The Atacama Cosmology Telescope: Relation Between Galaxy Cluster Optical
  Richness and Sunyaev-Zel'dovich Effect
  We present the measured Sunyaev-Zel'dovich (SZ) flux from 474
optically-selected MaxBCG clusters that fall within the Atacama Cosmology
Telescope (ACT) Equatorial survey region. The ACT Equatorial region used in
this analysis covers 510 square degrees and overlaps Stripe 82 of the Sloan
Digital Sky Survey. We also present the measured SZ flux stacked on 52
X-ray-selected MCXC clusters that fall within the ACT Equatorial region and an
ACT Southern survey region covering 455 square degrees. We find that the
measured SZ flux from the X-ray-selected clusters is consistent with
expectations. However, we find that the measured SZ flux from the
optically-selected clusters is both significantly lower than expectations and
lower than the recovered SZ flux measured by the Planck satellite. Since we
find a lower recovered SZ signal than Planck, we investigate the possibility
that there is a significant offset between the optically-selected brightest
cluster galaxies (BCGs) and the SZ centers, to which ACT is more sensitive due
to its finer resolution. Such offsets can arise due to either an intrinsic
physical separation between the BCG and the center of the gas concentration or
from misidentification of the cluster BCG. We find that the entire discrepancy
for both ACT and Planck can be explained by assuming that the BCGs are offset
from the SZ maxima with a uniform random distribution between 0 and 1.5 Mpc.
Such large offsets between gas peaks and BCGs for optically-selected cluster
samples seem unlikely given that we find the physical separation between BCGs
and X-ray peaks for an X-ray-selected subsample of MaxBCG clusters to have a
much narrower distribution that peaks within 0.2 Mpc. It is possible that other
effects are lowering the ACT and Planck signals by the same amount, with
offsets between BCGs and SZ peaks explaining the remaining difference between
measurements. (Abridged)
