Statistics of Dark Matter Substructure: II. Comparison of Model with
  Simulation Results
  We compare subhalo mass and velocity functions obtained from different
simulations with different subhalo finders among each other, and with
predictions from the new semi-analytical model of Jiang & van den Bosch (2014).
We find that subhalo mass functions (SHMFs) obtained using different subhalo
finders agree with each other at the level of ~ 20 percent, but only at the low
mass end. At the massive end, subhalo finders that identify subhaloes based
purely on density in configuration space dramatically underpredict the subhalo
abundances by more than an order of magnitude. These problems are much less
severe for subhalo velocity functions (SHVFs), indicating that they arise from
issues related to assigning masses to the subhaloes, rather than from detecting
them. Overall the predictions from the semi-analytical model are in excellent
agreement with simulation results obtained using the more advanced subhalo
finders that use information in six dimensional phase-space. In particular, the
model accurately reproduces the slope and host-mass-dependent normalization of
both the subhalo mass and velocity functions. We find that the SHMFs and SHVFs
have power-law slopes of 0.82 and 2.6, respectively, significantly shallower
than what has been claimed in several studies in the literature.
