Ion viscosity mediated by tangled Magnetic fields-An application to Black Hole Accretion disks

We derive expressions for a ``hybrid'' viscosity arising from Coulomb collisions between ions in the presence of tangled magnetic fields. Such magnetic fields are expected to be embedded in accretion flows onto black holes and other compact objects. Ion viscosity in the absence of magnetic fields has been shown to appreciable in hot accretion disks, but it was thought that the presence of the smallest of magnetic fields would effectively quench it. We show that the hybrid viscosity in hot (ion temperatures around 10^11-10^12 K) accretion disks results in values of the Shakura Sunyaev \alpha parameter around 0.01 to 0.1-0.5. We do not model the generation of the tangled magnetic fields; we merely assume its presence and assume it to be arbitrarily strong.