| We use numerical simulations of cosmological structure formation to study the distribution and evolution of galaxy clusters. We employ simulations in both WMAP1 and WMAP3 cosmologies, and simulated with and without the physics of galaxy formation, resulting in a sample of nearly 300 galaxy clusters spanning two decades in mass at the present epoch. We show that the mass weighted temperature of the intracluster medium and the Sunyaev-Zel'dovich (SZ) Compton Y integrated within a radius enclosing 500 times the critical density of the universe each correlates strongly with total cluster mass, and the mean relation is reasonably well described by a simple self-similar model. These relations exhibit remarkably little scatter (10-15%) independent of cluster mass and redshift. We find that the distribution of these quantities about the best fit scaling relations is not well fit by a log-normal distribution, but instead exhibits significant positive kurtosis. Additionally, we find that the residual from the best fit mass-temperature relation correlates with halo temperature, indicating a connection between halo merger history and the properties of the cluster gas. These results have significant implication for the ability of future SZ galaxy cluster surveys to self-calibrate the mass-observable relations and thus constrain cosmological parameters. |
