Heating and cooling of hot accretion flows by nonlocal radiation

We consider nonlocal effects that arise when radiation emitted at one radius of an accretion disk either heats or cools gas at other radii through Compton scattering. We discuss three situations: 1. Radiation from the inner regions of an advection-dominated flow Compton cooling gas at intermediate radii and Compton heating gas at large radii. 2. Soft radiation from an outer thin accretion disk Compton cooling a hot one- or two-temperature flow on the inside. 3. Soft radiation from an inner thin accretion disk Compton cooling hot gas in a surrounding one-temperature flow. We describe how previous results are modified by these nonlocal interactions. We find that Compton heating or cooling of the gas by the radiation emitted in the inner regions of a hot flow is not important. Likewise, Compton cooling by the soft photons from an outer thin disk is negligible when the transition from a cold to a hot flow occurs at a radius greater than some minimum R-tr,R-min. However, if the hot how terminates at R < R-tr,R-min, nonlocal cooling is so strong that the hot gas is cooled to a thin disk configuration in a runaway process. In the case of a thin disk surrounded by a hot one-temperature flow, we find that Compton cooling by soft radiation dominates over local cooling in the hot gas for M greater than or similar to 10(-3)alpha M-Edd and R less than or similar to 10(4)R(Schw). As a result, the maximum accretion rate for which an advection-dominated one-temperature solution exists decreases by a factor of similar to 10 compared with the value computed under an assumption of local energy balance.