On the asymptotic behavior of the super sonic interstellar gas flow which is made by spiral density wave, propagating in rapidly rotating galaxy disk

Nonlinear solutions for the large-scale flow of interstellar gas in the presence of a spiral gravitational field have received considerable attention because this model allows to explain a lot of observations for galaxy disks. However this investigations were forced to limit by numerable analysis of the problem because of its nonlinearity. In this paper we wish to carry out the analytical expression which allows us to describe the super sonic nonlinear interstellar gas flow in rapidly rotating galaxy disk which is made by the spiral density wave. One of characteristic parameters of theory is the amplitude of spiral density wave potential corresponding to separatrix, which separates super sonic flows from flows containing the jump from super sonic flows to subsonic. We have defined the dependence of perturbing potential value, under which the galaxy shock wave appeared with respect to the parameters characterizing the gas disk (such as sound speed in gas, disk rotation speed, "spiral design" rotation speed).