Investigating cluster astrophysics and cosmology with cross-correlation of the thermal Sunyaev-Zel'dovich effect and weak lensing

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, alpha(0), and the amplitude of the matter power spectrum, a 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 sigma(8) similar to 0.85 and a large fraction of non-thermal pressure (alpha(0) similar to 0.2-0.3). The tSZ-WL cross-correlation on the other hand prefers a significantly lower sigma(8) similar to 0.6 and low alpha(0) similar to 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 haloes. In such a model, the combined data prefer sigma(8) similar to 0.7 and alpha(0) similar to 0.2, consistent with predictions from hydrodynamical simulations.