Abstract <p>The regularity/chaoticity of orbits of 45 globular clusters in thecentral region of the Galaxy with a radius of 3.5 kpc, which aresubject to the greatest influence of the elongated rotating bar,is analyzed. Various methods of analysis are used, namely, themethods of calculating the maximum characteristic Lyapunovexponents (MCLE), MEGNO (Mean Exponential Growth factor of NearbyOrbits), the Poincaré section method, the frequency method basedon calculating fundamental frequencies, and a new method isproposed based on calculating the orbit amplitude spectrum as afunction of time and calculating the entropy of the amplitudespectrum as a measure of orbital chaos. Bimodality is found in thehistogram of the distribution of positive Lyapunov exponentscalculated in the classical version, without renormalizing theshadow orbit, which allows implementing a probabilistic method forGC classification, which is also a new approach. To construct theorbits of globular clusters, we used the gravitational potentialmodel with a bar in the form of a triaxial ellipsoid. Thefollowing bar parameters were adopted: mass <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(10^{10} M_{\odot}\)</EquationSource>  </InlineEquation>,length of the semi-major axis 5 kpc, angle of rotation of the baraxis 25<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({}^{\circ}\)</EquationSource>  </InlineEquation>, rotation velocity 40 km s<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({}^{-1}\)</EquationSource>  </InlineEquation> kpc<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({}^{-1}\)</EquationSource>  </InlineEquation>. Toform the 6D phase space required for integrating the orbits, weused the most accurate astrometric data to date from the Gaiasatellite (EDR3), as well as new refined average distances toglobular clusters. Globular clusters with regular and chaoticdynamics were classified. As the analysis showed, globularclusters with small pericentric distances and large eccentricitiesare most susceptible to the influence of the bar and demonstratethe greatest chaos. It is shown that the results of theclassification of globular clusters by the nature of their orbitaldynamics, obtained using the various analysis methods consideredin the work, correlate well with each other.</p>

Analysis of Orbital Dynamics of Globular Clusters in the Central Region of the Milky Way

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发表日期：

2025年9月1日

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A. T. Bajkova,
A. A. Smirnov,
V. V. Bobylev

摘要

Abstract

The regularity/chaoticity of orbits of 45 globular clusters in thecentral region of the Galaxy with a radius of 3.5 kpc, which aresubject to the greatest influence of the elongated rotating bar,is analyzed. Various methods of analysis are used, namely, themethods of calculating the maximum characteristic Lyapunovexponents (MCLE), MEGNO (Mean Exponential Growth factor of NearbyOrbits), the Poincaré section method, the frequency method basedon calculating fundamental frequencies, and a new method isproposed based on calculating the orbit amplitude spectrum as afunction of time and calculating the entropy of the amplitudespectrum as a measure of orbital chaos. Bimodality is found in thehistogram of the distribution of positive Lyapunov exponentscalculated in the classical version, without renormalizing theshadow orbit, which allows implementing a probabilistic method forGC classification, which is also a new approach. To construct theorbits of globular clusters, we used the gravitational potentialmodel with a bar in the form of a triaxial ellipsoid. Thefollowing bar parameters were adopted: mass \(10^{10} M_{\odot}\) ,length of the semi-major axis 5 kpc, angle of rotation of the baraxis 25 \({}^{\circ}\) , rotation velocity 40 km s \({}^{-1}\) kpc \({}^{-1}\) . Toform the 6D phase space required for integrating the orbits, weused the most accurate astrometric data to date from the Gaiasatellite (EDR3), as well as new refined average distances toglobular clusters. Globular clusters with regular and chaoticdynamics were classified. As the analysis showed, globularclusters with small pericentric distances and large eccentricitiesare most susceptible to the influence of the bar and demonstratethe greatest chaos. It is shown that the results of theclassification of globular clusters by the nature of their orbitaldynamics, obtained using the various analysis methods consideredin the work, correlate well with each other.