The power-law galaxies

Abstract

Axisymmetric galaxy models with simple distribution functions (DFs) that are sums of powers of the binding energy E and angular momentum component |$L_z$| are presented. They are useful for representing elliptical galaxies, as well as the bulges and haloes of spiral galaxies. The equipotentials are stratified on similar concentric spheroids. The rotation law can be asymptotically rising, flat or declining. The intrinsic and projected velocity dispersions are elementary. In the limit of vanishing core radius, the galaxies are scale-free, and the surface brightness is cusped. Composite models, in which a population of stars with a spheroidal density distribution is embedded within the halo, are easy to construct.