Critical points of density distribution of rapidly rotating superdense Newtonian polytropes

Abstract

An analytical representation of the density distribution of rapidly rotating superdense Newtonian polytropes is obtained in terms of polynomials in powers of flatness parameters e and the polytropic index approximating it with an error of 10−3. A scheme of the determination of critical points in the configuration density distribution is constructed. If n = 1.4, the values of the parameters characterizing an analytical representation of density near the critical points are obtained. The dynamics of critical points depending on the parameter e is studied. The formation of A 2- and A 3-type catastrophes is demonstrated. It is proven that a bubble domain in the shape of an elliptical torus is formed in the density distribution near the point e = 0.3503.