The local stellar velocity distribution of the Galaxy ⋆ Galactic structure and potential

The velocity distribution of neighbouring stars is deduced from the Hipparcos proper motions. We have used a classical Schwarzschild decomposition and also developed a dynamical model for quasi-exponential stellar discs. This model is a 3-D derivation of Shu's model in the framework of Stäckel potentials with three integrals of motion. We determine the solar motion relative to the local standard of rest (LSR) (U ⊙ = 9.7 ± 0.3 km s −1 , V ⊙ = 5.2 ± 1.0 km s −1 and W ⊙ = 6.7 ± 0.2 km s −1), the density and kinematic radial gradients, as well as the local slope of the velocity curve. We find out that the scale density length of the Galaxy is 1.8 ± 0.2 kpc. We measure a large kinematic scale length for blue (young) stars, R σr = 17 ± 4 kpc, while for red stars (predominantly old) we find R σr = 9.7 ± 0.8 kpc (or R σ 2 r = 4.8 ± 0.4 kpc). From the stellar disc dynamical model, we determine explicitly the link between the tangential-vertical velocity (v θ , v z) coupling and the local shape of the potential. Using a restricted sample of 3-D velocity data, we measure z o , the focus of the spheroidal coordinate system defining the best fitted Stäckel potential. The parameter z o is related to the tilt of the velocity ellipsoid and more fundamentally to the mass gradient in the galactic disc. This parameter is found to be 5.7±1.4 kpc. This implies that the galactic potential is not extremly flat and that the dark matter component is not confined in the galactic plane.