The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks

TL;DR

This study measures the turbulent magnetic Prandtl number in MHD turbulence within disks, finding it to be approximately unity, which influences magnetic field diffusion and angular momentum transport.

Contribution

It provides the first direct measurement of the turbulent magnetic Prandtl number in MHD turbulence in disk-like conditions.

Findings

The magnetic field perturbation decays exponentially with a rate proportional to k^2.

The turbulent magnetic Prandtl number Pr_{M,T} is approximately 1.

Magnetic field diffusion and angular momentum transport are characterized in a shearing box simulation.

Abstract

The magnetic Prandtl number Pr_M 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 Pr_{M,T} controls the rate of escape of vertical field from the disk; for Pr_{M,T} leq 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 Pr_{M,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 proportional to k^2, and that the implied Pr_{M,T} ~ 1.