The Hubble Space Telescope Survey of M31 Satellite Galaxies. III. Calibrating the Horizontal Branch as an Age Indicator for Nearby Galaxies

We present a new method for measuring the mean age of old/intermediate stellar populations in resolved, metal-poor ($\rm \langle[Fe/H]\rangle \lesssim -1.5$) galaxies using only the morphology of the horizontal branch (HB) and an estimate of the average metallicity. We calculate the ratio of blue-to-red HB stars and the mass-weighted mean ages of 27 M31 satellite galaxies that have star formation histories (SFHs) measured from Hubble Space Telescope-based color-magnitude diagrams (CMDs) that include the oldest Main Sequence Turn-off (MSTO) ages. We find a strong correlation between mean age, metallicity, and HB morphology, for stellar populations older than $\sim6$~Gyr. The correlation allows us to predict a galaxy's mean age from its HB morphology to a precision of $\lesssim 1$~Gyr. We validate our method by recovering the correct ages of Local Group galaxies that have robust MSTO-based ages and are not in our calibration sample. We also use our technique to measure the mean ages of isolated field galaxies KKR25 ($11.21^{+0.70}_{-0.65}$~Gyr) and VV124 ($11.03^{+0.73}_{-0.68}$~Gyr), which indicate that their main star formation episodes may have lasted several Gyr and support the picture that they achieved their early-type characteristics (e.g., low gas content, low star formation activity) in isolation and not through environment. Because the HB is $\sim80\times$ brighter than the oldest MSTO, our method can provide precise characteristic ages of predominantly old galaxies at distances $\sim 9$ times farther. We provide our calibrations in commonly used HST/ACS filters.