Chemical abundances of Seyfert 2 AGNs $-$II. N2 metallicity calibration based on SDSS

We present a semi-empirical calibration between the metallicity ($Z$) of Seyfert 2 Active Galactic Nuclei and the $N2$=log([N II]$\lambda$6584/H$\alpha$) emission-line intensity ratio. This calibration was derived through the [O III]$\lambda$5007/[O II]$\lambda$3727 versus $N2$ diagram containing observational data and photoionization model results obtained with the Cloudy code. The observational sample consists of 463 confirmed Seyfert 2 nuclei (redshift $z < 0.4$) taken from the Sloan Digital Sky Survey DR7 dataset. The obtained $Z$-$N2$ relation is valid for the range $0.3 < (Z/Z_{\odot}) < 2.0$ which corresponds to $-0.7 < \: (N2) < 0.6$. The effects of varying the ionization parameter ($U$), electron density and the slope of the spectral energy distribution on the $Z$ estimations are of the order of the uncertainty produced by the error measurements of $N2$. This result indicates the large reliability of our $Z-N2$ calibration. A relation between $U$ and the [O III]/[O II] line ratio, almost independent of other nebular parameter, was obtained.