E/B decomposition of CMB polarization pattern of incomplete sky: A pixel space approach

Abstract

CMB polarization pattern may be decomposed into gradient-like (E) and curl-like (B) mode, which provide invaluable information respectively. We have investigated E/B decomposition in pixel space. We find E/B mixing due to incomplete sky is localized in pixel-space, and negligible in the regions far away from the masked area. By estimating the expected local leakage power, we have diagnosed ambiguous pixels. Our criteria for ambiguous pixels (i.e. r c) is associated with the tensor-to-scalar ratio of B mode power spectrum, which the leakage power is comparable to. By setting rc to a lower value, we may reduce leakage level, but reduce sky fraction at the same time. Therefore, we have solved $\partial \Delta C-l/\partial r-{\rm c}$ = 0, and obtained the optimal rc, which minimizes the estimation uncertainty, given a foreground mask and noise level. We have applied our method to a simulated map blocked by a foreground (diffuse + point source) mask. Our simulation shows leakage power is smaller than primordial (i.e. unlensed) B mode power spectrum of tensor-to-scalar ratio r ∼ 1×10-3 at wide range of multipoles (50 ? l ? 2000), while allowing us to retain sky fraction ∼0.48. © ESO, 2010.