Radiation Pressure Supported AGN Tori with Hard X-Ray and Stellar   Heating
  The dynamics and structure of toroidal obscuration around AGN remain uncertain and controversial. In this paper we extend earlier work on the dynamical role of infrared radiation pressure by adding the effects of two kinds of distributed heating: Compton-heating due to hard X-rays from the nucleus and local starlight heating. We find numerical solutions to the axisymmetric hydrostatic equilibrium, energy balance, and photon diffusion equations including these effects. Within the regime of typical parameters, the two different sources of additional heating have very similar effects: the density profile within the torus becomes shallower both radially and vertically, but for plausible heating rates, there is only minor change (relative to the source-free case) in the distribution of column density with solid angle. The most interesting consequence of distributed heating is that it selects out a relatively narrow range of parameters permitting an equilibrium, particularly $(L/L_E)/\tau_T$. We discuss the implications of both the narrowness of the permitted range and its approximate coincidence with the range inferred from observations. 
Jiming Shi and Julian H. Krolik