An ACT measurement of the MaDCoWS mass-richness scaling relation

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≲z≲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 κ=1.84+0.15−0.14, where the
slope is defined as M∝λ^(κ) where λ 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. We conclude that the
original MaDCoWS survey's selection function is not well defined, and,
as such, reiterate the MaDCoWS collaboration's recommendation that the
sample is suited for probing cluster and galaxy evolution, but not
cosmological analyses.