Two-component galaxies with flat rotation curve

TL;DR

This paper introduces analytical models of two-component galaxies with flat rotation curves, analyzing their dynamical stability, phase-space consistency, and velocity dispersion profiles, providing tools for studying elliptical galaxy mass distributions.

Contribution

It presents new analytical models of two-component galaxies with gamma-model stellar density and r^(-2) total density, including phase-space and velocity dispersion analyses.

Findings

Models with gamma>4/17 are consistent if anisotropy radius exceeds a critical value.

Gamma=0 models are unphysical even when isotropic.

Explicit formulas for velocity dispersions are derived.

Abstract

Dynamical properties of two-component galaxy models whose stellar density distribution is described by a gamma-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 gamma and anisotropy radius. The explicit phase-space distribution function is recovered for integer values of gamma, and it is shown that while models with gamma>4/17 are consistent when the anisotropy radius is larger than a critical value (dependent on gamma), the gamma=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 center 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 modeling of the mass distribution of elliptical galaxies in studies combining stellar dynamics and gravitational lensing.