Thermal SZ Scaling

The thermal SZ effect signal from galaxy clusters scales with cluster mass, redshift, and the ICM thermal energy content, and these scaling relations — Y_SZ ∝ M^α (1+z)^β × E(z)^γ — are calibrated through joint analysis of X-ray observations, weak lensing mass measurements, and self-calibration within large cluster samples. The observed normalization and slope of the Y_SZ–M relation show systematic differences from ΛCDM predictions: the observed tSZ signal at fixed weak lensing mass is lower than predicted, while the Y_SZ–Y_X relation (comparing tSZ to X-ray spectroscopic mass proxy Y_X) agrees well with simulations. This implies the tension lies in the absolute mass calibration — specifically that the weak lensing masses are higher than the masses inferred from the SZ-calibrated scaling relations, consistent with the broader cluster hydrostatic mass bias discussion but now manifest in the scaling relation normalization.

Successive Collision Theory addresses the thermal SZ scaling tension through the gravitational superposition contribution to weak lensing mass. In SCT, weak lensing measures the total effective gravitational mass including the superposition term from overlapping nested frames, while the tSZ signal reflects only the thermal pressure of the baryonic ICM. The ratio Y_SZ/M_lensing is therefore systematically lower than Y_SZ/M_true (where M_true is the actual baryon-plus-compact-object mass) because M_lensing includes the non-thermal, non-SZ-producing superposition contribution. This produces the observed deficit in Y_SZ at fixed weak lensing mass without requiring systematic errors in either the tSZ measurements or the lensing analysis — both are correctly measuring what they claim, but they measure different components of the total effective gravitational mass.

The SCT prediction for the tSZ scaling relations is specific: the normalization offset between tSZ-inferred mass and lensing mass should scale with the depth of each cluster's embedding in the frame hierarchy, being larger for clusters in denser environments where the superposition contribution is greatest. This produces an environment-dependent scatter in the Y_SZ–M_lensing relation — clusters in filament nodes and supercluster cores should show lower Y_SZ/M_lensing ratios than clusters in lower-density environments at the same lensing mass. Current scatter in tSZ scaling relations is consistent with this prediction, and future surveys combining tSZ maps from CMB-S4 with weak lensing from Euclid will have sufficient statistical power to detect this environment-dependent normalization shift — a unique and falsifiable SCT prediction.