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 vertical bar V-phi - V-LSR vertical bar less than or similar to 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-phi), 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-phi color-coded phase space is also discussed.