Classifying orbits in galaxy models with a prolate or an oblate dark matter halo component

We explore the nature of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a disk, a spherical nucleus, and a flat biaxial dark matter halo component. In particular, we study the influence of all the involved parameters of the dynamical system, by computing both the percentage of chaotic orbits and the percentages of orbits of the main regular resonant families in each case. To distinguish between ordered and chaotic motion, we use the smaller alignment index (SALI) method to extensive samples of orbits by numerically integrating the equations of motion as well as the variational equations. Moreover, 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. Two cases are studied for every parameter: (i) the case where the halo component is prolate and (ii) the case where an oblate dark halo is present. Our numerical investigation indicates that all the dynamical quantities affect, more or less, the overall orbital structure. It was observed that the mass of the nucleus, the halo flattening parameter, the scale length of the halo, the angular momentum, and the orbital energy are the most influential quantities, while the effect of all the other parameters is much weaker. It was also found that all the parameters corresponding to the disk only have a minor influence on the nature of orbits. Furthermore, some other quantities, such as the minimum distance to the origin, the horizontal, and the vertical force, were tested as potential chaos detectors. Our analysis revealed that only general information can be obtained from these quantities. We also compared our results with early related work.Comment: Published in Astronomy & Astrophysics (A&A) journa

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

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.Comment: Published in Baltic Astronomy journal. arXiv admin note: previous papers with related context: arXiv:1404.4194, arXiv:1404.3961, arXiv:1309.560