The vertical gradients in the Galactic rotation derived from the proper motions of the UCAC4 PPMXL and PPM catalogues

Abstract

The paper deals with the kinematic analysis of the proper motions listed in huge modern astrometric catalogues UCAC4, PPMXL and XPM. Our approach is based on representation of the proper motions on the set of vector spherical harmonics. To study the stellar kinematics in the northern and southern galactic hemispheres separately the set of the orthonormal vector spherical harmonics defined on the latitude zone of the sphere was constructed. In the performing the separate solutions this approach concealed the correlations between the unknown parameters and made the solution trustworthy. It is shown that the kinematic analysis of the UCAC4, PPMXL and XPM proper motions in northern and southern Galactic hemispheres detects retardation of the Galaxy’s rotational velocity and acceleration of the expansion velocity of the stellar system with increasing the distance from the principal Galactic plane. The estimates of the vertical gradient of the Galactic rotation are UCAC4: 40.1 ± 0.2; PPMXL: 36.2 ± 0.4; XPM: 37.7 ± 0.1 km · s^−1 · kpc^−1, while the values of the vertical gradient of the expansion velocity turned out to be UCAC4: 11.9 ± 0.2; PPMXL: 19.0 ± 1.1; XPM: 10.9 ± 0.3 km · s^−1 · kpc^−1. Refs 16. Figs 1. Tables 4.

Keywords:

astrometry, stellar kinematics, proper motions, spherical harmonics