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Testing DARKexp against energy and density distributions of Millennium-II halos

We test the DARKexp model for relaxed, self-gravitating, collisionless systems against equilibrium dark matter halos from the Millennium-II simulation. While limited tests of DARKexp against simulations and observations have been carried out elsewhere, this is the first time the testing is done with a large sample of simulated halos spanning a factor of ~ 50 in mass, and using independent fits to density and energy distributions. We show that DARKexp, a one shape parameter family, provides very good fits to the shapes of density profiles, ρ(r), and differential energy distributions, N(E), of individual simulated halos. The best fit shape parameter $ϕ_{0}$ obtained from the two types of fits are correlated, though with scatter. Our most important conclusions come from ρ(r) and N(E) that have been averaged over many halos. These show that the bulk of the deviations between DARKexp and individual Millennium-II halos come from halo-to-halo fluctuations, likely driven by substructure, and other density perturbations. The average ρ(r) and N(E) are quite smooth and follow DARKexp very closely. The only deviation that remains after averaging is small, and located at most bound energies for N(E) and smallest radii for ρ(r). Since the deviation is confined to 3-4 smoothing lengths, and is larger for low mass halos, it is likely due to numerical resolution effects.