Abridged: We simulate a massive galaxy cluster in a LCDM Universe using three different approaches to solving the equations of non-radiative hydrodynamics: `classic Smoothed Particle Hydrodynamics (SPH); a novel SPH with a higher order dissipation sw
itch (SPHS); and adaptive mesh refinement (AMR). We find that SPHS and AMR are in excellent agreement, with both forming a well-defined entropy core that rapidly converges with increasing mass and force resolution. By contrast, SPH exhibits rather different behaviour. At low redshift, entropy decreases systematically with decreasing cluster-centric radius, converging on ever lower central values with increasing resolution. At higher redshift, SPH is in better agreement with SPHS and AMR but shows much poorer numerical convergence. We trace these discrepancies to artificial surface tension in SPH at phase boundaries. At early times, the passage of massive substructures close to the cluster centre stirs and shocks gas to build an entropy core. At later times, artificial surface tension causes low entropy gas to sink artificially to the centre of the cluster. We use SPHS to study the contribution of numerical versus physical dissipation on the entropy core, and argue that numerical dissipation is required to ensure single-valued fluid quantities in converging flows. However, provided this dissipation occurs 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 turbulence for galaxy cluster simulations. We conclude that entropy cores in non-radiative simulations of galaxy clusters are physical, resulting from entropy generation in shocked gas during cluster assembly, putting to rest the long-standing puzzle of cluster entropy cores in AMR simulations versus their apparent absence in classic SPH simulations.
We perform a detailed investigation into the disruption of central cusps via the transfer of energy from sinking massive objects. Constant density inner regions form at the radius where the enclosed mass approximately matches the mass of the infallin
g body. We explore parameter space using numerical simulations and give an empirical relation for the size of the resulting core within structures that have different initial cusp slopes. We find that infalling bodies always stall at the edge of these newly formed cores, experiencing no dynamical friction over many dynamical times. As applications, we consider the resulting decrease in the dark matter annihilation flux due to centrally destroyed cusps, and we present a new theory for the formation of close binary nuclei -- the `stalled binary model. We focus on one particularly interesting binary nucleus system, the dwarf spheroidal galaxy VCC 128 which is dark matter dominated at all radii. We show that its nuclei would rapidly coalesce within a few million years if it has a central dark matter cusp slope steeper than r^{-1}. However, if its initial dark matter cusp is slightly shallower than a log slope of -0.75 at ~0.1% of the virial radius, then the sinking nuclei naturally create a core equal to their observed separation and stall. This is close to the log slope measured a recent billion particle CDM halo simulation.
It is of great interest to measure the properties of substructures in dark matter halos at galactic and cluster scales. Here we suggest a method to constrain substructure properties using the variance of weak gravitational flexion in a galaxy-galaxy
lensing context. We show the effectiveness of flexion variance in measuring substructures in N-body simulations of dark matter halos, and present the expected galaxy-galaxy lensing signals. We show the insensitivity of the method to the overall galaxy halo mass, and predict the methods signal-to-noise for a space-based all-sky survey, showing that the presence of substructure down to 10^9 M_odot halos can be reliably detected.
