The Phase Space Structure of Dark Matter Halos

The phase space structure of dark matter halos can be used to measure the mass of the halo, infer mass accretion rates, and probe the effects of modified gravity. Previous studies showed that the splashback radius can be measured in position space using the slope of the density profile. Using N-body simulations, we show that the phase space structure of the dark matter halo does not end at this splashback radius. Instead, there exists a region where infalling, splashback, and virialized halos are mixed spatially. We model the distribution of the three kinematically distinct populations and show that there exists an "edge radius" beyond which a dark matter halo has no orbiting substructures. This radius is a fixed multiple of the splashback radius as defined in previous works, and can be interpreted as a radius which contains a fixed fraction of the apocenters of dark matter particles. Our results provide a firm theoretical foundation to the satellite galaxy model adopted in the companion paper by Tomooka et al., where we analyzed the phase space distribution of SDSS redMaPPer clusters.