Statistical analysis of undetected point sources in cosmic microwave background maps

Cosmic microwave background (CMB) temperature anisotropies follow a Gaussian statistical distribution in the standard inflationary model, but there are non-Gaussian contributions due to astrophysical foregrounds. The detection of the non-Gaussian signal due to extragalactic point sources and its distinction from the possible intrinsic non-Gaussianity is an issue of great importance in CMB analysis. The Mexican Hat Wavelet Family (MHWF), which has been proved very useful for the detection of extragalactic point sources, is applied here to the study of non-Gaussianity due to point sources in CMB maps. We carry out simulations of CMB maps with the characteristics of the forthcoming Planck mission at 70 and 100 GHz and filter them with the MHWF. By comparing the skewness and kurtosis of simulated maps with and without point sources, we are able to detect clearly the non-Gaussian signal due to point sources for flux limits as low as 0.4 Jy (70 GHz) and 0.3 Jy (100 GHz). The second and third members of the MHWF perform better in this respect than the Mexican Hat Wavelet (MHW1) and much better than the Daubechies 4 wavelet. We have also estimated the third order, K3, and fourth order, K4, cumulants produced by point sources at these Planck channels by means of a fit with the MHWF. The average relative errors with respect to the real values are below 12% for fluxes down to 0.6 Jy (70 GHz) and 0.4 Jy (100 GHz). The values of these cumulants allow us to distinguish between different source counts models. From the estimated cumulants and assuming a power law for the source number counts we are able to obtain the coefficients α and A of the differential number counts, α = 2.19 ± 0.46 (α = 2.26 ± 0.19), A = 24.3 ± 4.3 (A = 21.0 ± 4.2) for 70 (100) GHz, assuming a flux limit of 1 Jy. These results are consistent with the values obtained from simulations containing only point sources, which are: α = 2.32± 0.06 (α = 2.35± 0.16), A = 22.1 ± 1.5 (A = 20.0± 3.7) for 70 (100) GHz.