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

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 δ_l ~ π/γ_max, where γ_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.

11 pages

References in corpus (7)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra
• Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope
• The Atacama Cosmology Telescope: A Measurement of the 600< ell <8000 Cosmic Microwave Background Power Spectrum at 148 GHz
• Efficient Power Spectrum Estimation for High Resolution CMB Maps
• Data analysis methods for the cosmic microwave background
• CMB power spectrum estimation with non-circular beam and incomplete sky coverage
• Notes on bias and covariance matrix of the angular power spectrum on small sky maps

Cited by in corpus (3)

• Observation of Anisotropy in the Arrival Directions of Galactic Cosmic Rays at Multiple Angular Scales with IceCube
• Direct measurement of the angular power spectrum of cosmic microwave background temperature anisotropies in the WMAP Data
• Exploring the origin of the fine structures in the CMB temperature angular power spectrum