The velocity ellipsoid in the Galactic disc using Gaia DR1
  The stellar velocity ellipsoid of the solar neighbour is re-examined using
intermediate-old mono-abundances stellar groups with high quality chemistry
data together with parallaxes and proper motions from Gaia DR1. We find the
average velocity dispersion values for the three space velocity components for
the thin and thick disc of (\sigma_{U},\sigma_{V},\sigma_{W})_{thin} = (33 \pm
4, 28 \pm 2, 23 \pm 2) and (\sigma_{U},\sigma_{V},\sigma_{W})_{thick} = (57 \pm
6, 38 \pm 5, 37 \pm 4) km s^{-1}, respectively. The mean values of the ratio
between the semi-axes of the velocity ellipsoid for the thin disc are found to
be, \sigma_{V}/\sigma_{U} = 0.70 \pm 0.13 and \sigma_{W}/\sigma_{U} is 0.64 \pm
0.08, while for the thick disc \sigma_{V}/\sigma_{U} = 0.67 \pm 0.11 and
\sigma_{W}/\sigma_{U} is 0.66 \pm 0.11. Inputting these dispersions into the
linear Str\"omberg relation for the thin disc groups, we find the Sun's
velocity with respect to the LSR in Galactic rotation to be V_{\sun} = 13.9 \pm
3.4 km s^{-1}. A relation is found between the vertex deviation and the
chemical abundances for the thin disc, ranging from -5 to +40^{\circ} as
iron-abundance increases. For the thick disc we find a vertex deviation of
l_{uv} \sim -15^{\circ}. The tilt angle (l_{uw}) in the U-W plane for the thin
disc groups ranges from -10 to +15^\circ, but there is no evident relation
between l_{uw} and the mean abundances. However we find a weak relation for
l_{uw} as a function of iron abundances and \alpha-elements for most of the
groups in the thick disc, where the tilt angle decreases from -5 to -20^\circ
when [Fe/H] decreases and [\alpha/Fe] increases. The velocity anisotropy
parameter is independent of the chemical group abundances and its value is
nearly constant for both discs (\beta \sim 0.5), suggesting that the combined
disc is dynamically relaxed.
