  We use high-resolution N-body simulations to study the equilibrium density
profiles of dark matter halos in hierarchically clustering universes. We find
that all such profiles have the same shape, independent of halo mass, of
initial density fluctuation spectrum, and of the values of the cosmological
parameters. Spherically averaged equilibrium profiles are well fit over two
decades in radius by a simple formula originally proposed to describe the
structure of galaxy clusters in a cold dark matter universe. In any particular
cosmology the two scale parameters of the fit, the halo mass and its
characteristic density, are strongly correlated. Low-mass halos are
significantly denser than more massive systems, a correlation which reflects
the higher collapse redshift of small halos. The characteristic density of an
equilibrium halo is proportional to the density of the universe at the time it
was assembled. A suitable definition of this assembly time allows the same
proportionality constant to be used for all the cosmologies that we have
tested. We compare our results to previous work on halo density profiles and
show that there is good agreement. We also provide a step-by-step analytic
procedure, based on the Press-Schechter formalism, which allows accurate
equilibrium profiles to be calculated as a function of mass in any hierarchical
model.
