Statistical properties of X-ray clusters: Analytic and numerical comparisons

We compare the results of Eulerian hydrodynamic simulations of cluster formation against virial scaling relations between four bulk quantities: the cluster mass, the dark matter velocity dispersion, the gas temperature, and the cluster luminosity. The comparison is made for a large number of clusters at a range of redshifts in three different cosmological models (cold plus hot dark matter, cold dark matter, and open cold dark matter). We find that the analytic formulae provide a good description of the relations between three of the four numerical quantities. The fourth (luminosity) also agrees once we introduce a procedure to correct for the fixed numerical resolution. We also compute the normalizations for the virial relations and compare extensively to the existing literature, finding remarkably good agreement. The Press-Schechter prescription is calibrated with the simulations, again finding results consistent with other authors. We also examine related issues such as the size of the scatter in the virial relations, the effect of metallicity with a fixed passband, and the structure of the halos. All of this is done in order to establish a firm groundwork for the use of clusters as cosmological probes. Implications for the models are briefly discussed.