Inner Lindblad resonance in galaxies Nonlinear theory II Bars

For pt.I see Astrophys. J., vol.201, no.3, p.566 (1975). The properties of the orbits in a galaxy composed of an axisymmetric background and a weak bar are derived theoretically, by means of a new integral besides the Hamiltonian. Inside the inner Lindblad resonance (ILR) there is only one periodic orbit, while outside the resonance there are one unstable and two stable periodic orbits. The non periodic orbits surround one of the stable periodic orbits, or both of them. Unless the amplitude of the wave increases considerably inwards the orbits inside the ILR are oriented perpendicularly to the bar; the majority of the orbits outside the ILR and inside corotation are elongated along the bar, and the orbits outside corotation and inside the outer Lindblad resonance are oriented mainly perpendicularly to the bar. A comparison with numerical calculations of orbits in various models shows very good agreement. (8 refs).