The stellar velocity ellipsoid of the solar neighbour ( d < 200 pc ) 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 Strömberg 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 .