Deconstructing Thermal Sunyaev-Zel'dovich - Gravitational Lensing
  Cross-Correlations: Implications for the Intracluster Medium
  Recent first detections of the cross-correlation of the thermal
Sunyaev-Zel'dovich (tSZ) signal in Planck cosmic microwave background (CMB)
temperature maps with gravitational lensing maps inferred from the Planck CMB
data and the CFHTLenS galaxy survey provide new probes of the relationship
between baryons and dark matter. Using cosmological hydrodynamics simulations,
we show that these cross-correlation signals are dominated by contributions
from hot gas in the intracluster medium (ICM), rather than diffuse, unbound gas
located beyond the virial radius (the "missing baryons"). Thus, these
cross-correlations offer a tool with which to study the ICM over a wide range
of halo masses and redshifts. In particular, we show that the tSZ - CMB lensing
cross-correlation is more sensitive to gas in lower-mass, higher-redshift halos
and gas at larger cluster-centric radii than the tSZ - galaxy lensing
cross-correlation. Combining these measurements with primary CMB data will
constrain feedback models through their signatures in the ICM pressure profile.
We forecast the ability of ongoing and future experiments to constrain such ICM
parameters, including the mean amplitude of the pressure - mass relation, the
redshift evolution of this amplitude, and the mean outer logarithmic slope of
the pressure profile. The results are promising, with $\approx 5-20$% precision
constraints achievable with upcoming experiments, even after marginalizing over
cosmological parameters.
