The Galaxy in Action Space

It is generally better to think of galaxies as made of orbits rather than stars. Orbits in most axisymmetric potentials form a three-dimensional continuum. The natural coordinates for the description of this continuum are action integrals. Thus one is led to the view that our Galaxy inhabits a three-dimensional Euclidean space called action space. In this space the density of stars belonging to each galactic component is given by the distribution function of that component. The structure and evolution of the disk within action space is described. The most natural disk distribution function turns out to violate the classical relation between Oort’s constants and the ratio of principal velocity dispersions of disk stars. The Schwarzschild velocity ellipsoid is not a self-similar solution of the equation that governs the diffusion of disk stars through action space if scattering of stars by molecular clouds is the sole cause of the diffusion. A general procedure for choosing the distribution functions of hot components such as the classical populations II is described and illustrated by several worked examples.