Revealing the network of periodic orbits in galaxy models with a prolate or an oblate dark matter halo component

TL;DR

This study maps the positions and stability of periodic stellar orbits in galaxy models with prolate or oblate dark matter halos, revealing how various parameters influence orbital dynamics in the meridional plane.

Contribution

It introduces a sensitive numerical method to locate and analyze the stability of resonant periodic orbits in galaxy models with different dark matter halo shapes.

Findings

Mass of nucleus and disk significantly affect orbit stability.

Halo flattening and scale length influence orbit positions.

Key parameters like angular momentum and energy are most impactful.

Abstract

Locating the position of periodic orbits in galaxies is undoubtedly an issue of paramount importance. We reveal the position and the stability of periodic orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a disk, a spherical nucleus, and a biaxial dark matter halo component. In particular, we study how all the involved parameters of the dynamical system influence the position and the stability of all resonant families. To locate the position and measure the stability of periodic orbits we use a highly sensitive numerical code which is able to identify resonant periodic orbits of the type $n:m$. Two cases are studied for every parameter: (i) the case where the dark matter halo component is prolate and (ii) the case where an oblate dark matter halo is present. Our numerical exploration reveals that all the dynamical quantities affect, more or less, the position and the stability of the periodic orbits. It is shown that the mass of the nucleus, the mass of the disk, the halo flattening parameter, the scale length of the halo, the angular momentum, and the total orbital energy are the most influential quantities, while the effect of all other parameters is much weaker.