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 axial field and perturbation wavenumber geometry. Here we treat the problem more generally. Both axisymmetric and nonaxisymmetric cases are treated. Though seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron whistler waves, and since these have right-hand polarization, a helicity factor is also introduced into the stability problem. This factor is the product of the components of the angular velocity and magnetic field along the perturbation wavenumber, and it is destabilizing when negative. An important finding of our more general calculation is that unless the field and angular velocity are exactly aligned, it is always possible to find destabilizing wavenumbers. HEMFs can destabilize any differential rotation law, even those with angular velocity increasing outward. Regardless of the sign of the angular velocity gradient, the maximum growth rate is always given in magnitude by the local Oort A value of the disk, as in the standard magnetorotational instability. The role of HEMFs may prove crucial to understanding how turbulence is maintained in the low state of eruptive disk systems.