for all gas from 0.1 pc to large radii) for a smooth density model with the fiducial parameters listed in Table \[FiducialParameters\]. Middle: Clumpy gas column density distribution with same clumping parameters as those used in Figure \[BuildingUpSnapshot\], also integrated for all gas from 0.1 pc to large radii. Bottom: All parameters are the same as the panel above, but this time the column density is integrated from the sublimation radius outward (i.e. these are the dusty gas columns). []{data-label="ColumnDensityHistograms"}](f3b.png){width="\textwidth"}

![Top: Column density histogram (integrated for all gas from 0.1 pc to large radii) for a smooth density model with the fiducial parameters listed in Table \[FiducialParameters\]. Middle: Clumpy gas column density distribution with same clumping parameters as those used in Figure \[BuildingUpSnapshot\], also integrated for all gas from 0.1 pc to large radii. Bottom: All parameters are the same as the panel above, but this time the column density is integrated from the sublimation radius outward (i.e. these are the dusty gas columns). []{data-label="ColumnDensityHistograms"}](f3c.png){width="\textwidth"}

Monte Carlo Radiative Transfer
------------------------------

The Monte Carlo technique partitions the luminosity of the accreting black hole into equal-energy photon packets that probabilistically interact with the surrounding gas. The packets were transported in three dimensions 