How to count clustered galaxies

TL;DR

This paper develops an empirical correction method for galaxy number counts affected by clustering bias in confusion-limited surveys, improving accuracy in submillimetre galaxy studies.

Contribution

It introduces a novel approach combining 1- and 2-point statistics to measure and correct clustering bias in galaxy counts from confusion-limited data.

Findings

Clustering inflates counts by a factor of 1.6 at 500μm around 10mJy.

The method provides revised counts at 250, 350, and 500μm.

Bias correction improves the accuracy of galaxy evolution studies.

Abstract

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$\mu$m. Our results indicate that at 500$\mu$m clustering inflates the apparent counts by a factor of 1.6 around 10mJy and slightly suppresses the faintest sub-mJy counts, with milder effects at 350$\mu$m and 250$\mu$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 SCUBA-2 and CCAT, enabling unbiased exploitation of the full statistical information in current and future far-infrared and submillimetre surveys.