Scaling Relations in the Phase-Space Structure of Dark Matter Haloes

TL;DR

This paper identifies new scaling relations for the phase-space structure of simulated dark matter haloes, extending classical models and providing practical tools for approximating their distribution functions across various halo masses.

Contribution

It introduces novel scaling relations for the phase-space distribution functions and energy distributions of dark matter haloes, based on simulations, generalizing classical isothermal sphere models.

Findings

Scaling relations hold across broad energy ranges.

Relations depend on gravitational constant and NFW profile parameters.

Applicable to haloes over a wide mass range.

Abstract

We present new scaling relations for the isotropic phase-space distribution functions (DFs) and energy distributions of simulated dark matter haloes. These relations are inspired by those for the singular isothermal sphere with density profile $\rho(r)\propto r^{-2}$, for which the DF satisfies $f(E) \propto r_{\max}^{-2}(E)$ and the energy distribution satisfies $dM/dE \propto r_{\max}(E)$, with $r_{\max}(E)$ being the radius where the gravitational potential equals energy $E$. For the simulated haloes, we find $f(E)\propto r_{\max}^{-2.08}(E)$ and $dM/dE \propto r_{\max}(E)$ across broad energy ranges. In addition, the proportionality coefficients depend on the gravitational constant and the parameters of the best-fit Navarro-Frenk-White density profile. These scaling relations are satisfied by haloes over a wide mass range and provide an efficient method to approximate their DFs and energy distributions. Understanding the origin of these relations may shed more light on halo formation.