The metallicity dependence of RR Lyrae absolute magnitudes from synthetic horizontal-branch models

A grid of synthetic horizontal-branch (SHB) models based on horizontal-bran ch (HB) evolutionary tracks with improved physics has been constructed to r econsider the theoretical calibration of the dependence of M-upsilon(RR) on metallicity in globular clusters and the slope of the mean [M-V(RR)]-[Fe/H ] relation. The SHB models confirm Lee's earlier finding that the slope of the [M-V(RR)]-[Fe/H] relation is itself a function of the metallicity range considered and that, in addition, for a given [Fe/H] RR Lyrae luminosities depend on HE morphology. This is due to the fact that HE stars pass throug h the RR Lyrae instability strip at different evolutionary stages, dependin g on their original position on the HE. At [Fe/H] = -1.9, and for HE type 0 , the models yield M-V(RR)= 0.47 +/- 0.10. The mean slope for the zero-age HE models is 0.204. Since there is no simple universal relation between M-u psilon(RR) and metallicity that is applicable to all globular clusters, the HE morphology of each individual cluster must be taken into account, in ad dition to [Fe/H], in deriving the appropriate M-upsilon(RR). Taking HE morp hology into account, we find that the slope of the mean [M-V(RR)]-[Fe/H] re lation varies between 0.36 for the clusters with Galactocentric distances R -gc less than 6 kpc and 0.22 for clusters with 6 kpc < R-gc less than or eq ual to 20 kpc. Implications for interpreting observations of field RR Lyrae variables and for absolute globular cluster ages and Galactic chronology a re briefly discussed.