On the Observed Distributions of Black Hole Masses and Eddington Ratios From Radiation Pressure Corrected Virial Indicators

The application of the virial theorem to the broad-line region (BLR) of active galactic nuclei (AGNs) allows black hole (BH) mass estimates for large samples of objects at all redshifts. In a recent paper, we showed that ionizing radiation pressure onto BLR clouds affects virial BH mass estimates and we provided empirically calibrated corrections. More recently, a new test of the importance of radiation forces has been proposed: the M BH - relation has been used to estimate M BH for a sample of type-2 AGNs and virial relations (with and without radiation pressure) for a sample of type-1 AGNs extracted from the same parent population. The observed L/L Edd distribution based on virial BH masses is in good agreement with that based on M BH - only if radiation pressure effects are negligible, otherwise significant discrepancies are observed. In this Letter, we investigate the effects of intrinsic dispersions associated with the virial relations providing M BH , and we show that they explain the discrepancies between the observed L/L Edd distributions of type-1 and type-2 AGNs. These discrepancies in the L/L Edd distributions are present regardless of the general importance of radiation forces, which must be negligible only for a small fraction of sources with large L/L Edd . Average radiation pressure corrections should then be applied in virial M BH estimators until their dependence on observed source physical properties has been fully calibrated. Finally, the comparison between M BH and L/L Edd distributions derived from -based and virial estimators can constrain the variance of BLR physical properties in AGNs.