Shu-Rong Chen(NTU,TAM); Hsi-Yu Schive(NTU); Tzihong Chiueh(NTU)
Fuzzy dark matter (FDM), consisting of extremely light bosons with negligible self-interaction, is a viable dark matter candidate. It mimics cold dark matter (CDM) on large scales, such as the large-scale structures of the universe and the outer dark matter halo profile. On small scales, the FDM halo features a central core (soliton), in contrast to the cuspy CDM halo profile. The solitonic cores in different haloes are self-similar, meaning that all solitons have the same shape after rescaling. In this work, we extend this similarity to the entire halo and derive a self-similar solution in the Einstein-de Sitter cosmology. The solution has a central core similar to a soliton, surrounded by short-wavelength oscillations similar to the FDM halo granules. The total energy of this similarity solution is positive, in contrast to the negative energy of a virialized bound halo. We demonstrate by three-dimensional FDM simulations that the similarity solution is stable against small perturbations. With larger-amplitude perturbations, the solution will soon evolve into a virialized soliton-halo system similar to the halos formed in cosmological simulations.