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We present the stellar mass-[Fe/H] and mass-[Mg/H] relation of quiescentgalaxies in two galaxy clusters at $z\sim0.39$ and $z\sim0.54$. We derive theage, [Fe/H], and [Mg/Fe] for each individual galaxy using a full-spectrumfitting technique. By comparing with the relations for $z\sim0$ SDSS galaxies,we confirm our previous finding that the mass-[Fe/H] relation evolves withredshift. The mass-[Fe/H] relation at higher redshift has lower normalizationand possibly steeper slope. However, based on our sample, the mass-[Mg/H]relation does not evolve over the observed redshift range. We use a simpleanalytic chemical evolution model to constrain average outflow that thesegalaxies experience over their lifetime, via the calculation of mass-loadingfactor. We find that the average mass-loading factor $\eta$ is a power-lawfunction of galaxy stellar mass, $\eta \propto M_*^{-0.21\pm0.09}$. Themeasured mass-loading factors are consistent with the results of otherobservational methods for outflow measurements and with the predictions whereoutflow is caused by star formation feedback in turbulent disks.

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