Dissecting the Phase Space Snail Shell

The ongoing vertical phase-mixing, manifesting itself as a snail shell in the $Z-{V}_{Z}$ phase space, has been discovered with Gaia DR2 data. To better understand the origin and properties of the phase-mixing process, we study the vertical phase-mixing signatures in arches (including the classical "moving groups") of the ${V}_{R}-{V}_{\phi }$ phase space near the solar circle. Interestingly, the phase space snail shell exists only in the arches with $| {V}_{\phi }-{V}_{\mathrm{LSR}}| \,\lesssim 30$ km s^-1, I.e., stars on dynamically "colder" orbits. The snail shell becomes much weaker and eventually disappears for increasingly larger radial action (J_R), quantifying the "hotness" of orbits. Thus, one should pay closer attention to the colder orbits in future phase-mixing studies. We also confirm that the Hercules stream has two branches (at fast and slow V_φ), which may not be explained by a single mechanism, since only the fast branch shows the prominent snail shell feature. The hotter orbits may have phase-wrapped away already due to the much larger dynamical range in radial variation to facilitate faster phase-mixing. To explain the lack of a well-defined snail shell in the hotter orbits, the disk should have been perturbed at least 500 Myr ago. Our results offer more support to the recent satellite-disk encounter scenario than the internal bar-buckling perturbation scenario as the origin of the phase space mixing. The origin of the more prominent snail shell in the V_φ color-coded phase space is also discussed.