Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

Details Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

2006-07-10

arxiv.org/abs/astro-ph/0607174v2

Mon.Not.Roy.Astron.Soc.373:271-279,2006

Astronomy and Astrophysics

Astrophysics

18 pages, 10 figures, to be published in MNRAS

Scientific paper

In the presence of a strong $m=2$ component in a rotating galaxy, the phase space structure near corotation is shaped to a large extent by the {\it invariant manifolds} of the short period family of unstable periodic orbits terminating at L$_1$ or L$_2$. The main effect of these manifolds is to create robust {\it phase correlations} among a number of chaotic orbits large enough to support a {\it spiral} density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine-Gordon equation. Numerical examples are given in an N-Body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar-spiral pattern.

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