Relationship between Poincaré Sections and Spectral Characteristics of Orbits of Globular Clusters in the Central Region of the Galaxy

TL;DR

The study addresses whether chaos indicators from Poincaré sections align with spectral diagnostics for globular cluster orbits in the Galaxy’s central region, where the rotating bar strongly perturbs dynamics. It constructs a realistic Galactic potential combining axisymmetric and bar components, uses Gaia-based six-dimensional phase-space data for 45 GCs within 3.5 kpc, and applies Poincaré sections, frequency drift, and spectral entropy analyses to classify orbits. A key result is a complete 100% correspondence between Poincaré-section classifications and spectral characteristics, enabling the use of spectral analysis as a visual and objective alternative to Poincaré sections. The findings yield explicit lists of regular and chaotic globular clusters and demonstrate entropy-based gradations of chaos, with practical implications for understanding GC dynamics in bar-dominated galactic centers.

Abstract

In the paper, orbital dynamics, regular or chaotic, of globular clusters (GCs) in the central region of the Galaxy, which is subject to the greatest influence of the rotating bar, has been studied. Such methods for determining chaos as Poincaré sections and spectral methods have been compared. The relationship between the Poincaré sections and the spectral characteristics of the orbits has been estimated. The sample includes 45 globular clusters in the central region of the Galaxy with a radius of 3.5 kpc. To form the 6D-phase space required for integrating the orbits, the most accurate astrometric data to date from the Gaia satellite, as well as new refined average distances, have been used. The following, most realistic, bar parameters have been adopted: mass $10^{10} M_\odot$, length of the major semi-axis of the bar model in the form of a triaxial ellipsoid is 5 kpc, angle of rotation of the bar axis is $25^o$, rotation velocity is 40 km s$^{-1}$ kpc $^{-1}$. The result of the study is that a 100\% correlation between the classification by Poincaré sections and the spectral characteristics of the orbits has been established. Consequently, the classification by Poincaré sections can be replaced by a more visual analysis of the amplitude spectra of the orbits. Thus, two lists of GCs: with regular and chaotic dynamics have been compiled. The GCs with varying degrees of orbital chaos have separately been distinguish.

Figures (8)

• 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: Normalized power spectra of -coordinates (left), -coordinates (right) of the reference and shadow orbits as functions of time that are shown in black and red, respectively. The upper panels refer to GC of NGC 6266 with regular dynamics, and the lower panels refer to GC of NGC 6355 with chaotic dynamics.
• Figure 3: Orbits of globular clusters. In the panels from left to right: column (1), projections of orbits onto the plane ($X-Y$ ); column (2) radial values of the initial (reference) and perturbed (shadow) orbits as a function of time (reference orbits are shown in yellow, shadow orbits in purple); column (3), Poincaré sections $X-V_x$; column (4), $X$ - coordinates of Poincaré sections; column (5), $V_x$ - coordinates of the Poincaré sections; column (6), normalized power spectra - the values of the reference and shadow orbits as functions of time, shown in black and red, respectively; and column (7), illustration of the frequency method (the power spectrum of the first half of the time sequence is shown in red and the second half is shown in black). The names of the GCs are shown in the second panels from the left.
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