Stochastic model of ring structures in galaxies

The collective dynamics of an ensemble of density inhomogeneities in a rotating gravitating disk is examined, assuming that the inhomogeneities participate in the rotation of the disk and have small radial velocities. It is found that, if the contrasts of the inhomogeneities are positive, the isotropic geodesics are exponentially unstable. In this case, the collective gravitational field of the inhomogeneities is stochastic. It is shown that, with the passage of time, the inhomogeneities form a fragmented ring with nearly constant density contrast and position on the disk.