The SRG/eROSITA All-Sky Survey: Tracing the Large-Scale Structure with a clustering study of galaxy clusters

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. The ability of eROSITA onboard Spectrum-Roentgen-Gamma (SRG) to discover galaxy clusters allows probing the association of extended X-ray emission to dark matter haloes. We aim to measure the projected two-point correlation function to study the occupation of dark matter halos by clusters and groups detected by the first eROSITA all-sky survey (eRASS1). We create five volume-limited samples probing clusters with different redshift and X-ray luminosity. We interpret the correlation function with halo occupation distribution (HOD) and halo abundance matching (HAM) models. We simultaneously fit cosmological parameters and halo bias of a flux-limited sample of 6493 clusters with purity > 96%. Results. We obtain a detailed view of the halo occupation for eRASS1 clusters. The fainter population at low redshift (S0: LX = 4.63E43 erg/s, 0.1 < z < 0.2) is the least biased compared to dark matter, with b = 2.95 $\pm$ 0.21. The brightest clusters up to higher redshift (S4: LX = 1.77E44 erg/s , 0.1 < z < 0.6) exhibit a higher bias b = 4.34 $\pm$ 0.62. Satellite groups are rare, with a satellite fraction < 14.9% (8.1) for the S0 (S4) sample. We combine the HOD prediction with a HAM procedure to constrain the scaling relation between LX and mass in a new way and find a scatter of 0.36. We obtain cosmological constraints for the physical cold dark matter density 0.12+0.03-0.02 and an average halo bias b = 3.63+1.02-0.85. We model 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.