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)-sigma 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)-sigma 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 sigma-based and virial estimators can constrain the variance of BLR physical properties in AGNs.