The role of the radial orbit instability in dark matter halo formation and structure

For a decade, N-body simulations have revealed a nearly universal dark matter density profile, which appears to be robust to changes in the overall density of the universe and the underlying power spectrum. Despite its universality, the physical origin of this profile has not yet been well understood. Semianalytic models by Barnes and coworkers have suggested that the density structure of dark matter halos is determined by the onset of the radial orbit instability (ROI). We have tested this hypothesis using N-body simulations of collapsing dark matter halos with a variety of initial conditions. For dynamically cold initial conditions, the resulting halo structures are triaxial in shape, due to the mild aspect of the instability. We examine how variations in initial velocity dispersion affect the onset of the instability, and find that an isotropic velocity dispersion can suppress the ROI entirely, while a purely radial dispersion does not. The quantity σ²/v _c² is a criterion for instability, where regions with σ²/v_c² ≲ 1 become triaxial due to the ROI or other perturbations. We also find that the radial orbit instability sets a scale length at which the velocity dispersion changes rapidly from isotropic to radially anisotropic. This scale length is proportional to the radius at which the density profile changes shape, as is the case in the semianalytic models; however, the coefficient of proportionality is different by a factor of ∼2.5. We conclude that the radial orbit instability is likely to be a key physical mechanism responsible for the nearly universal profiles of simulated dark matter halos.