Integration of Poisson's equation for a disk galaxy of finite thickness

Abstract

Assuming a density perturbance in the form of an Archimedes spiral and an exponential decrease of matter density along the z-direction, Poisson's equation governing the perturbed gravitational field is solved with Hankel's integral transform and the method of steepest descent. For shortwave perturbances in the plane z=0, a simple analytical expression is given. In our approximation, the form of the perturbed field is determinate and is also an Archimedes spiral.