Hot and cooled baryons in smoothed particle hydrodynamic simulations of galaxy clusters: physics and numerics

We discuss an extended set of Tree+SPH( smoothed particle hydrodynamics) simulations of the formation of clusters of galaxies, with the goal of investigating the interplay between numerical resolution effects and star formation/feedback processes. Our simulations were all carried out in a concordance Lambda cold dark matter ( Lambda CDM) cosmology and include radiative cooling, star formation and energy feedback from galactic winds. The simulated clusters span the mass range M-vir similar or equal to ( 0.1 - 2.3) x 1015 h(-1) M-circle dot, with mass resolution varying by several decades. At the highest achieved resolution, the mass of gas particles is m(gas) similar or equal to 1.5 x 107 h(-1) M-circle dot, which allows us to resolve the virial region of a Virgo-like cluster with more than two million gas particles and with at least as many dark matter ( DM) particles. Our resolution study confirms that, in the absence of an efficient feedback mechanism, runaway cooling leads to about 35 per cent of baryons in clusters to be locked up in long lived stars at our highest resolution, with no evidence of convergence. However, including feedback causes the fraction of cooled baryons to converge at about 15 per cent already at modest resolution, which is much closer to the typical values inferred from observational data. Feedback also stabilizes other gas-related quantities, such as radial profiles of entropy, gas density and temperature, against variations due to changes in resolution. Besides the effects of mass resolution, we also investigate the influence of the gravitational force softening length and that of numerical heating of the gas induced by two-body encounters between DM and lighter gas particles. We also show that simulations where more DM than gas particles are used, such that mgas similar or equal to m(DM), show a significantly enhanced efficiency of star formation at z greater than or similar to 3, but they accurately reproduce at z = 0 the fraction of cooled gas and the thermodynamic properties of the intracluster gas. Our results are important for establishing and delineating the regime of numerical reliability of the present generation of hydrodynamical simulations of galaxy clusters.