Effects of observer peculiar motion on the isotropic background frequency spectrum: from monopole to higher multipoles

Abstract

The observer peculiar motion produces boosting effects in the background anisotropies with frequency spectral behaviours related to its spectrum. We study how the frequency spectrum of the background isotropic monopole emission is modified and transferred to the frequency spectra at higher multipoles, l. We perform the analysis in terms of spherical harmonic expansion up to a certain lmax, for various models from radio to far-IR. We derive a system of linear equations to obtain spherical harmonic coefficients and provide explicit solutions up to lmax=6 as linear combinations of the signals at N=lmax+1 colatitudes. The associated Legendre polynomials symmetry with respect to {\pi}/2 is used to separate the system into two subsystems, one for l=0 and even l, the other for odd l. This improves the solutions accuracy with respect to an arbitrary colatitudes choice. We apply the method to analytical or semi-analytical representions of monopole spectra, i.e. to four types of CMB distortions, four types of extragalactic backgrounds superimposed to the CMB Planckian spectrum and some combinations of them. We present our results in terms of spherical harmonic coefficients, relationships between the observed and intrinsic monopoles, maps, angular power spectra. We compare the method results with the ones obtained using more computationally demanding numerical integrations or map generation/inversion. The method is generalized to include the effect of the observer motion relative to the Sun. Its simplicity and efficiency can significantly alleviate the computational effort needed for accurate predictions and for the analysis of future data. We discuss the superposition of the CMB intrinsic anisotropies and of the effects induced by the observer motion, exploring for the possibility of constraining the intrinsic dipole embedded in the kinematic dipole, in the presence of CMB spectral distortions.