The cosmological evolution of quasar black hole masses

Abstract

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 ≃107 M⊙ and an upper limit of ≃3 × 109 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 Lbol/LEdd≃ 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 Mbh–σ and Mbh–Lbulge 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 (Mbh≥ 108 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 ≥108.5 M⊙ are in place by ≃2.