Very-long-baseline interferometry study of the flaring blazar TXS 1508+572 in the early Universe

High-redshift blazars provide valuable input to studies of the evolution of active galactic nuclei (AGN) jets and provide constraints on cosmological models. Detections at high energies ($0.1< E <100$ GeV) of these distant sources are rare, but when they exhibit bright gamma-ray flares, we are able to study them. However, contemporaneous multi-wavelength observations of high-redshift objects ($z>4$) during their different periods of activity have not been carried out so far. An excellent opportunity for such a study arose when the blazar TXS\,1508+572 ($z=4.31$) exhibited a gamma -ray flare in 2022 February in the $0.1-300$ GeV range with a flux 25 times brighter than the one reported in the in the fourth catalog of the Fermi Large Area Telescope. Our goal is to monitor the morphological changes, spectral index and opacity variations that could be associated with the preceding gamma -ray flare in TXS\,1508+572 to find the origin of the high-energy emission in this source. We also plan to compare the source characteristics in the radio band to the blazars in the local Universe ($z<0.1$). In addition, we aim to collect quasi-simultaneous data to our multi-wavelength observations of the object, making TXS\,1508+572 the first blazar in the early Universe ($z>4$) with contemporaneous multi-frequency data available in its high state. In order to study the parsec-scale structure of the source, we performed three epochs of very-long-baseline interferometry (VLBI) follow-up observations with the Very Long Baseline Array (VLBA) supplemented with the Effelsberg $100$-m Telescope at $15$, $22$, and $43$\,GHz, which corresponds to $80$, $117$, and $228$\,GHz in the rest frame of TXS\,1508+572 . In addition, one $86$\,GHz ($456$\,GHz) measurement was performed by the VLBA and the Green Bank Telescope during the first epoch. We present total intensity images from our multi-wavelength VLBI monitoring that reveal significant morphological changes in the parsec-scale structure of TXS\,1508+572 . The jet proper motion values range from $0.12$ mas/yr to $0.27$ mas/yr, which corresponds to apparent superluminal motion $ app -- $32.2\,c$. This is consistent with the high Lorentz factors inferred from the spectral energy distribution (SED) modeling for this source. The core shift measurement reveals no significant impact by the high-energy flare on the distance of the $43$-GHz radio core with respect to the central engine, that means this region is probably not affected by e.g., injection of new plasma as seen in other well-studied sources like CTA\,102. We determine the average distance from the $43$-GHz radio core to the central supermassive black hole to be $46.1 that corresponds to a projected distance of $0.32 pc. We estimate the equipartition magnetic field strength $1$ pc from the central engine to be on the order of $0.8$ G, and the non-equipartition magnetic field strength at the same distance to be about $1.7$ G, which values agree well with the magnetic field strength measured in low to intermediate redshift AGN. Based on our VLBI analysis, we propose that the gamma -ray activity observed in February 2022 is caused by a shock-shock interaction between the jet of TXS\,1508+572 and new plasma flowing through this component. Similar phenomena have been observed, for example, in CTA\,102 in a shock-shock interaction between a stationary and newly emerging component. In this case, however, the core region was also affected by the flare as the core shift stays consistent throughout the observations.