Illustration of 4 different critical resonant lines in the (r_p,r_a)-space. As defined in Eq. (41), a critical line is characterised by the resonant vectors m₁, m₂ and a location in action space. Each of the 4 plotted critical lines are associated with the same location , represented by the black dot. The critical lines correspond to various choices of resonant vectors m₁ and m₂ among the three inner, outer and corotation Lindblad resonances, respectively ILR, OLR and COR. One should also note that for m₁ = m₂, the critical lines go through the point .