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 {\it 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 $(1-b)=0.79^{+0.07}_{-0.10}$, 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 ($7\times10^{5}$--$3 \times10^{8}$)\,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.