Accounting for selection effects in the BH-bulge relations: No evidence for cosmological evolution

The redshift evolution of the black hole - bulge relations is an essential observational constraint for models of black hole - galaxy coevolution. In addition to the observational challenges for these studies, conclusions are complicated by the influence of selection effects. We demonstrate that there is presently no statistical significant evidence for cosmological evolution in the black hole-bulge relations, once these selection effects are taken into account and corrected for. We present a fitting method, based on the bivariate distribution of black hole mass and galaxy property, that accounts for the selection function in the fitting and is therefore able to recover the intrinsic black hole - bulge relation unbiased. While prior knowledge is restricted to a minimum, we at least require knowledge of either the sample selection function and the mass dependence of the active fraction, or the spheroid distribution function and the intrinsic scatter in the black hole - bulge relation. We employed our fitting routine to existing studies of the black hole-bulge relation at z~1.5 and z~6, using our current best knowledge of the distribution functions. There is no statistical significant evidence for positive evolution in the MBH-M* ratio out to z~2. At z~6 the current constraints are less strong, but we demonstrate that the large observed apparent offset from the local black hole-bulge relation at z~6 is fully consistent with no intrinsic offset. The method outlined here provides a tool to obtain more reliable constraints on black hole - galaxy co-evolution in the future.Comment: 13 pages, 8 figures, published in MNRA

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.Comment: 19 pages, 15 figures, accepted for publication in A&