[Paper Review] Chaos and the dynamical evolution of barred galaxies

Thanos Manos, E. Athanassoula|arXiv (Cornell University)|Oct 29, 2005

Stellar, planetary, and galactic studies3 citations

TL;DR

This paper applies the Smaller Alignment Index (SALI) method to study chaotic and ordered orbits in 2D and 3D Ferrers barred galaxy models, demonstrating SALI's effectiveness in distinguishing orbital chaos. It finds that increasing bar mass raises chaotic orbit fractions, while increasing bar's vertical scale length reduces chaos, revealing key dependencies on structural parameters in barred galaxy dynamics.

ABSTRACT

The dynamical evolution of barred galaxies depends crucially on the fraction and their spacial distribution of chaotic orbits in them. In order to distinguish between the two kinds of orbits, we use the Smaller Alignment Index (SALI) method, a very powerful method which can be applied to problems of galactic dynamics. Using model potentials, and taking into account the full 3D distribution of matter, we discuss how the distribution of chaotic orbits depends on the main model parameters, like the mass of the various components and the bar axial ratio.

Motivation & Objective

• To investigate the role of chaotic orbits in the dynamical evolution of barred galaxies.
• To apply the SALI method as a reliable tool for distinguishing ordered from chaotic motion in galactic potentials.
• To quantify how the fraction of chaotic and regular orbits depends on model parameters such as bar mass and axial ratio.
• To compare SALI results with traditional methods like Poincaré Surface of Section (PSS) in 2D systems.
• To extend the analysis to 3D galactic potentials with full 3D matter distribution.

Proposed method

• The SALI method is used to compute the alignment index of two initially orthogonal deviation vectors in phase space.
• The time evolution of SALI is calculated using the formula: SALI(t) = min{||v₁/||v₁|| + v₂/||v₂||||, ||v₁/||v₁|| - v₂/||v₂||||.
• The Hamiltonian model includes a rotating Ferrers bar, a Miyamoto disc, and a Plummer halo, with total energy conserved.
• Initial conditions are set in planes (x, p_y, z) and (x, p_y, p_z) with other coordinates and momenta zero to explore 3D orbit families.
• Orbits are classified as chaotic if SALI tends to zero (≈10⁻¹⁶) exponentially; regular if SALI fluctuates around a positive value.
• The fraction of chaotic and regular orbits is computed across different energy levels and model parameters.

Experimental results

Research questions

• RQ1 How does the SALI method compare to traditional Poincaré Surface of Section in detecting ordered and chaotic orbits in 2D barred galaxy models?
• RQ2 What is the dependence of chaotic orbit fraction on the bar mass in 3D barred galaxy potentials?
• RQ3 How does changing the vertical scale length (c) of the bar affect the level of orbital chaos in 3D models?
• RQ4 Can SALI effectively detect small regions of stability that are invisible to Poincaré sections?
• RQ5 How do the distributions of chaotic and regular orbits evolve with changes in total energy in the 2D system?

Key findings

• In 2D systems, SALI successfully distinguishes chaotic orbits (SALI → 0) from regular ones (SALI > 0), matching Poincaré Surface of Section results.
• The SALI method detects small stable regions in phase space that are not visible via Poincaré sections due to their low density.
• In 3D models, increasing the bar mass (M_bar) leads to a higher fraction of chaotic orbits, consistent with earlier 2D findings.
• Increasing the bar's vertical scale length (c) while keeping M_bar constant results in a more regular dynamical behavior, reducing chaos.
• The SALI method is effective and efficient for high-dimensional galactic systems where phase space visualization is infeasible.
• The study confirms that orbital chaos in barred galaxies is strongly influenced by bar mass and geometry, especially in 3D configurations.