How to make a clean separation between CMB E and B modes with proper foreground masking

Abstract

We investigate the E/B decomposition of CMB polarization on a masked sky. In real space, operators of E and B mode decomposition involve only differentials of CMB polarization. We may, therefore in principle, perform a clean E/B decomposition from incomplete sky data. Since it is impractical to apply second derivatives to observation data, we usually rely on spherical harmonic transformation and inverse transformation, instead of using real-space operators. In spherical harmonic representation, jump discontinuities in a cut sky produces Gibbs phenomenon, unless a spherical harmonic expansion is made up to an infinitely high multipole. By smoothing a foreground mask, we may suppress the Gibbs phenomenon effectively in a similar manner to apodization of a foreground mask discussed in other works. However, we incur foreground contamination by smoothing a foreground mask, because zero-value pixels in the original mask may be rendered non-zero by the smoothing process. In this work, we investigate an optimal foreground mask, which ensures proper foreground masking and suppresses Gibbs phenomenon. We apply our method to a simulated map of the pixel resolution comparable to the Planck satellite. The simulation shows that the leakage power is lower than unlensed CMB B mode power spectrum of tensor-to-scalar ratio $r\sim 1\times 10^{-7}$. We compare the result with that of the original mask. We find that the leakage power is reduced by a factor of $10^6\sim 10^9$ at the cost of a sky fraction $0.07$, and that the enhancement is highest at lowest multipoles. We confirm that all the zero-value pixels in the original mask remain zero in our mask. The application of this method to the Planck data will improve the detectability of primordial tensor perturbation.

v2: typos corrected, v3: matched with the published version (the clarity improved) v4: a typo corrected v5: a bibliography file error fixed

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Cited by in corpus (23)

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• Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses
• Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise
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• Constraining the topology of the Universe using the polarised CMB maps
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• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
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• Towards efficient and optimal analysis of CMB anisotropies on a masked sky
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• Fisher Matrix Optimization of Cosmic Microwave Background Interferometers
• Primordial Gravitational Waves and Rescattered Electromagnetic Radiation in the Cosmic Microwave Background
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