Global Relationships among the 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 metalabundance Z in the core region of clusters of galaxies. First, we confirm thatfundamental relations among rho_0, R, and T found by Fujita and Takahara arereproduced by another data catalogue. Second, we find that, when clusters havetwo components in their surface brightness distribution, the inner componentsalso satisfy the same fundamental relations on the assumption that the averagetemperature of the inner component is the same as that of the outer component.These results strengthen our interpretation that clusters form a two parameterfamily in terms of mass and rho_vir; larger rho_vir corresponds to earlierformation epoch. We argue that the inner components represent distinct darkmatter components which collapsed ahead of the outer components. Third, we alsofind a tight relation between S_gas and rho_vir both for the outer and innercomponents; S_gas is smaller for larger rho_vir but is larger than thatproduced through gravitational collapse alone for larger rho_vir. Althoughradiative cooling affects the thermal evolution, the tight relationshipdiscovered suggests the existence of stable heating sources or stable energytransmission mechanisms. Finally, we find that the iron abundance at thecenters of clusters is correlated with rho_vir for the inner components. Thisimplies that iron produced by Type Ia supernovae has more accumulated forclusters formed earlier. We briefly discuss the implications of these findings.Comment: 11 pages, to be published in PAS