beyond the sublimation radius, the exact choice of innermost radius has little effect on our results. Slices of the gas density for the model developed in this section, along with a simulation from @Hopkins2012-1, are shown in Figure \[DensitySlices\].

[ccccc]{} 0.3 & $3.4 \times 10^{24}$ & 1.5 & 1 & $10^8$\
\[FiducialParameters\]

![Top: An example of a slice through the smooth model density distribution with the fiducial parameters listed in Table \[FiducialParameters\], except $\overline{N}_\mathrm{H} = 1.0 \times 10^{25}$ cm$^{-2}$ (chosen to match the simulation in the bottom panel). Bottom: A density slice taken from a hydrodynamical simulation of gas accretion onto a central black hole (see @Hopkins2012-1). Note that the color map is truncated at $n = 10^3$ cm$^{-2}$, and the density in the model distribution continues to drop below this value. []{data-label="DensitySlices"}](f1a.png){width="50.00000%"}

![Top: An example of a slice through the smooth model density distribution with the fiducial parameters listed in Table \[FiducialParameters\], except $\overline{N}_\mathrm{H} = 1.0 \times 10^{25}$ cm$^{-2}$ (chosen to match the simulation in the bottom panel). Bottom: A density slice taken from a hydrodynamical simulation of gas accretion onto a central black hole (see @Hopkins2012-1). Note that the color map is truncated at $n = 10^3$ cm$^{-2}$, 