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Using synthetic horizontal-branch models, we have investigated the origin of the systematic variation in horizontal-branch (HB) morphology with galactocentric distance (R(sub 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(sub 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 approximately 5 Gyr) among the halo globular clusters. 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 approximately 2 Gyr.

Mass loss on the horizontal branch has been invoked in the literature to explain such phenomena as the color (mass) dispersion of the horizontal branch and the observed distribution of period changes in RR Lyrae stars. To test these claims, the Yale stellar evolution code was used to evolve horizontal branch models of masses 0.64, 0.66, 0.68, 0.70, and 0.72 solar mass with Z of 0.001, core mass of 0.4893, main-sequence helium abundance of 0.23, and constant mass loss rates of 0, 10(exp -10), 5 x 10(exp -10), and 10(exp -9) solar mass/yr. Mass loss was assumed to occur only in the instability strip, where a mechanism is most likely to exist. Synthetic horizontal branches, constructed from the models, show that mass loss on the horizontal branch cannot produce the observed color dispersion even for the highest mass-loss rate of 10(exp -9) solar mass/yr. Mass loss is unlikely to occur at a higher rate without significant effects on the horizontal branch morphology, which would destroy the good agreement between standard synthetic models without mass loss and observed horizontal branches. Periods and period changes were calculated for all models. The period changes are not significantly larger for models with mass loss. The effect of mass loss in clusters of other metallicities is discussed.

We have investigated the effect of the new Livermore OPAL opacities on the evolution of horizontal-branch (HB) stars. This work was motivated by the recent stellar pulsation calculations using the new Livermore opacities, which suggest that the masses of double-mode RR Lyrae stars are 0.1-0.2 solar mass larger than those based on earlier opacities. Unlike the pulsation calculations, we find that the effect of opacity change on the evolution of HB stars is not significant. In particular, the effect of the mean masses of RR Lyrae stars is very small, showing a decrease of only 0.01-0.02 solar mass compared to the models based on old Cox-Stewart opacities. Consequently, with the new Livermore OPAL opacities, both the stellar pulsation and evolution models now predict approximately the same masses for the RR Lyrae stars. Our evolutionary models suggest that the mean masses of the RR Lyrae stars are about 0.76 and about 0.71 solar mass for M15 (Oosterhoff group II) and M3 (group I), respectively. If (alpha/Fe) = 0.4, these values are decreased by about 0.03 solar mass. Variations of the mean masses of RR Lyrae stars with HB morphology and metallicity are also presented.

Recent abundance measurements of RR Lyrae variables in the Baade's window field of the Galactic nuclear bulge are examined, and the observed metallicity distributions of the RR Lyraes in different Galactic radial zones are compared with those predicted for the HB population models. It is shown that the observed systematic variation with Galactocentric distance is only explained if the age of the stellar population increases, in the mean, with decreasing R(G). Thus, the oldest stellar population, the RR Lyraes in the Galactic nuclear bulge, is indeed older than that in the halo.

Recent advances in our understanding of horizontal-branch (HB) stars and in precision CCD photometry make it possible to establish a chronology of the formation of the Galaxy from the fossil record. The Lee et al. HB evolutionary models and the inferred age-metallicity relation of the Galactic globular-cluster system are now strengthened by many pieces of supporting evidence. This provides valuable information regarding the formation chronology of the halo and disk. Moreover, there is strong evidence from RR Lyrae stars that the radial variation in HB morphology observed in the halo continues to the very center of the Galaxy, which suggests that the formation of the bulge and halo was an inside-out process. These two crucial pieces of information are combined to extend the Searle and Zinn picture of halo formation to include the formation of the bulge and disk. The emerging picture is consistent with the idea that galaxies formed as clusters and mergers of many small gas-rich subsystems, rather than by the rapid collapse of single large protogalactic clouds.

Recent developments in our understanding of RR Lyrae variables are discussed, with special emphasis on their role as distance indicators. The dependence of RR Lyrae luminosity on metallicity and horizontal-branch (HB) morphology is now well understood with many pieces of supporting evidence. This allows the determination of distances to several Local Group galaxies (LMC, M31, and M33) by constructing HB population models that reproduce the observed luminosity functions of RR Lyraes in these galaxies. The new RR Lyrae distances to M31 and M33 are some 15-37 percent larger than those adopted by de Vaucouleurs (1986) and by Aaronson et al. (1986), while they are in reasonable agreements with the recent results based on multicolor CCD photometry of classical Cepheids. This indicates that the large value of Hubble constant (90-100 km/s/Mpc) suggested by these authors may be due, at least in part, to the errors in distances to nearby calibrating galaxies.

The observed correlation between the RR Lyrae luminosity and Fe/H for all Omega Cen RR Lyrae stars for which Fe/H has been determined by the delta-S method is considered, and emphasis is placed on the lack of luminosity variation among the variables in Omega Cen. Model calculations are shown to suggest that the observed 'flat' correlation between the RR Lyrae luminosity and Fe/H for stars having Fe/H forbidden line less than -1.4 can be reproduced if the HB stars in Omega Cen obey the nonmonotonic behavior of the HB morphology with decreasing Fe/H similar to that observed in the Galactic globular cluster system. This is considered to be a natural consequence of recent HB evolutionary models suggesting that the RR Lyrae mean luminosity depends on HB morphology as well as metallicity.

The observed secular period changes of RR Lyrae stars in five globular clusters have been compared with those predicted by synthetic models of the horizontal branch (HB). It is shown that most of the observed number distributions of the period change rate beta could be attributed to evolutionary effects, if the random observational error is of order + or - 0.07 days/Myr in beta as suggested by the observers. The model calculations indicate that the mean rate of period change in RR Lyrae stars in globular clusters depends sensitively on their HB type, as is the case for the period shift at a given effective temperature. The distinct bias toward positive period changes in M15 and Omega Cen is evidence that most HB stars in the Oosterhoff group II clusters pass through the instability strip from blue to red toward the end of their core helium burning phase. If confirmed by future observations, this is strong support for the Lee et al. (1990) explanation of the Sandage (1957) period-shift effect.