Viscous and resistive effects on the magnetorotational instability with a net toroidal field

Abstract

Resistivity and viscosity have a significant role in establishing the energy levels in turbulence driven by the magnetorotational instability (MRI) in local astrophysical disk models. This study uses the Athena code to characterize the effects of a constant shear viscosity ν and Ohmic resistivity η in unstratified shearing box simulations with a net toroidal magnetic flux. A previous study of shearing boxes with zero net magnetic field performed with the ZEUS code found that turbulence dies out for values of the magnetic Prandtl number, P m = ν/η, below P m ∼ 1; for P m ≳ 1, time- and volume-averaged stress levels increase with P m. We repeat these experiments with Athena and obtain consistent results. Next, the influence of viscosity and resistivity on the toroidal field MRI is investigated both for linear growth and for fully developed turbulence. In the linear regime, a sufficiently large ν or η can prevent MRI growth; P m itself has little direct influence on growth from linear perturbations. By applying a range of values for ν and η to an initial state consisting of fully developed turbulence in the presence of a background toroidal field, we investigate their effects in the fully nonlinear system. Here, increased viscosity enhances the turbulence, and the turbulence decays only if the resistivity is above a critical value; turbulence can be sustained even when P m < 1, in contrast to the zero net field model. While we find preliminary evidence that the stress converges to a small range of values when ν and η become small enough, the influence of dissipation terms on MRI-driven turbulence for relatively large η and ν is significant, independent of field geometry. © 2009 The American Astronomical Society.