DM only density profile for our SfDM toy model with Λm³ = 0.1−0.3 × 10^-3 eV⁴/c⁸ (blue shaded) and a c₂₀₀ = 4ΛCDM NFW comparison profile (dashed black line) each with a virial mass of 10¹⁵M_⊙. Blue circles show the radii of the superfluid core for different Λm³ choices (the upper line represents a larger choice of Λm³, which results in a higher density and smaller core radius). Inside the core, the density is approximately constant, outside the core the density follows a strict isothermal 1 /r² power law. The inclusion of baryons in this model will not affect the general features too much, but will shrink the core radius slightly. The core radius can be increased by using a smaller value of Λm³, which we show in the following sections of the paper.