Relationship between Poincar\'e Sections and Spectral Characteristics of Orbits of Globular Clusters in the Central Region of the Galaxy

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 Poincar\'e sections and spectral methods have been compared. The relationship between the Poincar\'e 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 Poincar\'e sections and the spectral characteristics of the orbits has been established. Consequently, the classification by Poincar\'e 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.