2007ApJ...660..267B

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_ø-σ relation predicts fewer massive black holes than does the M_ø-L relation. This is because the σ-L relation in black hole samples currently available is inconsistent with that in the SDSS sample, on which the distributions of L or σ are based; the black hole samples have smaller L for a given σ or have larger σ for a given L. This is true whether L is estimated in the optical or in the NIR. If this is a selection rather than physical effect, then the M_ø-σ and M_ø-L relations currently in the literature are also biased from their true values. We provide a framework for describing the effect of this bias. We then combine it with a model of the bias to make an estimate of the true intrinsic relations. If we have correctly modeled the selection effect, then our analysis suggests that the bias in the <M_ø|σ> relation is likely to be small, whereas the <M_ø|L> relation is biased toward predicting more massive black holes for a given luminosity, and the M_ø-L relation is entirely a consequence of more fundamental relations between M_ø and σ and between σ and L. The intrinsic relation we find suggests that at fixed luminosity, older galaxies tend to host more massive black holes.