Programs to observe evolution in the Mbh-sigma or Mbh-L relations typicallycompare black-hole masses, Mbh, in high-redshift galaxies selected by nuclearactivity to Mbh in local galaxies selected by luminosity L, or stellar velocitydispersion sigma. Because AGN luminosity is likely to depend on Mbh, selectioneffects are different for high-redshift and local samples, potentiallyproducing a false signal of evolution. This bias arises because cosmic scatterin the Mbh-sigma and Mbh-L relations means that the mean log(L) or log(sigma)among galaxies that host a black hole of given Mbh, may be substantiallydifferent than the log(L) or log(sigma) obtained from inverting the Mbh-L orMbh-sigma relations for the same nominal Mbh. The bias is particularly strongat high Mbh, where the luminosity and dispersion functions of galaxies arefalling rapidly. The most massive black holes occur more often as rare outliersin galaxies of modest mass than in the even rarer high-mass galaxies, whichwould otherwise be the sole location of such black holes in the absence ofcosmic scatter. Because of this bias, Mbh will typically appear to be too largein the distant sample for a given L or sigma. For the largest black holes andthe largest plausible cosmic scatter, the bias can reach a factor of 3 in Mbhfor the Mbh-sigma relation and a factor of 9 for the Mbh-L relation.Unfortunately, the actual cosmic scatter is not known well enough to correctfor the bias. Measuring evolution of the Mbh and galaxy property relationsrequires object selection to be precisely defined and exactly the same at allredshifts.
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