A Very Simple Cusped Halo Model

Abstract

We introduce a very simple model of a dark halo. It is a close relative of Hernquist's model, being generated by the same transformation but this time applied to the logarithmic potential rather than the point mass. The density is proportional to (distance)${}^{-1}$ at small radii, whilst the rotation curve is flat at large radii. Isotropic and radially anisotropic distributions functions are readily found, and the intrinsic and line of sight kinematical quantities are available as simple formulae. We also provide an analytical approximation to the Hamiltonian as a function of the actions. As an application, we study the kinematic properties of stellar haloes and tracers in elliptical galaxies. We show that the radial velocity dispersion of a power-law population in a galaxy with a flat rotation curve always tends to the constant value. This holds true irrespective of the anisotropy or the lengthscales of the dark or luminous matter. An analogous result holds for the line of sight or projected velocity dispersion of a power-law surface brightness profile. The radial velocity dispersion of Population II stars in the Milky Way is a strongly declining function of Galactocentric radius. So, if the rotation curve is flat, we conclude that the stellar halo density cannot follow a power-law at large radii, but must decrease more sharply (like an Einasto profile) or be abruptly truncated at large radii. Both the starcount and kinematic data of the Milky Way stellar halo are well-represented by an Einasto profile with index $m\approx 2$ and effective radius $\approx 20$ kpc.

8 pages, 6 figures, MNRAS in press

References in corpus (4)

• High-resolution dark matter density profiles of THINGS dwarf galaxies: Correcting for non-circular motions
• A universal density slope - velocity anisotropy relation for relaxed structures
• Touching The Void: A Striking Drop in Stellar Halo Density Beyond 50 kpc
• Hamiltonians of Spherically Symmetric, Scale-Free Galaxies in Action-Angle Coordinates

Cited by in corpus (4)

• Action-based distribution functions for spheroidal galaxy components
• Made-to-Measure Dark Matter Haloes, Elliptical Galaxies and Dwarf Galaxies in Action Coordinates
• Miyamoto-Nagai discs embedded in the Binney logarithmic potential: analytical solution of the two-integrals Jeans equations
• The Doubloon Models of Dark Haloes