Thermal properties of two-dimensional advection-dominated accretion flow

We study the thermal structure of the widely adopted two-dimensional advect ion-dominated accretion how (ADAF) of Narayan & Yi. The critical radius for a given mass accretion rate, outside of which the optically thin hot solut ions do not exist in the equatorial plane, agrees with those of one-dimensi onal studies. However, we find that, even within the critical radius, there always exists a conical region of the flow, around the pole, which cannot maintain the assumed high electron temperature, regardless of the mass accr etion rate, in the absence of radiative heating. This could lead to a torus -like advection inflow shape since, in general, the ions too will cool down . We also find that Compton preheating is generally important and, if the r adiative efficiency, defined as the luminosity output divided by the mass a ccretion rate times the velocity of light squared, is above similar to 4 x 10(-3), the polar region of the flow is preheated above the virial temperat ure by Compton heating, which may result in time-dependent behavior or outf low while accretion continues in the equatorial plane. Thus, under most rel evant circumstances, ADAF solutions may be expected to be accompanied by po lar outflow winds. While preheating instabilities exist in ADAF, as for sph erical flows, the former are to some extent protected by their characterist ically higher densities and higher cooling rates, which reduce their suscep tibility to Compton driven overheating.