Cluster mass estimators from CMB temperature and polarization lensing

Upcoming Sunyaev–Zel'dovich surveys are expected to return ∼10 4 intermediate mass clusters at high redshift. Their average masses must be known to the same accuracy as desired for the dark energy properties. Internal to the surveys, the cosmic microwave background (CMB) potentially provides a source for lensing mass measurements whose distance is precisely known and behind all clusters. We develop statistical mass estimators from six quadratic combinations of CMB temperature and polarization fields that can simultaneously recover large-scale structure and cluster mass profiles. The performance of these estimators on idealized Navarro–Frenk–White (NFW) clusters suggests that surveys with a ∼1' beam and noise in uncontaminated temperature maps can make a ∼10σ detection, or equivalently a ∼10% mass measurement for each 10 3 set of clusters. With internal or external acoustic scale E -polarization measurements, the ET cross-correlation estimator can provide a stringent test for contaminants on a first detection at ∼1/3 the significance. For surveys that reach below , the EB cross-correlation estimator should provide the most precise measurements and potentially the strongest control over contaminants.