Cosmology from LOFAR Two-metre Sky Survey Data Release 2: Counts-in-cells statistics

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The second data release of the LOFAR Two-Metre Sky Survey (LoTSS-DR2) extends the first data release in terms of sky coverage and source density. It provides the largest radio source catalogue to date, including 4.4 million sources and covering 5,635 square degrees of the sky. Therefore, it provides an excellent opportunity for studies of the large-scale structure of the Universe. We investigated the statistical distribution of source counts in cells and we tested a computationally cheap method based on the counts in cells to estimate the two-point correlation function. We studied and compared three stochastic models for the counts in cells; these resulted in a Poisson distribution, a compound Poisson distribution, and a negative binomial distribution. By analysing the variance of counts in cells for various cell sizes, we fitted the reduced normalised variance to a single power-law model representing the angular two-point correlation function. Our analysis confirms that radio sources are not Poisson distributed, which is most likely due to multiple physical components of radio sources. Employing instead a Cox process, we show that there is strong evidence in favour of the negative binomial distribution above a flux-density threshold of 2 mJy. Additionally, the mean number of radio components derived from the negative binomial distribution is in good agreement with corresponding estimates based on the value-added catalogue of LoTSS-DR2. The scaling of the counts-in-cells normalised variance with cell size is in good agreement with a power-law model for the angular two-point correlation. At a flux-density threshold of 2 mJy and a signal-to-noise ratio of 7.5 for individual radio sources, we find that for a range of angular scales large enough to not be affected by the multi-component nature of radio sources, the value of the exponent of the power law ranges from -0.8 to -1.05. This closely aligns with findings from previous optical, infrared, and radio surveys of the large-scale structure. The multi-component nature of LoTSS radio sources is essential in order to understand the observed counts-in-cells statistics. The scaling of the counts-in-cells statistics with cell size provides a computationally efficient method for estimating the two-point correlation properties, offering a valuable tool for future large-scale structure studies.