Contributions of point extragalactic sources to the cosmic microwave background bispectrum

All the analyses of cosmic microwave background (CMB) temperature maps up to date show that CMB anisotropies follow a Gaussian distribution. On the other hand, astrophysical foregrounds, which hamper the detection of the CMB angular power spectrum, are not Gaussian-distributed on the sky. Therefore, they should give a sizeable contribution to the CMB bispectrum. In fact, the first-year data of the Wilkinson Microwave Anisotropy Probe (WMAP) mission have allowed the first detection of the extragalactic source contribution to the CMB bispectrum at 41 GHz and, at the same time, much tighter limits than before to non-Gaussian primordial fluctuations. In view of the above, and for achieving higher precision in current and future CMB measurements of non-Gaussianity, in this paper we discuss a comprehensive assessment of the bispectrum due to either uncorrelated or clustered extragalactic point sources in the entire frequency interval around the CMB intensity peak. Our calculations, based on current cosmological evolution models for sources, show that the reduced angular bispectrum due to point sources b(ps) should be detectable in all WMAP and Planck frequency channels. We also find agreement with the results for b(ps) at 41 GHz coming from the analysis of the first-year WMAP data. Moreover, by comparing b(ps) with the primordial reduced CMB bispectrum, we find that only the peak value of the primordial bispectrum (which appears at l similar or equal to 200) results in greater than b(ps) in a frequency window around the intensity peak of theCMB. The amplitude of this window basically depends on the capability of the source detection algorithms (i.e., on the achievable flux detection limit Slim for sources). Finally, our current results show that at low frequencies (i.e., nu less than or equal to 100 GHz) the angular bispectrum of a clustered distribution of sources does not seem substantially different from that of Poisson-distributed ones, by using realistic angular correlation functions suitable to apply to the relevant source populations. On the other hand, we also find that at higher frequencies (i.e., nu greater than or equal to 300 GHz) the clustering term can greatly enhance the normalization of b(ps).