Linear analysis of the Hall effect in protostellar disks

The effects of Hall electromotive forces (HEMFs) on the linear stability of protostellar disks are examined. Earlier work on this topic focused on axi al field and perturbation wavenumber geometry. Here we treat the problem mo re generally. Both axisymmetric and nonaxisymmetric cases are treated. Thou gh seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron w histler waves, and since these have right-hand polarization, a helicity fac tor is also introduced into the stability problem. This factor is the produ ct of the components of the angular velocity and magnetic field along the p erturbation wavenumber, and it is destabilizing when negative. An important finding of our more general calculation is that unless the field and angul ar velocity are exactly aligned, it is always possible to find destabilizin g wavenumbers. HEMFs can destabilize any differential rotation law, even th ose with angular velocity increasing outward. Regardless of the sign of the angular velocity gradient, the maximum growth rate is always given in magn itude by the local Oort A value of the disk, as in the standard magnetorota tional instability. The role of HEMFs may prove crucial to understanding ho w turbulence is maintained in the "low state" of eruptive disk systems.