Asymptotic Orbits in Barred Spiral Galaxies

TL;DR

This paper investigates the formation and longevity of spiral arms in barred spiral galaxies, attributing their persistence to the stickiness of chaotic orbits near unstable manifolds, supported by $N$-body simulations.

Contribution

It demonstrates that the long-lasting spiral patterns are due to chaotic orbit stickiness near unstable manifolds, providing a dynamical explanation for spiral structure persistence.

Findings

Spiral arms last over 10 bar rotations due to orbit stickiness.

Chaotic orbits near unstable manifolds support spiral structure.

Velocity minima loci correspond to density maxima and morphological features.

Abstract

We study the formation of the spiral structure of barred spiral galaxies, using an $N$-body model. The evolution of this $N$-body model in the adiabatic approximation maintains a strong spiral pattern for more than 10 bar rotations. We find that this longevity of the spiral arms is mainly due to the phenomenon of stickiness of chaotic orbits close to the unstable asymptotic manifolds originated from the main unstable periodic orbits, both inside and outside corotation. The stickiness along the manifolds corresponding to different energy levels supports parts of the spiral structure. The loci of the disc velocity minima (where the particles spend most of their time, in the configuration space) reveal the density maxima and therefore the main morphological structures of the system. We study the relation of these loci with those of the apocentres and pericentres at different energy levels. The diffusion of the sticky chaotic orbits outwards is slow and depends on the initial conditions and the corresponding Jacobi constant.