Testing for directionality in the Planck polarization and lensing data

TL;DR

This paper applies the D statistic to Planck 2018 polarization and lensing data to detect residual foreground contamination and directionality, finding no significant residuals or excess directionality in the analyzed maps.

Contribution

It demonstrates the effectiveness of the D statistic in detecting residual foregrounds and directionality in CMB polarization and lensing maps, with applications to Planck data.

Findings

No residual foreground contamination detected in Planck 2018 CMB maps.

The D statistic can detect percent-level foreground contamination with 95% confidence.

No excess directionality found in the Planck lensing potential map.

Abstract

In order to better analyse the polarization of the cosmic microwave background (CMB), which is dominated by emission from our Galaxy, we need tools that can detect residual foregrounds in cleaned CMB maps. Galactic foregrounds introduce statistical anisotropy and directionality to the polarization pseudo-vectors of the CMB, which can be investigated by using the D statistic of Bunn and Scott. This statistic is rapidly computable and capable of investigating a broad range of data products for directionality. We demonstrate the application of this statistic to detecting foregrounds in polarization maps by analysing the uncleaned Planck 2018 frequency maps. For the Planck 2018 CMB maps, we find no evidence for residual foreground contamination. In order to examine the sensitivity of the D statistic, we add a varying fraction of the polarized thermal dust and synchrotron foreground maps to the CMB maps and show the percent-level foreground contamination that would be detected with 95 percent confidence. We also demonstrate application of the D statistic to another data product by analysing the gradient of the minimum-variance CMB lensing potential map (i.e., the deflection angle) for directionality. We find no excess directionality in the lensing potential map when compared to the simulations provided by the Planck Collaboration.