Simulation-Based Cosmological Mass Calibration of XXL Galaxy Clusters using HSC Weak Lensing
We present a cosmological analysis of the X-ray-selected galaxy cluster sample from the XXL survey, employing a simulation-based inference (SBI) framework to jointly constrain cosmological parameters and X-ray scaling relations through forward modeling of cluster counts, X-ray observables, and weak-lensing measurements. Our analysis combines X-ray data from the XMM-XXL survey with shear measurements from the three-year shape catalog of the Hyper Suprime-Cam Subaru Strategic Program. The analysis focuses on the XXL C1 sample, comprising 171 clusters for abundance modeling, a subset of 86 clusters located within the XXL-N region for lensing-based mass calibration, and 162 clusters with X-ray temperature and luminosity measurements used to constrain scaling relations. Using the density-estimation likelihood-free inference (DELFI) algorithm, we construct a forward model with 12 parameters that incorporates the XXL selection function and cluster population modeling and accounts for key systematic effects including cluster miscentering, photometric redshift bias, and mass-dependent weak-lensing bias. Our SBI analysis yields a constraint on the cosmological parameter $S_8 \equiv σ_8 (Ω_{m}/0.3)^{0.5} = 0.867 \pm 0.063$, with an additional 3% systematic uncertainty from neural network stochasticity. The result is consistent with Planck and recent cluster-based measurements. The inferred temperature-mass relation is consistent with self-similar expectations within uncertainties, whereas the luminosity-temperature relation exhibits a slope steeper than the self-similar prediction. From the resulting posterior distribution of the forward model, we derive lensing-calibrated mass estimates for all individual XXL clusters with measured X-ray temperatures or luminosities. These results provide a self-consistent mass calibration for future multi-probe cosmological analyses of the XXL sample.