The large-scale anisotropies of the extragalactic infrared background and of the N(S) source counts

We provide comparative, theoretical analyses of the large-scale anisotropies in the intensity of an extragalactic integrated background ({DELTA}I/I) and in the N(S) source counts ({DELTA}N/N). We assume that such anisotropies are generated by small-amplitude density fluctuations on length scales exceeding the Local Supercluster radius, and special reference is made to the far-infrared background and to the IRAS source counts. We show that both {DELTA}I/I and {DELTA}N/N are determined by fluctuations in the source number density and by the Doppler shifts generated by the cosmic matter density perturbations. As a result, the source-count anisotropy {DELTA}N/N explicitly depends on the source spectral index, even in the limit of small length scales; simple Newtonian explanation is provided for this result. It is further shown that for a source luminosity function {PHI}(L) proportional to L^-2^ we simply have {DELTA}N/N = {DELTA}I/I for any flux level S. We study in detail the harmonic content of the anisotropies and prove its independence of the specific perturbation spectrum, provided that they are dominated by length scales much smaller than the Hubble radius (which is shown to be true for spectra used in current theories of galaxy formation). Finally we show that the ratio of the IRAS dipole to the cosmic background dipole can be used to infer the cosmic density parameter {OMEGA}_0_ only if the source spectral index is known.