= 0.1$ parsecs from the central black hole. Also, unless $\overline{N}_\mathrm{H}$ is being varied explicitly, $\rho_0$ is set so that the sightline-averaged column density is $3.4 \times 10^{24}$ cm$^{-2}$, with a mid-plane column density of $1.0 \times 10^{25}$ cm$^{-2}$. These values are consistent with the calculations from @Hopkins2010-1 of surface densities of $10^{11}$ – $10^{12}$ $M_\odot$ kpc$^{-2}$ for the central 10 parsecs surrounding the black hole. The fiducial parameters are summarized in Table \[FiducialParameters\].

For this smooth density model we use a two-dimensional grid with spherical polar $(r,\theta)$ coordinates, with logarithmic spacing in the radial coordinate and linear spacing in the angular coordinate. Our resolution is 192 radial zones and 64 $\theta$ zones for $\theta$ ranging from $0$ to $\pi/2$, with an assumed symmetry for $\theta \rightarrow \pi - \theta$. The radial zones span radii ranging from $r_0 = 0.1$ pc to an outer radius $r_\mathrm{out} =10^{20}$ cm ($\approx$ 32.4 pc). The 0.1 pc scale was chosen because it is a larger scale than the typical black hole accretion disk, but also small compared to the typical dust sublimation radius. We ignore all momentum deposition inside the 0.1 pc radius, and since nearly all the momentum deposition occurs at and 