To quantify how rare the bullet-cluster-like high-velocity merging systems are in the standard Λ cold dark matter (CDM) cosmology, we use a large-volume (27 h–3 Gpc3) cosmological N-body MICE simulation to calculate the distribution of infall velocities of subclusters around massive main clusters. The infall velocity distribution is given at (1-3)R200 of the main cluster (where R200 is similar to the virial radius), and thus it gives the distribution of realistic initial velocities of subclusters just before collision. These velocities can be compared with the initial velocities used by the non-cosmological hydrodynamical simulations of 1E0657-56 in the literature. The latest parameter search carried out by Mastropietro & Burkert has shown that an initial velocity of 3000 km/s at about 2R200 is required to explain the observed shock velocity, X-ray brightness ratio of the main and subcluster, X-ray morphology of the main cluster, and displacement of the X-ray peaks from the mass peaks. We show that such a high infall velocity at 2R200 is incompatible with the prediction of a ΛCDM model: the probability of finding 3000 km/s in (2-3)R200 is between 3.3x10–11 and 3.6x10–9. A lower velocity, 2000 km/s at 2R200, is also rare, and moreover, Mastropietro & Burkert have shown that such a low initial velocity does not reproduce the X-ray brightness ratio of the main and subcluster or morphology of the main cluster. Therefore, we conclude that the existence of 1E0657-56 is incompatible with the prediction of a ΛCDM model, unless a lower infall velocity solution for 1E0657-56 with ≲1800 km/s at 2R200 is found.
cosmology: theory - large-scale structure of universe - methods: statistical