Dashed lines with various symbols show six examples of the halo profiles normalized to the cosmic mean density. All haloes are found to possess a distinct inner core fitted extremely well by the soliton solution (solid lines). A detailed soliton fit for the largest halo is inset, where the error is the root-mean-square scatter of density in each radial bin. A Navarro–Frenk–White (NFW) profile representing standard CDM is also shown for comparison (black dot-dashed line, with a very large scale radius of 10 kpc), which fits well the profiles outside the cores. The yellow hatched area indicates the ρ300 of the dSph satellites around the Milky Way3,24, which is consistent with the majority of galaxy haloes formed in the ψDM simulations.