Using Spherical Harmonics in the Galactocentric Coordinate System to Study the Kinematics of Globular Star Clusters

The technique of spherical harmonics, both scalar and vector ones, has long been applied to analyze the astronomical data on a sphere, for example, in the representation of systematic errors, in stellar kinematics. Up to now, spherical harmonics have been used exclusively in heliocentric coordinate systems: the equatorial or Galactic one. To study the kinematics of the entire Galaxy (and not only the solar neighborhood), it is reasonable to pass to the Galactocentric coordinate system. The second release of the Gaia catalogue does not yet allow such an analysis to be performed for individual stars due to the relatively low accuracy of the parallaxes. However, such a study seems possible for globular star clusters, despite their small number. Although the kinematics of globular clusters was studied in detail in many papers, we want to test the method of analyzing the Galactocentric proper motions and radial velocities using spherical harmonics based on data from this catalogue.