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.
