Numerical simulations of nonideal MHD accretion disks

We present three-dimensional magnetohydrodynamic simulations of the nonlinear evolution of the magnetorotational instability (MRI) with a non-zero 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 constant coefficient of resistivity eta. 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 ReM ≲ 104, where the Reynolds number is defined in terms of the disk scale height and sound speed, ReM = csH/eta. 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.;We then extend our simulations to include isothermal stratified disks with a variable Ohmic resistivity. Our resistive profile is due to cosmic ray ionization at the disk surface. Both poloidal and azimuthal field geometries are considered. These simulations span four disk scale heights, over which the magnetic Reynolds number ReM varies by several orders of magnitude. For poloidal and azimuthal fields we find that layered accretion is a natural consequence of resistive stratification. The disk divides into an "active" zone whose nonlinear evolution is characterized by turbulent transport dominated by Maxwell stress at reduced saturation amplitudes, and a "dead" zone where the Reynolds stress is the dominant means of transport. The high Reynolds stress in the dead zone is driven by the flux of kinetic energy from the MRI supported turbulence in the active region. Aside from the flux of kinetic energy, interaction between the zones is insignificant. The Poynting flux through the boundary was minimal and decreased with increasing resistivity. In the dead zone the MRI is stabilized at values of ReM consistent with those obtained for the local simulations. Thus local simulations may be useful in determining which regions of a disk may support enhanced angular momentum transport. The results above suggest that the model for layered accretion may require modification. Transport in the dead zone may be non-neglible, thus resulting in a longer timescale over which accretion outburst events occur.