Abstract
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 a sharp drop in the density profile. Using N-body simulations, we model the distribution of the kinematically distinct infalling and orbiting populations of subhalos and halos. We show that the two are mixed spatially all the way to redge, which extends past the splashback radius defined by the drop in the spherically averaged density profile. This edge radius can be interpreted as a radius which contains a fixed fraction of the apocenters of dark matter particles. Our results highlight the possibility of measuring the outer boundary of a dark matter halo using its phase space structure and provide a firm theoretical foundation to the satellite galaxy model adopted in the companion paper (Tomooka et al. 2020), where we analyzed the phase space distribution of SDSS redMaPPer clusters.