On a non-local stability of self-gravitating stellar systems

Antonov's theory on a stability of collisionless self-gravitating systems is extended so as to include a differential rotation. For slowly rotating systems, the perturbation method is developed on the basis of a linearized Vlasov and Poisson equations with axi-symmetry. By means of this method, a marginal stability is analyzed for a series of Miyamoto's stellar disk models. It is shown that among these stellar disks a class is unstable for a velocity deviation due to the differential rotation. Its physical meaning is also discussed in connection with a characteristic shape of a density perturbation. (author)