Intra-cluster Summed Galaxy Colors
  Though cluster-summed luminosities have served as mass proxies,
cluster-summed colors have received less attention. Since galaxy colors have
given useful insights into dust content and specific star formation rates, this
research investigates possible correlations between cluster-summed colors and
various observable and intrinsic halo properties for clusters in subsamples of
TNG, SDSS, and Buzzard.
  Cluster color--magnitude space shows a peak towards the red and bright
corner, drawn there by bright red galaxies. Summing colors across a cluster
reduces the scatter in color spaces, since magnitude summing acts somewhat like
a weighted average. The correlation between these summed colors were $(73 \pm
24)\%$ across all three datasets. Summed colors and cluster properties
typically had low correlations but ranged up to $\sim 40\%$. The correlation
between color and mass didn't change significantly with richness threshold for
TNG and Buzzard, but for SDSS the correlation decreased dramatically with
increasing richness, passing from positive correlation to negative correlation
near a richness threshold of ten.
  We also looked at mass proxy scaling relations with richness or magnitude and
measured the reduction in mass scatter once we added cluster colors. The
reduction was generally insignificant, but several large reductions in mass
scatter occurred under certain circumstances: high-richness Buzzard
mass--magnitude relation saw a reduction of $(19 \pm 28)\%$ while low-richness
SDSS saw similar order reductions of $(16 \pm 8)\%$ and $(14 \pm 8)\%$ for the
mass--richness and mass--magnitude relations respectively. This first look at
summed cluster color shows potential in aiding mass proxies under certain
circumstances, but more deliberate and thorough investigations are needed to
better characterize and make use of cluster-summed colors.
