Spiral solitons in the flat gas disks of galaxies

Abstract

In the theory of spiral structure of galaxies, the theory of density waves in flat gravitating disks has achieved the greatest successes. A theory is developed in this study of the nonlinear perturbations of a thin self-gravitating disk at the limit of gravitational instability with allowance for nonlinear terms up to and including the fifth order. The critical value of the surface polytropic index below which explosive instability of the disk develops is reduced by virtue of the terms of fifth order of the nonlinearity by an amount proportional to the square of the perturbation amplitude. The correction to the amplitude and the small changes in the profile of the cubic solition depend on the velocity of the perturbations. The stability of the solitons is investigated and the corrections to the growth rates of the cubic solitons are obtained.