The GALAH survey and Gaia DR2: Linking ridges, arches and vertical waves
  in the kinematics of the Milky Way
  Gaia DR2 has revealed new small-scale and large-scale patterns in the
phase-space distribution of stars in the Milky Way. In cylindrical Galactic
coordinates $(R,\phi,z)$, ridge-like structures can be seen in the \vphiR{}
plane and asymmetric arch-like structures in the \vphivR{} plane. We show that
the ridges are also clearly present when the third dimension of the \vphiR{}
plane is represented by $\langle z \rangle$, $\langle V_z \rangle$, $\langle
V_R \rangle$, $\langle$[Fe/H]$\rangle$ and $\langle[\alpha/{\rm Fe}]\rangle$.
The maps suggest that stars along the ridges lie preferentially close to the
Galactic midplane ($|z|<0.2$ kpc), and have metallicity and $\alpha$ elemental
abundance similar to that of the Sun. We show that phase mixing of disrupting
spiral arms can generate both the ridges and the arches. It also generates
discrete groupings in orbital energy $-$ the ridges and arches are simply
surfaces of constant energy. We identify 8 distinct ridges in the \gaia{} data:
six of them have constant energy while two have constant angular momentum.
Given that the signature is strongest for stars close to the plane, the
presence of ridges in $\langle z \rangle$ and $\langle V_z \rangle$ suggests a
coupling between planar and vertical directions. We demonstrate, using N-body
simulations that such coupling can be generated both in isolated discs and in
discs perturbed by an orbiting satellite like the Sagittarius dwarf galaxy.
