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.
