# Snails Across Scales: Local and Global Phase-Mixing Structures as Probes of the Past and Future Milky Way

**Authors:** Suroor S. Gandhi, Kathryn V. Johnston, Jason A. S. Hunt, Adrian M. Price-Whelan, Chervin F. P. Laporte, David W. Hogg  
**arXiv:** [2107.03562](https://arxiv.org/abs/2107.03562)  
**Date:** 2021-07-08  
**Summary page:** https://www.summarizepaper.com/en/paper/2107.03562v1/

## Abstract

Signatures of vertical disequilibrium have been observed across the Milky Way's disk. These signatures manifest locally as unmixed phase-spirals in $z$--$v_z$ space ("snails-in-phase") and globally as nonzero mean $z$ and $v_z$ which wraps around as a physical spiral across the $x$--$y$ plane ("snails-in-space"). We explore the connection between these local and global spirals through the example of a satellite perturbing a test-particle Milky Way (MW)-like disk. We anticipate our results to broadly apply to any vertical perturbation. Using a $z$--$v_z$ asymmetry metric we demonstrate that in test-particle simulations: (a) multiple local phase-spiral morphologies appear when stars are binned by azimuthal action $J_\phi$, excited by a single event (in our case, a satellite disk-crossing); (b) these distinct phase-spirals are traced back to distinct disk locations; and (c) they are excited at distinct times. Thus, local phase-spirals offer a global view of the MW's perturbation history from multiple perspectives. Using a toy model for a Sagittarius (Sgr)-like satellite crossing the disk, we show that the full interaction takes place on timescales comparable to orbital periods of disk stars within $R \lesssim 10$ kpc. Hence such perturbations have widespread influence which peaks in distinct regions of the disk at different times. This leads us to examine the ongoing MW-Sgr interaction. While Sgr has not yet crossed the disk (currently, $z_{Sgr} \approx -6$ kpc, $v_{z,Sgr} \approx 210$ km/s), we demonstrate that the peak of the impact has already passed. Sgr's pull over the past 150 Myr creates a global $v_z$ signature with amplitude $\propto M_{Sgr}$, which might be detectable in future spectroscopic surveys.