Nonlinear evolution of the magnetorotational instability in ion-neutral disks

We carry out three-dimensional magnetohydrodynamical simulations of the magnetorotational (Balbus-Hawley) instability in weakly ionized plasmas. We adopt a formulation in which the ions and neutrals are treated as separate fluids coupled only through a collisional drag term. Ionization and recombination processes are not considered. The linear stability of the ion-neutral system has been previously considered by Blaes & Balbus. Here we extend their results to the nonlinear regime by computing the evolution of the Keplerian angular momentum distribution in the local shearing box approximation. We find significant turbulence and angular momentum transport when the collisional frequency is on the order of 100 times the orbital frequency Omega. At higher collision rates, the two-fluid system studied here behaves much like the fully ionized systems studied previously. At lower collision rates, the evolution of the instability is determined primarily by the properties of the ions, with the neutrals acting as a sink for the turbulence. Since in this regime saturation occurs when the magnetic field is superthermal with respect to the ion pressure, we find that the amplitude of the magnetic energy and the corresponding angular momentum transport rate is proportional to the ion density. Our calculations show that the ions and neutrals are essentially decoupled when the collision frequency is less than 0.01 Omega; in this case, the ion fluid behaves as in the single-fluid simulations and the neutrals remain quiescent. We find that purely toroidal initial magnetic field configurations are unstable to the magnetorotational instability across the range of coupling frequencies.