Dust in galaxy clusters: Modeling at millimeter wavelengths and impact
  on Planck cluster cosmology
  We have examined dust emission in galaxy clusters at millimeter wavelengths
using the Planck $857 \, {\rm GHz}$ map to constrain the model based on
Herschel observations that was used in studies for the Cosmic ORigins Explorer
(CORE) mission concept. By stacking the emission from Planck-detected clusters,
we estimated the normalization of the infrared luminosity versus mass relation
and constrained the spatial profile of the dust emission. We used this newly
constrained model to simulate clusters that we inject into Planck frequency
maps. The comparison between clusters extracted using these gas+dust
simulations and the basic gas-only simulations allows us to assess the impact
of cluster dust emission on Planck results. In particular, we determined the
impact on cluster parameter recovery (size, flux) and on Planck cluster
cosmology results (survey completeness, determination of cosmological
parameters). We show that dust emission has a negligible effect on the recovery
of individual cluster parameters for the Planck mission, but that it impacts
the cluster catalog completeness, reducing the number of detections in the
redshift range [0.3-0.8] by up to $\sim 9\%$. Correcting for this
incompleteness in the cosmological analysis has a negligible effect on
cosmological parameter measurements: in particular, it does not ease the
tension between Planck cluster and primary cosmic microwave background
cosmologies.
