Abstract

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.

中文翻译：

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在半圆心坐标系中使用球谐函数研究球状星团的运动学

摘要

长期以来，标量和矢量的球谐技术一直被用于分析球体上的天文数据，例如，恒星运动学中系统误差的表示。到目前为止，球谐已经专门用于日心坐标系：赤道或银河系。要研究整个银河系的运动学（不仅是太阳系附近的运动学），将其传递到以伽拉克为中心的坐标系是合理的。由于视差的准确性相对较低，Gaia目录的第二版尚未允许对单个恒星执行这种分析。然而，尽管球状星团的数量很少，但这种研究似乎仍可能进行。尽管许多论文都详细研究了球状星团的运动学，