The AURORA Survey: The Mass -- Metallicity and Fundamental Metallicity Relations at $z \sim 2.3$ Based Purely on Direct $T_e$ Metallicities

Abstract: We present new constraints on the Mass -- Metallicity (MZR) and Fundamental Metallicity Relations (FMR) using a sample of 34 galaxies at $1.38\leq~z\leq~3.5$ (median $z=2.28$). These galaxies have direct $T_e$ measurements from [O\sc{iii}]4363Å~and/or [O\sc{ii}]7320,7331Å~auroral emission lines detected with \textit{JWST}/NIRSpec as part of the AURORA survey. The detection of both oxygen auroral lines allows for dual-zone direct $T_e$ measurements and expands the dynamic range in $12+\log\mathrm{(O/H)}$ (7.68 to 8.65 dex), stellar mass ($10^{8}$ to $10^{10.4}$ M$\odot$), and star-formation rate ($1$ to $100$ M$\odot$ yr$^{-1}$) compared to previous direct $T_e$ studies of the high-redshift MZR and FMR. We characterize the $z\sim2$ MZR and find a slope of $0.27\pm0.04$ and normalization of $12+\log\mathrm{(O/H)} = 8.44\pm0.04$ at $10^{10}$ M$\odot$ with an intrinsic scatter of 0.10 dex, consistent with past strong-line MZR measurements. Comparisons with $z\sim2$ predictions from six simulations reveal that none reproduce our observed MZR normalization evolution between $z\sim0$ and $z\sim2$. This discrepancy suggests current models do not fully capture the chemical enrichment and feedback processes occurring at cosmic noon. However, all 34 galaxies are on or above the star-forming main sequence such that our sample may be biased towards lower $12+\log\mathrm{(O/H)}$ if the FMR persists at $z\sim2$. Correcting for this selection effect would increase O/H by $\approx0.1$ dex at 10$^{9.3}$ M$\odot$ (the median mass of our sample) bringing our MZR into better agreement with that of \texttt{TNG}. Lastly, we find our $z\sim2.3$ sample is consistent with the $z\sim0$ FMR within 0.1 dex in O/H, indicating that the smooth secular mechanisms regulating chemical enrichment, star formation, stellar mass, and outflows were in place at cosmic noon.