Low Masses and High Redshifts: The Evolution of the Mass-Metallicity
  Relation
  We present the first robust measurement of the high redshift mass-metallicity
(MZ) relation at 10^{8}< M/M_{\sun} < 10^{10}, obtained by stacking spectra of
83 emission-line galaxies with secure redshifts between 1.3 < z < 2.3. For
these redshifts, infrared grism spectroscopy with the Hubble Space Telescope
Wide Field Camera 3 is sensitive to the R23 metallicity diagnostic:
([OII]3726,3729 + [OIII] 4959,5007)/H\beta. Using spectra stacked in four mass
quartiles, we find a MZ relation that declines significantly with decreasing
mass, extending from 12+log(O/H) = 8.8 at M=10^{9.8} M_{\sun} to 12+log(O/H)=
8.2 at M=10^{8.2} M_{\sun}. After correcting for systematic offsets between
metallicity indicators, we compare our MZ relation to measurements from the
stacked spectra of galaxies with M>10^{9.5} M_{\sun} and z~2.3. Within the
statistical uncertainties, our MZ relation agrees with the z~2.3 result,
particularly since our somewhat higher metallicities (by around 0.1 dex) are
qualitatively consistent with the lower mean redshift z=1.76 of our sample. For
the masses probed by our data, the MZ relation shows a steep slope which is
suggestive of feedback from energy-driven winds, and a cosmological downsizing
evolution where high mass galaxies reach the local MZ relation at earlier
times. In addition, we show that our sample falls on an extrapolation of the
star-forming main sequence (the SFR-M_{*} relation) at this redshift. This
result indicates that grism emission-line selected samples do not have
preferentially high SFRs. Finally, we report no evidence for evolution of the
mass-metallicity-SFR plane; our stack-averaged measurements show excellent
agreement with the local relation.
