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 Faber-Jackson and 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.