Solutions of the linear perturbation equation for typical profiles of rest-mass density and axial velocity obtained from the simulations (left panel: pinching, symmetric mode; right panel: helical mode). The tail density is taken as ρ_t/ρ_j = 10³; the tail and jet velocities are v_t = 0.05 c and v_j = 0.95 c, respectively; and the sound speeds are c_s,t = 0.04 c and c_s,j = 0.54 c. The dashed and dotted lines show the line corresponding to phase velocities, w/k, equal to the relativistic composition of the velocity and sound speed for each of the flows, i.e. 0.98 c for the jet and 0.09 c for the tail. These velocities separate the solution plane in different allowed and forbidden regions (see e.g. Payne & Cohn 1985, for the non-relativistic case).