The Mass-metallicity Relation at Z 2 Accepted for Publication in Apj

We use a sample of 87 rest-frame ultraviolet-selected star-forming galaxies with mean spectroscopic redshift 〈z〉 = 2.26±0.17 to study the correlation between metallicity and stellar mass at high redshift. Using stellar masses determined from spectral energy distribution fitting to UnGRJKs (and Spitzer IRAC, for 37% of the sample) photometry, we divide the sample into six bins in stellar mass, and construct six composite Hα + [N II] spectra from all of the objects in each bin. We estimate the mean oxygen abundance in each bin from the [N II]/Hα ratio, and find a monotonic increase in metallicity with increasing stellar mass, from 12 + log(O/H) < 8.2 for galaxies with 〈M⋆〉 = 2.7 × 10 M⊙ to 12 + log(O/H) = 8.6 for galaxies with 〈M⋆〉 = 1.0 × 10 M⊙. The mass-metallicity relation at z ∼ 2 is offset from the local mass-metallicity relation by ∼ 0.3 dex, in the sense that galaxies of a given stellar mass have lower metallicity at high redshift. A corresponding metallicity-luminosity relation constructed by binning the galaxies according to rest-frame B magnitude shows no significant correlation. This lack of correlation is explained by the known large variation in the rest-frame optical mass-to-light ratio at z ∼ 2, and indicates that the correlation with stellar mass is more fundamental. We use the empirical relation between star formation rate density and gas density to estimate the gas fractions of the galaxies, finding an increase in gas fraction with decreasing stellar mass. The median gas fraction is more than two times higher than that found in local star-forming galaxies, providing a natural explanation for the lower metallicities of the z ∼ 2 galaxies. These gas fractions combined with the observed metallicities allow the estimation of the effective yield yeff as a function of stellar mass; in contrast to observations in the local universe which show a decrease in yeff with decreasing baryonic mass, we find a slight increase. Such a variation of metallicity with gas fraction is best fit by a model with supersolar yield and an outflow rate ∼ 4 times higher than the star formation rate. We conclude that the mass-metallicity relation at high redshift is driven by the increase in metallicity as the gas fraction decreases through star formation, and is likely modulated by metal loss from strong outflows in galaxies of all masses. Our ability to detect differential metal loss as a function of mass is limited by the small range of baryonic masses spanned by the galaxies in the sample, but there is no evidence for preferential loss of metals from low mass galaxies as has been suggested in the local universe. Subject headings: galaxies: abundances—galaxies: evolution—galaxies: high-redshift