Initial conditions for idealized clusters mergers, simulating 'El Gordo'

Simulations of isolated binary mergers of galaxy clusters are a useful tool to study the evolution of these objects. For exceptionally massive systems, they even represent the only viable way of simulation, because these are rare in typical cosmological simulations. We present a new practical model for these simulations based on the Hernquist dark matter profile. The hydrostatic equation is solved for a beta-model with beta = 2/3 in this potential and approximate expressions for X-ray brightness and Compton-y parameter are derived. We show in detail how to setup such a system using smoothed particle hydrodynamics. The theoretical and several numerical models are compared to observed scaling relations of galaxy clusters and satisfactory agreement with the self-similar relations is found. The model is then applied to investigate the observed cluster ACT-CT J0102-4915 'El Gordo', a particularly massive merging high-redshift cluster. We are able to reproduce the X-ray luminosity, Sunyaev-Zeldovich effect and dark matter core distance as well as the rough shape of the observed cluster for reasonable model parameters. The lack of sub-structure prevents us from obtaining the fluctuations observed in the wake of the system and we argue that the parent cluster of the system was highly disturbed even before the main merger observed today.