The local stellar velocity distribution of the Galaxy - Galactic structureand potential

The velocity distribution of neighbouring stars is deduced from the Hipparc os 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 Stackel poten tials 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 lo cal 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-sigma r = 17 +/- 4 kpc, while for red stars (pre dominantly old) we find R-sigma r = 9.7 +/- 0.8 kpc (or R-sigma r2 = 4.8 +/ - 0.4 kpc). From the stellar disc dynamical model, we determine explicitly the link bet ween the tangential-vertical velocity (v(theta), v(z)) coupling and the loc al 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 Stackel potential. The parameter z(o) is related to the tilt o f 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 extremely flat and that the dark matter component is not confined in the galactic plane.