Invariant manifolds and the response of spiral arms in barred galaxies

TL;DR

This paper demonstrates that invariant manifolds of unstable periodic orbits around Lagrangian points accurately predict spiral arm structures in barred galaxies, linking dynamical theory with observed galaxy morphology.

Contribution

It provides a theoretical framework connecting invariant manifolds with spiral patterns in barred galaxies, incorporating the effects of azimuthal displacement and boundary conditions.

Findings

Invariant manifolds reproduce spiral patterns when the spiral potential is included.

The azimuthal displacement of Lagrangian points is key to spiral formation.

Manifolds are related to morphological features in response models.

Abstract

The unstable invariant manifolds of the short-period family of periodic orbits around the unstable Lagrangian points $L_1$ and $L_2$ of a barred galaxy define loci in the configuration space which take the form of a trailing spiral pattern. In the present paper we investigate this association in the case of the self-consistent models of Kaufmann & Contopoulos (1996) which provide an approximation of real barred-spiral galaxies. We also examine the relation of `response' models of barred-spiral galaxies with the theory of the invariant manifolds. Our main results are the following: The invariant manifolds yield the correct form of the imposed spiral pattern provided that their calculation is done with the spiral potential term turned on. We provide a theoretical model explaining the form of the invariant manifolds that supports the spiral structure. The azimuthal displacement of the Lagrangian points with respect to the bar's major axis is a crucial parameter in this modeling. When this is taken into account, the manifolds necessarily develop in a spiral-like domain of the configuration space, delimited from below by the boundary of a banana-like non-permitted domain, and from above either by rotational KAM tori or by cantori forming a stickiness zone. We construct `spiral response' models on the basis of the theory of the invariant manifolds and examine the connection of the latter to the `response' models (Patsis 2006) used to fit real barred-spiral galaxies, explaining how are the manifolds related to a number of morphological features seen in such models.