The tilt of the velocity ellipsoid in the Milky Way with Gaia DR2
  The velocity distribution of stars is a sensitive probe of the gravitational
potential of the Galaxy, and hence of its dark matter distribution. In
particular, the shape of the dark halo (e.g. spherical, oblate, or prolate)
determines velocity correlations, and different halo geometries are expected to
result in measurable differences. Here we explore and interpret the
correlations in the $(v_R, v_z)$-velocity distribution as a function of
position in the Milky Way. We selected a high-quality sample of stars from the
Gaia DR2 catalogue and characterised the orientation of the velocity
distribution or tilt angle over a radial distance range of $[4-13]~$kpc and up
to $3.5~$kpc away from the Galactic plane while taking into account the effects
of the measurement errors. We find that the tilt angles change from spherical
alignment in the inner Galaxy ($R\sim4~$kpc) towards more cylindrical
alignments in the outer Galaxy ($R\sim11~$kpc) when using distances that take a
global zero-point offset in the parallax of $-29~\mu$as. However, if the
amplitude of this offset is underestimated, then the inferred tilt angles in
the outer Galaxy only appear shallower and are intrinsically more consistent
with spherical alignment for an offset as large as $-54~\mu$as. We further find
that the tilt angles do not seem to strongly vary with Galactic azimuth and
that different stellar populations depict similar tilt angles. Therefore we
introduce a simple analytic function that describes the trends found over the
full radial range. Since the systematic parallax errors in Gaia DR2 depend on
celestial position, magnitude, and colour in complex ways, it is not possible
to fully correct for them. Therefore it will be particularly important for
dynamical modelling of the Milky Way to thoroughly characterise the systematics
in astrometry in future Gaia data releases.
