Invariant manifolds in barred galaxy simulations. I. Material density waves

TL;DR

This study uses N-body simulations to show that invariant manifold theory effectively explains the origin and dynamics of spiral arms in barred galaxies, identifying specific stellar populations responsible for the structure.

Contribution

It demonstrates that manifold-compatible orbits form the backbone of spiral arms, linking invariant manifold theory with observable kinematic signatures in galaxy simulations.

Findings

Manifold-compatible particles generate the main spiral structure.

Low-energy particles exhibit quasi-circular motion.

Spiral arms are sustained by manifold-guided radial transport.

Abstract

We investigate the dynamical origin and kinematic signatures of spiral structure in an N-body simulation of an isolated barred galaxy, assessing whether invariant manifold theory provides a consistent dynamical framework to disentangle the disc particle populations and to identify those that genuinely build, trace, and sustain the spiral arms. We compute the Jacobi energy of disc particles and classify them relative to the energies of the equilibrium points, thereby isolating manifold-compatible orbits. We analyse their spatial distribution and velocity structure to characterise spiral-related streaming motions. The Jacobi constant provides a physically motivated dynamical separator that reveals three distinct kinematic populations: (i) low-energy particles on nearly circular orbits populating most of the disc, (ii) high-energy particles associated with banana orbits, and (iii) manifold-compatible particles originating near the bar and following transit orbits along the spiral arms. Only the manifold-compatible population generates the prominent outward-migrating ridge observed in the R - v_phi plane and reproduces the characteristic spiral streaming pattern. In contrast, the low-energy population exhibits a global quasi-circular motion with small perturbations induced by the self-gravity of the spiral structure. Our results demonstrate that the spiral arms are dynamically traced by the manifold-compatible population, which forms the backbone of the structure and drives effective radial transport. The bulk of low-energy disc particles responds to the spiral perturbation similarly to the traditional density wave picture, enhancing the density contrast caused by the invariant-manifold compatible particles. In this framework, barred spiral arms emerge as material structures sustained by manifold-guided transport, with the surrounding disc behaving as a system of material density waves.