Identifying resonances of the Galactic bar in Gaia DR2: II. Clues from angle space

The Milky Way disk exhibits intricate orbit substructure of still-debated dynamical origin. The angle variables $(\theta_\phi,\theta_R)$ -- which are conjugates to the actions $(L_z,J_R)$, and describe a star's location along its orbit -- are a powerful diagnostic to identify $l$:$m$ resonances via the orbit shape relation $\Delta \theta_R / \Delta \theta_\phi = -m/l$. In the past, angle signatures have been hidden by survey selection effects (SEs). Using test particle simulations of a barred galaxy, we demonstrate that \emph{Gaia} should allow us to identify the Galactic bar's Outer Lindblad Resonance ($l=+1, m=2$, OLR) in angle space. We investigate strategies to overcome SEs. In the angle data of the \emph{Gaia} DR2 RVS sample, we independently identify four candidates for the OLR and therefore for the pattern speed $\Omega_\text{bar}$. The strongest candidate, $\Omega_\text{bar}\sim1.4\Omega_0$, positions the OLR above the `Sirius' moving group, agrees with measurements from the Galactic center, and might be supported by higher-order resonances around the `Hercules/Horn'. But it misses the classic orbit orientation flip, as discussed in the companion study on actions. The candidate $\Omega_\text{bar}\sim1.2\Omega_0$ was also suggested by the action-based study, has the OLR at the `Hat', is consistent with \emph{slow bar} models, but still affected by SEs. Weaker candidates are $\Omega_\text{bar}=1.6\Omega_0$ and $1.74\Omega_0$. In addition, we show that the stellar angles do not support the `Hercules/Horn' being created by the OLR of a \emph{fast bar}. We conclude that -- to resolve if `Sirius' or `Hat' is related to the bar's OLR -- more complex dynamical explanations and more extended data with well-behaved SEs are required.