Measuring Polarized Emission in Clusters in the CMB S4 Era
  The next generation of CMB experiments (CMB Stage-4) will produce a
Sunyaev-Zel'dovich (SZ) cluster catalog containing $\sim10^{5}$ objects, two
orders of magnitudes more than currently available. In this paper, we discuss
the detectability of the polarized signal generated by scattering of the CMB
quadrupole on the cluster electron gas using this catalog. We discuss the
possibility of using this signal to measure the relationship between cluster
optical depth and mass. We find that the area of observation of S4 maximizes
the signal-to-noise (S/N) on the polarized signal but that this S/N is
extremely small for an individual cluster, of order 0.5% for a typical cluster
in our catalog, the main source of noise being the residual primordial E-mode
signal. However, we find that the signal could be detected using the full
cluster catalog and that the significance of the result will increase linearly
with the size of the CMB S4 telescope mirror.
