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.