Probing the diffuse baryon distribution with the lensing-tSZ cross-correlation

Approximately half of the Universe's baryons are in a form that has been hard to detect directly. However, the missing component can be traced through the cross-correlation of the thermal Sunyaev-Zeldovich (tSZ) effect with weak gravitational lensing. We build a model for this correlation and use it to constrain the extended baryon component, employing data from the Canada France Hawaii Lensing Survey and the Planck satellite. The measured correlation function is consistent with an isothermal beta-model for the halo gas pressure profile, and the 1- and 2-halo terms are both detected at the 4 sigma level. In addition, we measure the hydrostatic mass bias (1-b) = 0.79(-0.10)(+0.07), which is consistent with numerical simulation results and the constraints from X-ray observations. The effective temperature of the gas is found to be in the range (7 x 10(5)-3 x 10(8)) K, with approximately 50% of the baryons appearing to lie beyond the virial radius of the halos, consistent with current expectations for the warm-hot intergalactic medium.