Inner Lindblad resonance in galaxies. Nonlinear theory. III - The response density

Details Inner Lindblad resonance in galaxies. Nonlinear theory. III - The response density Inner Lindblad resonance in galaxies. Nonlinear theory. III - The response density

Jan 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979a%26a....71..221c&link_type=abstract

Astronomy and Astrophysics, vol. 71, no. 1-2, Jan. 1979, p. 221-244.

Astronomy and Astrophysics

Astrophysics

18

Celestial Mechanics, Galactic Evolution, Resonance, Space Density, Spiral Galaxies, Angular Momentum, Distribution Functions, Elliptical Orbits, Hamiltonian Functions, Integral Equations, Jacobi Integral, Nonlinear Equations, Tables (Data)

Scientific paper

The response of a galaxy to an imposed spiral field is calculated theoretically. Since the unperturbed distribution function (f) changes considerably near the inner Lindblad resonance, the final distribution function (f fin) is obtained by expressing f in terms of 'resonant' integrals of motion and the corresponding angles and then averaging over the angles. It is found that f fin outside the resonance consists of three parts, two corresponding to untrapped orbits and one to trapped orbits. The density response is determined by integrating f fin over all velocities. It is shown that the amplitude of the response is very large very near resonance and that, in the case of an imposed spiral field of amplitude that does not increase strongly inward, the response is almost in phase outside the resonance but quite out of phase inside it. It is concluded that this spiral field cannot be self-consistent unless it vanishes inside the resonance. The self-consistency equations are expressed explicitly in terms of both amplitude and phase, and some numerical applications are provided.

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