Kinematics of stars in the northern and southern galactic hemispheres

We use vector spherical harmonics for a kinematic analysis of the proper motions of stars from the Hipparcos, Tycho-2, and UCAC3 catalogues in the northern and southern Galactic hemispheres. We have found that the statistically reliable values of the Ogorodnikov-Milne model parameters M32+ and M32− have different signs in different hemispheres. This is a consequence of the Galaxy’s rotational retardation with distance from the principal Galactic plane. Based on various samples of stars from the above catalogues, we have obtained the following estimate for the magnitude of the vertical gradient of Galactic rotation velocity in the solar neighborhoods: (20.1 ± 2.9) < |∂V⊙/∂z| < (49.2 ± 0.8) km s−1 kpc−1. Another result that is revealed by our analysis of the parameters M13− and M13+ in different Galactic hemispheres is that the vertical gradient of expansion velocity for the stellar system ∂VR/∂z is positive in the northern hemisphere and negative in the southern one. This suggests that the expansion velocity VR increases with distance fromthe Galactic plane. We show that both these gradients give rise to an apparent acceleration of the solar motion along the x and y axes of the rectangular Galactic coordinate system. Our analysis of the parameters M21− and M12+ shows no significant differences in both hemispheres and has allowed us to determine the Oort parameters, to estimate the Galactic rotation velocity and period in the solar neighborhood, and to calculate the ratio of the epicyclic frequency to the angular velocity of Galactic rotation in the solar neighborhood. The derived diagonal elements of the velocity field deformation tensor suggest that the orientation of the rectangular Galactic coordinate system in space must be determined by taking into account not only the geometrical factors but also the dynamical ones. All these results agree well with these quantities estimated over the entire sphere by various authors.