# 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

## TL;DR

This study reports the first detection of the [O III]$\lambda$4363 emission line in a low-mass, high-redshift galaxy, enabling direct metallicity measurement and testing the applicability of local metallicity diagnostics at $z$=2.59.

## Contribution

It provides the lowest-mass galaxy at $z>2$ with a direct oxygen abundance measurement and validates the use of local strong-line metallicity relations and excitation diagnostics at high redshift.

## Key findings

- Detected [O III]$\lambda$4363 line at 4.2$\sigma$ in a $z$=2.59 galaxy
- Confirmed local strong-line metallicity calibrations are valid up to $z$=3.1
- Showed the $
m O_{32}$ vs. $
m R_{23}$ diagram as a redshift-invariant metallicity diagnostic

## Abstract

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 ($\rm EW_0\sim138$ A) at $z$ = 2.5918. Dwarf galaxies similar to A1689-217 are common at high redshift and likely responsible for reionization, yet few have been studied with detailed spectroscopy. We report a 4.2$\sigma$ detection of the electron-temperature-sensitive [O III]$\lambda$4363 emission line and use this line to directly measure an oxygen abundance of 12+$\log$(O/H) = 8.06 $\pm$ 0.12 ($\sim1/4\ \rm Z_\odot$). A1689-217 is the lowest mass galaxy at $z>$ 2 with 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 $\rm cm^{-3}$) and reddening ($E(B-V)\sim$ 0.39). We study relations between strong-line ratios and direct metallicities with A1689-217 and other galaxies with [O III]$\lambda$4363 detections at $z\sim0-3.1$, showing that the locally-calibrated, oxygen-based, strong-line relations are consistent from $z\sim0-3.1$. We also show additional evidence that the $\rm O_{32}$ vs. $\rm R_{23}$ excitation diagram can be utilized as a redshift-invariant, direct-metallicity-based, oxygen abundance diagnostic out to $z\sim$ 3.1. From this excitation diagram and the strong-line ratio $-$ metallicity plots, we observe that the ionization parameter at fixed O/H is consistent with no redshift 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 the Fundamental Metallicity Relation.