Constraints on the optical depth of galaxy groups and clusters
  Future data from galaxy redshift surveys, combined with high-resolutions maps of the cosmic microwave background, will enable measurements of the pairwise kinematic Sunyaev-Zel'dovich (kSZ) signal with unprecedented statistical significance. This signal probes the matter-velocity correlation function, scaled by the average optical depth ($\tau$) of the galaxy groups and clusters in the sample, and is thus of fundamental importance for cosmology. However, in order to translate pairwise kSZ measurements into cosmological constraints, external constraints on $\tau$ are necessary. In this work, we present a new model for the intra-cluster medium, which takes into account star-formation, feedback, non-thermal pressure, and gas cooling. Our semi-analytic model is computationally efficient and can reproduce results of recent hydrodynamical simulations of galaxy cluster formation. By calibrating the model using recent X-ray measurements of gas density profiles of clusters and $M_{\mathrm{gas}}-M$ relations of groups and clusters, we show that the integrated $\tau$ is constrained to better than 6% (with a confidence level of 95%), which sets the tightest constraints on the external prior on the optical depth of groups and clusters reported in the literature to date. Our strong prior on $\tau$ should significantly improve cosmological constraints derived from future pairwise kSZ measurements and shed new insights into the nature of dark energy, modified gravity, and neutrino mass. 
Samuel Flender, Daisuke Nagai, Michael McDonald
astro-ph.CO