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 quantiti es: the cluster mass, the dark matter velocity dispersion, the gas tem perature, and the cluster luminosity. The comparison is made for a lar ge number of clusters at a range of redshifts in three different cosmo logical models (cold plus hot dark matter, cold dark matter, and open cold dark matter). We find that the analytic formulae provide a good d escription of the relations between three of the four numerical quanti ties. The fourth (luminosity) also agrees once we introduce a procedur e to correct for the fixed numerical resolution. We also compute the n ormalizations for the virial relations and compare extensively to the existing literature, finding remarkably good agreement. The Press-Sche chter prescription is calibrated with the simulations, again finding r esults consistent with other authors. We also examine related issues s uch 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 o f clusters as cosmological probes. Implications for the models are bri efly discussed.