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 (SDSS), using virial BH mass estimators based on the, , and 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 - and -estimated BH masses are consistent with one another; and (3) the BH mass estimator may be more severely affected by a disk wind component than the and estimators, giving a positive bias in mass correlated with the - blueshift. Most SDSS quasars have virial BH masses in the range 10⁸-10⁹ M_. There is a clear upper mass limit of 10^10 M_ for active BHs at z 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 z 2. 3) has mean virial BH mass larger by 0. 12 dex than the whole sample. A broad absorption line (BAL) quasar subsample (with 1. 7 z 2. 2) has identical virial mass distribution as the nonBAL sample, with no mean offset. (Abridged)