Density Profiles of ΛCDM Clusters

We analyze the mass accretion histories (MAHs) and density profiles of cluster-size halos with virial masses of × 1014 h-1 M☉ in a flat ΛCDM cosmology. We find that most MAHs have a similar shape: an early merger-dominated mass increase followed by a more gradual accretion-dominated growth. For some clusters the intense merger activity and rapid mass growth continue until the present-day epoch. In agreement with previous studies, we find that the concentration of the density distribution is tightly correlated with the halo's MAH and with its formation redshift. During the period of fast mass growth, the concentration remains approximately constant and low, cv ≈ 3-4, while during the slow accretion stages the concentration increases with decreasing redshift as cv ∝ (1 + z)-1. We consider fits of three widely discussed analytic density profiles to the simulated clusters, focusing on the most relaxed inner regions. We find that there is no unique best-fit analytic profile for all the systems. At the same time, if a cluster is best fitted by a particular analytic profile at z = 0, the same is usually true at earlier epochs out to z ~ 1-2. The local logarithmic slope of the density profiles at 3% of the virial radius ranges from -1.2 to -2.0, a remarkable diversity for the relatively narrow mass range of our cluster sample. Interestingly, for all the studied clusters the logarithmic slope down to the smallest resolved scale (≲1% of the virial radius) becomes shallower with decreasing radius without reaching an asymptotic value. We do not find a clear correlation of the inner slope with the formation redshift or the shape of the halo's MAH. We do find, however, that during the period of rapid mass growth the density profiles can be well described by a single power law ρ(r) ∝ r-γ with γ ~ 1.5-2. The relatively shallow power-law slopes result in low concentrations at these stages of evolution, as the scale radius at which the density profiles reach the slope of -2 is at large radii. This indicates that the inner power law-like density distribution of halos is built up during the periods of rapid mass accretion and active merging, while the outer steeper profile is formed when the mass accretion slows down. To check the convergence and robustness of our conclusions, we resimulate one of our clusters by using 8 times as many particles and twice as good force resolution. We find good agreement between the two simulations in all the results discussed in our study.