Volume 531, July 2011
|Number of page(s)||8|
|Published online||06 June 2011|
How to make a clean separation between CMB E and B modes with proper foreground masking
Niels Bohr Institute & Discovery Center, Blegdamsvej 17, 2100 Copenhagen, Denmark
Received: 16 February 2011
Accepted: 4 April 2011
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 ~ 1 × 10-7. We compare the result with that of the original mask. We find that the leakage power is reduced by a factor of 106 ~ 109 at the cost of a sky fraction 0.07, and that 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.
Key words: cosmic background radiation / methods: data analysis
© ESO, 2011
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