Functional principal component analysis of radio-optical reference frame tie

TL;DR

This paper applies functional principal component analysis with vector spherical harmonics to evaluate and improve the robustness of the celestial reference frame link between Gaia and ICRF, identifying key deficiencies and guiding future enhancements.

Contribution

It introduces a novel application of functional principal component analysis to assess and optimize the Gaia-ICRF reference frame tie, highlighting the weakest link components.

Findings

Identifies the most uncertain vector fields on the sphere affecting the frame link.

Provides a robustness measure for least-squares solutions in reference frame modeling.

Guides future development of the ICRF for improved accuracy.

Abstract

The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs to be anchored in the radio-based International Celestial Reference Frame (ICRF) to provide a referenced and quasi-inertial celestial coordinate system. The link between the two fundamental frames is realized through two samples of distant extragalactic sources, mostly AGNs and quasars, but only the smaller sample of radio-loud ICRF sources with optical counterparts is available to determine the mutual orientation. The robustness of this link can be mathematically formulated in the framework of functional principal component analysis using a set of vector spherical harmonics to represent the differences in celestial positions of the common objects. The weakest eigenvectors are computed, which describe the greatest deficiency of the link. The deficient or poorly determined terms are specific vector fields on the sphere which carry the largest errors of absolute astrometry using Gaia in reference to the ICRF. This analysis provides guidelines to the future development of the ICRF maximizing the accuracy of the link over the entire celestial sphere. A measure of robustness of a least-squares solution, which can be applied to any linear model fitting problem, is introduced to help discriminate between reference frame tie models of different degrees.