The Metal Abundances across Cosmic Time ($\mathcal{MACT}$) Survey. II.
  Evolution of the Mass-Metallicity Relation over 8 Billion Years, using
  [OIII]$\lambda$4363\AA-based Metallicities
  We present the first results from MMT and Keck spectroscopy for a large
sample of $0.1\leq z\leq1$ emission-line galaxies selected from our narrow-band
imaging in the Subaru Deep Field. We measured the weak [OIII]$\lambda$4363
emission line for 164 galaxies (66 with at least 3$\sigma$ detections, and 98
with significant upper limits). The strength of this line is set by the
electron temperature for the ionized gas. Because the gas temperature is
regulated by the metal content, the gas-phase oxygen abundance is inversely
correlated with [OIII]$\lambda$4363 line strength. Our temperature-based
metallicity study is the first to span $\approx$8 Gyr of cosmic time and
$\approx$3 dex in stellar mass for low-mass galaxies, $\log{\left(M_{\rm
star}/M_{\rm sun}\right)}\approx6.0-9.0$. Using extensive multi-wavelength
photometry, we measure the evolution of the stellar mass--gas metallicity
relation and its dependence on dust-corrected star formation rate (SFR). The
latter is obtained from high signal-to-noise Balmer emission-line measurements.
Our mass-metallicity relation is consistent with Andrews & Martini at
$z\leq0.3$, and evolves toward lower abundances at a given stellar mass,
$\log{({\rm O/H})}\propto(1+z)^{-2.32^{+0.52}_{-0.26}}$. We find that galaxies
with lower metallicities have higher SFRs at a given stellar mass and redshift,
although the scatter is large ($\approx$0.3 dex), and the trend is weaker than
seen in local studies. We also compare our mass--metallicity relation against
predictions from high-resolution galaxy formation simulations, and find good
agreement with models that adopt energy- and momentum-driven stellar feedback.
We have identified 16 extremely metal-poor galaxies with abundances less than a
tenth of solar; our most metal-poor galaxy at $z\approx0.84$ is similar to I Zw
18.
