Context. The existence of supermassive black hole binaries (SMBHBs) is predicted by various cosmological and evolutionary scenarios for active galactic nuclei. These objects are considered as contributors into the gravitational wave (GW) background, as well as emitters of discrete GW bursts. Yet, SMBHBs remain a rather elusive class of extragalactic objects. Aims. Previously we have identified the quasar J2102+6015 as a potential SMBHB system on the basis of absolute astrometric very long baseline interferometry (VLBI) monitoring. Here we present another case, the source J0204+1514, exhibiting a similar oscillating astrometric pattern. Our aim is to analyse the evolution of SMBHBs as generators of GW and provide a physical 'multi-messenger'link between astrometric manifestation in the radio domain and GW emission. Methods. We analysed the available archive VLBI astrometry data that resulted in the detection of astrometric oscillations in the source J0204+1514. We assume these oscillations to be manifestations of orbital motion in a binary system. We estimated the parameters of the suspected SMBHB in this source and applied basic theoretical models to project its evolution towards coalescence. We also developed a simplified 'toy'model of SMBHBs consistent with the discovered astrometric oscillations and made quantitative predictions of GW emission of such sources using the case of J0204+1514 as an example potentially applicable to other SMBHBs. Results. We provide observational evidence of astrometric oscillations in the source J0204+1514. As an ad hoc result, we also provide a re-assessed estimate of the redshift of J2102+6015, z = 1.42. A toy model of the object containing a SMBHB with parameters consistent with the observed astrometric oscillations of the source J0204+1514 as an example enables us to consider GW emission as the cause of the system's orbital evolution. Conclusions. We conclude that astrometric VLBI monitoring has an appreciable potential for future detections of SMBHBs that could become multi-messenger targets for both electromagnetic (in radio domain) and GW astronomy. To outline the contours of a future physical model connecting SMBHB evolution with detectable GW manifestations, we present a toy model and, as an example, apply this toy model to the astrometrically oscillating source J0204+1514 described in this work. We also provide a justification for aiming future space-borne VLBI missions at direct imaging of SMBHBs as a synergistic contribution into future multi-messenger studies involving prospective GW facilities.

There is still a limited number of high-redshift (z > 3) active galactic nuclei (AGNs) whose jet kinematics have been studied with very long baseline interferometry (VLBI). Without a dedicated proper motion survey, regularly conducted astrometric VLBI observations of bright radio-emitting AGN with sensitive arrays can be utilized to follow changes in the jets, by means of high-resolution imaging and brightness distribution modelling. Here, we present a first-time VLBI jet kinematic study of NVSS J080518 + 614423 (z = 3.033) and NVSS J165844-073918 (z = 3.742), two flat-spectrum radio quasars that display milliarcsecond-scale jet morphology. Archi v al astrometric observ ations carried out mainly with the Very Long Baseline Array, supplemented by recent data taken with the European VLBI Network, allowed us to monitor changes in their radio structure in the 7.6-8.6 GHz frequency band, covering almost two decades. By identifying individual jet components at each epoch, we were able to determine the apparent proper motion for multiple features in both sources. Apparent superluminal motions range (1-14) c, and are found to be consistent with studies of other high-redshift AGN targets. Using the physical parameters derived from the brightness distribution modelling, we estimate the Doppler-boosting factors (δ≈11.2 and δ≈2.7), the Lorentz factors (Γ ≈7.4 and Γ ≈36.6), and the jet viewing angles (θ≈4.4°and θ≈8.0°), for NVSS J080518 + 614423 and NVSS J165844-073918, respectively. The data revealed a stationary jet component with negligible apparent proper motion in NVSS J165844-073918.

Radio-loud quasars at high redshift (z ≥ 4) are rare objects in the universe and rarely observed with Very Long Baseline Interferometry (VLBI). But some of them have flux density sufficiently high for monitoring of their apparent position. The instability of the astrometric positions could be linked to the astrophysical process in the jetted active galactic nuclei in the early universe. Regular observations of the high-redshift quasars are used for estimating their apparent proper motion over several years. We have undertaken regular VLBI observations of several high-redshift quasars at 2.3 GHz (S band) and 8.4 GHz (X band) with a network of five radio telescopes: 40 m Yebes (Spain), 25 m Sheshan (China), and three 32 m telescopes of the Quasar VLBI Network (Russia)—Svetloe, Zelenchukskaya, and Badary. Additional facilities joined this network occasionally. The sources have also been observed in three sessions with the European VLBI Network in 2018-2019 and one Long Baseline Array experiment in 2018. In addition, several experiments conducted with the Very Long Baseline Array in 2017-2018 were used to improve the time sampling and the statistics. Based on these 37 astrometric VLBI experiments between 2017 and 2021, we estimated the apparent proper motions of four quasars: 0901+697, 1428+422, 1508+572, and 2101+600.

The powerful high-redshift quasar J2102+6015 (at z = 4.575) may provide useful information for studying supermassive black hole growth, galaxy evolution and feedback in the early Universe. The source has so far been imaged with very-long-baseline interferometry (VLBI) at 2/8 GHz (S/X) bands only, showing complex compact structure. Its total radio spectrum peaks at ∼ 6 GHz in the rest frame. There is no sign of Doppler-boosted jet emission, and the separation of the two major features in its east-west oriented structure spanning ∼ 10 milliarcseconds does not change significantly on a timescale longer than a decade. However, VLBI astrometric monitoring observations suggest quasi-periodic (∼ 3 yr) variation in its absolute position. J2102+6015 is presumably a young radio source with jets misaligned with respect to the line of sight. Here we briefly report on our new high-resolution imaging observations made with the European VLBI Network (EVN) at 5 and 22 GHz frequencies in 2021 June, and give an overview of what is currently known about this peculiar, distant jetted active galactic nucleus.

We present and briefly discuss results of several studies of the source J2102+6015 with tentatively defined redshift z = 4.575 which demonstrates unusual properties in imaging and astrometric VLBI observations. Its properties might be considered as indications on the supermassive black hole binary which can be considered as a so far rare example of a high-redshift source of known electromagnetic and, possibly, predictable gravitational wave emissions.