Virialization of galaxy clusters and beyond

Using samples of structures identified by a multiscale decomposition from n umerical simulations, we analyze the scale dependence of the virialization of clusters. We find that beyond the scale of full virialization there exis ts a radius range over which clusters are quasi-virialized, i.e., while the internal structure of an individual cluster may depart substantially from dynamical relaxation, some statistical properties of the multiscale-identif ied clusters are approximately the same as those for the virialized systems . The dynamical reason for the existence of quasi virialization is that som e of the scaling properties of dynamically relaxed systems of cosmic gravit ational clustering approximately hold beyond the full virialization regime. This scaling can also be seen from a semianalytic calculation of the mass functions of collapsed and uncollapsed halos in the Press-Schechter formali sm. The "individual-statistical" duality of the quasi virialization provide s an explanation of the observed puzzle that the total masses of clusters d erived from virial theory are statistically the same as the masses determin ed from gravitational lensing, in spite of the presence of irregular config uration and substructures in individual clusters. It also explains the tigh t correlation between the velocity dispersion of optical galaxies and the t emperature of X-ray emitting gas. Consequently, the virial mass estimators based on the assumptions of isothermal and hydrostatic models are statistic ally applicable to scales on which the clusters are quasi-virialized. In th e quasi-virialization regime, the temperature functions of clusters also sh ow scaling. This feature is a useful discriminator among models. As a preli minary comparison with observation, the discriminator yields favor the mode ls of LCDM and OCDM.