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

Context. 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, τ)) and the birth metallicity gradient (∇[Fe/H](τ)) over time – quantities that are unknown and inferred under key assumptions. Aims. 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, τ) in a variety of galaxies. Methods. Using stellar disk particles, we tested the assumptions required in estimating R_birth, [Fe/H](0, τ), and ∇[Fe/H](τ) using recently proposed methods to understand when they are valid. Results. We show that ∇[Fe/H](τ) 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, τ) can be constrained and confirmed by requiring the R_birth distributions of mono-age, solar neighborhood populations to follow inside-out formation. Conclusions. 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.