Parallactic delay for geodetic VLBI and non-orthogonality of the fundamental axes

The Gaia optical astrometric mission has measured the precise positions of millions of objects in the sky, including extragalactic sources also observed by Very Long Baseline Interferometry (VLBI). In the recent Gaia EDR3 release, an effect of negative parallax with a magnitude of approximately $-17$ $μ$ as was reported, presumably due to technical reasons related to the relativistic delay model. A recent analysis of a 30-yr set of geodetic VLBI data (1993-2023) revealed a similar negative parallax with an amplitude of $-15.8 ± 0.5$ $μ$ as. Since both astrometric techniques, optical and radio, provide consistent estimates of this negative parallax, it is necessary to investigate the potential origin of this effect.