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 similar or equal to 10(7) M-circle dot and an upper limit of similar or equal to 3 x 10(9) M-circle dot, 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(-1)) show a clear upper boundary at L-bol/L-Edd similar or equal to 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 2dF quasar luminosity function, the number density of active black holes at z similar or equal to 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(8.5) M-circle dot are in place by similar or equal to 2.