The Direct-Method Oxygen Abundance of Typical Dwarf Galaxies at Cosmic High-Noon

We present a Keck/MOSFIRE, rest-optical, composite spectrum of 16 typical, gravitationally-lensed, star-forming, dwarf galaxies at $1.7 \lesssim z \lesssim 2.6$ ($z_{\rm{mean}}=2.30$), all chosen independent of emission-line strength. These galaxies have a median stellar mass of $\log(M_\ast/\rm{M_\odot})_{\rm{med}} = 8.29^{+0.51}_{-0.43}$ and a median star formation rate of $\rm{SFR_{H\alpha}^{med} = 2.25^{+2.15}_{-1.26}\ M_\odot\ yr^{-1}}$. We measure the faint, electron-temperature-sensitive, [O III] $\lambda$4363 emission line at $2.5\sigma$ ($4.1\sigma$) significance when considering a bootstrapped (statistical-only) uncertainty spectrum. This yields a direct-method oxygen abundance of $12+\log(\rm{O/H})_{\rm{direct}}=7.88^{+0.25}_{-0.22}$ ($0.15^{+0.12}_{-0.06}\ \rm{Z_\odot}$). We investigate the applicability at high-$z$ of locally-calibrated, oxygen-based, strong-line metallicity relations, finding that the local reference calibrations of arXiv:1805.08224 best reproduce ($\lesssim 0.12$ dex) our composite metallicity at fixed strong-line ratio. At fixed $M_\ast$, our composite is well-represented by the $z \sim 2.3$ direct-method stellar mass$\,-\,$gas-phase metallicity relation (MZR) of arXiv:1907.00013. When comparing to predicted MZRs from the IllustrisTNG and FIRE simulations, we find excellent agreement with the FIRE MZR. Our composite is consistent with no metallicity evolution, at fixed $M_\ast$ and SFR, of the locally-defined fundamental metallicity relation. We measure the doublet ratio [O II] $\lambda$3729/[O II] $\lambda3726 = 1.56 \pm 0.32$ ($1.51 \pm 0.12$) and a corresponding electron density of $n_e = 1^{+215}_{-0}\ \rm{cm^{-3}}$ ($n_e = 1^{+74}_{-0}\ \rm{cm^{-3}}$) when considering the bootstrapped (statistical-only) error spectrum. This result suggests that lower-mass galaxies have lower densities than higher-mass galaxies at $z \sim 2$.