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Signatures of vertical disequilibrium have been observed across the Milky Way’s (MW’s) disk. These signatures manifest locally as unmixed phase spirals inz–v_zspace (“snails-in-phase”), and globally as nonzero meanzandv_z, wrapping around the disk into physical spirals in thex–yplane (“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 az–v_zasymmetry metric, we demonstrate that in test-particle simulations: (a) multiple local phase-spiral morphologies appear when stars are binned by azimuthal actionJ_ϕ, 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 withinR≲ 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. Whilemore »Sgr has not yet crossed the disk (currently,z_Sgr≈ −6 kpc,v_z,Sgr≈ 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 globalv_zsignature with amplitude ∝M_Sgr, which might be detectable in future spectroscopic surveys.

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ABSTRACT In this work, we present two new ∼109 particle self-consistent simulations of the merger of a Sagittarius-like dwarf galaxy with a Milky Way (MW)-like disc galaxy. One model is a violent merger creating a thick disc, and a Gaia–Enceladus/Sausage-like remnant. The other is a highly stable disc which we use to illustrate how the improved phase space resolution allows us to better examine the formation and evolution of structures that have been observed in small, local volumes in the MW, such as the z−vz phase spiral and clustering in the vR−vϕ plane when compared to previous works. The local z−vz phase spirals are clearly linked to the global asymmetry across the disc: we find both 2-armed and 1-armed phase spirals, which are related to breathing and bending behaviours, respectively. Hercules-like moving groups are common, clustered in vR−vϕ in local data samples in the simulation. These groups migrate outwards from the inner galaxy, matching observed metallicity trends even in the absence of a galactic bar. We currently release the best-fitting ‘present-day’ merger snapshots along with the unperturbed galaxies for comparison.