Probing the statistical properties of CMB $B$-mode polarization through Minkowski Functionals

TL;DR

This paper uses Minkowski functionals to analyze the non-Gaussian features of lensed B-mode polarization maps in the CMB, revealing significant deviations and the impact of foreground residuals, aiding future experiments.

Contribution

It introduces Minkowski functional analysis to study the morphological properties of lensed B-mode maps and detect foreground residuals.

Findings

Deviations from Gaussianity are significant in B-mode maps.

Minkowski functionals can detect tiny foreground residuals.

Analysis provides a complementary method for foreground investigation.

Abstract

The detection of the magnetic type $B$-mode polarization is the main goal of future cosmic microwave background (CMB) experiments. In the standard model, the $B$-mode map is a strongly non-gaussian field due to the lensed component. Besides the two-point correlation function, the other statistics are also very important to dig the information of the polarization map. In this paper, we employ the Minkowski functionals to study the morphological properties of the lensed $B$-mode maps. We find that the deviations from Gaussianity are very significant for both full and partial-sky surveys. As an application of the analysis, we investigate the morphological imprints of the foreground residuals in the $B$-mode map. We find that even for very tiny foreground residuals, the effects on the map can be detected by the Minkowski functional analysis. Therefore, it provides a complementary way to investigate the foreground contaminations in the CMB studies.