The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks

The magnetic Prandtl number PrM is the ratio of viscosity to resistivity. In astrophysical disks the diffusion of angular momentum (viscosity) and magnetic fields (resistivity) are controlled by turbulence. Phenomenological models of the evolution of large scale poloidal magnetic fields in disks suggest that the turbulent magnetic Prandtl number PrM,T controls the rate of escape of vertical field from the disk; for PrM,T ≤ R/H vertical field diffuses outward before it can be advected inward by accretion. Here we measure field diffusion and angular momentum transport due to MHD turbulence in a shearing box, and thus PrM,T, by studying the evolution of a sinusoidal perturbation in the magnetic field that is injected into a turbulent background. We show that the perturbation is always stable, decays approximately exponentially, has decay rate ∝ k, and that the implied PrM,T ∼ 1. Subject headings: accretion, accretion disks, magnetohydrodynamics