Modeling the recent interactions between the Magellanic Clouds and Milky Way

The Large and Small Magellanic Clouds (LMC and SMC, respectively) are the largest satellite galaxies of the Milky Way (MW) and their interactions with each other have given rise to multiple stellar substructures in their periphery as well as the gaseous Magellanic Stream. To better understand the origin of the stellar substructures and constrain their past orbit, we model the past 2.5 Gyr of the interactions between the MW and the LMC and SMC using N-body simulations. Due to the strong interactions, analytical orbit integrations are insufficient to analyze the past galaxy orbits accurately. Therefore, we use a genetic algorithm in combination with N-body simulations to determine the LMC and SMC initial positions and velocities 2.5 Gyr ago that result in the Magellanic Clouds (MCs) arriving near their observed locations and velocities at the current time. After running ~8,000 simulations, our best matching model includes two close interactions between the MCs (940 Myr and 140 Myr ago) and reproduces some observed features of the MCs, including the LMC disc warp, a ring-shaped overdensity in the LMC, the tidal expansion of the SMC, and a greater distance dispersion on the eastern side of the SMC. The LMC disc warp is caused by the most recent interaction with the SMC, which occurred ~140 Myr before the present. The interaction causes global ripples in the LMC disc with a mean amplitude of 1.3 kpc.

💡 Research Summary

This paper presents a comprehensive dynamical reconstruction of the past 2.5 Gyr of interactions among the Milky Way (MW), the Large Magellanic Cloud (LMC), and the Small Magellanic Cloud (SMC). Recognizing that strong mutual tidal forces and dynamical friction render analytical orbit integrations unreliable, the authors combine a genetic algorithm (GA) with N‑body simulations to explore the nine‑dimensional space of initial positions, velocities, and orientations for the two satellite galaxies.

Observational constraints are drawn from Gaia EDR3 (red‑clump and red‑giant stars) and SDSS‑IV/APOGEE DR17 (line‑of‑sight velocities). The Gaia sample is cleaned using colour‑magnitude cuts, proper‑motion windows (0.9–2.8 mas yr⁻¹ in L MS, –0.6–1.4 mas yr⁻¹ in B MS), a parallax filter (π > 0.2 mas), and spatial selections in Magellanic Stream coordinates to isolate the stellar components of the Clouds and their tidal features.

The N‑body framework employs the pkdgrav code. Low‑resolution models consist of ~1.6 × 10⁵ stellar and ~2.4 × 10⁵ dark‑matter particles for the LMC (stellar mass 7.2 × 10⁹ M⊙, halo mass 1.76 × 10¹¹ M⊙), ~2.3 × 10⁴ stellar and ~2.9 × 10⁴ dark particles for the SMC (stellar mass 1.06 × 10⁹ M⊙, halo mass 2.02 × 10¹⁰ M⊙), and ~2.4 × 10⁴ stellar plus ~2.5 × 10⁴ dark particles for the MW (stellar mass 5.25 × 10¹⁰ M⊙, halo mass 1.16 × 10¹² M⊙). Each galaxy is first evolved in isolation for 6 Gyr to reach a relaxed configuration, then the three are combined and evolved for an additional 2.5 Gyr under the GA‑selected initial conditions.

The GA evaluates fitness as the inverse of the summed squared differences between simulated and observed three‑dimensional positions and velocities of the LMC and SMC at the “current time” (defined when the LMC crosses L MS = 0°). A penalty halves the fitness for any run where the two satellites approach within 15 kpc, discouraging unphysical mergers. Each generation runs 15 simulations in parallel; the best individual is always retained, while the rest are generated via weighted random selection, crossover, and Gaussian mutation (σ = 0.5 kpc for positions, 1–2 km s⁻¹ for velocities).

After roughly 8 000 simulations, the optimal solution features two close passages: the first ≈ 940 Myr ago and the second ≈ 140 Myr ago. The most recent encounter induces global ripples in the LMC disc with a mean vertical amplitude of 1.3 kpc (peaking near 2 kpc), reproducing the observed southern and northern warps that give the LMC a characteristic “U‑shape”. The model also generates a ring‑like stellar overdensity at ≈ 10–15 kpc from the LMC centre, matching the overdensity identified in SMASH data. For the SMC, the 140 Myr encounter creates a pronounced distance bimodality on its eastern side, consistent with historic photometric detections of a near and a far component.

To assess the robustness of the result, the authors performed higher‑resolution runs (10× particle count) for the best‑fit orbit and explored six variations of the LMC structural parameters: thicker disc (model B), thinner disc (C), hotter disc (D), more compact halo (F), and more diffuse halo (G). The disc thickness and temperature significantly affect warp amplitude—thinner, colder discs develop larger vertical excursions, while hotter discs damp the response. Halo concentration modestly influences the orbital decay but does not alter the qualitative morphology of the warps or overdensities.

Comparisons between simulated and observed maps of stellar density, proper motions (in L MS and B MS), and line‑of‑sight velocities show good agreement across the bulk of the Clouds. The simulated LMC warp reproduces both the southern warp identified by Choi et al. (2018) and the northern warp reported by Saha & Subramanian (2022). The ring‑shaped overdensity aligns with the outer stellar substructures reported by Nidever et al. (2019). The SMC’s eastern distance spread mirrors the bimodal distribution first noted by Hatzidimitriou & Hawkins (1989) and later confirmed spectroscopically.

Nevertheless, the purely collisionless N‑body approach cannot capture the detailed morphology of the gaseous Magellanic Stream, the Leading Arm, or the fine filamentary substructures observed in H I. The authors acknowledge that incorporating hydrodynamics, ram‑pressure stripping, and a hot Magellanic corona (as in Lucchini et al. 2020) will be necessary for a complete picture.

In the discussion, the paper emphasizes that the GA‑N‑body framework efficiently navigates a high‑dimensional parameter space, delivering a self‑consistent orbital history that simultaneously explains multiple observed stellar features. The identification of two distinct close passages provides a coherent timeline linking the LMC warp, the ring overdensity, and the SMC’s eastern distance bimodality. The authors suggest future work should integrate gas physics, star‑formation feedback, and the upcoming Gaia DR3 and LSST datasets to refine the model further and test its predictive power for yet‑unobserved substructures.

Overall, the study delivers a robust, observation‑driven dynamical model of the Magellanic system’s recent past, demonstrating the power of combining evolutionary algorithms with high‑resolution N‑body simulations for unraveling complex satellite‑host interactions.