(a) Stability indices, b₁, b₂, of the planar PL_1, 2 orbit (branch 1 and branch 2) as a function of the Jacobi constant (or energy), E_n, for bar mass M_b = 5. The vertical stability index, b₁, (black) corresponds to the stability of planar periodic orbits with respect to perturbations perpendicular to the orbital plane, while the planar stability index, b₂, (red) corresponds to the stability with respect to perturbations on the orbital plane. The three vertical lines correspond to the energy levels at which we investigated the phase space. (b) Characteristics of the two planar branches of the PL₁ family that are joined and disappear at the bifurcation point. (c) Branch 1 and (d) branch 2 planar PL₁ orbits plotted with the same colour as the corresponding energies (vertical lines) in Fig. 2a.