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

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 th...

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Bibliographic Details
Published in:arXiv.org 2003-04
Main Authors: Ansari, R, Bargot, S, Bourrachot, A, Couchot, F, Haïssinski, J, Henrot-Versillé, S, G Le Meur, Perdereau, O, Piat, M, Plaszczynski, S, Touze, F
Format: Article
Language:English
Subjects:
Big Bang theory
Cosmic microwave background
Focal plane
Scaling laws
Smoothness
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0301251