Partial CMB maps: bias removal and optimal binning of the angular power spectrum

Details Partial CMB maps: bias removal and optimal binning of the angular power spectrum Partial CMB maps: bias removal and optimal binning of the angular power spectrum

2009-10-24

arxiv.org/abs/0910.4623v2

Monthly Notices of the Royal Astronomical Society 405, 3 (2010) 1421-1430

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

11 pages

Scientific paper

10.1111/j.1365-2966.2010.16561.x

We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as \delta_l ~ \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_l, as obtained from the partial map projection on the spherical harmonic Ylm(l,m) basis. We have derived near optimal bands and weighting functions in l-space for power spectrum calculation using 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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