Particle Heating by Nonlinear Alfvenic Turbulence in ADAFs

Particle heating in advection-dominated accretion flows (ADAFs) by nonlinear MHD (Alfvenic) turbulence is investigated. Such turbulence with highly-fluctuating magnetic fields, $\tilde B\sim B_0$, is believed to be naturally produced by the magnetic shearing instability near the nonlinear saturation. It is shown that the energy is dissipated in the parallel cascade, which occurs due to nonlinear compressibility of high-amplitude turbulence, and predominantly heats protons, but not electrons. The conservative limit on the electron--to--proton heating fraction is $\delta\lesssim{\rm few}\times10^{-2}$.