The Black Hole Masses and Eddington Ratios of Type 2 Quasars
  Type 2 quasars are an important constituent of active galaxies, possibly
representing the evolutionary precursors of traditionally studied type 1
quasars. We characterize the black hole mass ($M_{\rm BH}$) and Eddington ratio
($L_{\rm bol}/L_{\rm Edd}$) for 669 type 2 quasars selected from the Sloan
Digital Sky Survey, using black hole masses estimated from the $M_{\rm
BH}-\sigma_{\ast}$ relation and bolometric corrections scaled from the
extinction-corrected $ [\rm O~{\scriptsize III}]~ \lambda 5007$ luminosity.
When stellar velocity dispersions cannot be measured directly from the spectra,
we estimate them from the core velocity dispersions of the narrow emission
lines $ \rm [O~{\scriptsize II}]~ \lambda\lambda 3726, 3729$, $ \rm
[S~{\scriptsize II}]~\lambda\lambda 6716, 6731$, and $[ \rm O~{\scriptsize
III}]~ \lambda 5007$, which are shown to trace the gravitational potential of
the stars. Energy input from the active nucleus still imparts significant
perturbations to the gas kinematics, especially to high-velocity, blueshifted
wings. Nonvirial motions in the gas become most noticeable in systems with high
Eddington ratios. The black hole masses of our sample of type 2 quasars range
from $M_{\rm BH}
  \approx 10^{6.5} $ to $10^{10.4} \, M_\odot$ (median $10^{8.2} \, M_\odot$).
Type 2 quasars have characteristically large Eddington ratios ($L_{\rm
bol}/L_{\rm Edd}~\approx 10^{-2.9}-10^{1.8}$; median $10^{-0.7}$), slightly
higher than in type~1 quasars of similar redshift; the luminosities of
$\sim$20% of the sample formally exceed the Eddington limit. The high Eddington
ratios may be consistent with the notion that obscured quasars evolve into
unobscured quasars.
