Relative density perturbation profiles ρ₁(ξ)/ρ₀(ξ) of the normal modes for the constant { E,V } case, obtained by solving Eq. (28). The modes should be truncated at a value ξ = Ξ where the corresponding velocity profile shown in Fig. D.3 vanishes, as marked by the vertical dotted lines, in order to satisfy the boundary conditions (11). Zeros are displayed. Only modes of lowest L at given Ξ are shown. Note that the core-halo structure described in Sect. 4.1.2 disappears between L = 0.021 and L = 0.022.