The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks
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 largescale 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} <= 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 vpropk ^{2}, and that the implied Pr_{M,T} ~ 1.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 2009
 DOI:
 10.1088/0004637X/697/2/1901
 arXiv:
 arXiv:0903.3757
 Bibcode:
 2009ApJ...697.1901G
 Keywords:

 accretion;
 accretion disks;
 MHD;
 Astrophysics  High Energy Astrophysical Phenomena;
 Astrophysics  Galaxy Astrophysics
 EPrint:
 15pages, 1 figure, accepted by ApJ