Instabilities in a Self-Gravitating Magnetized Gas Disk

Abstract

A linear stability analysis has been performed onto a self-gravitating magnetized gas disk bounded by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by self-gravity, usual Jeans gravitational instability and convection. In the direction parallel to the magnetic fields, the magnetic tension completely suppresses the convection. If the adiabatic index $γ$ is less than a certain critical value, the perturbations trigger the Parker as well as the Jeans instability in the disk. Consequently, the growth rate curve has two maxima: one at small wavenumber due to a combination of the Parker and Jeans instabilities, and the other at somewhat larger wavenumber mostly due to the Parker instability. In the horizontal direction perpendicular to the fields, the convection makes the growth rate increase monotonically upto a limiting value as the perturbation wavenumber gets large. However, at small wavenumbers, the Jeans instability becomes effective and develops a peak in the growth rate curve. Depending on the system parameters, the maximum growth rate of the convection may or may not be higher than the peak due to the Jeans-Parker instability. Therefore, a cooperative action of the Jeans and Parker instabilities can have chances to over-ride the convection and may develop large scale structures of cylindrical shape in non-linear stage. In thick disks the cylinder is expected to align its axis perpendicular to the field, while in thin ones parallel to it.