The SRG/eROSITA All-Sky Survey Tracing the large-scale structure with a clustering study of galaxy clusters

Context. The spatial distribution of galaxy clusters provides a reliable tracer of the large-scale distribution of matter in the Universe. The clustering signal depends on intrinsic cluster properties and cosmological parameters. Aims. The ability of eROSITA on board Spectrum-Roentgen-Gamma (SRG) to discover galaxy clusters allows the association of extended X-ray emission with dark matter haloes to be probed. We measured the projected two-point correlation function to study the occupation of dark matter haloes by clusters and groups detected by the first eROSITA all-sky survey (eRASS1). Methods. We created five volume-limited samples probing clusters with different redshifts and X-ray luminosity values. We interpreted the correlation function with halo occupation distribution (HOD) and halo abundance matching (HAM) models. We simultaneously fit the cosmological parameters and halo bias of a flux-limited sample of 6493 clusters with purity > 96%. Results. We obtained a detailed view of the halo occupation for eRASS1 clusters. The fainter population at low redshift (S0: (L) over bar (X) = 4.63 x 10(43) erg s(-1), 0.1 < z < 0.2) is the least biased compared to dark matter, with b = 2.95 +/- 0.21. The brightest clusters up to higher redshift (S4: (L) over bar (X) = 1.77 x 10(44) erg s(-1), 0.1 < z < 0.6) exhibit a higher bias b = 4.34 +/- 0.62. Satellite groups are rare, with a satellite fraction < 14.9% (8.1) for the S0 (S4) sample. We combined the HOD prediction with a HAM procedure to constrain the scaling relation between L-X and mass in a new way, and find a scatter of <sigma(Lx)> = 0.36. We obtain cosmological constraints for the physical cold dark matter density omega(c) = 0.12(-0.02)(+0.03) and an average halo bias b = 3.63(-0.85)(+1.02). Conclusions. We modelled the clustering of galaxy clusters with a HOD approach for the first time, paving the way for future studies combining eROSITA with 4MOST, SDSS, Euclid, Rubin, and DESI to unravel the cluster distribution in the Universe.