Detecting the polarization induced by scattering of the microwave
  background quadrupole in galaxy clusters
  We analyse the feasibility of detecting the polarization of the CMB caused by
scattering of the remote temperature quadrupole by galaxy clusters with
forthcoming CMB polarization surveys. For low-redshift clusters, the signal is
strongly correlated with the local large-scale temperature and polarization
anisotropies, and the best prospect for detecting the cluster signal is via
cross-correlation. For high-redshift clusters, the correlation with the local
temperature is weaker and the power in the uncorrelated component of the
cluster polarization can be used to enhance detection. We derive linear and
quadratic maximum-likelihood estimators for these cases, and forecast
signal-to-noise values for the SZ surveys of a Planck-like mission and SPTPol.
Our estimators represent an optimal `stacking' analysis of the polarization
from clusters. We find that the detectability of the effect is sensitive to the
cluster gas density distribution, as well as the telescope resolution, cluster
redshift distribution, and sky coverage. We find that the effect is too small
to be detected in current and near-future SZ surveys without dedicated
polarization follow-up, and that an r.m.s. noise on the Stokes parameters of
roughly 1 uK-arcmin for each cluster field is required for a 2-sigma detection,
assuming roughly 550 clusters are observed. We discuss and quantify potential
biases from the kinetic part of the signal caused by the relative motion of the
cluster with respect to the CMB, and from the background CMB polarization
behind the cluster, discussing ways in which these biases might be mitigated.
Our formalism should be important for next-generation CMB polarization
missions, which we argue will be able to measure this effect with high
signal-to-noise. This will allow for an important consistency test of the LCDM
model on scales that are inaccessible to other probes.
