Snails across Scales: Local and Global Phase-mixing Structures as Probes of the Past and Future Milky Way

Signatures of vertical disequilibrium have been observed across the Milky Way's (MW'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 ), wrapping around the disk into physical spirals in 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 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 less than or similar to 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) approximate to -6 kpc, v ( z,Sgr) approximate to 210 km s(-1)), 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 proportional to M (Sgr), which might be detectable in future spectroscopic surveys.