Heating and Cooling of Hot Accretion Flows by Non Local Radiation

We consider non-local effects which 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 non-local 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 $R_{tr,min}$. However, if the hot flow terminates at $R < R_{tr,min}$, non-local 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 $\dot{M} \gsim 10^{-3} \alpha \dot{M}_{Edd}$, and $R \lsim 10^4 R_{Schw}$. As a result, the maximum accretion rate for which an advection-dominated one-temperature solution exists, decreases by a factor of $\sim 10$, compared to the value computed under an assumption of local energy balance.