On the stability of a differentially rotating disk of stars

Stability and collective oscillations of an infinitely thin stellar disk of highly flattened galaxies are studied by utilizing the technique of the plasma kinetic theory. It is shown that the gravitationally (Jeans-) stable disk may still be unstable to oscillatory growing waves that propagate in the plane of a system. The cause of this spontaneous instability of small-amplitude gravity perturbations is the interaction of stars with spiral Jeans-stable (natural) waves at corotation resonance in a differentially rotating system. Typical growth rates of excited density waves are large and comparable in magnitude to the characteristic frequency of the disk rotation. The similar magneto-drift kinetic instability (overstability) of the inverse Landau damping type has been discussed first by Krall and Rosenbluth (1963, Phys. Fluids, 6, 254) in physics of an inhomogeneous plasma. The instability has an essential dependence on the differential rotation of the disk. It seems likely that by these kinetically unstable oscillations, one can explain a new type of small-amplitude recurrent spiral modes discovered in N-body simulations by Sellwood and Lin (1989, Monthly Not. Roy. Astron. Soc., 240, 991) and Donner and Thomasson (1994, Astron. Astrophys., 290, 785). Computational tests as well as desirable extensions to the theory are proposed.