Variations of angular momentum $L_z$ as an indicator of orbital chaos of globular clusters in the central region of the Galaxy with a bar

TL;DR

This paper introduces a new method using variations in the angular momentum component $L_z$ to identify orbital chaos in globular clusters near the Galactic center, demonstrating high correlation with existing techniques.

Contribution

It proposes a novel approach based on $L_z$ variations to analyze orbital chaos, validated against other classification methods.

Findings

Successfully classified 45 globular clusters into regular, chaotic, and weakly chaotic groups.

High correlation between the new $L_z$ variation method and traditional orbit classification techniques.

Provides a practical tool for studying orbital dynamics in barred galaxy potentials.

Abstract

It is shown how the violation of the invariance of the $Z$-component of the orbital angular momentum $L_z$ in the axially symmetric potential of the Galaxy with a bar can serve as an indicator of the degree of orbital chaos of globular clusters in the central region of the Galaxy. In this case, the higher the variations of $L_z$ of the orbit over a certain period of time, the higher the chaos of the orbit. In essence, a new method for analyzing orbital dynamics -- regular or chaotic -- is proposed. A high level of correlation between the results of orbit classification by the proposed method and the results of classification by other methods is shown. As a result, a sample of 45 globular clusters in the central region of the Galaxy with a radius of 3.5 kpc is divided into regular, chaotic, and weakly chaotic.