MHD turbulence in accretion disks: The importance of the magnetic Prandtl number

The magnetorotational instability (MRI) is the most likely source of MHD turbulence in accretion disks. Recently, it has been realized that microscopic diffusion coefficients (viscosity and resistivity) are important in determining the saturated state of the turbulence and thereby the rate of angular momentum transport. In this paper, we use a set of numerical simulations performed with a variety of numerical methods to investigate the dependance of α, the rate of angular momentum transport, on these coefficients. We show that α is an increasing function of the magnetic Prandtl number Pm, the ratio of viscosity over resistivity. In the absence of a mean field, we also find that MRI-induced MHD turbulence decays at low Pm.