Statistics of non-polarized points in the CMB polarization maps

TL;DR

This paper analyzes the distribution and geometry of non-polarized points in CMB polarization maps, using a new method to identify these points and test Gaussianity, revealing their relation to lensing and tensor-to-scalar ratio.

Contribution

It introduces a procedure to identify non-polarized points in pixelized CMB maps and explores their statistical properties and relation to cosmological parameters.

Findings

Total NPP density relates to lensing and tensor-to-scalar ratio r.

Lensing removes degeneracy of NPP count with r.

SMICA and NILC maps are consistent with Gaussian simulations.

Abstract

The non-polarized points (NPP) of the $Q$ and $U$ Stokes parameters of the CMB can be classified according to the geometry of the polarization field. We describe a procedure to identify these points in the pixelized sky and present the shape of the polarization angles in the vicinity of NPPs. We design a test of Gaussianity using the Kullback-Leibler divergence. We show that the total number density of non-polarized points of the E- and B-families is closely related to the presence of lensing and the tensor-to-scalar ratio $r$. We further show that in the absence of lensing, the total number of NPPs of all types does not depend on $r$, while the lensing effect removes this degeneracy. This analysis is applied to the CMB maps from the 2018 Planck release. We show that there is general consistency of SMICA and NILC maps compared to a reference set of Gaussian simulations. The strongest discrepancies are found in the Commander (with corresponding $p$-value $0.07$) and NILC ($p = 0.15$) maps.