Resolving the Structure of Cold Dark Matter Halos

TL;DR

This study probes how mass resolution and force softening affect the central density structure of cold dark matter halos in cosmological N-body simulations. Using multi-scale resimulations with a high-resolution region embedded in a larger volume, and a PKDGRAV treecode, the authors demonstrate that higher resolution yields significantly steeper inner cusps, with a converged slope near $\rho(r) \sim r^{-1.4}$ within about $1\%$ of the virial radius. They show that both particle number and softening influence the cusp, and that a substantial fraction of the central mass originates from early-formed subhalos, suggesting the inner structure is tied to the formation history rather than numerical artifacts. The findings imply stronger central densities than the traditional NFW profile, with important consequences for arc statistics and galaxy-halo dynamics, and indicate that even higher resolution may be required to fully characterize the inner CDM cusp.

Abstract

We examine the effects of mass resolution and force softening on the density profiles of cold dark matter halos that form within cosmological N-body simulations. As we increase the mass and force resolution, we resolve progenitor halos that collapse at higher redshifts and have very high densities. At our highest resolution we have nearly 3 million particles within the virial radius, several orders of magnitude more than previously used and we can resolve more than one thousand surviving dark matter halos within this single virialised system. The halo profiles become steeper in the central regions and we may not have achieved convergence to a unique slope within the inner 10% of the virialised region. Results from two very high resolution halo simulations yield steep inner density profiles, $ρ(r)\sim r^{-1.4}$. The abundance and properties of arcs formed within this potential will be different from calculations based on lower resolution simulations. The kinematics of disks within such a steep potential may prove problematic for the CDM model when compared with the observed properties of halos on galactic scales.