An alternative bosonic dark matter model is examined in detail via high-resolution simulations. These bosons have particle mass of order 10¡22eV and are non-interacting. If they do exist and can account for structure formation, these bosons must be condensed into the Bose-Einstein state and described by a coherent wave function. This matter, also known as Fuzzy Dark Matter (Hu, Barkana & Gruzinov, 2000), is speculated to be able, ‾rst, to eliminate the sub-galactic halos to solve the prob- lem of over-abundance of dwarf galaxies, and, second, to produce °at halo cores in galaxies suggested by some observations. Due to the limited dynamical range, our 10243 simulation literarily addresses cluster-size halos in an 100 h¡1Mpc box, rather than galaxy-size halos in an 1 h¡1Mpc box, by adopting 10¡26eV boson mass. However, since the SchrÄodinger-Poisson model studied in this work is a scale-free system, our results can be rescaled to a simulation box 100 times smaller. The sim- ulation results show that although this extremely light bosonic dark matter indeed suppresses low-mass halos, it can, to the contrary of expectation, yield singular halo cores. The density pro‾le of the singular halo is almost identical to the halo pro‾le of Navarro, Frenk & White (1997). Such a pro‾le seems to be independent of the formation processes via accretion or merger. We shall stress a caveat for rescaling from 100 h¡1Mpc to 1 h¡1Mpc box. The background density averaged over 100 h¡1Mpc is usually considered to represent the true background, but that averaged over 1 h¡1Mpc can be subject to large sample variance. Though our simulation, after rescaling, correspond to one of the many background densities, or e®ectively one of the many background cosmologies, we believe that the general trend obtained in this work remains valid in di®erent cosmologies.
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