Two-component galaxies with flat rotation curve

Abstract

Dynamical properties of two-component galaxy models whose stellar density distribution is described by a γ model while the total density distribution has a pure r-2 profile are presented. The orbital structure of the stellar component is described by Osipkov-Merritt anisotropy, while the dark matter halo is isotropic. After a description of minimum halo models, the positivity of the phase-space density (the model consistency) is investigated, and necessary and sufficient conditions for consistency are obtained analytically as a function of the stellar inner density slope γ and anisotropy radius. The explicit phase-space distribution function is recovered for integer values of γ, and it is shown that while models with γ > 4/17 are consistent when the anisotropy radius is larger than a critical value (dependent on γ), the γ = 0 models are unphysical even in the fully isotropic case. The Jeans equations for the stellar component are then solved analytically; in addition, the projected velocity dispersion at the centre and at large radii are also obtained analytically for generic values of the anisotropy radius, and it is found that they are given by remarkably simple expressions. The presented models, even though highly idealized, can be useful as starting point for more advanced modelling of the mass distribution of elliptical galaxies in studies combining stellar dynamics and gravitational lensing. © 2009 RAS.