Confusion noise and source clustering

The influence of source clustering on the distribution of fluctuations in integrated background radiations [the P(D) curve] is analyzed. The general framework to model the P(D) curve given the beam profile, the source counts (the log N-log S relation), and the source correlation functions is presented. It is then shown that an account of source clustering in terms of an excess variance [i.e., via the convolution of the model P(D) curves with a Gaussian] is generally inappropriate. Since the correct way to account for source clustering requires all of the n-point source correlation functions, and there is little or no observational information of these quantities for n > 2, simple models with few parameters are presented, namely, a Gaussian clustering model and a shot noise clustering model. To illustrate the effects of source clustering in the determination of source counts via analysis of confusion noise, simulations with the shot noise clustering model and a top-hat beam are generated and P(D) curves subsequently fitted. The amount by which source counts are overestimated if clustering is not properly accounted for is quantified.