Fuzzy dark matter is a hypothetical scalar particle whose mass is around 10^-22 eV, which is one of the alternatives to cold dark matter model to alleviate the small-scale problems. The quantum nature of FDM arises rich phenomena in small scale, such as soliton core and granular structures inside FDM halos.

For the first part in this talk, we focus on the granular structures and show an analytical model of the density profile. Using this model, we calculate a sub-galactic matter power spectrum and compare it with that obtained from the strong lens system SDSS J0252+0039.

Next we study how to determine a soliton core mass for a given halo mass. We compare the core-halo mass relation in our model and that obtained from the previous FDM simulations.