Observing the inner parsec-scale region of candidate neutrino-emitting blazars

Context. Many questions on the nature of astrophysical counterparts of high-energy neutrinos remain unanswered. There is increasing evidence of a connection between blazar jets and neutrino events, with the flare of the γ-ray blazar TXS 0506+056 in spatial and temporal proximity of IC 170922A representing one of the most outstanding associations of high-energy neutrinos with astrophysical sources reported so far. Aims. With the purpose of characterising potential blazar counterparts to high-energy neutrinos, we analysed the parsec-scale regions of γ-ray blazars in spatial coincidence with high-energy neutrinos, detected by the IceCube Observatory. Specifically, we intended to investigate peculiar radio properties of the candidate counterparts related to the neutrino production, such as radio flares coincident to the neutrino detection or features in jets morphology (limb brightening, transverse structures). Methods. We collected multi-frequency very-long-baseline interferometry (VLBI) follow-up observations of candidate counterparts of four high-energy neutrino events detected by IceCube between January 2019 and November 2020, with a focus on γ-ray associated objects. We analysed their radio characteristics soon after the neutrino arrival in comparison with archival VLBI observations and low-frequency radio observations. We discussed our results with respect to previous statistical works and studies on the case of TXS 0506+056. Results. We identified and analysed in detail five potential neutrino emitting blazars. Our results suggest an enhanced state of activity for one source, PKS 1725+123. However, the lack of adequate monitoring prior to the neutrino events was a limitation in tracing radio activity and morphological changes in all the sources. Conclusions. We suggest that PKS 1725+123 is a promising neutrino source candidate. For the other sources, our results alone do not reveal a strong connection between the radio activity state at the neutrino arrival. A larger number of VLBI and multi-wavelength follow-up observations of neutrino events is now essential to understand the neutrino production mechanisms in astrophysical sources.