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

TL;DR

This study probes whether globular clusters near the Galactic center exhibit regular or chaotic orbital motion under a rotating bar modeled as a triaxial ellipsoid. It combines seven chaos diagnostics, including a novel spectral-entropy approach, with Gaia EDR3 data to construct 6D orbits and classify cluster dynamics. A bimodal distribution in MCLE without shadow renormalization enables a probabilistic initial separation, which is refined by renormalized MCLE, MEGNO, Poincaré sections, frequency drift, and visual checks; a voting scheme yields 24 regular and 21 chaotic clusters, with chaotic cases linked to small pericenters and high eccentricities. The work introduces a practical, cross-validated framework for assessing chaos in barred potentials and enhances understanding of how the Galactic bar shapes GC orbital dynamics and stability.

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 Poincaré 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.

Figures (24)

• Figure 1: Calculated approximations of the MCLE without renormalization of the shadow orbit as a function of time for 45 GCs. Panels (a) and (b) -- the maximum time interval is 1200 billion years, (c) and (d) -- 20 billion years; in panels (a) and (c) the functions are presented in a linear scale, in (b) and (d) -- in a logarithmic one.
• Figure 2: Histogram of the distribution of MCLE approximations: (a) -- without renormalization of the shadow orbit for 45 GCs at $t = 12$ billion years; (b) with renormalization of the shadow orbit, on the interval of 120 billion years. Approximation of the histogram in panel (a) by two Gaussians (red line) allows implementing the probabilistic method of separating GCs with regular and chaotic orbits (left and right Gaussians, respectively).
• Figure 3: Typical examples of the $\ln (\frac{D_t}{D_0})$ dependence for regular (a) and chaotic (b) orbits in the case of calculating the MCLE without renormalizing the shadow orbit. Here, discrete KK samples act as time t, the time step is 0.1 million years, i.e. $t=0.1\times KK$ million years. Examples are given for NGC6266 (regular orbit) and NGC6355 (chaotic orbit). The $\ln (\frac{D_t}{D_0})$ dependences in the case of renormalizing the shadow orbit are given in panel (c) for NGC6266 and panel (d) for NGC6355. Panels (a) and (b) are shown for a time interval of 100 billion years, panels (c) and (d) -- for 120 billion years.
• Figure 4: MEGNO approximations for 45 GCs on a time interval of 270 billion years (a). Histogram of the distribution of MEGNO approximations and its approximation by two Gaussians (red line), allowing to implement a probabilistic method for separating GCs with regular and chaotic orbits (b). "MEGNO -- MCLE" diagram (c).
• Figure 5: Poincaré sections: (a) for NGC6266 (regular orbit); (b) NGC6355 (chaotic orbit).