BASS XXX: Distribution Functions of DR2 Eddington-ratios, Black Hole Masses, and X-ray Luminosities

We determine the low-redshift X-ray luminosity function (XLF), active black hole mass function (BHMF), and Eddington-ratio distribution function (ERDF) for both unobscured (Type 1) and obscured (Type 2) active galactic nuclei (AGN) using the unprecedented spectroscopic completeness of the BAT AGN Spectroscopic Survey (BASS) data release 2. In addition to a straightforward 1/Vmax approach, we also compute the intrinsic distributions, accounting for sample truncation by employing a forward modeling approach to recover the observed BHMF and ERDF. As previous BHMFs and ERDFs have been robustly determined only for samples of bright, broad-line (Type 1) AGNs and/or quasars, ours is the first directly observationally constrained BHMF and ERDF of Type 2 AGN. We find that after accounting for all observational biases, the intrinsic ERDF of Type 2 AGN is significantly skewed towards lower Eddington ratios than the intrinsic ERDF of Type 1 AGN. This result supports the radiation-regulated unification scenario, in which radiation pressure dictates the geometry of the dusty obscuring structure around an AGN. Calculating the ERDFs in two separate mass bins, we verify that the derived shape is consistent, validating the assumption that the ERDF (shape) is mass independent. We report the local AGN duty cycle as a function of mass and Eddington ratio, by comparing the BASS active BHMF with the local mass function for all SMBH. We also present the log N-log S of Swift-BAT 70-month sources.