The cusp-halo relation

TL;DR

This paper introduces a predictive framework and a new density profile model for the central cusps of dark matter halos, which are crucial for understanding warm dark matter scenarios.

Contribution

It provides a method to predict the cusp coefficient for each halo and introduces the cusp-NFW profile, along with a code package for implementation.

Findings

The cusp coefficient A can be predicted for individual halos.

The cusp-NFW profile accurately models halos with prompt cusps.

The framework aids in studying warm dark matter models.

Abstract

Simulations have established that each halo of collisionless dark matter is expected to contain a $\rho = A r^{-1.5}$ density cusp at its center. This prompt cusp is a relic of the halo's earliest moments and has a mass comparable to the cutoff scale in the spectrum of initial density perturbations. In this work, we provide a framework to predict for each halo the coefficient $A$ of its central cusp. We also present a "cusp-NFW" functional form that accurately describes the density profile of a halo with a prompt cusp at its center. Accurate characterization of each halo's central cusp is of particular importance in the study of warm dark matter models, for which the spectral cutoff is on an astrophysically relevant mass scale. To facilitate easy incorporation of prompt cusps into any halo modeling approach, we provide a code package that implements the cusp-halo relation and the cusp-NFW density profile.