An Improved and Physically-Motivated Scheme for Matching Galaxies with
  Dark Matter Halos
  The simplest scheme for predicting real galaxy properties after performing a
dark matter simulation is to rank order the real systems by stellar mass and
the simulated systems by halo mass and then simply assume monotonicity - that
the more massive halos host the more massive galaxies. This has had some
success, but we study here if a better motivated and more accurate matching
scheme is easily constructed by looking carefully at how well one could predict
the simulated IllustrisTNG galaxy sample from its dark matter computations. We
find that using the dark matter rotation curve peak velocity, $v_{max}$, for
normal galaxies reduces the error of the prediction by 30% (18% for central
galaxies and 60% for satellite systems) - following expectations from the
physics of monolithic collapse. For massive systems with halo mass $>$
10$^{12.5}$ M$_{\odot}$ hierarchical merger driven formation is the better
model and dark matter halo mass remains the best single metric. Using a new
single variable that combines these effects, $\phi$ $=$
$v_{max}$/$v_{max,12.7}$ + M$_{peak}$/(10$^{12.7}$ M$_{\odot}$) allows further
improvement and reduces the error, as compared to ranking by dark matter mass
at $z=0$ by another 6% from $v_{max}$ ranking. Two parameter fits -- including
environmental effects produce only minimal further impact.
