Analysis of astrometric catalogues with vector spherical harmonics

TL;DR

This paper introduces a method using vector spherical harmonics to compare and analyze stellar catalogues, revealing systematic effects and rotational properties with advantages of invariance and model independence.

Contribution

It presents a novel spectral decomposition technique for astrometric data analysis based on vector spherical harmonics, highlighting its theoretical and practical benefits.

Findings

Identified systematic effects in FK5 compared to Hipparcos

Extracted rotation and dipole acceleration in Gaia QSO data

Demonstrated invariance properties and transformation behaviors

Abstract

Comparison of stellar catalogues with position and proper motion components using a decomposition on a set of orthogonal vector spherical harmonics. We show the theoretical and practical advantages of this technique as a result of invariance properties and the independence of the decomposition from a prior model. We describe the mathematical principles used to perform the spectral decomposition, evaluate the level of significance of the multipolar components and examine the transformation properties under space rotation. The principles are illustrated with a characterisation of the systematic effects in the FK5 catalogue compared to Hipparcos and with an application to the extraction of the rotation and dipole acceleration in the astrometric solution of QSOs expected from Gaia.