Identifying AGNs from X-ray detections$-$II: Metallicity calibrations for the ${\mathrm{N}}_2{\mathrm{O}}_2$ and ${\mathrm{N}}_2{\mathrm{S}}_2$ 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 ${\mathrm{N}}_2{\mathrm{O}}_2$ and ${\mathrm{N}}_2{\mathrm{S}}_2$ 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$-$10 keV X-ray luminosity ($L_{\mathrm{X}}$) 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 $8.0\lesssim 12+\log (O/H)\lesssim 9.1$ ($0.2\lesssim Z/Z_{\odot }\lesssim 2.6$). The ${\mathrm{N}}_2{\mathrm{O}}_2$ and ${\mathrm{N}}_2{\mathrm{S}}_2$ indices trace co-spatial emitting volumes within the narrow-line regions (NLRs), enabling this framework to resolve the significant $L_{\mathrm{X}}$-driven systematic biases we previously identified in the standard ${\mathrm{N}}_2$ and ${\mathrm{N}}_2{\mathrm{O}}_3$ indices. While the ${\mathrm{N}}_2{\mathrm{O}}_2$ ratio proves to be virtually independent of nebular structural variations, the ${\mathrm{N}}_2{\mathrm{S}}_2$ index exhibits a subtle, yet discernible, electron density ($N_{\mathrm{e}}$) susceptibility due to the low critical density ($N_{\mathrm{c}}$) of the [S II]$\lambda \lambda 6716,6731$ doublet. Nevertheless, both diagnostics yield highly precise metallicity constraints with tight root-mean-square residual dispersions of $\sim 0.081$ dex for ${\mathrm{N}}_2{\mathrm{O}}_2$ and $\sim 0.121$ dex for ${\mathrm{N}}_2{\mathrm{S}}_2$. We propose the ${\mathrm{N}}_2{\mathrm{O}}_2$ and ${\mathrm{N}}_2{\mathrm{S}}_2$ calibrations as highly optimized, unbiased metallicity tracers for AGNs.

18 pages, 8 figures, accepted for publication by MNRAS; DOI: 10.1093/mnras/stag1563