On the Cosmological Evolution of Quasar Black-hole Masses

Virial black-hole mass estimates are presented for 12698 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 M⊙ and an upper limit of ≃ 3 × 10 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 (FWHM≥ 2000 km s) show a clear upper boundary at Lbol/LEdd ≃ 1, suggesting that the Eddington luminosity is still a relevant physical limit to the accretion rate of luminous broadline quasars at z ≤ 2. By combining the black-hole mass distribution of the SDSS quasars with the 2dF quasar luminosity function, the number density of active black holes at z ≃ 2 is estimated as a function of mass. 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 M⊙ are in place by ≃ 2.