Simulation-Based Cosmological Mass Calibration of XXL Galaxy Clusters using HSC Weak Lensing

TL;DR

This work addresses the challenge of deriving robust cosmological constraints from XXL galaxy clusters in the presence of complex selection and systematics by adopting a simulation-based, likelihood-free forward-modeling approach. The authors jointly constrain cosmology and X-ray scaling relations using a 12-parameter SBI framework that forward-models cluster counts, X-ray observables, and weak-lensing data from HSC, while explicitly accounting for miscentering, photo-$z$ bias, and mass-dependent lensing biases. They report a constraint on $S_8 \equiv \sigma_8(\Omega_m/0.3)^{0.5}$ of $0.867 \pm 0.063$ with an additional 3% systematic from neural-network stochasticity, finding consistency with Planck and other cluster measurements; the inferred $T$--$M$ relation agrees with self-similar expectations while the $L$--$T$ relation is steeper than self-similar. From the forward model posterior, they derive lensing-calibrated masses for XXL clusters and provide a self-consistent mass calibration for future multi-probe analyses of the XXL sample, demonstrating the viability and value of SBI methods in cluster cosmology.

Abstract

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.

Figures (2)

• Figure 1: Number counts of galaxy clusters as a function of redshift. The red histogram displays the observed XXL C1 clusters from the combined northern and southern regions. The blue histogram represents the mean redshift distribution of synthetic XXL-detected clusters, generated from approximately 5,000 posterior samples inferred via SBI. The blue error bars indicate the confidence intervals marginalized over all parameter uncertainties, while the magenta error bars represent the expected Poisson noise of the observed data. Note that the posterior uncertainties (blue) generally exceed the Poisson noise (magenta), reflecting the additional variance propagated from scaling relation and cosmological uncertainties.
• Figure 2: The temperature--luminosity distribution of observed XXL C1 galaxy clusters (red points and histograms) compared with the distribution from synthetic cluster samples generated using approximately 5,000 posterior samples inferred via SBI. The error bars indicate the 68% confidence intervals of the simulated distributions, while the shaded blue contours correspond to the 68% and 95% confidence levels of the posterior predictive distribution.