Magnetic field configurations, relative chemical potential perturbations, and velocity fields produced by the models I, II, III, and IV. For B, lines represent the poloidal magnetic field lines labeled by the corresponding value of α. For models I–III, color represents the poloidal potential α, while in model IV, it represents the toroidal magnetic field B_ϕ. For χ_n and χ_c, color represents their local value. For v_n and v_ad, lines represent the poloidal component and color its magnitude; these are computed through the explicit semi-analytic approach described in Sect. 3.1 using the background NS model with the HHJ EoS.