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Recent detections of the cross-correlation of the thermal Sunyaev-Zel'dovich (tSZ) effect and weak gravitational lensing (WL) enable unique studies of cluster astrophysics and cosmology. In this work, we present constraints on the amplitude of the non-thermal pressure fraction in galaxy clusters, ₀, and the amplitude of the matter power spectrum, ₈, using measurements of the tSZ power spectrum from Planck, and the tSZ-WL cross-correlation from Planck and the Red Cluster Sequence Lensing Survey. We fit the data to a semi-analytic model with the covariance matrix using N-body simulations. We find that the tSZ power spectrum alone prefers ₈ 0. 85 and a large fraction of non-thermal pressure (₀ 0. 2-0. 3). The tSZ-WL cross-correlation on the other hand prefers a significantly lower ₈ 0. 6, and low ₀ 0. 05. We show that this tension can be mitigated by allowing for a steep slope in the stellar-mass-halo-mass relation, which would cause a reduction of the gas in low-mass halos. In such a model, the combined data prefer ₈ 0. 7 and ₀ 0. 2, consistent with predictions from hydrodynamical simulations.
Osato et al. (Mon,) studied this question.