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Fig. D.1


Relative density perturbation profiles ρ1(ξ)/ρ0(ξ) and velocity profiles of the normal modes for the constant { T,V } case, obtained by solving Eq. (18). The profiles should be truncated at a value ξ = Ξ where the velocity profile vanishes, to satisfy boundary conditions (11). The vertical dotted line indicates where the system should be truncated to obtain the mode of lowest L for fixed Ξ: for L =  −0.02 and L = 0 only this mode is entirely displayed, while for L = 0.02 two modes are displayed, depending on which zero of the velocity profile is chosen. In the case L = 0, the total density ρ(t) = ρ0 + ρ1(t) at the point ξ = 4.07 remains unchanged, that is, unperturbed; this is one of the relevant points listed by Lynden-Bell & Wood (1968).

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