Precise C-N-O Abundances of Individual Galaxies in the First Billion Years from Ultra-Deep, Rest-UV-to-Optical JWST Spectroscopy

We present ultra-deep JWST/NIRSpec $R\sim 1000$ spectroscopy of nine star-forming galaxies at $z=6.0-8.3$ in the GOODS-N field, drawn from the Origins of Metal Enrichment in Galaxies at cosmic dAwn (OMEGA) survey. Paired with ancillary ultra-deep G140M observations, the G395M integrations from OMEGA yield continuous rest-frame UV-to-optical coverage and the full suite of diagnostics needed for precise characterisations and measures of the chemical abundances of these systems. Crucially, the auroral [O,{\scriptsize III}],$\lambda$4363 line is detected in every galaxy, enabling the determination of electron temperatures and direct oxygen abundances of $12+\log (\mathrm{O}\mathrm{/}\mathrm{H})=7.14-8.18$, independent of strong-line calibrations that dominate systematics at these redshifts. We couple direct oxygen abundances with measurements of rest-frame UV emission-line strengths and ratios to infer the physical properties of our sample. Most importantly, we trace the relationship between oxygen abundance and both C/O and N/O abundance ratios with high fidelity, demonstrating robustly that $z=6.0-8.3$ galaxies follow the local trend in C/O vs. O/H, and that inferences regarding N/O are sensitive to the choice of rest-frame UV (\niv] or \niii]) or optical ([\nii]) tracers. This pilot study demonstrates the power of combining ultra-deep JWST/NIRSpec $R\sim 1000$ rest-frame UV and optical spectroscopy, which now requires statistical samples to uncover the nebular properties of the full population of $z\ge 6$ star-forming galaxies.