Dark Matter Halo Profiles in Scale-Free Cosmologies

TL;DR

This study investigates how the inner density slopes of dark matter halos depend on the initial power spectrum slope in scale-free cosmologies, finding a correlation but no convergence to a universal slope.

Contribution

It demonstrates the dependence of halo inner slopes on the spectral index and challenges the notion of a universal central density slope in dark matter halos.

Findings

Inner slope $\alpha$ correlates with spectral index $n$

Normalizing by $r_{-2}$ removes slope differences

No evidence for a universal central slope

Abstract

We explore the dependence of the central logarithmic slope of dark matter halo density profiles $\alpha$ on the spectral index $n$ of the linear matter power spectrum $P(k)$ using cosmological $N$-body simulations of scale-free models (i.e. $P(k) \propto k^n$). For each of our simulations we identify samples of well resolved haloes in dynamical equilibrium and we analyse their mass profiles. By parameterising the mass profile using a ``generalised'' Navarro, Frenk & White profile in which the central logarithmic slope $\alpha$ is allowed to vary while preserving the $r^{-3}$ asymptotic form at large radii, we obtain preferred central slopes for haloes in each of our models. There is a strong correlation between $\alpha$ and $n$, such that $\alpha$ becomes shallower as $n$ becomes steeper. However, if we normalise our mass profiles by $r_{-2}$, the radius at which the logarithmic slope of the density profile is -2, we find that these differences are no longer present. We conclude that there is no evidence for convergence to a unique central asymptotic slope, at least on the scales that we can resolve.