The Mass Profile and Accretion History of Cold Dark Matter Halos
  We use the Millennium Simulation series to study the relation between the
accretion history (MAH) and mass profile of cold dark matter halos. We find
that the mean density within the scale radius, r_{-2} (where the halo density
profile has isothermal slope), is directly proportional to the critical density
of the Universe at the time when the main progenitor's virial mass equals the
mass enclosed within r_{-2}. Scaled to these characteristic values of mass and
density, the mean MAH, expressed in terms of the critical density of the
Universe, M(\rho_{crit}(z)), resembles that of the enclosed density profile,
M(<\rho >), at z=0. Both follow closely the NFW profile, suggesting that the
similarity of halo mass profiles originates from the mass-independence of halo
MAHs. Support for this interpretation is provided by outlier halos whose
accretion histories deviate from the NFW shape; their mass profiles show
correlated deviations from NFW and are better approximated by Einasto profiles.
Fitting both M(<\rho >) and M(\rho_{crit}) with either NFW or Einasto profiles
yield concentration and shape parameters that are correlated, confirming and
extending earlier work linking the concentration of a halo with its accretion
history. These correlations also confirm that halo structure is insensitive to
initial conditions: only halos whose accretion histories differ greatly from
the NFW shape show noticeable deviations from NFW in their mass profiles. As a
result, the NFW profile provides acceptable fits to hot dark matter halos,
which do not form hierarchically, and for fluctuation power spectra other than
CDM. Our findings, however, predict a subtle but systematic dependence of mass
profile shape on accretion history which, if confirmed, would provide strong
support for the link between accretion history and halo structure we propose
here.
