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

We present three-dimensional magnetohydrodynamic simulations of the nonline ar evolution of the magnetorotational instability (MRI) with a nonzero ohmi c resistivity. The simulations begin from a homogeneous (unstratified) dens ity distribution and use the local shearing-box approximation. The evolutio n of a variety of initial held configurations and strengths is considered f or several values of the constant coefficient of resistivity eta. For unifo rm vertical and toroidal magnetic fields, we find unstable growth consisten t with the linear analyses; finite resistivity reduces growth rates and, wh en large enough, stabilizes the MRI. Even when unstable modes remain, resis tivity has significant effects on the nonlinear state. The properties of th e saturated state depend on the initial magnetic field configuration. Tn si mulations with an initial uniform vertical field, the MRI is able to suppor t angular momentum transport even for large resistivities through the quasi -periodic generation of axisymmetric radial channel solutions rather than t hrough the maintenance of anisotropic turbulence. Reconnective processes ra ther than parasitic instabilities mediate the resurgent channel solution in this case. Simulations with zero-net Bur show that the angular momentum tr ansport and the amplitude of magnetic energy after saturation are significa ntly reduced by finite resistivity, even at levels where the linear modes a re only slightly affected. The MRI is unable to sustain angular momentum tr ansport and turbulent how against diffusion for Re-M less than or similar t o 10(4), where the Reynolds number is defined in terms of the disk scale he ight and sound speed, Re-M = c(s)H/eta. As this is close to the Reynolds nu mbers expected in low, cool states of dwarf novae, these results suggest th at finite resistivity may account for the low and high angular momentum tra nsport rates inferred for these systems.