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 with the counts of individual sources detected with high-resolution instruments. If the beamwidth corresponds to a sizable fraction of the clustering size, as in the case of Planck/High Frequency Instrument (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-mu m 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 as a result of clustering continues to be important above the canonical 5 sigma detection limit. Detailed simulations confirm the reliability of our approach. As the ratio of the beamwidth 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/Spectral and Photometric Imaging REceiver (SPIRE) 500-mu m survey the enhancement of the bright source counts as a result of clustering is important.