Title: The Galaxy Clustering Crisis in Abundance Matching,
Abstract: Galaxy clustering on small scales is significantly under-predicted by
sub-halo abundance matching (SHAM) models that populate (sub-)haloes with
galaxies based on peak halo mass, $M_{\rm peak}$. SHAM models based on the peak
maximum circular velocity, $V_{\rm peak}$, have had much better success. The
primary reason $M_{\rm peak}$ based models fail is the relatively low abundance
of satellite galaxies produced in these models compared to those based on
$V_{\rm peak}$. Despite success in predicting clustering, a simple $V_{\rm
peak}$ based SHAM model results in predictions for galaxy growth that are at
odds with observations. We evaluate three possible remedies that could "save"
mass-based SHAM: (1) SHAM models require a significant population of "orphan"
galaxies as a result of artificial disruption/merging of sub-haloes in modern
high resolution dark matter simulations; (2) satellites must grow significantly
after their accretion; and (3) stellar mass is significantly affected by halo
assembly history. No solution is entirely satisfactory. However, regardless of
the particulars, we show that popular SHAM models based on $M_{\rm peak}$
cannot be complete physical models as presented. Either $V_{\rm peak}$ truly is
a better predictor of stellar mass at $z\sim 0$ and it remains to be seen how
the correlation between stellar mass and $V_{\rm peak}$ comes about, or SHAM
models are missing vital component(s) that significantly affect galaxy
clustering.