How does the Structure of Spherical Dark Matter Halos Affect the Types of Orbits in Disk Galaxies?

TL;DR

This study investigates how the scale length of spherical dark matter halos influences stellar orbit types in disk galaxies, revealing that more concentrated halos promote regular orbits while less concentrated ones increase chaos.

Contribution

It provides a detailed analysis of the effect of dark matter halo scale length on orbital dynamics using SALI and spectral methods, highlighting the relationship between halo concentration and orbital regularity.

Findings

Highly concentrated halos favor regular orbits.

Less concentrated halos increase the percentage of chaotic orbits.

The orbital structure varies significantly with halo scale length.

Abstract

The main objective of this work is to determine the character of orbits of stars moving in the meridional $(R,z)$ plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical dark matter halo component. In particular, we try to reveal the influence of the scale length of the dark matter halo on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when this parameter varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our numerical computations reveal that when the dark matter halo is highly concentrated, that is when the scale length has low values the vast majority of star orbits move in regular orbits, while on the other hand in less concentrated dark matter halos the percentage of chaos increases significantly. We also compared our results with early related work.