Turbulent resistivity evaluation in magnetorotational instability generated turbulence

¹ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: g.lesur@damtp.cam.ac.uk
² Laboratoire d'Astrophysique, UJF CNRS, BP 53, 38041 Grenoble Cedex 9, France

Received: 3 April 2009
Accepted: 26 June 2009

Abstract

Context. MRI turbulence is a leading mechanism for the generation of an efficient turbulent transport of angular momentum in an accretion disk through a turbulent viscosity effect. It is believed that the same process could also transport large-scale magnetic fields in disks, reshaping the magnetic structures in these objects. This process, known as turbulent resistivity, has been suggested and used in several accretion-ejection models and simulations to produce jets. Still, the efficiency of MRI-driven turbulence to transport large-scale magnetic fields is largely unknown.

Aims. We present new analytical and numerical results aiming at quantifying the turbulent resistivity produced by MRI-driven turbulence in accretion disks.

Methods. We investigate this problem both analytically and numerically. We introduce a linear calculation of the MRI in the presence of a spatially inhomogeneous mean magnetic field. We show that, in this configuration, MRI modes lead to an efficient magnetic field transport, on the order of the angular momentum transport. We next use fully non linear simulations of MRI turbulence to compute the turbulent resistivity in several magnetic configurations.

Results. We find that the turbulent resistivity is on the order of the turbulent viscosity in all our simulations, although somewhat lower. The variations in the turbulent resistivity are correlated with the variation in the turbulent viscosity as a function of the imposed mean field. Finally, the turbulent resistivity tensor is found to be highly anisotropic with a diffusion coefficient 3 times greater in the radial direction than in the vertical direction.

Conclusions. These results support the possibility of driving jets from turbulent disks; the resulting jets may not be steady.