The Electron-Temperature-Based Oxygen Abundance of Dwarf Galaxies at the Peak of Cosmic Star Formation

At $z \sim 2$, where cosmic star formation peaks, little is known about the galaxy stellar mass ($M_\ast$), star formation rate (SFR), and oxygen abundance (or gas-phase metallicity; O/H) parameter space in which typical dwarf galaxies lie ($M_\ast \leqslant 10^9\ \rm{M_\odot}$). This is due to current technological limitations as well as uncertainty about the accuracy of indirectly-measured metallicities at high-$z$. Consequently, our models and understanding of galaxy formation and evolution are largely unconstrained in this mass regime.Here we present a sample, one of the first of its kind, of 16 representative, star-forming, gravitationally-lensed dwarf galaxies at $1.7 \lesssim z \lesssim 2.6$ ($z_{\rm{mean}}=2.30$) with a median $M_\ast$ of log($M_\ast$/$\rm{M_\odot}$)$_{\rm{med}}$ = 8.29 and a median SFR of $\rm{SFR_{H\alpha}^{med} = 2.25\ M_\odot\ yr^{-1}}$. Sample spectroscopy and photometry were taken with the Keck Multi-Object Spectrometer For InfraRed Exploration and the \textit{Hubble Space Telescope}, respectively. Study of these galaxies is done largely via a composite emission-line spectrum of the sample, from which we detect the faint, electron-temperature-sensitive, auroral emission line, [O III] $\lambda$4363, with which we directly estimate metallicity. Within this sample, we also independently study the $z=2.59$ galaxy, A1689-217, which yields a rare, individual detection of [O III] $\lambda$4363 at high-$z$. In assessing indirect, locally-calibrated, strong-line metallicity relations at high-$z$, we find certain strong-line ratios are insensitive to metallicities around those we directly measure. Other indices show greater utility, but have metallicity calibrations that vary in applicability based on the high-$z$ and calibration samples considered. We do show evidence supporting the creation of a redshift-invariant, empirical metallicity relation within the $\rm{O_{32}}$ vs. $\rm{R_{23}}$ excitation diagram. Our stacked sample shows excellent agreement with the direct-method $M_\ast\,-\,$O/H relation (MZR) of Sanders et al. (2020) and disagrees with other high-$z$ MZRs displaying significantly shallower slopes. We also find excellent agreement with the MZR from the Feedback In Realistic Environments simulations after recalculating our stellar masses, which likely underestimate contributions from older stellar populations under our fiducial assumptions. Finally, we find consistency with a redshift-invariant fundamental metallicity relation (FMR), though note a large scatter in dwarf galaxy metallicities