Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components

TL;DR

This paper introduces an efficient pixel-space algorithm for separating pure E and B polarization components in CMB maps, effectively removing ambiguous modes caused by incomplete sky coverage, applicable to arbitrary geometries.

Contribution

The paper presents a novel, scalable method for E/B separation in CMB polarization maps that handles arbitrary geometries without requiring complete mode bases.

Findings

Efficient removal of ambiguous modes in polarization maps.

Applicable to maps with arbitrary sky coverage geometries.

Scales cubically with boundary pixel count.

Abstract

Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of "ambiguous" modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into "pure" E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels on the boundary of the map.