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

TL;DR

This study investigates the impact of E-to-B leakage in partial sky surveys on CMB B-mode polarization analysis, revealing that morphological statistics are sensitive to leakage effects, which are crucial for accurate primordial gravitational wave detection.

Contribution

The paper demonstrates that morphological statistical tools can detect E-to-B leakage residuals in CMB polarization maps, highlighting their importance in primordial B-mode signal analysis.

Findings

Leakage effects are negligible in power spectrum, skewness, kurtosis analyses.

Morphological tools detect leakage at high confidence levels.

Leakage significantly contaminates morphological analyses of B-modes.

Abstract

One of the main goals of modern cosmology is to search for primordial gravitational waves by looking on their imprints in the B-type polarization in the cosmic microwave background radiation. However, this signal is contaminated by various sources, including cosmic weak lensing, foreground radiations, instrumental noises, as well as the E-to-B leakage caused by the partial sky surveys, which should be well understood to avoid the misinterpretation of the observed data. In this paper, we adopt the E/B decomposition method suggested by Smith in 2006, and study the imprints of E-to-B leakage residuals in the constructed B-type polarization maps, $\mathcal{B}(\hat{n})$, by employing various statistical tools. We find that the effects of E-to-B leakage are negligible for the $\mathcal{B}$-mode power spectrum, as well as the skewness and kurtosis analyses of $\mathcal{B}$-maps. However, if employing the morphological statistical tools, including Minkowski functionals and/or Betti numbers, we find the effect of leakage can be detected at very high confidence level, which shows that in the morphological analysis, the leakage can play a significant role as a contaminant for measuring the primordial B-mode signal and must be taken into account for a correct explanation of the data.