Constraints on the optical depth of galaxy groups and clusters

Abstract

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.