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, \rho(r), and differential energy distributions, N(E), of
individual simulated halos. The best fit shape parameter $\phi_{0}$ obtained
from the two types of fits are correlated, though with scatter. Our most
important conclusions come from \rho(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 \rho(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 \rho(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.
