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

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.

29 pages, 22 figures, 7 tables, JCAP accepted

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• Tracking down the origin of superbubbles and supergiant shells in the Magellanic Clouds with Minkowski tensor analysis
• Morphology of CMB fields -- effect of weak gravitational lensing
• Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
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• Probing CMB Polarization Gaussianity with the Statistics of Unpolarized Points: Non-Gaussianity of Planck Data and Prospects for Future B-Mode Measurements
• Statical properties of CMB B-mode polarisation in a partial sky analysis