Selection bias in the M_BH-sigma and M_BH-L correlations and its consequences
Abstract
It is common to estimate black hole abundances by using a measured correlation between black hole mass and another more easily measured observable such as the velocity dispersion or luminosity of the surrounding bulge. The correlation is used to transform the distribution of the observable into an estimate of the distribution of black hole masses. However, different observables provide different estimates: the M_BH-sigma relation predicts fewer massive black holes than does the M_BH-L relation. This is because the sigma-L relation in black hole samples currently available is inconsistent with that in the SDSS sample, from which the distributions of L or sigma are based: the black hole samples have smaller L for a given sigma. The sigma-L relation in the black hole samples is similarly discrepant with that in the ENEAR sample of nearby early-type galaxies. This suggests that current black hole samples are biased towards objects with abnormally large velocity dispersions for their luminosities. If this is a selection rather than physical effect, then the M_BH-sigma and M_BH-L relations currently in the literature are also biased from their true values. We provide estimates of this bias, and hence, of the true intrinsic relations. Our analysis suggests that the bias in the relation is likely to be small, whereas the relation is biased towards predicting more massive black holes for a given luminosity. In addition, it is likely that the M_BH-L relation is entirely a consequence of more fundamental relations between M_BH and sigma, and between sigma and luminosity.Keywords
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