The cosmological dependence of cluster density profiles

We use N-body simulations to study the shape of mean cluster density and velocity profiles in the nonlinear regime formed via gravitational instability. The dependence of the final structure on both cosmology and initial density field is examined, using a grid of cosmologies and scale- free initial power spectra P (k) is proportional to kⁿ^. Einstein-de Sitter, open ({OMEGA₀_ = 0. 2 and 0. 1) and flat, low density (OMEGA₀_ = 0. 2, λ₀_ = 0. 8) models are examined, with initial spectral indices n = - 2, - 1 and 0. For each model, we stack clusters in an appropriately scaled manner to define an average density profile in the nonlinear regime. The profiles are well fit by a power law p (r) is proportional to r^-α^ for radii whereas the local density contrast is between 100 and 3000. This covers 99% of the cluster volume. We find a clear trend toward steeper slopes (larger α's) with both increasing n and decreasing OMEGA₀_. The OMEGA₀_ dependence is partially masked by the n dependence; these is degeneracy in the values of α between the Einstein-de Sitter and flat, low-density cosmologies. However, the profile slopes in the open models are consistently higher than the OMEGA = 1 values for the range of n examined. Cluster density profiles are thus potentially useful cosmological diagnostics. We find no evidence for a constant density core in any of the models, although the density profiles do tend to flatten at small radii. Much of the flattening is due to the force softening required by the simulations. An attempt is made to recover the unsoftened profiles assuming angular momentum invariance. The recovered profiles in Einstein-de Sitter cosmologies are consistent with a pure power law up to the highest density contrasts (10⁶^) accessible with our resolution. The low-density models show significant deviation from a power law above density contrasts ~10⁵^. We interpret this curvature as reflecting the non- scale-invariant nature of the background cosmology in these models. These results are at the limit of our resolution and so should be tested in future using simulations with larger numbers of particles. Such simulations will also provide insight on the broader problem of understanding, in a statistical sense, the full phase space structure of collapsed, cosmological halos.