© The Authors 2025

1. Introduction

Some supermassive black holes at the center of galaxies generate collimated jets of ionized relativistic particles, which are accelerated by the strong magnetic fields surrounding the black hole and the accretion disk. These highly energetic and luminous jets propagate through the host galaxy and beyond, interacting with the interstellar (ISM), intergalactic, and intracluster media (ICM). Temperature, density, and pressure differences between the plasma in the jet and the surrounding medium influence the jet’s expansion by altering its shape and profile and by affecting its direction and expansion speed.

The relativistic jet in the radio galaxy 3C 84 (NGC 1275), located in the Perseus Cluster, is a valuable source of information about the interactions between the ICM and the parsec-scale jet. NGC 1275 is at the center of a strong cooling flow cluster, where large amounts of inflowing gas are reheated by the galaxy’s active nucleus. The galaxy also displays bright X-ray emission (Forman et al. 1972), and observations by Chandra have shown pairs of opposed bubbles in the ICM located at different distances and directions relative to the 3C 84 radio source (Fabian et al. 2003). A proposed explanation for these structures is that they are inflated by a precessing and restarting of a jet–counterjet pair (Dunn et al. 2006).

3C 84 is also a variable radio source (Dent 1966; Pauliny-Toth & Kellermann 1966) and has been observed since the 1950s through multiple Very Long Baseline Interferometry (VLBI) observations at both millimeter and centimeter wavelengths. Giovannini et al. (2018) and Savolainen et al. (2023) provide a historical overview of the radio observations of 3C 84, of which we give a short summary here. The source presents various lobe-like structures south and north of the core, on parsec (e.g., Walker et al. 2000; Asada et al. 2006) to kiloparsec (Pedlar et al. 1990) scales, which may indicate a repeatedly restarting jet. Observations at the parsec scale from the 2010s have shown the presence of a dim radio lobe (C2; Nagai et al. 2010) and a bright radio lobe (C3), the latter of which is connected to the core (see the top-left panel in our Fig. 2; Nagai et al. 2014). The C2 component was ejected in the early 1960s during a period of increasing brightness that lasted until the mid 1980s, before dropping in the 1990s and early 2000s (Nesterov et al. 1995). C3 was emitted around 2003 (Suzuki et al. 2012; Nagai et al. 2017) during a second period of high brightness. While C3 propagated from the core through a limb-brightened structure, the propagation of C2 happened through a jet with a centrally peaked morphology. In more recent years, higher-resolution observations have been able to resolve the internal structure of the parsec-scale jet in 3C 84. Giovannini et al. (2018) presented results at 22 GHz from a global array of ground antennas plus the space antenna RadioAstron (Kardashev & Khartov 2013). The reconstructed image clearly shows strong limb-brightening and a wide opening angle near the core, followed by a quasi-cylindrical jet profile. The jet ends with a bright spot with surrounding diffuse emission. Giovannini et al. (2018) suggest that the cylindrical profile may be due to the jet connecting C1 to C3 being embedded in a uniform-pressure cavity carved by past activity of the jet. This is supported by other observations by RadioAstron at 5 GHz (Savolainen et al. 2023), which show that the C2 and C3 components are both surrounded by low-intensity emission from a cocoon-like structure. Savolainen et al. (2023) discuss that, in the interaction between the C3 structure and the ISM, energy is transferred to the ISM, heating the gas that forms the cocoon. They also suggest that the cocoon-like structure could be caused by the jet moving through a multiphase medium consisting of gas clouds of different sizes and densities. The embedding of the jet in a clumpy medium is supported by results from Nagai et al. (2017) and Kino et al. (2018, 2021). In particular, Kino et al. (2021) analyzed 43 GHz images of 3C 84 from the Very Long Baseline Array (VLBA) from 2012 to 2020. They tracked the motion of a hot spot and, in 2016−2017, observed a year-long frustration phase, during which the hot spot followed a circular trajectory after reaching the edge of C3, rather than propagating farther through the jet. They attribute this event to a collision between the head of the jet and a compact dense cloud. After the collision, the jet breaks through the cloud, deviating its expansion direction to the west and transitioning from an FR II- to FR I-class radio lobe morphology. However, despite the significant number of studies, observations of 3C 84 have provided either repeated images of the jet at low resolution (Kino et al. 2018, 2021) or hard-to-repeat single-epoch images at high resolution (Giovannini et al. 2018). This hinders a proper study of the kinematics of the plasma in the jets and the dynamics of the jet expansion.

In this work we present a reimaging of all 121 VLBA observations of 3C 84 at 43 GHz obtained by the BEAM-ME monitoring program (Jorstad & Marscher 2016) from 2010 to 2023 obtained using the regularized maximum likelihood (RML) imaging method eht-imaging (Chael et al. 2018). With eht-imaging, we obtained images of the parsec-scale jet at a resolution of ∼80 μas. This is ∼2−3 times higher than the nominal beam used to convolve CLEAN images, whose average across different epochs is (280, 150) μas. RML methods produce super-resolved images by incorporating reasonable prior assumptions that regularize the image. These methods have proven to achieve higher fidelity at super-resolution than CLEAN (see, e.g., Fuentes et al. 2023). Thanks to the combination of the super-resolving power of RML methods and the constant monitoring by the BEAM-ME program, we were able to observe, for the first time, the evolution of the overall and internal structure dynamics of the parsec-scale jet, over a 12-year period. The images we present resolve the hot spots and the internal structure of the jet, as well as the connection between the limb-brightened structure and the core. At this resolution, it is also possible to resolve the front of the jet head, discerning the expansion of the jet from the motion of components through the jet. We considered the source redshift, z, to be 0.0176 (Strauss et al. 1992). In continuity with previous publications on 3C 84, we assumed a Λ cold dark matter cosmology with H₀ = 70.7 km s⁻¹ Mpc⁻¹, Ω_M = 0.27, and Ω_Λ = 0.73; this means that 1 mas in the image plane corresponds to 0.35 pc.

In Sect. 2 we provide details of the observed data and explain the method used to image them. In Sect. 3 we present the imaging results, provide a quantitative estimate of the jet’s speed and direction, and discuss the evolution of the jet in the context of previous observations of the source. We summarize and discuss our results in Sect. 4.

2. Data and imaging

2.1. Observations

We analyzed data from the BEAM-ME monitoring program conducted by Boston University (previously named VLBA-BU-BLAZAR)¹, which observes multiple gamma-ray blazars and radio sources using the VLBA at 43 and 86 GHz (Jorstad & Marscher 2016). We focused on total intensity observations of the radio source 3C 84 in the Perseus cluster, at 43 GHz, conducted on a roughly monthly basis from late 2010 until early 2023, resulting in a total of 121 individual epochs.

The BEAM-ME data are already fully calibrated and self-calibrated to the CLEAN images provided in the archive. However, to avoid any bias from possible residual calibration errors or from the self-calibration, we chose to run the first imaging step using only closure quantities. The archival data were already time averaged with a 30 s interval, so no additional time averaging was performed before imaging.

2.2. Imaging procedure

The data were imaged using eht-imaging, a forward modeling imaging method for VLBI observations (Chael et al. 2018). This method defines the image as a discrete square matrix of flux density values, I = {I_ij}, and optimizes these values to minimize the objective function:

$$\begin{array}{c}\hfill J(\mathbf{I})={\displaystyle \sum _{\mathrm{D}}}{\alpha }_{\mathrm{D}}{\chi }_{\mathrm{D}}^2(\mathbf{I},\mathbf{d})-{\displaystyle \sum _{\mathrm{R}}}{\beta }_{\mathrm{R}}{S}_{\mathrm{R}}(\mathbf{I}),\end{array}$$(1)

where the first sum runs over the reduced χ² of different data products D computed from the image I and the observed data d, while the second sum runs over various regularizers R that impose additional correlations among pixel values, thus constraining the possible solutions to the ill-posed problem of VLBI imaging (The Event Horizon Telescope Collaboration 2019). The coefficients α_D and β_R that weight the data terms and the regularizers are hyperparameters of the method.

The imaging procedure followed these steps:

1. Iteratively apply eht-imaging’s optimization step, using only log closure amplitudes and closure phases as data products in the objective function. Stop the optimization when the reduced χ² of both data products decreases by less than 2% in a single step.

2. Perform self-calibration of amplitudes and phases to the obtained image, to correct potential residual station-based errors.

3. Reapply eht-imaging’s optimization steps, this time using both complex visibilities and closure quantities as data products in the objective function. Stop the optimization when the χ² of both data products decreases by less than 1%.

The eht-imaging’s optimization step mentioned in point 1 and 3 consists of alternating between a series of quasi-Newton gradient descent steps and blurring of the resulting image with a Gaussian kernel with a full width at half maximum (FWHM) equal to 1.5 times the nominal resolution of the array (∼150 μas). The blurring step prevents the optimizer from getting trapped in local minima of the objective function. The images obtained with this procedure provide a good fit to the data, with an average reduced visibility χ² of 1.61. We note that, in most cases, the images obtained after step 1 are very similar to those obtained after step 3, meaning that the closure quantities are sufficient to constrain the images and that self-calibration only provides small refinements to the final images. The gains obtained from the self-calibration step were negligible, which was expected since the archival data were already self-calibrated using CLEAN imaging.

2.2.1. Field of view.

The field of view was increased linearly from 5.1 mas for the earliest epoch to 13.2 mas for the latest one, following the growth of the emitting region in the jet, as seen in the archival CLEAN images. Accordingly, the number of pixels was increased from 170 to 440, while the pixel size remained constant at 30 μas².

2.2.2. Initialization image.

The initialization image for the optimization process was chosen to be an elliptical Gaussian with major axis rotated 6° clockwise from the north, with (FWHM_x, FWHM_y) values ranging linearly from (385, 1375) μas to (910, 3250) μas to match the average direction and increasing dimensions of the jet. For a few epochs (specifically, from April 30, 2022, to December 6, 2022), the optimizer would not converge if initialized to a Gaussian. We attribute this to the combination of a suboptimal coverage and a complex jet morphology, which could not be well approximated by a Gaussian. In these cases, we initialized the optimizer to the CLEAN image provided by the BEAM-ME program, blurred with a Gaussian kernel of FWHM equal to twice the nominal resolution of the array. We tested the effect of initializing with the CLEAN image instead of a Gaussian on the other epochs and found that the final image was not noticeably affected by the choice of prior image.

2.2.3. Regularizers.

We made minimal use of regularizers, since the uv coverage of the array is sufficiently dense. In step 1 of the imaging procedure, the total flux of the image cannot be constrained by closure amplitudes, so we used a flux regularizer to constrain it to the maximum amplitude of the shortest baseline. In both steps 1 and 2, we used the entropy regularizer to constrain the emission in the center of the image and the ℓ₁ regularizer to encourage sparsity, since significant portions of the images were expected to have no emission. The exact regularizers’ weights, along with other imaging parameters, are reported in Table 1.

2.2.4. Images.

Imaging results from all epochs are presented in Fig. 1 and in the corresponding online movie (Movie 1), while Fig. 2 shows the comparison between CLEAN and eht-imaging images for a few selected epochs. The eht-imaging images we obtained are consistent with the CLEAN images provided by the BEAM-ME program, but in higher resolution. This enables a more precise detection of the outlines of the bright limbs and the edge of the jet head, as well as the resolution of intra-jet features and the jet orientation at the subparsec scale.

Fig. 1. Radio source 3C 84 as observed from 2010 to 2023 by the VLBA at 43 GHz and imaged with eht-imaging. The black vertical lines mark the dates of the observation epoch corresponding to each image. The time evolution of the source is shown in the online movie (Movie 1).

Fig. 2. Comparison between images of radio source 3C 84 from VLBA observations at 43 GHz obtained with the CLEAN (left) and eht-imaging (right) imaging methods.

3. Jet analysis

The sequence of jet images in Fig. 1 reveals various features of the jet evolution. In the first images (corresponding to epochs in late 2010), the jet presents clear limb-brightening, with the two limbs originating from an unresolved core and undergoing a slight counterclockwise bending. The limb-brightened structure extends until the core, to which it connects at a high opening angle, confirming the analysis from Giovannini et al. (2018), which resolved the limb structure at a distance of 0.03 mas (or 350 gravitational radii de-projected). Over the years, the limb-brightening persists as the jet increases in length, reaching ∼4 times its initial size. A dim emission feature (C2) is evident in the bottom-right part of the jet in 2011−2013. From 2014, C2 gradually becomes dimmer and more elongated, as if dragged by the expanding C3 component. A single localized bright spot from C2 is still visible in 2015, before the component disappears into the diffuse emission on the right side of the jet, barely visible above the noise level until 2019. A detailed analysis of the C2 component is beyond the scope of the present paper, but future works may extract information about the energy exchange associated with its disappearance.

The jet launching direction changes over the years, slowly rotating counterclockwise from 2011 to 2015, slowly rotating back to the initial direction from 2015 to 2016, maintaining the same direction during 2017−2018, then drastically rotating clockwise from 2019 to 2022. From 2019, the core undergoes a severe twisting due to the clockwise rotation, which complicates its structure, while in 2017 a secondary component appears west of the core and persists until the end of the considered time window. A complex picture of the core was already described by Punsly et al. (2021), who modeled the core structure with two or three components aligned in the east-west direction. The 2019 twist is also reported by Park et al. (2024a), who describe the ejection of a knot east of the core (Paraschos et al. 2022) and track its motions as it abruptly changes direction toward the south. Park et al. (2024a) suggest that the knot’s deflection may be due to the jet colliding with a dense clumpy cloud. In our images, however, we do not see the ejection of an individual knot, but rather we observe emission appearing west of the core because of the twisting of the jet rails. This scenario also explains the apparent southward deflection of the knot, which moves along the preexisting jet structure.

Various components can be tracked moving along the jet (Hodgson et al. 2021), notably a bright spot is seen approaching the head of the jet, “bouncing” against it and then dissipating, in the time span between late 2015 and early 2017. Our results confirm the hot spot’s counterclockwise trajectory reported by Kino et al. (2021). However, our images show that the hot spot appears at the end of 2015 and dissipates at the beginning of 2018 as the jet pierces through the lobe. The 2015 hot spot’s flip and the 2018 hot spot’s breakout reported by Kino et al. (2021), should be attributed to a component mismatch caused by insufficient resolution.

At the end of 2010, the jet presents a straight morphology. However, a lobe begins to form in late 2011 and undergoes a significant expansion from early 2013 to early 2017. The inflation coincides with a slowdown in the jet’s expansion velocity, followed, in 2018, by a burst through the inflated bubble and an increase in the expansion speed. This confirms the abrupt morphological transition from an FR II- to FR I-class radio lobe observed by Kino et al. (2021), to which we add a gradual opposite transition from FR I to FR II observed from 2010 to 2013. From late 2020 to the end of the considered epochs, some portions of the jet appear darkened. This could be caused by a lower local emissivity, a change in the viewing angle, or the presence of an absorbing foreground. With respect to this last hypothesis, it should be noted that 3C 84 is likely surrounded by an accretion disk associated with ionized gas, which absorbs and obscures the inner section of the counterjet (Walker et al. 2000; Fujita & Nagai 2016).

Some of our images also show the presence of an emission region north of the core. From 2011 to 2013 we detect a persistent emission 0.5 mas northwest of the core, while from 2017 we detect a more diffuse emission 2−3 mas north of the core, coinciding with the N1 component detected by Fujita & Nagai (2016). However, in some epochs, the emission cannot be detected above the noise level of the image background. Whenever the northern emission is detected in the CLEAN images, it is also visible in the corresponding images from eht-imaging, which proves the ability of eht-imaging to recover diffuse structures. We consider the northern emission to be produced by the counterjet of the radio source, partially obscured by the accretion disk. If both the NW and N emitting regions were to be attributed to the counterjet, it would mean that the latter also presents a winding and irregular profile like its southern counterpart. However, the emission that we detect is diffuse and barely above the noise level of the images. Because of this, we are not able to use it to constrain the core shift and we chose not to include further analysis of the counterjet in this work.

3.1. Feature extraction

Traditionally, VLBI images of relativistic jets have been analyzed by fitting Gaussian components to the bright features of the jet and tracking the motion of these components over time, which is known as “model fitting”. This was the best approach to analyzing jet dynamics when the resolution was not sufficient to resolve features inside the jets. However, new super-resolution imaging methods such as eht-imaging now allow us to resolve intra-jet features (see Janssen et al. 2021; Fuentes et al. 2023; Savolainen et al. 2023; Park et al. 2024b), making it unnecessary to approximate and oversimplify jet images using a set of Gaussians. In these cases, model fitting is not an adequate tool. Instead, case-by-case methods should be chosen, depending on the features visible in the image. Because of the winding and evolving jet structure observed in our images of 3C 84, we characterized the jet by measuring its maximum radial expansion from the core (see Sect. 3.5) and by tracing the profiles of the two bright limbs, from which we computed the overall jet outline and the jet launching direction (see Sect. 3.4).

3.2. Alignment

To compare features extracted from images at different epochs, it is crucial that the images are properly aligned. To align the images with respect to the jet core, we applied the following steps:

1. Locate the brightest pixel in each image. In a few cases the brightest pixel is not located in the core, but in the C3 component. In those cases the brightest pixel is replaced by a randomly chosen pixel from the core.

2. Apply a circular mask of 1 mas radius, centered in the brightest point, setting to zero every pixel outside the mask.

3. Shift each image by the amount that maximizes the cross-correlation between the masked image and the masked image of the previous epoch.

This procedure was effective for correctly aligning all epochs except those between November 3 and 6, 2021. For those epochs, a simple cross-correlation alignment was not effective because of the rapid twisting of the core region, so an additional shift, linearly spaced from 35 μas up to 246 μas, was applied after the cross-correlation shift.

3.3. Edge fitting

The most straightforward way to characterize the features present in the jet is to outline its edges by tracking the position of the two bright limbs. For this purpose, as shown in Fig. 3, we considered circular sections of the image, centered around the jet core. We find the two highest emission peaks along each of these profiles and assign their positions to the two bright edges, creating two sets of points outlining each edge (blue points in Fig. 3). In some sections, the position of one or both limbs could not be detected using this method. In such cases, the limb position was determined by interpolating between the positions in the preceding and following sections. The overall jet outline (white points in Fig. 3) was determined by the set of midpoints of the distance segments between each point of one limb and the other limb.

Fig. 3. Example of the fitted edges and jet direction for the jet in epoch July 21, 2021. Dark blue points represent fitted edge points, while light blue points represent interpolated edge points. White points represent the jet outline. A subset of the circular sections used to detect the edge points is shown as thin white lines.

3.4. Jet launching direction

The local jet direction at each section of the jet is defined by the vector tangent to the jet outline curve. We determined the initial jet launching direction by averaging the tangent vectors corresponding to the segments of the jet outline within 90 μas from the core, to avoid resolution-induced biases. The standard deviation associated with the average was assigned as the error on the measured direction. The left panel in Fig. 4 shows the angle corresponding to the jet launching direction as a function of time. The points in blue represent the measured direction from each epoch, while the orange lines indicate the average and standard deviation of a Gaussian process (GP) regression to the data. The right panel in Fig. 4 shows the average jet launching direction from the GP regression with the angle plotted in angular coordinates for a more intuitive representation of the directional shift. The plot shows that the orientation of the jet within the first 0.03 pc from the core undergoes several irregular oscillations. We observe a 20° oscillation from the beginning of 2011 to the end of 2012, a 40° oscillation from early 2013 to early 2017, a 10° shift until early 2018, followed by a clear 60° shift until 2021 and a constant trend in late 2021 and 2022. The overall change in the jet’s orientation spans 80 degrees.

Fig. 4. Top: Details of the core region in 3C 84 for six selected epochs. Bottom left: Angle of the jet launching direction as a function of time. The angle is measured east of north. The measured direction from each epoch is shown in blue and the average of a GP regression to the data in orange. The orange shading indicates the 1 sigma (dark shade) and 3 sigma (light shade) uncertainty from the GP regression. Bottom right: Average direction from the GP regression, plotted in angular coordinates for a more intuitive representation of the direction change. Red corresponds to earlier epochs and blue to later epochs.

A change in the direction of the jet has been proposed by Dunn et al. (2006) to explain the presence of X-ray holes at different orientations with respect to the core on kiloparsec scales. They suggest two possible causes for jet precession: a binary black hole system would make the jet of the primary black hole undergo a regular precession (Katz 1997), while an instability in the accretion disk or a misalignment between the black hole spin and the accretion disk axis could cause the disk to warp, resulting in a stochastic jet precession (Pringle 1997). However, they estimate a precession timescale on the order of 10⁷ years. Here instead we observe a drastic irregular variation in the jet’s direction over a timescale of a few years. It is possible that the jet in 3C 84 undergoes precession cycles over different timescales. It should also be noted that, since monitoring of 3C 84 began, at least two epochs of jet activity, with different properties and directions, have been observed, one from the 1960s related to the ejection of C2, and the other from the 2000s, associated with the expansion of C3 and the direction oscillations reported above. Therefore, the presence of X-ray holes at different orientations could also be due to different activity phenomena associated with different jet orientations and properties.

3.5. Jet length and expansion speed

To measure the jet length, we first computed the longitudinal intensity profile of the jet by identifying the highest intensity value of the image along circular sections centered on the core. We defined the jet length, as projected in the image plane, as the maximum distance from the core reached by the head of the jet. The head of the jet was identified as the point where the longitudinal jet profile dropped below the average noise floor, which was computed as the mean image value, in a portion of the image not covered by the jet. The threshold value was adjusted for epochs from June 2016 to January 2017 to accommodate for a significantly higher noise floor and for epochs from May to September 2021 to take into account the darkening of portions of the jet. The darkening appears in various portions of the jet in later epochs, but it affects the measurement of the jet length only in mid 2021 because a darkened portion coincides with the jet head, as shown, for example, in the lower panel of Fig. 2 or in Fig. 3. The uncertainty associated with the jet length measurements was taken as the pixel size used in the imaging process (30 μas), under the assumption that the limited resolution is the main source of uncertainty for this measurement.

Figure 5 shows the jet length as a function of time. As visible in the online movie, three different trends are evident. Until the end of 2012 the jet length increases linearly, from the beginning of 2013 to the beginning of 2017 the increase occurs at a lower rate, and finally, from 2017, the expansion occurs at a higher speed than the initial one. A possible explanation for the speed change, is that the jet propagates across a medium with different densities, possibly shaped by past activity of the jet. For each of these three expansion regimes, we performed a linear fit to the jet length to compute the expansion velocity. The residuals of the linear fits are shown in the lower panel of Fig. 5 and do not show significant trends, meaning that the expansion in each regime was indeed occurring at a constant speed. From the measured velocities projected in the image plane, we computed the true de-projected velocities of the jet front, accounting for special relativistic effects and assuming an inclination of θ = 18° (Tavecchio & Ghisellini 2014).

Fig. 5. Top: Measured jet length as a function of time (points) and piece-wise linear fit (continuous line). Uncertainties on the measurements are not shown because the error bars are smaller than the size of the points. Bottom: Residuals of the linear fits.

Table 2 reports the values of the apparent speed in the image plane and the de-projected physical speed. The reduced χ² values of the linear fits are also reported in Table 2 and show that the uncertainties are properly estimated for the first two regimes, while they might be slightly underestimated in the last case. This might be due to some portions of the jet being obscured in the latest epochs, which causes a higher uncertainty in the detection of the jet head. Previous estimates of the speed of the 3C 84 jet head, in our considered time period, measured an average apparent speed of 0.27 ± 0.02 c between 2007 and 2013 (Hiura et al. 2018), and an average apparent speed of 0.33 between 2003 and 2020 (Kino et al. 2021). Weaver et al. (2022) measured the apparent speed of the components in 3C 84 in the period from 2010 to 2019, through model fitting. The speed of the components is not necessarily the same speed of the jet expansion, but it can be useful to compare the two. In the period between 2010 and 2012, the apparent speed of components C2, C3, and C6 are 0.27 c, 0.21 c, and 0.34 c, which match our estimate of the expansion speed of 0.29 c. In the period between 2013 and 2015, Weaver et al. (2022) reported a speed of 0.84 c for component C9, matching the observation of the hot spot frustration, which moves at a higher speed than the jet expansion. Finally, from 2016 to 2019, they report component C10 moving at a speed of 1.38 c, indicating a drastic increase in velocity, which matches our measured expansion speed increase. Regarding the jet expansion after 2017, Kam et al. (2024) report measurements of the velocity of four subcomponents propagating from C3 after the jet breaks through the inflated bubble. In the time period between 2017 and 2022, they measure apparent speeds between 0.46 c and 1.35 c, indicating that short-lived components inside the jet may travel faster than the jet front itself.

4. Conclusions

In this paper we present and discuss the parsec-scale structure of 3C 84. We show images from 121 VLBA observations at 43 GHz from late 2010 to early 2023, and we performed a quantitative kinematic analysis of the jet’s expansion and precession. Studying the restarted jet in 3C 84 is important to understanding how the ISM interacts with the jet, affecting its direction, morphology, and propagation speed, and how, in return, the ISM is affected by the irregular jet activity.

Thanks to the super-resolution enabled by the RML imaging method eht-imaging, our images resolve the internal structure of the jet, its profile and edges, and different bright components moving inside the jet. The images were obtained using a standard iterative procedure in eht-imaging, mostly relying on closure quantities to avoid bias from residual calibration errors and with minimal use of regularizers. The images were later aligned with respect to the jet core by maximizing the cross-correlation between subsequent images.

We confirm the presence of a limb-brightened structure that connects to the unresolved core at a wide opening angle (Giovannini et al. 2018). In the initial observations, a dim component (C2) was still present in the bottom-right side of the jet but disappeared completely around 2019. During the 12-year period of observations, the restarted jet grew in length, expanding toward the south. In the most recent images, starting from 2020, some portions of the far side of the jet appear darkened. The direction at which the jet emerges from the core varies across the years. We measured the jet direction within 0.03 pc of the core and observed it undergoing various irregular oscillations, spanning an overall angle of 80°, including a fast 60° orientation change from 2019 to 2021. The parsec-scale jet gradually transitioned from an FR I- to an FRhb II-like morphology from 2010 to 2013, while in 2017 it abruptly transitioned back to an FR I-like morphology. We measured the expansion speed of the jet head (C3 component) and observed three separate regimes of linear expansion. The first regime corresponds to the FR I – FR II transition, the second to the inflation of the jet head in the FR II state, and the third to the expansion following the FR II – FR I transition. We measure apparent speeds of 0.29 ± 0.01 c, 0.228 ± 0.004 c, and 0.61 ± 0.01 c, respectively. We confirm previous observations of a hot spot frustration during the epochs preceding the jet’s abrupt FR II – FR I transition (Kino et al. 2021). The hot spot is observed following a counterclockwise trajectory around the lobe of the jet head. However, contrary to prior observations, we distinguish the frustrated hot spot from other components present before 2016 and after 2017. In some of our images, especially from 2017, we detect a diffuse emission north of the core, which we interpret as being produced by the counterjet that is partially obscured by the accretion disk. However, the emission is barely above the noise level of the images, so we did not rely on it for the analysis of the jet features.

Overall, our results indicate that the jet is propagating in an irregular ISM that is characterized by the presence of clumps of denser material, which affects the jet’s speed, direction, and morphology. The presence of localized absorbing gas in front of the jet may also be an explanation for its local darkening, which alternatively may be due to an increase in the viewing angle or a change in emissivity. The observed evolution of the parsec-scale jet suggests that the presence of radio lobes may be a temporary stage in the evolution of a jet, caused by density differences in the ambient medium. In 3C 84 this seems to be confirmed by the presence of ancient lobes at multiple scales. The limb-brightening suggests a possible spine-sheath structure, where the inner part of the jet moves at a higher speed than the outer part, and could explain the bright gamma-ray emission observed by Abdo et al. (2009). Limb-brightening could also be caused by a higher number of emitting electrons, which are accelerated in the interaction between the jet and the ISM (Stawarz & Ostrowski 2002). Park et al. (2024b) also suggest that a higher emissivity in the jet boundary layer, due to an interaction with a dense medium, may be at the origin of the observed limb-brightening in NGC 315. Possible reasons for the irregular jet precession include an instability in the disk or a misalignment between the angular momentum of the accretion disk and the spin of the black hole (Dunn et al. 2006; Pringle 1997), which may cause a warping of the disk and a stochastic variation in the jet’s direction.

Our results show that by using innovative super-resolving imaging methods, it is possible to resolve complex features in the jet structure, which were previously accessible only at higher observing frequencies or with significantly longer baselines. This marks a change in how jet features can be analyzed, shifting from the fitting of simple Gaussian components to more specific analyses adapted to the jet morphology. For example, similar to Park et al. (2024b), our eht-imaging images clearly highlight the limb-brightening structure, which allowed us to trace the jet edges and precisely track the changes in the jet direction over time. Future imaging of jet sources with new imaging methods could uncover additional cases of limb-brightening that were previously undetectable due to insufficient resolution.

Data availability

Movie associated to Fig. 1 is available at https://www.aanda.org

Acknowledgments

We thank Marie-Lou Gendron-Marsolais (Université Laval and IAA-CSIC) for useful discussions on this work. The project that gave rise to these results received the support of a fellowship from “la Caixa” Foundation (ID 100010434), with fellowship code LCF/BQ/DI22/11940027. Authors M. Foschi, J. L. Gómez and A. Fuentes acknowledge financial support from the Severo Ochoa grant CEX2021-001131-S funded by MCIN/AEI/10.13039/501100011033. The work at the IAA-CSIC was supported in part by the Spanish Ministerio de Economía y Competitividad (grant number PID2022-140888NB-C21). I.C. is supported by the KASI-Yonsei Postdoctoral Fellowship program. This study makes use of VLBA data from the VLBA-BU Blazar Monitoring Program (BEAM-ME and VLBA-BU-BLAZAR; http://www.bu.edu/blazars/BEAM-ME.html), funded by NASA through the Fermi Guest Investigator grants, the latest is 80NSSC23K1508. The VLBA is an instrument of the National Radio Astronomy Observatory. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated by Associated Universities, Inc.

References

All Tables

All Figures

	Fig. 1. Radio source 3C 84 as observed from 2010 to 2023 by the VLBA at 43 GHz and imaged with eht-imaging. The black vertical lines mark the dates of the observation epoch corresponding to each image. The time evolution of the source is shown in the online movie (Movie 1).
In the text

	Fig. 2. Comparison between images of radio source 3C 84 from VLBA observations at 43 GHz obtained with the CLEAN (left) and eht-imaging (right) imaging methods.
In the text

	Fig. 3. Example of the fitted edges and jet direction for the jet in epoch July 21, 2021. Dark blue points represent fitted edge points, while light blue points represent interpolated edge points. White points represent the jet outline. A subset of the circular sections used to detect the edge points is shown as thin white lines.
In the text

Fig. 4. Top: Details of the core region in 3C 84 for six selected epochs. Bottom left: Angle of the jet launching direction as a function of time. The angle is measured east of north. The measured direction from each epoch is shown in blue and the average of a GP regression to the data in orange. The orange shading indicates the 1 sigma (dark shade) and 3 sigma (light shade) uncertainty from the GP regression. Bottom right: Average direction from the GP regression, plotted in angular coordinates for a more intuitive representation of the direction change. Red corresponds to earlier epochs and blue to later epochs.

In the text

	Fig. 5. Top: Measured jet length as a function of time (points) and piece-wise linear fit (continuous line). Uncertainties on the measurements are not shown because the error bars are smaller than the size of the points. Bottom: Residuals of the linear fits.
In the text