Plasma streaming from the distant blazar 3C 345 has been reconstructed as a continuous, high-resolution movie, allowing astronomers to measure how the jet’s flow changes from place to place rather than tracking only its brightest moving features. The result also challenges the idea that those bright features are traveling shock waves.
The new approach, called kine, was designed to solve a basic problem in very long baseline interferometry, or VLBI. Radio telescopes can resolve structures in powerful jets launched by supermassive black holes, but conventional imaging generally produces separate pictures from individual observations. That makes it difficult to follow rapid or irregular changes in the source at high resolution.
Kine instead treats the observations as pieces of a single evolving scene. It uses a neural representation of the source that takes position and time as inputs and learns a continuous description of the radio emission. The resulting model can be sampled at times between actual observations, while information from multiple epochs is used simultaneously during reconstruction.
The researchers demonstrated the method using 116 observations of the blazar 3C 345 made at 15 GHz with the Very Long Baseline Array between 1995 and 2022 as part of the MOJAVE monitoring program. 3C 345 has a relativistic jet extending about 13 milliarcseconds on the reconstructed images. Its inner jet travels westward from a bright compact core before becoming a diffuse plume that bends northward.
The reconstruction reaches an average effective resolution of about 113 microarcseconds and a dynamic range of roughly 5.1 × 10⁵. In comparisons with traditional CLEAN imaging, the dynamic reconstruction produced about 140 times the dynamic range of the conventional images.
The authors emphasize that these gains depend on the quality and amount of observational data rather than representing a fixed improvement independent of the dataset. Tests using synthetic observations modeled on the 3C 345 data found effective dynamic-image resolutions between about 100 and 125 microarcseconds, with an average of 113 microarcseconds.
The movie reveals the jet’s local flow
The continuous reconstruction makes it possible to apply an image-analysis technique known as optical flow. Rather than identifying individual bright blobs and measuring how far they travel between observations, optical flow estimates the local motion of emission across the reconstructed video.
That distinction matters for 3C 345 because the jet contains both a continuous plasma flow and occasional bright, compact features. In the reconstructed movie, material is continuously expelled from the core. Some bright features initially move ballistically, then turn toward the jet axis roughly 2–3 milliarcseconds from the core before disappearing into the diffuse plume.
The optical-flow measurements show that the fastest average apparent flow reaches about 12 times the speed of light, with an uncertainty of 0.2 times the speed of light, between 1 and 3 milliarcseconds from the core in the southern part of the jet. The average apparent speed falls to about 9–11c within the first 5 milliarcseconds and to about 5–8c farther out in the diffuse emission. For the reported viewing angles, the maximum apparent speed corresponds to a physical speed of about 0.997c.
The spread in measured apparent speeds is also substantial. The standard deviation ranges from about 3c to 6c without a strong dependence on location, which the authors interpret as evidence that the plasma flow is turbulent and undergoes significant changes in apparent speed.
The reconstructed velocity field can also be integrated to trace trajectories through the jet. When the researchers used it to follow the bright components that had previously been measured with Gaussian model fitting, the resulting trajectories agreed with those earlier measurements. That agreement provided a check on the optical-flow analysis while allowing it to go beyond discrete components and measure the flow between them.
Synthetic-data tests likewise found that kine combined with optical flow could accurately recover apparent velocities in the 3C 345 dataset up to at least about 23c, above the maximum speeds measured in the real observations.
Bright features move almost as fast as the surrounding flow
That comparison produces the study’s central physical result.
The bright components in the inner jet have apparent speeds of about 10–13c. The average bulk plasma flow in the same region is about 9–12c. The two measurements are therefore of the same order.
This is important because the bright components in 3C 345 have previously been interpreted as traveling shocks. A shock is a pattern moving through the plasma, so its pattern speed need not be the same as the speed of the material itself. If the features were strong shocks, the researchers would expect a substantial difference between the shock’s pattern speed and the underlying plasma flow.
They do not see that difference in 3C 345.
Instead, the comparable speeds suggest that the bright components may be localized regions within the plasma with greater emissivity rather than strongly shocked regions. The authors note, however, that similar pattern and flow speeds can also occur under certain conditions in which protons are not highly relativistic.
Polarization provides another test of the shock idea
The researchers then turned to the jet’s polarization to test that interpretation.
Kine reconstructs the Stokes parameters needed to follow the evolution of linear polarization as well as total intensity. Across multiple epochs, the electric vector position angles show a recurring pattern: they align with the jet along its spine and become perpendicular near the jet boundary. The pattern persists in the time-averaged polarization map.
The polarization structure is consistent with a long-lasting toroidal magnetic field threading the jet, potentially produced by a large-scale helical field dominated by its toroidal component, according to the authors. When bright features are ejected, they disrupt the underlying polarization pattern as they travel through the jet.
A strong shock should leave another signature. If a shock compresses the magnetized plasma, the compression can increase the ordering of the magnetic field and produce locally higher fractional linear polarization in the shocked region. Given the predominantly toroidal magnetic-field pattern inferred for 3C 345, the researchers would therefore expect the bright features to coincide with localized increases in fractional polarization if they were strong shocks.
That correlation is absent.
The peaks in fractional polarization do not spatially coincide with the bright features in total intensity. The passage of a bright feature slightly disrupts the surrounding polarization pattern, but it does not produce the expected local polarization peak. This further disfavors the strong-shock interpretation.
Combining the polarization evidence with the comparison between component and bulk-flow speeds, the researchers interpret the bright features as regions of enhanced emissivity associated with locally amplified magnetic fields. They propose that plasma turbulence increases the magnetic pressure in these regions and that Doppler boosting further increases their brightness when they are ejected southward. This is presented as an interpretation of the observations rather than a directly measured property of the features.
What the new imaging changes
The distinction between a bright moving feature and the plasma carrying it could not be made with the earlier component-based analysis alone. Gaussian model fitting measures the motion of discrete components, but it does not provide the underlying flow speed between those components.
Kine’s continuous representation changes that by combining information from many observations and producing a smooth video that can be analyzed locally in both space and time. Its neural network represents the brightness distribution continuously, while the simultaneous treatment of epochs helps recover structures that individual observations may not constrain as well.
The validation tests also showed that the method can interpolate between observations while preserving motion. For data with the coverage and quality of the 3C 345 observations, reliable motion-preserving interpolation was possible for frames up to six months from the nearest observation. The longest interpolation used in the study was 5.7 months.
On the real 3C 345 observations, the average dynamic range was about 3.6 × 10³ for CLEAN, 4.9 × 10⁴ for static kine reconstruction and 5.1 × 10⁵ for dynamic kine reconstruction. The corresponding measured resolutions were 141 microarcseconds for static kine and 106 microarcseconds for dynamic kine, compared with a nominal CLEAN resolution of 475 microarcseconds. The authors regard the synthetic-data tests as the more conservative basis for their resolution conclusions because the real-data comparison lacks a known ground truth.
The method is not limited to 3C 345. The authors describe kine as applicable to VLBI datasets that are static or dynamic, single-epoch or multi-epoch, and fully polarimetric. It was originally developed for horizon-scale observations of Sagittarius A* with the Event Horizon Telescope, where source variability can occur on timescales shorter than the observation itself.
For the 116 epochs of 3C 345 data, optimizing the network took about 1.3 hours on four NVIDIA A100 GPUs. The authors also report that processing four days of M87* Event Horizon Telescope observations took about 20 minutes on one A100.
For 3C 345, the immediate result is a different picture of what its moving bright features represent. The observations do not provide evidence that those features are strongly shocked regions. Instead, their speeds, polarization behavior and relationship to the surrounding flow lead the researchers to interpret them as Doppler-boosted regions of enhanced emissivity associated with local increases in magnetic pressure. The authors stress that this conclusion challenges the current shock models for 3C 345 specifically, while systematic application of the technique to other sources will be needed to determine whether the result extends beyond this jet.
The study was published in Nature.
