Einasto Profiles and the Dark Matter Power Spectrum
  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.
