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

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

2003-01-14

arxiv.org/abs/astro-ph/0301251v3

Mon.Not.Roy.Astron.Soc.343:552,2003

Astronomy and Astrophysics

Astrophysics

8 pages, 8 figures

Scientific paper

10.1046/j.1365-8711.2003.06694.x

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.

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