The Baryonic Collapse Efficiency of Galaxy Groups in the RESOLVE and ECO
  Surveys
  We examine the z = 0 group-integrated stellar and cold baryonic (stars + cold
atomic gas) mass functions (group SMF and CBMF) and the baryonic collapse
efficiency (group cold baryonic to dark matter halo mass ratio) using the
RESOLVE and ECO survey galaxy group catalogs and a galform semi-analytic model
(SAM) mock catalog. The group SMF and CBMF fall off more steeply at high masses
and rise with a shallower low-mass slope than the theoretical halo mass
function (HMF). The transition occurs at group-integrated cold baryonic mass
M_coldbary ~ 10^11 Msun. The SAM, however, has significantly fewer groups at
the transition mass ~ 10^11 Msun and a steeper low-mass slope than the data,
suggesting that feedback is too weak in low-mass halos and conversely too
strong near the transition mass. Using literature prescriptions to include hot
halo gas and potential unobservable galaxy gas produces a group BMF with slope
similar to the HMF even below the transition mass. Its normalization is lower
by a factor of ~2, in agreement with estimates of warm-hot gas making up the
remaining difference. We compute baryonic collapse efficiency with the halo
mass calculated two ways, via halo abundance matching (HAM) and via dynamics
(extended all the way to three-galaxy groups using stacking). Using HAM, we
find that baryonic collapse efficiencies reach a flat maximum for groups across
the halo mass range of M_halo ~ 10^11.4-12 Msun, which we label "nascent
groups." Using dynamics, however, we find greater scatter in baryonic collapse
efficiencies, likely indicating variation in group hot-to-cold baryon ratios.
Similarly, we see higher scatter in baryonic collapse efficiencies in the SAM
when using its true groups and their group halo masses as opposed to
friends-of-friends groups and HAM masses.
