Contributions of Point Extragalactic Sources to the Cosmic Microwave Background Bispectrum

All the analyses of Cosmic Microwave Background (CMB) temperature mapsup--to--date show that CMB anisotropies follow a Gaussian distribution. On theother hand, astrophysical foregrounds which hamper the detection of the CMBangular power spectrum, are not Gaussian distributed on the sky. Therefore,they should give a sizeable contribution to the CMB bispectrum. In fact, thefirst year data of the Wilkinson Microwave Anisotropy Probe (WMAP) mission haveallowed the {\it first} detection of the extragalactic source contribution tothe CMB bispectrum at 41 GHz and, at the same time, much tighter limits thanbefore to non--Gaussian primordial fluctuations. In view of the above and forachieving higher precision in current and future CMB measurements ofnon--Gaussianity, in this paper we discuss a comprehensive assessment of thebispectrum due to either uncorrelated and clustered extragalactic point sourcesin the whole frequency interval around the CMB intensity peak. Ourcalculations, based on current cosmological evolution models for sources, showthat the reduced angular bispectrum due to point sources, $b_{ps}$, should bedetectable in all WMAP and Planck frequency channels. We also find agreementwith the results on $b_{ps}$ at 41 GHz coming from the analysis of the firstyear WMAP data. Moreover, by comparing $b_{ps}$ with the primordial reduced CMBbispectrum, we find that only the peak value of the primordial bispectrum(which appears at $l\simeq 200$) results greater than $b_{ps}$ in a frequencywindow around the intensity peak of the CMB. The amplitude of this windowbasically depends on the capability of the source detection algorithms (i.e.,on the achievable flux detection limit, $S_{lim}$, for sources).Comment: 26 pages, 6 Figures, use AasTex5.0, ApJ, in press, Oct. 10, 2003 Issu