Biases in virial black hole masses: An SDSS perspective

We compile black hole (BH) masses for ∼60,000 quasars in the redshift range 0.1 ≲ z ≲ 4.5 included in the Fifth Data Release of the Sloan Digital Sky Survey, using virial BH mass estimators based on the Hβ, Mg II, and C IV emission lines. Within our sample, the widths of the three lines follow lognormal distributions, with means and dispersions that do not depend strongly on luminosity or redshift. The Mg II- and Hβ-estimated BH masses are consistent with one another, but there is a positive bias between the C IV- and Mg II-estimated BH masses correlated with the C IV-Mg II blueshift, suggesting that the C IV estimator is more severely affected by a disk wind. If the underlying BH mass distribution decreases with mass and the Eddington ratio distribution at fixed true BH mass has nonzero width, we show that the measured virial BH mass and Eddington ratio distributions within finite luminosity bins are subject to Malmquist bias. We present a model that reproduces the observed virial mass distribution, quasar luminosity function, and line width distribution of our sample; it has an underlying BH mass distribution dN/d log M ∝ M^-2.6 and a lognormal true Eddington ratio distribution at fixed true mass with dispersion 0.4 dex and mean dependent on BH mass. In this model, the observed viral mass ( Eddington ratio) distribution for the SDSS sample is biased high (low) by ∼0.6 dex within finite luminosity bins. Finally, we compare virial BH masses of radio and broad absorption line quasars with ordinary quasars matched in redshift and luminosity.