Identifying AGNs from X-ray detections---I: Metallicity calibrations in AGNs with X-ray luminosity as the primary input parameter

Abstract

We present the first semi-empirical strong-line calibrations to determine metallicity in Active Galactic Nuclei (AGNs) that use the directly observable X-ray luminosity ($Ł_{\rm X}$) instead of the dimensionless ionization parameter ($U$). The calibrations are derived from an extensive grid of photoionization models computed with the {\sc Cloudy} code, which are compared with observational data of Seyfert nuclei from the Burst Alert Telescope (BAT) AGN Spectroscopic Survey (BASS). In this first paper, we develop new calibrations for two key optical metallicity diagnostics based on the $N2$ and $O3N2$ indices, which are valid in a metallicity range of $8.0 \lesssim \logOH \lesssim 9.1\, {\rm or}\, 0.2 \lesssim (Z/Z_{\odot}) \lesssim 2.6$, with precision of $1σ\approx 0.22$ dex ($N2$) and $\approx 0.20$ dex ($O3N2$). We systematically investigate the influence of the AGN spectral index $(\aox)$, narrow-line region (NLR) gas density (\Ne), the characteristic peak temperature of the Big Blue Bump $(T_{\rm BB})$, and $Ł_{\rm X}$. We find a strong, opposing secondary dependence on $Ł_{\rm X}$ for both indices. We demonstrate that neglecting this parameter overlooks systematic offsets intrinsic to the diagnostics, leading to metallicity errors of up to $\sim 1.0$ dex, particularly for the least and most luminous sources. This framework offers a more precise characterization of chemical enrichment in the NLRs of AGNs by leveraging their intrinsic X-ray emission to mitigate these systematic biases.

Figures (8)

• Figure 1: Electron density distribution derived from our observational sample. The blue dashed line represents densities, $N_\mathrm{e}(\text{[S~ii]})$, derived from the [S ii]$\lambda\lambda6716,6731$ doublet (557 objects; median $\approx 580 \pm 413\,\mathrm{cm}^{-3}$). The red dash-dotted line corresponds to densities, $N_\mathrm{e}(\text{[Ar~iv]})$, from the [Ar iv]$\lambda\lambda4711,4740$ doublet (248 objects, median $\approx 3467\pm 864\,\mathrm{cm}^{-3}$). Vertical lines indicate the median values. The $p$--$value$ from the Kolmogorov-Smirnov (KS) test (p_KS) is $4.55 \times 10^{-134}$, confirming that the distributions are statistically distinct and trace stratified NLRs in the AGNs.
• Figure 2: Logarithmic residuals of derived gas-phase metallicity ($\Delta \log Z$ in dex) resulting from variations in the inner radius ($r_{\mathrm{in}}$) of the photoionized cloud for the $N2$ (left panel) and $O3N2$ (right panel) diagnostics. The residuals are plotted as a function of the baseline metallicity derivation ($r_{\mathrm{in}} = 0.3$ pc). To evaluate the extreme spatial boundaries of the GRAVITY2024 sample, the derived metallicities were analytically recalculated assuming fixed constant radii of $r_{\mathrm{in}} = 0.028$ pc (blue squares) and $r_{\mathrm{in}} = 1.33$ pc (red triangles). The green circles represent the scenario where $r_{\mathrm{in}}$ is continuously coupled to the AGN luminosity (i.e. $R \propto L^{0.5}$), effectively evaluating the grid at a constant ionization parameter ($U$) corresponding to a pivot luminosity of $L_{\mathrm{X}} = 10^{43.5}$ erg s$^{-1}$. The dashed horizontal line indicates zero residual. The mean absolute deviations $\left(\overline{\Delta}\right)$ provided in the legend demonstrate that incorporating the $R \propto L^{0.5}$ correlation significantly reduces systematic bias across the sample compared to assuming unscaled extreme spatial boundaries.
• Figure 3: Diagnostic diagram of log([O iii]$\lambda 5007$/[O ii]$\lambda 3727$) versus log([N ii]$\lambda6584$/H$\alpha$) from the models and the observational sample of Seyfert 2s. Each panel represents a grid of photoionization models calculated for specific values of the ionizing spectral index ($\alpha_{\mathrm{ox}}$) and logarithm of electron density ($N_{\rm e}$ [cm$^{-3}$]), as indicated in the top-left corner of each subplot. The rows correspond to $\alpha_{\mathrm{ox}}$ values of -2.0, -1.7, -1.4, -1.1, and -0.8 (from bottom to top), while columns correspond to $N_{\rm e}$ values from $\rm 10^2\, to \, 10^4\,cm^{-3}$ (top to bottom). All models assume a blackbody temperature $T_{\rm BB} = 100\,000 {\rm K}$ for the ionizing continuum. Within each panel, solid lines represent models of constant metallicity ($Z/\, \mathrm{Z}_{\odot} = \rm 0.20, 0.50, 0.75, 1.00, and\, 2.60$, with colors indicated in the main legend at the top of the figure), varying with $\log L_{\mathrm{X}}$. Dashed lines represent models of constant X-ray luminosity ($\log L_{\mathrm{X}} = 38, 40, 42, 44, 46, 48$, with colors also indicated in the main legend), varying with metallicity. The red filled squares show the observational data from the BASS DR2. In the bottom-right corner of each subplot, two coverage percentages are provided, each associated with a total object count ($N_{\rm L}$ or $N_{\rm G}$): Percentages indicate the coverage fraction, defined as the proportion of the plotted data points ($N_{\rm L}$) and the total BPT-selected AGN sample ($N_{\rm G}$) that fall within the boundaries of the model grid (see § \ref{['bass_data']}). Note that while the total sample sizes $N_{\rm L}$ and $N_{\rm G}$ (denominators) remain constant across all panels, the coverage percentages vary depending on the specific model parameters ($N_{\rm e}$ and $\alpha_{\mathrm{ox}}$) used.
• Figure 4: Same as Figure \ref{['fig_2']} but for the diagnostic diagram of log([O iii]$\lambda5007$/[O ii]$\lambda 3727$) versus log([O iii]$\lambda 5007$/ [N ii]$\lambda6584$).
• Figure 5: Metallicity calibrations based on the $N2$ and $O3N2$ strong-line indices, derived from interpolating photoionization model results onto the observed BASS DR2 data. Left column:$Z/Z_{\odot}$ as a function of the log([N ii]$\lambda6584$/H$\alpha$) ratio ($N2$). Right column:$Z/Z_{\odot}$ as a function of the log([O iii]$\lambda 5007$/[N ii]$\lambda6584$) ratio ($O3N2$). In both columns, each panel explores the effect of a different model parameter on the estimated metallicity. The colored markers represent the interpolated metallicity estimates ($Z_{\rm est}$) obtained for each observational data point from a subset of the model grid, while the lines are the corresponding polynomial fits (Equations \ref{['cal_1']} and \ref{['cal_2']}). The dashed black line in each panel represents the global fit using all model data. From top to bottom, the rows vary the $\alpha_{\mathrm{ox}}$, $N_{\rm e}$ in cm$^{-3}$, $\log L_{\mathrm{X}}$, and the $T_ {\rm BB}$ in K. The coefficients for each fit are presented in Table \ref{['table_2']}.