Simulating Galaxy Clusters

Galaxy clusters are the largest gravitationally bound objects in the universe. They are also among the rarest objects in the universe. While these two facts about galaxy clusters may seem disparate, they are in fact intimately related. Our current theory of the origin and evolution of galaxy clusters places them within the broader context of cosmological structure formation in which galaxies, galaxy groups, galaxy clusters, and galaxy superclusters all arise from gravitational instability amplifying perturbations in the cold dark matter density field in an expanding universe. At early times the perturbations are linear in amplitude, and are extremely well described by a Gaussian random field with a known power spectrum (the ΛCDM power spectrum; cf. Fig. 2). At later times, density perturbations become nonlinear and collapse into gravitationally bound systems. The shape of the ΛCDM power spectrum is such that structure forms from the “bottom up”, with galaxies forming first and clusters forming later. It just so happens that we live in a universe in which cluster-scale perturbations collapsed rather recently (since z ∼ 1), which accounts for their rarity as well as their sometimes complex substructure. As cluster-scale perturbations collapse, they bring in all matter within a sphere of comoving radius of about 15 Mpc, which includes galaxies, intergalactic gas, and anything else in that patch of the universe. Because the escape velocity of galaxy clusters is of order 1000 km/s, everything but relativistic particles become trapped in the cluster potential well. For this reason it is often said that clusters represent a fair sample of the universe. This is true from the standpoint of their matter content. However, from the standpoint of cosmological structure this could not be further from the truth. Galaxy clusters form and evolve in the rarest peaks (∼ 3σ) of the density field (Fig. 1). Galaxy formation begins sooner in such regions, and the galaxies evolve due to internal and external processes which are somewhat different from the general field (e.g., ram pressure stripping). Galaxy clusters are interesting objects in their own right, and for decades have been extensively studied in the optical, Xray, and radio wavebands [65]. More recently this has been extended to the microwave, infrared, and extreme UV [66, 67], motivated in part by the fact that galaxy clusters are excellent cosmological probes. Because of their large size and high X-ray luminosities, they can be seen to great distances. As discussed in this volume and in [67], galaxy clusters can also be seen in absorption/emission against the cosmic microwave background (CMB) via the Sunyaev-Zeldovich effect (SZE). As discussed by Rephaeli elsewhere in these proceedings, the SZE is redshift independent, meaning that deep microwave surveys should detect all galaxy clusters in a particular