Effect of clustering on extragalactic source counts with low-resolution instruments

In the presence of strong clustering, low-resolution surveys measure the summed contributions of groups of sources within the beam. The counts of bright intensity peaks are therefore shifted to higher flux levels compared to the counts of individual sources detected with high-resolution instruments. If the beam-width corresponds a sizable fraction of the clustering size, as in the case of Planck/HFI, one actually detects the fluxes of clumps of sources. We argue that the distribution of clump luminosities can be modelled in terms of the two- and three-point correlation functions, and apply our formalism to the Planck/HFI 850 micron surveys. The effect on counts is found to be large and sensitive also to the evolution of the three-point correlation function; in the extreme case that the latter function is redshift-independent, the source confusion due to clustering keeps being important above the canonical 5*sigma detection limit. Detailed simulations confirm the reliability of our approach. As the ratio of the beam-width to the clustering angular size decreases, the observed fluxes approach those of the brightest sources in the beam and the clump formalism no longer applies. However, simulations show that also in the case of the Herschel/SPIRE 500 micron survey the enhancement of the bright source counts due to clustering is important.