VLBI Diagnostics of Off-axis Jets in Radio Flares of Tidal Disruption Events

Abstract: The origin of late-time radio flares in tidal disruption events remains unclear. In particular, the peculiar radio flare observed in AT2018hyz has motivated two leading scenarios: a delayed outflow launched $\sim1000\,\rm days$ after discovery, or an off-axis relativistic jet directed far from our line of sight. Very long baseline interferometry (VLBI) imaging provides the most direct way to distinguish between these scenarios. In this paper, we calculate synthetic radio images for both models and examine their observational signatures. The motion of the emission centroid is the most powerful diagnostic for breaking the degeneracy. In the delayed-outflow scenario, the centroid motion is confined within a non-relativistic distance, whereas in the off-axis jet scenario it exhibits apparent superluminal motion. Detecting such superluminal motion would therefore provide a smoking-gun signature of the off-axis jet interpretation. We also find that the jet image exhibits characteristic features, including a non-monotonic evolution of the image aspect ratio. These results are expected to be generic and applicable to other jetted explosions, such as microquasars and gamma-ray bursts.