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.