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Constraints on the Distance Moduli, Helium and Metal Abundances, and Ages of Globular Clusters from their RR Lyrae and Non-Variable Horizontal-Branch Stars. I. M3, M15, and M92

Up-to-date isochrones, zero-age horizontal branch (ZAHB) loci, and evolutionary tracks for core He-burning stars are applied to the color-magnitude diagrams (CMDs) of M3, M15, and M92, focusing in particular on their RR Lyrae populations. Periods for ab- and c-type variables are calculated using the latest theoretical calibrations of log P_ab and log P_c as a function of luminosity, mass, effective temperature, and metallicity. Our models are generally able to reproduce the measured periods to well within the uncertainties implied by the stellar properties on which pulsation periods depend, as well as the mean periods and cluster-to-cluster differences in <P_ab> and <P_c>, on the assumption of well-supported values of E(B-V), (m-M)_V, and [Fe/H]. While many of the RR Lyrae in M3 lie close to the same ZAHB that fits the faintest HB stars at bluer or redder colors, the M92 variables are all significantly evolved stars from ZAHB locations on the blue side of the instability strip. M15 appears to contain a similar population of HB stars as M92, along with additional helium-enhanced populations not present in the latter which comprise most of its RR Lyrae stars. The large number of variables in M15 and the similarity of the observed values of <P_ab> and <P_c> in M15 and M92 can be explained by HB models that allow for variations in Y. Similar ages (~12.5 Gyr) are found for all three clusters, making them significantly younger than the field halo subgiant HD 140283. Our analysis suggests a preference for stellar models that take diffusive processes into account.