<div>The conventional VLBI relativistic delay model refers to the time epoch when the signal passes one of two stations of an interferometer baseline. Before, 2002, this model was used as part of the correlation procedure. Since 2002, a new correlation procedure has been adopted in which the VLBI group delays refers to the time epoch of signal passage at the geocenter. A new alternative to the conventional VLBI model delay should be introduced to follow that change because the discrepancy between the two relativistic geometrical delay models is up to 6 ps for ground-based VLBI experiments. In addition, a miscalculation of the signal arrival moment to the geocentre or the "reference station" may cause a larger modelling error (up to 50 ps) which would directly affect the radio telescope positions with a corresponding formal error of 15 mm. This is particularly essential for upcoming geodetic VLBI observations as the final goal of 1-mm accuracy needs to be achieved.</div> Presented at the Journées 2023: Temps et Relativité Générale (Time and General Relativity)

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 μas 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 μas. 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. We developed the extended group relativistic delay model to incorporate the additional parallactic effect for radio sources at distances less than 1 Mpc and found that the apparent annual signal might appear due the non-orthogonality of the fundamental axes, which are defined by the positions of the reference radio sources themselves. Unlike the conventional parallactic ellipse, the apparent annual effect in this case appears as a circular motion for all objects independently of their ecliptic latitude. The measured amplitude of this circular effect is within a range of 10–15 μas that is consistent with the ICRF3 stability of the fundamental axis. This annual circular effect could also arise if a Gödel-type cosmological metric were applied, suggesting that, in the future, this phenomenon could be used to indicate global cosmic rotation. <b>Citation:</b> Titov O, Osetrova A. Parallactic delay for geodetic VLBI and non-orthogonality of the fundamental axes. <i>Publications of the Astronomical Society of Australia</i>. 2024;41:e111. doi:10.1017/pasa.2024.111