The dynamical structure of dark matter halos with universal properties

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 $ρ/σ_r^3$, and a linear $β-γ$ 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 $β(r)$ with arbitrary asymptotic values $β_0$ and $β_\infty$. 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.