Constraints on star formation driven galaxy winds from the mass-metallicity relation at z=0

We extend a chemical evolution model relating galaxy stellar mass and gas-phase oxygen abundance (the massmetallicity 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 similar to 0 total galaxy cold gas fractions and the massmetallicity 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 massmetallicity relation; without winds, gas-to-stellar mass ratios greater than or similar to 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 fractionstellar mass relation does not strongly affect our conclusions on how the wind efficiencies must scale with galaxy mass. Because theoretical descriptions of the mass loading factor , where is the mass outflow rate and is the star formation rate, are often cast in terms of the depth of the galaxy potential well, which is in turn linked to the host halo virial velocity vvir, we use one of the latest abundance matching analyses to describe outflow efficiencies in terms of vvir rather than stellar mass. Despite systematic uncertainties in the normalization and slope of the massmetallicity relation, we show that the metal expulsion efficiency xi(w)= (Zw/Zg)eta(w) (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 xi w >> 1 and xi w alpha v(vir)(-3) or steeper. In contrast, momentum- or energy-driven outflow models suggest that eta(w) should scale as v(vir)(-1) or v(vir)(-2), respectively, implying that the Z(w-)M(*) relation should be shallower than the Zg-M-* relation.