Superfluid-only density profile for aDM-only system with central gravitational potential Φ₀ = −10¹² m² s^-2 and Λm³ = 0.3 × 10^-3 eV⁴/c⁸.The “true” core radius at which the effect of phonons disappears completely is where the superfluid density drops to zero. However, in the modelling presented in this paper, DM is considered to be entirely in the normal-phase (non-superfluid) beyond the radius at which the tangential pressure is matched (what we call R_c). This matching radius is illustrated by a square for the isothermal case, and a circle shows the NFW normal-phase case. We show this to emphasise that our method truncates any superfluid phonon effects at a smaller radius than the true radius of the superfluid matter. This is a feature of our simplified model, and more complex models will have to be constructed in the future to fully understand the superfluid paradigm.