A dynamics-based density profile for dark haloes -- III. Parameter space

TL;DR

This paper analyzes a new density profile model for dark matter haloes, exploring its parameter space and how these parameters relate to halo properties like mass and accretion history.

Contribution

It provides a detailed analysis of the parameter space of a truncated Einasto profile and clarifies how profile parameters relate to halo formation and accretion.

Findings

Parameters are non-degenerate in averaged profiles.

The truncation radius correlates with accretion rate.

The shape parameter alpha depends on accretion rate, not mass.

Abstract

In the previous paper of this series, we proposed a new function to fit halo density profiles out to large radii. This truncated Einasto profile models the inner, orbiting matter as $\rho_{\rm orb} \propto \exp \left[-2/\alpha\ (r / r_{\rm s})^\alpha - 1/\beta\ (r / r_{\rm t})^\beta \right]$ and the outer, infalling term as a power-law overdensity. In this paper, we analyse the resulting parameter space of scale radius $r_{\rm s}$, truncation radius $r_{\rm t}$, steepening $\alpha$, truncation sharpness $\beta$, infalling normalisation $\delta_1$, and infalling slope $s$. We show that these parameters are non-degenerate in averaged profiles, and that fits to the total profiles generally recover the underlying properties of the orbiting and infalling terms. We study the connection between profile parameters and halo properties such as mass (or peak height) and accretion rate. We find that the commonly cited dependence of $\alpha$ on peak height is an artefact of fitting Einasto profiles to the actual, truncated profiles. In our fits, $\alpha$ is independent of mass but dependent on accretion rate. When fitting individual halo profiles, the parameters exhibit significant scatter but otherwise follow the same trends. We confirm that the entire profiles are sensitive to the accretion history of haloes, and that the two radial scales $r_{\rm s}$ and $r_{\rm t}$ particularly respond to the formation time and recent accretion rate. As a result, $r_{\rm t}$ is a more accurate measure of the accretion rate than the commonly used radius where the density slope is steepest.