The Sunyaev Zel'dovich (SZ) effect is sensitive to the pressure of ionized
gas inside galaxy clusters. The gas pressure responds to changes in the
gravitational potential of the cluster, which is dominated by the host dark
matter halo. Changes in halo concentration therefore impact the SZ signal, with
implications for cosmological and other analyses of SZ-selected clusters. We
investigate the concentration-SZ relation in theory and simulations. We find
that the impact of concentration on the inner SZ profile (R≲0.75R200c​) can be captured with standard polytropic gas models. However, we
find that such models do a poor job of reproducing the outer SZ profiles (R≳0.75R200c​) and the relation between the integrated SZ signal, Y,
and concentration. This disagreement results from a sharp truncation of the gas
pressure profile near the splashback radius, likely caused by virial shocks. We
develop a simple description of the truncation that leads to a good match with
simulated SZ profiles out to several R200c​ for clusters of varying mass
and concentration, and that also accurately predicts the concentration-Y
relationship. Finally, we determine how inference of the linear bias parameter
and splashback radius for SZ-selected clusters can be biased by ignoring the
concentration dependence of the SZ signal.Comment: 15 pages, 11 figures; comments welcome