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 of Active
Galactic Nuclei allows Black Hole 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 MBH-sigma relation has been used to
estimate MBH for a sample of type-2 AGN and virial relations (with and without
radiation pressure) for a sample of type-1 AGN extracted from the same parent
population. The observed L/LEdd distribution based on virial BH masses is in
good agreement with that based on MBH-sigma only if radiation pressure effects
are negligible, otherwise significant discrepancies are observed. In this paper
we investigate the effects of intrinsic dispersions associated to the virial
relations providing MBH, and we show that they explain the discrepancies
between the observed L/LEdd distributions of type-1 and type-2 AGN. These
discrepancies in the L/LEdd 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/LEdd. Average radiation pressure corrections
should then be applied in virial MBH estimators until their dependence on
observed source physical properties has been fully calibrated. Finally, the
comparison between MBH and L/LEdd distributions derived from sigma-based and
virial estimators can constrain the variance of BLR physical properties in AGN.
