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

This paper proposes that Very Long Baseline Interferometry (VLBI) imaging can definitively distinguish between delayed outflow and off-axis jet scenarios for late-time radio flares in tidal disruption events by detecting the presence of apparent superluminal motion in the emission centroid, which serves as a unique signature of the off-axis jet model.

Original authors: Tatsuya Matsumoto

Published 2026-07-22

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CC BY 4.0

Original authors: Tatsuya Matsumoto

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a grand, cosmic stage where stars sometimes meet their dramatic end. When a star wanders too close to a supermassive black hole, the black hole's gravity can rip the star apart in a violent event called a Tidal Disruption Event (TDE). It's like a cosmic spaghetti monster slurping up a noodle. Usually, these events are bright and short-lived, but sometimes, they throw a surprise party: a radio flare that appears a thousand days after the initial explosion, long after everyone thought the show was over.

To figure out what's causing these late-night radio parties, astronomers use two main ideas. One idea is that the black hole was just slow to start cooking, launching a slow-moving cloud of gas (an outflow) a thousand days late. The other idea is that a super-fast, laser-beam jet of particles was launched right at the start, but it was pointed in the wrong direction, away from Earth. Because it was pointed away, we couldn't see it until it slowed down enough for its light to catch up to us. The big question is: which one is it? The answer matters because it tells us how black holes behave and how they launch these powerful jets. To solve this mystery, we need to look at the "footprints" these events leave on the sky, not just how bright they are.

In this paper, the author, Tatsuya Matsumoto, acts like a cosmic detective creating a simulation to see what these two suspects would look like if we could take a high-resolution photo of them with a giant telescope called VLBI (Very Long Baseline Interferometry). Instead of just guessing, he built a computer model to generate "synthetic radio images" for both the "late slow cloud" and the "early fast jet pointed away" scenarios.

The main finding is that the two suspects leave very different footprints, specifically in how the center of their light moves across the sky. If it's the "late slow cloud," the center of the light stays put, wobbling only a tiny bit like a slow-moving boat. But if it's the "early fast jet pointed away," the center of the light zooms across the sky faster than the speed of light! This is called "superluminal motion," and it's a trick of perspective that only happens with things moving at near-light speeds. The paper suggests that spotting this super-fast movement would be the "smoking gun" proof that the event was actually a jet, not a delayed cloud.

The paper also finds that the shape of the jet's image changes in a weird, non-boring way. At first, the jet looks like a round disk, similar to the slow cloud. But as time goes on, the jet's image stretches out and changes its shape, becoming elongated in a specific direction before settling down. This changing shape is another clue that helps tell the two scenarios apart.

The author is careful to note that these results come from computer simulations, not from having actually taken the photo yet. While the math is solid, we haven't caught the culprit in the act with a telescope just yet. However, the paper argues that if we can get a high-resolution image of events like AT2018hyz (the specific event that sparked this mystery), we should be able to see this super-fast motion or the changing shape. If we do, it will confirm that the universe is launching powerful jets even when they seem to be hiding from us. If we don't see it, then the "late slow cloud" theory might be the winner. Until we look, the mystery remains, but this paper gives us the exact map of what to look for.

Problem Statement
The physical origin of late-time radio flares in tidal disruption events (TDEs) remains uncertain. This ambiguity is particularly acute for the event AT2018hyz, which exhibited a sudden, luminous radio flare approximately 1000 days after its optical discovery. Two primary scenarios have been proposed to explain this phenomenon: (1) a delayed outflow launched roughly 700–1000 days after the initial disruption, potentially driven by accretion disk state transitions; and (2) an off-axis relativistic jet launched near the time of discovery but oriented far from the observer's line of sight, whose emission was initially suppressed by relativistic beaming effects. Current analyses relying solely on radio light curves and spectra cannot distinguish between these models, as both can reproduce the observed temporal and spectral evolution.

Methodology
The authors employ a semi-analytical framework to compute synthetic radio images, light curves, and spectra for both the delayed outflow and off-axis jet scenarios. The methodology assumes a piecewise spherical approximation for the outflow dynamics, where fluid elements evolve as part of a spherically symmetric flow. The emitting region is modeled as a thin shell sweeping up a circumnuclear medium (CNM) with a power-law density profile.

Key components of the calculation include:

Dynamics: The outflow evolution is calculated based on energy conservation, accounting for the transition from relativistic to Newtonian regimes. For jetted scenarios, lateral expansion is neglected, assuming the jet maintains its original top-hat geometry.
Radiative Transfer: The observed flux is derived by integrating synchrotron emissivity over the emitting volume, explicitly accounting for cosmological redshift and the equal-arrival-time surface (EATS) effect. The intensity distribution is calculated using the radiative transfer equation under the thin-shell approximation.
Imaging: Synthetic radio intensity maps are generated at 5 GHz. The study focuses on the evolution of the emission centroid position and the image aspect ratio (the ratio of widths in the direction of motion versus perpendicular to it) as primary diagnostics.

Key Contributions and Results
The paper presents synthetic radio images and light curves for AT2018hyz under both proposed models, calibrated to match observed light curve slopes and spectral peaks. The primary findings are:

Centroid Motion as a Diagnostic: The motion of the emission centroid is identified as the most powerful diagnostic for breaking the degeneracy between the two scenarios.
- Delayed Outflow: In the delayed outflow scenario, the emission centroid remains confined to the origin (or moves within a non-relativistic distance $\lesssim c\beta T$ ), reflecting the spherical symmetry of the outflow.
- Off-axis Jet: In the off-axis jet scenario, the approaching jet exhibits apparent superluminal motion. The emission centroid moves outward at superluminal speeds before the jet decelerates to the Newtonian regime. As the counter-jet eventually becomes visible and contributes to the emission, the centroid moves backward, eventually returning toward the origin. Detecting such superluminal motion would provide a "smoking-gun" signature of the off-axis jet interpretation.
Image Morphology and Aspect Ratio:
- The delayed outflow produces a disk-like image with limb brightening, maintaining a roughly circular shape until deceleration significantly alters the expansion rate.
- The off-axis jet initially appears as a filled disk but undergoes a characteristic non-monotonic evolution in its aspect ratio. As the jet decelerates from relativistic to Newtonian speeds, the geometry of the EATS changes, causing the image to elongate perpendicular to the motion (Y-direction) before the aspect ratio reaches a minimum and subsequently increases, asymptotically approaching a constant value determined by the viewing angle ( $\cos \theta_{obs}$ ).
Parameter Constraints:
- For the delayed outflow model, the authors infer a kinetic energy of $\sim 10^{52}$ erg, consistent with a Newtonian outflow launched $\sim 700$ days post-discovery.
- For the off-axis jet model, the fit requires a significantly higher isotropic-equivalent energy ( $\sim 10^{56}$ erg) to sustain relativistic motion until $\sim 2000$ days. While this energy is larger than typical jetted TDEs, it is required by the observation that the jet has not yet decelerated to the Newtonian phase.

Significance
The paper asserts that Very Long Baseline Interferometry (VLBI) imaging offers the most direct method to distinguish between delayed outflows and off-axis jets in TDEs. The detection of superluminal centroid motion would definitively confirm the off-axis jet scenario. Furthermore, the authors argue that these results are generic and applicable to other relativistic transients, such as microquasars and gamma-ray bursts, due to the self-similar nature of blast wave evolution. The study also suggests that if VLBI resolution is insufficient to resolve the source structure, precise astrometry of the emission centroid using optical or infrared telescopes (e.g., JWST) could still detect the characteristic motion, provided the source is sufficiently bright to overcome stellar contamination in the host galaxy's nuclear region.

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