Identifying AGNs from X-ray detections—II: Metallicity calibrations for the N2O2 and N2S2 diagnostics

Abstract Emission-line ratios from ions with nearly identical ionization potentials offer a robust solution to the degeneracies inherent to traditional active galactic nuclei (AGNs) metallicity diagnostics. We introduce new semi-empirical metallicity calibrations for the N2O2 and N2S2 diagnostics, explicitly designed to isolate the chemical abundance from the incident radiation field. By coupling an extensive grid of cloudy photoionization simulations directly to the intrinsic 2–10 keV X-ray luminosity (LX) and benchmarking against Seyfert 2 nuclei from the Burst Alert Telescope AGN Spectroscopic Survey (BASS), we establish robust relations valid across the metallicity regime of 8.0 ≲ 12 + log (O/H) ≲ 9.1 (0.2 ≲ Z/Z⊙ ≲ 2.6). The N2O2 and N2S2 indices trace co-spatial emitting volumes within the narrow-line regions (NLRs), enabling this framework to resolve the significant LX-driven systematic biases we previously identified in the standard N2 and O3N2 indices. While the N2O2 ratio proves to be virtually independent of nebular structural variations, the N2S2 index exhibits a subtle, yet discernible, electron density (Ne) susceptibility due to the low critical density (Nc) of the $\mathrm{[S\, \textsc {ii}]}\lambda \lambda 6716,6731$ doublet. Nevertheless, both diagnostics yield highly precise metallicity constraints with tight root-mean-square residual dispersions of ∼0.081 dex for N2O2 and ∼0.121 dex for N2S2. We propose the N2O2 and N2S2 calibrations as highly optimized, unbiased metallicity tracers for AGNs.