About the connection between the $C_{\ell }$ power spectrum of the Cosmic Microwave Background and the ${\Gamma }_m$ Fourier spectrum of rings on the sky

Abstract

In this article we present and study a scaling law of the $m{\Gamma }_m$ CMB Fourier spectrum on rings which allows us (i) to combine spectra corresponding to different colatitude angles (e.g. several detectors at the focal plane of a telescope), and (ii) to recover the $C_l$ power spectrum once the ${\Gamma }_m$ coefficients have been measured. This recovery is performed numerically below the 1% level for colatitudes $\Theta >80^{\circ }$ degrees. In addition, taking advantage of the smoothness of the $C_l$ and of the ${\Gamma }_m$, we provide analytical expressions which allow to recover one of the spectrum at the 1% level, the other one being known.

8 pages, 8 figures

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• Cosmic Microwave Background Anisotropies
• The Cosmic Microwave Background Anisotropy Power Spectrum measured by Archeops
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Cited by in corpus (4)

• Xspect, estimation of the angular power spectrum by computing cross-power spectra with analytical error bars
• The CMB temperature power spectrum from an improved analysis of the Archeops data
• Data analysis methods for the cosmic microwave background
• CMB polarization analysis on circular scans