Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978mnras.182..457n&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 182, Feb. 1978, p. 457-472.
Astronomy and Astrophysics
Astronomy
12
Density Wave Model, Galactic Structure, Spiral Galaxies, Angular Momentum, Nonlinearity, Star Distribution, Wave Dispersion, Wave Scattering
Scientific paper
A nonlinear theory of spiral density waves is developed using the tight-winding approximation. When the amplitude of the wave exceeds a certain critical value, the wave satisfies a nonlinear dispersion relation. An exact solution to this system is found using the technique of inverse scattering. Contrary to the case for linear waves, the nonlinear waves are shown to be spirals which do not tend to wind up. The nonlinear term deduced is a nonlinear frequency shift in the epicyclic frequency. The theory gives a maximum amplitude roughly midway between corotation and the Lindblad resonances as well as a minimum at corotation. All resonances will be broadened. The nonlinear term deduced can saturate the wave amplitude in a spiral galaxy without gas. Observational implications of this are discussed.
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