Using transport coefficients of cosmic rays in turbulent magnetic fields to determine hybrid viscosity in hot accretion disks around AGN

The nature of the viscosity operative in hot, two-temperature accretion disks around AGN has been a long-standing, unsolved problem. It has been previously suggested that protons, in conjunction with the turbulent magnetic field that is likely to exist in the accretion disk, might be crucial in providing this viscosity. Several authors have recently determined diffusion coefficients for charged particles (cosmic rays) propagating in turbulent magnetic fields by means of extensive Monte Carlo simulations. We use the diffusion coefficients for protons determined by these simulations to find the effective mean free path for protons in hot accretion disks. This in turn yields good estimates of the viscosity due to energetic protons embedded in the turbulent magnetic field of a hot, two-temperature accretion disk. We combine this with a simple two-temperature accretion disk model to determine the Shakura-Sunyaev $\alpha$ viscosity parameter arising out of this mechanism. We find that protons diffusing in the turbulent magentic field embedded in a hot accretion d isk provide a physically reasonable source of viscosity in hot accretion disks around AGN.