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We present Keck/MOSFIRE and Keck/LRIS spectroscopy of A1689-217, a lensed(magnification $\sim7.9$), star-forming (SFR $\sim$ 16 $\rm M_\odot\ yr^{-1}$),dwarf (log($M_\ast/M_\odot$) = $8.07-8.59$), Ly$\alpha$-emitter ($\rmEW_0\sim138$ A) at $z$ = 2.5918. Dwarf galaxies similar to A1689-217 are commonat high redshift and likely responsible for reionization, yet few have beenstudied with detailed spectroscopy. We report a 4.2$\sigma$ detection of theelectron-temperature-sensitive [O III]$\lambda$4363 emission line and use thisline to directly measure an oxygen abundance of 12+$\log$(O/H) = 8.06 $\pm$0.12 ($\sim1/4\ \rm Z_\odot$). A1689-217 is the lowest mass galaxy at $z>$ 2with an [O III]$\lambda$4363 detection. Using the rest-optical emission lines,we measure A1689-217's other nebular conditions including electron temperature($T_e$([O III]) $\sim$ 14,000 K), electron density ($n_e\sim$ 220 $\rmcm^{-3}$) and reddening ($E(B-V)\sim$ 0.39). We study relations betweenstrong-line ratios and direct metallicities with A1689-217 and other galaxieswith [O III]$\lambda$4363 detections at $z\sim0-3.1$, showing that thelocally-calibrated, oxygen-based, strong-line relations are consistent from$z\sim0-3.1$. We also show additional evidence that the $\rm O_{32}$ vs. $\rmR_{23}$ excitation diagram can be utilized as a redshift-invariant,direct-metallicity-based, oxygen abundance diagnostic out to $z\sim$ 3.1. Fromthis excitation diagram and the strong-line ratio $-$ metallicity plots, weobserve that the ionization parameter at fixed O/H is consistent with noredshift evolution. Although A1689-217 is metal-rich for its $M_\ast$ and SFR,we find it to be consistent within the large scatter of the low-mass end of theFundamental Metallicity Relation.

astrophysical journal/the astrophysical journal

The Detection of [O III]$\lambda$4363 in a Lensed, Dwarf Galaxy at $z$ =  2.59: Testing Metallicity Indicators and Scaling Relations at High Redshift  and Low Mass