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Global Relationships among Physical Properties of Galaxy Cluster Cores

Using X-ray data, we investigate interrelations between gas density rho_0, virial density rho_vir, core radius R, temperature T, entropy S_gas, and metal abundance Z in the core region of clusters of galaxies. First, we confirm that fundamental relations among rho_0, R, and T found by Fujita and Takahara are reproduced by another data catalogue. Second, we find that, when clusters have two components in their surface brightness distribution, the inner components also satisfy the same fundamental relations on the assumption that the average temperature of the inner component is the same as that of the outer component. These results strengthen our interpretation that clusters form a two parameter family in terms of mass and rho_vir; larger rho_vir corresponds to earlier formation epoch. We argue that the inner components represent distinct dark matter components which collapsed ahead of the outer components. Third, we also find a tight relation between S_gas and rho_vir both for the outer and inner components; S_gas is smaller for larger rho_vir but is larger than that produced through gravitational collapse alone for larger rho_vir. Although radiative cooling affects the thermal evolution, the tight relationship discovered suggests the existence of stable heating sources or stable energy transmission mechanisms. Finally, we find that the iron abundance at the centers of clusters is correlated with rho_vir for the inner components. This implies that iron produced by Type Ia supernovae has more accumulated for clusters formed earlier. We briefly discuss the implications of these findings.