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An empirical prediction for stellar metallicity distributions in nearby galaxies

We combine star-formation histories derived from observations of high redshift galaxies with measurements of the z~0 relation between gas-phase metallicity, stellar mass, and star formation rate to make an explicit and completely empirical connection between near-field and distant galaxy observations. Our approach relies on two basic assumptions: 1) galaxies' average paths through time in stellar mass vs. star formation rate space are represented by a family of smooth functions that are determined by the galaxies' final stellar mass, and 2) galaxies grow and become enriched with heavy elements such that they always evolve along the mass--metallicity--star formation rate relation. By integrating over these paths, we can track the chemical evolution of stars in galaxies in a model independent way, without the need for explicit assumptions about gas inflow, outflow, or star formation efficiency. Using this approach, we present predictions of stellar metallicity (i.e., O/H) distribution functions for present day star-forming galaxies of different stellar masses and the evolution of the alpha-element stellar metallicity-mass relation since z~1. The metallicity distribution functions are fairly well described as Gaussians, truncated at high metallicity, with power-law tails to low metallicity. We find that the stellar metallicity distribution for Milky Way mass galaxies is in reasonable agreement with observations for our Galaxy, and that the predicted stellar mass vs. mean stellar metallicity relation at z=0 agrees quite well with results derived from galaxy surveys. This validates the assumptions that are implicit in our simple approach. Upcoming observations will further test these assumptions and their range of validity, by measuring the mean stellar mass-metallicity relation up to z~1, and by measuring the stellar metallicity distributions over a range of galaxy masses.