oMEGACat IV: Constraining Ages of Omega Centauri sub-giant branch stars with HST and MUSE

We present age estimates for over 8100 sub-giant branch (SGB) stars in Omega Centauri ($\omega$ Cen) to study its star formation history. Our large data set, which combines multi-wavelength HST photometry with MUSE metallicities, provides an unprecedented opportunity to measure individual stellar ages. We do this by fitting each star's photometry and metallicity with theoretical isochrones, that are embedded with an empirical [C+N+O]-[Fe/H] relation specifically for $\omega$ Cen. The bulk of the stars have ages between 13 and 10 Gyr, with the mean stellar age being 12.08$\pm$0.01 Gyrs and the median age uncertainty being 0.68 Gyrs. From these ages we construct the most complete age-metallicity relation (AMR) for $\omega$ Cen to date. We find that the mean age of stars decreases with increasing metallicity and find two distinct streams in the age-metallicity plane, hinting at different star formation pathways. We derive an intrinsic spread in the ages of 0.75$\pm$0.01 Gyr for the whole cluster, with the age spread showing a clear increase with metallicity. We verify the robustness of our age estimations by varying isochrone parameters and constraining our systematics. We find the C+N+O relation to be the most critical consideration for constraining the AMR. We also present the SGB chromosome map with age information. In the future, these stellar ages could be combined with chemical abundances to study age differences in subpopulations, and uncover the chemical evolution history of this massive nuclear star cluster.