Inner Lindblad resonance in galaxies Nonlinear theory III The response density

For pt.II see ibid., vol.61, no.4, p.477 (1977). The authors calculate theoretically the response of a galaxy to an imposed spiral field. The unperturbed (axisymmetric) distribution function, f, changes considerably near the inner Lindblad resonance; the final distribution function, f/sub fin/, is found by expressing f in terms of the 'resonant' integrals of motion and the corresponding angles, and averaging over the angles. Outside resonance the final distribution function is composed of three parts, two of them corresponding to trapped orbits, and one to untrapped orbits. The density response is found by integrating f/sub fin/ over all velocities. Away from the resonance the response can be expressed analytically. The physical meaning of the various terms of the response is discussed. Very near resonance the amplitude of the response is very large. The author also follows the azimuth of the response maximum going through the resonance. (11 refs).