The Metallicity Dependence of RR Lyrae Absolute Magnitudes from Synthetic Horizontal-Branch Models

A grid of synthetic horizontal-branch (SHB) models based on horizontal-branch (HB) evolutionary tracks with improved physics has been constructed to reconsider the theoretical calibration of the dependence of M v (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 HB morphology. This is due to the fact that HB stars pass through the RR Lyrae instability strip at different evolutionary stages, depending on their original position on the HB. At [Fe/H] = -1.9, and for HB type 0, the models yield M V (RR) = 0.47 ± 0.10. The mean slope for the zero-age HB models is 0.204. Since there is no simple universal relation between M v (RR) and metallicity that is applicable to all globular clusters, the HB morphology of each individual cluster must be taken into account, in addition to [Fe/H], in deriving the appropriate M v (RR). Taking HB morphology into account, we find that the slope of the mean ⟨ M V (RR)⟩-[Fe/H] relation 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 ≤ 20 kpc. Implications for interpreting observations of field RR Lyrae variables and for absolute globular cluster ages and Galactic chronology are briefly discussed.