The Tau of Galaxy Clusters

The recent emergence of detections of the kinetic Sunyaev-Zel'dovich (kSZ) effect through cross-correlation techniques is encouraging for the prospects of future cosmic microwave background (CMB) experiments. Extracting information on the large-scale velocity fields and constraining cosmological parameters from such kSZ measurements requires an understanding of the optical depth to CMB photons through halos. Using cosmological hydrodynamic simulations we find that there exists a low-scatter relation between the optical depth and thermal Sunyaev-Zel'dovich (tSZ) signal of halos within a physical aperture. We propose that such a relation can be used to break the degeneracy between optical depth and line-of-sight velocity in kSZ measurements. The limiting factors in our proposal are systematic uncertainties associated with the sub-grid physics models in the simulations, which we calculate to be less than 10 percent. We discuss future observational measurements that could potentially be used to mitigate the systematic uncertainties in this scaling relation.