.