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 Program

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-star,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 (approximate to 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-star,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 C-R is used as the mass proxy, based on which individual halo masses M are obtained at the given C-R in a population modelling, while accounting for systematic uncertainties in the weak-lensing modelling through a simulation-calibrated weak-lensing mass-to-halo-mass (M-WL-M-z) relation. The count rate (C-R-M-z) and BCG stellar mass (M-star,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 C-R-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 (B-BCG) and redshift (gamma(BCG)) trends, due to the parameter degeneracy arising from the sample selection and the limited sample size. By adopting an informative prior on gamma(BCG) to break the B-BCG-gamma(BCG) degeneracy, we obtain a M-star,M- BCG-M-z relation with the mass slope increasing to B-BCG = 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 approximate to 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.