  An analytical model is presented for the postcollapse equilibrium structure
of virialized objects which condense out of a low-density cosmological
background universe, either matter-dominated or flat with a cosmological
constant. This generalizes the model we derived previously for an Einstein-de
Sitter (EdS) universe. The model is based upon the assumption that cosmological
haloes form from the collapse and virialization of top-hat density
perturbations and are spherical, isotropic, and isothermal. This leads to the
prediction of a unique, nonsingular, truncated isothermal sphere (TIS), a
particular solution of the Lane-Emden equation (modified for nonzero
cosmological constant). The size and virial temperature are unique functions of
the mass and redshift of formation of the object for a given background
universe. The central density is roughly proportional to the critical density
of the universe at the epoch of collapse. This TIS model is in good agreement
with observations of the internal structure of dark matter--dominated haloes on
scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many
of the average properties of haloes in simulations of the Cold Dark Matter
(CDM) model to good accuracy, suggesting that it is a useful analytical
approximation for haloes which form from realistic initial conditions. Our TIS
model matches the density profiles of haloes in CDM N-body simulations outside
the innermost region, while avoiding the steep central cusp of the latter which
is in apparent conflict with observations. The TIS model may also be relevant
to nonstandard CDM models, like self-interacting dark matter, recently proposed
to resolve this conflict.
