Issue A&A Volume 507, Number 1, November III 2009 Page(s) 19 - 28 Section Astrophysical processes DOI 10.1051/0004-6361/200912752 Published online 03 September 2009

A&A 507, 19-28 (2009)
DOI: 10.1051/0004-6361/200912752

Turbulent resistivity driven by the magnetorotational instability

S. Fromang^{1, 2} and J. M. Stone<sup>3

1</sup>  CEA, Irfu, SAp, Centre de Saclay, 91191 Gif-sur-Yvette, France
    e-mail: sebastien.fromang@cea.fr
²  UMR AIM, CEA-CNRS-Univ. Paris VII, Centre de Saclay, 91191 Gif-sur-Yvette, France
³  Department of Astrophysical Sciences, Peyton Hall, Ivy Lane, Princeton University, NJ 08544, USA

Received 23 June 2009 / Accepted 1 September 2009

Abstract
Aims. We measure the turbulent resistivity in the nonlinear regime of the MRI, and evaluate the turbulent magnetic Prandtl number.
Methods. We perform a set of numerical simulations with the Eulerian finite volume codes Athena and Ramses in the framework of the shearing box model. We consider models including explicit dissipation coefficients and magnetic field topologies such that the net magnetic flux threading the box in both the vertical and azimuthal directions vanishes.
Results. We first demonstrate good agreement between the two codes by comparing the properties of the turbulent states in simulations having identical microscopic diffusion coefficients (viscosity and resistivity). We find the properties of the turbulence do not change when the box size is increased in the radial direction, provided it is elongated in the azimuthal direction. To measure the turbulent resistivity in the disk, we impose a fixed electromotive force on the flow and measure the amplitude of the saturated magnetic field that results. We obtain a turbulent resistivity that is in rough agreement with mean field theories like the Second Order Smoothing Approximation. The numerical value translates into a turbulent magnetic Prandtl number  Pm_t of order unity. Pm_t appears to be an increasing function of the forcing we impose. It also becomes smaller as the box size is increased in the radial direction, in good agreement with previous results obtained in very large boxes.
Conclusions. Our results are in general agreement with other recently published papers studying the same problem but using different methodology. Thus, our conclusion that  Pm_t is of order unity appears robust.

Key words: accretion, accretion disks -- magnetohydrodynamics (MHD) -- methods: numerical

© ESO 2009

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