TSZ KSZ Statistics

The thermal and kinetic Sunyaev-Zeldovich effects encode complementary information about galaxy clusters: tSZ measures the thermal energy of the ICM while kSZ measures the bulk momentum. Their joint statistics — cross-correlations, bispectra, and higher-order moments combining both effects — provide constraints on both the ICM thermodynamic state and the cluster peculiar velocity field simultaneously. Analyses of the tSZ-kSZ cross-correlation and the kSZ auto-power spectrum in combined CMB datasets from ACT, SPT, and Planck find joint amplitudes and correlation structures that show mild but persistent deviations from ΛCDM predictions calibrated on the Planck cosmological parameters. The kSZ amplitude in particular, when analyzed via pairwise momentum estimators, is systematically lower than predicted from the Planck σ₈-Ω_m combination, consistent with the S₈ tension but adding an independent momentum-space measurement of structure growth.

Successive Collision Theory addresses the joint tSZ-kSZ statistics through the combination of the locally suppressed growth factor (explaining the kSZ amplitude deficit) and the gravitational superposition (modifying the tSZ normalization). The kSZ pairwise momentum is sensitive to the large-scale velocity field, which in SCT is suppressed in the local universe by the enhanced Λ_eff within the KBC supervoid — the same mechanism that explains the S₈ tension and the kinematic SZ dipole anomaly. The tSZ signal is modified by the superposition mechanism as described in the thermal SZ tensions. Their joint statistics in SCT therefore show correlated deviations from ΛCDM: the kSZ is low because peculiar velocities are suppressed, while the tSZ normalization deficit reflects the superposition pressure redistribution. The cross-correlation between tSZ and kSZ carries information about the spatial correlation between thermal and kinetic energy, which in SCT is organized by the angular momentum inheritance of the cluster population rather than by random hierarchical assembly.

The angular momentum organization of cluster motions in SCT introduces a non-Gaussian component to the joint tSZ-kSZ statistics that is absent from ΛCDM predictions. Because cluster peculiar velocities in SCT are partially organized along the inherited angular momentum field — producing coherent bulk flows aligned with filaments and the collision geometry — the kSZ auto-power spectrum has enhanced large-scale power compared to the isotropic random-velocity assumption of ΛCDM. This large-scale coherent kSZ contribution adds to the two-point statistics at low multipoles in a way that depends on the orientation of the angular momentum field relative to the line of sight. In directions along the collision axis, the coherent bulk flow contribution to kSZ is strongest; perpendicular to the collision axis it is weakest. This anisotropic kSZ signal is a unique SCT prediction for joint tSZ-kSZ statistics testable with full-sky CMB survey data.