Biases in Virial Black Hole Masses: An SDSS Perspective

We compile black hole (BH) masses for $\sim 60,000$ quasars in the redshift range $0.1 \lesssim z \lesssim 4.5$ included in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS), using virial BH mass estimators based on the \hbeta, \MgII, and \CIV emission lines. We find that: (1) within our sample, the widths of the three lines follow log-normal distributions, with means and dispersions that do not depend strongly on luminosity or redshift;(2) the \MgII- and \hbeta-estimated BH masses are consistent with one another; and (3) the \CIV BH mass estimator may be more severely affected by a disk wind component than the \MgII and \hbeta estimators, giving a positive bias in mass correlated with the \CIV-\MgII blueshift. Most SDSS quasars have virial BH masses in the range $10^8-10^9 M_\odot$. There is a clear upper mass limit of $\sim 10^{10} M_\odot$ for active BHs at $z \gtrsim 2$, decreasing at lower redshifts. Making the reasonable assumptions that the underlying BH mass distribution decreases with mass and that the Eddington ratio distribution at fixed BH mass has non-zero width, we show that the measured virial BH mass distribution and Eddington ratio distribution are subject to Malmquist bias. A radio quasar subsample (with $1.5\lesssim z\lesssim 2.3$) has mean virial BH mass larger by $\sim 0.12$ dex than the whole sample. A broad absorption line (BAL) quasar subsample (with $1.7\lesssim z\lesssim 2.2$) has identical virial mass distribution as the nonBAL sample, with no mean offset. (Abridged)