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It is common to estimate black hole abundances by using a measuredcorrelation between black hole mass and another more easily measured observablesuch as the velocity dispersion or luminosity of the surrounding bulge. Thecorrelation is used to transform the distribution of the observable into anestimate of the distribution of black hole masses. However, differentobservables provide different estimates: the Mbh-sigma relation predicts fewermassive black holes than does the Mbh-L relation. This is because the sigma-Lrelation in black hole samples currently available is inconsistent with that inthe SDSS sample, from which the distributions of L or sigma are based: theblack hole samples have smaller L for a given sigma or have larger sigma for agiven L. This is true whether L is estimated in the optical or in the NIR. Ifthis is a selection rather than physical effect, then the Mbh-sigma and Mbh-Lrelations currently in the literature are also biased from their true values.We provide a framework for describing the effect of this bias. We then combineit with a model of the bias to make an estimate of the true intrinsicrelations. While we do not claim to have understood the source of the bias, oursimple model is able to reproduce the observed trends. If we have correctlymodeled the selection effect, then our analysis suggests that the bias in the<Mbh|sigma> relation is likely to be small, whereas the <Mbh|L> relation isbiased towards predicting more massive black holes for a given luminosity. Inaddition, it is likely that the Mbh-L relation is entirely a consequence ofmore fundamental relations between Mbh and sigma, and between sigma and L. Theintrinsic relation we find suggests that at fixed luminosity, older galaxiestend to host more massive black holes.Comment: 12 pages, 7 figures. Accepted by ApJ. We have added a figure showing  that a similar bias is also seen in the K-band. A new appendix describes the  BH samples as well as the fits used in the main tex

Selection Bias in theM•‐σ andM•‐LCorrelations and Its Consequences

Selection Bias in theM_•‐σ andM_•‐LCorrelations and Its Consequences