On the distribution of matter in disk-shaped galaxies of finite thickness

Abstract

For an axisymmetric galaxy with an exponential density decrease along the z-direction, the relation between the projected surface density and the rotation curve is investigated. The peculiar motions of stars are neglected. Revised forms of Toomre's formulae for an infinitely thin disk galaxy are obtained. It is found that with a finite thickness, matter is more concentrated towards the centre; the projected surface density in the central part of our Galaxy comes out about 9% higher than is given by Toomre's model.