Parker-Jeans Instability of Gaseous Disks

The magnetohydrodynamical instability of self-gravitating magnetized gaseous disks is investigated by means of a normal-mode analysis. The growth rates and eigenfunctions of unstable perturbations are obtained numerically. The perturbed disks are shown graphically. Self-gravitating magnetized gaseous disks, in general, suffer from two kinds of instabilities, the Jeans and Parker types. The former is driven by self-gravity and the latter by a nonuniform magnetic field. These two kinds of instabilities coexist in our model and have different characteristics. In our equilibrium model disk, the Jeans mode has a larger growth rate than does the Parker mode, when either the magnetic field is weak or the wavelength of the perturbation is long. The Parker instability dominates when the magnetic field is strong and the wavelength is short. The Jeans instability disturbs mainly the high-density region near the midplane; the Parker instability disturbs mainly the low-density region far from the midplane. The growth rate of the Jeans instability is maximum when the wave vector of the perturbation is parallel to the magnetic field. On the other hand, that of the Parker instability is maximum when the wavenumber in the direction perpendicular to the magnetic field is infinitely large.