Observational Selection Effects and the M-_ Relation

Abstract

We examine the possibility that the observed relation between black hole mass and host-galaxy stellar velocity dispersion (the M -_ relation) is biased by an observational selection effect, the difficulty of detecting a black hole whose sphere of influence is smaller than the telescope resolution. In particular, we critically investigate recent claims that the M -_ relation only represents the upper limit to a broad distribution of black hole masses in galaxies of a given velocity dispersion. We find that this hypothesis can be rejected at a high confidence level, at least for the early-type galaxies with relatively high velocity dispersions (median 268 km s –1 ) that comprise most of our sample. We also describe a general procedure for incorporating observational selection effects in estimates of the properties of the M -_ relation. Applying this procedure we find results that are consistent with earlier estimates that did not account for selection effects, although with larger error bars. In particular, (1) the width of the M -_ relation is not significantly increased, (2) the slope and normalization of the M -_ relation are not significantly changed, and (3) most or all luminous early-type galaxies contain central black holes at zero redshift. Our results may not apply to late-type or small galaxies, which are not well represented in our sample.