A Low-mass Model of The Milky Way: The Disk Warp Resulting from A Galaxy Merger

Previous studies have shown that disk warps can result from galaxy mergers. Recent research indicates a noticeable decline in the rotation curve (RC) of the Milky Way (MW), suggesting the need for a new low-mass model to describe its dynamical features. This study constructs a new Gaia-Sausage-Enceladus (GSE) merger model to characterize the RC features of our galaxy. We use the GIZMO code to simulate mergers with various orbital parameters to investigate how the disk warp evolves under different conditions. This simulation demonstrates the evolutionary mechanism of disk warp, which arises due to the asymmetric gravitational potential of the dark matter (DM) halo generated universally by galaxy mergers. The results indicate that the tilt angle of the DM halo partly reflects the gravitational strength at the $Z=0$ plane, while the gravitational strength on the disk plane reflects the amplitude of disk warp. We identify a dual-regime interaction mechanism driven by the asymmetric halo potential. On short timescales, we find a distinct anti-correlation between the halo’s tilt angle and the disk’s warp amplitude, indicating a `seesaw’ mechanism of angular momentum exchange. On secular timescales, however, dynamical friction drives a global alignment, causing both the halo tilt and the warp amplitude to decay simultaneously. Furthermore, we demonstrate that high-inclination mergers can sustain long-lived prograde precession, where the persistent yet decaying gravitational torque maintains the prograde bending mode against differential wind-up.

💡 Research Summary

This paper presents a new low‑mass model of the Milky Way (total mass ≈2.4 × 10¹¹ M⊙) that simultaneously reproduces the recently reported steep decline in the Galactic rotation curve and the long‑lived S‑shaped warp of the stellar disk. The authors build on their previous Gaia‑Sausage‑Enceladus (GSE) merger framework, updating it to reflect the lower total mass implied by recent Gaia DR3 analyses (Jiao et al. 2023; Ou et al. 2023). Using the GIZMO hydrodynamics code together with initial conditions generated by the DICE package, they simulate a gas‑rich GSE progenitor (total mass 7.2 × 10¹⁰ M⊙, gas fraction 0.92) colliding with a Milky Way progenitor at redshift ≈ 2 (virial mass 1.8 × 10¹¹ M⊙, stellar mass ≈1.5 × 10¹⁰ M⊙, gas fraction 0.667). Both dark‑matter halos are modeled with Einasto profiles (α_MW = 3.5, α_GSE = 3.25) to reproduce the observed rapid outer‑radius decline of the rotation curve.

The orbital configuration is deliberately extreme: a highly eccentric (e = 0.9) retrograde encounter with opposite spin orientations, and a suite of inclination angles (15°, 30°, 45°, 55°, 60°, 75°) is explored while keeping all other parameters fixed. The merger completes within ≈3 Gyr, with the first pericentric passage occurring at ≈1 Gyr. The particle mass resolution (10⁵ M⊙) is sufficient to resolve vertical bending modes in the disk.

Key results are as follows. (1) The merger rapidly reshapes the dark‑matter halo: mass becomes strongly concentrated within ≈0.2 R_vir, the outer halo develops a pronounced oblate shape and a measurable triaxiality, and the short axis tilts relative to the disk plane by 5–15°. (2) The asymmetric halo potential excites a vertical bending mode in the stellar disk. The warp amplitude (A_warp) reaches its maximum within ≈0.5 Gyr after the merger and exhibits an anti‑correlation with the halo tilt angle during this early phase—a “seesaw” exchange of angular momentum between halo and disk. (3) On secular timescales, dynamical friction damps the relative motion, causing both the halo tilt and A_warp to decay exponentially. The decay accelerates inside ≈0.5 R_vir where the halo becomes more spherical. (4) High‑inclination mergers (≥45°) generate a persistent prograde torque that drives a long‑lived precession of the bending mode with periods of 1–2 Gyr. This torque counteracts differential winding, allowing the warp to survive for several gigayears despite the secular damping. (5) The simulated rotation curve matches the observed decline beyond ≈15 kpc, confirming that the chosen Einasto parameters and low total mass correctly reproduce the outer‑disk dynamics.

The authors interpret these findings as evidence for a two‑regime interaction mechanism. In the first, short‑term regime, the halo’s asymmetric potential and the disk’s vertical response are coupled in a seesaw fashion, rapidly transferring angular momentum. In the second, long‑term regime, dynamical friction aligns the halo and disk, leading to simultaneous attenuation of both tilt and warp. The persistence of the warp in high‑inclination cases demonstrates that a single major merger can provide a universal, long‑lived source of disk warping, consistent with the high incidence of warps in external spiral galaxies.

Overall, the paper advances our understanding of Milky Way dynamics by (i) showing that a low‑mass Milky Way model can still accommodate the GSE merger, (ii) quantifying the halo‑disk angular‑momentum exchange that produces the warp, (iii) revealing the secular alignment process that eventually damps the warp, and (iv) highlighting the role of orbital inclination in sustaining a prograde bending mode. These results bridge the gap between cosmological hierarchical assembly and the detailed vertical structure of galactic disks, offering a coherent explanation for both the observed rotation curve decline and the enduring warp of the Milky Way.