within a radius of less than 100 parsecs. Taken together, these effects can help to explain both the $M_\mathrm{BH}$ - $\sigma$ relation [@Ferrarese2000; @Gebhardt2000; @Tremaine2002] and the existence of galactic outflows observed at speeds of thousands of km s$^{-1}$. The results, particularly those of @DeBuhr2011-2, also suggest that line-driven winds may be insufficient to drive observed outflows, and that a large amount of momentum ($\gtrsim 3 \, L/c$) may need to be deposited via absorption by dust grains during the period when the SMBH is optically thick to both ultraviolet and far-infrared radiation, the time when most black hole growth is believed to occur [@Fabian1999; @Hopkins2005-1].

A large uncertainty in the numerical calculations referenced above is the amount of radiative momentum deposited within the central unresolved radius. The velocity and mass-loss rate of the resulting wind depend sensitively on this coupling. Moreover, in those studies the momentum was deposited in a spherically symmetric manner. In reality, multidimensional effects, such as the tendency for radiation to escape out the rarefied, polar regions of the gas distribution, will be crucial. These effects have been considered by several previous studies. @Pier1992-1 computed the radiation forces exerted on a torus modelled as a constant 