Darkness Visible: N-Body Simulations of Dark Matter Spikes in Hernquist Haloes

TL;DR

This paper presents fully numerical simulations of dark matter spikes in Hernquist haloes, introduces an empirical density profile based on simulations, and discusses implications for dark matter detection and gravitational wave signals.

Contribution

It provides the first fully numerical simulation of dark matter spikes in Hernquist haloes and proposes a new empirical density profile dependent on a single mass-ratio parameter.

Findings

Spike radius scales differently than theoretical predictions.

Significant depletion of outer halo in high mass-ratio systems.

Empirical profile deviates from previous approximations.

Abstract

Dark matter is theorised to form massive haloes, which could be further condensed into so-called spikes when a black hole grows at the centre of such a halo. The existence of these spikes is instrumental for several dark matter detection schemes such as indirect detection and imprints on gravitational wave inspirals, but all previous work on their formation has been (semi-)analytical. We present fully numerically simulated cold dark matter spikes using the SWIFT code. Based on these results, we propose a simple empirical density profile - dependent on only a single mass-ratio parameter between the black hole and total mass - for dark matter spikes grown in Hernquist profiles. We find that the radius of the spike scales differently compared to theoretical predictions, and show a depletion of the outer halo that is significant for high mass-ratio systems. We critically assess approximations of the spike as used in the field, show that our profile significantly deviates, and contextualise the potential influence for future dark matter detections by simulating binary black hole inspirals embedded in our profile.