The Hall instability of weakly ionized, radially stratified, rotating disks

Cool weakly ionized gaseous rotating disk, are considered by many models as the origin of the evolution of protoplanetary clouds. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Thus, a hierarchy of successive fragmentations into smaller and smaller pieces as a part of the Kant-Laplace theory of formation of the planetary system remains valid also for contemporary cosmogony. Traditionally, axisymmetric magnetohydrodynamic (MHD), and recently Hall-MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against nonaxisymmetric perturbations in compressible rotating fluids in external magnetic field is proposed as a viable mechanism for the azimuthal fragmentation of the protoplanetary disk and thus perhaps initiating the road to planet formation. The Hall instability is excited due to the combined effect of the radial stratification of the disk and the Hall electric field, and its growth rate is of the order of the rotation period.