What sets the central structure of dark matter haloes?

Abstract

Dark matter (DM) haloes forming near the thermal cut-off scale of the density perturbations are unique, since they are the smallest objects and form through monolithic gravitational collapse, while larger haloes contrastingly have experienced mergers. While standard cold dark matter (CDM) simulations readily produce haloes that follow the universal Navarro-Frenk-White (NFW) density profile with an inner slope, $\rho \propto r^{-\alpha}$, with $\alpha=1$, recent simulations have found that when the free-streaming cut-off expected for the CDM model is resolved, the resulting haloes follow nearly power-law density profiles of $\alpha\sim1.5$. In this paper, we study the formation of density cusps in haloes using idealized $N$-body simulations of the collapse of proto-haloes. When the proto-halo profile is initially cored due to particle free-streaming at high redshift, we universally find $\sim r^{-1.5}$ profiles irrespective of the proto-halo profile slope outside the core and large-scale non-spherical perturbations. Quite in contrast, when the proto-halo has a power-law profile, then we obtain profiles compatible with the NFW shape when the density slope of the proto-halo patch is shallower than a critical value, $\alpha_{\rm ini} \sim 0.3$, while the final slope can be steeper for $\alpha_{\rm ini}\ga 0.3$. We further demonstrate that the $r^{-1.5}$ profiles are sensitive to small scale noise, which gradually drives them towards an inner slope of $-1$, where they become resilient to such perturbations. We demonstrate that the $r^{-1.5}$ solutions are in hydrostatic equilibrium, largely consistent with a simple analytic model, and provide arguments that angular momentum appears to determine the inner slope.