Partial CMB maps: bias removal and optimal binning of the angular power spectrum
Résumé
We present a semi-analytical method to investigate the systematic and statistical effects of the calculated angular power spectrum, when partial (incomplete) spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as $\delta \ell \sim \pi/\gamma_{max}$, where $\gamma_{max}$ is the effective maximum extent of the partial spherical maps. We propose a correction algorithm to reduce systematic effects on the estimated $C_\ell$, as obtained from the partial map projection on the spherical harmonic $\ylm{\ell}{m}$ basis. We have derived near optimal bands and weighting functions in $\ell$-space for power spectrum calculation on small maps, and a correction algorithm for partially masked spherical maps, that contain information on the angular correlations on all scales.
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