Thermal properties of two-dimensional advection-dominated accretion flow

We study the thermal structure of the widely adopted two-dimensional advection-dominated accretion flow (ADAF) of Narayan & Yi. The critical radius for a given mass accretion rate, outside of which the optically thin hot solutions do not exist in the equatorial plane, agrees with those of one-dimensional 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 accretion 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 radiative efficiency, defined as the luminosity output divided by the mass accretion rate times the velocity of light squared, is above ∼ 4 × 10^-3, the polar region of the flow is preheated above the virial temperature by Compton heating, which may result in time-dependent behavior or outflow while accretion continues in the equatorial plane. Thus, under most relevant circumstances, ADAF solutions may be expected to be accompanied by polar outflow winds. While preheating instabilities exist in ADAF, as for spherical flows, the former are to some extent protected by their characteristically higher densities and higher cooling rates, which reduce their susceptibility to Compton driven overheating.