The Circular Velocity Function of Group Galaxies
  A robust prediction of $\Lambda{\rm CDM}$ cosmology is the halo circular
velocity function (CVF), a dynamical cousin of the halo mass function. The
correspondence between theoretical and observed CVFs is uncertain, however:
cluster galaxies are reported to exhibit a power-law CVF consistent with
$N$-body simulations, but that of the field is distinctly Schechter-like,
flattened relative to $\Lambda{\rm CDM}$ expectations at circular velocities
$v_c \lesssim 200\, {\rm km\, s^{-1}}$. Groups offer a powerful probe of the
role environment plays in this discrepancy as they bridge the field and
clusters. Here, we construct the CVF for a large, mass- and
multiplicity-complete sample of group galaxies from the Sloan Digital Sky
Survey. Using independent photometric $v_c$ estimators, we find no transition
from a field- to $\Lambda{\rm CDM}$-shaped CVF above $v_c = 50\, {\rm km\,
s^{-1}}$ as a function of group halo mass. All groups with $12.4 \lesssim \log
M_{\rm halo} / M_{\odot} \lesssim 15.1$ (Local Group analogs to rich clusters)
display similar Schechter-like CVFs marginally suppressed at low-$v_c$ compared
to that of the field. Conversely, some agreement with $N$-body results emerges
for samples saturated with late-type galaxies, with isolated late-types
displaying a CVF similar in shape to $\Lambda{\rm CDM}$ predictions. We
conclude that the flattening of the low-$v_c$ slope in groups is due to their
depressed late-type fractions -- environment affecting the CVF only to the
extent that it correlates with this quantity -- and that previous cluster
analyses may suffer from interloper contamination. These results serve as
useful benchmarks for cosmological simulations of galaxy formation.
