Solitons in the dark: First approach to non-linear structure formation with fuzzy dark matter

We present the results of a full cosmological simulation with the new code SCALAR , where dark matter is in the form of fuzzy dark matter (FDM), described by a light scalar field with a mass of m B = 2.5 × 10 −22 eV and evolving according to the Schrödinger-Poisson system of equations. In comoving units, the simulation volume is 2.5 h −1 Mpc on a side, with a resolution of 20 h −1 pc at the highest refinement level. While the resulting large-scale resolution prevents us from studying the general properties of the FDM structure formation, the extremely high small-scale resolution allows a detailed analysis of the formation and evolution of central solitonic cores, which are found to leave their imprints on dark matter density profiles, resulting in shallower central densities, and on rotation curves, producing an additional circular velocity peak at small radii from the centre. Despite the limitations on the large-scale resolution, we find that the suppression of structures due to the quantum nature of the scalar field reveals indications of a shallower halo mass function in the low-mass end compared to the case of a ΛCDM simulation, in which dark matter is expected to cluster at all mass scales even if it was evolved with the same initial conditions as used for FDM. Furthermore, we verify the scaling relations characterising the solution to the Schrödinger–Poisson system for both isolated and merging haloes, and we find that they are preserved by merging processes. We characterise each FDM halo in terms of the dimensionless quantity Ξ ∝ E halo / M halo 3 , and we show that the core mass is tightly linked to the halo mass by the core–halo mass relation M core / M halo ∝ Ξ 1/3 . We also show that the core surface density of the simulated FDM haloes does not follow the scaling with the core radius, as observed for dwarf galaxies. This is a challenge for the FDM model as the sole explanation of core formation