Magnetic viscosity by localized shear flow instability in magnetized accretion disks

摘要

Differentially rotating disks are subject to the axisymmetric instability for perfectly conducting plasma in the presence of poloidal magnetic fields. For nonaxisymmetric perturbations, the authors find localized unstable eigenmodes whose eigenfunction is confined between two Alfven singularities at (omega)(sub d) = (+-) (omega)(sub A), where (omega)(sub d) is the Doppler-shifted wave frequency, and (omega)(sub A) = k(parallel)v(sub A) is the Alfven frequency. The radial width of the unstable eigenfunction is (Delta)x (approximately) (omega)(sub A)/(Ak(sub y)), where A is the Oort's constant, and k(sub y) is the azimuthal wave number. The growth rate of the fundamental mode is larger for smaller value of k(sub y)/k(sub z). The maximum growth rate when k(sub y)/k(sub z) (approximately) 0.1 is (approximately) 0.2(Omega) for the Keplerian disk with local angular velocity (Omega). It is found that the purely growing mode disappears when k(sub y)/k(sub z) > 0.12. In a perfectly conducting disk, the instability grows even when the seed magnetic field is infinitesimal. Inclusion of the resistivity, however, leads to the appearance of an instability threshold. When the resistivity (eta) depends on the instability-induced turbulent magnetic fields (delta)B as (eta)((delta)B(sup 2)), the marginal stability condition self-consistently determines the (alpha) parameter of the angular momentum transport due to the magnetic stress. For fully ionized disks, the magnetic viscosity parameter (alpha)(sub B) is between 0.001 and 1. The authors' three-dimensional MHD simulation confirms these unstable eigenmodes. It also shows that the (alpha) parameter observed in simulation is between 0.01 and 1, in agreement with theory. The observationally required smaller (alpha) in the quiescent phase of accretion disks in dwarf novae may be explained by the decreased ionization due to the temperature drop.