The impact of the uncertainty in single-epoch virial black hole mass estimates on the observed evolution of the black hole-bulge scaling relations

Recent observations of the black hole (BH)-bulge scaling relations usually report positive redshift evolution, with higher redshift galaxies harboring more massive BHs than expected from the local relations. All of these studies focus on broad line quasars with BH mass estimated from virial estimators based on single-epoch spectra. Since the sample selection is largely based on quasar luminosity, the cosmic scatter in the BH-bulge relation introduces a statistical bias leading to on average more massive BHs given galaxy properties at high redshift (i.e., the Lauer et al. bias). We here emphasize a previously underappreciated statistical bias resulting from the uncertainty of single-epoch virial BH mass estimators and the shape of the underlying (true) BH mass function, which leads to on average overestimation of the true BH masses at the high-mass end. We demonstrate that the latter virial mass bias can contribute a substantial amount to the observed excess in BH mass at fixed bulge properties, comparable to the Lauer et al. bias. The virial mass bias is independent of the Lauer et al. bias; hence if both biases are at work, they can largely (or even fully) account for the observed BH mass excess at high redshift.