We extend a chemical evolution model relating galaxy stellar mass and
gas-phase oxygen abundance (the mass-metallicity relation) to explicitly
consider the mass-dependence of galaxy gas fractions and outflows. Using
empirically derived scalings of galaxy mass with halo virial velocity in
conjunction with the most recent observations of z~0 total galaxy cold gas
fractions and the mass-metallicity relation, we place stringent global
constraints on the magnitude and scaling of the efficiency with which star
forming galaxies expel metals. We demonstrate that under the assumptions that
metal accretion is negligible and the stellar initial mass function does not
vary, efficient outflows are required to reproduce the mass-metallicity
relation; without winds, gas-to-stellar mass ratios >~ 0.3 dex higher than
observed are needed. Moreover, z=0 gas fractions are low enough that while they
have some effect on the magnitude of outflows required, the slope of the gas
fraction--stellar mass relation does not strongly affect our conclusions on how
the wind efficiencies must scale with galaxy mass. Despite systematic
uncertainties in the normalization and slope of the mass-metallicity relation,
we show that the metal expulsion efficiency zetaw=(Zw/Zg)etaw (where Zw is the
wind metallicitiy and Zg is the interstellar medium metallicity) must be both
high and scale steeply with mass. Specifically, we show that zetaw >> 1 and
zetaw proportional to vvir^-3 or steeper. In contrast, momentum- or
energy-driven outflow models suggest that etaw should scale as vvir^-1 or
vvir^-2, respectively, implying that the Zw-Mstar relation should be shallower
than the Zg-Mstar relation. [abridged]Comment: MNRAS, in press; 22 pages, 13 figures. Several structural changes,
including a new section on varying the IMF (yield
