Empirical derivation of the metallicity evolution with time and radius using TNG50 Milky Way and Andromeda analogues

Recent works use a linear birth metallicity gradient to estimate the evolution of the Fe/H profile in the Galactic disk over time, and infer stellar birth radii (R$_ birth $) from Fe/H and age measurements. These estimates rely on the evolution of Fe/H at the Galactic center ( Fe/H (0, tau )) and the birth metallicity gradient (nabla Fe/H over time --- quantities that are unknown and inferred under key assumptions. In this work, we use the sample of Milky Way and Andromeda analogues from the TNG50 simulation to investigate the ability to recover Fe/H (R, tau ) in a variety of galaxies. Using stellar disk particles, we tested the assumptions required in estimating R$_ birth Fe/H (0, tau ), and nabla Fe/H using recently proposed methods to understand when they are valid. We show that nabla Fe/H can be recovered in most galaxies to within 26 from the range in Fe/H across age, with better accuracy for more massive and stronger barred galaxies. We also find that the true central metallicity is unrepresentative of the genuine disk Fe/H profile; thus we propose to use a projected central metallicity instead. About half of the galaxies in our sample do not have a continuously enriching projected central metallicity, with a dilution in Fe/H correlating with mergers. Most importantly, galaxy-specific Fe/H (R, tau ) can be constrained and confirmed by requiring the R$_ birth $ distributions of mono-age, solar neighborhood populations to follow inside-out formation. We conclude that examining trends with R$_ birth $ is valid for the Milky Way disk and similarly structured galaxies, where we expect R$_ birth $ can be recovered to within 20 assuming today's measurement uncertainties in TNG50.