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Delayed phase mixing in the self-gravitating Galactic disc

T. Asano, T. Antoja

TL;DR

This study addresses biases in dating past Galactic perturbations from Gaia phase spirals by incorporating the disc's self-gravity. By comparing a high-resolution self-consistent $N$-body MW–Sgr simulation with contracted-potential test-particle runs, the authors show that self-gravity introduces a delayed, non-winding phase lasting several hundred million years, causing underestimation of the excitation time when neglected. They reproduce this delay qualitatively with an analytical self-gravitating shearing-box model and quantify a solar-neighborhood lag of about $\Delta t \sim 0.3$ Gyr, leading to a revised elapsed time of $t_{\mathrm{elapsed}} \approx t_{\mathrm{fit}} + \Delta t \approx 0.6$–$1.2$ Gyr, more consistent with Sgr’s pericentre passage. The work highlights that accurate dynamical dating of perturbations requires self-gravity in Galactic-disc models and provides a practical correction for the phase-spiral clock.

Abstract

The Gaia phase spiral is considered to work as a dynamical clock for dating past perturbations, but most of the previous studies neglected the disc's self-gravity, potentially biasing estimates of the phase spiral's excitation time. We aim to evaluate the impact of self-gravitating effects on the evolution of vertical phase spirals and to quantify the bias introduced in estimating their excitation time when such effects are ignored. We analysed a high-resolution, self-consistent $N$-body simulation of the MW-Sagittarius dwarf galaxy (Sgr) system, alongside four test particle simulations in potentials contracted from the $N$-body snapshots. In each case, we estimated the winding time of phase spirals by measuring the slope of the density contrast in the vertical angle-frequency space. In test particle models, the phase spiral begins winding immediately after Sgr's pericentre passage, and the winding time closely tracks the true elapsed time since the Sgr's pericentre 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 $\gtrsim$ 300 Myr before a clear spiral forms, leading to systematic underestimation of excitation times. An analytical shearing-box model with self-gravity, developed by Widrow (2023), qualitatively reproduces this delay, supporting its origin in the disc's self-gravitating response. Assuming that self-gravity affects phase mixing in the MW to the same degree as the $N$-body model, the lag induced by self-gravity is estimated to be $\sim$ 0.3 Gyr in the solar neighbourhood. Accounting for this delay revises the inferred age of the MW's observed phase spiral to $\sim$0.6-1.2 Gyr, in better agreement with the Sgr's pericentre passage. (shortened for arXiv)

Delayed phase mixing in the self-gravitating Galactic disc

TL;DR

This study addresses biases in dating past Galactic perturbations from Gaia phase spirals by incorporating the disc's self-gravity. By comparing a high-resolution self-consistent -body MW–Sgr simulation with contracted-potential test-particle runs, the authors show that self-gravity introduces a delayed, non-winding phase lasting several hundred million years, causing underestimation of the excitation time when neglected. They reproduce this delay qualitatively with an analytical self-gravitating shearing-box model and quantify a solar-neighborhood lag of about Gyr, leading to a revised elapsed time of – Gyr, more consistent with Sgr’s pericentre passage. The work highlights that accurate dynamical dating of perturbations requires self-gravity in Galactic-disc models and provides a practical correction for the phase-spiral clock.

Abstract

The Gaia phase spiral is considered to work as a dynamical clock for dating past perturbations, but most of the previous studies neglected the disc's self-gravity, potentially biasing estimates of the phase spiral's excitation time. We aim to evaluate the impact of self-gravitating effects on the evolution of vertical phase spirals and to quantify the bias introduced in estimating their excitation time when such effects are ignored. We analysed a high-resolution, self-consistent -body simulation of the MW-Sagittarius dwarf galaxy (Sgr) system, alongside four test particle simulations in potentials contracted from the -body snapshots. In each case, we estimated the winding time of phase spirals by measuring the slope of the density contrast in the vertical angle-frequency space. In test particle models, the phase spiral begins winding immediately after Sgr's pericentre passage, and the winding time closely tracks the true elapsed time since the Sgr's pericentre 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 -body simulation exhibits an initial, coherent vertical oscillation lasting 300 Myr before a clear spiral forms, leading to systematic underestimation of excitation times. An analytical shearing-box model with self-gravity, developed by Widrow (2023), qualitatively reproduces this delay, supporting its origin in the disc's self-gravitating response. Assuming that self-gravity affects phase mixing in the MW to the same degree as the -body model, the lag induced by self-gravity is estimated to be 0.3 Gyr in the solar neighbourhood. Accounting for this delay revises the inferred age of the MW's observed phase spiral to 0.6-1.2 Gyr, in better agreement with the Sgr's pericentre passage. (shortened for arXiv)

Paper Structure

This paper contains 14 sections, 22 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Simulations
  3. N-body simulation
  4. Test particle simulations
  5. Phase spirals
  6. Unwinding phase spirals
  7. Method
  8. Results
  9. Discussion
  10. Analytical models
  11. Implications for the Milky Way
  12. Conclusions
  13. Supplementary figures from the test particle models
  14. Shearing box model

Figures (15)

  • Figure 1: Vertical forces due to Sgr (upper panel) and the DM wake (lower panel). The forces are evaluated along circular orbits at $R=8$ kpc, and the colours of the lines indicate the azimuth $\phi=\Omega_{\mathrm{8\,kpc}} t + \phi_0$. Vertical dashed lines indicate the times of Sgr's pericentre passages.
  • Figure 2: Amplitude of the perturbing force as a function of $R$ and $t$. The colour maps represent the force amplitudes due to Sgr (first panel), the DM wake (second panel), and their ratio (third panel). The vertical dashed lines indicate the times of Sgr's pericentre passages.
  • Figure 3: Phase spirals in the TP (Static) model (first row), TP (Sgr) model (second row), TP (Wake) model (third row), TP (Sgr+Wake) model (fourth row), and $N$-body model (fifth row). Each panel shows the density contrast in the $\sqrt{J_z}\cos\theta_z$-$\sqrt{J_z}\sin\theta_z$ space for 18 bins of $\theta_{\phi}$ at $R_g=8$ kpc.
  • Figure 4: Time evolution of the phase spiral. From left to right, columns correspond to the different models: TP (Static), TP (Sgr), TP (Wake), TP (Sgr+Wake), and $N$-body model. From top to bottom, time increases from $t=0$ Gyr to 0.88 Gyr.
  • Figure 5: An example of phase spiral unwinding. Top left: density contrast in the $\sqrt{J_z}\cos\theta_z$--$\sqrt{J_z}\sin\theta_z$ space. Top middle: the same data mapped into the $\sqrt{J_z}$--$\theta_z$ space. Top right: the filtered $\sqrt{J_z}$--$\theta_z$ map. The red dots indicate the phase of the $k=1$ Fourier mode. Bottom left: the phase of the $k=1$ Fourier mode mapped into the $\Omega_z$--$\theta_z$ space, where $\Omega_z$ is the vertical frequency. The blue line shows the best-fit linear model. Bottom right: the $\sqrt{J_z}$--$\theta_z$ map reconstructed from the fitting result.
  • ...and 10 more figures