Selection Bias in Observing the Cosmological Evolution of the M•-σ and M•-L Relationships

Programs to observe evolution in the M_•-σ or M_•-L relations typically compare black hole masses, M_•, in high-redshift galaxies selected by nuclear activity to M_• in local galaxies selected by luminosity L or velocity dispersion σ. Because active galactic nucleus luminosity can depend on M_•, selection effects are different for the two samples, potentially producing a false signal of evolution. Cosmic scatter in the M_• relations means that the mean logL or logσ among galaxies that host a black hole of given M_• may be substantially different than the logL or logσ obtained from inverting the M_•-L or M_•-σ relations for the same nominal M_•. The bias is strongest at high M_•, where the luminosity and dispersion functions of galaxies fall rapidly. The most massive black holes occur more often as rare outliers in galaxies of modest mass than in the even rarer high-mass galaxies, which would otherwise be the sole location of such black holes in the absence of cosmic scatter. Because of this bias, M_• will typically appear to be too large in the distant sample for a given L or σ. For the largest black holes and the largest plausible cosmic scatter, the bias can reach a factor of 3 in M_• for the M_•-σ relation and 9 for the M_•-L relation. Unfortunately, the cosmic scatter is not known well enough to correct for the bias. Measuring evolution of the M_• relations requires object selection to be precisely defined and exactly the same at all redshifts.