The entropy core in galaxy clusters: numerical and physical effects in cosmological grid simulations

A flat distribution of low gas entropy in the core region of galaxy clusters is a feature commonly found in Eulerian cosmological simulations, at variance with most standard simulations of smoothed particle hydrodynamics fashion. From the literature, it is still unclear whether this difference is entirely due to numerical artefacts (e.g. spurious transfer from gravitational energy to thermal energy), physical mechanisms (e.g. enhanced mixing in Eulerian codes) or a mixture of both. This issue is related to many still open lines of research in the characterization of the dynamical evolution of the baryons in galaxy clusters: the origin of the cool-core/non-cool-core bi-modality, the diffusion of metals within galaxy clusters, the interplay between active galactic nuclei (AGN) and the intra-cluster medium, etc. In this work, we aim at constraining to what extent the entropy core is affected by numerical effects, and which are the physical reasons for its production in cosmological runs. To this end, we run a set of 30 high-resolution re-simulations of a similar to 3 x 1014 M-circle dot h-1 cluster of galaxies with a quiet dynamical history, using modified versions of the cosmological adaptive mesh refinement code enzo and investigating many possible (physical and numerical) details involved in the production of entropy in simulated galaxy clusters. We report that the occurrence of a flat entropy core in the innermost region of a massive cluster is mainly due to hydrodynamical processes resolved by the numerical code (e.g. shocks and mixing motions) and that additional spurious effects of numerical origin (e.g. artificial heating due to softening effects) affect the size and level of the entropy core only in a minor way. Using Lagrangian tracers we show that the entropy profile of non-radiative simulations is produced by a mechanism of 'sorting in entropy' which takes place with regularity during the cluster evolution. The evolution of tracers illustrates that the flat entropy core is caused by physical mixing of subsonic motions (mostly driven by accreted sub-clumps) within the shallow inner cluster potential. Several re-simulations were also produced for the same cluster object with the addition of radiative cooling, uniform pre-heating at high redshift (z = 10) and late (z < 1) thermal energy feedback from AGN activity in the cluster, in order to assess the effects of such mechanisms on the final entropy profile of the cluster. We report on the infeasibility of balancing the catastrophic cooling (and recovering a flat entropy profile) by means of the investigated trials for AGN activity alone, while for a sub-set of pre-heating models, or AGN feedback plus pre-heating models, a flat entropy distribution similar to non-radiative runs can be obtained with a viable energy requirement. Complementary analysis is presented also for a major merger cluster, obtaining similar results and achieving a generally good consistency with X-ray data for the entropy distribution in real galaxy clusters.