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 $z\sim 0.39$ and $z\sim 0.54$. 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 $z\sim 0$ SDSS 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 average outflow that these galaxies experience over their lifetime, via the calculation of mass-loading factor. We find that the average mass-loading factor $\eta$ is a power-law function of galaxy stellar mass, $\eta \propto M_{\ast }^{-0.21\pm 0.09}$. 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.