We use cosmological hydrodynamic simulations with enriched galactic
outflows to compare predictions for the galaxy mass-metallicity (M* − Z)
with observations at z ≈ 2 from Erb et al. (2006). With no outflows
included galaxies are over-enriched, indicating that outflows are required
not only to suppress star formation and enrich the IGM but also to lower
galaxy metal content. The observed M* − Z slope is matched both in
our model without winds as well as in our favored outflow model where the
outflow velocity scales as the escape velocity, but is too steep in
a model with constant outflow speeds. If outflows are too widespread
at early times, the IGM out of which smaller galaxies form can become
pre-polluted, resulting in a low-mass flattening of the M* − Z relation
that is inconsistent with data. Remarkably, the same momentum-driven
wind model that provides the best agreement with IGM enrichment data
also yields the best agreement with the z ≈ 2 M* − Z relation,
showing the proper outflow scaling and strength to match the observed
slope and amplitude. In this model, the M* − Z relation evolves slowly
from z = 6 → 2; an (admittedly uncertain) extrapolation to z = 0
broadly matches local M* − Z observations. Overall, the M* − Z
relation provides critical constraints on galactic outflow processes
during the heyday of star formation in the Universe.