Evolution of the Stellar Mass–Metallicity Relation. II. Constraints on Galactic Outflows from the Mg Abundances of Quiescent Galaxies

We present the stellar mass–[Fe/H] and mass–[Mg/H] relation of quiescent galaxies in two galaxy clusters at z ~ 0.39 and z ~ 0.54. We derive the age, [Fe/H], and [Mg/Fe] for each individual galaxy using a full-spectrum fitting technique. By comparing with the relations for z ~ 0 Sloan Digital Sky Survey galaxies, we confirm our previous finding that the mass–[Fe/H] relation evolves with redshift. The mass–[Fe/H] relation at higher redshift has lower normalization and possibly steeper slope. However, based on our sample, the mass–[Mg/H] relation does not evolve over the observed redshift range. We use a simple analytic chemical evolution model to constrain the average outflow that these galaxies experience over their lifetime, via the calculation of mass-loading factor. We find that the average mass-loading factor η is a power-law function of galaxy stellar mass, η ∝ M*^(−0.21±0.09). The measured mass-loading factors are consistent with the results of other observational methods for outflow measurements and with the predictions where outflow is caused by star formation feedback in turbulent disks.