The post-collapse equilibrium structure of cosmological haloes in a low-density universe

An analytical model is presented for the post-collapse equilibrium structure of virialized objects that 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, non-singular, truncated isothermal sphere (TIS), a particular solution of the Lane–Emden equation (suitably modified when Λ≠0). 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 that 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 non-standard CDM models, such as that for self-interacting dark matter, recently proposed to resolve this conflict.