Selection bias in observing the cosmological evolution of the M○-σ and M○- L relationships

Programs to observe evolution in the M-center dot-sigma or M-center dot-L relations typically compare black hole masses, M-center dot, in highredshift galaxies selected by nuclear activity to M-center dot in local galaxies selected by luminosity L or velocity dispersion sigma. Because active galactic nucleus luminosity can depend on M-center dot, selection effects are different for the two samples, potentially producing a false signal of evolution. Cosmic scatter in the M-center dot relations means that the mean log L or log sigma among galaxies that host a black hole of given M-center dot may be substantially different than the log L or log sigma obtained from inverting the M-center dot-L or M-center dot-sigma relations for the same nominal M-center dot. The bias is strongest at high M-center dot, 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-center dot will typically appear to be too large in the distant sample for a given L or sigma. For the largest black holes and the largest plausible cosmic scatter, the bias can reach a factor of 3 in M-center dot for the M-center dot-sigma relation and 9 for theM(center dot)-L relation. Unfortunately, the cosmic scatter is not known well enough to correct for the bias. Measuring evolution of the M-center dot relations requires object selection to be precisely defined and exactly the same at all redshifts.