Efficiency of pseudo-spectrum methods for estimation of Cosmic Microwave Background B-mode power spectrum

Estimation of the B-mode angular power spectrum of polarized anisotropies of the cosmic microwave background (CMB) is a key step towards a full exploitation of the scientific potential of this probe. In the context of pseudo-spectrum methods the major challenge is related to a contamination of the B-mode spectrum estimate with residual power of much larger E-mode. This so-called E-to-B leakage is unavoidably present whenever an incomplete sky map is only available, as is the case for any realistic observation. The leakage has to be then minimized or removed and ideally in such a way that neither a bias nor extra variance is introduced. In this paper, we compare from these two perspectives three different methods proposed recently in this context Refs. Smith 2006, Zhao & Baskaran 2010, Kim & Naselsky 2010, which we first introduce within a common algebraic framework of the so-called chi-fields and then study their performance on two different experimental configurations - one corresponding to a small-scale experiment covering 1% of the sky motivated by current ground-based or balloon-borne experiments and another - to a nearly full-sky experiment, e.g., a possible CMB B-mode satellite mission. We find that though all these methods allow to reduce significantly the level of the E-to-B leakage, it is the method of Smith 2006, which at the same time ensures the smallest error bars in all experimental configurations studied here, owing to the fact that it permits straightforwardly for an optimization of the sky apodization of the polarization maps used for the estimation. For a satellite-like experiment, this method enables a detection of B-mode power spectrum at large angular scales but only after appropriate binning. The method of Zhao & Baskaran 2010 is a close runner-up in the case of a nearly full sky coverage.