Evolution of the density profiles of dark matter haloes

We use numerical simulations in a ΛCDM cosmology to model density profiles in a set of sixteen dark matter haloes with resolutions of up to seven million particles within the virial radius. These simulations allow us to follow robustly the formation and evolution of the central cusp over a large mass range of 10 to 10 M⊙, down to approximately 0.5% of the virial radius, and from redshift 5 to the present, covering a larger range in parameter space than previous works. We confirm that the cusp of the density profile is set at redshifts of two or greater and remains remarkably stable to the present time, when considered in non-comoving coordinates. Motivated by the diversity and evolution of halo profile shapes, we fit our haloes to the two parameter profile, ρ ∝ 1 (cγr/rvir) [1+(cγr/rvir)] , where the steepness of the cusp is given by the asymptotic inner slope parameter, γ, and its radial extent is described by the concentration parameter, cγ (with cγ defined as the virial radius divided by the concentration radius). In our simulations, we find γ ≃ 1.4− 0.08Log10(M/M∗) for haloes of 0.01M∗ to 1000M∗, with a large scatter of ∆γ ∼ ±0.3, where M∗ is the redshift dependent characteristic mass of collapsing haloes; and cγ ≃ 8.(M/M∗) , with a large M/M∗ dependent scatter roughly equal to ±cγ . Our redshift zero haloes have inner slope parameters ranging approximately from r (i.e. Navarro, Frenk, & White) to r (i.e. Moore et al. ), with a median of roughly r. This two parameter profile fit works well for all types haloes in our simulations, whether or not they show evidence of a steep asymptotic cusp. We also model a cluster in power law cosmologies of P ∝ k, with n = (0, -1, -2, -2.7). Here we find that the concentration radius and the inner cusp slope are a both function of n, with larger concentration radii and shallower cusps for steeper power spectra. We have completed a thorough resolution study and find that the minimum resolved radius is well described by the mean interparticle separation over a range of masses and redshifts. The trend of steeper and more concentrated cusps for smaller M/M∗ haloes clearly shows that dwarf sized ΛCDM haloes have, on average, significantly steeper density profiles within the inner few percent of the virial radius than inferred from recent observations. Code to reproduce this profile can be downloaded from http://www.icc.dur.ac.uk/∼reed/profile.html.