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

R. Ansari (1) , S. Bargot (1) , A. Bourrachot (1) , F. Couchot (1) , J. Haïssinski (1) , S. Henrot-Versillé (1) , G. Le Meur (1) , O. Perdereau (1) , M. Piat (2) , Stéphane Plaszczynski (1) , F. Touze (1)

1 LAL - Laboratoire de l'Accélérateur Linéaire
2 IAS - Institut d'astrophysique spatiale

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.

Domaines: Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Astrophysique [astro-ph]

R. Ansari, S. Bargot, A. Bourrachot, F. Couchot, J. Haïssinski, et al.. 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. Monthly Notices of the Royal Astronomical Society, 2003, 343 (2), pp.552-558. ⟨10.1046/j.1365-8711.2003.06694.x⟩. ⟨hal-00007648⟩