oMEGACat. IX. Chemical Tagging of Omega Centauri Populations with Machine-Learning-Inferred Abundances from the MUSE Spectrograph

We present chemical abundance measurements for 7,302 red giant branch stars within the half-light radius (~5') of $ω$ Centauri ($ω$ Cen), derived from MUSE spectra using the neural network model DD-Payne. DD-Payne effectively identifies spectral features of C, N, and O for [Fe/H]>-1.0 dex; Mg for [Fe/H]>-1.5 dex; and Na, Ca, and Ba for all metallicities. By combining these measurements with previous high-resolution studies, we create the most comprehensive picture of $ω$ Cen's rich chemical evolutionary history. For the first time, we map elemental variations across the entire chromosome diagram, which is widely used to identify multiple populations. We analyze the median chemical abundance trends as functions of age and metallicity for different subpopulations. The DD-Payne measurements of [C/Fe], [N/Fe], and [O/Fe] extend literature trends to higher metallicities and show continuous abundance-metallicity relations, with [(C+N+O)/Fe] increasing steadily with [Fe/H]. [Ca/Fe] and the s-process element [Ba/Fe] also increase with metallicity across all populations. For [Ba/Fe], the chemically enhanced (P2) populations are more enriched than primordial (P1) and the intermediate (Im) populations. Furthermore, [N/Fe] correlates strongly with stellar age while [Ca/Fe] and [Ba/Fe] exhibits a weaker age dependence. Using these abundance-metallicity-age relations, we evaluate different formation scenarios of $ω$ Cen proposed in the literature. Our study demonstrates that combining MUSE with machine learning enables large-sample stellar abundance measurements in crowded cluster cores, overcoming the limitations of fiber-fed spectroscopy for studying multiple stellar populations and their evolutionary histories.