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,multi-wavelength 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 Mpc/h 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-Zeldovich (SZ) signals for samples of thousands of halos with M_200 > 5 times 10^{13} Msun/h 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 Msun/h 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). 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.

Effects of Selection and Covariance on X-ray Scaling Relations of Galaxy Clusters

We explore how the behavior of galaxy cluster scaling relations are affected by flux-limited selection biases and intrinsic covariance among observable properties. Our models presume log-normal covariance between luminosity (L) and temperature (T) atfixed mass (M), centered on evolving, power-law mean relations as a function of host halo mass. Selection can mimic evolution; the lm and lt relations from shallow X-ray flux-limited samples will deviate from mass-limited expectations at nearly all scales while the relations from deep surveys ($10^{-14} cgsflux$) become complete, and therefore unbiased, at masses above $sims 2 times 10^{14} hinv msol$. We derive expressions for low-order moments of the luminosity distribution at fixed temperature, and show that the slope and scatter of the lt relation observed in flux-limited samples is sensitive to the assumed lt correlation coefficient. In addition, lt covariance affects the redshift behavior of halo counts and mean luminosity in a manner that is nearly degenerate with intrinsic population evolution.