Nonspherical similarity solutions for dark halo formation

We carry out fully 3-dimensional simulations of evolution from self-similar, spherically symmetric linear perturbations of a Cold Dark Matter 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 axis ratios of order 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 first pericentre and at first apocentre after infall. They are well approximated by the NFW 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 fit 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 LCDM initial conditions and so can be considered approximately universal.

Caustics in growing Cold Dark Matter Haloes

We simulate the growth of isolated dark matter haloes from self-similar and spherically symmetric initial conditions. Our N-body code integrates the geodesic deviation equation in order to track the streams and caustics associated with individual simulation particles. The radial orbit instability causes our haloes to develop major-to-minor axis ratios approaching 10 to 1 in their inner regions. They grow similarly in time and have similar density profiles to the spherical similarity solution, but their detailed structure is very different. The higher dimensionality of the orbits causes their stream and caustic densities to drop much more rapidly than in the similarity solution. This results in a corresponding increase in the number of streams at each point. At 1% of the turnaround radius (corresponding roughly to the Suns position in the Milky Way) we find of order 10^6 streams in our simulations, as compared to 10^2 in the similarity solution. The number of caustics in the inner halo increases by a factor of several, because a typical orbit has six turning points rather than one, but caustic densities drop by a much larger factor. This reduces the caustic contribution to the annihilation radiation. For the region between 1% and 50% of the turnaround radius, this is 4% of the total in our simulated haloes, as compared to 6.5% in the similarity solution. Caustics contribute much less at smaller radii. These numbers assume a 100 GeV c^-2 neutralino with present-day velocity dispersion 0.03 cm s^-1, but reducing the dispersion by ten orders of magnitude only doubles the caustic luminosity. We conclude that caustics will be unobservable in the inner parts of haloes. Only the outermost caustic might potentially be detectable.