Delayed phase mixing in the self-gravitating Galactic disc

¹ Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franquès, 1, 08028 Barcelona, Spain
² Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franquès, 1, 08028 Barcelona, Spain
³ Institut d’Estudis Espacials de Catalunya (IEEC), c. Gran Capità 2–4, 08034 Barcelona, Spain

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 13 October 2025
Accepted: 13 February 2026

Abstract

Context. The discovery of the phase spiral in the vertical position–velocity (z–v_z) distribution of the solar neighbourhood stars revealed the Milky Way (MW) disc disequilibrium. The phase spiral is considered to work as a dynamical clock for dating past perturbations, but some previous studies neglected the disc self-gravity, which might bias estimates of the phase spiral excitation time.

Aims. We revisit self-gravitating effects on the evolution of vertical phase spirals and quantify the bias introduced in estimating their excitation time when these effects are ignored.

Methods. We analysed a high-resolution self-consistent N-body simulation of the MW interaction with the Sagittarius dwarf galaxy (Sgr), alongside four test-particle simulations in potentials constructed from the N-body snapshots. In the test-particle simulations, we used static and time-dependent potentials that included (or excluded) Sgr and the dark matter (DM) wake. In each case, we estimated the winding time of phase spirals by measuring the slope of the density contrast in the vertical angle–frequency (θ_z–Ω_z) space.

Results. In test-particle models, the phase spiral immediately begins to wind after the Sgr pericentric passage, and the winding time closely tracks the true elapsed time since the Sgr pericentric passage. Adding the DM wake yields only a modest (<100 Myr) reduction of the winding time relative to Sgr alone. By contrast, the self-consistent N-body simulation exhibits an initial coherent vertical oscillation lasting ≳300 Myr before a clear spiral forms, leading to a systematic underestimation of the excitation times. An analytical shearing-box model with self-gravity, developed in a previous study, qualitatively reproduces this delay. This supports the hypothesis that it originates in the response of the self-gravitating disc.

Conclusions. Assuming that self-gravity affects phase mixing in the MW to the same degree as the N-body model, we estimated the lag induced by self-gravity to be ∼0.3 Gyr in the solar neighbourhood. Accounting for this delay revises the inferred age of the observed phase spiral of the MW to ∼0.6–1.2 Gyr, which agrees better with the Sgr pericentric passage. An accurate dynamical dating of past perturbations thus requires models that include the self-gravitating response of the Galactic disc.