Why do only some galaxy clusters have cool cores?

Flux-limited X-ray samples indicate that about half of rich galaxy clusters have cool cores. Why do only some clusters have cool cores while others do not? In this paper, cosmological N-body + Eulerian hydrodynamic simulations, including radiative cooling and heating, are used to address this question as we examine the formation and evolution of cool core (CC) and noncool core (NCC) clusters. These adaptive mesh refinement simulations produce both CC and NCC clusters in the same volume. They have a peak resolution of 15.6 h(-1) kpc within a (256 h(-1) Mpc)(3) box. Our simulations suggest that there are important evolutionary differences between CC clusters and their NCC counterparts. Many of the numerical CC clusters accreted mass more slowly over time and grew enhanced CCs via hierarchical mergers; when late major mergers occurred, the CCs survived the collisions. By contrast, NCC clusters experienced major mergers early in their evolution that destroyed embryonic CCs and produced conditions that prevented CC reformation. As a result, our simulations predict observationally testable distinctions in the properties of CC and NCC beyond the core regions in clusters. In particular, we find differences between CC versus NCC clusters in the shapes of X-ray surface brightness profiles, between the temperatures and hardness ratios beyond the cores, between the distribution of masses, and between their supercluster environs. It also appears that CC clusters are no closer to hydrostatic equilibrium than NCC clusters, an issue important for precision cosmology measurements.