Novel $z\sim~10$ auroral line measurements extend the gradual offset of the FMR deep into the first Gyr of cosmic time

Abstract: The mass assembly and chemical enrichment of the first galaxies provide key insights into their star-formation histories and the earliest stellar populations at cosmic dawn. Here we compile and utilize new, high-quality spectroscopic JWST/NIRSpec Prism observations from the JWST archive. We extend the wavelength coverage beyond the standard pipeline cutoff up to 5.5$\mu$m, enabling a detailed examination of the rest-frame optical emission-line properties for galaxies at $z\approx 10$. The improved calibration allows us to detect H$\beta$ and the [OIII]$\lambda\lambda 4959,5007$ doublet and resolve the auroral [OIII]$\lambda 4363$ line for the 11 galaxies in our sample ($z=9.3-10.0$) to obtain direct $T_e$-based metallicity measurements. We find that all galaxies show high ionisation fields and electron temperatures, with derived metallicities in the range $12+\log {\rm (O/H)} = 7.1 - 8.3$, consistent with previous strong-line diagnostics at high-z. We derive an empirical relation for $M_{\rm UV}$ and 12+log(O/H) at $z\approx 10$, useful for future higher-z studies, and show that the sample galaxies are `typical' star-forming galaxies though with relatively high specific star-formation rates and with evidence for bursty star formation. Combining the rest-frame optical line analysis and detailed UV to optical SED modelling, we determine the mass-metallicity relation and the fundamental-metallicity relation of the sample, pushing the redshift frontier of these measurements to $z=10$. These results, together with literature measurements, point to a gradually decreasing MZR at higher redshifts, with a break in the FMR at $z\approx 3$, decreasing to metallicities $\approx 3\times$ lower at $z=10$ than observed during the majority of cosmic time at $z=0-3$, likely caused by massive pristine gas inflows diluting the observed metal abundances during early galaxy assembly at cosmic dawn.