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We investigate the evolution of galaxy gas-phase metallicity (O/H) over therange $z=0-3.3$ using samples of $\sim300$ galaxies at $z\sim2.3$ and $\sim150$galaxies at $z\sim3.3$ from the MOSDEF survey. This analysis crucially utilizesdifferent metallicity calibrations at $z\sim0$ and $z>1$ to account forevolving ISM conditions. We find significant correlations between O/H andstellar mass ($M_*$) at $z\sim2.3$ and $z\sim3.3$. The low-mass power law slopeof the mass-metallicity relation is remarkably invariant over $z=0-3.3$, suchthat $\textrm{O/H}\propto M_*^{0.30}$ at all redshifts in this range. At fixed$M_*$, O/H decreases with increasing redshift as dlog(O/H)/d$z=-0.11\pm0.02$.We find no evidence that the fundamental metallicity relation between $M_*$,O/H, and star-formation rate (SFR) evolves out to $z\sim3.3$, with galaxies at$z\sim2.3-3.3$ having O/H within 0.04~dex of local galaxies matched in $M_*$and SFR on average. We employ analytic chemical evolution models to placeconstraints on the mass and metal loading factors of galactic outflows. Theefficiency of metal removal increases toward lower $M_*$ at fixed redshift, andtoward higher redshift at fixed $M_*$. These models suggest that the slope ofthe mass-metallicity relation is set by the scaling of the metal loading factorof outflows with $M_*$, not by the change in gas fraction as a function of$M_*$. The evolution toward lower O/H at fixed $M_*$ with increasing redshiftis driven by both higher gas fraction (leading to stronger dilution of ISMmetals) and higher metal removal efficiency, with models suggesting that botheffects contribute approximately equally to the observed evolution. Theseresults suggest that the processes governing the smooth baryonic growth ofgalaxies via gas flows and star formation hold in the same form over at leastthe past 12~Gyr.

The MOSDEF Survey: The Evolution of the Mass-Metallicity Relation from $z=0$ to $z\sim3.3$