Methods for pixel domain correction of EB leakage

Abstract

In observation of the cosmic microwave background (CMB) polarization, "EB leakage" refers to the artificial B-mode signal coming from the leakage of E-mode signal when part of the sky is unavailable or excluded. Correction of such leakage is one of the preconditions for detecting primordial gravitational waves via the CMB B-mode signal. In this work, we design two independent methods for correcting the EB leakage directly in the pixel domain using standard definitions of the Eand B-modes. The two methods give consistent results, and both are fast and easy to implement. Tests on a CMB simulation containing zero initial B-mode show an efficient suppression of the EB leakage. When combined with the MASTER method to reconstruct the full-sky B-mode spectrum in simulations with a relatively simple mask, the error from EB-leakage is suppressed further by more than one order of magnitude at the recombination bump, and up to three orders of magnitude at higher multipoles, compared to a "pure" MASTER scheme under the same conditions. Meanwhile, although the final power spectrum estimation benefits from apodization, the pixel domain correction itself is done without apodization, and thus the methods offer more freedom in choosing an apodization based on specific requirements.

General solutions of the leakage in integral transforms and applications to the EB-leakage and detection of the cosmological gravitational wave background

“…Interestingly, as shown by Fig. 1, for pure CMB signal, the error bars of the recycling method [3] are roughly only 30% bigger than the ideal error bars, thus the result of the recycling method is an excellent approximation of the BUE, especially when computed at a higher resolution. However, as mentioned above, this must to be further tested if non-Gaussian and non-analytic prior information is taken into account.…”

“…We know from Figure 1 that the BUE only gives 20-30% improvement compared to the recycling method used in [3,4], which is sufficiently fast. Meanwhile, it was shown by Figure 6 of [9] that for ≈ 100, the error of the fisher estimator is no less than 50% of the pseudo-C method.…”

“…Therefore, the BBE can be easily obtained as long as a fast algorithm of the integral transform is available, e.g., the fast Fourier transforms (FFT). This is extremely convenient, and is exactly the idea of the recycling method used in [3] to correct the EB-leakage for detecting the CGW. It is also possible to use an extra window function W (p) that smooths the edge of the region, which is the conventional way of reducing the leakage.…”

“…It is reasonable to expect that, for each given sky coverage that is incomplete, there is going to be an unbeatable minimal error coming from the EB-leakage, which will set an upper limit of the ability to detect the CGW, even if all other issues are perfectly solved. In [3,4], we presented the best blind estimate (BBE) of the EB-leakage, but one problem still remains: when there is some reasonable prior information, can we improve the estimation of the EB-leakage? If the answer is yes, to what extent?…”

Statistics of CMB polarization angles

“…However, it is important to stress, that component separation and extraction of the primordial CMB polarised signal usually takes place in Q, U domain and only then is converted into E/B components. This conversion is not local and for different masks is accompanied by the presence of different E-to-B leakage terms [5][6][7][8][9].…”