A model of a spiral galaxy with finite thickness

Abstract

A first-order asymptotic solution (rapid phase variation) of the Poisson's equation for the three-dimensional potential in a special model is applied to a stationary, polytropic gas disk. After considering the vertical motion and the three-dimensional distributions of the physical parameters, a dispersion relation is derived. Numerical examples are calculated for the Schmidt model galaxy and for a thick galaxy to illustrate the variation of the wave number with height which may possibly account for certain observed facts about spiral arms.