Open AccessConcerning the connection between the C ℓ power spectrum of the cosmic microwave background and the Γ m Fourier spectrum of rings on the sky
Author(s) -
Ansari R.,
Bargot S.,
Bourrachot A.,
Couchot F.,
Haïssinski J.,
HenrotVersillé S.,
Le Meur G.,
Perdereau O.,
Piat M.,
Plaszczynski S.,
Touze F.
Publication year - 2003
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2003.06694.x
Subject(s) - physics , cosmic microwave background , telescope , spectrum (functional analysis) , astrophysics , spectral line , sky , microwave , spectral density , fourier transform , connection (principal bundle) , optics , scaling , smoothness , cardinal point , astronomy , anisotropy , mathematical analysis , geometry , telecommunications , quantum mechanics , computer science , mathematics
In this article we present and study a scaling law of the m Γ 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 ℓ power spectrum once the Γ m coefficients have been measured. This recovery is performed numerically below the 1 per cent level for colatitudes Θ > 80° . In addition, taking advantage of the smoothness of C ℓ and of Γ 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.