New metallicity calibration for Seyfert 2 galaxies based on the N2O2 index

We derive a new relation between the metallicity of Seyfert 2 Active Galactic Nuclei (AGNs) and the intensity of the narrow emission-lines ratio $N2O2$=log([N II]$\lambda$6584/[O II]$\lambda$3727). The calibration of this relation was performed determining the metallicity ($Z$) of a sample of 58 AGNs through a diagram containing the observational data and the results of a grid of photoionization models obtained with the Cloudy code. We find the new $Z/Z_\odot$-$N2O2$ relation using the obtained metallicity values and the corresponding observational emission line intensities for each object of the sample. Estimations derived through the use of this new calibration indicate that narrow line regions of Seyfert 2 galaxies exhibit a large range of metallicities ($0.3 \: < \: Z/Z_{\odot} \: < \:2.0$), with a median value $Z \approx Z_{\odot}$. Regarding the possible existence of correlations between the luminosity $L(\rm H\beta$), the electron density, and the color excess E(B$-$V) with the metallicity in this kind of objects, we do not find correlations between them.