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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 λ1240/He II λ1640, C43 = log(C IV λ1549 + C IIIλ1909)/He II λ1640], and C III]λ1909/C IV λ1549 emission-line intensity ratios. A metallicity-independent calibration between the ionization parameter and the C III]λ1909/C IV λ1549 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. 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 an 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.
Dors et al. (Tue,) studied this question.