The Hydrostatic Mass Bias and the ${\sigma }_8$ Tension: A Multi-Probe Forecast for Stage-IV/V Surveys

Abstract

The hydrostatic mass bias ($b_{\mathrm{HSE}}$) is a leading systematic uncertainty in cluster cosmology and a principal source of degeneracy with ${\sigma }_8$ and ${\Omega }_m$. We investigate the capability of Stage-IV CMB and optical surveys to calibrate $b_{\mathrm{HSE}}$ using tomographic cross-correlations between the thermal Sunyaev--Zel'dovich (tSZ) effect, galaxy clustering, and weak lensing. We perform a Fisher forecast incorporating realistic survey noise, foreground modeling for clustered CIB and radio sources, and full marginalization over cosmological and astrophysical nuisance parameters, including per-bin galaxy bias perturbations, photometric redshift shifts, intrinsic alignments, and baryonic feedback modeled with HMCode2020. With optimized tomographic binning (10 lens and 5 source bins for LSST; 6 lens and 5 source bins for CSST), we forecast marginalized constraints of $0.98\%$ for SO+LSST, $1.60\%$ for CMB-S4+LSST, and $2.40\%$ for CMB-S4+CSST. Tomography improves $b_{\mathrm{HSE}}$ precision by factors of approximately three relative to non-tomographic analyses, reflecting the role of redshift information in breaking the $b_{\mathrm{HSE}}$--${\sigma }_8$ degeneracy. Optical-only probes provide no direct constraint on $b_{\mathrm{HSE}}$, whereas inclusion of tSZ-containing spectra enables percent-level calibration under realistic systematic assumptions. The results demonstrate that multi-probe tomographic analyses with Stage-IV surveys can achieve robust control of hydrostatic mass bias, strengthening cluster-based constraints on structure growth.

arXiv comment20 pages, 7 figures, 3 tables. Published in The Astrophysical Journal, 1004, 103 (2026). We have added useful citations in this version

References in corpus (47)

• The Structure of Cold Dark Matter Halos
• Efficient Computation of CMB anisotropies in closed FRW models
• Halo Models of Large Scale Structure
• Toward a halo mass function for precision cosmology: the limits of universality
• The Simons Observatory: Science goals and forecasts
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Cosmological Parameters from Observations of Galaxy Clusters
• Chandra Cluster Cosmology Project III: Cosmological Parameter Constraints
• The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests
• The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the Y_SZ-M_500 relation
• Dark matter halo concentrations in the Wilkinson Microwave Anisotropy Probe year 5 cosmology
• Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies
• KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics
• Testing X-ray Measurements of Galaxy Clusters with Cosmological Simulations
• The BAHAMAS project: Calibrated hydrodynamical simulations for large-scale structure cosmology
• The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters
• HMcode-2020: Improved modelling of non-linear cosmological power spectra with baryonic feedback
• Cosmology from the Chinese Space Station Optical Survey (CSS-OS)
• Core Cosmology Library: Precision Cosmological Predictions for LSST
• The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and its Implications for Structure Growth
• Effect of Photometric Redshift Uncertainties on Weak Lensing Tomography
• CMB-S4: Forecasting Constraints on Primordial Gravitational Waves
• On the Cluster Physics of Sunyaev-Zel'dovich Surveys II: Deconstructing the Thermal SZ Power Spectrum
• Hydrodynamic Simulation of Non-thermal Pressure Profiles of Galaxy Clusters
• The Effective Number Density of Galaxies for Weak Lensing Measurements in the LSST Project
• KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey
• Baryons, Neutrinos, Feedback and Weak Gravitational Lensing
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Cluster Abundances, Weak Lensing, and Galaxy Correlations
• Weak-Lensing Mass Calibration of ACTPol Sunyaev-Zel'dovich Clusters with the Hyper Suprime-Cam Survey
• Testing Sunyaev-Zel'dovich measurements of the hot gas content of dark matter haloes using synthetic skies
• SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field
• Introduction to the Chinese Space Station Survey Telescope (CSST)
• Cross-correlation of DES Y3 lensing and ACT/$Planck$ thermal Sunyaev Zel'dovich Effect II: Modeling and constraints on halo pressure profiles
• Constraining Cluster Virialization Mechanism and Cosmology using Thermal-SZ-selected clusters from Future CMB Surveys
• The Simons Observatory: Galactic Science Goals and Forecasts
• Forecast of Neutrino Cosmology from the CSST Photometric Galaxy Clustering and Cosmic Shear Surveys
• Assessing the Importance of Noise from Thermal Sunyaev-Zel{'}dovich Signals for CMB Cluster Surveys and Cluster Cosmology
• Transitioning from Stage-III to Stage-IV: Cosmology from galaxy$\times$CMB lensing and shear$\times$CMB lensing
• Cross Correlation between the Thermal Sunyaev-Zel'dovich Effect and Projected Galaxy Density Field
• Future Cosmology: New Physics and Opportunity from the China Space Station Telescope (CSST)
• Freeform three-mirror anastigmatic large-aperture telescope and receiver optics for CMB-S4
• Joint Modelling of Astrophysical Systematics for Cosmology with LSST Cosmic Shear
• Results and forecasts on cosmic inflation from weak lensing
• The impact of baryons on the sparsity of simulated galaxy clusters from The Three Hundred Project
• Mitigating Nonlinear Systematics in Weak Lensing Surveys II: Stability and Diagnostics with Intrinsic Alignment
• Euclid: Modelling observational effects in cluster counts and cluster clustering
• Implications of SPT and eROSITA cosmologies for Planck cluster number counts and t-SZ power spectrum