LOCAL SHEAR INSTABILITIES IN WEAKLY IONIZED, WEAKLY MAGNETIZED DISKS

We extend the analysis of axisymmetric magnetic shear instabilities fr om ideal magnetohydrodynamic (MHD) flows to weakly ionized plasmas wit h coupling between ions and neutrals caused by collisions, ionization, and recombination. As part of the analysis, we derive the single-flui d MI-ID dispersion relation without invoking the Boussinesq approximat ion. This work expands the range of applications of these instabilitie s from fully ionized accretion disks to molecular disks in galaxies an d, with somewhat more uncertainty, to protostellar disks. Instability generally requires the angular velocity to decrease outward, the magne tic field strengths to be subthermal, and the ions and neutrals to be sufficiently well coupled. If ionization and recombination processes c an be neglected on an orbital timescale, adequate coupling is achieved when the collision frequency of a given neutral with the ions exceeds the local epicyclic frequency. When ionization equilibrium is maintai ned on an orbital timescale, a new feature is present in the disk dyna mics: in contrast to a single-fluid system, subthermal azimuthal field s can affect the axisymmetric stability of weakly ionized two-fluid sy stems. We discuss the underlying causes for this behavior. Azimuthal f ields tend to be stabilizing under these circumstances, and good coupl ing between the neutrals and ions requires the collision frequency to exceed the epicyclic frequency by a potentially large secant factor re lated to the magnetic field geometry. When the instability is present, subthermal azimuthal fields may also reduce the growth rate unless th e collision frequency is high, but this is important only if the field strengths are very subthermal and/or the azimuthal field is the domin ant field component. We briefly discuss our results in the context of the Galactic center circumnuclear disk, and suggest that the shear ins tability might be present there, and be responsible for the observed t urbulent motions.