The formation of entropy cores in non-radiative galaxy cluster simulations: SPH versus AMR
We simulate the formation and evolution of a massive galaxy c luster in aΛCDM Universe using three different approaches to solving the equations of h ydrodynamics in the absence of radiative cooling: one based on the ‘classic’ Smoothed Partic le Hydrodynamics (SPH) method; one based on a novel SPH algorithm with a higher order dissipa tion switch (SPHS); and one based on an adaptive mesh refinement (AMR) method. We find that SPHS and the AMR code are in excellent agreement with one another: in both, the sph rically averaged entropy profile forms a well-defined core that rapidly converges with increa sing mass and force resolution. By contrast, in agreement with previous work, SPH exhibits r ather different behaviour. At low redshift, the entropy profile shows a systematic decreas e with decreasing cluster-centric radius, converging on ever lower central entropy with incre asing resolution. At higher redshift (z ∼ 1), SPH is in better agreement with the other codes but shows mu ch poorer numerical convergence. We trace the reason for these discrepancies to a known artificial surface tension in SPH that appears at phase boundaries. At early times, the p assage of massive substructures close to the cluster centre during its violent assembly stir s and shocks the gas to build up an entropy core. At late times, the artificial surface tension c auses low entropy gas – that ought to mix with the higher entropy gas – to sink artificially to the c ntre of the cluster. We use SPHS – in which we can fully control the amount of numeri cal dissipation – to study the contribution of numerical versus physical dissip ation on the resultant entropy core. We argue that numerical dissipation is required to ensure si ngle-valued fluid quantities in converging flows. However, provided this dissipation occur s only at the resolution limit, and provided that it does not propagate errors to larger scales, its effect is benign. There is no requirement to build ‘sub-grid’ models of unresolved turbule nc for galaxy cluster simulations. We conclude that entropy cores in non-radiative simulation s f galaxy clusters are physical, resulting from entropy generation in shocked gas during the cluster assembly process. This finally puts to rest the long-standing puzzle of cluster entro py cores in AMR simulations versus their apparent absence in classic SPH simulations.