Vertical waves in the solar neighbourhood in Gaia DR2
  The vertical structure and dynamics of stars in our local Galactic
neighbourhood contains much information about the local distribution of visible
and dark matter and of perturbations to the Milky Way disc. We use data on the
positions and velocities of stars in the solar neighbourhood from \gaia\ DR2
and large spectroscopic surveys to investigate the vertical number counts and
mean-velocity trend as a function of distance from the local Galactic
mid-plane. We perform a detailed measurement of the wave-like North-South
asymmetry in the vertical number counts, which reveals a number of deficits at
heights $\approx 0.4\,\mathrm{kpc}$, $\approx 0.9\,\mathrm{kpc}$, and $\approx
1.5\,\mathrm{kpc}$, and peaks at $\approx 0.2\,\mathrm{kpc}$, $\approx
0.7\,\mathrm{kpc}$, and $\approx 1.1\,\mathrm{kpc}$. We find that the asymmetry
pattern is independent of colour. The mean vertical velocity is almost constant
to $<1\,\mathrm{km\,s}^{-1}$ within a few 100 pc from the mid-plane and then
displays a North-South symmetric dip at $\approx0.5\,\mathrm{kpc}$ with an
amplitude of $\approx 2\,\mathrm{km\,s}^{-1}$ that is a plausible velocity
counterpart to the main number-count dip at a similar height. Thus, with \gaia\
DR2 we confirm at high fidelity that the local Galactic disc is undergoing a
wave-like oscillation and a dynamically-consistent observational picture of the
perturbed local vertical structure emerges for the first time. We also present
the most precise and accurate determination of the Sun's height above the local
Galactic mid-plane, correcting for any asymmetry in the vertical density:
$z_\odot = 20.8 \pm 0.3\,\mathrm{pc}$.
