  Galaxy clusters are an important tool for cosmology, and their detection and
characterization are key goals for current and future surveys. Using data from
the Wide-field Infrared Survey Explorer (WISE), the Massive and Distant
Clusters of WISE Survey (MaDCoWS) located 2,839 significant galaxy
overdensities at redshifts $0.7\lesssim z\lesssim 1.5$, which included
extensive follow-up imaging from the Spitzer Space Telescope to determine
cluster richnesses. Concurrently, the Atacama Cosmology Telescope (ACT) has
produced large area mm-wave maps in three frequency bands along with a large
catalog of Sunyaev-Zeldovich (SZ) selected clusters, as part of its Data
Release 5 (DR5). Using the maps and cluster catalog from DR5, we explore the
scaling between SZ mass and cluster richness. We use complementary radio survey
data from the Very Large Array, submillimeter data from Herschel, and ACT
224~GHz data to assess the impact of contaminating sources on the SZ signals.
We then use a hierarchical Bayesian model to fit the mass-richness scaling
relation. We find that MaDCoWS clusters have submillimeter contamination which
is consistent with a gray-body spectrum, while the ACT clusters are consistent
with no submillimeter emission on average. We find the best fit ACT SZ mass vs.
MaDCoWS richness scaling relation has a slope of $\kappa =
1.84^{+0.15}_{-0.14}$, where the slope is defined as $M\propto
\lambda_{15}^{\kappa}$ where $\lambda_{15}$ is the richness. Additionally, we
find that the approximate level of in-fill of the ACT and MaDCoWS cluster SZ
signals to be at the percent level

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics