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

We explore the origin of phase-space substructures 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, seen in the second Gaia data release. We use a collisionless N-body simulation with co-spatial thin and thick discs to study the orbital structure close to the Outer Lindblad Resonance (OLR) of the bar. We find that a prominent, long-lived ridge associated to the bar OLR is formed in the $V_{\phi}-r$ plane, and show how OLR orbits populate it and occupy the $E-L_z$ plane. This ridge translates to streams in the $V_{\phi}$-$V_r$ plane and we examine which closed periodic and trapped librating orbits are responsible for the observed features in this plane. 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. The changing libration amplitude of orbits in the $V_{\phi}$-$V_r$ plane 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 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 observed features.