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

Abstract

The regularity/chaoticity of orbits of 45 globular clusters in the central region of the Galaxy with a radius of 3.5 kpc, which are subject to the greatest influence of the elongated rotating bar, is analyzed. Various methods of analysis are used, namely, the methods of calculating the maximum characteristic Lyapunov exponents (MCLE), MEGNO (Mean Exponential Growth factor of Nearby Orbits), the Poincar\'e section method, the frequency method based on calculating fundamental frequencies, and a new method is proposed based on calculating the orbit amplitude spectrum as a function of time and calculating the entropy of the amplitude spectrum as a measure of orbital chaos. Bimodality is found in the histogram of the distribution of positive Lyapunov exponents calculated in the classical version, without renormalizing the shadow orbit, which allows implementing a probabilistic method for GC classification, which is also a new approach. To construct the orbits of globular clusters, we used the gravitational potential model with a bar in the form of a triaxial ellipsoid. The following bar parameters were adopted: mass $10^{10} M_\odot$, length of the semi-major axis 5 kpc, angle of rotation of the bar axis 25$^o$, rotation velocity 40 km s$^{-1}$ kpc$^{-1}$. To form the 6D-phase space required for integrating the orbits, we used the most accurate astrometric data to date from the Gaia satellite (EDR3), as well as new refined average distances to globular clusters. Globular clusters with regular and chaotic dynamics were classified.