# Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

## TL;DR

This study uses dynamical Monte Carlo simulations to analyze the orbital behavior of old neutron stars in 3-D galactic potentials, revealing mostly regular orbits with some chaos in triaxial halos, which aids understanding of galactic dynamics.

## Contribution

It introduces a detailed analysis of neutron star orbits in axisymmetric and triaxial potentials using Poincare sections and Lyapunov exponents, highlighting the stability and chaos in phase space.

## Key findings

- Most orbits are regular with two degrees of freedom.
- Chaotic trajectories are rare and depend on halo orientation.
- Invariant tori and curves are identified around stable orbits.

## Abstract

We describe the dynamical behavior of isolated old (> 1 G yr) objects-like Neutron Stars (NSs). These isolated NSs are evolved under smooth, time-independent, 3-D gravitational potentials, axisymmetric and with a triaxial dark halo. We analysed the geometry of the dynamics and applied the Poincare section method for comparing the influence of different birth velocity distributions. The inspection of the maximal asymptotic Lyapunov (Lambda) exponent shows that the dynamical behaviors of the selected orbits are nearly the same as the regular orbits with two degrees of freedom, both in axisymmetric and triaxial when (phi, q_z)= (0,0). Conversely, a few chaotic trajectories are found with a rotated triaxial halo when (phi, q_z)= (90, 1.5). The tube orbits preserve the direction of their circulation around either the long or short axis as appeared in the triaxial potential, even when every initial condition leads to different orientations. The Poincare section method shows that there are 2-D invariant tori and invariant curves (islands) around stable periodic orbits that bound to the surface of 3-D tori. The regularity of the several prototypical orbits offer the means to identify the phase space regions with localized motions and to determine their environment in different models, because they can occupy significant parts of phase-space depending on the potential. This is of particular importance in Galactic Dynamics.