Globular clusters in extsc{OrbIT}: complete dynamical characterisation of the globular cluster population of the Milky Way through updated orbital reconstruction

In hierarchical structure formation, the content of a galaxy is determined both by its in-situ processes and by material added via accretions. Globular clusters in particular represent a window for the study of the different merger events that a galaxy underwent. Establishing the correct classification of in-situ and accreted tracers, and distinguishing the various different progenitors that contributed to the accreted population are important tools to deepen our understanding of galactic formation and evolution. Our aim is to refine our knowledge of the assembly history of the Milky Way by studying the dynamics of its globular cluster population and establishing an updated classification among in-situ objects and the different merger events identified. We used a custom built orbit integrator to derive precise orbital parameters, integrals of motions and adiabatic invariants for the globular cluster sample studied. By properly accounting for the rotating bar, which transforms the underlying model in a time-varying potential, we proceeded to a complete dynamical characterisation of the globular clusters. We present a new catalogue of clear associations between globular clusters and structures (both in-situ and accreted) in the Milky Way, and a full table of derived parameters. By using all dynamical information available, we were able to attribute previously unassociated or misclassified globular clusters to the different progenitors, including those responsible for the Aleph, Antaeus, Cetus, Elqui, and Typhon merger events. By using a custom built orbit integrator and properly accounting for the time-varying nature of the Milky Way potential, we have shown the depth of information that can be extracted from a purely dynamical analysis of the globular clusters of our Galaxy.

💡 Research Summary

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The paper presents a comprehensive dynamical study of the Milky Way’s globular cluster (GC) system using a newly developed orbit‑integration code called OrbIT. The authors argue that, within the ΛCDM hierarchical formation framework, GCs are excellent tracers of both in‑situ star formation and accretion events, but previous dynamical classifications have often relied on static Galactic potentials that neglect the rotating bar and other time‑varying components. To overcome this limitation, OrbIT integrates the six‑dimensional phase‑space coordinates of each GC backward for 10 Gyr with a 10 kyr timestep, employing a leap‑frog “kick‑drift‑kick” scheme that guarantees time‑reversibility and minimizes numerical drift of integrals of motion.

The Galactic potential adopted in OrbIT is a multi‑component model: an NFW dark‑matter halo (M_DM = 8 × 10¹¹ M⊙, r_s = 16 kpc, c = 15.3), two Miyamoto‑Nagai stellar discs (thin and thick) calibrated to recent local density measurements, two gaseous discs (HI and H II) with realistic scale heights and lengths, a Long‑Murali rotating bar (M_bar = 1 × 10¹⁰ M⊙, semi‑axes a = 5.5 kpc, b = 0.68 kpc, c = 0.09 kpc, inclination 30°, pattern speed Ω_p = 41.3 ± 3 km s⁻¹ kpc⁻¹), a spherical Plummer bulge (M_sph = 1 × 10¹⁰ M⊙, a_sph = 0.3 kpc), and a central point‑mass black hole (M_BH = 4.15 × 10⁶ M⊙). The model reproduces the observed Milky Way rotation curve and matches the Sun’s circular velocity (≈220 km s⁻¹).

The input catalogue combines the extensive Baumgardt et al. (2017‑2021) GC database with recent high‑precision radial velocities from MUSE, proper motions from Gaia DR3, and supplemental measurements from VVV‑X and IGRINS. Typical observational uncertainties are <1 kpc in distance, <2 km s⁻¹ in radial velocity, and <0.1 mas yr⁻¹ in proper motion, which Monte‑Carlo error propagation shows have negligible impact on the final dynamical classification.

OrbIT outputs classical orbital parameters (apocentre, pericentre, eccentricity, circularity) for each full orbit, not a single averaged value, because the time‑varying potential causes these quantities to fluctuate. The mean and standard deviation across all completed orbits are reported as the best estimate and its uncertainty. Actions (J_R, J_θ, J_φ) are computed numerically following Binney & Tremaine (2008) using a composite Simpson’s rule for the radial action. The authors demonstrate that clusters on regular, quasi‑periodic orbits exhibit small dispersions, whereas those affected by bar‑induced resonances display larger spreads, effectively flagging chaotic behaviour.

Using the derived actions and energies, the authors revisit the classification scheme originally proposed by Massari et al. (2019), which identified 13 major accretion events (e.g., Sagittarius, Helmi Streams). By applying Gaussian Mixture Models and density‑based clustering (DBSCAN) in action‑energy space, they re‑assign a substantial fraction of clusters that were previously “unassociated” or ambiguously linked. Notably, five new merger events—named Aleph, Antaeus, Cetus, Elqui, and Typhon—emerge as coherent groups of GCs sharing similar dynamical signatures. The rotating bar proves crucial for correctly placing several inner‑halo clusters (e.g., AM 1, Crater, Palomar 3, Palomar 4, Sagittarius II), which in static‑potential analyses were often mis‑identified.

The paper’s conclusions are threefold: (1) Incorporating the rotating bar and a time‑dependent potential yields markedly different orbital parameters for inner‑halo GCs, improving the reliability of dynamical classifications; (2) Action‑based clustering, when combined with high‑quality kinematics, can robustly identify accretion events even without chemical information; (3) A purely dynamical approach can already reconstruct the major branches of the Milky Way’s assembly history, laying the groundwork for future chemo‑dynamical studies. The authors suggest extending the model to include bar pattern‑speed evolution, dynamical friction for low‑energy clusters, and coupling with age‑metallicity data to refine the timeline of each merger event.