Concerning the connection between the C ℓ power spectrum of the cosmic microwave background and the <MATH>Γ m </MATH> Fourier spectrum of rings on the sky.

ABSTRACT In this article we present and study a scaling law of the mΓ[sub m] cosmic microwave background Fourier spectrum on rings that allows us to (i) combine spectra corresponding to different colatitude angles (e.g. several detectors at the focal plane of a telescope) and (ii) recover the C[sub ℓ] power spectrum once the Γ[sub m] coefficients have been measured. This recovery is performed numerically below the 1 per cent level for colatitudes Θ &gt; 80&#176; . In addition, taking advantage of the smoothness of C[sub ℓ] and of Γ[sub m] , we provide analytical expressions that allow the recovery of one of the spectra at the 1 per cent level, the other one being known. [ABSTRACT FROM AUTHOR]