The Hall instability in magnetized rotating disks

Full Text: The dynamics of rotating gaseous disks under the influence of a magnetic field is of great importance to numerous astrophysical phenomena. Of particular importance is the study of the various instabilities that may arise within the rotating disks whose inverse growth rates are comparable to the rotation period. Such instabilities are believed to hold the key to the solution of such persistent problems as the outwards transport of angular momentum in rotating disks. The rediscovery of the magneto-rotational instability (MRI) within astrophysical context gave the sign to a series of extensive investigations of magnetohydrodynamic (MHD) instabilities in such configurations. In this work the importance of the Hall electromotive force to such astrophysical objects as protostellar disks is introduced and discussed. It is shown that in addition to modifying the classical MRI instabilities, the Hall effect gives rise to a new family of instabilities when it is acting in a density stratified environment. That new family of wave propagation phenomena are characterized by the emergence of the Hall drift velocity VHD = li2Ωi/L where li and Ωi are the inertial length and Larmor frequency of the ions, respectively, and L is a measure of the density inhomogeneity length. In particular it is shown that a slow quasi electrostatic mode may become unstable for short enough inhomogeneity length scales . That mode is termed the Hall instability and the domains of its existence in astrophysical parameter space is investigated and presented