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: L̄_X = 4.63 × 10⁴³ 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: L̄_X = 1.77 × 10⁴⁴ 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 ⟨σ_Lx⟩ = 0.36. We obtain cosmological constraints for the physical cold dark matter density ω_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.