Physical Sciences and Mathematics Commons^™

E/B Decomposition Of Finite Pixelized Cmb Maps, Emory F. Bunn, Matias Zaldarriaga, Max Tegmark, Angelica De Oliveira-Costa

Physics Faculty Publications

Separation of the E and B components of a microwave background polarization map or a weak lensing map is an essential step in extracting science from it, but when the map covers only part of the sky and/or is pixelized, this decomposition cannot be done perfectly. We present a method for decomposing an arbitrary sky map into a sum of three orthogonal components that we term ‘‘pure E,’’ ‘‘pure B,’’ and ‘‘ambiguous.’’ The fluctuations in the pure E and B maps are due only to the E and B power spectra, respectively, whereas the source of those in …