Bias-Hardened CMB Lensing with Polarization

Polarization data will soon provide the best avenue for measurements of the CMB lensing potential, although it is potentially sensitive to several instrumental effects including beam asymmetry, polarization angle uncertainties, sky coverage, as well as analysis choices such as masking. We derive "bias-hardened" lensing estimators to mitigate these effects, at the expense of somewhat larger reconstruction noise, and test them numerically on simulated data. We find that the mean-field bias from masking is significant for the EE quadratic lensing estimator, however the bias-hardened estimator combined with filtering techniques can mitigate the mean field. On the other hand, the EB estimator does not significantly suffer from the mean-field from the point source masking and survey window function. The contamination from beam asymmetry and polarization angle uncertainties, however, can generate mean-field biases for the EB estimator. These can also be mitigated using bias-hardened estimators, with at most a factor of ~ 3 degradation of noise level compared to the conventional approach.