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

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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), the density and kinematic radial gradients, as well as the local slope of the velocity curve. From the stellar disc dynamical model, we determine explicitly the link between the tangential-vertical velocity (vθ, vz) coupling and the local shape of the potential. Using a restricted sample of 3-D velocity data, we measure zₒ, the focus of the spheroidal coordinate system defining the best fitted Stäckel potential. The parameter zₒ 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.