Einasto Profiles and the Dark Matter Power Spectrum

TL;DR

This study investigates dark matter halo density profiles and mass accretion histories using N-body simulations, revealing that halo structures are influenced by initial power spectrum steepness and retain memory of their formation environment.

Contribution

It demonstrates how the Einasto profile shape parameter varies with peak height and initial power spectrum slope, linking halo structure to initial conditions.

Findings

Density profiles are similar despite different MAHs.

The Einasto shape parameter increases with peak height.

Profile curvature depends on the initial power spectrum slope.

Abstract

We study the mass accretion histories (MAHs) and density profiles of dark matter halos using N-body simulations of self-similar gravitational clustering from scale-free power spectra, $P(k)\propto k^n$. We pay particular attention to the density profile curvature, which we characterize using the shape parameter, $\alpha$, of an Einasto profile. In agreement with previous findings our results suggest that, despite vast differences in their MAHs, the density profiles of virialized halos are remarkably alike. Nonetheless, clear departures from self-similarity are evident: for a given spectral index, $\alpha$ increases slightly but systematically with "peak height", $\nu\equiv\delta_{sc}/\sigma(M,z)$, regardless of mass or redshift. More importantly, however, the "$\alpha-\nu$" relation depends on $n$: the steeper the initial power spectrum, the more gradual the curvature of both the mean MAHs and mean density profiles. These results are consistent with previous findings connecting the shapes of halo mass profiles and MAHs and imply that dark matter halos are not structurally self-similar but, through the merger history, retain a memory of the linear density field from which they form.