The Circular Velocity Function of Group Galaxies

A robust prediction of $\mathrm{\Lambda }\mathrm{C}\mathrm{D}\mathrm{M}$ 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 $\mathrm{\Lambda }\mathrm{C}\mathrm{D}\mathrm{M}$ expectations at circular velocities $v_c\lesssim 200\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$. 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 $\mathrm{\Lambda }\mathrm{C}\mathrm{D}\mathrm{M}$-shaped CVF above $v_c = 50, {\rm km, s^{-1}}$asafunctionofgrouphalomass\mathrm{.}Allgroupswith$12.4 \lesssim \log M_{\rm halo} / M_{\odot} \lesssim 15.1$ (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 $\mathrm{\Lambda }\mathrm{C}\mathrm{D}\mathrm{M}$ 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.