Prospects for extending the Mass-Metallicity Relation to low mass at
  high redshift: a case study at z~1
  We report J-band MOSFIRE spectroscopy of a low-mass
(log$(M_*/M_\odot)=8.62^{+0.10}_{-0.06}$) star-forming galaxy at $z=0.997$
showing the detection of [NII] and [SII] alongside a strong H$\alpha$ line. We
derive a gas-phase metallicity of
log$(\text{O}/\text{H})=7.99^{+0.13}_{-0.23}$, placing this object in a region
of $M_* - Z$ space that is sparsely populated at this redshift. Furthermore,
many existing metallicity measurements in this $M_* - z$ regime are derived
from only [NII]/H$\alpha$ (N2), a diagnostic widely used in high-redshift
metallicity studies despite the known strong degeneracy with the ionization
parameter and resulting large systematic uncertainty. We demonstrate that even
in a regime where [NII] and [SII] are at the detection limit and the
measurement uncertainty associated with the [NII]/[SII] ratio is high (S/N~3),
the more sophisticated Dopita et al. diagnostic provides an improved constraint
compared to N2 by reducing the systematic uncertainty due to the ionization
parameter. This approach does not, however, dispel uncertainty associated with
stochastic or systematic variations in the nitrogen-to-oxygen abundance ratio.
While this approach improves upon N2, future progress in extending metallicity
studies into this low-mass regime will require larger samples to allow for
stochastic variations, as well as careful consideration of the global trends
among dwarf galaxies in all physical parameters, not just metallicity.
