On the ridges, undulations & streams in Gaia DR2: Linking the topography of phase-space to the orbital structure of an N-body bar

We explore the origin of phase-space substructures revealed by the second Gaia data release in the disc of the Milky Way, such as the ridges in the $V_{\phi}$-$r$ plane, the undulations in the $V_{\phi}$-$r$-$V_r$ space and the streams in the $V_{\phi}$-$V_r$ plane. We use a collisionless N-body simulation with co-spatial thin and thick discs, along with orbit integration, to study the orbital structure close to the Outer Lindblad Resonance (OLR) of the bar. We find that a prominent, long-lived ridge is formed in the $V_{\phi}$-$r$ plane due to the OLR which translates to streams in the $V_{\phi}$-$V_r$ plane and examine which closed periodic and trapped librating orbits are responsible for these features. We find that orbits which carry out small librations around the $x_1(1)$ family are preferentially found at negative $V_r$, giving rise to a `horn'-like feature, while orbits with larger libration amplitudes, trapped around the $x_1(2)$ and $x_1(1)$ families, constitute the positive $V_r$ substructure, i.e. the Hercules-like feature. This changing libration amplitude of orbits will translate to a changing ratio of thin/thick disc stars, which could have implications on the metallicity distribution in this plane. We find that a scenario in which the Sun is placed close to the OLR gives rise to a strong asymmetry in $V_r$ in the $V_{\phi}$-$V_r$ plane (i.e. Hercules vs. `the horn') and subsequently to undulations in the $V_{\phi}$-$r$-$V_r$ space. We also explore a scenario in which the Sun is placed closer to the bar corotation and find that the bar perturbation $alone$ cannot give rise to the these features.