VISCOUS AND RESISTIVE EFFECTS ON THE MAGNETOROTATIONAL INSTABILITY WITH A NET TOROIDAL FIELD

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 nu and Ohmic resistivity eta 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 = nu/eta, below P-m similar to 1; for P-m greater than or similar to 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 nu or eta can prevent MRI growth; P-m itself has little direct influence on growth from linear perturbations. By applying a range of values for nu and eta 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 nu and eta become small enough, the influence of dissipation terms on MRI-driven turbulence for relatively large eta and nu is significant, independent of field geometry.