Efficiency of pseudospectrum methods for estimation of the cosmic microwave background B-mode power spectrum

The estimation of the B-mode angular power spectrum of polarized anisotropies of the cosmic microwave background is a key step towards a full exploitation of the scientific potential of this probe. In the context of pseudospectrum methods the major challenge is related to a contamination of the B-mode spectrum estimate with the residual power of the much larger E-mode. This so-called E-to-B leakage is unavoidably present whenever only an incomplete sky map is 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 [K. M. Smith, Phys. Rev. D 74, 083002 (2006); W. Zhao and D. Baskaran, Phys. Rev. D 82, 023001 (2010); J. Kim and P. Naselsky, Astron. Astrophys. 519, A104 (2010)], which we first introduce within a common algebraic framework of the so-called χ 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 cosmic microwave background B-mode satellite mission. We find that although all these methods allow us to reduce significantly the level of the E-to-B leakage, it is the method of Smith that at the same time ensures the smallest error bars in all experimental configurations studied here, owing to the fact that it permits straightforwardly 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 the B-mode power spectrum at large angular scales but only after appropriate binning. The method of Zhao and Baskaran is a close runner-up in the case of a nearly full-sky coverage.