Updated indicators of oxygen metallicity for high-$z$ galaxies

Abstract: Recent work has demonstrated that widely used strong-line oxygen abundance indicators, such as O3N2, $\rm R23$, and $\widehat{\rm R}$, suffer from large uncertainties when applied to high-redshift galaxies. We show that this loss of precision primarily arises because, at fixed \Oabund, galaxies span a wide dynamic range in ionization parameter and nitrogen enrichment. Here we develop updated indicators that explicitly incorporate both effects via the proxies O32 and N2O2. We define ${\rm R}{\rm u}\equiv \rm R23+α_1 O32+α_2 N2O2$, $\widehat{\rm R}{\rm u}\equiv \rm \widehat{R}+β1 O32+β_2 N2O2$, and ${\rm O}{\rm u}\equiv \rm O3N2+γ1 O32+γ_2 N2O2$, and calibrate \Oabund~as low-order polynomials in each composite indicator. Applied to a JWST sample with $T{\rm e}$-method abundances, the updated indicators substantially tighten the correlations with \Oabund, boosting adjusted coefficients of determination from $\mathbb{R}^2\lesssim 0$ (classical indicators) to $\mathbb{R}^2\gtrsim 0.5$ for the full sample and to $\sim 0.7$ at $z>2$. The residuals reveal a redshift evolution in the mapping between \Oabund, strong lines, ionization, and nitrogen enrichment, with a pivotal turning point near the cosmic noon ($z\sim 2$). Our calibrations provide a practical, physically grounded path to precise metallicity measurements in the JWST era and a firmer basis for quantifying early chemical enrichment and feedback.