Fuzzy Aquarius: evolution of a Milky-way like system in the Fuzzy Dark Matter scenario

We present the first high-resolution zoom-in simulation of a Milky-way-like halo extracted from the Aquarius Project in the Fuzzy Dark Matter (FDM) framework. We use the N-body code AX-GADGET, based on a particle oriented solution of the Schr\"{o}dinger-Poisson equations, able to detail the complexity of structure formation while keeping track of the quantum effects in FDM. The halo shows a cored density profile, with a core size of several kpc for a FDM mass of $m_{\chi}=2.5h \times 10^{-22}\ {\rm eV}/c^2$. A flattening is observed also in the velocity profile, representing a distinct feature of FDM dynamics. We provide a quantitative analysis of the impact of fuzziness on satellites in terms of abundance, mass, distance and velocity distribution functions and their evolution with redshift. Very interestingly, we show that all collapsed structures, despite showing a flat density profile at $z=0$, do not reach the solitonic ground-state at the time of formation: on the contrary, they asymptotically converge to it on a timescale that depends on their mass and formation history. This implies that current limits on FDM mass - obtained by applying simple scaling relations to observed galaxies - should be taken with extreme care, since single objects can significantly deviate from the expected asymptotic behavior during their evolution.