Inner Lindblad resonance in galaxies - Nonlinear theory. IV - Self-consistent bars

Astronomy and Astrophysics – Astrophysics

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Galaxies, Nonlinear Equations, Resonance, Self Consistent Fields, Space Density, Astrodynamics, Density Wave Model, Linearization, Perturbation Theory, Poisson Equation

Scientific paper

A discussion is presented of various approaches for consideration of the requirement that response density should be equal to the imposed density if a galaxy is to be self-consistent, with attention to the difficulties posed by near resonances. After a comparison of the nonlinear approach with several linear alternatives, a linear approach is formulated which does not introduce any infinities at resonances and a nonlinear self-consistency equation is derived in the case of a bar and its linearized version. It is found that, while amplitude decreases outwards near the Lindblad resonances in all linear solutions and many nonlinear ones, the amplitude increases near the resonances in other solutions. A comparison of corresponding linear and nonlinear solutions establishes regions of agreement and discrepancy.

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