Accurate Model of the Projected Velocity Distribution of Galaxies in
  Dark Matter Halos
  We present a percent-level accurate model of the line-of-sight velocity
distribution of galaxies around dark matter halos as a function of projected
radius and halo mass. The model is developed and tested using synthetic galaxy
catalogs generated with the UniverseMachine run on the Multi-Dark Planck 2
N-body simulations. The model decomposes the galaxies around a cluster into
three kinematically distinct classes: orbiting, infalling, and interloping
galaxies. We demonstrate that: 1) we can statistically distinguish between
these three types of galaxies using only projected line-of-sight velocity
information; 2) the halo edge radius inferred from the line-of-sight velocity
dispersion is an excellent proxy for the three-dimensional halo edge radius; 3)
we can accurately recover the full velocity dispersion profile for each of the
three populations of galaxies. Importantly, the velocity dispersion profiles of
the orbiting and infalling galaxies contain five independent parameters --
three distinct radial scales and two velocity dispersion amplitudes -- each of
which is correlated with mass. Thus, the velocity dispersion profile of galaxy
clusters has inherent redundancies that allow us to perform nontrivial
systematics check from a single data set. We discuss several potential
applications of our new model for detecting the edge radius and constraining
cosmology and astrophysics using upcoming spectroscopic surveys.
