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.
