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, $\sigma_8$, 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 $\sigma_8 \sim 0.85$ and a large
fraction of non-thermal pressure ($\alpha_0 \sim 0.2$-$0.3$). The tSZ-WL
cross-correlation on the other hand prefers a significantly lower $\sigma_8
\sim 0.6$, and low $\alpha_0 \sim 0.05$. 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 $\sigma_8 \sim 0.7$ and $\alpha_0 \sim 0.2$,
consistent with predictions from hydrodynamical simulations.
