The dynamical structure of dark matter halos with universal properties

TL;DR

This paper introduces a family of analytical phase-space distribution functions that accurately reproduce the universal properties of dark matter halos observed in simulations, offering insights into their formation and structure.

Contribution

It presents a new set of self-consistent, analytical distribution functions based on Dehnen-McLaughlin models that incorporate universal halo properties and allow flexible anisotropy profiles.

Findings

Distribution functions accurately reproduce universal halo properties

Able to generate diverse velocity anisotropy profiles

Provides a new tool for understanding dark matter halo formation

Abstract

$N$-body simulations have unveiled several apparently universal properties of dark matter halos, including a cusped density profile, a power-law pseudo phase-space density $\rho/\sigma_r^3$, and a linear $\beta-\gamma$ relation between the density slope and the velocity anisotropy. We present a family of self-consistent phase-space distribution functions $F(E,L)$, based on the Dehnen-McLaughlin Jeans models, that incorporate these universal properties very accurately. These distribution functions, derived using a quadratic programming technique, are analytical, positive and smooth over the entire phase space and are able to generate four-parameter velocity anisotropy profiles $\beta(r)$ with arbitrary asymptotic values $\beta_0$ and $\beta_\infty$. We discuss the orbital structure of six radially anisotropic systems in detail and argue that, apart from its use for generating initial conditions for $N$-body studies, our dynamical modeling provides a valuable complementary approach to understand the processes involved in the formation of dark matter halos.