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

A new method for determining the nature of the orbital motion (chaotic or regular) of globular clusters in the central region of the Galaxy with a radius of 3.5 kpc, which are most affected by the bar, is proposed. The method is based on calculating the orbital power spectrum as a function of time and calculating the entropy of the power spectrum as a measure of orbital chaos. The sample includes 45 globular clusters. To form the 6D phase space required for integrating the orbits, the most accurate astrometric data to date from the Gaia satellite (Vasiliev \& Baumgardt, 2021) were used, as well as new refined average distances (Baumgardt \& Vasiliev, 2021). Orbits of globular clusters are obtained in a non-axisymmetric potential with a bar in the form of a triaxial ellipsoid embedded in an axisymmetric potential, traditionally used by us to construct orbits of globular clusters, described in detail in the paper by Bajkova et al. (2023a). The following, most realistic, bar parameters are adopted: mass $10^{10} M_\odot$, length of the major semi-axis 5 kpc, angle of rotation of the bar axis 25$^o$, angular velocity of rotation 40 km s$^{-1}$ kpc$^{-1}$. A list of 23 globular clusters with regular dynamics and 22 globular clusters with chaotic dynamics is determined. The correlation of the obtained classification of globular clusters with the classification obtained by us using other methods in the work of Bajkova et al. (2024a) was determined.