Non-spherical similarity solutions for dark halo formation

We carry out fully three-dimensional simulations of evolution from self-similar, spherically symmetric linear perturbations of a cold dark matter (CDM)-dominated Einstein-de Sitter universe. As a result of the radial orbit instability, the haloes which grow from such initial conditions are triaxial with major-to-minor axial ratios of the order of 3:1. They nevertheless grow approximately self-similarly in time. In all cases, they have power-law density profiles and near-constant velocity anisotropy in their inner regions. Both the power-law index and the value of the velocity anisotropy depend on the similarity index of the initial conditions, the former as expected from simple scaling arguments. Halo structure is thus not 'universal' but remembers the initial conditions. On larger scales the density and anisotropy profiles show two characteristic scales, corresponding to particles at the first pericentre and at the first apocentre after infall. They are well approximated by the Navarro-Frenk-White model only for one value of the similarity index. In contrast, at all radii within the outer caustic the pseudo-phase-space density can be fitted by a single power law with an index which depends only very weakly on the similarity index of the initial conditions. This behaviour is very similar to that found for haloes formed from Lambda CDM initial conditions and so can be considered approximately universal.