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

¹ Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 70101, Taiwan
² Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse 1, 85748 Garching, Germany
³ INAF, Osservatorio di Astrofisica e Scienza dello Spazio, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
⁴ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁵ Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
⁶ Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
⁷ Core Research for Energetic Universe, Hiroshima University, 1-3-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
⁸ IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France
⁹ Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141 Taipei 10617, Taiwan
¹⁰ Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
¹¹ Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-Cho, Inage-Ku, Chiba 263-8522, Japan
¹² Argelander-Institut für Astronomie (AIfA), Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
¹³ Institute of Physics, National Yang Ming Chiao Tung University, 1001 University Road, Hsinchu 30010, Taiwan

^⋆ Corresponding author: inchiu@phys.ncku.edu.tw

Received: 1 April 2025
Accepted: 17 September 2025

Abstract

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 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_⋆, 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 (γ_BCG) trends, due to the parameter degeneracy arising from the sample selection and the limited sample size. By adopting an informative prior on γ_BCG to break the B_BCG–γ_BCG degeneracy, we obtain a 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 ≈ 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.