Turbulence and particle heating in advection-dominated accretion flows

We extend and reconcile recent work on turbulence and particle heating in advection-dominated accretion hows. For approximately equipartition magnetic fields, the turbulence primarily heats the electrons. For weaker magnetic fields, the protons are primarily heated. The division between electron and proton heating occurs between beta similar to 5 and beta similar to 100 (beta is the ratio of gas to magnetic pressure), depending on unknown details of how Alfven waves are converted into whistlers on scales of the proton Larmor radius. We also discuss the possibility that magnetic reconnection could be a significant source of electron heating.