The mass-metallicity relation of SDSS quasars
  Active galactic nuclei (AGNs) are characterized by a clear correlation
between luminosity and metallicity (L_AGN-Z_AGN relation). The origin of this
correlation is not clear. It may result from a relation between the black hole
mass (M_BH) and metallicity, or from a relation between the accretion rate
(L/L_Edd) and metallicity. To investigate the origin of the L_AGN-Z_AGN
relation, we use optical spectra of 2383 quasars at 2.3 < z < 3.0 from the
Sloan Digital Sky Survey. By using this data set, we have constructed composite
spectra of 33 subsamples in intervals of both M_BH and L/L_Edd. From these
composite spectra we measure emission-line flux ratios that are sensitive to
the metallicity of the broad line region (BLR); specifically, NV/CIV, NV/HeII,
(SiIV+OIV])/CIV, and AlIII/CIV. We find that there is a significant correlation
between M_BH and Z_BLR as inferred from all four metallicity-sensitive
emission-line flux ratios. This result strongly suggests that the observed
L_AGN-Z_AGN relation is mostly a consequence of the M_BH-Z_AGN relation. The
relation between M_BH and Z_BLR is likely a consequence of both the M_BH-M_bul
relation and of the mass-metallicity relation in the host galaxy. We also find
that L/L_Edd correlates with the emission line flux ratios involving NV (more
specifically, NV/CIV and NV/HeII), while it does not correlate with the other
two metallicity sensitive emission line flux ratios, i.e., (SiIV+OIV])/CIV and
AlIII/CIV. These correlations indicate that the emission-line flux ratios
involving NV depend on both metallicity and relative abundance of nitrogen. We
suggest that the relation between L/L_Edd and those line ratios involving
nitrogen, is caused by a delay of the black hole accretion rate relative to the
onset of nuclear star formation of about 10^8 years, which is the timescale
required for the nitrogen enrichment.
