Kinematical and chemical vertical structure of the Galactic thick disk I. Thick disk kinematics

The variation of the kinematical properties of the Galactic thick disk with Galactic height Z are studied by means of 412 red giants observed in the direction of the south Galactic pole up to 4.5 kpc from the plane. We confirm the non-null mean radial motion toward the Galactic anticenter found by other authors, but we find that it changes sign at |Z|=3 kpc, and the proposed inward motion of the LSR alone cannot explain these observations. The rotational velocity decreases with |Z| by -30 km/s/kpc, but the data are better represented by a power-law with index 1.25, similar to that proposed from the analysis of SDSS data. All the velocity dispersions increase with |Z|, but the vertical gradients are small. The dispersions grow proportionally, with no significant variation of the anisotropy. The ratio sigma_U/sigma_W=2 suggests that the thick disk could have formed from a low-latitude merging event. The vertex deviation increases with Galactic height, reaching ~20 degrees at |Z|=3.5 kpc. The tilt angle also increases, and the orientation of the ellipsoid in the radial-vertical plane is constantly intermediate between the alignment with the cylindrical and the spherical coordinate systems. The tilt angle at |Z|=2 kpc coincides with the expectations of MOND, but an extension of the calculations to higher |Z| is required to perform a conclusive test. Finally, between 2.5 and 3.5 kpc we detect deviations from the linear trend of many kinematical quantities, suggesting that some kinematical substructure could be present.