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 study addresses orbital chaos of globular clusters in the Milky Way’s central region under a barred potential. It introduces a chaos indicator based on the time variation of the Z-component angular momentum, $Digl(rac{L_z}{|L_z(1)|}igr)$, computed from long-term orbit integrations in a bar-perturbed Galactic potential and validated against multiple established diagnostics. The method yields a strong correlation with previous chaos indicators and partitions 45 central GCs into regular, chaotic, and weakly chaotic groups, demonstrating the utility of $L_z$-variations as a practical chaos proxy in barred galaxies. This approach provides a quantitative, implementable tool for probing GC dynamics near the Galactic center and enhances understanding of the dynamical role of the Galactic bar.

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.

Figures (2)

• Figure 1: Rotation curve of the Galaxy with an axisymmetric potential without a bar (black line) and a non-axisymmetric potential including a bar (red line).
• Figure 2: Graphic illustration of the new method for determining the orbital dynamics of a GC based on the magnitude of the variation $D(L_z/L_z(1))$: (a) diagram $D(L^n_z/|L_z^n(1)|$ -- Jacobi integral", (b) histogram of the distribution of variations $D(L^n_z/|L_z^n(1)|$, (c) values of variations in $D(L^n_z/|L_z^n(1)|$ for all 45 GCs, (d) degree of orbital regularity of all 45 GCs, determined by the "voting" method.