Radio Jet Proper-motion Analysis of Nine Distant Quasars above Redshift 3.5

Our focus is on the jet kinematics of a sample of high-redshift blazars at z ∼ 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 ${t}_{\mathrm{gap}}=\tfrac{{D}_{\min }}{{\mu }_{\mathrm{comp}}}$, where D_min is the minimum distance that can be distinguished between available epochs, usually depending on the observing resolution and frequency. Here μ_comp denotes the proper motion of a well-identified component. In the case of VLBI measurements, D_min can be measured in mas, μ_comp in mas yr⁻¹, and thus t_gap in yr. For high-redshift radio jets, their μ_comp could be much smaller than their low-redshift counterparts due to the cosmological time dilation, thus a large t_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 ≲ z ≲ 4.5. We used the Astrogeo database ⁹ 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 Database ¹⁰ (NASA/IPAC Extragalactic Database (NED), 2019) 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). Because 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 subsample for the jet proper-motion study, according to the following criteria:

• 1.  
  The redshift is 3.5 ≲ z ≲ 4.5.
• 2.  
  The flux density at 8.4 GHz is S_{8. 4} > 50 mJy to enable high-dynamic-range imaging.
• 3.  
  The source shows the resolved jet structure in the existing 8.4 GHz archival images, a premise for being able to measure the jet component motion.
• 4.  
  Multiple epochs of VLBI imaging are available at 8.4 GHz. A minimum time gap t_gap ≈ 7 yr can be estimated by assuming a moderate jet component speed of 10c and D_min from the 3σ position error. A rough estimate of ≈0.2 for the position error is based on the 10% restoring-beam size of typical 8.4 GHz VLBA observations. The corresponding μ_comp is 0.08−0.09 mas yr⁻¹ for 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 decl. (Dec. > −40°). The latter is because the archival data were mostly obtained with the VLBA located in 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.

Table 2. Information on the High-z Quasars Selected for This Jet Proper-motion Study from Astrogeo

Name	R.A. (J2000)	Decl. (J2000)	z	Nepoch	Epoch Range	Reference
(1)	(2)	(3)	(4)	(5)	(6)	(7)
J0048+0640	00h48m587231	+06d40m06475	3.580	5	2004−2018	Gurvits et al. (1999)
J0753+4231	07h53m033375	+42d31m30765	3.595	4	1995−2018	Hewett & Wild (2010)
J1230−1139	12h30m555560	−11d39m09795	3.528	3	1996−2018	Drinkwater et al. (1997)
J1316+6726	13h16m272015	+67d26m24262	3.515	4	1995−2018	Richards et al. (2009)
J1421−0643	14h21m077556	−06d43m56356	3.689	5	1997−2018	Ellison et al. (2001)
J1445+0958	14h45m164653	+09d58m36073	3.552	6	1997−2018	Hewett & Wild (2010)
J1606+3124	16h06m085184	+31d24m46458	4.560	4	1996−2018	Healey et al. (2008)
J1939−1002	19h39m572566	−10d02m41521	3.787	5	1996−2019	Lanzetta et al. (1991)
J2102+6015	21h02m402191	+60d15m09837	4.575	4	1994−2018	Sowards-Emmerd et al. (2004)

Notes. Columns: (1) source name, (2)–(3) source equatorial coordinates R.A. and decl., (4) redshift, (5) number of available VLBI epochs at 8.4 GHz for this study, (6) time range spanned by the VLBI observations, (7) literature reference for the redshift.

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We have collected images from the Astrogeo archive for a total of 39 epochs for these 9 sources, with 3–6 epochs per source and a maximum time span of ∼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 is 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 nine 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.

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 10 VLBA antennas participated in the observations (see Table B1. 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. Because the target sources are all compact and bright (S_{8. 4} > 50 mJy), a fringe search can be done using them as calibrators, so a standard continuum observation mode was used. A total of 6 hr of observation time was divided into two sessions: BZ064A (2 hr) and BZ064B (4 hr), 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 hr on-source time. This allowed us to reach a fairly good (u,v) coverage and high image quality. We refer to Table B1 for the details of the observations.

After observations, the data were correlated with a 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) over 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 language, ¹¹ 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 split 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, bright calibrator sources (J2148+0657 for BZ064A and 3C 273 for BZ064B; Table B1) 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 subbands. 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 subband (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 minute. The data from the Astrogeo archive have been calibrated, so we just conducted the imaging and model fitting following similar steps to Difmap as above. The imaging parameters of the proposed observation are listed in Table B2. Basic information on the archival VLBI observations is given in Table B3.

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 nonlinear 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. Because 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 an 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 that were not treated as physical components were applied to account for the extra flux density. These components are also listed in Table B5.

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., $\tfrac{{\theta }_{\mathrm{beam}}}{{\rm{S}}/{\rm{N}}}$, where S/N 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).

Extremely high brightness temperatures observed in AGN cores, close to or above the inverse-Compton limit (Kellermann & Pauliny-Toth 1969) are usually considered to be 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:

$$\begin{eqnarray}&&{T}_{{\rm{B}}}=1.22\times {10}^{12}(1+z)\displaystyle \frac{{S}_{\nu }}{{\theta }_{\mathrm{comp}}^{2}{\nu }^{2}}\,{\rm{K}},\end{eqnarray} \tag{ 1 }$$

where S_ν is the flux density of the VLBI component (in Jy), ν the observing frequency (in GHz), and θ_comp is the diameter (FWHM) of the circular Gaussian component (in mas). The estimated T_B,obs values for the VLBI components in each source are listed in Table B5.

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_B,eq (Readhead 1994). This can be considered as the intrinsic brightness temperature of the relativistic jet. Observed brightness temperatures above the limit (T_B,eq ≈ 5 × 10¹⁰ 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_B,obs values as δ = T_B,obs/T_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_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 ∼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. First, we used the T_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_B,obs values were omitted, reducing the impact of possible model-fitting biases due to some potentially poor-quality data. The average T_B,obs is likely more characteristic of the quiescent states of the AGN core. The resulting average T_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_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_B,int for each of our observed sources, taking the actual rest-frame frequencies into account. The extrapolated T_B,int values are in the range of (1.1−1.4) × 10¹⁰ 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_B,int, confirming that they contain highly relativistic jets with Doppler-boosted radio emission. We calculated their Doppler factors, which 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_B,eq, suggesting that the equipartition assumption probably does not apply in these regions. The brightness temperatures of the 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.

Because the cosmological time dilation is proportional to (1 + z), the jets in the high-redshift sample appear to change 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 (≳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 B4. We fitted the linear proper motion along the R.A. (μ_x ) and decl. (μ_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 B2 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 the terminal hot spots S and N in J1606+3124 is 0.013 ± 0.002 mas yr⁻¹ (1.60 ± 0.25 c), and between the hot spot S and the inner jet knot C is 0.006 ± 0.002 mas yr⁻¹ (0.74 ± 0.25 c). This leads to a hot-spot advance speed of 0.8c (An et al. 2022a). The separation speed between the eastern and western components in J2102+6015 is 0.023 ± 0.011 mas yr⁻¹ (2.8 ± 1.4 c) (Zhang et al. 2021). In the third CSO in our sample, J0048+0640, we obtained a separation speed of 0.005 ± 0.002 mas yr⁻¹ (0.6 ± 0.2 c), giving a hot-spot advance speed of ∼0.3 c.

The apparent jet component speeds in the core–jet sources are in the range of 1.4c−17.5c, 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.

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 those presented here are still very rare. For sources at lower redshifts, Lister et al. (2019) found that the distribution of Lorentz factors peaks between Γ = 5−15, with a shallow tail reaching Γ ≈ 50. The misaligned parent population of low-Γ 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 broadband 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 Equations (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 (Γ > 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., θ < θ_crit, where the critical angle ${\theta }_{\mathrm{crit}}=\arcsin ({{\rm{\Gamma }}}^{-1})$). In such cases, a minor change in the viewing angle would greatly increase the jet's 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 pieces of evidence, including higher Lorentz factors and smaller viewing angles, support these sources belonging to the blazar class.

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 a prominent well-resolved mas-scale radio jet structure. Also, because of the cosmological time dilation, reliably detecting positional changes in jet components requires a decades-long history of VLBI monitoring observations. Thanks to the accumulated astrometric snapshot VLBI data, here we could derive jet proper motions for another six high-redshift blazars. This increases the available proper-motion sample in the early universe substantially (Table 3).

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 (μ–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 μ–z relation is consistent with the predictions of the ΛCDM cosmology and distribution of jet Lorentz factors where the vast majority of the jets have Γ ≲ 25. For a given Lorentz factor, the apparent jet component speed cannot exceed $\sqrt{{{\rm{\Gamma }}}^{2}-1}\approx {\rm{\Gamma }}$ (e.g., Urry & Padovani 1995). To better populate the high-redshift region, we added our own proper-motion measurements to the μ–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, β_app ≳ 40, are only found at z ≲ 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 μ ≈ 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 populate the high-redshift end of the apparent proper-motion–redshift diagram with reliable jet proper motions measured with VLBI.

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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 ∼3.8 mas, consistent 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_B is 7.0 ± 1.3 × 10¹⁰ K for NE and 4.6 ± 3.9 × 10¹⁰ 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 multifrequency total flux density measurements of z > 3 AGNs with the RATAN-600 radio telescope show a peaked spectrum for J0048+0640 with ν_peak ≈ 4 GHz in the observer's frame (Sotnikova et al. 2021), reinforcing that it is a young CSO source.

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 ν_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 the source being 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_B of NE1 and NE2 are 8.4 ± 1.7 × 10¹⁰ K and 1.4 ± 0.4 × 10¹⁰ K, respectively. We estimate the maximum proper motion of the jet to be 0.018 ± 0.001 mas yr⁻¹ (1.8 ± 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 of ∼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 a \higher accuracy.

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 ∼0.10 mas yr⁻¹, corresponding to an apparent transverse speed of ∼12c. The mean T_B of this source is 3.4 ± 2.7 × 10¹⁰ 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°, 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).

The redshift of this source is from photometric measurements, but with a very high probability (∼95%, Richards et al. 2009). Because 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 three available epochs, and we did not detect a significant (i.e., ≥3σ) outward motion due to the significant positional errors and the short time period. The mean T_B of the core component is 13.3 ± 5.5 × 10¹⁰ K, indicating strong nonthermal 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 14.2c, 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.

This source shows a typical core–jet radio structure. The mean T_B is 4.2 ± 2.1 × 10¹⁰ K. This source is a prominent high-z blazar. Previous studies have discovered large kiloparsec-scale radio and X-ray jets extending toward the northeast of this nucleus (Worrall et al. 2020). Our VLBI images reveal the parsec-scale jet structure, showing three jet components moving away from the core radially toward the northeast direction. The position angle of the parsec-scale jet is consistent with that of the kiloparsec-scale jet (about 30°). The estimated maximum jet proper motion is ∼0.15 mas yr⁻¹ (∼16c).

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 nonflat radio spectrum, and the lack of parsec-scale structural evolution (see Punsly et al. 2015 and the references therein). Previous multiband 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. Because 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 ± 0.01 mas yr⁻¹. The mean T_B of this source is 15.5 ± 6.4 × 10¹⁰ 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).

This source was previously identified as a flat-spectrum radio quasar (FSRQ) (Healey et al. 2007; Torniainen et al. 2007; Coppejans et al. 2016). However, further radio spectral studies based on simultaneous multifrequency 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 a high-redshift CSO source. Additional results and a detailed discussion of the CSO identification have been presented elsewhere (An et al. 2022a).

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 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_B of this source is 21.4 ± 6.7 × 10¹⁰ K, which greatly exceeds the equipartition value and indicates strong Doppler boosting with δ ≥ 4.

Because the jet component J1 is weak and diffuse at most available epochs, we just measured the proper motions of J2 and J3. The resulting jet proper motion is −0.014 ± 0.001 mas yr⁻¹ for J2 and 0.005 ± 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).

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 nature of the source, 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 ± 0.011 mas yr⁻¹ was obtained. The details are presented in a separate paper (Zhang et al. 2021).