On the Use of Vector Spherical Harmonics

TL;DR

This paper compares three commonly used vector spherical harmonics systems in astronomy to address inconsistencies and facilitate better comparison of results across studies.

Contribution

It provides a detailed comparison of the three main VSH systems used in astrometry and stellar astronomy, clarifying their differences and aiding standardization.

Findings

Identifies differences between the three VSH systems.

Highlights potential issues in comparing results from different VSH approaches.

Provides guidance for selecting and applying VSH systems in astronomical research.

Abstract

In many astronomical works, the structure of vector fields is analyzed, such as the differences in the celestial object coordinates in catalogs or the celestial object velocities, by decomposition into vector spherical harmonics (VSH). This method has shown high efficiency in many studies, but, at the same time, comparing the results obtained by different authors can cause difficulties associated with different approaches to building the VSH system and even with their different designations. To facilitate this task, this paper provides a comparison of the three VSH systems most often used in works on astrometry and stellar astronomy.