The cosmological evolution of quasar black hole masses

Virial black hole mass estimates are presented for 12 698 quasars in the redshift interval 0.1 ≤ z ≤ 2.1 , based on modelling of spectra from the Sloan Digital Sky Survey (SDSS) first data release. The black hole masses of the SDSS quasars are found to lie between ≃10 7 M ⊙ and an upper limit of ≃3 × 10 9 M ⊙ , entirely consistent with the largest black hole masses found to date in the local Universe. The estimated Eddington ratios of the broad‐line quasars (full width at half‐maximum ≥ 2000 km s −1 ) show a clear upper boundary at L bol / L Edd ≃ 1 , suggesting that the Eddington luminosity is still a relevant physical limit to the accretion rate of luminous broad‐line quasars at z ≤ 2 . By combining the black hole mass distribution of the SDSS quasars with the two degree field (2dF) quasar luminosity function, the number density of active black holes at z ≃ 2 is estimated as a function of mass. In addition, we independently estimate the local black hole mass function for early‐type galaxies using the M bh –σ and M bh – L bulge correlations. Based on the SDSS velocity dispersion function and the Two Micron All Sky Survey (2MASS) K ‐band luminosity function, both estimates are found to be consistent at the high‐mass end ( M bh ≥ 10 8 M ⊙ ) . By comparing the estimated number density of active black holes at z ≃ 2 with the local mass density of dormant black holes, we set lower limits on the quasar lifetimes and find that the majority of black holes with mass ≥10 8.5 M ⊙ are in place by ≃2.