Semi-empirical metallicity calibrations based on ultraviolet emission lines of type-2 AGNs

We derived two semi-empirical calibrations between the metallicity of the Narrow Line Region (NLR) of type-2 Active Galactic Nuclei and the rest-frame of the N V$\lambda$1240/He II$\lambda1640$, C43=log[(C IV$\lambda1549$+C III]$\lambda1909$)/HeII$\lambda1640$] and C III]$\lambda1909$/C IV$\lambda1549$ emission-line intensity ratios. A metallicity-independent calibration between the ionization parameter and the C III]$\lambda1909$/C IV$\lambda1549$ emission-lines ratio was also derived. These calibrations were obtained comparing ratios of measured UV emission-line intensities, compiled from the literature, for a sample of 77 objects (redshift $0 \: < \: z \: < \: 3.8$) with those predicted by a grid of photoionization models built with the Cloudy code. Using the derived calibrations, it was possible to show that the metallicity estimations for NLRs are lower by a factor of about 2-3 than those for Broad Line Regions (BLRs). Besides we confirmed the recent result of the existence of a relation between the stellar mass of the host galaxy and its NLR metallicity. We also derived a $M-Z$ relation for the objects in our sample at $1.6 \: < \: z \: < \: 3.8$. This relation seems to follow the same trend as the ones estimated for Star Forming galaxies of similar high redshifts but for higher masses.