Beyond Feedback: Disentangling Baryonic Effects with tSZ times FRB Cross-Correlations

Standard observational probes lack the sensitivity to characterize the interplay between feedback-driven gas ejection and non-thermal pressure support in groups and clusters, and current models lack the framework to disentangle it. Recent first detections of the tSZ times FRB cross-power spectrum (Takahashi et al, 2025; Sharma et al 2026) have been interpreted as constraining AGN feedback and sigma 8, but the baryon models used do not independently parameterize non-thermal pressure support, leaving feedback efficiency and gas thermodynamics degenerate. We demonstrate that this cross-correlation provides sensitivity to the thermal and non-thermal structure of cluster gas that neither observable alone can achieve, because the tSZ effect traces electron pressure while FRBs trace solely electron density. Using the Baryon Pasting (BP) framework, which separately parameterizes feedback efficiency epsilon f and non-thermal pressure amplitude A nt, we show that their joint constraint breaks this degeneracy. In the noise-free limit, adding the cross-power spectrum reduces r cond from 0.96 to 0.08 (a 12-fold reduction) and improves the joint figure of merit by a factor of 19, with the constraining power concentrated at cluster interior scales (3000). Recent detections are consistent with our fiducial model and disfavor weak feedback (epsilon f 95% 2.40--3.67 times 10-6 across datasets). With 5 times10 4 FRBs from DSA-2000 combined with SO, we forecast 3.8% fractional precision on A nt, improving to 2.3% with CMB-HD. These constraints directly inform the hydrostatic mass bias, with immediate implications for cluster-based cosmological inference from eROSITA, SO, and CMB-HD.