Axisymmetric Magnetorotational Instability in Viscous Accretion Disks

Abstract

Axisymmetric magnetorotational instability (MRI) in viscous accretion disks is investigated by linear analysis and two-dimensional nonlinear simulations. The linear growth of the viscous MRI is characterized by the Reynolds number defined as RMRI≡ ν2/ν,ω where νA is the Alfvén velocity, ν is the kinematic viscosity, and ω is the angular velocity of the disk. Although the linear growth rate is suppressed considerably as the Reynolds number decreases, the nonlinear behavior is found to be almost independent of RMRI. At the nonlinear evolutionary stage, a two-channel flow continues growing and the Maxwell stress increases until the end of calculations even though the Reynolds number is much smaller than unity. A large portion of the injected energy to the system is converted to the magnetic energy. The gain rate of the thermal energy, on the other hand, is found to be much larger than the viscous heating rate. Nonlinear behavior of the MRI in the viscous regime and its difference from that in the highly resistive regime can be explained schematically by using the characteristics of the linear dispersion relation. Applying our results to the case with both the viscosity and resistivity, it is anticipated that the critical value of the Lundquist number SMRI ≡ ν2/n{right tail}ω, for active turbulence depends on the magnetic Prandtl number SMRI.c α Pm1/2 in the regime of Pm » 1 and remains constant when Pm « 1, where Pm ≡ S MRI/RMRI = ν/n{right tail} and n{right tail} is the magnetic diffusivity. © 2008. The American Astronomical Society. All rights reserved.