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 frequency maps. For the Planck CMB maps, we find no evidence for residual foreground contamination; however, we detect an excess directionality due to anisotropic noise, which can be dealt with through careful simulations. 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 that roughly per-cent-level foreground contamination would be detected with 95 per cent 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.

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Copyright © 2019 The Authors. This article first appeared in Monthly Notices of the Royal Astronomical Society 490, no. 3 (December 2019): 3404–13. doi:10.1093/mnras/stz2777

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