Low redshift AGN in the Hamburg/ESO Survey: II. The active black hole
  mass function and the distribution function of Eddington ratios
  We estimated black hole masses and Eddington ratios for a well defined sample
of local (z<0.3) broad line AGN from the Hamburg/ESO Survey (HES), based on the
Hbeta line and standard recipes assuming virial equilibrium for the broad line
region. The sample represents the low-redshift AGN population over a wide range
of luminosities, from Seyfert 1 galaxies to luminous quasars. From the
distribution of black hole masses we derived the active black hole mass
function (BHMF) and the Eddington ratio distribution function (ERDF) in the
local universe, exploiting the fact that the HES has a well-defined selection
function. While the directly determined ERDF turns over around L/L_Edd ~ 0.1,
similar to what has been seen in previous analyses, we argue that this is an
artefact of the sample selection. We employed a maximum likelihood approach to
estimate the intrinsic distribution functions of black hole masses and
Eddington ratios simultaneously in an unbiased way, taking the sample selection
function fully into account. The resulting ERDF is well described by a
Schechter function, with evidence for a steady increase towards lower Eddington
ratios, qualitatively similar to what has been found for type~2 AGN from the
SDSS. Comparing our best-fit active BHMF with the mass function of inactive
black holes we obtained an estimate of the fraction of active black holes, i.e.
an estimate of the AGN duty cycle. The active fraction decreases strongly with
increasing black hole mass. A comparison with the BHMF at higher redshifts also
indicates that, at the high mass end, black holes are now in a less active
stage than at earlier cosmic epochs. Our results support the notion of
anti-hierarchical growth of black holes, and are consistent with a picture
where the most massive black holes grew at early cosmic times, whereas at
present mainly smaller mass black holes accrete at a significant rate.
