The Hydrostatic Mass Bias and the $\sigma_8$ Tension: A Multi-Probe Forecast for Stage-IV/V Surveys

TL;DR

This paper forecasts how multi-probe, tomographic analyses combining CMB and optical surveys can precisely calibrate hydrostatic mass bias, reducing its degeneracy with cosmological parameters and improving constraints on structure growth.

Contribution

It introduces a comprehensive Fisher forecast for Stage-IV surveys demonstrating the effectiveness of tomographic cross-correlations in calibrating hydrostatic mass bias.

Findings

Tomographic analysis improves $b_{HSE}$ precision by a factor of three.

Optical-only probes cannot constrain $b_{HSE}$ directly.

Multi-probe approaches achieve percent-level calibration of hydrostatic mass bias.

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.