An analytic distribution function for a massless cored stellar system in a cuspy dark matter halo

TL;DR

This paper derives analytical distribution functions for spherical, massless cored stellar systems within cuspy dark matter halos, matching observed velocity dispersions in dwarf galaxies, useful for simulations.

Contribution

It provides the first analytical distribution functions for cored stellar systems embedded in cuspy halos with specific velocity anisotropy, enabling realistic initial conditions for simulations.

Findings

Derived analytical distribution functions for specific stellar-halo models.

Models reproduce velocity dispersion profiles similar to dwarf spheroidal galaxies.

Applicable for generating initial conditions in N-body simulations.

Abstract

We demonstrate the existence of distribution functions that can be used to represent spherical massless cored stellar systems embedded in cuspy dark matter halos with constant mildly tangential velocity anisotropy. In particular, we derive analytically the functional form of the distribution function for a Plummer stellar sphere in a Hernquist dark halo, for \beta_0 = -0.5 and for different degrees of embedding. This particular example satisfies the condition that the central logarithmic slope of the light profile \gamma_0 > 2 \beta_0. Our models have velocity dispersion profiles similar to those observed in nearby dwarf spheroidal galaxies. Hence they can be used to generate initial conditions for a variety of problems, including N-body simulations that may represent dwarf galaxies in the Local Group.