Comparison of Hectospec Virial Masses with SZE Measurements
  We present the first comparison of virial masses of galaxy clusters with
their Sunyaev-Zel'dovich Effect (SZE) signals. We study 15 clusters from the
Hectospec Cluster Survey (HeCS) with MMT/Hectospec spectroscopy and published
SZE signals. We measure virial masses of these clusters from an average of 90
member redshifts inside the radius $r_{100}$. The virial masses of the clusters
are strongly correlated with their SZE signals (at the 99% confidence level
using a Spearman rank-sum test). This correlation suggests that $Y_{SZ}$ can be
used as a measure of virial mass. Simulations predict a powerlaw scaling of
$Y_{SZ}\propto M_{200}^\alpha$ with $\alpha\approx$1.6. Observationally, we
find $\alpha$=1.11$\pm$0.16, significantly shallower (given the formal
uncertainty) than the theoretical prediction. However, the selection function
of our sample is unknown and a bias against less massive clusters cannot be
excluded (such a selection bias could artificially flatten the slope).
Moreover, our sample indicates that the relation between velocity dispersion
(or virial mass estimate) and SZE signal has significant intrinsic scatter,
comparable to the range of our current sample. More detailed studies of scaling
relations are therefore needed to derive a robust determination of the relation
between cluster mass and SZE.
