Metal-poor stars. V. Horizontal-branch morphology

Using theoretical models for horizontal-branch stars, various observational quantities such as color-magnitude (c-m) diagrams have been synthesized. The proposal that there is a dispersion in mass along the horizontal branch (NB) produces a good fit to observed c-m diagrams. In fact, it is so easy to achieve a fit in the c-m diagram that the parameters inv6lved cannot be effectively limited, but still some important results emerge. It seems highly likely that some parameter other than age along a single evolutionary track must vary on the NB. The details of evolutionary tracks have only a minor effect on the appearance of the NB. As the heavy-element abundance Z varies from cluster to cluster, either the helium abundance must vary or the mean mass loss must vary. The "second parameter" affecting the NB is discussed in detail. Either helium variations of the order of 0.03 or age variations on the order of a billion years can account for the anomalous c-m diagrams. With certain assumptions the blueness of the NB is not a monotonic function of Z. Conclusive identification of the second parameter must await an adequate theory for mass loss along the red-giant branch and observations of the CNO abundances in the clusters. An effort to combine evolutionary theory with pulsation theory is largely unsuccessful. Quantities such as the fraction of RR Lyrae stars in the fundamental mode are extremely sensitive functions of the opacity used in the pulsation calculations. None of the presently proposed theoretical transition curves from fundamental to first harmonic variables is satisfactory. General trends such as a difference in mass and luminosity for the two Oosterhoff classes can be understood. The NB in the (surface gravity, effective temperature)-plane is briefly considered. Subject headings: horizontal-branch stars - interiors, stellar - RR Lyrae stars