Kinematical analysis of proper motions independent of the systematic drift of parallaxes on the sky

Abstract

The paper deals with the particular features of the kinematical analysis of proper motions when the parallaxes are unavailable and the Solar motion can not be removed from proper motions. Our approach is based on representation of parallaxes on the set of spherical harmonics. We propose a method of calculating the kinematic parameters of the stellar velocity field which ignores the systematic drift of parallaxes on the sky. The numerical simulations gave evidence that our method is able to get precise values of the Solar apex coordinates and to evaluate the kinematical parameters of the 3-D Ogorodnikov— Milne model up to the three first order coefficients of the parallaxes expansion on a set of the spherical functions. A remarkable feature of the proposed method is the possibility to construct the shape of the figure which is formed by deviations of parallaxes from the sphere corresponding to the average parallaxes of the stars under consideration. It is worthwhile to underline that all this is done when the values of parallaxes are completely unavailable. Here, the information comes from the “Solar terms” of proper motions which are generated by the products of the parallaxes and the Solar motion components with respect to the centroid of the stars. Refs 14. Tables 4.

Keywords:

astrometry, stellar kinematics, proper motions, spherical harmonics