# Radio Jet Proper Motion Analysis of Nine Distant Quasars above Redshift 3.5

Yingkang Zhang11affiliation: SKA Regional Centre Joint Lab, Shanghai
Astronomical Observatory, CAS, Nandan Road 80, Shanghai, 200030, China;
e-mail<EMAIL_ADDRESS>, Tao An 11affiliation: SKA Regional Centre Joint
Lab, Shanghai Astronomical Observatory, CAS, Nandan Road 80, Shanghai, 200030,
China; e-mail<EMAIL_ADDRESS>22affiliation: SKA Regional Centre Joint Lab,
Peng Cheng Lab, Shenzhen, 518066, China , Sándor Frey33affiliation: Konkoly
Observatory, ELKH Research Centre for Astronomy and Earth Sciences, Konkoly
Thege Miklós út 15-17, H-1121 Budapest, Hungary 44affiliation: CSFK, MTA
Centre of Excellence, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
55affiliation: Institute of Physics, ELTE Eötvös Loránd University, Pázmány
Péter sétány 1/A, H-1117 Budapest, Hungary , Krisztina Éva
Gabányi33affiliation: Konkoly Observatory, ELKH Research Centre for Astronomy
and Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
44affiliation: CSFK, MTA Centre of Excellence, Konkoly Thege Miklós út 15-17,
H-1121 Budapest, Hungary 66affiliation: Department of Astronomy, Institute of
Geography and Earth Sciences, ELTE Eötvös Loránd University, Pázmány Péter
sétány 1/A, H-1117 Budapest, Hungary 77affiliation: ELKH-ELTE Extragalactic
Astrophysics Research Group, ELTE Eötvös Loránd University, Pázmány Péter
sétány 1/A, H-1117 Budapest, Hungary , Yulia Sotnikova88affiliation: Special
Astrophysical Observatory of RAS, Nizhny Arkhyz, 369167, Russia

###### Abstract

Up to now, jet kinematic studies of radio quasars have barely reached beyond
the redshift range at $z>3.5$. This significantly limits our knowledge of
high-redshift jets, which can provide key information for understanding the
jet nature and the growth of the black holes in the early Universe. In this
paper, we selected 9 radio-loud quasars at $z>3.5$ which display milliarcsec-
scale jet morphology. We provided evidence on the source nature by presenting
high-resolution very long baseline interferometry (VLBI) images of the sample
at 8.4 GHz frequency and making spectral index maps. We also consider Gaia
optical positions that are available for 7 out of the 9 quasars, for a better
identification of the jet components within the radio structures. We find that
6 sources can be classified as core–jet blazars. The remaining 3 objects are
more likely young jetted radio sources, compact symmetric objects. By
including multi-epoch archival VLBI data, we also obtained jet component
proper motions of the sample and estimated the jet kinematic and geometric
parameters (Doppler factor, Lorentz factor, viewing angle). Our results show
that at $z>3.5$, the jet apparent transverse speeds do not exceed 20 times the
speed of light ($c$). This is consistent with earlier high-redshift quasar
measurements in the literature and the tendency derived from low-redshift
blazars that fast jet speeds ($>40\,c$) only occur at low redshifts. The
results from this paper contribute to the understanding of the cosmological
evolution of radio AGN.

High-redshift galaxies (734), Radio active galactic nuclei (2134), Quasars
(1319), Supermassive black holes (1663), Very long baseline interferometry
(1769)

††software: AIPS (Greisen, 2003), Difmap (Shepherd, 1997)

##  1 Introduction

Active galactic nuclei (AGNs) are the most powerful persistent objects in the
Universe, luminous across the whole range of the electromagnetic spectrum.
They can be found from the local Universe up to very high redshifts. AGNs have
been observed throughout almost the entire history of the Universe, providing
important information for studying the co-evolution of supermassive black
holes (SMBHs) and their host galaxies. The most distant quasars discovered so
far are ULAS J134208.10+092838.61 at redshift $z=7.54$ (Bañados et al., 2018b)
and J0313$-$1806 at $z=7.64$ (Wang et al., 2021). Representing the end era of
the cosmic reionization, they offer important clues to explore this episode
when the neutral hydrogen gas in the Universe became ionized. More than 300
quasars with $z>5.7$ are known to date, most of which were discovered in
optical observations (Bañados et al., 2015; Jiang et al., 2016; Shen et al.,
2019). In recent years, in addition to traditional near-infrared spectroscopic
observations, X-ray and mm-wavelength radio observations have also contributed
to the discovery of quasars with $z>6$ (e.g., Maiolino et al., 2005; Medvedev
et al., 2020). Among these high-redshift AGNs, SMBHs with masses exceeding
$10^{9}M_{\odot}$ are found. Although there is an observational bias that the
most massive and highly accreting black holes are the easiest to observe due
to sensitivity limitations, at least the existence of these SMBHs indicates
that they have completed their rapid growth in less than one tenth of the
current age of the Universe. The formation and rapid growth of the first SMBHs
is one of the mysteries of current cosmology and AGN astrophysics.

Relativistic jets are thought to play an important role in promoting rapid
accretion of early AGNs. If a significant fraction of the gravitational energy
can be channeled into forming and maintaining relativistic jets, then their
black holes can remain at high-rate accretion for a long time (Jolley &
Kuncic, 2008; Ghisellini et al., 2013). In this sense, the dynamical
properties and the lifetime of the high-redshift jets are key to testing this
scenario. Although the number of high-$z$ AGNs discovered has been increasing
over the years (Jiang et al., 2016; Wang et al., 2019), their radio
counterparts are less intensely studied. An important reason is that only
$\sim 10\%$ of optically detected quasars have active radio counterparts. The
ratio of radio-loud and radio-quiet AGNs seems to be consistent at high
redshifts and in the local Universe (Bañados et al., 2015), but it has also
been suggested that the fraction of radio-loud AGNs tends to evolve with
redshift (Diana et al., 2022). Producing relativistic jets is not only one of
the ways of AGN energy release (Blandford et al., 2019), but also has an
important impact on the feedback to the environment in the host galaxy
(Fabian, 2012). To date, the role of jets in the formation and evolution of
first SMBHs remains an open question.

The extreme subclass of AGNs are blazars, remarkable for their high bulk
Lorentz factors in the jet plasma, the small viewing angles of the jets with
respect to the line of sight, and thus the large Doppler-boosting factors.
Blazars make up nearly half of the radio-loud AGNs with flux density $S_{\rm
1.4GHz}>100$ mJy in the high-redshift population (Sotnikova et al., 2021). The
jets of high-redshift blazars are typically short, possibly due to the
projection effect caused by the small viewing angle. Perhaps also the
environment of the early galaxies is not favorable for the development of
large-scale jets. In the latter case, the relativistic electrons in the
extended jets are heavily depleted via inverse-Compton scattering by the
enhanced number density of cosmic microwave background (CMB) photons in the
high-redshift Universe (Ghisellini et al., 2014). Also, the interaction
between the jet and the dense interstellar medium may cause a large amount of
the jet’s mechanical energy to be consumed and the growth of the jet to be
stalled (An et al., 2022a). Typical radio images of the distant jetted AGNs
are characterized by compact flat-spectrum cores or core–jet structures. Very
long baseline interferometry (VLBI), with its unique high-resolution
capability, provides a direct way to probe the pc-scale compact structure and
jet properties of high-$z$ AGNs.

To date, there are only six radio-loud quasars imaged with VLBI at extremely
high redshifts ($z>6$). Their VLBI morphologies indicate different types of
radio sources. They do not show a strong tendency towards highly-beamed
sources (i.e. blazars) that would be expected from a selection effect caused
by relativistic beaming. Here we list the radio-loud quasars at $z>5$ with
VLBI imaging available in the literature (Table 1). As one can see, most of
the objects are marked as a compact quasar. These sources show a compact
structure or minor extension on milliarcsec (mas) angular scale (down to a few
tens of pc in linear scale). They typically do not have very high brightness
temperatures or show flat radio spectrum. Their VLBI studies suggest that
these compact high-redshift quasars could be young jetted AGNs in the early
Universe (see references in Table 1). The observing wavelengths of current
VLBI facilities are typically at a few cm, and the corresponding rest-frame
frequencies of high-redshift quasars are much higher than those of their local
counterparts studied at the same observing frequency. The emitted frequency is
$(1+z)$ times the observed frequency. This makes the steep-spectrum jets
relatively fainter and could cause the lack of radio quasars observed with
prominent extended jets at high redshifts (e.g. Gurvits et al., 2015;
Krezinger et al., 2022).

Table 1: Information about the high-redshift ($z>5$) radio quasars with VLBI
imaging observations from the literature

Name | $z$ | Ref. for $z$ | Ref. for VLBI | Radio morphology
---|---|---|---|---
$z>6$
J1129$+$1846 | 6.82 | 1 | 16 | Compact quasar
J2331$+$1129 | 6.57 | 2 | 17 | Compact quasar
J2318$-$3113 | 6.44 | 3 | 18 | Compact quasar
J1429$+$5447 | 6.18 | 4,5 | 19 | Compact quasar
J1427$+$3312 | 6.12 | 6 | 20,21 | CSO candidate
J0309$+$2717 | 6.10 | 7 | 22 | Core–jet blazar
$z>5$
J2228$+$0110 | 5.95 | 8 | 23 | Compact quasar
J2329$-$1520 | 5.84 | 9 | 24 | CSO candidate
J0836$+$0054 | 5.77 | 10 | 25,26 | Compact quasar
J1530$+$1049 | 5.72 | 11 | 27 | MSO galaxy
J0906$+$6930 | 5.47 | 12 | 12,28,29 | Core–jet blazar
J1026$+$2542 | 5.25 | 13 | 30,31 | Core–jet blazar
J0131$-$0321 | 5.13 | 14 | 32 | Compact blazar
J0913$+$5919 | 5.18 | 15 | 33 | Compact quasar

Note. — Columns: (1) source name in J2000 format; (2) source redshift; (3)
reference for the source redshift: 1–Bañados et al. (2021), 2–Koptelova &
Hwang (2022), 3–Decarli et al. (2018), 4–Willott et al. (2010), 5–Wang et al.
(2011), 6–McGreer et al. (2006), 7–Belladitta et al. (2020), 8–Zeimann et al.
(2011), 9–Bañados et al. (2018a), 10–Fan et al. (2001), 11–Saxena et al.
(2018), 12–Romani et al. (2004), 13–Ahn et al. (2012), 14–Yi et al. (2014),
15–Anderson et al. (2001); (4) reference for VLBI image: 16–Momjian et al.
(2021), 17–Frey et al. 2022 (in prep.), 18–Zhang et al. (2022), 19–Frey et al.
(2011), 20–Frey et al. (2008), 21–Momjian et al. (2008), 22–Spingola et al.
(2020), 23–Cao et al. (2014), 24–Momjian et al. (2018), 25–Frey et al. (2005),
26–Frey et al. (2003), 27–Gabányi et al. (2018) , 28–Zhang et al. (2017),
29–An et al. (2020b), 30–Frey et al. (2013), 31–Frey et al. (2015), 32–Gabányi
et al. (2015), 33–Momjian et al. (2004); (5) source morphology in VLBI images
and classification.

The small sample significantly limits our knowledge of high-redshift jets. It
was found that there are two distinct cosmological epochs of SMBH formation:
the number density of non-jetted AGNs hosting SMBHs peaks at $z\sim 2-2.5$,
while the formation of SMBHs in jetted AGNs took place earlier, at $z\sim 4$
(Sbarrato et al., 2015; Sbarrato, 2021, and references therein). This seems to
indicate that black holes with powerful jets grow faster than those of the
same mass but without jets. Thus, observational studies of jetted AGNs at
$z\sim 4$ can bring us crucial information about the rapid growth of the first
black holes. Moreover, the sample size of radio-loud AGNs in this cosmic
period is much larger than during the cosmic reionization ($z\gtrsim 7$),
facilitating statistical studies.

The kinematics of high-redshift jets provides key information for
understanding the jet nature. In particular, VLBI can measure the jet proper
motion and independently calculate the Doppler-boosting factor, which can be
used to estimate the bulk Lorentz factor and viewing angle of the jet flow.
These place strong observational constraints on the modeling of the spectral
energy distribution (SED) of the jet (Sbarrato et al., 2022). Current
detections of jet proper motions of high-redshift ($z\gtrsim 4$) AGNs are
limited to a few sources (Veres et al., 2010; Frey et al., 2015; Perger et
al., 2018; An et al., 2020b; Zhang et al., 2020). All these are blazars, with
apparent superluminal speeds distributed in a wide range from $2\,c$ to about
$20\,c$, where $c$ denotes the speed of light. In contrast, the jets of high-
redshift galaxies move at mildly relativistic speeds (An et al., 2022a),
consistent with the traditional notion of their large viewing angle, without
strong beaming effects. More proper motion measurements help extend our
understanding of the nature and geometry of high-redshift jets.

In the present work, we provide new high-quality VLBI images of nine high-
redshift radio-loud quasars. By combining archival multi-frequency, multi-
epoch VLBI data as well as optical data, we classify their source nature and
determine for the first time their jet proper motions and other radio
properties on pc scales. This work increases the size of the proper motion
sample of $z>3.5$ jets by a factor of two. The subsequent sections of the
paper are organized as follows. In Section 2, we describe the method of sample
selection, the new Very Long Baseline Array (VLBA) observations, and the data
processing. Section 3 presents the new VLBI images which are used as the
reference for source classification. Section 4 contains the analysis and
discussion of the jet kinematics. Section 5 summarizes the main results and
conclusions of this paper. Comments on individual target sources are given in
Appendix A, extended tables and figures can be found in Appendix B. Throughout
this paper, we use the cosmological parameters derived from a flat $\Lambda$
Cold Dark Matter ($\Lambda$CDM) model (Komatsu et al., 2011) with
$\Omega_{\mathrm{m}}=0.27$, $\Omega_{\Lambda}=0.73$, and $H_{0}=70$ km
s-1Mpc-1.

##  2 Target Selection and VLBI Observations

###  2.1 The Selected High-redshift Sample

Our focus is on the jet kinematics of a sample of high-redshift blazars at
$z\sim 4$. To measure the proper motion of the jet, at least two epochs of
VLBI observations at the same observing frequency are required, preferably
with similar $(u,v)$ coverage at each epoch. The time interval between epochs
should also be taken into account when measuring jet proper motions at high
redshifts. The minimum time gap between epochs can be estimated as
$t_{\mathrm{gap}}=\frac{D_{\mathrm{min}}}{\mu_{\mathrm{comp}}}$, where
$D_{\mathrm{min}}$ is the minimum distance that can be distinguished between
available epochs, usually depending on the observing resolution and frequency.
Here $\mu_{\mathrm{comp}}$ denotes the proper motion of a well-identified
component. In the case of VLBI measurements, $D_{\mathrm{min}}$ can be
measured in mas, $\mu_{\mathrm{comp}}$ in mas yr-1, and thus
$t_{\mathrm{gap}}$ in yr. For high-redshift radio jets, their
$\mu_{\mathrm{comp}}$ could be much smaller than their low-redshift
counterparts due to the cosmological time dilation, thus a large
$t_{\mathrm{gap}}$ is usually needed to obtain reliable measurements. This is
one of the reasons why only a few $z>4$ jet proper motions have been measured
so far.

To select suitable AGNs, we first checked the VLBI archive database for radio
sources with $3.5\lesssim z\lesssim 4.5$. We used the Astrogeo
database111http://astrogeo.org/ to build our sample, which is currently the
largest collection of VLBI imaging data available. It accumulates data from a
series of astrometric and geodetic VLBI surveys such as the VLBA Calibrator
Surveys (VCS, Beasley et al., 2002; Fomalont et al., 2003; Petrov et al.,
2005, 2006; Kovalev et al., 2007; Petrov et al., 2008; Petrov, 2016), the
United States Naval Observatory surveys (USNO; Hunt et al., 2021), and various
other projects. The Astrogeo database now provides more than 100,000 VLBI
images of more than 17,000 AGNs, mostly observed in snapshot mode at 2.3 and
8.4 GHz. Although the quality of the snapshot images is not very high, we only
focus on compact radio structures from bright radio sources with flux
densities above $50$ mJy, so these images are sufficient for our research
purposes. By cross-matching the list with the NASA/IPAC Extragalactic
Database222 http://ned.ipac.caltech.edu (NASA/IPAC Extragalactic Database
(2019), NED) and some large optical spectroscopic projects (e.g., Sloan
Digital Sky Survey Data Releases 9 and 12, Ahn et al., 2012; Pâris et al.,
2017), over 60 $z>3.5$ quasars are found (the full sample will be given in our
subsequent study). Since VLBI is sensitive to compact sources with high
brightness temperatures, the high-redshift extragalactic sources detected in
the flux density-limited VLBI surveys are all radio-loud jetted AGNs. From
this parent sample, we then selected a sub-sample for the jet proper motion
study, according to the following criteria:

  * •

The redshift is $3.5\lesssim z\lesssim 4.5$.

  * •

The flux density at 8.4 GHz is $S_{\mathrm{8.4}}>50$ mJy, to enable high
dynamic range imaging.

  * •

The source shows resolved jet structure in the existing 8.4-GHz archival
images, a premise for being able to measure jet component motion.

  * •

Multiple epochs of VLBI imaging are available at 8.4 GHz. A minimum time gap
$t_{\mathrm{gap}}\approx 7$ yr can be estimated, by assuming a moderate jet
component speed $10\,c$ and $D_{\mathrm{min}}$ from 3-$\sigma$ position error.
A rough estimate of $\approx 0.2$ for the position error is based on the 10%
restoring beam size of typical 8.4-GHz VLBA observations. The corresponding
$\mu_{\mathrm{comp}}$ is $0.08-0.09$ mas yr-1for the given redshift range.

Based on the above criteria, we selected nine targets whose detailed
information can be found in Table 2. There is no other bias in this sample,
except for the limitation on the flux density and the declination
($\mathrm{Dec.}>-40\arcdeg$). The latter is because the archival data were
mostly obtained with the VLBA located on the northern hemisphere. In
particular, our sample selection did not restrict the AGN optical properties.
At the time of selecting the present sample, J1606+3124 met our criteria.
However, a subsequent study (An et al., 2022a) found that its optical
classification and redshift are debatable and need further confirmation. An et
al. (2022a) suggest that the source is more likely a high-redshift radio
galaxy rather than a quasar.

We have collected images from the Astrogeo archive for a total of 39 epochs
for these nine sources, with 3–6 epochs per source and a maximum time span of
$\sim 24$ yr (which equals approximately $4$ yr in the source’s rest frame).
In snapshot mode, a target is observed in a few scans (observation time
segments), each lasting for a few minutes. Scans of multiple sources are
interleaved to ensure that each source has good $(u,v)$ coverage. Our selected
target sources are routinely monitored in the VLBA calibrator surveys, the
$(u,v)$ coverage at 8.4 GHz are similar from epoch to epoch, and the prominent
components can be clearly imaged with similar quality, even with limited
sensitivity.

In order to obtain high-quality images of high-$z$ AGNs for better
identification of the radio components and classification of their radio
structures, we initiated a new epoch of VLBA observations of the selected 9
sources. The new data are used together with the archival data for jet
kinematic studies. Details of the new VLBA observations are presented in the
next subsection.

Table 2: Information about the high-$z$ quasars selected for this jet proper
motion study from Astrogeo

Name | RA (J2000) | Dec (J2000) | $z$ | $N_{\mathrm{epoch}}$ | Epoch range | Reference
---|---|---|---|---|---|---
J0048$+$0640 | 00h48m58.7231s |  $+$06d40m06.475s | 3.580 | 5 | 2004$-$2018 | Gurvits et al. (1999)
J0753$+$4231 | 07h53m03.3375s |  $+$42d31m30.765s | 3.595 | 4 | 1995$-$2018 | Hewett & Wild (2010)
J1230$-$1139 | 12h30m55.5560s |  $-$11d39m09.795s | 3.528 | 3 | 1996$-$2018 | Drinkwater et al. (1997)
J1316$+$6726 | 13h16m27.2015s |  $+$67d26m24.262s | 3.515 | 4 | 1995$-$2018 | Richards et al. (2009)
J1421$-$0643 | 14h21m07.7556s |  $-$06d43m56.356s | 3.689 | 5 | 1997$-$2018 | Ellison et al. (2001)
J1445$+$0958 | 14h45m16.4653s |  $+$09d58m36.073s | 3.552 | 6 | 1997$-$2018 | Hewett & Wild (2010)
J1606$+$3124 | 16h06m08.5184s |  $+$31d24m46.458s | 4.560 | 4 | 1996$-$2018 | Healey et al. (2008)
J1939$-$1002 | 19h39m57.2566s |  $-$10d02m41.521s | 3.787 | 5 | 1996$-$2019 | Lanzetta et al. (1991)
J2102$+$6015 | 21h02m40.2191s |  $+$60d15m09.837s | 4.575 | 4 | 1994$-$2018 | Sowards-Emmerd et al. (2004)

Note. — Columns: (1) source name, (2)–(3) source equatorial coordinates right
ascension and declination, (4) redshift, (5) number of available VLBI epochs
at 8.4 GHz for this study, (6) time range spanned by the VLBI observations,
(7) literaure reference for the redshift.

###  2.2 VLBA Observations and Data Reduction

The VLBA observations (project code: BZ064, PI: Y. Zhang) were conducted on
2017 February 5 and 2017 March 19 at 8.4 GHz. Nine out of the ten VLBA
antennas participated in the observations (see Table 4. The observations were
performed using the DDC (digital downconverter) system with a baseband
bandwidth of 128 MHz, divided into 256 spectral channels of 500 kHz each,
using four baseband channels (IFs) of left and right circular polarization and
2-bit sampling. This configuration results in a total data rate of 2048 Mbit
s-1. Since the target sources are all compact and bright
($S_{\mathrm{8.4}}>50$ mJy), fringe search can be done using themselves as
calibrators, so a standard continuum observation mode was used. A total of 6 h
of observation time was divided into two sessions: BZ064A (2 h) and BZ064B (4
h), according to the distribution of the right ascensions of the 9 target
sources (see Table 2). During the observations, pointing on sources in the
same group were alternated, each obtaining about 0.5 h on-source time. This
allowed us to reach a fairly good $(u,v)$ coverage and high image quality. We
refer to Table 4 for the details of the observations.

After observations, the data were correlated with 2-s integration time using
the DiFX correlator (Deller et al., 2011) in Socorro (New Mexico, USA). The
correlated data were then downloaded to the China Square Kilometre Array (SKA)
Regional Centre prototype (An et al., 2019) via the internet for further
calibration and imaging. We calibrated the data using the VLBI data processing
pipeline developed by our group (An et al., 2022b). The main steps of the
procedure are detailed below. We used the US National Radio Astronomy
Observatory (NRAO) Astronomical Image Processing System (AIPS) software
package (Greisen, 2003) to calibrate the amplitude and phase of the visibility
data. Our pipeline is written in Python language333http://www.python.org,
using ParselTongue as an interface to convert AIPS tasks into Python scripts
(Kettenis et al., 2006), so that most of the operations can be executed
automatically.

The pipeline first loaded the data into AIPS and performed a couple of tasks
to assist the user in inspecting the data quality. Input parameters (names for
fringe finders, bandpass calibrators and target sources, reference antenna,
solution intervals, etc.) were determined manually. Then the pipeline
automatically conducted the amplitude, phase, and bandpass calibrations, and
splitted the visibility data into single-source files. The procedures and
parameters used in our experiment are described as follows. The visibility
amplitudes were calibrated using the antenna gain curves and system
temperatures measured at each station during the observations. The AIPS
procedure VLBATECR was then used to correct for atmospheric opacity as well.
Next, the bright calibrator sources (J2148$+$0657 for BZ064A and 3C 273 for
BZ064B; Table 4) were used to calibrate the delays and global phase errors of
the instruments using the FRING task. This operation calibrated and aligned
the delays and phases between different sub-bands. Next, global fringe fitting
was performed on all sources and the resulting gain solutions were
interpolated and applied to calculate and remove the phase errors. We checked
and found that over 98% of the phase solutions were successful. Finally, the
antenna-based bandpass functions were solved by using data from the
calibrators and applied to correct the target sources’ visibility data. At
this point, the initial calibration was complete. The calibrated data were
exported to an external single-source FITS file by averaging over each sub-
band (128 MHz each) and a time interval of 2 s.

After calibration, together with the archival calibrated visibility data
obtained from the Astrogeo archive, all single-source data files exported from
AIPS were loaded into the Caltech Difmap software package (Shepherd, 1997) for
final imaging and model-fitting. The hybrid mapping process consists of
several iterations of CLEAN and self-calibration. Final CLEAN images were
obtained after a few iterations of phase and amplitude self-calibration,
repeated by gradually reducing the solution intervals from a few hours to 1
min. The data from the Astrogeo archive have been calibrated, so we just
conducted the imaging and model-fitting following similar steps in Difmap as
above.

To parameterize the core and the jet components, we conducted model fitting on
the self-calibrated visibility data in Difmap. This utilizes the
Levenberg–Marquardt non-linear least-squares minimization technique in the
visibility domain (Shepherd, 1997). During the processing, we followed the
rules of continuity and simplicity, assuming that most components move
downstream of the jet and the number of jet components does not change much
over the successive epochs. Since we care more about the change in the
position of the jet components, most components are fitted with circular
Gaussian brightness distribution models. Very few components whose structure
was too compact were fitted with a point source model. In a few cases, the jet
components showed extended structure and could not be adequately fitted by a
single circular Gaussian model. These features could result from diffuse
emission or newly ejected components along the jet trajectory. Regarding this,
several point-source models which were not treated as physical components were
applied to account for the extra flux density. These components are also
listed in Table 8.

Fomalont (1999) introduced a method to estimate the uncertainty of the fitted
model component parameters. This method considers only the statistical error
of the image and is therefore closely related to the image quality, while the
actual error in the observed data is often higher than the statistical error.
For the peak brightness and integrated flux density of each component, we
considered an additional 5% calibration uncertainty originating from the
measured gain curves and system temperatures. For the position of each
component, we found that the Fomalont (1999) method underestimates the actual
error of the snapshot observations. Due to the short observing time, the
sparse $(u,v)$ coverage of the archival Astrogeo data could result in side
lobes. In such conditions, we chose to identify components based on our own
long-track VLBA observations, and used the synthesized beam size instead of
the fitted component size to calculate the position error, i.e.,
$\frac{\theta_{\rm beam}}{\rm SNR}$, where SNR denotes the signal-to-noise
ratio. In such snapshot observations, our conservative estimation of the
errors provided a more reasonable assessment of the observed properties of the
jet, and similar applications are common in large VLBA surveys (e.g. the
MOJAVE survey; Lister et al., 2009, 2016, 2019).

##  3 Results

Here we show mas-resolution images of the nine high-$z$ radio-loud quasars and
classify their radio structures by combining their radio morphology, radio
spectrum, and Gaia optical astrometric data. Figure 1 displays the high-
quality images obtained from our VLBA observations in 2017. The lowest noise
level of the images is $\sim 0.1$ mJy beam-1 (Table 5), close to the thermal
noise level. The components marked with labels are from the model fitting
results from Section 2.2; their parameters can be found in Table 8. Our new
VLBA observations are more sensitive than the archival astrometric snapshot
data from Astrogeo, thus the models fitted to our own 2017 VLBA data are used
as a reference. Certain model components are too weak or too diffuse to be
detected in some lower-quality images. Those components are not used for
proper motion determination. Since these sources were intentionally chosen to
have a resolved structure in VLBI images (see Section 2), all images
demonstrate a rich jet structure but present two different types of
characteristics:

  * •

In six sources (J1230+1139, J1316+6726, J1421$-$0643, J1445+0958,
J1939$-$1002, and J2102+6015), the brightest component is located at one end
of the radio structure. J1230+1139, J1316+6726, and J1445+0958 show a large
jet bending ($\approx 90\arcdeg$) within 2 mas. J1421$-$0643 and J1939$-$1002
display linear collimated structure. A faint diffuse feature can be seen at 20
mas from the brightest component in J1939$-$1002\. In the image of J2102+6015,
there are two faint discrete components to the west of the brightest component
(see also in Zhang et al., 2021).

  * •

The other three sources (J0048+0640, J0753+4231, and J1606+3124) show two
compact components with comparable brightness at either end of the radio
structure.

The archival Astrogeo images show similar structures, with minor differences
because faint components are not always detected in the less sensitive
snapshot observations. An example is J1 component in J1939$-$1002\. Basic
information on the archival VLBI observations is given in Table 6.

A conclusive classification of radio structures from VLBI images alone is not
always possible, and for this reason, we searched optical astrometric data of
these sources from the Gaia (Gaia Collaboration et al., 2016) Early Data
Release 3 (Gaia Collaboration et al., 2021) via the Gaia archive (Gaia
collaboration, 2020). For quasars, the optical nucleus detected by Gaia
corresponds to the accretion disk, with some contribution from the innermost
part of the synchrotron-emitting jet (e.g. Plavin et al., 2019). It better
represents the central black hole than the radio core, which is the
synchrotron self-absorbed jet base at the given frequency. We found Gaia data
for 7 of our 9 sources. The remaining two (J1606+3124 and J2102+6015) appear
too weak in optical, which is consistent with their identification as a galaxy
(see below for a detailed discussion).

In Figure 1, we marked the Gaia positions with crosses whose size represents
the 3-sigma positional errors. By comparing optical positions with the mas-
scale radio structure of the 7 sources, we found the following:

  * •

J0048+0640: the Gaia position lies between the two components, NE and SW.
Considering the comparable brightness of NE and SW components and their almost
equal distances from the optical nucleus, we can classify J0048+0640 as a
compact symmetric object (CSO; Phillips & Mutel, 1982).

  * •

J0753+4231: the optical position is close to the northernmost component NE2,
so this AGN may be a core–jet source. The brightest VLBI component is NE1,
with a separation of about 2 mas downstream along the jet. NE1 may be a moving
knot or a standing shock in the jet.

  * •

J1230+1139: the optical position is close to the brightest component C, but
with a significant deviation. The situation is similar to that of J0753+4231.
Moreover, there is a clear extension from component C toward the optical
position, indicating that the radio core is weaker than the bright jet knot.

  * •

J1316+6726: the Gaia position corresponds to the brightest radio component C
within the positional uncertainty. This AGN is classified as a core–jet
source.

  * •

J1421$-$0643, J1445+0968, and J1939$-$1002: core–jet sources with their
optical nuclei and radio cores in good positional agreement.

|  |
---|---|---

|  |
---|---|---

|  |
---|---|---

Figure 1: Naturally weighted images of the 9 high-redshift sources after deep
cleaning, derived from our VLBA observations at 8.4 GHz in 2017. The lowest
contours represent $\pm 4$ times of the rms noise, and the positive contour
levels increase by a factor of 2. The image parameters are listed in Table 5.
The green crosses mark the optical positions detected by Gaia, the bar length
are 3 times the Gaia positional errors reported in
https://gea.esac.esa.int/archive.

Since the astrometric/geodetic snapshot observations found in the Astrogeo
database are carried out in dual frequency bands (either at around 2 and 8
GHz, or at 4 and 8 GHz), the simultaneous dual-frequency observations with the
same pointing centers enable us to produce spectral index maps for each target
source. This can assist in the classification of their radio structure. In
making the spectral index maps, we first selected a set of 2/8-GHz
($S/X$-band) data with relatively high-quality images for each source, and
performed the same hybrid mapping procedure. We set the same image size, pixel
size, and restoring beam size for both bands. Model fitting was also performed
on the self-calibrated 2-GHz visibility data to identify the optically thin
components that were used for calculating the offset between the $S/X$ image
brightness peaks, in order to properly align them. The spectral index maps
were finally made using our Python script which follows similar calculations
as done in the AIPS task COMB. Features with brightness lower than 3 times the
rms noise in the 2-GHz maps were omitted to make the spectral index images
clearer and more reliable.

The resulting spectral index images are shown in Figure 3 (The spectral index
$\alpha$ is defined as $S\propto\nu^{\alpha}$, where $S$ is the flux density
and $\nu$ the frequency). J0048+0640 shows a steep spectrum throughout the
whole emission structure (mainly NE and SW components), reinforcing its
classification as a CSO. The southern component of J0753+4231 has a steep
spectrum and the northern component has a flat spectrum, which is consistent
with its core–jet classification. In J1230+1139, J1316+6726, J1421$-$0643,
J1445+0958, and J1939$-$1002, the flattest spectrum (or rising spectrum with
positive spectral index) appears at one end of the radio structure,
corresponding to the position of the optical nucleus, and the rest of the
structure shows a steep spectrum. This information supports that the flat-
spectrum components are associated with the radio cores and these sources are
core–jet quasars. J1606+3124 lacks a distinct flat-spectrum component, and it
is most likely a CSO (see the discussion in An et al., 2022a). Based on its
VLBI images, J2102+6015 is a rather peculiar object. Both its eastern and
western parts have relatively flat spectra. In the higher-resolution images,
the eastern component is resolved into three sub-components (Frey et al.,
2018). However, none of the VLBI components have detectable proper motion
(Zhang et al., 2021). The spectral index map supports that J2102+6015 could be
a CSO candidate (see Zhang et al., 2021).

In summary, the mas-scale morphology, the radio spectral index map, and, where
Gaia data are available, the cross-match between the optical nucleus and radio
components all together suggest the CSO classification of the radio structure
in J0048+0640, J1606+3124, and J2102+6015. The other 6 high-redshift quasars
are core–jet sources.

##  4 Discussion

In this section, we focus on the jet proper motion and discuss the properties
of the relativistic jets in our sample of high-redshift jetted AGNs.

###  4.1 Core Brightness Temperature and Doppler Boosting

Extremely high brightness temperatures observed in AGN cores, close to or
above the inverse-Compton limit (Kellermann & Pauliny-Toth, 1969), are usually
considered as due to the beaming effect of relativistic jets pointing close to
the observer’s line of sight. VLBI observations can be used directly to
measure the brightness temperature:

$T_{\mathrm{B}}=1.22\times
10^{12}(1+z)\frac{S_{\nu}}{\theta_{\mathrm{comp}}^{2}\nu^{2}}\,{\mathrm{K}},$
(1)

where Sν is the flux density of the VLBI component (in Jy), $\nu$ the
observing frequency (in GHz), and $\theta_{\mathrm{comp}}$ is the diameter
(full width at half-maximum, FWHM) of the circular Gaussian component (in
mas). The estimated $T_{\mathrm{B,obs}}$ values for the VLBI components in
each source are listed in Table 8.

The radio core is conventionally defined as the optically-thick section of the
jet base in the vicinity of the central SMBH. For radio-loud quasars with a
core-jet structure, the core is usually the brightest and most compact
component in the VLBI image. Assuming that the magnetic field energy density
and the particle energy density are in an equipartition state, the brightness
temperature will have a maximum value called equipartition brightness
temperature, $T_{\mathrm{B,eq}}$ (Readhead, 1994). This can be considered as
the intrinsic brightness temperature of the relativistic jet. Observed
brightness temperatures above the limit ($T_{\mathrm{B,eq}}\approx 5\times
10^{10}$ K) are generally considered to be caused by the Doppler boosting
effect of beamed jets. The Doppler factor can be estimated from the observed
$T_{\mathrm{B,obs}}$ values as $\delta=T_{\mathrm{B,obs}}/T_{\mathrm{B,eq}}$.

We must be aware that the equipartition estimate of the Doppler factor is
valid for the optically thick parts of the jet, where the frequency of the
$T_{\mathrm{B,obs}}$ measurement should be close to the spectral peak of the
source. For the high-redshift quasars in our sample, the observed 8.4 GHz
corresponds to a rest-frame frequency of $\sim 40$ GHz, which most likely
exceeds the spectral peak frequencies. To estimate the Doppler factors of our
sample, we adopted the following approach to obtain appropriate values.
Firstly, we used the $T_{\mathrm{B,obs}}$ values measured from all the 8-GHz
($X$-band) epochs to calculate an average brightness temperature for each
source. During the averaging calculations, the extreme $T_{\mathrm{B,obs}}$
values were omitted, reducing the impact of possible model-fitting biases due
to some potentially poor-quality data. The average $T_{\mathrm{B,obs}}$ is
likely more characteristic to the quiescent states of the AGN core. The
resulting average $T_{\mathrm{B,obs}}$ for each source can be found among the
individual comments on the sources (Appendix A).

Recently, Cheng et al. (2020) estimated the correlation between the observed
$T_{\mathrm{B,obs}}$ and the frequencies, based on large VLBA surveys of
compact radio AGNs at multiple frequencies. They found that the spectral peaks
are at around 7 GHz in the rest frame of the sources. Based on the empirical
correlation from Cheng et al. (2020), and using the equipartition brightness
temperature as the intrinsic brightness temperature that is valid at the
spectral peak frequency, we can then estimate the intrinsic brightness
temperature $T_{\mathrm{B,int}}$ for each of our observed sources, taking the
actual rest-frame frequencies into account. The extrapolated
$T_{\mathrm{B,int}}$ values are in the range of $(1.1-1.4)\times 10^{10}$ K
for the sources in our sample.

From the estimates above, we find that all the six core–jet sources in our
sample have high core brightness temperatures exceeding the extrapolated
$T_{\mathrm{B,int}}$, confirming that they contain highly relativistic jets
with Doppler-boosted radio emission. We calculated their Doppler factors that
can be found in Table 3. The brightness temperatures of J1316+6726,
J1445+0958, and J1939$-$1002 are high and these values have prominent temporal
variations. For J0753+4231, the brightest jet component NE1 has the highest
brightness temperature. The three CSOs, J0048+0640, J1606+3124, and
J2102+6015, do not have identifiable cores, but the brightness temperatures of
their hot spots exceed $T_{\mathrm{B,eq}}$, suggesting that the equipartition
assumption probably does not apply in these regions. The brightness
temperatures of J0048+0640 hot spots show a significant decrease at epochs
2017 September 18 and 2018 January 18, while a significant increase in the
component size occurs. This can be explained by the adiabatic expansion of the
hot spots.

###  4.2 Jet Proper Motion

Since the cosmological time dilation is proportional to $(1+z)$, the jets in
the high-redshift sample appear changing slower. Thus reliable component
proper motion measurements require VLBI observations spanning a longer time
interval in the observer’s frame (e.g. Frey et al., 2015; Perger et al., 2018;
An et al., 2020b; Zhang et al., 2020).

Using our fitted Gaussian model components, we measured apparent proper
motions based on the time evolution of the separation of core and jet
components. For components that are too close to the core, their fitted
positions may be affected by the finite restoring beam size and perhaps newly
ejected features. On the other hand, components too far away from the core
($\gtrsim 10$ mas) are usually weak and diffuse, their positional
uncertainties are too large. Therefore, we excluded these components from our
proper motion determination.

Finally, we derived proper motions for 18 jet features from 9 target sources.
The results are shown in Table 7. We fitted the linear proper motion along the
RA ($\mu_{x}$) and Dec ($\mu_{y}$) directions separately, using a least-
squares method, and then calculated the total proper motion as
$\sqrt{\mu_{x}^{2}+\mu_{y}^{2}}$. For the core–jet sources, we calculated the
rate of change of the jet component position relative to the core with time.
For CSO sources, we calculated the separation speed of the two opposite hot
spots using a particular terminal hot spot as a reference. Assuming that both
hot spots advance with the same speed, the advance speed of a particular hot
spot is half of the calculated separation speed.

Figure 4 demonstrates the jet component trajectories and proper motion fitting
results of the VLBI components in the sample. For each source, we selected the
most appropriate jet components for proper motion measurements: they have data
from the most epochs, are clearly distinguishable in VLBI images, and have the
smallest positional errors.

The detailed radio properties of two CSOs, J1606+3124 and J2102+6015, have
been presented before (An et al., 2022a; Zhang et al., 2021), so we only
briefly summarize the results here. The separation speed between terminal hot
spots S and N in J1606+3124 is $0.013\pm 0.002$ mas yr-1 ($1.60\pm 0.25\,c$),
and between the hot spot S and the inner jet knot C is $0.006\pm 0.002$ mas
yr-1 ($0.74\pm 0.25\,c$). This leads to a hot spot advance speed of $0.8\,c$
(An et al., 2022a). The separation speed between the eastern and western
components in J2102+6015 is $0.023\pm 0.011$ mas yr-1 ($2.8\pm 1.4\,c$) (Zhang
et al., 2021). In the third CSO in our sample, J0048+0640, we obtained a
separation speed of $0.005\pm 0.002$ mas yr-1 ($0.6\pm 0.2\,c$), giving a hot
spot advance speed of $\sim 0.3\,c$.

The apparent jet component speeds in the core–jet sources are in the range of
$1.4-17.5\,c$, consistent with the known proper motions in low-redshift radio-
loud quasars (e.g. Piner et al., 2012; Lister et al., 2019). The maximum speed
is close to that of the fastest high-$z$ jet observed before (Zhang et al.,
2020), but lower than the maximum value found in low-redshift AGNs. The
quasars J1230$-$1139, J1316+6726, and J1445+0958 contain fast-moving
components in the outer part of the jets. These large proper motions could be
caused by the projection effect of a large jet bending.

###  4.3 Lorentz Factors and Viewing Angles

High-redshift blazar sources are potentially valuable for studying the
cosmological evolution of radio source number density and SMBH accretion.
Understanding the distribution of the jet Lorentz factors is fundamental for
assessing the number density of AGNs with jets misaligned with respect to the
line of sight. These constitute the mostly hidden parent population of highly-
beamed jetted sources (blazars). The latter objects are more easily detectable
in flux density-limited observations, because of their Doppler-boosted
emission. Kinematic measurements of high-redshift AGN jets and estimates of
jet Lorentz factors such as presented here are still very rare. For sources at
lower redshifts, Lister et al. (2019) found that the distribution of Lorentz
factors peaks between $\Gamma=5-15$, with a shallow tail reaching
$\Gamma\approx 50$. The misaligned parent population of low-$\Gamma$ jetted
sources is larger because those jets require very small viewing angles to be
detected as blazars.

The Lorentz factor can be obtained by fitting the broad-band spectral energy
distribution (SED) of a blazar (e.g. Boettcher et al., 1997), or directly from
VLBI observations. Based on the Doppler factor and the apparent superluminal
speed of the jet derived from the VLBI observations, we can estimate the bulk
Lorentz factor and viewing angle (see Eqs. B5 and B7 in Ghisellini et al.,
1993). The bulk Lorentz factors and jet viewing angles are calculated for five
core–jet sources (with the exception of J1316$+$6726, due to the lack of valid
proper motion measurements). The results are presented in Table 3, along with
values for other high-$z$ radio quasars taken from the literature. Two
sources, J1230$-$1139 and J1421$-$0643, show relatively large Lorentz factors,
which exceed the typical maximum values ($\Gamma>20$, e.g. Kellermann et al.,
2004) based on the $\beta_{\mathrm{app,max}}$ for the studied high-redshift
sources. In the relativistic beaming model (see Appendix A in Urry & Padovani,
1995), this can happen when the viewing angle is very small (i.e.
$\theta<\theta_{\mathrm{crit}}$, where the critical angle
$\theta_{\mathrm{crit}}=\arcsin(\Gamma^{-1})$). In such cases, a minor change
in the viewing angle would greatly increase the jet apparent speed. An
alternative possibility could be that the sizes of the VLBI cores are
overestimated, which could be caused by the overlap of the emitting components
or variability. This will lead to a decrease in the estimated Doppler factor.
Both cases above are common in blazars with core–jet structures. These
observational evidences, including higher Lorentz factors and smaller viewing
angles, support that these sources belong to the blazar class.

Table 3: VLBI kinematic parameters measured for high-$z$ radio quasars

Name | $z$ | $\beta$ | $\delta$ | $\Gamma$ | $\theta$ | Ref.
---|---|---|---|---|---|---
J0753$+$4231 | 3.59 | 1.8$\pm$0.1 | 6.0$\pm$1.2 | 3.4$\pm$0.5 | 5.3$\pm$2 | 1
J1230$-$1139 | 3.53 | 10.3$\pm$0.8 | 2.4$\pm$1.9 | 23.3$\pm$16.9 | 10.5$\pm$1.1 | 1
J1421$-$0643 | 3.69 | 15.9$\pm$0.3 | 3.0$\pm$1.5 | 44.2$\pm$20.9 | 6.9$\pm$0.3 | 1
J1445$+$0958 | 3.55 | 12.9$\pm$0.6 | 11.1$\pm$4.6 | 13.1$\pm$1.1 | 5.1$\pm$1.8 | 1
J1939$-$1002 | 3.79 | 0.5$\pm$0.1 | 16.5$\pm$5.2 | 8.3$\pm$2.6 | 0.2$\pm$0.2 | 1
J0906$+$6930 | 5.47 | 2.5$\pm$0.8 | 6.0$\pm$0.8 | 3.6$\pm$0.5 | 6.8$\pm$2.2 | 2
J1026$+$2542 | 5.27 | 12.5$\pm$ 3.9 |  $\gtrsim$ 5 |  $\gtrsim$ 12.5 | 4.6 | 3
J1430$+$4204 | 4.72 | 19.5$\pm$1.9 | 22.2$\pm$10.6 | 14.6$\pm$3.8 | 2.2$\pm$1.6 | 4
J2134$-$0419 | 4.33 | 4.1$\pm$ 2.7 | 3–8 | 2–7 | 3–20 | 5

Note. — Columns: (1) J2000 source name; (2) redshift; (3) apparent transverse
speed of the fastest jet component, in the unit of $c$; (4) Doppler factor
estimated from the VLBI core brightness temperature; (5) bulk Lorentz factor;
(6) jet viewing angle in $\arcdeg$; (7) reference for the estimated
parameters: 1–this paper, 2–An et al. (2020b), 3–Frey et al. (2015), 4–Zhang
et al. (2020), 5–Perger et al. (2018)

###  4.4 High-redshift Quasars in the Apparent Proper Motion–Redshift Diagram

Except for J0906+6930 (Zhang et al., 2017; An et al., 2020b), J1026+2542 (Frey
et al., 2015), J1430+4204 (Zhang et al., 2020), and J2134$-$0419 (Perger et
al., 2018), there are no robust proper motion measurements in other quasar
jets at $z>3.5$. The main reason is the lack of known sources that are
sufficiently bright with prominent well-resolved mas-scale radio jet
structure. Also, because of the cosmological time dilation, reliably detecting
positional changes in jet components requires decades-long history of VLBI
monitoring observations. Thanks to the accumulated astrometric snapshot VLBI
data, here we could derive jet proper motions for another 6 high-redshift
blazars. This increases the available proper motion sample in the early
Universe substantially (Table 3).

Figure 2: The apparent proper motion–redshift ($\mu-z$) diagram based on the
latest VLBI observations of radio jets. Down triangles: this work; up
triangles: from the literature, see Table 3; circles: Piner et al. (2012)
measured at 8.4 GHz; squares: Britzen et al. (2008) measured at 5 GHz; plus
signs: Lister et al. (2021) measured at 15 GHz. The solid lines represent the
maximum apparent speed $\beta_{\mathrm{app,max}}$ with the given bulk Lorentz
factors $\Gamma=20$ and 40.

An even larger sample of high-redshift jet proper motions could eventually
become useful to constrain cosmological model parameters through the apparent
proper motion–redshift ($\mu-z$) relation (e.g. Cohen et al., 1988; Vermeulen
& Cohen, 1994; Kellermann et al., 1999). Earlier studies based on large but
lower-redshift source samples (Figure 2) found that the upper bound on the
$\mu-z$ relation is consistent with the predictions of the $\Lambda$CDM
cosmology and a distribution of jet Lorentz factors where the vast majority of
the jets have $\Gamma\lesssim 25$. For a given Lorentz factor, the apparent
jet component speed cannot exceed $\sqrt{\Gamma^{2}-1}\approx\Gamma$ (e.g.
Urry & Padovani, 1995). To better populate the high-redshift region, we added
our own proper motion measurements to the $\mu-z$ diagram constructed from
literature data (Figure 2). Large VLBI surveys (Britzen et al., 2008; Piner et
al., 2012; Lister et al., 2021) at lower redshifts, as well as measurements
for individual high-redshift quasars are considered. From our sample studied
here, only the highest jet component speeds of each source are plotted. Note
that VLBI observations made at different frequencies (ranging from 5 to 15
GHz) are collected in Figure 2. This may result in systematically different
apparent proper motion values (e.g. Kellermann et al., 2004). Nevertheless,
the general trend in which our new measurements also fit is clearly seen: jets
with the fastest apparent proper motion, $\beta_{\mathrm{app}}\gtrsim 40$, are
only found at $z\lesssim 2$. Given that our estimated Lorentz factors reach
about 40 (Table 3), it is expected that with larger samples of high-redshift
quasars, their apparent proper motions could be as high as $\mu\approx 0.4$
mas yr-1 (Figure 2), without violating the current cosmological paradigm and
without requiring extremely high bulk Lorentz factors in the jet. Our study
helps populating the high-redshift end of the apparent proper motion–redshift
diagram with reliable jet proper motions measured with VLBI.

##  5 Summary

In this paper, we reported new 8.4-GHz VLBA observations of 9 high-redshift
($z>3.5$) jetted quasars. Based on archival dual-band (usually 2- and 8-GHz)
astrometric VLBI data and our high-quality VLBA data taken in 2017, we
presented high-resolution radio images and spectral index maps of each source
in the sample. Accurate optical positions from Gaia were also considered for 7
out of the 9 sources, in the context of their mas-scale radio structure. By
fitting the source visibility data with circular Gaussian brightness
distribution model components, and using appropriate component identifications
across multiple observing epochs, kinematic properties of the jets were
derived.

In our sample, six sources (J0753+4231, J1230$-$1139, J1316+6726,
J1421$-$0643, J1445+0958, and J1939$-$1002) were classified as core–jet
blazars. These sources have flat-spectrum (or inverted-spectrum) features at
the brighter end of the radio structure (the so-called cores), which also
closely correspond to the position of the optical nucleus where Gaia
measurements are available. The brightness temperatures of their VLBI cores
all exceed the estimated equipartition threshold. In the framework of the
relativistic beaming model, we also estimated the jet kinematic and geometric
parameters (Doppler factor, Lorentz factor, and jet viewing angle) of these
core–jet blazars (except for J1316+6726 due to the lack of valid proper motion
measurements). The results are presented in Table 3.

Three sources in our sample (J0048+0640, J1606+3124, and J2102+6015) were
classified as CSOs or CSO candidates. The spectral index maps of J0048+0640
and J1606+3124 show steep-spectrum emission at both sides of their jet ends.
For J2102+6015, its eastern and western features have relatively flat (or
inverted) spectra, and none of the VLBI components have detectable proper
motion (see also Zhang et al., 2021). The maximum jet proper motion detected
in our sample is $\sim 0.15$ mas yr-1, corresponding to an apparent jet speed
of $\sim 18\,c$. The range of our jet proper motions shows good consistency
with low-redshift quasars, where large values of $\beta_{\mathrm{app}}$ only
appear at low redshifts (e.g. Piner et al., 2012; Lister et al., 2019). Our
study substantially increases the sample of high-redshift radio quasars with
reliable jet proper motions measured with VLBI. It may serve as an important
starting point for accumulating data for future studies of high-redshift AGN
jets.

This research was funded by National Key R&D Programme of China under grant
number 2018YFA0404603 and the China–Hungary project funded by the the Ministry
of Science and Technology of China and Chinese Academy of Sciences. YKZ was
sponsored by Shanghai Sailing Program under grant number 22YF1456100. This
research was supported by the Hungarian National Research, Development and
Innovation Office (NKFIH), grant number OTKA K134213. This work is supported
by the Ministry of science and higher education of Russia under the contract
075-15-2022-262. The National Radio Astronomy Observatory is a facility of the
National Science Foundation operated under cooperative agreement by Associated
Universities, Inc. We acknowledge the use of data from the Astrogeo Center
database maintained by Leonid Petrov. VLBA

##  Appendix A Comments on Individual Sources

###  A.1 J0048$+$0640

The first VLBI image of this source was made at 5 GHz from a European VLBI
Network (EVN) observation in 1996. It showed a double-component source
extended along the northeast–southwest direction (Paragi et al., 1999). The
two components were separated by $\sim 3.8$ mas, consistently with our 8.4-GHz
imaging results. The source is marginally resolved at 2.3 GHz and clearly
resolved into two components at 8.4 GHz (Figure 1). In producing the spectral
index image, we used the midpoints of the 2.3- and 8.4-GHz images for the
alignment (the two components can be extracted from the best-quality 2.3-GHz
data with model fitting). Both the NE and SW components exhibit flat spectra
and high brightness temperatures. The average $T_{\mathrm{B}}$ is $7.0\pm
1.3\times 10^{10}$ K for NE and $4.6\pm 3.9\times 10^{10}$ K for SW, with the
Gaia nucleus positioned in between. The possibility of gravitational lensing
can be ruled out because the two components would violate the preservation of
surface brightness (see e.g. Spingola et al., 2019; Casadio et al., 2021).
Considering the source compactness, it is very unlikely to be a dual AGN, but
this scenario is difficult to rule out with observations at other wavebands
because of the insufficient resolution. The most likely explanation is that
J0048$+$0640 is a CSO. No significant proper motion was detected between the
two components over a 14-yr time baseline. Recent multi-frequency total flux
density measurements of $z>3$ AGNs with the RATAN-600 radio telescope show a
peaked spectrum for J0048$+$0640 with $\nu_{\mathrm{peak}}\approx 4$ GHz in
the observer’s frame (Sotnikova et al., 2021), reinforcing that it is a young
CSO source.

###  A.2 J0753$+$4231

The source was included in the CSO candidate sample of CSOs observed in the
northern sky (COINS) and VLBA Imaging and Polarimetry Survey (VIPS) (Peck &
Taylor, 2000; Helmboldt et al., 2007; Tremblay et al., 2016). In recent
studies of the radio spectra of high-$z$ quasars, this source was also
identified as a candidate MHz-peaked spectrum source with
$\nu_{\mathrm{peak}}<1$ GHz in the observer’s frame (e.g. Mingaliev et al.,
2013; Sotnikova et al., 2021). In our study, J0753$+$4231 shows a double
structure in both the 2.3- and 8.4-GHz images. The Gaia position and the
spectral index map support that the source is a one-sided core–jet quasar
rather than a CSO. The core should be located in the outermost NE2 component.
The average brightness temperatures $T_{\mathrm{B}}$ of NE1 and NE2 are
$8.4\pm 1.7\times 10^{10}$ K and $1.4\pm 0.4\times 10^{10}$ K, respectively.
We estimate the maximum proper motion of the jet to be $0.018\pm 0.001$ mas
yr-1 ($1.8\pm 0.1\,c$) using NE2 (core) as the reference point. In a previous
study, Britzen et al. (2008) also detected four components at 5 GHz, and
conducted proper motion measurements based on three VLBI epochs, leading to a
maximum speed $\sim 0.1$ mas yr-1. Compared to their proper motions, our
measured value is much smaller, but it is based on a longer time period (22
yr) and has higher accuracy.

###  A.3 J1230$-$1139

The 8.4-GHz image of this source shows a prominent curved jet that bends from
the west to the southwest at a projected distance of about 45 pc. Two
components, J1 and J2, are detected in the curved southwest jet section, and
J3 is located where the jet bends. The brightest component is C, but it is not
a radio core. The extension east of C shows a flat spectrum and should host
the core. The maximum proper motion is $\sim 0.10$ mas yr-1, corresponding to
an apparent transverse speed of $\sim 12\,c$. The mean $T_{\mathrm{B}}$ of
this source is $3.4\pm 2.7\times 10^{10}$ K. The relatively lower brightness
temperature may be due to the presence of self-absorption in the core,
resulting in an underestimate of the flux density and an overestimate of its
size. The estimated viewing angle of the innermost jet is around $10\arcdeg$,
derived from the Doppler factor and maximum apparent jet speed, classifying it
as a blazar. The source also shows significant variability, consistent with
its blazar identification. It shares similar high-resolution jet properties
with other high-$z$ blazars (e.g. Zhang et al., 2020; An et al., 2020b).

###  A.4 J1316$+$6726

The redshift of this source is from photometric measurements, but with a very
high probability ($\sim 95\%$, Richards et al., 2009). Since the jet is well-
separated from the core, we included it in our sample and tried to check its
high-$z$ nature by determining its jet proper motions following the method
introduced by An et al. (2020a). In the VLBI images of this source, a weak and
extended jet can be found at around 8 mas southeast of the bright core
component, with a sharp bending at a projected distance of 60 pc from the
core. The jet is only marginally detected at 3 available epochs, and we did
not detect a significant (i.e. $\geq 3\sigma$) outward motion due to the
significant positional errors and the short time period. The mean
$T_{\mathrm{B}}$ of the core component is $13.3\pm 5.5\times 10^{10}$ K,
indicating strong non-thermal emission. The apparent inward motion needs to be
verified by future observations. If this proper motion is caused by the motion
of a newly-formed jet component in the core, then the new jet speed along the
jet direction is $14.2\,c$, which does not exceed the expected proper motion
upper limit for a high-$z$ jet (see an example of the opposite situation in An
et al., 2020a), and thus its photometric redshift can be considered plausible.

###  A.5 J1421$-$0643

This source shows a typical core–jet radio structure. The mean
$T_{\mathrm{B}}$ is $4.2\pm 2.1\times 10^{10}$ K. This source is a prominent
high-$z$ blazar. Previous studies have discovered large kpc-scale radio and
X-ray jets extending towards the northeast of this nucleus (Worrall et al.,
2020). Our VLBI images reveal the pc-scale jet structure, showing three jet
components moving away from the core radially toward the northeast direction.
The position angle of the pc-scale jet is consistent with that of the kpc-
scale jet (about $30\arcdeg$). The estimated maximum jet proper motion is
$\sim 0.15$ mas yr-1 ($\sim 16\,c$).

###  A.6 J1445$+$0958

This object, also known as OQ 172, has a rich jet structure starting toward
the west and turning the south. It was once identified as a GHz-peaked
spectrum (GPS) galaxy due to the less variable radio and optical emission, the
non-flat radio spectrum and the lack of pc-scale structural evolution (see
Punsly et al., 2015, and the references therein). Previous multi-band VLBI
observations revealed a clockwise jet trajectory from high-frequency to low-
frequency images, which was attributed to the interaction between the
relativistic jet and the narrow-line region medium (Liu et al., 2017). In our
image at 8.4 GHz, the emission of the jet that bends from west to south was
modeled and analyzed. Since the jet is becoming weak and diffuse in the
southern tail, barely detected in the less sensitive archival snapshot
observations, we only fit the brighter jet section in the northern part
(Figure 1). From seven epochs spanning 21 yr, we were able to obtain jet
proper motion in J1445$+$0958 for the first time. Among the three jet
components, J1 stands out as the fastest one, with a proper motion of 0.13
$\pm$ 0.01 mas yr-1. The mean $T_{\mathrm{B}}$ of this source is $15.5\pm
6.4\times 10^{10}$ K, suggesting a highly beamed jet. From the spectral index
map, the high brightness temperature, and the Gaia optical position, the
source could be a blazar. Although its GPS-type radio spectrum is inconsistent
with the typically flat spectrum of low-redshift blazars, it is not
unprecedented in high-redshift quasars (e.g. Sotnikova et al., 2021).

###  A.7 J1606$+$3124

This source was previously identified as a flat-spectrum radio quasar (Healey
et al., 2007; Torniainen et al., 2007; Coppejans et al., 2016). However,
further radio spectral studies based on simultaneous multi-frequency
observations suggested that the source is a GPS radio galaxy in the early
Universe (RATAN-600, Mingaliev et al., 2012; Sotnikova et al., 2019). In our
study, by analyzing the spectral index map and the archival radio spectra, we
conclude that the source could be the a high-redshift CSO source. Additional
results and a detailed discussion of the CSO identification have been
presented elsewhere (An et al., 2022a).

###  A.8 J1939$-$1002

The VLBI morphology resembles a core–jet radio source. The two compact jet
components lie close to the bright core, and a distant jet component (J1) is
in the northeastern direction at a distance of about 22 mas. This distant
feature shows a slight change in the position angle. It could possibly be
explained by the rise of the Doppler-boosted region caused by the helical jet
path, which is usually seen in flat-spectrum radio quasars (FSRQs) (e.g.
Alberdi et al., 2000; Hong et al., 2004). However, the possibility of jet
interaction with the surrounding interstellar medium (ISM) cannot be ruled out
either (e.g. Gómez et al., 2000; An et al., 2020b). The mean $T_{\mathrm{B}}$
of this source is $21.4\pm 6.7\times 10^{10}$ K, which well exceeds the
equipartition value and indicates strong Doppler boosting with $\delta\geq 4$.

Since the jet component J1 is weak and diffuse at most available epochs, we
just measured proper motions of J2 and J3. The resulting jet proper motion is
$-0.014\pm 0.001$ mas yr-1 for J2 and $0.005\pm 0.001$ mas yr-1 for J3. The
apparent inward jet motion is physically meaningless. Despite position errors,
the curved jet motion across the line of sight and the newly-emerging features
that move beyond the time separations among the available epochs could be the
possible reasons for the negative proper motion of J2 (see e.g. Lister et al.,
2013, 2016).

###  A.9 J2102$+$6015

Previous studies of this source claim it as an FSRQ with moderate Doppler
boosting effects (Coppejans et al., 2016), but recent works prefer
J2102$+$6015 to be a GPS radio source (e.g. Coppejans et al., 2017; Frey et
al., 2018). We find further interesting characteristics of this source.
Considering the high-resolution images, the spectral index behavior, and the
component separation speeds, we believe this high-$z$ AGN is most likely a
CSO. From the deep imaging and model-fitting results, we found that neither
the E nor the W features are unresolved. To further constrain the source
nature, we collected more high-resolution VLBI data from further epochs, and
used somewhat more conservative positional error estimates (i.e. one-tenth of
the restoring beam size) to conduct component identification and proper motion
estimates. A more robust proper motion estimate of 0.023 $\pm$ 0.011 mas yr-1
was obtained. The details are presented in a separate paper (Zhang et al.,
2021).

##  Appendix B Tables and Figures

Table 4 lists the basic observing information for the proposed VLBA session
BZ064. Table 5 presents the parameters of the VLBI CLEAN images for each
target source in our VLBA observation BZ064. Table 6 lists the 8-GHz VLBI
imaging parameters of the target sources based on their archival VLBA
experiments. Table 7 is showing the jet proper motion parameters of the major
jet components within each source in our sample, which were estimated based on
our multi-epoch 8.4 GHz VLBA observations. Table 8 catalogued the parameters
of the brightness distribution models (Gaussian or point-source models) that
are used to fit the target sources in the visibility domain. Figure 3 shows
the spectral index maps of the sources in our sample, made from their
simultaneous 2.3 and 8,4 GHz VLBA images. Figure 4 demonstrates how the jet
components move with respect to their ”cores” (optically thick radio cores or
referencing components) in our sample and exhibits the fitted results of their
radial motions and position angle changes.

Table 4: Information on our VLBA observations

Code | Freq. | Date | Target | Calibrators | Participating telescopesa
---|---|---|---|---|---
| (GHz) | (yyyy-mm-dd) |  |  |
BZ064A | 8.4 | 2017-02-05 | J0048$+$0640 | 2145$+$0657 | BR, FD, HN, LA, NL, OV, PT, SC
… | … | … | J1939$-$1002 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC
… | … | … | J2102$+$6015 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC
BZ064B | 8.4 | 2017-03-19 | J0753$+$4231 | 3C273, 3C345 | BR, FD, HN, LA, MK, NL, OV, PT, SC
… | … | … | J1230$-$1139 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC
… | … | … | J1316$+$6726 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC
… | … | … | J1421$-$0643 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC
… | … | … | J1445$+$0958 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC
… | … | … | J1606$+$3124 | … | BR, FD, HN, LA, MK, NL, OV, PT, SC

aafootnotetext: VLBA telescopes participating in the observations: BR
(Brewster), FD (Fort Davis), HN (Hancock), KP (Kitt Peak), LA (Los Alamos), MK
(Mauna Kea), NL (North Liberty), OV (Owens Valley), PT (Pie Town), SC (Saint
Croix)

Table 5: Parameters of the CLEAN images from the present VLBA observations at
8.4 GHz

Name | Date | $S_{\mathrm{peak}}$ | $B_{\mathrm{maj}}$ | $B_{\mathrm{min}}$ | PA | $\sigma$
---|---|---|---|---|---|---
| yyyy-mm-dd | (mJy beam-1) | (mas) | (mas) | (∘) | (mJy beam-1)
J0048$+$0640 | 2017-02-05 | 53.9 | 2.6 | 1.2 | 24.8 | 0.1
J0753$+$4231 | 2017-03-19 | 164.6 | 2.9 | 1.6 |  $-$74.2 | 0.1
J1230$-$1139 | 2017-03-19 | 55.0 | 2.4 | 1.0 | 6.0 | 0.1
J1316$+$6726 | 2017-03-19 | 92.6 | 2.3 | 0.9 |  $-$8.7 | 0.1
J1421$-$0643 | 2017-03-19 | 85.6 | 2.2 | 0.9 |  $-$2.1 | 0.1
J1445$+$0958 | 2017-03-19 | 244.0 | 1.9 | 0.7 |  $-$0.5 | 0.2
J1606$+$3124 | 2017-03-19 | 326.4 | 2.4 | 0.9 | 9.4 | 0.2
J1939$-$1002 | 2017-02-05 | 355.5 | 2.1 | 0.8 | 0.7 | 0.1
J2102$+$6015 | 2017-02-05 | 99.9 | 2.7 | 0.8 |  $-$1.6 | 0.1

Note. — Columns: (1) J2000 source name; (2) date of the observation; (3) peak
intensity of the image; (4)–(5) major and minor axes from the FWHM size of the
elliptical Gaussian restoring beam; (6) position angle of the beam major axis,
measured from north to east; (7) the rms noise of the post-fit image.

Table 6: Basic information on the archival VLBA experiments at 7.6–8.7 GHz
($X$ band)

Name | Date | Code | Freq. | $S_{\mathrm{peak}}$ | $\sigma$ | $B_{\mathrm{maj}}$ | $B_{\mathrm{min}}$ | PA | BW
---|---|---|---|---|---|---|---|---|---
| yyyy-mm-dd |  | (GHz) | (mJy beam-1) | (mJy beam-1) | (mas) | (mas) | (∘) | (MHz)
J0048$+$0640 | 2004-04-30 | bp110a | 8.6 | 67.4 | 1.15 | 2.2 | 1.0 | 4.2 | 8 $\times$ 4
.. | 2004-05-08 | bp110 | 8.6 | 72.3 | 1.19 | 2.1 | 0.9 | 7.6 | 8 $\times$ 4
.. | 2014-08-09 | bg219e | 8.7 | 53.4 | 0.25 | 2.6 | 1.2 | 18.9 | 32 $\times$ 12
.. | 2017-09-18 | uf001q | 8.7 | 49.0 | 0.47 | 4.9 | 1.7 |  $-$13.9 | 32 $\times$ 12
.. | 2018-01-18 | ug002a | 8.7 | 54.5 | 0.22 | 3.4 | 1.0 |  $-$18.1 | 32 $\times$ 12
J0753$+$4231 | 1996-06-07 | bb023 | 8.3 | 163.5 | 1.03 | 1.9 | 0.9 | -6.5 | 8 $\times$ 4
.. | 2015-03-17 | bg219i | 8.7 | 166.1 | 0.46 | 1.4 | 1.1 |  $-$18.9 | 32 $\times$ 12
.. | 2017-05-27 | uf001i | 8.7 | 135.0 | 0.35 | 1.5 | 1.0 | 12.1 | 32 $\times$ 12
.. | 2018-06-09 | ug002j | 8.7 | 118.5 | 0.31 | 1.6 | 1.1 | 9.9 | 32 $\times$ 12
J1230$-$1139 | 1997-05-07 | bb023 | 8.3 | 114.6 | 1.37 | 2.4 | 0.9 | 1.4 | 8 $\times$ 4
.. | 2017-07-16 | uf001n | 8.7 | 55.6 | 0.90 | 2.0 | 0.9 |  $-$6.4 | 32 $\times$ 12
.. | 2018-07-01 | ug002k | 8.7 | 56.9 | 0.78 | 2.2 | 1.0 |  $-$2.0 | 32 $\times$ 12
J1316$+$6726 | 1995-04-19 | bb023 | 8.3 | 131.9 | 6.10 | 2.5 | 0.9 |  $-$9.3 | 4 $\times$ 4
.. | 2005-07-20 | bk124 | 8.6 | 81.2 | 0.45 | 2.2 | 1.3 | 40.8 | 8 $\times$ 4
.. | 2014-12-20 | bg219f | 8.7 | 63.4 | 0.19 | 1.5 | 1.0 |  $-$86.7 | 32 $\times$ 12
J1421$-$0643 | 1997-05-07 | bb023 | 8.3 | 137.1 | 0.86 | 2.3 | 0.9 |  $-$3.2 | 8 $\times$ 4
.. | 2015-01-22 | bg219g | 8.7 | 61.2 | 0.28 | 2.1 | 0.9 |  $-$1.7 | 32 $\times$ 12
.. | 2015-03-17 | bg219i | 8.7 | 87.6 | 0.41 | 2.1 | 0.9 | 0.6 | 32 $\times$ 12
.. | 2017-02-19 | uf001c | 8.7 | 70.8 | 0.28 | 2.0 | 0.8 | 4.0 | 32 $\times$ 12
.. | 2018-03-26 | ug002d | 8.7 | 86.3 | 0.22 | 2.3 | 1.0 | 1.6 | 32 $\times$ 12
J1445$+$0958 | 1997-01-10 | bf025 | 8.3 | 161.3 | 1.42 | 1.9 | 1.0 | 1.0 | 8 $\times$ 4
.. | 1999-05-10 | rdv15 | 8.6 | 182.3 | 0.72 | 1.2 | 0.9 |  $-$8.6 | 8 $\times$ 4
.. | 2001-07-05 | rdv29 | 8.6 | 207.4 | 1.47 | 1.6 | 0.9 | 0.7 | 8 $\times$ 4
.. | 2005-06-22 | bl129 | 8.3 | 304.3 | 0.81 | 2.2 | 1.0 |  $-$4.6 | 8 $\times$ 4
.. | 2008-04-02 | rdv68 | 8.6 | 224.6 | 2.03 | 0.7 | 0.5 | 9.0 | 8 $\times$ 4
.. | 2018-03-26 | ug002d | 8.7 | 216.5 | 0.92 | 2.0 | 0.9 |  $-$2.9 | 32 $\times$ 12
J1606$+$3124 | 1996-05-15 | bb023 | 8.3 | 304.4 | 0.90 | 2.1 | 0.9 |  $-$18.2 | 8 $\times$ 4
.. | 2014-08-09 | bg219e | 8.7 | 337.0 | 0.33 | 2.1 | 1.1 | 20.9 | 32 $\times$ 12
.. | 2017-09-18 | uf001q | 8.7 | 323.6 | 0.88 | 3.2 | 1.6 |  $-$25.5 | 32 $\times$ 12
.. | 2018-03-26 | ug002d | 8.7 | 270.1 | 0.36 | 1.8 | 1.1 | 4.2 | 32 $\times$ 12
J1939$-$1002 | 1997-01-10 | bf025 | 8.3 | 246.7 | 0.80 | 2.1 | 0.9 |  $-$1.2 | 8 $\times$ 4
.. | 1997-05-07 | bb023 | 8.3 | 318.7 | 0.85 | 2.3 | 0.9 |  $-$1.0 | 8 $\times$ 4
.. | 1998-10-01 | rdv11 | 8.6 | 318.6 | 0.55 | 2.5 | 0.9 |  $-$1.6 | 4 $\times$ 4
.. | 2006-07-11 | rdv57 | 8.6 | 285.6 | 2.16 | 2.3 | 0.7 |  $-$5.6 | 8 $\times$ 4
.. | 2019-02-04 | sb072d2 | 7.6 | 350.2 | 0.39 | 2.4 | 1.1 | 5.4 | 32 $\times$ 8
J2102$+$6015 | 1994-08-12 | bb023 | 8.3 | 136.9 | 3.06 | 2.2 | 0.9 |  $-$65.4 | 4 $\times$ 4
.. | 2006-12-18 | bp133 | 8.6 | 92.4 | 0.71 | 1.4 | 1.2 |  $-$56.7 | 8 $\times$ 4
.. | 2017-05-01 | uf001h | 8.7 | 99.0 | 0.17 | 1.3 | 1.1 | 13.2 | 32 $\times$ 12
.. | 2018-06-09 | ug002j | 8.7 | 94.4 | 0.17 | 1.5 | 1.1 |  $-$14.0 | 32 $\times$ 12

Note. — Columns: (1) J2000 source name; (2) observing date; (3) project code;
(4) observing frequency; (5) peak intensity of the image; (6) rms noise,
(7)-(8) major and minor FWHM axes of the elliptical Gaussian restoring beam;
(9) position angle of the beam major axis, measured from north to east; (10)
observing bandwidth of each IF $\times$ number of IFs.

Table 7: Jet component proper motions

Name | Comp. | $\mu_{\mathrm{rad}}$ | $\mu_{x}$ | $\mu_{y}$ | $|\mu_{\mathrm{tot}}|$ | $|\beta_{\mathrm{rad}}|$ | $|\beta_{\mathrm{tot}}|$ | $\mathrm{PA}_{\mathrm{var}}$
---|---|---|---|---|---|---|---|---
J0048+0640 | SW | 0.005$\pm$0.002 | 0.001$\pm$0.001 |  $-$0.005$\pm$0.002 | 0.005$\pm$0.002 | 0.6$\pm$0.2 | 0.6$\pm$0.2 |  $-$0.1$\pm$0.1
J0753+4231 | SW2 | 0.003$\pm$0.005 |  $-$0.003$\pm$0.004 |  $-$0.002$\pm$0.009 | 0.004$\pm$0.006 | 0.3$\pm$0.6 | 0.4$\pm$0.7 | 0.0$\pm$0.0
… | SW1 | 0.013$\pm$0.003 |  $-$0.006$\pm$0.002 |  $-$0.013$\pm$0.004 | 0.014$\pm$0.004 | 1.5$\pm$0.3 | 1.6$\pm$0.4 |  $-$0.1$\pm$0.0
… | NE1 | 0.016$\pm$0.001 |  $-$0.016$\pm$0.001 |  $-$0.009$\pm$0.002 | 0.018$\pm$0.001 | 1.8$\pm$0.1 | 2.1$\pm$0.1 | 0.3$\pm$0.1
J1230$-$1139 | J1 | 0.093$\pm$0.007 |  $-$0.087$\pm$0.005 |  $-$0.055$\pm$0.011 | 0.103$\pm$0.007 | 10.3$\pm$0.8 | 11.4$\pm$0.8 |  $-$0.6$\pm$0.1
… | J2 | 0.026$\pm$0.004 |  $-$0.057$\pm$0.003 |  $-$0.088$\pm$0.006 | 0.105$\pm$0.005 | 2.9$\pm$0.4 | 11.7$\pm$0.6 |  $-$1.8$\pm$0.1
… | J3 |  $-$0.021$\pm$0.006 |  $-$0.018$\pm$0.004 |  $-$0.044$\pm$0.010 | 0.048$\pm$0.009 |  $-$2.3$\pm$0.7 | 5.3$\pm$1.0 |  $-$0.9$\pm$0.1
J1316+6726 | J1 |  $-$0.128$\pm$0.115 | 0.192$\pm$0.142 | 0.231$\pm$0.101 | 0.300$\pm$0.119 |  $-$14.2$\pm$12.8 | 33.4$\pm$13.3 |  $-$1.9$\pm$0.8
J1421$-$0643 | J2 | 0.140$\pm$0.003 | 0.126$\pm$0.002 | 0.065$\pm$0.005 | 0.142$\pm$0.003 | 15.9$\pm$0.3 | 16.1$\pm$0.3 | 0.3$\pm$0.1
… | J3 | 0.081$\pm$0.001 | 0.064$\pm$0.001 | 0.051$\pm$0.001 | 0.082$\pm$0.001 | 9.2$\pm$0.1 | 9.3$\pm$0.1 |  $-$0.6$\pm$0.1
… | J4 | 0.140$\pm$0.009 | 0.102$\pm$0.006 | 0.116$\pm$0.015 | 0.154$\pm$0.012 | 15.9$\pm$1.0 | 17.5$\pm$1.4 |  $-$3.5$\pm$0.5
J1445+0958 | J1 | 0.116$\pm$0.005 |  $-$0.049$\pm$0.004 |  $-$0.122$\pm$0.008 | 0.131$\pm$0.008 | 12.9$\pm$0.6 | 14.7$\pm$0.8 |  $-$1.5$\pm$0.1
… | J2 | 0.085$\pm$0.001 |  $-$0.089$\pm$0.001 |  $-$0.005$\pm$0.002 | 0.089$\pm$0.001 | 9.5$\pm$0.1 | 10.0$\pm$0.1 | 0.7$\pm$0.1
J1606+3124 | S-N | 0.013$\pm$0.002 | 0.002$\pm$0.002 | 0.014$\pm$0.004 | 0.014$\pm$0.004 | 1.6$\pm$0.2 | 1.7$\pm$0.5 | 0.1$\pm$0.0
… | S-C | 0.006$\pm$0.002 | 0.004$\pm$0.002 | 0.008$\pm$0.003 | 0.009$\pm$0.003 | 0.7$\pm$0.2 | 1.1$\pm$0.3 | 0.1$\pm$0.0
J1939$-$1002 | J2 |  $-$0.014$\pm$0.001 |  $-$0.007$\pm$0.001 |  $-$0.013$\pm$0.002 | 0.015$\pm$0.002 |  $-$1.6$\pm$0.1 | 1.7$\pm$0.2 |  $-$0.1$\pm$0.0
… | J3 | 0.005$\pm$0.001 |  $-$0.013$\pm$0.001 | 0.007$\pm$0.001 | 0.015$\pm$0.001 | 0.5$\pm$0.1 | 1.7$\pm$0.1 |  $-$0.7$\pm$0.1
J2102+6015 | W | 0.020$\pm$0.010 |  $-$0.021$\pm$0.010 | 0.000$\pm$0.010 | 0.021$\pm$0.010 | 2.5$\pm$1.2 | 2.6$\pm$1.2 | 0.0$\pm$0.0

Note. — Columns: (1) J2000 source name; (2) component identifier; (3)–(6)
fitted proper motion in mas yr-1: $\mu_{\mathrm{rad}}$ – the jet radial
motion; $\mu_{x}$, $\mu_{y}$ – proper motion components along the right
ascension and declination axes, respectively; $\mu_{\mathrm{tot}}$: total
proper motion calculated from $\mu_{x}$ and $\mu_{y}$; (7)–(8) apparent
transverse speed of jet radial ($\beta_{\mathrm{rad}}$) and total
($\beta_{\mathrm{tot}}$) motions, respectively, in units of $c$; (9) change of
the jet position angle, in $\arcdeg$ yr-1.

Table 8: Model fitting parameters

Name | Epoch | Comp. | $S_{\mathrm{peak}}$ | $S_{\mathrm{int}}$ | $R$ | PA | $\theta_{\mathrm{comp}}$ | $T_{\mathrm{B}}$
---|---|---|---|---|---|---|---|---
| yyyymmdd |  | (mJy beam-1) | (mJy) | (mas) | ($\arcdeg$) | (mas) | ($\times 10^{10}$ K)
J0048$+$0640 | 20040430 | NE | 66.8$\pm$3.5 | 71.5$\pm$3.9 | … | … | 0.31$\pm$0.05 | 5.5$\pm$1.2
… | … | SW | 39.1$\pm$2.1 | 40.7$\pm$2.3 | 4.33$\pm$0.03 |  $-$142.5$\pm$0.4 | 0.27$\pm$0.06 | 4.2$\pm$1.3
… | 20040508 | NE | 71.7$\pm$3.7 | 75.8$\pm$4.1 | … | … | 0.27$\pm$0.04 | 7.8$\pm$1.7
… | … | SW | 42.1$\pm$2.2 | 42.7$\pm$2.4 | 4.22$\pm$0.03 |  $-$142.0$\pm$0.3 | 0.18⋆ | 9.9$\pm$3.9
… | 20140809 | NE | 50.3$\pm$2.5 | 50.4$\pm$2.5 | … | … | 0.22$\pm$0.01 | 7.8$\pm$0.7
… | … | P1a | 15.7$\pm$0.8 | 5.7$\pm$0.3 | 1.93$\pm$0.02 |  $-$148.2$\pm$0.5 | 0.17⋆ | …
… | … | SW | 53.5$\pm$2.7 | 58.2$\pm$2.9 | 4.40$\pm$0.00 |  $-$143.0$\pm$0.1 | 0.45$\pm$0.01 | 2.1$\pm$0.1
… | 20170205 | NE | 44.2$\pm$2.2 | 42.5$\pm$2.2 | … | … | 0.22$\pm$0.03 | 6.9$\pm$1.2
… | … | P2a | 22.7$\pm$1.2 | 6.5$\pm$0.4 | 1.42$\pm$0.02 |  $-$154.7$\pm$0.6 | 0.15⋆ | …
… | … | SW | 58.5$\pm$2.9 | 64.6$\pm$3.3 | 4.33$\pm$0.01 |  $-$143.0$\pm$0.1 | 0.49$\pm$0.02 | 2.2$\pm$0.2
… | 20170918 | NE | 20.2$\pm$1.5 | 18.7$\pm$1.8 | … | … | 0.64⋆ | 0.3$\pm$0.2
… | … | SW | 48.6$\pm$2.7 | 51.6$\pm$3.2 | 4.08$\pm$0.08 |  $-$133.6$\pm$1.1 | 0.66$\pm$0.15 | 0.9$\pm$0.3
… | 20180118 | NE | 44.6$\pm$3.2 | 56.3$\pm$4.6 | … | … | 0.75$\pm$0.19 | 0.8$\pm$0.3
… | … | SW | 54.5$\pm$3.1 | 65.0$\pm$4.0 | 4.41$\pm$0.05 |  $-$142.1$\pm$0.7 | 0.62$\pm$0.10 | 1.2$\pm$0.3
J0753$+$4231 | 19960607 | NE2(core) | 13.1$\pm$0.9 | 12.1$\pm$1.1 | … | … | 0.27⋆ | 1.4$\pm$0.9
… | … | NE1 | 162.7$\pm$8.2 | 182.0$\pm$9.2 | 1.73$\pm$0.06 |  $-$150.0$\pm$0.2 | 0.39$\pm$0.12 | 9.7$\pm$0.6
… | … | SW1 | 19.4$\pm$1.2 | 14.0$\pm$1.2 | 9.30$\pm$0.08 |  $-$136.3$\pm$0.3 | 0.24⋆ | …
… | … | SW2 | 16.2$\pm$1.0 | 43.0$\pm$2.7 | 10.66$\pm$0.08 |  $-$138.5$\pm$0.3 | 1.56$\pm$0.09 | …
… | 20150317 | NE2(core) | 13.6$\pm$1.5 | 15.5$\pm$2.1 | … | … | 0.51$\pm$0.02 | 0.4$\pm$0.3
… | … | NE1 | 165.6$\pm$8.4 | 180.2$\pm$9.2 | 2.06$\pm$0.12 |  $-$143.0$\pm$0.3 | 0.37$\pm$0.24 | 9.6$\pm$0.9
… | … | SW1 | 32.9$\pm$1.7 | 31.7$\pm$1.6 | 9.60$\pm$0.12 |  $-$136.1$\pm$0.1 | 0.51$\pm$0.02 | …
… | … | SW2 | 20.1$\pm$1.2 | 36.4$\pm$2.2 | 10.71$\pm$0.13 |  $-$138.2$\pm$0.2 | 1.45$\pm$0.08 | …
… | 20170319 | NE2(core) | 19.2$\pm$1.1 | 17.3$\pm$1.2 | … | … | 0.34⋆ | 1.2$\pm$0.6
… | … | NE1 | 165.6$\pm$8.3 | 172.6$\pm$8.7 | 2.09$\pm$0.06 |  $-$144.7$\pm$0.2 | 0.38$\pm$0.13 | 9.5$\pm$0.7
… | … | SW1 | 41.1$\pm$2.3 | 59.0$\pm$3.4 | 9.82$\pm$0.08 |  $-$137.3$\pm$0.3 | 1.25$\pm$0.10 | …
… | … | SW2 | 8.6$\pm$0.7 | 11.6$\pm$1.1 | 11.84$\pm$0.15 |  $-$141.6$\pm$0.6 | 1.38$\pm$0.27 | …
… | 20170527 | NE2(core) | 15.6$\pm$1.0 | 16.0$\pm$1.1 | … | … | 0.27$\pm$0.02 | 1.6$\pm$0.8
… | … | NE1 | 134.7$\pm$6.8 | 148.9$\pm$7.6 | 2.07$\pm$0.04 |  $-$145.1$\pm$0.2 | 0.39$\pm$0.09 | 7.4$\pm$0.6
… | … | SW1 | 31.3$\pm$1.6 | 29.5$\pm$1.5 | 9.58$\pm$0.04 |  $-$136.7$\pm$0.1 | 0.48$\pm$0.02 | …
… | … | SW2 | 20.2$\pm$1.1 | 31.9$\pm$1.7 | 10.68$\pm$0.05 |  $-$138.3$\pm$0.1 | 1.35$\pm$0.04 | …
… | 20180609 | NE2(core) | 14.4$\pm$1.0 | 14.1$\pm$1.1 | … | … | 0.27⋆ | 1.4$\pm$0.9
… | … | NE1 | 118.3$\pm$6.0 | 129.2$\pm$6.6 | 2.10$\pm$0.06 |  $-$144.9$\pm$0.3 | 0.40$\pm$0.12 | 6.0$\pm$0.6
… | … | SW1 | 30.1$\pm$1.5 | 27.6$\pm$1.4 | 9.62$\pm$0.06 |  $-$136.6$\pm$0.1 | 0.49$\pm$0.02 | …
… | … | SW2 | 20.8$\pm$1.1 | 27.8$\pm$1.5 | 10.74$\pm$0.06 |  $-$138.4$\pm$0.1 | 1.31$\pm$0.05 | …
J1230$-$1139 | 19970507 | C(core) | 117.8$\pm$6.1 | 128.8$\pm$6.8 | … | … | 0.37$\pm$0.04 | 7.4$\pm$1.2
… | … | J3 | 33.7$\pm$2.1 | 21.8$\pm$1.8 | 2.91$\pm$0.05 |  $-$32.2$\pm$1.0 | 0.26⋆ | …
… | … | J2 | 66.2$\pm$3.4 | 76.2$\pm$3.9 | 3.01$\pm$0.01 |  $-$51.8$\pm$0.3 | 0.55$\pm$0.03 | …
… | … | J1 | 14.3$\pm$1.1 | 20.1$\pm$1.8 | 3.52$\pm$0.09 |  $-$90.0$\pm$1.4 | 0.80$\pm$0.18 | …
… | 20170319 | C(core) | 65.6$\pm$3.8 | 76.2$\pm$4.9 | … | … | 0.55$\pm$0.09 | 2.0$\pm$0.5
… | … | J3 | 14.9$\pm$1.6 | 41.1$\pm$4.8 | 2.56$\pm$0.15 |  $-$49.2$\pm$3.4 | 1.80$\pm$0.30 | …
… | … | J2 | 14.3$\pm$1.8 | 12.7$\pm$2.3 | 3.55$\pm$0.18 |  $-$86.8$\pm$2.9 | 0.51⋆ | …
… | … | J1 | 10.6$\pm$1.4 | 10.5$\pm$1.9 | 5.39$\pm$0.19 |  $-$102.4$\pm$2.0 | 0.52⋆ | …
… | 20170716 | C(core) | 57.1$\pm$3.1 | 65.2$\pm$3.8 | … | … | 0.43$\pm$0.06 | 2.6$\pm$0.5
… | … | J3 | 8.5$\pm$1.7 | 30.5$\pm$6.4 | 2.37$\pm$0.26 |  $-$52.8$\pm$6.2 | 1.82$\pm$0.51 | …
… | … | J2 | 7.8$\pm$1.0 | 8.1$\pm$1.3 | 3.62$\pm$0.15 |  $-$90.8$\pm$2.3 | 0.47$\pm$0.30 | …
… | … | J1 | 7.7$\pm$1.0 | 7.5$\pm$1.3 | 5.27$\pm$0.15 |  $-$101.9$\pm$1.6 | 0.43⋆ | …
… | 20180701 | C(core) | 58.1$\pm$3.4 | 69.1$\pm$4.5 | … | … | 0.56$\pm$0.09 | 1.6$\pm$0.4
… | … | J3 | 7.9$\pm$1.4 | 24.6$\pm$4.8 | 2.42$\pm$0.26 |  $-$51.6$\pm$6.1 | 1.75$\pm$0.51 | …
… | … | J2 | 17.0$\pm$1.6 | 19.8$\pm$2.3 | 3.48$\pm$0.12 |  $-$89.5$\pm$1.9 | 0.62$\pm$0.23 | …
… | … | J1 | 2.2$\pm$0.7 | 4.6$\pm$1.5 | 6.28$\pm$0.43 |  $-$100.3$\pm$3.9 | 1.12$\pm$0.86 | …
J1316$+$6726 | 19950419 | C(core) | 125.3$\pm$6.8 | 128.6$\pm$7.5 | … | … | 0.20⋆ | 25.5$\pm$11.6
… | 20050720 | C(core) | 84.9$\pm$4.5 | 88.2$\pm$4.8 | … | … | 0.29$\pm$0.06 | 7.5$\pm$2.0
… | 20141220 | C(core) | 63.6$\pm$3.2 | 64.0$\pm$3.2 | … | … | 0.10$\pm$0.01 | 48.8$\pm$5.4
… | … | J1 | 0.9$\pm$0.2 | 4.2$\pm$0.9 | 8.06$\pm$0.26 | 157.3$\pm$1.8 | 3.24$\pm$0.51 | …
… | 20170319 | C(core) | 92.6$\pm$4.6 | 93.6$\pm$4.7 | … | … | 0.20$\pm$0.00 | 18.0$\pm$1.0
… | … | J3 | 37.3$\pm$1.9 | 1.3$\pm$0.1 | 0.78$\pm$0.01 | 110.3$\pm$0.3 | 0.79$\pm$0.01 | …
… | … | J2 | 1.1$\pm$0.1 | 1.3$\pm$0.1 | 3.33$\pm$0.08 | 112.3$\pm$1.3 | 0.68$\pm$0.15 | …
… | … | J1 | 1.4$\pm$0.1 | 5.3$\pm$0.4 | 7.76$\pm$0.07 | 152.8$\pm$0.5 | 2.89$\pm$0.15 | …
… | 20180705 | C(core) | 86.9$\pm$4.4 | 89.7$\pm$4.5 | … | … | 0.21$\pm$0.01 | 14.3$\pm$1.0
… | … | J1 | 0.3$\pm$0.2 | 5.9$\pm$3.7 | 7.77$\pm$0.75 | 151.0$\pm$5.5 | 3.60$\pm$1.50 | …
J1421$-$0643 | 19970507 | C(core) | 136.6$\pm$6.8 | 146.6$\pm$7.4 | … | … | 0.38$\pm$0.01 | 8.2$\pm$0.5
… | … | J3 | 43.4$\pm$2.2 | 14.0$\pm$0.8 | 0.79$\pm$0.01 | 68.7$\pm$1.0 | 0.13⋆ | …
… | … | J2 | 20.8$\pm$1.2 | 19.7$\pm$1.4 | 2.68$\pm$0.05 | 50.2$\pm$1.0 | 0.25⋆ | …
… | … | J1 | 27.2$\pm$1.7 | 47.2$\pm$3.1 | 4.08$\pm$0.05 | 57.5$\pm$0.8 | 1.12$\pm$0.11 | …
… | 20150122 | C(core) | 60.2$\pm$3.0 | 66.5$\pm$3.4 | … | … | 0.44$\pm$0.01 | 2.6$\pm$0.2
… | … | J4 | 22.0$\pm$1.1 | 14.9$\pm$0.8 | 0.96$\pm$0.02 | 68.2$\pm$1.2 | 0.48$\pm$0.04 | …
… | … | J3 | 18.1$\pm$1.0 | 21.8$\pm$1.3 | 2.20$\pm$0.04 | 57.8$\pm$0.9 | 0.63$\pm$0.07 | …
… | … | J2 | 10.9$\pm$0.8 | 27.8$\pm$2.1 | 5.15$\pm$0.07 | 56.4$\pm$0.8 | 1.56$\pm$0.14 | …
… | 20150317 | C(core) | 85.0$\pm$4.3 | 92.3$\pm$4.6 | … | … | 0.43$\pm$0.01 | 3.9$\pm$0.2
… | … | J4 | 32.1$\pm$1.6 | 24.7$\pm$1.3 | 0.89$\pm$0.01 | 72.2$\pm$0.8 | 0.61$\pm$0.02 | …
… | … | J3 | 24.7$\pm$1.3 | 31.7$\pm$1.6 | 2.26$\pm$0.01 | 57.3$\pm$0.3 | 0.73$\pm$0.02 | …
… | … | J2 | 14.0$\pm$0.9 | 37.4$\pm$2.4 | 5.15$\pm$0.05 | 56.3$\pm$0.6 | 1.58$\pm$0.10 | …
… | 20170219 | C(core) | 70.0$\pm$3.6 | 81.4$\pm$4.3 | … | … | 0.46$\pm$0.04 | 3.0$\pm$0.4
… | … | J4 | 23.4$\pm$1.3 | 25.0$\pm$1.5 | 1.22$\pm$0.03 | 64.0$\pm$1.4 | 0.54$\pm$0.06 | …
… | … | J3 | 22.2$\pm$1.2 | 23.3$\pm$1.4 | 2.30$\pm$0.03 | 59.0$\pm$0.8 | 0.43$\pm$0.07 | …
… | … | J2 | 9.7$\pm$1.0 | 30.7$\pm$3.3 | 5.36$\pm$0.12 | 56.4$\pm$1.2 | 1.66$\pm$0.23 | …
… | 20170319 | C(core) | 82.8$\pm$4.2 | 92.8$\pm$4.7 | … | … | 0.42$\pm$0.02 | 4.3$\pm$0.4
… | … | J4 | 29.1$\pm$1.5 | 36.7$\pm$2.0 | 1.19$\pm$0.02 | 61.7$\pm$1.1 | 0.68$\pm$0.05 | …
… | … | J3 | 20.0$\pm$1.1 | 17.7$\pm$1.1 | 2.39$\pm$0.03 | 56.0$\pm$0.8 | 0.20⋆ | …
… | … | J2 | 12.5$\pm$1.2 | 29.8$\pm$3.1 | 5.79$\pm$0.11 | 56.6$\pm$1.1 | 1.47$\pm$0.22 | …
… | 20180326 | C(core) | 79.0$\pm$4.4 | 97.3$\pm$5.7 | … | … | 0.50$\pm$0.07 | 3.0$\pm$0.6
… | … | J4 | 23.0$\pm$1.4 | 28.6$\pm$2.0 | 1.28$\pm$0.06 | 65.9$\pm$2.6 | 0.61$\pm$0.11 | …
… | … | J3 | 20.7$\pm$1.3 | 23.3$\pm$1.7 | 2.35$\pm$0.06 | 57.6$\pm$1.5 | 0.47$\pm$0.12 | …
… | … | J2 | 8.3$\pm$1.3 | 30.3$\pm$4.8 | 5.40$\pm$0.22 | 56.4$\pm$2.3 | 1.66$\pm$0.44 | …
J1445$+$0958 | 19970110 | C(core) | 155.0$\pm$7.9 | 161.1$\pm$8.3 | … | … | 0.38$\pm$0.02 | 9.0$\pm$0.9
… | … | J3 | 22.3$\pm$2.5 | 12.5$\pm$2.7 | 1.29$\pm$0.14 | 46.6$\pm$6.0 | 0.41⋆ | …
… | … | J2 | 84.4$\pm$4.5 | 100.3$\pm$5.6 | 1.20$\pm$0.03 |  $-$118.1$\pm$1.2 | 0.69$\pm$0.05 | …
… | … | J1 | 38.0$\pm$2.9 | 54.6$\pm$4.8 | 3.32$\pm$0.08 |  $-$110.8$\pm$1.4 | 0.83$\pm$0.16 | …
… | 19990510 | C(core) | 178.3$\pm$9.4 | 193.3$\pm$10.5 | … | … | 0.34$\pm$0.03 | 12.1$\pm$1.8
… | … | J2 | 93.1$\pm$5.1 | 142.8$\pm$8.0 | 1.17$\pm$0.02 |  $-$119.3$\pm$1.1 | 0.77$\pm$0.04 | …
… | … | J1 | 24.1$\pm$3.2 | 73.8$\pm$10.3 | 3.38$\pm$0.13 |  $-$111.0$\pm$2.2 | 1.46$\pm$0.26 | …
… | 20010705 | C(core) | 206.6$\pm$10.7 | 215.0$\pm$11.4 | … | … | 0.29$\pm$0.03 | 18.4$\pm$2.9
… | … | J2 | 83.8$\pm$4.5 | 112.6$\pm$6.3 | 1.18$\pm$0.02 |  $-$116.7$\pm$1.1 | 0.70$\pm$0.05 | …
… | … | J1 | 32.7$\pm$2.0 | 51.1$\pm$3.3 | 3.27$\pm$0.04 |  $-$109.1$\pm$0.7 | 0.82$\pm$0.08 | …
… | 20050622 | C(core) | 300.4$\pm$15.0 | 278.1$\pm$14.0 | … | … | 0.15$\pm$0.01 | 99.7$\pm$10.1
… | … | J3 | 192.8$\pm$9.7 | 32.4$\pm$1.8 | 0.61$\pm$0.01 | 32.9$\pm$0.6 | 0.09⋆ | …
… | … | J2 | 76.1$\pm$4.0 | 99.1$\pm$5.4 | 1.31$\pm$0.03 |  $-$109.1$\pm$1.2 | 0.87$\pm$0.05 | …
… | … | J1 | 50.5$\pm$3.0 | 69.9$\pm$4.5 | 3.21$\pm$0.05 |  $-$109.1$\pm$0.9 | 0.88$\pm$0.10 | …
… | … | JF2 | 10.2$\pm$1.7 | 27.2$\pm$4.7 | 6.09$\pm$0.24 |  $-$137.7$\pm$2.2 | 1.99$\pm$0.48 | …
… | … | JF1a | 5.0$\pm$1.5 | 46.5$\pm$13.8 | 12.12$\pm$0.45 |  $-$166.7$\pm$2.1 | 4.59$\pm$0.89 | …
… | 20080402 | C(core) | 222.5$\pm$11.8 | 224.7$\pm$12.5 | … | … | 0.17$\pm$0.02 | 59.1$\pm$11.0
… | … | J3 | 110.0$\pm$6.2 | 67.8$\pm$4.8 | 0.51$\pm$0.02 | 40.9$\pm$1.8 | 0.09⋆ | …
… | … | J2 | 21.0$\pm$2.6 | 91.7$\pm$11.7 | 2.05$\pm$0.07 |  $-$105.0$\pm$2.0 | 1.03$\pm$0.14 | …
… | … | J1 | 11.6$\pm$1.2 | 18.7$\pm$2.2 | 4.17$\pm$0.05 |  $-$116.4$\pm$0.8 | 0.37$\pm$0.11 | …
… | 20170319 | C(core) | 247.9$\pm$12.5 | 213.9$\pm$10.8 | … | … | 0.26$\pm$0.01 | 24.9$\pm$2.3
… | … | J3 | 204.1$\pm$10.3 | 122.9$\pm$6.3 | 0.72$\pm$0.01 | 40.7$\pm$0.6 | 0.10⋆ | …
… | … | J3 | 24.2$\pm$2.0 | 27.8$\pm$2.8 | 1.12$\pm$0.09 |  $-$108.1$\pm$4.5 | 0.78$\pm$0.18 | …
… | … | J2 | 57.7$\pm$3.5 | 74.6$\pm$4.9 | 2.82$\pm$0.05 |  $-$103.4$\pm$0.9 | 0.62$\pm$0.09 | …
… | … | J1 | 15.8$\pm$1.7 | 35.7$\pm$4.2 | 6.16$\pm$0.13 |  $-$138.7$\pm$1.2 | 1.39$\pm$0.26 | …
… | … | JF1a | 4.7$\pm$1.6 | 42.9$\pm$14.5 | 12.26$\pm$0.45 |  $-$169.9$\pm$2.1 | 3.44$\pm$0.89 | …
… | 20180326 | C(core) | 199.2$\pm$10.0 | 170.2$\pm$8.6 | … | … | 0.31$\pm$0.01 | 13.0$\pm$1.0
… | … | J3 | 174.6$\pm$8.8 | 110.8$\pm$5.7 | 0.75$\pm$0.01 | 39.7$\pm$0.6 | 0.09⋆ | …
… | … | J3 | 25.6$\pm$1.7 | 47.6$\pm$3.4 | 1.32$\pm$0.06 |  $-$99.4$\pm$2.7 | 1.28$\pm$0.13 | …
… | … | J2 | 55.7$\pm$3.0 | 74.4$\pm$4.2 | 2.85$\pm$0.03 |  $-$104.3$\pm$0.6 | 0.77$\pm$0.06 | …
… | … | J1 | 8.3$\pm$1.4 | 32.6$\pm$5.7 | 5.40$\pm$0.22 |  $-$137.3$\pm$2.4 | 2.26$\pm$0.45 | …
… | … | JF1a | 3.2$\pm$0.8 | 39.0$\pm$10.3 | 11.48$\pm$0.36 |  $-$168.6$\pm$1.8 | 4.34$\pm$0.71 | …
J1606$+$3124 | 19960515 | S | 372.8$\pm$19.1 | 314.5$\pm$16.0 | … | … | 0.58$\pm$0.01 | 10.8$\pm$0.6
… | … | C | 70.0$\pm$4.0 | 79.4$\pm$4.9 | 2.49$\pm$0.01 |  $-$19.9$\pm$0.3 | 0.39$\pm$0.02 | 5.2$\pm$0.5
… | … | N | 34.8$\pm$2.2 | 48.5$\pm$3.3 | 7.97$\pm$0.02 |  $-$17.3$\pm$0.2 | 0.75$\pm$0.03 | …
… | 20140809 | S | 383.3$\pm$19.4 | 444.3$\pm$22.7 | … | … | 0.58$\pm$0.01 | 11.7$\pm$0.8
… | … | C | 77.6$\pm$4.3 | 99.4$\pm$5.8 | 2.60$\pm$0.02 |  $-$17.7$\pm$0.6 | 0.64$\pm$0.03 | 2.2$\pm$0.2
… | … | N | 26.9$\pm$1.9 | 39.9$\pm$3.0 | 8.29$\pm$0.03 |  $-$17.0$\pm$0.4 | 0.87$\pm$0.07 | …
… | 20170319 | S | 334.2$\pm$16.8 | 347.4$\pm$17.6 | … | … | 0.44$\pm$0.02 | 17.3$\pm$1.4
… | … | S0 | 9.0$\pm$1.7 | 21.2$\pm$4.3 | 1.12$\pm$0.05 |  $-$24.8$\pm$1.4 | 0.13⋆ | …
… | … | C | 67.0$\pm$3.7 | 80.9$\pm$4.7 | 2.66$\pm$0.01 |  $-$17.4$\pm$0.6 | 0.53$\pm$0.03 | 2.8$\pm$0.3
… | … | N | 24.0$\pm$1.4 | 34.3$\pm$2.0 | 8.28$\pm$0.08 |  $-$16.3$\pm$0.4 | 0.75$\pm$0.06 | …
… | 20170918 | S | 328.3$\pm$16.7 | 326.2$\pm$16.8 | … | … | 0.53$\pm$0.01 | 10.4$\pm$0.6
… | … | C | 63.4$\pm$3.7 | 95.4$\pm$5.9 | 2.49$\pm$0.02 |  $-$15.7$\pm$0.8 | 0.61$\pm$0.04 | 2.3$\pm$0.4
… | … | N | 29.7$\pm$2.0 | 38.7$\pm$2.9 | 8.14$\pm$0.02 |  $-$16.6$\pm$0.3 | 1.16$\pm$0.04 | …
… | 20180326 | S | 275.1$\pm$13.9 | 296.5$\pm$15.1 | … | … | 0.47$\pm$0.01 | 11.9$\pm$0.7
… | … | S0 | 10.0$\pm$1.7 | 24.4$\pm$4.5 | 1.11$\pm$0.02 |  $-$3.0$\pm$1.3 | 0.14⋆ | …
… | … | C | 71.1$\pm$3.9 | 82.1$\pm$4.7 | 2.63$\pm$0.01 |  $-$16.6$\pm$0.6 | 0.57$\pm$0.03 | 2.3$\pm$0.3
… | … | N | 26.0$\pm$1.4 | 36.0$\pm$2.1 | 8.24$\pm$0.02 |  $-$16.1$\pm$0.3 | 0.76$\pm$0.04 | …
J1939$-$1002 | 19970110 | C(core) | 238.6$\pm$11.9 | 207.2$\pm$10.4 | … | … | 0.09$\pm$0.01 | 236.6$\pm$27.0
… | … | J3 | 174.0$\pm$8.7 | 86.7$\pm$4.4 | 1.06$\pm$0.01 | 15.9$\pm$0.3 | 0.08⋆ | …
… | … | JXa | 82.4$\pm$4.4 | 12.3$\pm$1.6 | 1.14$\pm$0.02 |  $-$160.4$\pm$1.2 | 0.17⋆ | …
… | … | J2 | 32.7$\pm$2.0 | 37.9$\pm$2.6 | 3.63$\pm$0.05 | 9.2$\pm$0.8 | 0.53$\pm$0.10 | …
… | … | J1 | 3.9$\pm$0.5 | 5.5$\pm$0.9 | 23.63$\pm$0.18 | 31.5$\pm$0.4 | 0.72$\pm$0.36 | …
… | 19970507 | C(core) | 314.6$\pm$15.8 | 302.6$\pm$15.2 | … | … | 0.42$\pm$0.01 | 14.3$\pm$0.9
… | … | J3 | 204.3$\pm$10.3 | 93.1$\pm$4.9 | 1.21$\pm$0.01 | 9.4$\pm$0.4 | 0.11⋆ | …
… | … | JXa | 18.2$\pm$1.6 | 11.2$\pm$1.6 | 1.16$\pm$0.11 |  $-$97.3$\pm$5.3 | 0.38⋆ | …
… | … | J2 | 47.3$\pm$2.6 | 55.1$\pm$3.2 | 3.65$\pm$0.03 | 7.4$\pm$0.5 | 0.65$\pm$0.07 | …
… | … | J1 | 5.1$\pm$0.7 | 5.2$\pm$1.0 | 24.05$\pm$0.19 | 26.4$\pm$0.5 | 0.52⋆ | …
… | 19981001 | C(core) | 308.8$\pm$15.5 | 286.9$\pm$14.4 | … | … | 0.27$\pm$0.01 | 31.9$\pm$2.1
… | … | J3 | 205.3$\pm$10.3 | 84.0$\pm$4.3 | 1.14$\pm$0.01 | 13.1$\pm$0.3 | 0.09⋆ | …
… | … | J2 | 44.6$\pm$2.4 | 52.2$\pm$2.9 | 3.56$\pm$0.03 | 8.1$\pm$0.5 | 0.74$\pm$0.06 | …
… | … | J1 | 1.5$\pm$0.6 | 7.5$\pm$3.1 | 21.28$\pm$0.61 | 28.2$\pm$1.7 | 2.19$\pm$1.23 | …
… | 20060711 | C(core) | 282.4$\pm$14.8 | 327.2$\pm$17.7 | … | … | 0.38$\pm$0.04 | 17.7$\pm$2.7
… | … | J2 | 21.9$\pm$4.3 | 49.5$\pm$10.6 | 3.08$\pm$0.24 | 8.9$\pm$4.4 | 1.12$\pm$0.48 | …
… | 20170205 | C(core) | 352.5$\pm$17.6 | 365.0$\pm$18.3 | … | … | 0.38$\pm$0.01 | 20.9$\pm$1.1
… | … | J3 | 210.4$\pm$10.5 | 66.6$\pm$3.4 | 1.14$\pm$0.01 | 0.9$\pm$0.2 | 0.07⋆ | …
… | … | JXa | 76.6$\pm$4.0 | 36.5$\pm$2.2 | 1.46$\pm$0.02 |  $-$159.1$\pm$0.7 | 0.14⋆ | …
… | … | J2 | 31.5$\pm$1.8 | 30.0$\pm$1.9 | 3.34$\pm$0.03 | 6.9$\pm$0.6 | 0.19⋆ | …
… | 20190204 | C(core) | 347.7$\pm$17.4 | 337.5$\pm$16.9 | … | … | 0.39$\pm$0.01 | 22.3$\pm$1.2
… | … | J3 | 193.2$\pm$9.7 | 49.1$\pm$2.6 | 1.32$\pm$0.01 |  $-$0.8$\pm$0.3 | 0.10⋆ | …
… | … | JXa | 153.4$\pm$7.7 | 35.9$\pm$1.9 | 1.37$\pm$0.01 |  $-$163.7$\pm$0.3 | 0.10⋆ | …
… | … | J2 | 38.5$\pm$2.0 | 36.1$\pm$2.0 | 3.31$\pm$0.03 | 5.9$\pm$0.5 | 0.64$\pm$0.06 | …
… | … | J1 | 2.7$\pm$0.5 | 8.8$\pm$1.6 | 21.93$\pm$0.27 | 29.1$\pm$0.7 | 2.75$\pm$0.53 | …
J2102$+$6015 | 19940812 | E0 | 138.4$\pm$7.7 | 145.1$\pm$8.8 | … | … | 0.25$\pm$0.07 | 22.2$\pm$4.6
… | 20061218 | E0 | 91.2$\pm$4.6 | 48.6$\pm$2.4 | … | … | 0.31$\pm$0.01 | 4.6$\pm$0.3
… | … | E2 | 64.6$\pm$3.3 | 36.9$\pm$1.9 | 0.54$\pm$0.01 |  $-$95.7$\pm$0.90 | 0.83$\pm$0.02 | …
… | … | E1 | 74.7$\pm$3.8 | 54.1$\pm$2.8 | 0.58$\pm$0.01 | 90.2$\pm$0.92 | 0.65$\pm$0.02 | …
… | … | W0 | 5.4$\pm$0.4 | 5.3$\pm$0.5 | 9.84$\pm$0.07 |  $-$89.2$\pm$0.43 | 0.29⋆ | …
… | 20170205 | E0 | 101.3$\pm$5.1 | 121.6$\pm$6.1 | … | … | 0.60$\pm$0.00 | 3.3$\pm$0.2
… | … | E1 | 26.8$\pm$1.4 | 9.8$\pm$0.6 | 0.79$\pm$0.01 | 79.7$\pm$0.67 | 0.08⋆ | …
… | … | E2 | 34.7$\pm$1.8 | 25.6$\pm$1.3 | 0.79$\pm$0.01 |  $-$98.2$\pm$0.52 | 0.78$\pm$0.01 | …
… | … | C | 1.3$\pm$0.2 | 1.3$\pm$0.3 | 4.68$\pm$0.15 |  $-$88.2$\pm$1.86 | 0.36⋆ | …
… |  | W0 | 2.4$\pm$0.3 | 5.5$\pm$0.7 | 9.94$\pm$0.10 |  $-$88.8$\pm$0.59 | 1.36$\pm$0.21 | …
… | 20170501 | E0 | 102.5$\pm$5.1 | 115.3$\pm$5.8 | … | … | 0.60$\pm$0.01 | 2.9$\pm$0.2
… | … | E2 | 51.0$\pm$2.6 | 25.5$\pm$1.3 | 0.82$\pm$0.01 |  $-$102.5$\pm$0.44 | 0.77$\pm$0.01 | …
… | … | E1 | 31.0$\pm$1.6 | 6.2$\pm$0.5 | 0.92$\pm$0.02 | 80.3$\pm$1.03 | 0.13⋆ | …
… | … | W0 | 3.0$\pm$0.3 | 5.2$\pm$0.5 | 10.12$\pm$0.09 |  $-$89.5$\pm$0.49 | 1.06$\pm$0.17 | …
… | 20180609 | E0 | 94.2$\pm$4.7 | 103.2$\pm$5.2 | … | … | 0.58$\pm$0.00 | 2.8$\pm$0.1
… | … | E1 | 36.3$\pm$1.8 | 5.9$\pm$0.3 | 0.81$\pm$0.00 | 111.1$\pm$0.27 | 0.07⋆ | …
… | … | E2 | 43.4$\pm$2.2 | 22.0$\pm$1.1 | 0.82$\pm$0.00 |  $-$103.2$\pm$0.27 | 0.78$\pm$0.01 | …
… | … | P1a | 18.5$\pm$1.0 | 5.1$\pm$0.3 | 1.09$\pm$0.02 | 44.5$\pm$0.80 | 0.13⋆ | …
… | … | W2b | 2.3$\pm$0.2 | 2.5$\pm$0.3 | 10.70$\pm$0.10 |  $-$89.6$\pm$0.56 | 0.41$\pm$0.21 | …

^a^afootnotetext: These components could be part of a diffuse emission or
newly ejected components that cannot be fully fitted with the nearby Gaussian
components. For such components, a point-source model was used to account for
the extra flux density.

^b^bfootnotetext: The W feature of J2102+6015 can be fitted with 3 components
(W0, W1, and W2), W2 represents the westernmost component. See details in
Zhang et al. 2021.

^*^*footnotetext: Upper limit of the component size.

Note. — Columns: (1) J2000 source name; (2) observing date; (3) component
identifier; (4) peak intensity of the component; (5) integrated flux density
of the component through Gaussian model fitting; (6) separation of the
component from core; (7) position angle of the component with respect to the
core, measured from north to east; (8) FWHM size of the fitted Gaussian model
component.

|  |
---|---|---

|  |
---|---|---

|  |
---|---|---

Figure 3: Spectral index maps of our sample, based on simultaneous 2.3- and
8.4-GHz observations. In each map, the background contours represent the
2.3-GHz image. They start from 3 times of its rms noise and increase by a
factor of 2. The bottom left ellipse are the restored beams of the 2.3-GHz map
and the epochs used for the imaging are shown at bottom right. Figure 4:
Proper motions of the fitted jet components. For each line, the left panel is
a sketch map of the component motions with respect to the core component
(marked with a star). The middle panel represents the change of relative
radial distances of the components. The right panel is the corresponding
position angle change.  Figure 5: Jet proper motions (continued) Figure 6: Jet
proper motions (continued)

## References

  * Ahn et al. (2012) Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2012, ApJS, 203, 21, doi: 10.1088/0067-0049/203/2/21
  * Alberdi et al. (2000) Alberdi, A., Gómez, J. L., Marcaide, J. M., Marscher, A. P., & Pérez-Torres, M. A. 2000, A&A, 361, 529
  * An et al. (2022a) An, T., Wang, A., Zhang, Y., et al. 2022a, MNRAS, 511, 4572, doi: 10.1093/mnras/stac205
  * An et al. (2022b) An, T., Wu, X., Lao, B., et al. 2022b, arXiv e-prints, arXiv:2206.13022.  https://arxiv.org/abs/2206.13022
  * An et al. (2019) An, T., Wu, X.-P., & Hong, X. 2019, Nature Astronomy, 3, 1030, doi: 10.1038/s41550-019-0943-4
  * An et al. (2020a) An, T., Zhang, Y., & Frey, S. 2020a, MNRAS, 497, 2260, doi: 10.1093/mnras/staa2132
  * An et al. (2020b) An, T., Mohan, P., Zhang, Y., et al. 2020b, Nature Communications, 11, 143, doi: 10.1038/s41467-019-14093-2
  * Anderson et al. (2001) Anderson, S. F., Fan, X., Richards, G. T., et al. 2001, AJ, 122, 503, doi: 10.1086/321168
  * Bañados et al. (2018a) Bañados, E., Carilli, C., Walter, F., et al. 2018a, ApJL, 861, L14, doi: 10.3847/2041-8213/aac511
  * Bañados et al. (2015) Bañados, E., Venemans, B. P., Morganson, E., et al. 2015, ApJ, 804, 118, doi: 10.1088/0004-637X/804/2/118
  * Bañados et al. (2018b) Bañados, E., Venemans, B. P., Mazzucchelli, C., et al. 2018b, Nat., 553, 473, doi: 10.1038/nature25180
  * Bañados et al. (2021) Bañados, E., Mazzucchelli, C., Momjian, E., et al. 2021, ApJ, 909, 80, doi: 10.3847/1538-4357/abe239
  * Beasley et al. (2002) Beasley, A. J., Gordon, D., Peck, A. B., et al. 2002, ApJS, 141, 13, doi: 10.1086/339806
  * Belladitta et al. (2020) Belladitta, S., Moretti, A., Caccianiga, A., et al. 2020, A&A, 635, L7, doi: 10.1051/0004-6361/201937395
  * Blandford et al. (2019) Blandford, R., Meier, D., & Readhead, A. 2019, ARA&A, 57, 467, doi: 10.1146/annurev-astro-081817-051948
  * Boettcher et al. (1997) Boettcher, M., Mause, H., & Schlickeiser, R. 1997, A&A, 324, 395.  https://arxiv.org/abs/astro-ph/9604003
  * Britzen et al. (2008) Britzen, S., Vermeulen, R. C., Campbell, R. M., et al. 2008, A&A, 484, 119, doi: 10.1051/0004-6361:20077717
  * Cao et al. (2014) Cao, H. M., Frey, S., Gurvits, L. I., et al. 2014, A&A, 563, A111, doi: 10.1051/0004-6361/201323328
  * Casadio et al. (2021) Casadio, C., Blinov, D., Readhead, A. C. S., et al. 2021, MNRAS, 507, L6, doi: 10.1093/mnrasl/slab082
  * Cheng et al. (2020) Cheng, X. P., An, T., Frey, S., et al. 2020, ApJS, 247, 57, doi: 10.3847/1538-4365/ab791f
  * Cohen et al. (1988) Cohen, M. H., Barthel, P. D., Pearson, T. J., & Zensus, J. A. 1988, ApJ, 329, 1, doi: 10.1086/166352
  * Coppejans et al. (2016) Coppejans, R., Frey, S., Cseh, D., et al. 2016, MNRAS, 463, 3260, doi: 10.1093/mnras/stw2236
  * Coppejans et al. (2017) Coppejans, R., van Velzen, S., Intema, H. T., et al. 2017, MNRAS, 467, 2039, doi: 10.1093/mnras/stx215
  * Decarli et al. (2018) Decarli, R., Walter, F., Venemans, B. P., et al. 2018, ApJ, 854, 97, doi: 10.3847/1538-4357/aaa5aa
  * Deller et al. (2011) Deller, A. T., Brisken, W. F., Phillips, C. J., et al. 2011, PASP, 123, 275, doi: 10.1086/658907
  * Diana et al. (2022) Diana, A., Caccianiga, A., Ighina, L., et al. 2022, MNRAS, 511, 5436, doi: 10.1093/mnras/stac364
  * Drinkwater et al. (1997) Drinkwater, M. J., Webster, R. L., Francis, P. J., et al. 1997, MNRAS, 284, 85, doi: 10.1093/mnras/284.1.85
  * Ellison et al. (2001) Ellison, S. L., Yan, L., Hook, I. M., et al. 2001, A&A, 379, 393, doi: 10.1051/0004-6361:20011281
  * Fabian (2012) Fabian, A. C. 2012, ARA&A, 50, 455, doi: 10.1146/annurev-astro-081811-125521
  * Fan et al. (2001) Fan, X., Narayanan, V. K., Lupton, R. H., et al. 2001, AJ, 122, 2833, doi: 10.1086/324111
  * Fomalont (1999) Fomalont, E. B. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 180, Synthesis Imaging in Radio Astronomy II, ed. G. B. Taylor, C. L. Carilli, & R. A. Perley, 301
  * Fomalont et al. (2003) Fomalont, E. B., Petrov, L., MacMillan, D. S., Gordon, D., & Ma, C. 2003, AJ, 126, 2562, doi: 10.1086/378712
  * Frey et al. (2013) Frey, S., Fogasy, J. O., Paragi, Z., & Gurvits, L. I. 2013, MNRAS, 431, 1314, doi: 10.1093/mnras/stt249
  * Frey et al. (2008) Frey, S., Gurvits, L. I., Paragi, Z., & É. Gabányi, K. 2008, A&A, 484, L39, doi: 10.1051/0004-6361:200810040
  * Frey et al. (2003) Frey, S., Mosoni, L., Paragi, Z., & Gurvits, L. I. 2003, MNRAS, 343, L20, doi: 10.1046/j.1365-8711.2003.06869.x
  * Frey et al. (2015) Frey, S., Paragi, Z., Fogasy, J. O., & Gurvits, L. I. 2015, MNRAS, 446, 2921, doi: 10.1093/mnras/stu2294
  * Frey et al. (2011) Frey, S., Paragi, Z., Gurvits, L. I., Gabányi, K. É., & Cseh, D. 2011, A&A, 531, L5, doi: 10.1051/0004-6361/201117341
  * Frey et al. (2005) Frey, S., Paragi, Z., Mosoni, L., & Gurvits, L. I. 2005, A&A, 436, L13, doi: 10.1051/0004-6361:200500112
  * Frey et al. (2018) Frey, S., Titov, O., Melnikov, A. E., de Vicente, P., & Shu, F. 2018, A&A, 618, A68, doi: 10.1051/0004-6361/201832771
  * Gabányi et al. (2015) Gabányi, K. E., Cseh, D., Frey, S., et al. 2015, MNRAS, 450, L57, doi: 10.1093/mnrasl/slv046
  * Gabányi et al. (2018) Gabányi, K. É., Frey, S., Gurvits, L. I., Paragi, Z., & Perger, K. 2018, Research Notes of the American Astronomical Society, 2, 200, doi: 10.3847/2515-5172/aaec82
  * Gaia collaboration (2020) Gaia collaboration. 2020, Gaia EDR3, Version 1, European Space Agency, doi: 10.5270/esa-1ugzkg7
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Ghisellini et al. (2014) Ghisellini, G., Celotti, A., Tavecchio, F., Haardt, F., & Sbarrato, T. 2014, MNRAS, 438, 2694, doi: 10.1093/mnras/stt2394
  * Ghisellini et al. (2013) Ghisellini, G., Haardt, F., Della Ceca, R., Volonteri, M., & Sbarrato, T. 2013, MNRAS, 432, 2818, doi: 10.1093/mnras/stt637
  * Ghisellini et al. (1993) Ghisellini, G., Padovani, P., Celotti, A., & Maraschi, L. 1993, ApJ, 407, 65, doi: 10.1086/172493
  * Gómez et al. (2000) Gómez, J.-L., Marscher, A. P., Alberdi, A., Jorstad, S. G., & García-Miró, C. 2000, Science, 289, 2317, doi: 10.1126/science.289.5488.2317
  * Greisen (2003) Greisen, E. W. 2003, Astrophysics and Space Science Library, Vol. 285, AIPS, the VLA, and the VLBA, 109
  * Gurvits et al. (2015) Gurvits, L. I., Frey, S., & Paragi, Z. 2015, in Extragalactic Jets from Every Angle, Proceedings of the International Astronomical Union, ed. F. Massaro, C. C. Cheung, E. Lopez, & A. Siemiginowska, Vol. 313, 327–328
  * Gurvits et al. (1999) Gurvits, L. I., Kellermann, K. I., & Frey, S. 1999, A&A, 342, 378.  https://arxiv.org/abs/astro-ph/9812018
  * Healey et al. (2007) Healey, S. E., Romani, R. W., Taylor, G. B., et al. 2007, ApJS, 171, 61, doi: 10.1086/513742
  * Healey et al. (2008) Healey, S. E., Romani, R. W., Cotter, G., et al. 2008, ApJS, 175, 97, doi: 10.1086/523302
  * Helmboldt et al. (2007) Helmboldt, J. F., Taylor, G. B., Tremblay, S., et al. 2007, ApJ, 658, 203, doi: 10.1086/511005
  * Hewett & Wild (2010) Hewett, P. C., & Wild, V. 2010, MNRAS, 405, 2302, doi: 10.1111/j.1365-2966.2010.16648.x
  * Hong et al. (2004) Hong, X. Y., Jiang, D. R., Gurvits, L. I., et al. 2004, A&A, 417, 887, doi: 10.1051/0004-6361:20031784
  * Hunt et al. (2021) Hunt, L. R., Johnson, M. C., Cigan, P. J., Gordon, D., & Spitzak, J. 2021, AJ, 162, 121, doi: 10.3847/1538-3881/ac135d
  * Jiang et al. (2016) Jiang, L., McGreer, I. D., Fan, X., et al. 2016, ApJ, 833, 222, doi: 10.3847/1538-4357/833/2/222
  * Jolley & Kuncic (2008) Jolley, E. J. D., & Kuncic, Z. 2008, MNRAS, 386, 989, doi: 10.1111/j.1365-2966.2008.13082.x
  * Kellermann & Pauliny-Toth (1969) Kellermann, K. I., & Pauliny-Toth, I. I. K. 1969, ApJL, 155, L71, doi: 10.1086/180305
  * Kellermann et al. (1999) Kellermann, K. I., Vermeulen, R. C., Zensus, J. A., Cohen, M. H., & West, A. 1999, New A Rev., 43, 757, doi: 10.1016/S1387-6473(99)00093-7
  * Kellermann et al. (2004) Kellermann, K. I., Lister, M. L., Homan, D. C., et al. 2004, ApJ, 609, 539, doi: 10.1086/421289
  * Kettenis et al. (2006) Kettenis, M., van Langevelde, H. J., Reynolds, C., & Cotton, B. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 497
  * Komatsu et al. (2011) Komatsu, E., Smith, K. M., Dunkley, J., et al. 2011, ApJS, 192, 18, doi: 10.1088/0067-0049/192/2/18
  * Koptelova & Hwang (2022) Koptelova, E., & Hwang, C.-Y. 2022, ApJL, 929, L7, doi: 10.3847/2041-8213/ac61e0
  * Kovalev et al. (2007) Kovalev, Y. Y., Petrov, L., Fomalont, E. B., & Gordon, D. 2007, AJ, 133, 1236, doi: 10.1086/511157
  * Krezinger et al. (2022) Krezinger, M., Perger, K., Gabányi, K. É., et al. 2022, ApJS, 260, 49, doi: 10.3847/1538-4365/ac63b8
  * Lanzetta et al. (1991) Lanzetta, K. M., Wolfe, A. M., Turnshek, D. A., et al. 1991, ApJS, 77, 1, doi: 10.1086/191596
  * Lister et al. (2021) Lister, M. L., Homan, D. C., Kellermann, K. I., et al. 2021, ApJ, 923, 30, doi: 10.3847/1538-4357/ac230f
  * Lister et al. (2009) Lister, M. L., Cohen, M. H., Homan, D. C., et al. 2009, AJ, 138, 1874, doi: 10.1088/0004-6256/138/6/1874
  * Lister et al. (2013) Lister, M. L., Aller, M. F., Aller, H. D., et al. 2013, AJ, 146, 120, doi: 10.1088/0004-6256/146/5/120
  * Lister et al. (2016) —. 2016, AJ, 152, 12, doi: 10.3847/0004-6256/152/1/12
  * Lister et al. (2019) Lister, M. L., Homan, D. C., Hovatta, T., et al. 2019, ApJ, 874, 43, doi: 10.3847/1538-4357/ab08ee
  * Liu et al. (2017) Liu, Y., Jiang, D. R., Gu, M., & Gurvits, L. I. 2017, MNRAS, 468, 2699, doi: 10.1093/mnras/stx617
  * Maiolino et al. (2005) Maiolino, R., Cox, P., Caselli, P., et al. 2005, A&A, 440, L51, doi: 10.1051/0004-6361:200500165
  * McGreer et al. (2006) McGreer, I. D., Becker, R. H., Helfand, D. J., & White, R. L. 2006, ApJ, 652, 157, doi: 10.1086/507767
  * Medvedev et al. (2020) Medvedev, P., Sazonov, S., Gilfanov, M., et al. 2020, MNRAS, 497, 1842, doi: 10.1093/mnras/staa2051
  * Mingaliev et al. (2013) Mingaliev, M. G., Sotnikova, Y. V., Mufakharov, T. V., Erkenov, A. K., & Udovitskiy, R. Y. 2013, Astrophysical Bulletin, 68, 262, doi: 10.1134/S1990341313030036
  * Mingaliev et al. (2012) Mingaliev, M. G., Sotnikova, Y. V., Torniainen, I., Tornikoski, M., & Udovitskiy, R. Y. 2012, A&A, 544, A25, doi: 10.1051/0004-6361/201118506
  * Momjian et al. (2021) Momjian, E., Bañados, E., Carilli, C. L., Walter, F., & Mazzucchelli, C. 2021, AJ, 161, 207, doi: 10.3847/1538-3881/abe6ae
  * Momjian et al. (2018) Momjian, E., Carilli, C. L., Bañados, E., Walter, F., & Venemans, B. P. 2018, ApJ, 861, 86, doi: 10.3847/1538-4357/aac76f
  * Momjian et al. (2008) Momjian, E., Carilli, C. L., & McGreer, I. D. 2008, AJ, 136, 344, doi: 10.1088/0004-6256/136/1/344
  * Momjian et al. (2004) Momjian, E., Petric, A. O., & Carilli, C. L. 2004, AJ, 127, 587, doi: 10.1086/381300
  * NASA/IPAC Extragalactic Database (2019) (NED) NASA/IPAC Extragalactic Database (NED). 2019, NASA/IPAC Extragalactic Database (NED), IPAC, doi: 10.26132/NED1.  https://catcopy.ipac.caltech.edu/dois/doi.php?id=10.26132/NED1
  * Paragi et al. (1999) Paragi, Z., Frey, S., Gurvits, L. I., et al. 1999, A&A, 344, 51.  https://arxiv.org/abs/astro-ph/9901396
  * Pâris et al. (2017) Pâris, I., Petitjean, P., Ross, N. P., et al. 2017, A&A, 597, A79, doi: 10.1051/0004-6361/201527999
  * Peck & Taylor (2000) Peck, A. B., & Taylor, G. B. 2000, ApJ, 534, 90, doi: 10.1086/308746
  * Perger et al. (2018) Perger, K., Frey, S., Gabányi, K. É., et al. 2018, MNRAS, 477, 1065, doi: 10.1093/mnras/sty837
  * Petrov (2016) Petrov, L. 2016, arXiv e-prints, arXiv:1610.04951.  https://arxiv.org/abs/1610.04951
  * Petrov et al. (2005) Petrov, L., Kovalev, Y. Y., Fomalont, E., & Gordon, D. 2005, AJ, 129, 1163, doi: 10.1086/426920
  * Petrov et al. (2006) Petrov, L., Kovalev, Y. Y., Fomalont, E. B., & Gordon, D. 2006, AJ, 131, 1872, doi: 10.1086/499947
  * Petrov et al. (2008) —. 2008, AJ, 136, 580, doi: 10.1088/0004-6256/136/2/580
  * Phillips & Mutel (1982) Phillips, R. B., & Mutel, R. L. 1982, A&A, 106, 21
  * Piner et al. (2012) Piner, B. G., Pushkarev, A. B., Kovalev, Y. Y., et al. 2012, ApJ, 758, 84, doi: 10.1088/0004-637X/758/2/84
  * Plavin et al. (2019) Plavin, A. V., Kovalev, Y. Y., & Petrov, L. Y. 2019, ApJ, 871, 143, doi: 10.3847/1538-4357/aaf650
  * Punsly et al. (2015) Punsly, B., Marziani, P., Kharb, P., O’Dea, C. P., & Vestergaard, M. 2015, ApJ, 812, 79, doi: 10.1088/0004-637X/812/1/79
  * Readhead (1994) Readhead, A. C. S. 1994, ApJ, 426, 51, doi: 10.1086/174038
  * Richards et al. (2009) Richards, G. T., Myers, A. D., Gray, A. G., et al. 2009, ApJS, 180, 67, doi: 10.1088/0067-0049/180/1/67
  * Romani et al. (2004) Romani, R. W., Sowards-Emmerd, D., Greenhill, L., & Michelson, P. 2004, ApJL, 610, L9, doi: 10.1086/423201
  * Saxena et al. (2018) Saxena, A., Marinello, M., Overzier, R. A., et al. 2018, MNRAS, 480, 2733, doi: 10.1093/mnras/sty1996
  * Sbarrato (2021) Sbarrato, T. 2021, Galaxies, 9, 23, doi: 10.3390/galaxies9020023
  * Sbarrato et al. (2015) Sbarrato, T., Ghisellini, G., Tagliaferri, G., et al. 2015, MNRAS, 446, 2483, doi: 10.1093/mnras/stu2269
  * Sbarrato et al. (2022) —. 2022, arXiv e-prints, arXiv:2203.09527.  https://arxiv.org/abs/2203.09527
  * Shen et al. (2019) Shen, Y., Wu, J., Jiang, L., et al. 2019, ApJ, 873, 35, doi: 10.3847/1538-4357/ab03d9
  * Shepherd (1997) Shepherd, M. C. 1997, Astronomical Society of the Pacific Conference Series, Vol. 125, Difmap: an Interactive Program for Synthesis Imaging, 77
  * Sotnikova et al. (2021) Sotnikova, Y., Mikhailov, A., Mufakharov, T., et al. 2021, MNRAS, 508, 2798, doi: 10.1093/mnras/stab2114
  * Sotnikova et al. (2019) Sotnikova, Y. V., Mufakharov, T. V., Majorova, E. K., et al. 2019, Astrophysical Bulletin, 74, 348, doi: 10.1134/S1990341319040023
  * Sowards-Emmerd et al. (2004) Sowards-Emmerd, D., Romani, R. W., Michelson, P. F., & Ulvestad, J. S. 2004, ApJ, 609, 564, doi: 10.1086/421239
  * Spingola et al. (2020) Spingola, C., Dallacasa, D., Belladitta, S., et al. 2020, A&A, 643, L12, doi: 10.1051/0004-6361/202039458
  * Spingola et al. (2019) Spingola, C., McKean, J. P., Massari, D., & Koopmans, L. V. E. 2019, A&A, 630, A108, doi: 10.1051/0004-6361/201935427
  * Torniainen et al. (2007) Torniainen, I., Tornikoski, M., Lähteenmäki, A., et al. 2007, A&A, 469, 451, doi: 10.1051/0004-6361:20066892
  * Tremblay et al. (2016) Tremblay, S. E., Taylor, G. B., Ortiz, A. A., et al. 2016, MNRAS, 459, 820, doi: 10.1093/mnras/stw592
  * Urry & Padovani (1995) Urry, C. M., & Padovani, P. 1995, PASP, 107, 803, doi: 10.1086/133630
  * Veres et al. (2010) Veres, P., Frey, S., Paragi, Z., & Gurvits, L. I. 2010, A&A, 521, A6, doi: 10.1051/0004-6361/201014957
  * Vermeulen & Cohen (1994) Vermeulen, R. C., & Cohen, M. H. 1994, ApJ, 430, 467, doi: 10.1086/174424
  * Wang et al. (2019) Wang, F., Yang, J., Fan, X., et al. 2019, ApJ, 884, 30, doi: 10.3847/1538-4357/ab2be5
  * Wang et al. (2021) —. 2021, ApJL, 907, L1, doi: 10.3847/2041-8213/abd8c6
  * Wang et al. (2011) Wang, R., Wagg, J., Carilli, C. L., et al. 2011, ApJL, 739, L34, doi: 10.1088/2041-8205/739/1/L34
  * Willott et al. (2010) Willott, C. J., Delorme, P., Reylé, C., et al. 2010, AJ, 139, 906, doi: 10.1088/0004-6256/139/3/906
  * Worrall et al. (2020) Worrall, D. M., Birkinshaw, M., Marshall, H. L., et al. 2020, MNRAS, 497, 988, doi: 10.1093/mnras/staa1975
  * Yi et al. (2014) Yi, W.-M., Wang, F., Wu, X.-B., et al. 2014, ApJL, 795, L29, doi: 10.1088/2041-8205/795/2/L29
  * Zeimann et al. (2011) Zeimann, G. R., White, R. L., Becker, R. H., et al. 2011, ApJ, 736, 57, doi: 10.1088/0004-637X/736/1/57
  * Zhang et al. (2020) Zhang, Y., An, T., & Frey, S. 2020, Science Bulletin, 65, 525, doi: 10.1016/j.scib.2020.01.008
  * Zhang et al. (2022) Zhang, Y., An, T., Wang, A., et al. 2022, A&A, 662, L2, doi: 10.1051/0004-6361/202243785
  * Zhang et al. (2017) Zhang, Y., An, T., Frey, S., et al. 2017, MNRAS, 468, 69, doi: 10.1093/mnras/stx392
  * Zhang et al. (2021) —. 2021, MNRAS, 507, 3736, doi: 10.1093/mnras/stab2289