11institutetext:  Department of Astronomy, Institute of Physics and Astronomy,
ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest,
Hungary 22institutetext: Konkoly Observatory, HUN-REN Research Centre for
Astronomy and Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121 Budapest,
Hungary 33institutetext: CSFK, MTA Centre of Excellence, Konkoly Thege Miklós
út 15-17, H-1121 Budapest, Hungary 44institutetext: Dipartimento di Fisica e
Astronomia, Università di Bologna, Via P. Gobetti 93/2, 40129 Bologna, Italy
55institutetext: INAF Istituto di Radioastronomia, via Gobetti 101, 40129,
Bologna, Italy 66institutetext: INAF Osservatorio Astronomico di Brera, Via E.
Bianchi 46, 23807, Merate, Italy 77institutetext: Shanghai Astronomical
Observatory, Key Laboratory of Radio Astronomy and Technology, Chinese Academy
of Sciences, 80 Nandan Road, Shanghai 200030, China 88institutetext: Institute
of Physics and Astronomy, ELTE Eötvös Loránd University, Pázmány Péter sétány
1/A, H-1117 Budapest, Hungary 99institutetext: HUN-REN–ELTE Extragalactic
Astrophysics Research Group, Eötvös Loránd University, Pázmány Péter sétány
1/A, H-1117 Budapest, Hungary

# Revealing faint compact radio jets at redshifts above 5 with very long
baseline interferometry

M. Krezinger,,, E-mail<EMAIL_ADDRESS>G. Baldini 44 M.
Giroletti 55 T. Sbarrato 66 G. Ghisellini 66 G. Giovannini, 4455 T. An 77
K. É. Gabányi,,, 11992233 S. Frey,, 223388

(Received XX June 2024 / Accepted XX Yyyyy 2024)

###### Abstract

Context. Over the past two decades, our knowledge of the high-redshift $(z>5)$
radio quasars has expanded, thanks to dedicated high-resolution very long
baseline interferometry (VLBI) observations. Distant quasars provide unique
information about the formation and evolution of the first galaxies and
supermassive black holes in the Universe. Powerful relativistic jets are
likely to have played an essential role in these processes. However, the
sample of VLBI-observed radio quasars is still too small to allow meaningful
statistical conclusions.

Aims. We extend the list of the VLBI observed radio quasars to investigate how
the source structure and physical parameters are related to radio loudness.

Methods. We assembled a sample of 10 faint radio quasars located at $5<z<6$
with their radio-loudness indices spanning between $0.9-76$. We observed the
selected targets with the European VLBI Network (EVN) at 1.7 GHz. The
milliarcsecond-scale resolution of VLBI at this frequency allows us to probe
the compact innermost parts of radio-emitting relativistic jets. In addition
to the single-band VLBI observations, we collected single-dish and low-
resolution radio interferometric data to investigate the spectral properties
and variability of our sources.

Results. The detection rate of this high-redshift, low-flux-density sample is
$90\%$, with only one target (J0306$+$1853) remaining undetected. The other 9
sources appear core-dominated and show a single, faint and compact radio core
on this angular scale. The derived radio powers are typical of FRII radio
galaxies and quasars. By extending our sample with other VLBI-detected $z>5$
sources from the literature, we found that the core brightness temperatures
and monochromatic radio powers tend to increase with radio loudness.

###### Key Words.:

radio continuum: galaxies — galaxies: active — galaxies: high-redshift —
galaxies: jets

##  1 Introduction

There are currently several hundred quasars known at redshift $z>5$ and their
number is increasing (e.g. Fan et al., 1999; Bañados et al., 2016; Jiang et
al., 2016; Wang et al., 2019; Onken et al., 2022; DESI Collaboration et al.,
2023; Yue et al., 2023). Their studies provide essential information about how
galaxies formed and evolved in the early Universe. Quasars can be divided into
two populations based on their radio-loudness parameter, i.e. the radio-to-
optical power ratio usually expressed as
$R_{\mathrm{4400\,\AA}}=L_{\mathrm{5\,GHz}}/L_{\mathrm{4400\,\AA}}$
(Kellermann et al., 1989, 2016) or
$R_{\mathrm{2500\,\AA}}=L_{\mathrm{5\,GHz}}/L_{\mathrm{2500\,\AA}}$ (Sramek &
Weedman, 1980). Radio-loud quasars (RLQs) are defined with $R>10$ and they
represent only $\sim 10\%$ of the known quasars (e.g. Begelman et al., 1984;
Ivezić et al., 2002), also at high redshifts (Bañados et al., 2015). Their
radio emission originates mainly from powerful relativistic plasma jets (e.g.
Padovani et al., 2015; Blandford et al., 2019). On the other hand, the nature
of the the emission of radio-quiet quasars (RQQs, $R\leq 10$) is less obvious.
RQQs make up the majority of the active galactic nuclei (AGN) population at
every redshift, therefore their study is crucial for understanding the nature
of AGN in general. They are thought not to host high-power jets. Their radio
emission generally originates from star-forming activity in their host galaxy,
accretion disk winds, coronal emission, or shock regions due to the
interaction between the outflows and interstellar clouds (Panessa et al.,
2019). These mechanisms operate at different spatial scales and radio
frequencies. Recently, Sbarrato et al. (2021) revealed that at high redshifts,
some massive ($M>10^{10}\,\mathrm{M_{\odot}}$) RQQs host powerful relativistic
jets, which seems to be at odds with the above model.

The distant AGN are known to host supermassive black holes (SMBHs) with
$M_{\mathrm{BH}}>3\times 10^{8}\,\mathrm{M_{\odot}}$, with the majority being
more massive than $10^{9}\,\mathrm{M_{\odot}}$ (e.g. Wang et al., 2013; Shen
et al., 2019; Sbarrato, 2021). Detecting preferentially these objects is
clearly a selection bias, as they are the most powerful sources of radiation,
easily observable even from vast distances corresponding to high redshifts.
The presence of $M_{\mathrm{BH}}\gtrsim 10^{8-9}\,\mathrm{M_{\odot}}$ black
holes raises important questions about the formation and evolution of the
first SMBHs in the Universe. Volonteri (2012) and Inayoshi et al. (2020)
reviewed the possible mechanisms to build up SMBHs in excess of
$10^{9}\,\mathrm{M_{\odot}}$ in less than 1 Gyr. It can only be achieved via
fast accretion in a super-Eddington regime, or assuming black hole seeds of
$\sim 10^{4}\,\mathrm{M_{\odot}}$ as a starting point not to violate the
Eddington limit. Jets might play an important role in assembling such massive
early black holes. This can be explained by a simple model (e.g. Ghisellini et
al., 2013; Sbarrato, 2021; Sbarrato et al., 2022) where the relativistic jets
carry away some of the released gravitational energy, allowing for a faster
accretion at the same observed luminosity. The distribution of jets in the
early Universe, whether they are connected to RLQs or RQQs, is important to
understand their link to the formation of the first SMBHs.

Another intriguing observational result regarding the high-redshift AGN,
inferred by the presence of blazars (i.e. sources with their jets aligned
close to the line of sight, $\theta\lesssim 10\degr$), is that the fraction of
the most massive ($>10^{9}\,\mathrm{M_{\odot}}$) black holes hosted in radio-
loud (jetted) AGN is larger than those found in RQQs at $z>4$ compared to more
recent cosmological epochs (Ghisellini et al., 2013; Sbarrato et al., 2015;
Sbarrato, 2021). It appears that high-redshift AGN with the most massive black
holes prefer to have relativistic jets. There are a few scenarios that can
explain the problem of missing RQQs. Volonteri et al. (2011) proposed the idea
that the difference might be due to internal and external absorption
mechanisms in AGN, or lower bulk Lorentz factors in jets in the early
Universe. It is also possible that the current survey sensitivity causes bias.
At high redshift, Ghisellini et al. (2015a) found the radio lobes dimmed due
to the interaction of their electrons with photons of the cosmic microwave
background. The early galaxies may also be obscured by a dense dust bubble
surrounding the central region of the AGN (Ghisellini & Sbarrato, 2016) and
only the most powerful jets are able to penetrate this bubble, sweeping away
most of the material along their path. The absence of direct link between
radio-loudness and jet presence raises the question whether there is a missing
population of relativistic jets hosted in RQQs. Or we are simply
misclassifying a fraction of blazar candidates based on X-ray and low-
resolution radio observations (e.g. Cao et al., 2017; Coppejans et al., 2016;
Krezinger et al., 2022).

To reliably observe jets in RQQs, pc-scale resolution is required, because the
radio emission on this scale is closely associated with the central engine. On
the other hand, low-resolution observations (arcsec-scale) trace the total
radio flux density, a composite emission of the different mechanisms, which
cannot be directly linked to the optical, X-ray or infrared emissions coming
from the AGN. However, low-resolution interferometric surveys are the starting
point for any follow-up radio jet study. The Faint Images of the Radio Sky at
Twenty-Centimeters (FIRST, White et al., 1997) survey catalogue at 1.4-GHz and
the recent, still ongoing multi-epoch Very Large Array Sky Survey (VLASS, Lacy
et al., 2020; Gordon et al., 2020, 2021) provide essential spectral and
structural information in help to select targets for high-resolution
observations. The technique of very long baseline interferometry (VLBI) can
achieve pc-scale linear resolution at cm wavelengths and is capable to
distinguish between compact emission with high brightness temperature and a
more extended radio feature. Only a few dozens of RQQs have been observed with
VLBI (Blundell & Beasley, 1998; Middelberg et al., 2004; Ulvestad et al.,
2005; Giroletti & Panessa, 2009; Panessa & Giroletti, 2013; Herrera Ruiz et
al., 2016; Krezinger et al., 2020; Wang et al., 2023a), and very few that can
be found at high redshift (i.e. $z>4$, Klöckner et al., 2009; Sbarrato et al.,
2021).

VLBI can provide useful astrometric information as well. Phase-referenced VLBI
observations (Beasley & Conway, 1995), where nearby calibrator sources provide
relative astrometric positions for the targeted radio-emitting features, can
be accurate to milliarcsecond (mas) level. This accuracy is comparable to the
precise optical astrometric data from the recent 3rd Data Release (DR3) of the
Gaia mission (Gaia Collaboration et al., 2016, 2023). The optical position, if
available, in addition to the VLBI radio position, adds further relevant
astrophysical and morphological information about the source. The optical
position marks the location of the AGN accretion disk or, in some cases, its
blend with the optical synchrotron emission of the innermost sub-mas scale jet
(Plavin et al., 2019). Unlike the optical, the VLBI intensity peak pinpoints
the brightest and most compact emission feature, the self-absorbed base of the
jet (i.e. the core), or sometimes a shock front (i.e. a hotspot in a lobe) in
an extended radio source (Kovalev et al., 2017).

In this paper, we present VLBI observations of ten $z>5$ radio quasars with
different radio-loudness indices. This way, we expect to cover a variety of
radio-emitting AGN in order to understand whether the radio-loudness cut is
meaningful in terms of the presence of relativistic jets at such high
redshifts. The experiment was carried out with the European VLBI Network (EVN)
combined with e-MERLIN (Enhanced Multi-Element Radio-Linked Interferometer
Network) antennas at the frequency of 1.7 GHz in 2022. The sensitivity and
high angular resolution of the EVN allow us to detect compact core–jet
features. With the inclusion of e-MERLIN stations, it is also possible to
detect extended ($\sim 0\aas@@fstack{\prime\prime}1$) emission if present. The
goal was to investigate the nature of these sources using high-resolution VLBI
imaging data, together with radio spectral information found in the
literature, and the recent Gaia DR3 optical positions where available. By
involving literature data about other known $z>5$ quasars as well, we
investigate how the mas-scale properties are related to the radio loudness of
the sources.

In Section 2, we introduce the sample of 10 objects targeted with the EVN. In
Section 3, the details of the observations and data reduction are provided.
Our result are given in Section 4 and discussed in Section 5. The findings of
this study are summarised in Section 6. Throughout this paper, we assume a
standard flat $\Lambda$ Cold Dark Matter cosmological model with
$\Omega_{\mathrm{m}}=0.3$, $\Omega_{\mathrm{\Lambda}}=0.7$, and $H_{0}=70$ km
s-1 Mpc-1, and used these parameters in the cosmology calculator of Wright
(2006). In this model, the typical linear scale is $\sim 6$ pc mas-1 and the
luminosity distance of our sources is $\sim 50$ Gpc.

##  2 Target sample

With this study, we aim at extending the list of the VLBI-observed high-
redshift radio-quiet quasars. To this end, we searched for faint radio
emitters among the sources in the catalogue of the known $z>5$ quasars
compiled by Ross & Cross (2020). From this catalogue, the nine sources with
the lowest radio power were selected. These have VLASS detection but have not
been observed with VLBI yet. Their 2.7-GHz VLASS flux densities are ranging
between $1\,\mathrm{mJy}<S_{\mathrm{2.7\,GHz}}<11\,\mathrm{mJy}$. Six of them
were also detected in the 1.4-GHz FIRST survey. The 10th target, SDSS
J0306$+$1853, having one of the most massive known SMBHs among quasars at
$z>5$ with 1.1$\times 10^{10}$ M⊙ (Wang et al., 2015), is also included in the
sample. It was previously investigated by Sbarrato et al. (2021) and found to
be unresolved on arcsecond scales with the Karl G. Jansky Very Large Array
(JVLA), suggesting the presence of a compact radio jet. Its flux densities
were 0.25 mJy and 0.09 mJy at 1.5 and 5 GHz frequencies, respectively
(Sbarrato et al., 2021). There were no other radio observations of this
quasar.

Table 1 contains the parameters of the selected radio sources. Since all but
one of them have VLASS detection, for the sake of simplicity and uniformity,
we calculated the radio loudness index using the 2.7-GHz flux density as
$R=L_{\mathrm{2.7\,GHz}}/L_{\mathrm{4400\,A}}$. In the case of J0306$+$1853
which is not detected in VLASS, we used the flux densities and spectral index
derived by Sbarrato et al. (2021) to estimate the 2.7-GHz radio power. The 10
sources in our sample have radio loudness in the range $0.9\leq R\leq 76$.

Table 1: List of the target sources and information on their respective phase-
reference calibrators used in the EVN observations.

Source ID | $z$ | $D_{\mathrm{L}}$ | Linear scale | $S_{\mathrm{2.7}}$ | $S_{\mathrm{1.4}}$ | $R$ | Phase | Separation
---|---|---|---|---|---|---|---|---
|  | [Mpc] | [pc mas-1] | [mJy] | [mJy] | [$L_{\mathrm{2.7\,GHz}}/L_{\mathrm{4400\,A}}$] | calibrator | [°]
J0306$+$1853 | 5.3631 | 50596 | 6.06 | 0.15 (0.01)∗ | … | 0.9 | J0259+1925 | 1.79
J0616$-$1338 | 5.5802 | 53030 | 5.94 | 1.3 (0.2) | … | 9.3 | J0618$-$1418 | 0.80
J0741$+$2520 | 5.1943 | 48767 | 6.16 | 4.2 (0.2) | 2.9 (0.1) | 6.5 | J0746+2549 | 1.12
J0747$+$1153 | 5.2604 | 49493 | 6.12 | 1.5 (0.2) | … | 8.6 | J0749+1057 | 1.02
J0901$+$1615 | 5.6305 | 53585 | 5.91 | 2.9 (0.4) | 3.9 (0.2) | 76.1 | J0905+1541 | 1.10
J1034$+$2033 | 5.0106 | 46748 | 6.28 | 3.9 (0.3) | 3.9 (0.1) | 20.4 | J1036+2203 | 1.59
J1614$+$4640 | 5.3136 | 50077 | 6.09 | 4.0 (0.2) | 1.7 (0.1) | 20.3 | J1616+4632 | 0.31
J2239$+$0030 | 5.0906 | 47624 | 6.23 | 1.0 (0.2) | 1.4 (0.1) | 29.9 | J2239+0128 | 0.98
J2245$+$0024 | 5.1706 | 48393 | 6.18 | 1.4 (0.2) | 0.9 (0.1) | 58.0 | J2247+0000 | 0.66
J2344$+$1653 | 5.0006 | 46638 | 6.28 | 10.5 (0.2) | … | 24.3 | J2347+1709 | 0.85

Notes. Col. 1 – source name derived from J2000 equatorial coordinates; Col. 2
– spectroscopic redshift and its reference in the upper index (1: Wang et al.
(2015), 2: Yang et al. (2019), 3: McGreer et al. (2009), 4: Yang et al.
(2016), 5: Bañados et al. (2015), 6: Wang et al. (2016)); Col. 3 – luminosity
distance; Col. 4 – linear scale at the source redshift; Col. 5 – VLASS 2.7-GHz
flux density (uncertainty in parentheses). ∗ The 2.7-GHz flux density
calculated using the spectral index from Sbarrato et al. (2021); Col. 6 –
FIRST 1.4-GHz flux density (uncertainty in parentheses); Col. 7 – radio-
loudness parameter; Col. 8 – phase-reference calibrator source name; Col. 9 –
angular separation between the target and calibrator sources.

##  3 Observations and data reduction

###  3.1 EVN observations

The selected 10 faint radio sources were observed with the EVN at a single
frequency band centred around 1.66 GHz. The observations were carried out in
two sessions under the project code EG119 (PI: G. Baldini), one with 9 targets
in 2022 June 3 (EG119A) and another with J0306$+$1853 as the only target in
2022 October 22 (EG119B). In addition to the elements of the EVN, antennas of
the e-MERLIN were also included in the VLBI network. Since the targets are
faint sources, it was necessary to use the technique of phase referencing
(Beasley & Conway, 1995). In this observing mode, the radio telescopes were
nodding between a nearby bright compact calibrator source and the given
target, in repeating cycles. In our case, within the 8.5-min cycle time, 6.5
min was spent on the weak target source, the rest was spent on the calibrator
and with antenna slewing. The EG119B run had a shorter, 7-min cycle time, of
which 4.6 min was spent on the target source. The total bandwidth of 128 MHz
was divided into four 32-MHz wide intermediate frequency channels (IFs), each
further divided into 64 spectral channels. The data were recorded with 1024
Mbps data rate, in left and right circular polarizations. Bright compact
fringe-finder sources were also scheduled in the experiments, J0646$+$4451,
J1642$+$3948, and J2253$+$1608 in EG119A, and 3C 84 in EG119B. Overall, 15
radio telescopes participated in the experiments: Jodrell Bank Mk2
($38\,\mathrm{m}\times 25\,\mathrm{m}$ diameter, United Kingdom), Westerbork
($25$ m, The Netherlands), Effelsberg ($100$ m, Germany), Medicina ($32$ m,
Italy), Noto ($32$ m, Italy), Onsala ($25$ m, Sweden), Tianma ($65$ m, China),
Urumqi ($25$ m, China), Toruń ($32$ m, Poland), Hartebeesthoek ($26$ m, South
Africa) and the e-MERLIN antennas in the United Kingdom: Cambridge ($32$ m),
Darnhall, Defford, Knockin, and Pickmere ($25$ m each). Urumqi participated in
the EG119A experiment only. The data were processed at the Joint Institute for
VLBI European Research Infrastructure Consortium (JIVE, Dwingeloo, The
Netherlands) with the SFXC software correlator (Keimpema et al., 2015) with 2
s integration time. Typical $(u,v)$ coverages for the two project segments are
shown in Fig. 1.

Figure 1: Typical $(u,v)$ coverages for low-declination targets in the EG119A
(top) and EG119B (bottom) project segments.

###  3.2 Data reduction

The data were calibrated using the NRAO Astronomical Image Processing System
(aips) software package (Greisen, 2003), following a standard procedure (e.g.
Diamond, 1995). As the first step after loading the raw correlated data, the
interferometric visibility amplitudes were calibrated using the antenna gain
curves and the system temperatures measured at each telescope. Then, the data
were corrected for the dispersive ionospheric delay using total electron
content maps derived from global navigation satellite systems data. Phase
changes due to the time variation of the source parallactic angle were also
corrected for radio telescopes with azimuth–elevation mount. An initial
correction of instrumental phases and delays was performed using a 1-min scan
on a strong fringe-finder source. Then global fringe-fitting (Schwab & Cotton,
1983) was performed on the phase-reference and fringe-finder calibrators.
These calibrated visibility data were exported to the Difmap software package
(Shepherd et al., 1994), where we carried out hybrid mapping. The process
involved several iterations of the clean deconvolution algorithm (Högbom,
1974) and phase-only self-calibration (Pearson & Readhead, 1984), followed by
a few rounds of amplitude and phase self-calibration with decreasing solution
intervals. Antenna-based median gain correction factors, if in excess of $\pm
5\%$, were applied to the visibility amplitudes in aips. The clean model
components of the calibrators produced in Difmap were transferred to aips as
inputs for a repeated fringe-fitting of the calibrator data. By taking the
phase-reference calibrator source structure into account, we could improve
phase solutions. The fringe-fit solutions obtained for the phase-reference
calibrators were interpolated to the respective target source data. The
calibrated visibility data of the target sources were then exported from aips.

The final target source images were produced with Difmap (Shepherd et al.,
1994). To reduce the image noise, we applied natural weighting, where weights
were calculated as the reciprocal of the amplitude errors (uvweight $0,-1$).
The dirty images were shifted to make the brightness peak coincide with the
origin at (0,0) relative right ascension and declination. Following a standard
mapping procedure for weak (mJy-level) targets, only a few rounds of clean
iterations were performed without self-calibration. After reaching an
insignificant peak-to-noise level (below $\sim 5\sigma$) in the residual
images, we performed a final clean iteration involving $1000$ steps with a
very small loop gain $(0.01)$. The purpose of this last step is to smooth the
noise features in the final images. The resulting images are presented in Fig.
2 and their parameters are listed in Table 2. The phase-referenced VLBI
positions of the sources were obtained from the images using the aips task
maxfit.

The e-MERLIN stations participating in the interferometer network provided
relatively short baselines and thus allowed us to check whether there is $\sim
100$-mas scale extended emission in our sources. In Difmap, we applied a taper
to the visibility data to reduce the weight of the longer baselines (uvtaper
0.5, 12). This way we increased the sensitivity to detect possible extended
emission. We set the full width at half maximum (FWHM) of the Gaussian taper
at the baseline length of 12 million wavelengths (M$\lambda$).

In addition to producing the clean images, circular Gaussian brightness
distribution model components were also fitted to the visibility data
(Pearson, 1995) in Difmap. This allows us to quantitatively characterise
component sizes and flux densities (Table 3). In the absence of self-
calibration, the effect of coherence loss (Martí-Vidal et al., 2010) on the
peak brightness and flux density values has to be considered. To estimate the
level of correction for coherence loss, we imaged and modelled the calibrator
sources with and without performing phase self-calibration, and found an
average model flux density difference of $25\%$. Therefore, the fitted flux
densities and the peak brightness values were multiplied by a factor of
$1.25$. This factor can still be considered as a lower limit because it does
not take into account the fact that the calibrator data have been fringe
fitted, and their visibility phases are already corrected to a better degree
than for the targets. Note that our correction factor is consistent with
estimates found for other EVN experiments (e.g. Mosoni et al., 2006; Gabányi
et al., 2019; Krezinger et al., 2022).

The uncertainties of the parameters of the fitted Gaussian model components
were estimated following the method of Fomalont (1999). For the flux
densities, an additional $5\%$ error was added in quadrature, to account for
the VLBI absolute amplitude calibration uncertainty (e.g. An et al., 2012;
Frey et al., 2015).

##  4 Results

The naturally weighted 1.7-GHz EVN images are presented in Fig. 2. The image
parameters are listed in Table 2. Out of the $10$ target sources, $9$ were
successfully detected as a compact core. The tapering described in Sect. 3.2
did not reveal extended emission around any of the compact cores in the
detected $9$ sources. Only 3 (namely J1034$+$2033, J1614$+$4640, and
J2344$+$1653) of the brighter sources cloud be imaged at higher resolution
with applying uniform weighting. J0306$+$1853 was found to be non-detected
even after applying different data weighting schemes and tapering. The upper
limit to the brightness of this source is $113\leavevmode\nobreak\ \mu$Jy
beam-1 ($5\leavevmode\nobreak\ \sigma$) using the same natural weighting
applied for the images in Fig. 2 and corrected for $25$% coherence loss. The
parameters derived for the sources are given in Table 3.

Figure 2: Naturally weighted EVN images at $1.7$ GHz. Red crosses mark the
Gaia DR3 optical position in the four cases where it is available. The size of
the crosses indicates the $3\sigma_{\mathrm{pos}}$ uncertainty (see Sect.
5.2). The lowest contours are drawn at $\pm 3$ times the image noise and the
positive contours increase by a factor of 2. The restoring beam is shown in
the bottom-left corner. Table 2 contains the image parameters and the
coordinates corresponding to the images centres. Table 2: The 1.7-GHz VLBI
image parameters and source positions.

Source ID | RAVLBI | DecVLBI | Peak intensity | Restoring beam |  $1\sigma$ noise
---|---|---|---|---|---
| [$\mathrm{h\leavevmode\nobreak\ min\leavevmode\nobreak\ s}$] | [∘ ′ ′′] | [mJy beam-1] | [mas $\times$ mas] | [∘] | [mJy beam-1]
J0616$-$1338 | 06 16 24.37784 (0.00016) |  $-13$ 38 06.4239 (0.0024) | 1.08 (0.09) | 11.4 $\times$ 3.8 | 71.5 | 0.04
J0741$+$2520 | 07 41 54.71629 (0.00008) | +25 20 29.5594 (0.0012) | 0.81 (0.06) | 4.6 $\times$ 3.6 | 13.4 | 0.03
J0747$+$1153 | 07 47 49.17454 (0.00008) | +11 53 52.4652 (0.0012) | 0.76 (0.06) | 4.6 $\times$ 3.8 | 37.2 | 0.03
J0901$+$1615 | 09 01 32.64577 (0.00008) | +16 15 06.7575 (0.0012) | 1.15 (0.08) | 4.7 $\times$ 3.9 | 34.3 | 0.04
J1034$+$2033 | 10 34 18.64033 (0.00009) | +20 33 00.1247 (0.0013) | 1.68 (0.12) | 5.1 $\times$ 3.7 | 8.8 | 0.05
J1614$+$4640 | 16 14 25.14299 (0.00013) | +46 40 28.9963 (0.0019) | 2.57 (0.10) | 8.4 $\times$ 3.9 | 4.0 | 0.03
J2239$+$0030 | 22 39 07.56146 (0.00008) | +00 30 22.5944 (0.0012) | 0.78 (0.06) | 4.9 $\times$ 3.6 | 34.8 | 0.02
J2245$+$0024 | 22 45 24.27741 (0.00009) | +00 24 14.1389 (0.0013) | 0.45 (0.04) | 5.4 $\times$ 3.9 | 49.8 | 0.02
J2344$+$1653 | 23 44 33.49974 (0.00009) | +16 53 16.5598 (0.0013) | 3.36 (0.23) | 5.2 $\times$ 3.9 | 34.7 | 0.10

Notes. Col. 1 – source name; Col. 2 – right ascension with its uncertainty in
seconds (in parentheses); Col. 3 – declination with its uncertainty in
arcseconds (in parentheses); Col. 4 – image peak intensity; Col. 5 – restoring
beam major and minor axes (FWHM); Col. 6 – position angle of the restoring
beam major axis, measured from north through east; Col. 7 – $1\sigma$ image
noise level.

The 1.7-GHz redshift-corrected brightness temperatures were calculated
following (Condon et al., 1982):

$T_{\mathrm{b}}=1.22\times
10^{12}\,(1+z)\frac{S_{\nu}}{\theta^{2}\nu^{2}}\,\,[\mathrm{K}],$ (1)

where $z$ is the redshift, $S_{\nu}$ the integrated flux density of the core
in Jy, $\theta$ the fitted circular Gaussian component diameter (FWHM) in mas,
and $\nu$ the observing frequency in GHz. To check whether the sources are
resolved by the interferometer, we calculated the minimum resolvable size
following the formula of Kovalev et al. (2005). We found that each of our
sources are resolved. It should be noted here that the slightly resolved
structure could also be partly an effect of visibility phase decorrelation.

To investigate the compactness of the sources on the VLBI scale, we adopted
the method presented by Lee et al. (2008). They define the compactness as the
ratio of the core flux density to the total flux density of the clean
components obtained during the imaging,
$S_{\mathrm{core}}/S_{\mathrm{clean}}$. Here $S_{\mathrm{core}}$ is equal to
the modelled flux density, $S_{\mathrm{1.7}}$, while $S_{\mathrm{clean}}$ is
obtained by integrating the flux density contained in the clean components in
a 15-mas radius region around the core. The $S_{\mathrm{clean}}$ values are
consistent with the modelled flux densities within $10\%$, which indicates
that the sources are core-dominated, as seen from their appearance in the VLBI
images (Fig. 2).

Another way to characterise the compactness of the sources is to investigate
the ratio of their VLBI flux density to the total flux density. However, this
indicator gives information about the difference in the radio emission between
pc and kpc scales. We calculated the ratio of the 1.7-GHz VLBI flux density
obtained from Gaussian model fits ($S_{\mathrm{1.7}}$) to the total flux
density ($S_{\mathrm{VLA,1.7}}$). The latter values are estimated using the
derived spectral indices or log-parabolic spectral fits (see more in Section
5.3).

Using the formula of Hogg et al. (2002), we calculated the core and total
1.7-GHz redshift-corrected monochromatic radio powers, $P_{\mathrm{1.7,core}}$
and $P_{\mathrm{1.7,total}}$, respectively:

$P_{\nu}=1.20\times
10^{20}\,D_{\mathrm{L}}^{2}S_{\nu}(1+z)^{-1-\alpha}\,\,[\mathrm{W}\,\mathrm{Hz}^{-1}].$
(2)

In this equation, $D_{\mathrm{L}}$ refers to the source luminosity distance in
Mpc unit, $\alpha$ is the radio spectral index (see Table 4), and
$S_{\nu}=S_{\mathrm{1.7}}$ for $P_{\mathrm{1.7,core}}$ (assuming the same
spectral index for the VLBI-scale emission as derived from the total flux
densities), while $S_{\nu}=S_{\mathrm{VLA,1.7}}$ for $P_{\mathrm{1.7,total}}$.
We applied $\alpha=0$ to sources with peaked spectrum because the spectral
shape in the frequency range where the K-correction is applied is close to
flat (see Fig. 3).

Table 3: The derived physical parameters of the sources.

Source ID | $S_{\mathrm{1.7}}$ | $\theta_{\mathrm{1.7}}$ | $T_{\mathrm{b,1.7}}$ | $S_{\mathrm{clean}}$ | $S_{\mathrm{VLA,1.7}}$ | $S_{\mathrm{1.7}}/S_{\mathrm{VLA,1.7}}$ | $P_{\mathrm{1.7,core}}$ | $P_{\mathrm{1.7,total}}$
---|---|---|---|---|---|---|---|---
| [mJy] | [mas] | [$10^{8}$ K] | [mJy] | [mJy] |  | [1026 W Hz-1] | [1026 W Hz-1]
J0306$+$1853 | $<0.11^{*}$ | … | … | … | 0.23 (0.01) | … | … | 0.57 (0.08)
J0616$-$1338 | 1.86 (0.27) | 2.3 (0.1) | 10.6 (2.0) | 1.86 | … | … | 3.86 (0.73) | …
J0741$+$2520 | 2.69 (0.36) | 8.5 (0.5) | 1.0 (0.2) | 2.54 | 3.33 (0.41) | 0.81 (0.21) | 1.24 (0.22) | 1.54 (0.26)
J0747$+$1153 | 1.79 (0.24) | 4.0 (0.2) | 3.1 (0.6) | 1.81 | … | … | 1.66 (0.29) | …
J0901$+$1615 | 3.06 (0.39) | 8.4 (0.5) | 1.3 (0.2) | 3.19 | 3.68 (0.17) | 0.82 (0.15) | 3.96 (0.70) | 4.75 (0.62)
J1034$+$2033 | 3.46 (0.46) | 3.2 (0.2) | 9.2 (1.6) | 3.56 | 4.18 (0.14) | 0.83 (0.14) | 1.51 (0.27) | 1.83 (0.22)
J1614$+$4640 | 3.45 (0.35) | 1.5 (0.1) | 41.7 (4.9) | 3.96 | 2.95 (0.41) | 1.23 (0.29) | 1.73 (0.27) | 1.41 (0.29)
J2239$+$0030 | 1.36 (0.18) | 2.2 (0.1) | 7.7 (1.4) | 1.56 | 1.06 (0.21) | 1.28 (0.42) | 1.06 (0.19) | 0.83 (0.19)
J2245$+$0024 | 0.76 (0.12) | 4.0 (0.3) | 1.3 (0.3) | 0.76 | 1.31 (0.14) | 0.58 (0.16) | 0.35 (0.07) | 0.60 (0.09)
J2344$+$1653 | 7.03 (0.89) | 1.9 (0.1) | 53.0 (8.9) | 6.67 | 14.13 (0.47) | 0.50 (0.08) | 9.31 (1.61) | 18.71 (2.27)

Notes. ∗ non-detection, an upper limit to the peak brightness is given in mJy
beam-1; the errors are shown in parentheses; Col. 1 – source name; Col. 2 –
1.7-GHz fitted core flux density, with errors shown in parentheses; Col. 3 –
fitted FWHM of the core component; Col. 4 – redshift-corrected 1.7-GHz
brightness temperature; Col. 5 – cleaned flux density integrated within the
central 15-mas radius area; Col. 6 – 1.7-GHz total flux density estimated
using the derived spectral indices and log-parabolic coefficients (see Table
4); Col. 7 – ratio of the measured VLBI and the calculated total 1.7-GHz flux
densities; Col. 8 – 1.7-GHz monochromatic radio power for the core and its
uncertainty; Col. 9 – 1.7-GHz total monochromatic radio power and its
uncertainty.

##  5 Discussion

###  5.1 The origin and the nature of the radio emission

The high detection rate of compact pc-scale jets in RQQs in this study (3
sources out of 4 were detected) contrasts with the low detection rates seen in
low-redshift RQQ samples (Baldi et al., 2018, 2021; Wang et al., 2023a, b).
This potentially suggests an interesting evolution in the jet properties
and/or launch mechanisms of RQQs with cosmic time. Selection effects still
could play a role in this contradiction. It should be noted when the results
are compared with the low-redhsift samples that the rest-frame frequencies for
our 1.7-GHz measurements at $5<z<6$ are equal to $\sim 10-12$ GHz. The
difference between the rest-frame frequencies could cause bias in the
comparison. Nevertheless, the detected sources may represent the tip of the
iceberg, the brightest, most luminous of the high-redshift RQQ population.
Further deeper VLBI observations probing fainter sources would test whether
the high detection rate holds. It is possible that the RLQ/RQQ dichotomy
itself becomes increasingly blurred at high redshifts, if a larger fraction of
AGN have relativistic jets due to different accretion physics or environmental
conditions in the early Universe.

The sources detected in our sample appear to be highly core-dominated. They
seem to lack extended emission due to the losses coming from scattering with
cosmic microwave background (CMB) photons (Ghisellini et al., 2015a), or
perhaps the pc-scale jets are beamed towards the observer. It is also possible
that these radio AGN are very young, powerful, and intrinsically small sources
(O’Dea & Saikia, 2021). The derived brightness temperatures (see Table 3) all
exceed $T_{\mathrm{b}}=10^{6}$ K by at least two orders of magnitude, clearly
indicating non-thermal radio emission related to AGN activity and ruling out
star formation in the host galaxy as the primary source of radio emission
(Condon, 1992; Kewley et al., 2000; Middelberg et al., 2011). The AGN-
associated activity may include jets, outflows and coronal emission (Panessa
et al., 2019). The compactness and the derived $T_{\mathrm{b}}\sim 10^{8-9}$ K
values strengthen the case for the presence of plasma jets in our sources.
Jetted radio sources often show relativistically enhanced radio emission,
depending on the jet inclination to the line of sight and the bulk speed of
the plasma. The jet emission is considered Doppler-boosted when
$T_{\mathrm{b}}$ exceeds the equipartition value of $T_{\mathrm{b,eq}}\approx
5\times 10^{10}$ K (Readhead, 1994). Having the highest measured
$T_{\mathrm{b}}=(5.3\pm 0.9)\times 10^{9}$ K in our sample, the radio emission
in none of these sources appears Doppler-boosted, suggesting their jets are
not aligned close to the line of sight. However, VLBI imaging at higher
observing frequency and thus with better angular resolution might be able to
reveal higher brightness temperatures in these sources, depending on the shape
of the radio spectrum.

The pc-scale morphology of the radio structures in this sample of 9 VLBI-
detected AGN is generally similar to what is seen in other high-redshift VLBI
samples (e.g. Coppejans et al., 2016; Krezinger et al., 2022). There is no
clear sign of extended emission beyond a few mas radius or other jet component
in addition to the compact core. The only exception is J2344$+$1653, where the
$S_{\mathrm{1.7}}/S_{\mathrm{VLA,1.7}}$ ratio is $0.50\pm 0.08$. It suggests
the presence of a diffuse ($\sim 0.1-1\arcsec$) emission around the compact
core which is resolved out by the EVN. This could also apply for J2245$+$0024,
but the uncertainties are larger for that source (Table 3).

###  5.2 Gaia optical astrometric positions

The Gaia astrometric space mission provides the most accurate optical
positions available nowadays for AGN (Gaia Collaboration et al., 2016, 2023).
Thanks to the sensitivity of Gaia, its catalogue contains even some faint
distant AGN. Comparing their coordinates with the radio positions derived from
VLBI observations which have similar (mas or sub-mas) accuracy, additional
information on the nature of the investigated sources could be revealed. The
optical position of a quasar is generally linked to the thermal emission
originating from the accretion disk (Kovalev et al., 2017; Plavin et al.,
2019). On the other hand, the radio emission corresponds to the synchrotron
self-absorbed base of the jet with $\tau_{\nu}$ = 1 optical depth at the given
frequency $\nu$, or possibly a compact hotspot associated with a shock front
between the jet and the surrounding medium. The radio core is usually the
brightest and most compact region of the jet and can be pinpointed with VLBI
observations (e.g. Fey et al., 1997). Up to a few mas offset between radio and
optical AGN positions can occur and its position angle is found to
statistically coincide with the VLBI jet direction (Petrov et al., 2019). For
faint radio sources like the typical high-redshift quasars, revealing a
significant Gaia–VLBI positional mismatch exceeding the typical values could
help constraining the source classification and the nature of compact radio
emission, as it would suggest an extended structure with a quasar jet
misaligned with respect to the line of sight.

Out of the ten targets in our sample, five (namely J0306$+$1853, J0741$+$2520,
J0747$+$1153, J1034$+$2033, and J2344$+$1653) have been detected by Gaia. The
Gaia positions are marked with red crosses in Fig. 2. The uncertainties of the
optical positions from the Gaia DR3 (Gaia Collaboration et al., 2023) are
within 3 mas. The astrometric excess noise is only significant in the case of
J0747$+$115, where we added it to the formal position error in quadrature.
Since the quasar J0306$+$1853 remained undetected with the EVN, we could not
derive its accurate radio position to be compared with the Gaia position. The
Gaia–VLBI positional offsets are ranging between $1.3-1.8$ mas. An offset can
be considered significant if the optical position differs by more than
$3\sigma_{\mathrm{pos}}$, where
$\sigma_{\mathrm{pos}}=\sqrt{\sigma_{\mathrm{VLBI}}^{2}+\sigma_{\mathrm{Gaia}}^{2}}$,
the square root of the sum of squares of the VLBI and the Gaia positional
uncertainties. Based on this criterion, we find the optical–radio offsets
insignificant. This in fact indicates that the detected radio features could
be related to the inner jet, located close to the central engine.

###  5.3 Continuum radio spectra

We collected the available single-dish and low-resolution radio
interferometric observations from the literature for the targets, in order to
build their total flux density spectra. The investigated quasars are faint
($S_{\mathrm{2.7}}<11$ mJy, Table 1), thus they are often below the detection
thresholds of shallow surveys. The main sources of the flux density
measurements are the GMRT (Giant Metrewave Radio Telescope) and uGMRT
(upgraded GMRT) observations of radio-loud quasars at $z>5$ (Shao et al.,
2020, 2022) and various surveys carried out with the VLA (Table 4). The
continuum spectra for the ten sources in our sample are shown in Fig. 3. There
are two objects, J0616$-$1338 and JJ0747$+$1153, where only the 2.7-GHz VLASS
measurements are available. For the rest of the sample, we fitted the spectral
data points to characterise their continuum spectrum (black-coloured fits in
Fig. 3). In four cases, we assumed a power-law radio spectrum
$S\propto\nu^{\alpha}$, where $S$ is the flux density, $\nu$ the frequency,
and $\alpha$ the spectral index. Power-law spectra are called steep if
$\alpha<-0.5$, flat if $-0.5\leq\alpha\leq 0$, and inverted if $\alpha>0$. In
the case of four sources (J0741$+$2520, J1034$+$2033, J1614$+$4640, and
J2245$+$0024) with an apparently curved spectral shape, we found that the
choice of a log-parabolic function in the form of $\log
S=a(\log\nu-\log\leavevmode\nobreak\ \nu_{0})^{2}+b$ resulted in lower
$\chi^{2}$ values than using the power-law function. In the formula above,
$\nu_{0}$ is the turnover frequency corresponding to the peak flux density
$S_{0}$, while $a$ and $b$ are numerical constants (e.g. Coppejans et al.,
2017). The log-parabolic fit can be characterised by the $\nu_{0}$ and $S_{0}$
values. Given that some sources in our sample lack low-frequency data points,
it is possible that the their spectra are in fact also peaked. Peaked
continuum radio spectra seem to be common for bright $z>3$ radio quasars
(Sotnikova et al., 2021). Also, Shao et al. (2022) found that $z>5$ radio-loud
quasars tend to show evidence for spectral turnover at rest-frame frequencies
of $\sim 1-50$ GHz.

In Table 4, we give the flux densities and the derived spectral parameters,
i.e. the spectral indices in the case of power-law fits, and the peak
frequency ($\nu_{0}$) and flux density ($S_{0}$) values for log-parabolic
fits. Out of the four sources whose flux densities versus frequency are best
described with a power-law function, two show flat and two steep spectrum. The
four peaked spectra have their maxima between $1-5$ GHz which corresponds to
$\sim 6-30$ GHz in the rest frame of the sources. The fitted $\nu_{0}$ and
$S_{0}$ values are consistent within the uncertainties with the results of
Shao et al. (2022) who also found these sources having peaked spectra. The
difference between our and their analyses is that we also included the 1.4-GHz
FIRST and 2.7-GHz VLASS data points.

Deriving spectral indices of the compact VLBI components would require VLBI
measurements in at least two different frequency bands taken preferably at
around the same time, to avoid possible effects of variability. If the source
is compact enough that the VLBI flux density is comparable to the low-
resolution measurements, the VLBI flux density can be included in the total
flux density spectral analyses to help constrain the fit. We found the
compactness of J0616$-$1338 and J0747$+$1153 to be close to unity (Table 3),
therefore we used our 1.7-GHz EVN measurements together with the 2.7-GHz VLASS
data to derive their spectral index (red-coloured fits in Fig. 3).
J0616$-$1338 has steep spectrum with $\alpha^{\mathrm{2.7\leavevmode\nobreak\
GHz}}_{\mathrm{1.7\leavevmode\nobreak\ GHz}}=-0.72\pm 0.49$, although the
large uncertainty allows for a flat spectrum as well. J0747$+$1153 has
formally a flat spectrum, but the uncertainty is also large because there are
only two spectral points available, at relatively close frequencies.

Figure 3: Radio continuum spectra of the ten sources in our sample. Black
points indicate total flux density data from single-dish and low-resolution
interferometric measurements. The black dashed lines show the best-fit
spectrum (power-law or log-parabolic). The parameters of the spectral fits are
given in the insets and listed in Table 4. The red data points are the 1.7-GHz
EVN flux density measurements presented in this paper. The red dashed-dotted
lines for J0616$-$1338 and J0747$+$1153 show the power-law function fitted to
the only available two flux density data points (VLASS and EVN), with the
assumption that all the radio emission is confined to a small spatial scale
corresponding to the compact VLBI component. Table 4: Total flux density data
used collected from the literature.

Source ID | $\alpha$ | $S_{\mathrm{323\leavevmode\nobreak\ MHz}}$ | $S_{\mathrm{720\leavevmode\nobreak\ MHz}}$ | $S_{\mathrm{1.4\leavevmode\nobreak\ GHz}}$ | $S_{\mathrm{2.4\leavevmode\nobreak\ GHz}}$ | $S_{\mathrm{2.7\leavevmode\nobreak\ GHz}}$ | $S_{\mathrm{5\leavevmode\nobreak\ GHz}}$ | $S_{\mathrm{8.6\leavevmode\nobreak\ GHz}}$
---|---|---|---|---|---|---|---|---
|  | [mJy] | [mJy] | [mJy] | [mJy] | [mJy] | [mJy] | [mJy]
J0306$+$1853 |  $-0.87$ (0.08) |  |  |  0.25 (0.01)1 |  |  |  0.09 (0.01)1 |
J0616$-$1338 |  $-0.74$ (0.49)∗ |  |  |  |  | 1.33 (0.22) |  |
J0741$+$2520 |  $S_{0}=$ 3.5 (0.4) |  1.80 (0.19)4 |  1.89 (0.08)5 |  2.97 (0.14)3 |  3.27 (0.03)5 |  4.23 (0.24)2 |  3.89 (0.05)5 |  2.46 (0.02)5
|  $\nu_{0}=$ 2.7 (1.1) |  |  |  |  |  |  |
J0747$+$1153 |  $-0.37$ (0.39)∗ |  |  |  |  |  1.50 (0.17)2 |  |
J0901$+$1615 |  $-0.48$ (0.22) |  |  |  3.99 (0.15)3 |  |  2.92 (0.41)2 |  |
J1034$+$2033 |  $S_{0}=$ 4.3 (0.2) |  2.97 (0.19)4 |  4.08 (0.07)5 |  3.85 (0.14)3 |  3.94 (0.06)5 |  3.99 (0.29)2 |  2.92 (0.04)5 |  1.88 (0.03)5
|  $\nu_{0}=$ 1.2 (0.1) |  |  |  |  |  |  |
J1614$+$4640 |  $S_{0}=$ 3.3 (0.5) |  0.81 (0.19)4 |  1.34 (0.01)5 |  2.16 (0.14)3 |  4.06 (0.16)5 |  4.00 (0.23)2 |  3.13 (0.08)5 |  1.96 (0.10)5
|  $\nu_{0}=$ 2.9 (0.7) |  |  |  |  |  |  |
J2239$+$0030 |  $-0.31$ (0.19) |  1.80 (0.39)4 |  |  1.40 (0.10)3 |  |  1.04 (0.22)2 |  |
|  |  |  |  1.22 (0.08)6 |  |  |  |
|  |  |  |  0.68 (0.16)7 |  |  |  |
J2245$+$0024 |  $S_{0}=$ 1.7 (0.2) |  |  |  0.93 (0.09)3 |  1.65 (0.06)5 |  1.44 (0.15)2 |  1.75 (0.03)5 |  1.40 (0.03)5
|  $\nu_{0}=$ 4.1 (1.2) |  |  |  1.52 (0.06)6 |  |  |  |
J2344$+$1653 |  $-0.62$ (0.08) |  |  |  15.7 (0.7)8 |  |  10.12 (0.24)2 |  |

Notes. ∗ two-point spectral index derived from 1.7-GHz VLBI and 2.7-GHz VLASS
flux density measurements; Col. 1 – source designation; Col. 2 – fitted power-
law spectral index; where log-parabolic function was fitted, we give values
$S_{0}$ in mJy and $\nu_{0}$ in GHz; Col. 3–9 – flux densities at the various
frequencies and their uncertainties collected from the literature; numbers in
the upper indices are references to the measurements: 1: Sbarrato et al.
(2021), 2: VLASS, 3: FIRST, 4: Shao et al. (2020), 5: Shao et al. (2022), 6:
Hodge et al. (2011), 7: Heywood et al. (2016), and 8: Condon et al. (1998).

###  5.4 Variability

Variability is an indicator of relativistic jet or coronal emission for radio-
quiet AGN (e.g. Wang et al., 2023b) and of powerful jets in high-redshift
radio-loud AGN (e.g. Sotnikova et al., 2024). Due to the lack of measurements
performed at the same frequencies and with similar angular resolution in
multiple observing epochs, our ability the investigate flux density
variability is limited. However, the targets can be investigated by comparing
the high-resolution VLBI flux densities with single-dish and low-resolution
radio interferometric data. It should be noted that the estimated total flux
density values themselves may be affected by long-term variability since the
measurements at different frequencies used to determine the spectral shapes
and spectral indices were not simultaneous. If
$S_{\mathrm{1.7}}/S_{\mathrm{VLA,1.7}}>1.1$, we consider the source variable.
Only two of the sources (J1614$+$4640 and J2239$+$0030) fulfil this criterion,
although the large uncertainties make the possible variabilities indefinite.
The possible explanation for ratios below 0.9 is that a significant fraction
of the total radio emission originates from an extended region resolved out
with VLBI. Nevertheless, variability cannot be ruled out in these cases, just
the data available at present are not sufficient to claim it.

Krezinger et al. (2022) found about half of their 13 targets in a $4\lesssim
z\lesssim 4.5$ radio quasar sample to be variable, while in a larger $z>4.5$
sample containing the then-known 30 VLBI-detected source, Coppejans et al.
(2016) concluded that only about $20\%$ of the targets are significantly
variable. In recent studies, Wang et al. (2023a, b) investigated RQQs and RLQs
at $z\lesssim 0.5$ and found that core-dominated RQQs with flat/inverted
spectrum have more pronounced variability, while steep-spectrum jet-dominated
RQQs show negligible variability. Our findings, albeit limited by the
available data, do not contradict with the findings cited above.

###  5.5 The non-detection of J0306+1853

J0306$+$1853 remained undetected in our EVN–e-MERLIN observation. Earlier,
Sbarrato et al. (2021) observed this source with the VLA at 1.5 and 5 GHz. At
both frequencies, they found the source unresolved with point-like structure
on arcsecond scale. The derived spectral index ($-0.87\pm 0.06$, see also our
Table 4) indicates a steep spectrum and thus an extended structure. However,
the VLA detection raised the possibility of the presence of a sub-arcsecond
compact jet structure. The radio loudness $R_{4400\AA}=0.7$ (Sbarrato et al.,
2021) indicates that the source is radio-quiet. The sensitivity of the EVN
observation allowed us to reach $113\leavevmode\nobreak\ \mu$Jy beam-1
($5\leavevmode\nobreak\ \sigma$) detection limit, which would have been
sufficient to detect a mas-scale compact source with the 1.5-GHz VLA flux
density of 252 $\mu$Jy with a signal-to-noise ratio of $\sim 10$. Based on our
non-detection, the radio emission of J0306$+$1853 is apparently resolved out
on mas to $\sim 0\aas@@fstack{\prime\prime}1$ angular scales. It seems less
likely but still possible that J0306$+$1853 is variable.

###  5.6 The radio loudness–brightness temperature relation at high redshift

There are two commonly used definitions of the radio-loudness parameter.
Kellermann et al. (1989, 2016) defined $R_{4400\AA}$ as the fraction of the
rest-frame 5-GHz radio and the optical power at 4400 Å. On the other hand,
Sramek & Weedman (1980) defined $R_{2500\AA}$ based on the 2500 Å optical
power. To investigate the relation between radio loudness and other physical
parameters, focusing on high-redshift quasars, we collected all the available
$z>5$ sources from the literature, altogether 48 objects, which have either
any radio-loudness index ($R_{4400\AA}$ or $R_{2500\AA}$) published, or L-band
($1.4-1.7$ GHz) VLBI observation available, or both. SMBH masses were also
collected from the literature where available, for about one third of the
sample. We found that the mean $M_{\mathrm{SMBH}}$ at $z>5$ is $4.4\times
10^{9}$ M⊙ All the collected sources are listed in Table 5 with their radio-
loudness indices, brightness temperature, SMBH mass, L-band flux densities and
monochromatic powers, along with the respective references. The choice of the
L band is motivated by the fact that this is the most commonly used frequency
band for $z>5$ quasar VLBI observations, and this way we can also include our
9 newly-detected sources in the sample.

For the VLBI observations, we took data and references from Table 1 of
Krezinger et al. (2022) as a starting point, and collected the derived
redshift-corrected brightness temperatures. We extended this sample with the
few sources that have been published since then: VIK J2318$-$3113 (Zhang et
al., 2022), J0141$-$5427 (Gabányi et al., 2023), and J1702$+$1301 (Liu et al.,
2024). There are currently 24 sources known with L-band VLBI observations,
including the 9 presented in this paper. Out of these 24 sources, 7 have only
lower limit to $T_{\mathrm{b}}$. Each source has a single epoch of
observation. The bottom left panel in Fig. 4 shows the L-band brightness
temperatures as a function of redshift. The median $T_{\mathrm{b}}$ is
$5.9\times 10^{8}$ K. The measured $T_{\mathrm{b}}$ values show a generally
decreasing trend with increasing redshift. Also, the jet emission of only a
small fraction of these sources appears Doppler-boosted
($T_{\mathrm{b}}\gtrsim 5\times 10^{10}$ K) at L-band.

We found 43 sources with published $R_{4400\AA}$ and 23 sources with
$R_{2500\AA}$ values, with 21 overlapping objects. In the cases where multiple
$R$ values are published for a given source, we considered the value published
most recently. Because of variability, the $R$ value may depend on the epochs
when the luminosities were measured. It is usually not feasible to measure the
radio and optical luminosities at the same time. Therefore strong variability
of certain sources can influence the $R$ indices when there are optical
magnitudes or radio flux density measurements available at different epochs.
Another uncertainty of $R$ is caused by the choice of spectral indices assumed
when performing K-correction, i.e. calculating the rest-frame 5-GHz or 4400
$\AA$ luminosities. Considering all these caveats, it is not surprising to
find occasionally very different $R$ values in the literature for many
sources. However, the plot showing $R_{2500\AA}$ as a function of
$R_{4400\AA}$ values (top left panel of Fig. 4) for the $z>5$ sources where
both values are available indicates that in most cases the values of the two
radio-loudness indices are not markedly different. This justifies their use
together when analysing the general properties of the sample.

The top right panel of Fig. 4 displays the distribution of $T_{\mathrm{b}}$ as
a function of radio-loudness parameters $R_{4400\AA}$ and $R_{2500\AA}$. Based
on this plot, a general trend of increasing brightness temperature with
increasing radio loudness can be seen. It appears that, despite the
uncertainties described above, the sources with higher $R$ index have higher
$T_{\mathrm{b}}$ in L band. Since the radio loudness is proportional to the
total flux density and the brightness temperature to the core flux density
(Eq. 1), the existence of such a relation is not surprising if the radio
emission is confined to the compact AGN core region. Populating the parameter
space where the coverage is more incomplete (i.e. $R<10$ and $R>100$), this
relation could be constrained further. The high-redshift regime of the $R-z$
diagram started to be built up in the recent years (Belladitta et al., 2019;
Bañados et al., 2021), with more and more distant extragalactic radio sources
identified. The bottom right panel of Fig. 4 shows the $R_{4400\AA}$ and
$R_{2500\AA}$ (where there was no available $R_{4400\AA}$ value) indices of
AGN at $z>5$ as a function of redshift. The median values of the collected
$R_{4400\AA}$ and $R_{2500\AA}$ indices are are 35 and 90, respectively.

Figure 4: Top left: The $R_{\mathrm{2500\,\AA}}$ index as a function of
$R_{\mathrm{4400\,\AA}}$ for sources where both values are available in the
literature. The dashed line represents
$R_{\mathrm{2500\,\AA}}=R_{\mathrm{4400\,\AA}}$. Top right: The redshift-
corrected L-band brightness temperatures as a function of radio loudness. The
sources presented in this paper are marked with triangles. Bottom left: The
redshift-corrected L-band brightness temperature measurements for all $z>5$
AGN published to date, including those presented in this paper (triangles), as
a function of redshift. Bottom right: The
$R_{\mathrm{4400\,\AA}}=L_{\mathrm{5\,GHz}}/L_{\mathrm{4400\,\AA}}$ and
$R_{\mathrm{2500\,\AA}}=L_{\mathrm{5\,GHz}}/L_{\mathrm{2500\,\AA}}$ (where
$R_{\mathrm{4400\,\AA}}$ is not available) radio-loudness indices of $z>5$
sources as a function of redshift.

###  5.7 The radio power distribution at high redshift

The derived core and total monochromatic radio powers of our sources at $1.7$
GHz are in the range of $\sim 10^{25-27}$ W Hz-1. These radio powers are
typical of Fanaroff–Riley type II (FRII, Fanaroff & Riley, 1974) radio
galaxies and quasars, spanning from the low-end to the the high-power regime
(e.g. Giovannini et al., 2001; Giovannini, 2004; Sbarrato et al., 2021). The
phenomenological division line between FRI and FRII sources is at
$P_{\mathrm{total}}\approx 10^{25}$ W Hz-1 (Fanaroff & Riley, 1974), but it is
based on low-frequency observations. It appears that while these sources can
be classified as radio-quiet, they in fact have radio powers typical of a 3C
radio galaxy, i.e. $\gtrsim 10^{25}$ W Hz-1 (e.g. Giovannini et al., 2001;
Giovannini, 2004; Sbarrato et al., 2021).

We checked the sample of $z>5$ sources collected from the literature for
published L-band total and core flux densities and monochromatic radio powers.
We used the flux densities to calculate the total ($P_{\mathrm{total}}$) and
core ($P_{\mathrm{core}}$) K-corrected monochromatic radio powers (see Eq. 2)
in cases where these values were not available. We assumed $\alpha=0$ for
calculating all $P_{\mathrm{total}}$ values, and those $P_{\mathrm{core}}$
values where $\alpha$ was not published. The collected parameters are listed
in Table 5 along with their references.

The top panel of Fig. 5 shows the comparison of $P_{\mathrm{total}}$ and
$P_{\mathrm{core}}$ for $z>5$ sources, where both values were available. The
dashed line indicates $P_{\mathrm{total}}=P_{\mathrm{core}}$. Sources lying
above this line have more extended emission, since the total power is higher
than the core power. The sources become more core-dominated and more likely to
be beamed as the distance from the line decreases. The sources scattering
close to the $P_{\mathrm{total}}=P_{\mathrm{core}}$ line or slightly below,
like some of our sources, can also be affected by variability. The colouring
in the top panel of Fig. 5 reveals that in general the higher the radio
loudness the less core-dominated the source appears. This implies that the
radio emission responsible for the high radio loudness tends to originate from
the kpc-scale radio structure rather than the compact pc-scale region.

We found that our sources, although appearing core-dominated, do not show
evidence for relativistically beamed radio jets based on the derived
brightness temperatures (Table 3). One reason could be that the
$T_{\mathrm{b}}$ values are underestimated, by slightly overestimating the
modelled size of the VLBI core component. However, this cannot be responsible
for the nearly $2$ orders of magnitude difference from the equipartition
brightness temperature. A possible physical explanation is that the radio
emission region of these sources is intrinsically small, confined to sub-kpc
scales. Gigahertz-peaked spectrum (GPS) radio sources and compact symmetric
objects (CSOs) (e.g. Wilkinson et al., 1994; An & Baan, 2012; O’Dea & Saikia,
2021) are known to be young jetted AGN with compact radio structure, without
beamed radio jets and diffuse extended emission. In fact, a few known CSOs can
be found among high-redshift sources (e.g. Frey et al., 2008; Momjian et al.,
2008; An et al., 2022; Krezinger et al., 2022). The GPS and CSO nature of the
sources could be supported by their peaked spectrum (e.g. Tremblay et al.,
2016). In our sample, only 4 of the sources have peaked spectra (Fig. 3), but
except for J2239$+$0030, all the others have poor low-frequency coverage in
their flux density measurements, retaining the possibility that their spectrum
is actually peaked.

The middle panels of Fig. 5 display the relation between the radio-loudness
indices and the derived radio powers, similar to the $T_{\mathrm{b}}-R$ plot
in Sect. 5.6. Both the $P_{\mathrm{total}}$ and $P_{\mathrm{core}}$ values
show a steadily increasing trend. Since $R$ is proportional to the $5$-GHz
total radio power, this trend is not surprising for $P_{\mathrm{total}}$. The
bottom panels of Fig. 5 show the $P_{\mathrm{total}}$ and $P_{\mathrm{core}}$
values for AGN at $z>5$ as a function of redshift. Median values for both the
collected $P_{\mathrm{total}}$ and $P_{\mathrm{core}}$ are around $2\times
10^{26}$ W Hz-1.

Figure 5: The sources presented in this paper are marked with triangles. Top:
The comparison of L-band core monochromatic radio power and the L-band total
monochromatic radio power for $z>5$ sources where both values are available.
The dashed line represents the $P_{\mathrm{total}}=P_{\mathrm{core}}$. The
colours indicate the source radio loudness. Middle: The total (left) and core
(right) monochromatic radio powers of $z>5$ sources as a function of radio
loudness. Bottom: The total (left) and core (right) monochromatic radio powers
as a function of redshift.

##  6 Conclusion

In this paper, we present the results of 1.7-GHz VLBI observation of 10 high-
redshift ($5<z<6$) radio quasars using the EVN and e-MERLIN arrays. The
sources have different radio-loudness indices spanning a wide range of $\sim
10^{-1}-10^{2}$. Out of the 10 sources, 9 have been successfully detected.
They all show a single faint but compact mas-scale radio core component. The
90% detection rate for this faint sample is impressive and demonstrates the
effectiveness of the observing strategy and the sensitivity of the VLBI
network used. This opens the way for future VLBI studies of many more similar
$z>5$ sources. Further improvements in VLBI sensitivity expected in the future
from e.g. the first phase of the Square Kilometre Array (Paragi et al., 2015)
or the Five-hundred-meter Aperture Spherical Radio Telescope core array (Jiang
et al., 2024) are promising for advancing this work.

The sample presented here increases the number of known VLBI-observed $z>5$
radio AGN by about $40\%$. These high-resolution interferometric observations,
combined with additional low-resolution radio data obtained from the
literature, helped derive properties such as the origin of the radio emission,
compactness, flux density variability, and spectral indices. The brightness
temperatures obtained confirm the AGN origin of the radio emission and suggest
that the emission in none of these sources is Doppler-enhanced. The derived
monochromatic powers are comparable to those of the luminous FRII radio
galaxies and quasars. As J0306$+$1853 remained undetected at mas scale, we
have not been able to reveal the compact jet expected by Sbarrato et al.
(2021). We found that five of the sources have Gaia optical astrometric
positions. One of them is J0306$+$1853 with no VLBI detection, but the optical
positions of the other four AGN were found to be consistent with the VLBI
radio core positions within the uncertainties.

Notably, we did not find crucial differences in the morphology and the derived
physical parameters between our detected 3 RQQ and 6 RLQ sources. These
sources appear core-dominated with high radio power, despite being in the
transition region of RQQs to RLQs. With no compelling evidence for Doppler-
boosted jet emission, it is possible that these are young jetted AGN whose
radio emission is confined to a small region around the central SMBH.

By examining this sample, supplemented with other $z>5$ sources detected with
VLBI at L-band from the literature, we found that the core brightness
temperatures and monochromatic radio powers tend to increase with increasing
radio loudness. However, for the $R-T_{\mathrm{b}}$ relation, the radio-quiet
and the extreme radio-loud regimes are still undersampled. High-resolution
VLBI observations of many more radio-emitting AGN at $z>5$ would be desirable,
even though it is challenging because the spectral turnover is shifting to
lower frequencies as $z$ increases. Sensitive higher-frequency and therefore
higher-resolution VLBI observations of the investigated 9 detected sources
would provide tighter constraints on the brightness temperature, and
information on the spectral properties of the cores.

###### Acknowledgements.

The EVN is a joint facility of independent European, African, Asian and North
American radio astronomy institutes. Scientific results from data presented in
this publication are derived from the following EVN project code: EG102. The
e-MERLIN is a National Facility operated by the University of Manchester at
Jodrell Bank Observatory on behalf of STFC. This work presents results from
the European Space Agency (ESA) space mission Gaia. Gaia data are being
processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding
for the DPAC is provided by national institutions, in particular the
institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia
mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website
is https://archives.esac.esa.int/gaia. This research has made use of the
NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the
National Aeronautics and Space Administration. M.K. thanks for the support
from the ÚNKP-23-3 New National Excellence Program of the Ministry for Culture
and Innovation from the source of the National Research, Development and
Innovation Fund. We thank the Hungarian National Research, Development and
Innovation Office (NKFIH, grant no. OTKA K134213) for support. This work was
also supported by HUN-REN and the NKFIH excellence grant TKP2021-NKTA-64. T.A.
thanks for the support from the National SKA Program of China
(2022SKA0120102).

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##  Appendix A Radio loudness and brightness temperatures

Table 5: Values and references for the collected radio-loudness indices,
L-band brightness temperatures, core flux densities, monochromatic powers, and
black hole masses for the $z>5$ radio AGN listed with increasing redshift.

Redshift | Source ID | $R_{\mathrm{4400\,\AA}}$ | Ref. | $R_{\mathrm{2500\,\AA}}$ | Ref. | $T_{\mathrm{b,L-band}}$ | Ref. | $S_{\mathrm{total,L-band}}$ | Ref. | $S_{\mathrm{core,L-band}}$ | Ref. | $P_{\mathrm{total,L-band}}$ | Ref. | $P_{\mathrm{core,L-band}}$ | Ref. | $M_{\mathrm{SMBH}}$ | Ref.
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  [$10^{8}$ K] |  | [mJy] |  | [mJy] |  |  [$10^{26}$ W Hz-1] |  |  [$10^{2}6$ W Hz-1] |  | $10^{8}M_{\odot}$ |
5.00 |  J2344$+$1653 | 82 | 32 | 108 | 32 | 53.0 (8.9) | 0 |  |  | 7.0 (0.9) | 0 | 18.7 (2.3) | 0 | 9.3 (1.6) | 0 |  |
5.00 |  J0141$-$5427 |  |  | 12000 | 5 | 420 (310) | 18 | 160 | 5 | 80.3 (8.4) | 18 | 419 | 0 | 30.4 (5.3) | 0 | 8 | 5
5.00 |  GB6J162956$+$095959 | 3162 | 8 | 2300 | 5 |  |  | 32.3 (0.1) | 35 |  |  | 84.4 (0.3) | 0 |  |  |  |
5.01 |  J1146$+$4037 | 81 | 4 | 108 | 4 | 52.1 (2.9) | 14 |  |  | 15.5 (0.8) | 14 |  |  | 18.3 (2.3) | 14 |  |
5.01 |  J1034$+$2033 | 32 | 8 | 66 | 4 | 9.2 (1.6) | 0 | 3.9 (0.1) | 35 | 3.5 (0.5) | 0 | 1.8 (0.2) | 0 | 1.5 (0.3) | 0 |  |
5.02 |  J1013$+$3518 | 32 | 8 |  |  |  |  | 1.1 (0.1) | 35 |  |  | 3.0 (0.3) | 0 |  |  |  |
5.09 |  J2239$+$0030 | 35 | 32 | 46 | 32 | 7.7 (1.4) | 0 | 1.4 (0.1) | 35 | 1.4 (0.2) | 0 | 0.8 (0.2) | 0 | 1.1 (0.2) | 0 |  |
5.11 |  J0913$+$5919 | 509 | 4 | 674 | 4 | 420 | 38 | 17.6 (0.1) | 35 | 19.4 (0.1) | 38 | 48.3 (0.3) | 0 | 8.3 (0.9) | 0 |  |
5.16 |  J2245$+$0024 | 72 | 4 | 94 | 4 | 1.3 (0.3) | 0 | 0.9 (0.1) | 35 | 0.8 (0.1) | 0 | 0.6 (0.1) | 0 | 0.4 (0.1) | 0 |  |
5.18 |  J0131$-$0321 | 63 | 4 | 83 | 4 | 2800 | 16 | 33.7 (0.1) | 35 | 64.4 (0.3) | 16 | 95.8 (0.3) | 0 | 30 | 16 | 110 | 19
5.19 |  J0741$+$2521 | 9 | 4 | 12 | 4 | 1.0 (0.2) | 0 | 2.9 (0.1) | 35 | 2.7 (0.4) | 0 | 1.5 (0.3) | 0 | 1.2 (0.2) | 0 |  |
5.24 |  J2329$+$3003 |  |  | 47 | 26 |  |  |  |  |  |  |  |  |  |  |  |
5.26 |  J0747$+$1153 |  |  |  |  | 3.1 (0.6) | 0 |  |  | 1.8 (0.2) | 0 |  |  | 1.7 (0.3) | 0 |  |
5.27 |  J1026$+$2542 | 3981 | 8 | 5200 | 27 | 23000 | 15 | 239.4 (0.1) | 35 | 180.4 (0.5) | 15 | 708.9 (0.3) | 0 | 56 | 15 |  |
5.31 |  J1614$+$4640 | 16 | 4 | 21 | 4 | 41.7 (4.5) | 0 | 2.2 (0.1) | 35 | 3.6 (0.4) | 0 | 1.4 (0.3) | 0 | 1.7 (0.3) | 0 |  |
5.32 |  PSO J191$+$86 | 337 | 7 |  |  |  |  | 74.2 (2.3) | 10 |  |  | 117 | 7 |  |  | 24 | 7
5.36 |  J0306$+$1853 | 0.7 | 28 |  |  |  |  | 0.3 | 28 |  |  | 0.6 (0.1) | 0 |  |  | 110 | 36
5.36 |  GB6J164856$+$460341 | 631 | 8 | 400 | 5 |  |  | 49.9 (0.1) | 35 |  |  | 153.6 (0.3) | 0 |  |  |  |
5.47 |  J1702$+$1301 | 1100 | 32 |  |  | 20 | 24 | 28.3 (0.4) | 24 | 8.4 (0.1) | 24 | 91.2 (1.3) | 0 | 4.5 (0.5) | 0 |  |
5.47 |  J0906$+$6930 | 1585 | 8 | 2373 | 26 |  |  |  |  |  |  |  |  |  |  |  |
5.58 |  J0616$-$1338 |  |  |  |  | 10.6 (2.0) | 0 |  |  | 1.9 (0.3) | 0 |  |  | 3.9 (0.7) | 0 |  |
5.63 |  J0901$+$1615 | 79.4 | 8 |  |  | 1.3 (0.2) | 0 | 3.9 (0.1) | 35 | 3.1 (0.4) | 0 | 4.8 (0.6) | 0 | 3.9 (0.7) | 0 |  |
5.68 |  PJ055$-$00 | 178 | 2 | 83 | 26 |  |  | 2.1 (0.1) | 2 |  |  | 7.5 (0.5) | 0 |  |  |  |
5.72 |  J1530$+$1049 |  |  |  |  |  |  | 7.3 (0.1) | 35 | 1.7 | 17 | 25.9 (0.4) | 0 | 0.9 | 0 |  |
5.72 |  J0203$+$0012 | 4.3 | 2 |  |  |  |  | 0.20 (0.02) | 2 |  |  | 0.7 (0.1) | 0 |  |  |  |
5.77 |  0836$+$0054 | 11 | 4 | 15 | 4 | 0.3 | 12 | 1.1 (0.1) | 35 | 1.1 | 12 | 4.0 (0.4) | 0 | 4.3 | 12 | 83 | 30
5.77 |  J0927$+$2001 | 1.9 | 2 |  |  |  |  | 0.05 (0.01) | 2 |  |  | 0.18 (0.04) | 0 |  |  | 49 | 30
5.82 |  J0002$+$2550 | 1.3 | 2 |  |  |  |  | 0.09 (0.01) | 2 |  |  | 0.34 (0.04) | 0 |  |  | 48 | 30
5.84 |  P352$-$15 | 1000 | 25 | 1352 | 26 | 1.3 | 25 | 14.9 (0.7) | 10 | 1.2 (0.1) | 25 | 56.0 (2.6) |  | 0.6 (0.1) | 0 |  |
5.88 |  J2242$+$0334 | 55 | 22 | 58 | 26 |  |  | 0.19 (0.03) | 22 |  |  | 0.7 (0.1) | 0 |  |  |  |
5.90 |  J1335$+$3533 | 0.9 | 2 |  |  |  |  | 0.03 (0.01) | 2 |  |  | 0.12 (0.04) | 0 |  |  | 29 | 30
5.90 |  J1411$+$1217 | 1.2 | 2 |  |  |  |  | 0.06 (0.02) | 2 |  |  | 0.2 (0.1) | 0 |  |  | 5 | 11
5.92 |  J2053$+$0047 | 44 | 2 |  |  |  |  | 0.4 (0.1) | 2 |  |  | 1.7 (0.5) | 0 |  |  |  |
5.95 |  J2228$+$0110 | 34 | 4 | 46 | 4 | 3.1 | 9 | 0.3 (0.1) | 2 | 0.3 (0.1) | 9 | 1.2 (0.2) | 0 | 0.2 (0.1) | 0 |  |
6.02 |  J0818$+$1722 | 0.8 | 21 |  |  |  |  | 0.13 (0.03) | 21 |  |  | 0.5 (0.1) | 0 |  |  |  |
6.07 |  J1034$-$1425 | 1.5 | 21 |  |  |  |  | 0.17 (0.04) | 21 |  |  | 0.7 (0.2) | 0 |  |  |  |
6.09 |  J1602$+$4228 | 1.7 | 21 |  |  |  |  | 0.16 (0.04) | 21 |  |  | 0.7 (0.2) | 0 |  |  | 24 | 30
6.10 |  PSO J0309$+$27 | 2500 | 6 | 1521 | 26 | 2.7 (0.2) | 31 | 23.7 (0.1) | 10 | 8.0 (0.1) | 31 | 98.5 |  | 5.4 (0.6) | 0 |  |
6.11 |  J1558$-$0724 | 1.8 | 21 |  |  |  |  | 0.12 (0.04) | 21 |  |  | 0.5 | 0 |  |  |  |
6.12 |  J1427 $+$3312 | 77 | 21 | 16 | 4 | 0.9 (0.2) | 13 | 1.0 (0.1) | 35 | 1.5 | 13 | 4.3 (0.4) | 0 | 1.8 | 13 | 11 | 30
6.13 |  J1319$+$0950 | 2.4 | 2 |  |  |  |  | 0.6 (0.2) | 22 |  |  | 2.7 (0.7) | 0 |  |  | 21 | 34
6.14 |  J1609$+$3041 | 28.3 | 2 |  |  |  |  | 0.5 (0.1) | 2 |  |  | 2.0 (0.6) | 0 |  |  | 43 | 30
6.20 |  J0227$-$0605 | 16.5 | 22 |  |  |  |  | 0.3 (0.1) | 22 |  |  | 1.4 (0.3) | 0 |  |  | 2 | 30
6.21 |  J1429$+$5447 | 118 | 21 |  |  | 14.0 (0.6) | 37 | 3.00 (0.04) | 21 | 3.3 (0.1) | 37 | 12.9 (0.2) | 0 | 13.5 (1.5) | 37 | 18 | 30
6.30 |  J0100$+$2802 | 0.5 | 28 |  |  | 0.2 (0.1) | 23 | 0.10 (0.03) | 21 | 0.09 (0.02) | 23 | 0.5 (0.1) | 0 | 0.07 (0.01) | 0 | 120 | 36
6.42 |  J1148$+$5251 | 0.7 | 2 |  |  |  |  | 0.06 (0.01) | 2 |  |  | 0.3 (0.1) | 0 |  |  | 87 | 30
6.44 |  VIK J2318$-$3113 | 69 | 21 |  |  | 4.0 (1.7) | 33 | 0.6 (0.1) | 21 | 0.6 (0.1) | 33 | 3.0 (0.2) | 0 | 0.63 | 33 | 6 | 20
6.82 |  P172$+$18 | 70 | 26 | 90 | 26 | 0.5 (0.1) | 26 | 0.5 | 3 | 0.4 (0.1) | 26 | 2.7 | 0 | 0.3 (0.1) | 0 |  |

Notes. Col. 1 – source redshift; Col. 2 – source designation; Col. 3-4 –
$R_{\mathrm{4400\,\AA}}=L_{\mathrm{5\,GHz}}/L_{\mathrm{4400\,\AA}}$ radio-
loudness index and reference number; Col. 5-6 –
$R_{\mathrm{2500\,\AA}}=L_{\mathrm{5\,GHz}}/L_{\mathrm{2500\,\AA}}$ radio-
loudness index and reference number; Col. 7-8 – L-band core brightness
temperature (with uncertainty in parentheses) and reference number; Col. 9-10
– L-band total flux density (with uncertainty in parentheses) and reference
number; Col. 11-12 – L-band core flux density (with uncertainty in
parentheses) and reference number; Col. 13-14 – L-band total radio power (with
uncertainty in parentheses) and reference number; Col. 15-16 – L-band core
radio power (with uncertainty in parentheses) and reference number; Col. 17-18
– estimated black hole mass and reference number. The literature references
are the following. 0: This paper; 1:An et al. (2023); 2: Bañados et al.
(2015); 3: Bañados et al. (2021); 4: Shao et al. (2022); 5: Belladitta et al.
(2019); 6: Belladitta et al. (2020); 7: Belladitta et al. (2023); 8:
Caccianiga et al. (2024); 9: Cao et al. (2014); 10: Condon et al. (1998); 11:
De Rosa et al. (2011); 12: Frey et al. (2003); 13: Frey et al. (2008); 14:
Frey et al. (2010); 15: Frey et al. (2015); 16: Gabanyi et al. (2015); 17:
Gabányi et al. (2018); 18: Gabányi et al. (2023); 19: Ghisellini et al.
(2015b); 20: Ighina et al. (2021); 21: Keller et al. (2024); 22: Liu et al.
(2021); 23: Liu et al. (2022); 24: Liu et al. (2024); 25: Momjian et al.
(2018); 26: Momjian et al. (2021); 27: Sbarrato et al. (2012); 28: Sbarrato et
al. (2021); 29: Shao et al. (2022); 30: Shen et al. (2019); 31: Spingola et
al. (2020); 32: Yang et al. (2016); 33: Zhang et al. (2022); 34: Wang et al.
(2013); 35: White et al. (1997); 36: Wu et al. (2015); 37: Frey et al. (2011);
38: Coppejans et al. (2016)