The HectoMAP Cluster Survey: Spectroscopically Identified Clusters and
  their Brightest Cluster Galaxies (BCGs)
  We apply a friends-of-friends (FoF) algorithm to identify galaxy clusters and
we use the catalog to explore the evolutionary synergy between BCGs and their
host clusters. We base the cluster catalog on the dense HectoMAP redshift
survey (2000 redshifts deg$^{-2}$). The HectoMAP FoF catalog includes 346
clusters with 10 or more spectroscopic members. We list these clusters and
their members (5992 galaxies with a spectroscopic redshift). We also include
central velocity dispersions ($\sigma_{*, BCG}$) for all of the FoF cluster
BCGs, a distinctive feature of the HectoMAP FoF catalog. HectoMAP clusters with
higher galaxy number density (80 systems) are all genuine clusters with a
strong concentration and a prominent BCG in Subaru/Hyper Suprime-Cam images.
The phase-space diagrams show the expected elongation along the line-of-sight.
Lower-density systems include some false positives. We establish a connection
between BCGs and their host clusters by demonstrating that
$\sigma_{*,BCG}/\sigma_{cl}$ decreases as a function of cluster velocity
dispersion ($\sigma_{cl}$), in contrast, numerical simulations predict a
constant $\sigma_{*, BCG}/\sigma_{cl}$. Sets of clusters at two different
redshifts show that BCG evolution in massive systems is slow over the redshift
range $z < 0.4$. The data strongly suggest that minor mergers may play an
important role in BCG evolution in these clusters ($\sigma_{cl} \gtrsim 300$ km
s$^{-1}$). For systems of lower mass ($\sigma_{cl} < 300$ km s$^{-1}$), the
data indicate that major mergers may play a significant role. The coordinated
evolution of BCGs and their host clusters provides an interesting test of
simulations in high density regions of the universe.
