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We derived two semi-empirical calibrations between the metallicity of theNarrow Line Region (NLR) of type-2 Active Galactic Nuclei and the rest-frame ofthe N V$\lambda$1240/He II$\lambda1640$, C43=log[(C IV$\lambda1549$+CIII]$\lambda1909$)/HeII$\lambda1640$] and C III]$\lambda1909$/C IV$\lambda1549$emission-line intensity ratios. A metallicity-independent calibration betweenthe ionization parameter and the C III]$\lambda1909$/C IV$\lambda1549$emission-lines ratio was also derived. These calibrations were obtainedcomparing ratios of measured UV emission-line intensities, compiled from theliterature, for a sample of 77 objects (redshift $0 \: < \: z \: < \: 3.8$)with those predicted by a grid of photoionization models built with the Cloudycode. Using the derived calibrations, it was possible to show that themetallicity estimations for NLRs are lower by a factor of about 2-3 than thosefor Broad Line Regions (BLRs). Besides we confirmed the recent result of theexistence of a relation between the stellar mass of the host galaxy and its NLRmetallicity. 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 asthe ones estimated for Star Forming galaxies of similar high redshifts but forhigher masses.

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