On the Age Calibration of Open Clusters using Red Clump Stars

In this study, we extend the dust-independent Hatzidimitriou (1991) relation between cluster age and $d_{B-R}$ color difference between the red giant branch (RGB) and red clump to younger cluster ages. We perform membership analysis on fourteen galactic open clusters using Gaia DR3 astrometry, then compute the difference in color of the RGB and red clump $d_{B-R}$ using Gaia photometry. We also compute $d_{B-R}$ for five fields surrounding Small Magellanic Cloud (SMC) clusters. We find that the trend derived from older clusters does not extrapolate to younger ages and becomes double-valued. We confirm that $d_{B-R}$ is independent of metallicity. Current stellar evolutionary isochrones do not quantitatively reproduce the trend and furthermore predict an increased color gap with a decrease in metallicity that is not echoed in the data. Integrated light models based on current isochrones exaggerate the color change over the $-0.5 <$ [Fe/H] $< 0$ interval at the few-percent level.