The abundance of galaxy clusters in modified Newtonian dynamics: cosmological simulations with massive neutrinos

We present a new particle mesh cosmological N-body code for accurately solving the modified Poisson equation of the quasi-linear formulation of modified Newtonian dynamics (MOND). We generate initial conditions for the Angus cosmological model, which is identical to ? cold dark matter (?CDM) except that the CDM is switched for a single species of thermal sterile neutrinos. We set the initial conditions at z= 250 for a (512 Mpc h-1)3 box with 2563 particles, and we evolve them down to z= 0. We clearly demonstrate the ability of MOND to develop the large-scale structure in a hot dark matter cosmology and contradict the naive expectation that MOND cannot form galaxy clusters. We find that the correct order of magnitude of X-ray clusters (with TX > 4.5 keV) can be formed, but that we overpredict the number of very rich clusters and seriously underpredict the number of lower mass clusters. We present evidence that suggests the density profiles of our simulated clusters are compatible with those of the observed X-ray clusters in MOND. As a last test, we computed the relative velocity between pairs of haloes within 10 Mpc and find that pairs with velocities larger than 3000 km s-1, like the bullet cluster, can form without difficulty.