The Tilt of the Local Velocity Ellipsoid as Seen by Gaia
  The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7,224,631
stars with full six-dimensional phase space information. Bayesian distances of
these stars are available from the catalogue of Sch\"onrich et al. (2019). We
exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of
the Sun. We find that the tilt of the disc-dominated RVS sample is accurately
described by the relation $\alpha = (0.952 \pm 0.007)\arctan (|z|/R)$, where
($R,z$) are cylindrical polar coordinates. This corresponds to velocity
ellipsoids close to spherical alignment (for which the normalising constant
would be unity) and pointing towards the Galactic centre. Flattening of the
tilt of the velocity ellipsoids is enhanced close to the plane and Galactic
centre, whilst at high elevations far from the Galactic center the population
is consistent with exact spherical alignment. Using the LAMOST catalogue
cross-matched with Gaia DR2, we construct thin disc and halo samples of
reasonable purity based on metallicity. We find that the tilt of thin disc
stars straddles $\alpha = (0.909-1.038)\arctan (|z|/R)$, and of halo stars
straddles $\alpha = (0.927-1.063)\arctan (|z|/R)$. We caution against the use
of reciprocal parallax for distances in studies of the tilt, as this can lead
to serious artefacts.
