The mass profile and accretion history of cold dark matter haloes
We use the Millennium Simulation series to investigate the relation between the accretion history and mass profile of cold dark matter (CDM) haloes. We find that the mean inner 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 virial mass of the main progenitor equals the mass enclosed within r(-2). Scaled to these characteristic values of mass and density, the average mass accretion history, expressed in terms of the critical density of the Universe, M((crit)(z)), resembles that of the enclosed density profile, M( >), at z = 0. Both follow closely the Navarro, Frenk & White (NFW) profile, which suggests that the similarity of halo mass profiles originates from the mass-independence of halo accretion histories. Support for this interpretation is provided by outlier haloes 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( >) and M((crit)) with either NFW or Einasto profiles yield concentration and shape parameters that are correlated, confirming and extending earlier work that has linked the concentration of a halo with its accretion history. These correlations also confirm that halo structure is insensitive to initial conditions: only haloes whose accretion histories differ greatly from the NFW shape show notable deviations from NFW in their mass profiles. As a result, the NFW profile provides acceptable fits to hot dark matter haloes, 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.