Dynamical study of 2D and 3D barred galaxy models

TL;DR

This paper analyzes the dynamics of 2D and 3D barred galaxy models, distinguishing between regular and chaotic orbits using the SALI method, and explores how orbit types vary with initial conditions and galactic regions.

Contribution

It applies the SALI method to classify orbit regularity in 2D and 3D galaxy models, providing new insights into the distribution of orbit types across different galactic regions.

Findings

Regions near the (x,y) plane are mainly populated by regular orbits.

The fraction of regular orbits varies with the Jacobi constant in 3D models.

The inner and outer regions of the galaxy tend to have more regular orbits.

Abstract

We study the dynamics of 2D and 3D barred galaxy analytical models, focusing on the distinction between regular and chaotic orbits with the help of the Smaller ALigment Index (SALI), a very powerful tool for this kind of problems. We present briefly the method and we calculate the fraction of chaotic and regular orbits in several cases. In the 2D model, taking initial conditions on a Poincar\'{e} $(y,p_y)$ surface of section, we determine the fraction of regular and chaotic orbits. In the 3D model, choosing initial conditions on a cartesian grid in a region of the $(x, z, p_y)$ space, which in coordinate space covers the inner disc, we find how the fraction of regular orbits changes as a function of the Jacobi constant. Finally, we outline that regions near the $(x,y)$ plane are populated mainly by regular orbits. The same is true for regions that lie either near to the galactic center, or at larger relatively distances from it.