Abstract
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 $\simeq10^{7}\Msun$ and an upper limit of $\simeq 3\times 10^{9}\Msun$, 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\geq 2000 kms^{-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 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-types using the
M
bh
−σ
and
M
bh
−
L
bulge
correlations. Based on the SDSS velocity dispersion function and the 2MASS
K−
band luminosity function, both estimates are found to be consistent at the high-mass end ($M_{bh}\geq 10^{8}\Msun$). 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 $\geq 10^{8.5}\Msun$ are in place by
≃2
.