Determining the nature of orbits in a three-dimensional galaxy model hosting a BL Lacertae object

TL;DR

This study models the orbital dynamics in a galaxy with a BL Lacertae object, analyzing how parameters like nucleus mass and galaxy shape influence regular and chaotic motions through numerical experiments.

Contribution

It introduces a 3D dynamical model for galaxies hosting BL Lacertae objects and investigates the effects of various parameters on orbital chaos using numerical and analytical methods.

Findings

Parameters like nucleus mass affect chaos degree

Existence of local integrals near stable periodic points

Correlations between model parameters and orbital behavior

Abstract

A three-dimensional dynamical model for a galaxy hosting a BL Lacertae object is constructed. The model consists of a logarithmic potential representing an elliptical host galaxy with a bulge of radius $c_b$ and a dense massive nucleus. Using numerical experiments, we try to distinguish between regular and chaotic motion in both 2D and 3D system. In particular, we investigate how the basic parameters of our model, such as the mass of the nucleus, the internal perturbation and the flattening parameters influence the amount and the degree of chaos. Interesting correlations are presented for both 2D and 3D dynamical models. Our numerical results are explained and supported using elementary theoretical arguments and analytical calculations. Of particular interest, is the local integral of motion which have been found to exist in the vicinity of stable periodic points. The obtained numerical outcomes of the present research, are linked and also compared with several data derived from observations.