How to count clustered galaxies
Obtaining robust galaxy number counts is crucial for understanding galaxy evolution, and submillimetre counts in particular have proven valuable for revising subgrid physics models in cosmological simulations. In confusion-limited surveys, which are common at these wavelengths, statistical methods such as $P(D)$ fluctuation analysis are required to recover counts of faint, unresolved galaxies. However, the standard $P(D)$ framework assumes that galaxies are Poisson-distributed, whereas in reality galaxies are clustered. Using simulations, we demonstrate that this clustering systematically biases $P(D)$-derived number counts, and present an empirical method that simultaneously measures and corrects for this bias by combining the 1- and 2-point statistics in the map, thereby maximising the information extracted from the data. Applying this method to deep Herschel-SPIRE observations of the GOODS-N field, we provide revised galaxy number counts at 250, 350 and 500 $μ$m. Our results indicate that at 500 $μ$m clustering inflates the apparent counts by a factor of 1.6 around 10 mJy and slightly suppresses the faintest sub-mJy counts, with milder effects at 350 $μ$m and 250 $μ$m owing to the smaller beam sizes. This methodology is broadly applicable to other confusion-limited data sets with well-characterised beam and noise properties, including Spitzer, SCUBA-2, and the upcoming CCAT, enabling unbiased exploitation of the full statistical information in many surveys in the mid-IR to radio wavebands.