Identifying resonances of the Galactic bar in Gaia DR2: I. Clues from
  action space
  Action space synthesizes the orbital information of stars and is well-suited
to analyse the rich kinematic substructure of the disc in the \emph{Gaia} DR2
radial velocity sample (RVS). We revisit the strong perturbation induced in the
Milky Way (MW) disc by an $m=2$ bar, using test particle simulations and the
actions $(J_R,L_z,J_z)$ estimated in an axisymmetric potential. These make
three useful diagnostics cleanly visible. (1.) We use the well-known
characteristic flip from outward to inward motion at the Outer Lindblad
Resonance (OLR, $l=+1,m=2$), which occurs along the axisymmetric resonance line
(ARL) in $(L_z,J_R)$, to identify in the \emph{Gaia} action data three
candidates for the bar's OLR and pattern speed $\Omega_\text{bar}$:
$1.85\Omega_0$, $1.20\Omega_0$, and $1.63\Omega_0$ (with $\sim0.1\Omega_0$
systematic uncertainty). The \emph{Gaia} data is therefore consistent with both
slow and fast bar models in the literature, but disagrees with recent
measurements of $\sim1.45\Omega_0$. (2.) For the first time, we demonstrate
that bar resonances -- especially the OLR -- cause a gradient in vertical
action $\langle J_z \rangle$ with $L_z$ around the ARL via "$J_z$-sorting" of
stars. This could contribute to the observed coupling of $\langle v_R \rangle$
and $\langle | v_z | \rangle$ in the Galactic disc. (3.) We confirm prior
results that the behaviour of resonant orbits is well approximated by
scattering and oscillation in $(L_z,J_R)$ along a slope $\Delta J_R/\Delta L_z
= l/m$ centered on the $l$:$m$ ARL. Overall, we demonstrate that
axisymmetrically estimated actions are a powerful diagnostic tool even in
non-axisymmetric systems.
