Organised randoms: Learning and correcting for systematic galaxy clustering patterns in KiDS using self-organising maps

We present a new method for the mitigation of observational systematic effects in angular galaxy clustering through the use of corrective random galaxy catalogues. Real and synthetic galaxy data from the Kilo Degree Survey's (KiDS) 4th Data Release (KiDS-1000) and the Full-sky Lognormal Astro-fields Simulation Kit package, respectively, are used to train self-organising maps to learn the multivariate relationships between observed galaxy number density and up to six systematic-tracer variables, including seeing, Galactic dust extinction, and Galactic stellar density. We then create `organised' randoms; random galaxy catalogues with spatially variable number densities, mimicking the learnt systematic density modes in the data. Using realistically biased mock data, we show that these organised randoms consistently subtract spurious density modes from the two-point angular correlation function w(ϑ), correcting biases of up to 12σ in the mean clustering amplitude to as low as 0.1σ, over an angular range of 7 − 100 arcmin with high signal-to-noise ratio. Their performance is also validated for angular clustering cross-correlations in a bright, flux-limited subset of KiDS-1000, comparing against an analogous sample constructed from highly complete spectroscopic redshift data. Each organised random catalogue object is a clone carrying the properties of a real galaxy, and is distributed throughout the survey footprint according to the position of the parent galaxy in systematics space. Thus, sub-sample randoms are readily derived from a single master random catalogue through the same selection as applied to the real galaxies. Our method is expected to improve in performance with increased survey area, galaxy number density, and systematic contamination, making organised randoms extremely promising for current and future clustering analyses of faint samples.