The mass-metallicity relation of SDSS quasars

Active galactic nuclei (AGNs) are characterized by a clear correlation between luminosity and metallicity (LAGN-ZAGN relation). The origin of this correlation is not clear. It may result from a relation between the black hole mass (MBH) and metallicity, or from a relation between the accretion rate (L/LEdd) and metallicity. To investigate the origin of the LAGN-ZAGN 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 constructed composite spectra of 33 subsamples in intervals of both MBH and L/LEdd. From these composite spectra we measured emission-line flux ratios that are sensitive to the metallicity of the broad line region (BLR): specifically, N vλ1240/C ivλ1549, N vλ1240/He iiλ1640, (Si ivλ1398+O iv]λ1402)/C ivλ1549, and Al iiiλ1857/C ivλ1549. We find that there is a significant correlation between MBH and ZBLR as inferred from all four metallicity-sensitive emission-line flux ratios. This result strongly suggests that the observed LAGN-ZAGN relation is mostly a consequence of the MBH-ZAGN relation. The relation between MBH and ZBLR is likely a consequence of both the MBH-Mbul relation and of the mass-metallicity relation in the host galaxy. We also find that L/LEdd correlates with the emission line flux ratios involving N v (more specifically, N v/C iv and N v/He ii), while it does not correlate with the other two metallicity sensitive emission line flux ratios, i.e., (Si iv+O iv])/C iv and Al iii/C iv. These correlations indicate that the emission-line flux ratios involving N v depend on both the metallicity and relative abundance of nitrogen. We suggest that the relation between L/LEdd 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 108 years, which is the timescale required for the nitrogen enrichment.