Relative Ages of Nine Inner Milky Way Globular Clusters from Proper-motion-cleaned Color–Magnitude Diagrams*

Our picture of the age-metallicity relation for Milky Way globular clusters (MWGCs) is still highly incomplete, and the majority of MWGCs lack self-consistent age measurements. Here, we exploit deep, homogenous multi-epoch Hubble Space Telescope (HST) imaging of nine MWGCs located towards the inner Milky Way to measure their relative ages, in most cases for the first time. Our relative age measurements are designed to be directly comparable to the large set of MWGC ages presented by VandenBerg et al. (2013, V13), using identical filters, evolutionary models, and bolometric corrections, extended to the higher extinction values relevant to our target clusters. Adopting the V13 MWGC age scale, our relative age measurements imply that our target clusters are consistently very old, with a mean age of 12.9$\pm$0.4 Gyr, with the exception of the young metal-rich MWGC NGC 6342. We perform two tests to validate the precision of our methodology, and discuss the implications of our target cluster loci in the MWGC age-metallicity plane. In addition, we use our fully self-consistent bolometric corrections to assess the systematic impact of variations in the total-to-selective extinction ratio $R_{V}$ on relative age measurements.