Selection effects in the black hole-bulge relation and its evolution

Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: aschulze@aip.de

Received: 24 June 2011
Accepted: 9 September 2011

Abstract

We present an investigation of sample selection effects that influence the observed black hole-bulge relations and its evolution with redshift. We provide a common framework in which all kinds of selection effects on the M_•-bulge relations can be investigated, but our main emphasis is on the consequences of using broad-line AGN with virial estimates of black hole masses and their host galaxies to search for evolution in the BH-bulge relation. We identified relevant sources of bias that were not discussed in the literature so far. A particularly important effect is caused by the fact that the active fraction among SMBHs varies considerably with BH mass, in the sense that high-mass BHs are less likely to be active than lower mass ones. In the connection with intrinsic scatter of the BH-bulge relation this effect implies a bias towards a low BH mass at given bulge property. This effect adds to the bias caused by working with luminosity or flux limited samples that were already discussed by others. A quantitative prediction of these biases requires (i) a realistic model of the sample selection function, and (ii) knowledge of relevant underlying distribution functions: the distribution of spheroid properties such as velocity dispersions or masses; the active fraction as a function of BH mass, or alternatively the active black hole mass function; and the Eddington ratio distribution function. We employed our formalism together with recently determined distribution functions to investigate how much existing studies of the M_•-bulge relation using AGN hosts might suffer from selection biases. For low-redshift AGN samples we can naturally reproduce the flattening of the relation observed in some studies without having to invoke intrinsic differences in the BH-bulge relation between active and inactive galaxies. When extending our analysis to higher redshift samples we are clearly hampered by limited empirical constraints on the various relevant distribution functions. Using a best-guess approach for these distributions we estimate the expected magnitude of sample selection biases for a number of recent observational attempts to study the M_•-bulge evolution. In no case do we find statistically significant evidence for an evolving M_•-bulge relation. While the observed apparent offsets in M_• /M_Bulge  from the local relation can be quite large, the sample selection bias estimated from our formalism is typically of the same magnitude. We suggest a possible practical approach to circumvent several of the most problematic issues connected with AGN selection; this could become a powerful diagnostic in future investigations.