Vertical Phase Mixing across the Galactic Disk

By combining the {\it LAMOST} and Gaia} data, we investigate vertical phase mixing across Galactic disk. Our results confirm existence of space snail shells (or spirals) from 6 to 12 kpc. We find that grouping stars by guiding radius ($R_{g}$), instead present ($R$) further enhances shell signal in following aspects: (1) clarity shape is increased; (2) more wraps can be seen; (3) spaces are less affected lack closer disk mid-plane due extinction; (4) amplified greater radial ranges. Compared $R$-based shell, quantitatively measured shapes similar, except $R_{g}$-based show with better contrast. These lines evidence lead conclusion (angular momentum) a fundamental parameter tracing Results our test particle simulations impulse approximation verify particles grouped according $R_{g}$ reveal well-defined sharper features. comparing profiles pitch angle between observation simulation, external perturbation constrained $\sim$500$-$700 Myr ago. For future study, it recommended use additional constraints on orbital hotness (ellipticity) improve snail.