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One of the main goals of modern cosmology is to search for primordialgravitational waves by looking on their imprints in the B-type polarization inthe cosmic microwave background radiation. However, this signal is contaminatedby various sources, including cosmic weak lensing, foreground radiations,instrumental noises, as well as the E-to-B leakage caused by the partial skysurveys, which should be well understood to avoid the misinterpretation of theobserved data. In this paper, we adopt the E/B decomposition method suggestedby Smith in 2006, and study the imprints of E-to-B leakage residuals in theconstructed B-type polarization maps, $\mathcal{B}(\hat{n})$, by employingvarious statistical tools. We find that the effects of E-to-B leakage arenegligible for the $\mathcal{B}$-mode power spectrum, as well as the skewnessand kurtosis analyses of $\mathcal{B}$-maps. However, if employing themorphological statistical tools, including Minkowski functionals and/or Bettinumbers, we find the effect of leakage can be detected at very high confidencelevel, which shows that in the morphological analysis, the leakage can play asignificant role as a contaminant for measuring the primordial B-mode signaland must be taken into account for a correct explanation of the data.

Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis