The SRG/eROSITA All-Sky Survey

We present the weak-lensing mass calibration and constrain the relation between the stellar mass of the brightest cluster galaxy (BCG), halo mass, and redshift (M⋆, BCG–M–z) for a sample of 124 galaxy clusters and groups at redshift 0.1 < z < 0.8 from the first Data Release of the eROSITA All-Sky Survey (eRASS1), using data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program. The cluster survey is conducted by the eROSITA X-ray telescope aboard the Spectrum-Roentgen-Gamma (SRG) space observatory. The cluster sample is X-ray-selected and optically confirmed with a negligibly low contamination rate (≈5%). On the basis of individual clusters, the shear profiles g+ of 96 clusters are derived using the HSC Three-Year (HSC-Y3) weak-lensing data, while the BCG stellar masses M⋆, BCG of 101 clusters are estimated using the SED template fitting to the HSC five-band (grizY) photometry. The observed X-ray photon count rate CR is used as the mass proxy, based on which individual halo masses M are obtained at the given CR in a population modelling, while accounting for systematic uncertainties in the weak-lensing modelling through a simulation-calibrated weak-lensing mass-to-halo-mass (MWL–M–z) relation. The count rate (CR–M–z) and BCG stellar mass (M⋆, BCG–M–z) relations are simultaneously constrained in forward modelling and population modelling. In agreement with the results based on the weak-lensing data from the DES and KiDS surveys, we obtain a CR–M–z relation with a self-similar redshift scaling and a mass trend that is steeper than the self-similar prediction. We cannot simultaneously place stringent constraints on the power-law indices of the mass (BBCG) and redshift (γBCG) trends, due to the parameter degeneracy arising from the sample selection and the limited sample size. By adopting an informative prior on γBCG to break the BBCG–γBCG degeneracy, we obtain a M⋆, BCG–M–z relation with the mass slope increasing to BBCG = 0.38 ± 0.11. Informed by the prior, our results suggest that the BCG stellar mass at a fixed halo mass has remained stable with a moderate increase at a level of (20±8)% since redshift z ≈ 0.8. This finding supports the picture of the rapid-then-slow BCG formation, where the majority of the stellar mass must have been assembled at a much earlier cosmic time.