Two body relaxation in CDM simulations
Abstract
N-body simulations of the hierarchical formation of cosmic structures suffer from the problem that the first objects to form always contain just a few particles. Although relaxation is not an issue for virialised objects containing millions of particles, collisional processes will always dominate within the first structures that collapse. First we quantify how the relaxation varies with resolution, softening, and radius within isolated equilibrium and non-equilibrium cuspy haloes. We then show how this numerical effect propagates through a merging hierarchy by measuring the local relaxation rates of each particle throughout the hierarchical formation of a dark matter halo. The central few percent of the final structures suffer from high degrees of relaxation - a region which one might naively think is well resolved at the final time since the haloes contain approximately 10^6 particles. The entire haloes have a degree of relaxation larger than unity which implies that the energy of any particle has been numerical changed by of order itself. We show that relaxation will flatten a cusp in just a few mean relaxation times of a halo. We explore the effect of resolution on the degree of relaxation and we find that increasing N slowly reduces the degree of relaxation proportional to N^{-0.25} rather than proportional to 1/N as expected from the Vlasov equation. Cluster mass objects suffer most from relaxation since they form relatively late and therefore more of the particles spend more time in small N haloes.Keywords
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