[Paper Review] Detecting chaotic and ordered motion in barred galaxies

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

Galaxies: Formation, Evolution, Phenomena3 citations

TL;DR

This paper applies the Smaller Alignment Index (SALI) method to 3D barred galaxy potentials to distinguish chaotic from regular orbits, demonstrating that increased bar mass enhances chaos while greater bar thickness promotes regular motion; slow bars also yield higher percentages of regular orbits, confirming prior 2D findings in a 3D dynamical framework.

ABSTRACT

A very important issue in the area of galactic dynamics is the detection of chaotic and ordered motion inside galaxies. In order to achieve this target, we use the Smaller ALignment Index (SALI) method, which is a very suitable tool for this kind of problems. Here, we apply this index to 3D barred galaxy potentials and we present some results on the chaotic behavior of the model when its main parameters vary.

Motivation & Objective

• To detect and quantify chaotic versus regular motion in three-dimensional barred galaxy models.
• To investigate how variations in bar mass, thickness, and pattern speed affect orbital dynamics in 3D potentials.
• To extend previous 2D findings on orbital stability in barred galaxies to a full 3D dynamical framework.
• To validate the effectiveness of the SALI method in classifying orbital behavior in complex galactic potentials.

Proposed method

• The SALI method is used to distinguish chaotic from regular orbits by tracking the evolution of two initially orthogonal deviation vectors.
• The SALI is computed at each time step as the minimum of the sum and difference norms of the normalized deviation vectors.
• For chaotic orbits, SALI tends to zero; for regular orbits, it fluctuates around a positive value.
• The method is applied to a 3D Ferrers potential composed of a Miyamoto sphere, Plummer disc, and Ferrers bar.
• Initial conditions are set in two different planes to explore how orbital population selection affects results.
• Systematic variations in bar mass, bar length along the z-axis, and pattern speed are used to assess their impact on orbital stability.

Experimental results

Research questions

• RQ1 How does increasing the mass of the bar component affect the fraction of chaotic orbits in a 3D barred galaxy model?
• RQ2 How does increasing the thickness of the bar (longer z-axis) influence the prevalence of regular versus chaotic motion?
• RQ3 How does the pattern speed of the bar affect the percentage of regular orbits in 3D dynamical systems?
• RQ4 Does the choice of initial conditions (plane of integration) alter the observed distribution of chaotic and regular orbits?
• RQ5 Can the SALI method reliably classify orbital types in realistic 3D barred galaxy potentials?

Key findings

• Increasing the bar mass leads to a higher percentage of chaotic orbits, confirming earlier 2D results by Athanassoula et al. (1983).
• A thicker bar, achieved by increasing the length of the z-axis, results in a more regular dynamical behavior, reducing chaotic motion.
• Slower bars exhibit a greater proportion of regular orbits, indicating that pattern speed is a key factor in orbital stability.
• The SALI method successfully distinguishes between chaotic and regular orbits in 3D barred galaxy models with high reliability.
• The choice of initial conditions (e.g., in (x, py, z) vs. (x, py, pz)) leads to measurable differences in the distribution of chaotic and regular orbits.
• The method reveals that orbital behavior is sensitive to structural parameters such as bar mass and scale, even in three dimensions.