The SRG/eROSITA All-Sky Survey. The weak-lensing mass calibration and the stellar mass-to-halo mass relation from the Hyper Suprime-Cam Subaru Strategic programme

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 ( for a sample of $124$ galaxy clusters and groups at redshift $0.1<̊edshift<0.8$ from the first Data Release of the All-Sky Survey ( using data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program. The cluster survey is conducted by the 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 of $96$ clusters are derived using the HSC Three-Year (HSC-Y3) weak-lensing data, while the BCG stellar masses of $101$ clusters are estimated using the SED template fitting to the HSC five-band (grizY) photometry. The observed X-ray photon count rate ̊ate is used as the mass proxy, based on which individual halo masses are obtained at the given ̊ate in a population modelling, while accounting for systematic uncertainties in the weak-lensing modelling through a simulation-calibrated weak-lensing mass-to-halo-mass ( relation. The count rate (̊ate-- and BCG stellar mass ( 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 ̊ate-- 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 ( and redshift ( trends, due to the parameter degeneracy arising from the sample selection and the limited sample size. By adopting an informative prior on to break the degeneracy, we obtain a relation with the mass slope increasing to Bbcg = 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 łeft(20±8̊ight) since redshift ̊edshift≈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.