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

TL;DR

This paper introduces a semi-analytical method to correct systematic biases and optimize binning in the angular power spectrum derived from incomplete CMB maps, improving accuracy in cosmological analyses.

Contribution

It proposes a correction algorithm for partial spherical maps and derives near-optimal binning and weighting functions for power spectrum estimation.

Findings

Reduction of systematic bias in partial map power spectra

Derivation of near-optimal binning strategies

Effective correction for incomplete spherical data

Abstract

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.