Ripples spreading across the Galactic disc (Asano et al. 2025)

Abstract

Context. Gaia data have revealed vertically asymmetric phase-space structures in the Milky Way (MW) disc, such as phase spirals, indicating vertical oscillations. These oscillations exhibit two distinct modes: the bending mode and the breathing mode, associated with one-arm and two-arm phase spirals, respectively. The mechanisms driving these modes remain debated, with both external and internal origins proposed.
Aims. This study aims to explore the excitation mechanisms of the bending and breathing modes and their subsequent evolution in the MW disc, focusing on the interplay between direct perturbations from the Sagittarius dwarf galaxy and indirect contributions from tidally induced spiral arms.
Methods. We perform high-resolution $N$-body simulations with five billion particles to model the interaction between an MW-like disc galaxy and a Sagittarius dwarf-like satellite. These simulations resolve fine phase-space structures, enabling analysis of the bending and breathing modes at both macroscopic (global bending and breathing waves) and microscopic (local phase spirals) scales.
Results. Our simulations demonstrate that the satellite’s perturbation directly excites the bending mode and induces spiral arms in the galactic disc. These spiral arms, in turn, excite the breathing mode, making it an indirect consequence of the satellite interaction. Initially, the bending mode dominates, but it rapidly decays due to horizontal mixing. In contrast, the breathing mode persists for a longer duration, sustained by the spiral arms, leading to a transition from a bending-dominated to a breathing-dominated state. This transition progresses faster in the inner galaxy than in the outer regions. The simulations successfully reproduce the one-arm phase spiral observed in the solar neighbourhood and reveal two-arm phase spirals, particularly in the inner galaxy, associated with spiral arm-induced breathing modes. The two-arm phase spirals emerge approximately 200–-250 Myr after the bending-to-breathing transition.
Conclusions. Our findings highlight the combined effects of direct satellite perturbations and indirect spiral arm dynamics in shaping the vertical structure of the MW disc. The emergence of the two-arm phase spiral after the bending-to-breathing transition suggests that the MW disc experienced a significant perturbation more than $\sim$400 Myr ago, likely caused by the Sagittarius dwarf galaxy. This study underscores the importance of considering the dynamic interplay between direct and indirect mechanisms in understanding the vertical dynamics of the MW disc.

Face-on maps

Delayed phase mixing in the self-gravitating Galactic disc (Asano & Antoja 2026)

Phase spiral as a dynamical clock of our Galaxy

The phase spiral provides direct evidence that the Milky Way is not in dynamical equilibrium, demonstrating that its disc was recently perturbed by a major event, such as a close encounter with a satellite galaxy. Because the spiral winds up over time, it can be used as a dynamical clock to estimate when the perturbation occurred. This is achieved by mapping the phase spiral from ($z$, $v_z$) space into frequency—angle ($\Omega_z$, $\theta_z$) space, where the spiral transforms into a stripe pattern (zebra diagram; Frankel et al. 2023). The slope of this stripe is equal to the time elapsed since the disc was perturbed (Darragh-Ford et al. 2023).

This method assumes that stars orbit in a static gravitational potential and therefore neglects the self-gravity of the disc, that is, the time evolution of the disc potential. In reality, however, the disc’s self-gravity influences the evolution of the phase spiral and can bias the inferred dynamical age. Darling & Widrow (2019) showed that phase spirals in N-body (i.e. self-gravitating) simulations are systematically less tightly wound than those in test-particle (i.e. non-self-gravitating) simulations. Widrow (2023) later confirmed this result using an analytical model.

Building on these studies, we quantified the effect of self-gravity on estimates of the dynamical age of the phase spiral. To do so, we analysed the high-resolution N-body simulation of Asano et al. (2025) together with test-particle simulations in gravitational potentials constructed from snapshots of the N-body model.

The Winding Delay

We found that, following a perturbation, a self-gravitating disc does not begin winding into a phase spiral immediately. Instead, it first undergoes a coherent vertical oscillation, moving up and down almost like a rigid plate, for approximately 300 Myr before the spiral pattern starts to develop. During this initial stage, the spiral exhibits little or no winding. Consequently, purely kinematic models that neglect self-gravity systematically underestimate the time elapsed since the perturbation.

In the Solar neighbourhood, we roughly estimated that self-gravity introduces a winding delay of approximately 0.3 Gyr. Accounting for this delay revises the inferred age of the Milky Way’s observed phase spiral from 0.3—0.9 Gyr to 0.6—1.2 Gyr. This older age is in much better agreement with the timing of the previous pericentric passage of the Sagittarius dwarf galaxy.

Independently, Tavangar et al. (2026) recently performed a similar analysis using an N-body simulation by Hunt et al. (2021) and reached a broadly consistent conclusion. Their results also show a delay in the onset of phase-spiral winding, although there are some differences, such as the radial dependence of the delay. Further work is needed to better understand the role of self-gravity in the formation and evolution of phase spirals and its implications for reconstructing the dynamical history of the Milky Way.