Isotropy-Violation Diagnostics for $B$-mode Polarization Foregrounds to the Cosmic Microwave Background

TL;DR

This paper introduces an isotropy-violation diagnostic for polarized galactic foregrounds in CMB B-mode data, applying it to Planck data to identify cleaner sky regions and potential foreground features.

Contribution

It develops a harmonic-space isotropy-violation test using bipolar spherical harmonics to detect and map polarized foreground contamination in CMB B-mode observations.

Findings

Identified low-foreground regions near the South Galactic Pole and BICEP field.

Detected a possible foreground feature in the BICEP region.

Compared isotropy-violation results with local power spectrum methods.

Abstract

Isotropy-violation statistics can highlight polarized galactic foregrounds that contaminate primordial $B$-modes in the Cosmic Microwave Background (CMB). We propose a particular isotropy-violation test and apply it to polarized Planck 353 GHz data, constructing an map that indicates $B$-mode foreground dust power over the sky. We build our main isotropy test in harmonic space via the bipolar spherical harmonic basis, and our method helps us to identify the least-contaminated directions. By this measure, there are regions of low foreground in and around the BICEP field, near the South Galactic Pole, and in the Northern Galactic Hemisphere. There is also a possible foreground feature in the BICEP field. We compare our results to those based on the local power spectrum, which is computed on discs using a version of the method of Planck Int.~XXX (2016). The discs method is closely related to our isotropy-violation diagnostic. We pay special care to the treatment of noise, including chance correlations with the foregrounds. Currently we use our isotropy tool to assess the cleanest portions of the sky, but in the future such methods will allow isotropy-based null tests for foreground contamination in maps purported to measure primordial $B$-modes, particularly in cases of limited frequency coverage.