Massive Halos in Millennium Gas Simulations: Multivariate Scaling Relations

The joint likelihood of observable cluster signals reflects the astrophysical evolution of the coupled baryonic and dark matter components in massive halos, and its knowledge will enhance cosmological parameter constraints in the coming era of large, multiwavelength cluster surveys. We present a computational study of intrinsic covariance in cluster properties using halo populations derived from Millennium Gas Simulations (MGS). The MGS are re-simulations of the original 500 h −1 Mpc Millennium Simulation performed with gas dynamics under two different physical treatments: shock heating driven by gravity only ( GO ) and a second treatment with cooling and preheating ( PH ). We examine relationships among structural properties and observable X-ray and Sunyaev–Zel'dovich (SZ) signals for samples of thousands of halos with M 200 ⩾ 5 × 10 13 h −1 M ☉ and z < 2. While the X-ray scaling behavior of PH model halos at low redshift offers a good match to local clusters, the model exhibits non-standard features testable with larger surveys, including weakly running slopes in hot gas observable–mass relations and ∼10% departures from self-similar redshift evolution for 10 14 h −1 M ☉ halos at redshift z ∼ 1. We find that the form of the joint likelihood of signal pairs is generally well described by a multivariate, log-normal distribution, especially in the PH case which exhibits less halo substructure than the GO model. At fixed mass and epoch, joint deviations of signal pairs display mainly positive correlations, especially the thermal SZ effect paired with either hot gas fraction ( r = 0.88/0.69 for PH / GO at z = 0) or X-ray temperature ( r = 0.62/0.83). The levels of variance in X-ray luminosity, temperature, and gas mass fraction are sensitive to the physical treatment, but offsetting shifts in the latter two measures maintain a fixed 12% scatter in the integrated SZ signal under both gas treatments. We discuss halo mass selection by signal pairs, and find a minimum mass scatter of 4% in the PH model by combining thermal SZ and gas fraction measurements.