The coalescence of invariant manifolds and the spiral structure of barred galaxies

Abstract

In a previous paper (Voglis et al. 2006a, paper I) we demonstrated that, in a rotating galaxy with a strong bar, the unstable asymptotic manifolds of the short period family of unstable periodic orbits around the Lagrangian points L${}_1$ or L${}_2$ create correlations among the apocentric positions of many chaotic orbits, thus supporting a {\it spiral} structure beyond the bar. In the present paper we present evidence that the unstable manifolds of {\it all} the families of unstable periodic orbits near and beyond corotation contribute to the same phenomenon. Our results refer to a N-Body simulation, a number of drawbacks of which, as well as the reasons why these do not significantly affect the main results, are discussed. We explain the dynamical importance of the invariant manifolds as due to the fact that they produce a phenomenon of `stickiness' slowing down the rate of chaotic escape in an otherwise non-compact region of the phase space. We find a stickiness time of order 100 dynamical periods, which is sufficient to support a long-living spiral structure. Manifolds of different families become important at different ranges of values of the Jacobi constant. The projections of the manifolds of all the different families in the configuration space produce a pattern due to the `coalescence' of the invariant manifolds. This follows closely the maxima of the observed $m=2$ component near and beyond corotation. Thus, the manifolds support both the outer edge of the bar and the spiral arms.

19 pages, 12 figures, accepted for publication from MNRAS

References in corpus (3)

• The formation of spiral arms and rings in barred galaxies
• On the origin of rR_1 ring structures in barred galaxies
• Chaotic motion and spiral structure in self-consistent models of rotating galaxies

Cited by in corpus (13)

• Dawes Review 4: Spiral Structures in Disc Galaxies
• Orbital structure in barred spiral galaxies
• Invariant manifolds and the response of spiral arms in barred galaxies
• Spiral arm formation mechanisms: Spiral Structure in Barred galaxies. Observational constraints to spiral arm formation mechanisms
• The behavior of the pitch angle of spiral arms depending on optical wavelength
• Manifold spirals, disc-halo interactions and the secular evolution in N-body models of barred galaxies
• Structures induced by companions in galactic discs
• Inner and outer rings are not strongly coupled with stellar bars
• The shock-induced star formation sequence resulting from a constant spiral pattern speed
• Orbital and escape dynamics in barred galaxies -- IV. Heteroclinic connections
• Study of chaos in rotating galaxies using extended force-gradient symplectic methods
• Perturbed precessing ellipses as the building blocks of spiral arms in a barred galaxy with two pattern speeds
• Capturing the short-term characteristics of a barred galaxy from a single snapshot