The GALAH survey: Elemental abundances in open clusters using joint effective temperature and surface gravity photometric priors

The ability to measure precise and accurate stellar effective temperatures ($T_{\rm{eff}}$) and surface gravities ($\log(g)$) is essential in determining accurate and precise abundances of chemical elements in stars. Measuring $\log(g)$ from isochrones fitted to colour-magnitude diagrams of open clusters is significantly more accurate and precise compared to spectroscopic $\log(g)$. By determining the ranges of ages, metallicity, and extinction of isochrones that fit the colour-magnitude diagram, we constructed a joint probability distribution of $T_{\rm{eff}}$ and $\log(g)$. The joint photometric probability shows the complex correlations between $T_{\rm{eff}}$ and $\log(g)$, which depend on the evolutionary stage of the star. We show that by using this photometric prior while fitting spectra, we can acquire more precise spectroscopic stellar parameters and abundances of chemical elements. This reveals higher-order abundance trends in open clusters like traces of atomic diffusion. We used photometry and astrometry provided by the \textit{Gaia} DR3 catalogue, Padova isochrones, and Galactic Archaeology with HERMES (GALAH) DR4 spectra. We analysed the spectra of 1979 stars in nine open clusters, using MCMC to fit the spectroscopic abundances of 26 elements, $T_{\rm{eff}}$, $\log(g)$, $v_{\rm{mic}}$, and $v_{\rm{broad}}$. We found that using photometric priors improves the accuracy of abundances and $\log(g)$, which enables us to view higher-order trends of abundances caused by atomic diffusion in M67 and Ruprecht 147.