The effect of resistivity on the nonlinear stage of the magnetorotational instability in accretion disks

We present three-dimensional magnetohydrodynamic simulations of the nonlinear evolution of the magnetorotational instability (MRI) with a nonzero ohmic resistivity. The simulations begin from a homogeneous (unstratified) density distribution and use the local shearing-box approximation. The evolution of a variety of initial field configurations and strengths is considered for several values of the constant coefficient of resistivity η. For uniform vertical and toroidal magnetic fields, we find unstable growth consistent with the linear analyses; finite resistivity reduces growth rates and, when large enough, stabilizes the MRI. Even when unstable modes remain, resistivity has significant effects on the nonlinear state. The properties of the saturated state depend on the initial magnetic field configuration. In simulations with an initial uniform vertical field, the MRI is able to support angular momentum transport even for large resistivities through the quasi-periodic generation of axisymmetric radial channel solutions rather than through the maintenance of anisotropic turbulence. Reconnective processes rather than parasitic instabilities mediate the resurgent channel solution in this case. Simulations with zero-net flux show that the angular momentum transport and the amplitude of magnetic energy after saturation are significantly reduced by finite resistivity, even at levels where the linear modes are only slightly affected. The MRI is unable to sustain angular momentum transport and turbulent flow against diffusion for Re_M ≲ 10⁴, where the Reynolds number is defined in terms of the disk scale height and sound speed, Re_M = c_s H/η. As this is close to the Reynolds numbers expected in low, cool states of dwarf novae, these results suggest that finite resistivity may account for the low and high angular momentum transport rates inferred for these systems.