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We estimated black hole masses and Eddington ratios for a well defined sampleof local (z<0.3) broad line AGN from the Hamburg/ESO Survey (HES), based on theHbeta line and standard recipes assuming virial equilibrium for the broad lineregion. The sample represents the low-redshift AGN population over a wide rangeof luminosities, from Seyfert 1 galaxies to luminous quasars. From thedistribution of black hole masses we derived the active black hole massfunction (BHMF) and the Eddington ratio distribution function (ERDF) in thelocal universe, exploiting the fact that the HES has a well-defined selectionfunction. 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 anartefact of the sample selection. We employed a maximum likelihood approach toestimate the intrinsic distribution functions of black hole masses andEddington ratios simultaneously in an unbiased way, taking the sample selectionfunction fully into account. The resulting ERDF is well described by aSchechter function, with evidence for a steady increase towards lower Eddingtonratios, qualitatively similar to what has been found for type~2 AGN from theSDSS. Comparing our best-fit active BHMF with the mass function of inactiveblack 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 withincreasing black hole mass. A comparison with the BHMF at higher redshifts alsoindicates that, at the high mass end, black holes are now in a less activestage than at earlier cosmic epochs. Our results support the notion ofanti-hierarchical growth of black holes, and are consistent with a picturewhere the most massive black holes grew at early cosmic times, whereas atpresent mainly smaller mass black holes accrete at a significant rate.

Low redshift AGN in the Hamburg/ESO Survey: II. The active black hole mass function and the distribution function of Eddington ratios