The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks

Details The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks

2009-03-22

arxiv.org/abs/0903.3757v1

Astrophys.J.697:1901-1906,2009

Astronomy and Astrophysics

Astrophysics

High Energy Astrophysical Phenomena

15pages, 1 figure, accepted by ApJ

Scientific paper

10.1088/0004-637X/697/2/1901

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.

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