Exploring Chaotic Motion of a Particle in the Centre of a Galaxy with a Prolate Halo

TL;DR

This paper investigates how the combined gravitational effects of a supermassive black hole and a prolate halo influence particle motion, revealing conditions that lead to chaotic or regular orbits using pseudo-Newtonian modeling.

Contribution

It introduces a model combining a pseudo-Newtonian SMBH potential with a prolate halo to analyze chaotic dynamics in galaxy centers.

Findings

SMBH spin affects the degree of chaos in particle orbits.

Prolate halo components can induce or suppress chaos depending on parameters.

The system exhibits both regular and chaotic motion influenced by SMBH and halo properties.

Abstract

The majority of galaxies are known to have supermassive black holes (SMBHs) at their core, which have a tremendous gravitational pull on the objects around them. When embedded within extended matter distributions such as prolate, shell-like halos, they give rise to complex gravitational fields that often drive nearby particles into chaotic orbits. The inherently nonlinear nature of such motion, shaped by general relativity, makes direct analysis highly challenging. To overcome this, pseudo-Newtonian potentials are used to approximate relativistic effects within a Newtonian framework. In this study, we model the central SMBH using the Artemova-Bjornsson-Novikov (1996) potential to mimic the rotational effects of a Kerr-like black hole. The surrounding prolate halo is treated as an axisymmetric, shell-like mass distribution, represented through a multipole expansion including dipole and quadrupole components. Poincare sections and the Maximum Lyapunov Exponent (MLE) reveal how the SMBH-halo system drives both order and chaos, with the SMBH spin modulating the dynamics by enhancing or suppressing chaos depending on its direction and magnitude.