The evolution of chaos in active galaxy models with an oblate or a prolate dark halo component

TL;DR

This study examines how the shape and size of a dark halo influence chaotic motion in galaxy models, revealing exponential and linear relationships between chaos extent, halo scale-length, and flatness.

Contribution

It introduces a detailed analysis of chaos evolution in galaxy models with oblate or prolate dark halos, highlighting new quantitative relationships and theoretical insights.

Findings

Chaos extent decreases exponentially with halo scale-length.

Linear relationship between chaos extent and halo flatness parameter.

Critical angular momentum correlates linearly with halo flatness.

Abstract

The evolution of chaotic motion in a galactic dynamical model with a disk, a dense nucleus and a flat biaxial dark halo component is investigated. Two cases are studied: (i) the case where the halo component is oblate and (ii) the case where a prolate halo is present. In both cases, numerical calculations show that the extent of the chaotic regions decreases exponentially as the scale-length of the dark halo increases. On the other hand, a linear relationship exists between the extent of the chaotic regions and the flatness parameter of the halo component. A linear relationship between the critical value of the angular momentum and the flatness parameter is also found. Some theoretical arguments to support the numerical outcomes are presented. An estimation of the degree of chaos is made by computing the Lyapunov Characteristic Exponents. Comparison with earlier work is also made.