On the global stability of rotating magnetized disks

Global modes of the magnetic shear instability in horizontally unbounded rotating disks are studied by solving the linear eigenvalue problem. Nonaxisymmetry and finite diffusivities are allowed for. The instability exists in a range of the magnetic field amplitudes between the minimum value, B-min, imposed by the finite diffusivities and the maximum amplitude, B-max, brought about by the finite thickness of the disk. The unstable modes for the magnetic field close to the lower and upper bounds occupy different regions in the disk. The critical rotation rates for onset of the instability for the excitations with various axial and vertical symmetries are estimated and their dependencies on the external magnetic field amplitude are defined. The axisymmetric modes with symmetric magnetic field and antisymmetric velocity relative to the disk mid-plane are most easily excited. The effective diffusivity produced by the supernova explosions is small enough for the instability to be active in the galactic disk. The possibility of the global hydromagnetic dynamos excited by the instability in astrophysical disks is discussed.