Zones of anomalous activity of the magnetorotational instability in protostellar disks

A criterion for the magnetorotational instability of a protostellar disk in which the dust particles are assumed to be well mixed with the gas over the entire disk volume has been obtained within the framework of Hall magnetohydrodynamics. It is shown that the dusty plasma component affects significantly the Hall current and, under certain conditions, can cause its direction to be reversed compared to the case of a weakly ionized electron-ion plasma. A significant expansion of the range of wave numbers for unstable magnetic fluctuations is a consequence of the Hall current reversal. The spatial localization of the regions of protostellar disks in which not only the long-wavelength Alfvén disturbances but also the short-wavelength ones are subject to the magnetorotational instability is investigated. Possible physical consequences of the presence of anomalously active zones in cold disks for their structure and evolution are pointed out.