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 ~=10⁷ M_solar and an upper limit of ~=3 × 10⁹ M_solar, 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>= 10⁸ M_solar). 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_solar are in place by ~=2.