# Radio-loud Quasars above Redshift 4: VLBI Imaging of an Extended Sample

Máté Krezinger Department of Astronomy, Institute of Geography and Earth
Sciences, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117
Budapest, Hungary  Konkoly Observatory, ELKH Research Centre for Astronomy and
Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
Krisztina Perger Konkoly Observatory, ELKH Research Centre for Astronomy and
Earth Sciences, Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
Krisztina Éva Gabányi Department of Astronomy, Institute of Geography and
Earth Sciences, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A,
H-1117 Budapest, Hungary  ELKH-ELTE Extragalactic Astrophysics Research Group,
Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
Konkoly Observatory, ELKH Research Centre for Astronomy and Earth Sciences,
Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary  Sándor Frey Konkoly
Observatory, ELKH Research Centre for Astronomy and Earth Sciences, Konkoly
Thege Miklós út 15-17, H-1121 Budapest, Hungary  Institute of Physics, ELTE
Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
Leonid I. Gurvits Joint Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991
PD Dwingeloo, The Netherlands  Department of Astrodynamics and Space Missions,
Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
Zsolt Paragi Joint Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD
Dwingeloo, The Netherlands  Tao An Shanghai Astronomical Observatory, Key
Laboratory of Radio Astronomy, Chinese Academy of Sciences, 80 Nandan Road,
Shanghai 200030, China  Yingkang Zhang Shanghai Astronomical Observatory, Key
Laboratory of Radio Astronomy, Chinese Academy of Sciences, 80 Nandan Road,
Shanghai 200030, China  Hongmin Cao School of Physics and Electrical
Information, Shangqiu Normal University, 298 Wenhua Road, Shangqiu, Henan
476000, China  Tullia Sbarrato INAF – Osservatorio Astronomico di Brera, via
E. Bianchi 46, I-23807 Merate, Italy Máté Krezinger<EMAIL_ADDRESS>
###### Abstract

High-redshift radio sources provide plentiful opportunities for studying the
formation and evolution of early galaxies and supermassive black holes.
However, the number of known radio-loud active galactic nuclei (AGN) above
redshift 4 is rather limited. At high redshifts, it appears that blazars, with
relativistically beamed jets pointing towards the observer, are in majority
compared to radio-loud sources with jets misaligned with respect to the line
of sight. To find more of these misaligned AGN, milliarcsec-scale imaging
studies carried out with very long baseline interferometry (VLBI) are needed,
as they allow us to distinguish between compact core–jet radio sources and
those with more extended emission. Previous high-resolution VLBI studies
revealed that some of the radio sources among blazar candidates in fact show
unbeamed radio emission on milliarcsecond scales. The most accurate optical
coordinates determined with the Gaia astrometric space mission are also useful
in the classification process. Here, we report on dual-frequency imaging
observations of 13 high-redshift ($4<z<4.5$) quasars at 1.7 and 5 GHz with the
European VLBI Network. This sample increases the number of $z>4$ radio sources
for which VLBI observations are available by about a quarter. Using structural
and physical properties, such as radio morphology, spectral index,
variability, brightness temperature, as well as optical coordinates, we
identified six blazars and six misaligned radio AGNs, with the remaining one
tentatively identified as blazar.

Extragalactic radio sources (508) — Radio active galactic nuclei (2134) —
Quasars (1319) — High-redshift galaxies (734) — Interferometry (808)

††facilities: EVN, e-MERLIN††software:  aips (Greisen, 2003), Difmap
(Shepherd, 1997), Astropy (Astropy Collaboration et al., 2013, 2018),
Matplotlib (Hunter, 2007)

##  1 Introduction

Studying the high-redshift Universe can help better understand how are
galaxies formed and evolved. Active galactic nuclei (AGN) are of special value
for this purpose because they are luminous and already present in the early
Universe, less than about a billion years (redshift $z\gtrsim 6$) after the
Big Bang. AGN are powered by accreting supermassive black holes (SMBHs) with
masses of $\sim 10^{6}-10^{10}$ M⊙ and located in the center of the galaxies.
In some objects, two-sided relativistic plasma jets are launched along the
axis perpendicular to the accretion disk. High-redshift AGN offer a key to
understand the evolution of their host galaxies (e.g. Best et al., 2005;
Fabian, 2012; Morganti et al., 2013) as they set constrains on the properties
of the accretion process and the black hole growth (e.g. Wyithe & Loeb, 2012;
Page et al., 2014). There is still much to learn about these objects, and the
sample of high-redshift AGN is limited.

Only about $10\%$ of the AGN population are radio-loud with (highly energetic)
synchrotron-emitting jets (Ivezić et al., 2002). These are the radio quasars
that are the easiest to observe from extreme distances. They are called
blazars when their jet points nearly towards the observer with $\theta\lesssim
10\arcdeg$ (Urry & Padovani, 1995), where $\theta$ is the inclination angle of
the jet axis with respect to the line of sight. Because of relativistic
beaming effects, the blazar jets are Doppler-boosted, which could make their
emission dominate most of the AGN spectrum. Given limited sensitivity of the
instruments, blazars with enhanced strong synchrotron emission are expected to
be the most easily detected in the radio AGN population at a given redshift.
Blazars have characteristic properties in their X-ray and $\gamma$-ray
emission (e.g. Sbarrato et al., 2013; Ghisellini et al., 2015), flat radio
spectrum, and compact radio structure with brightness temperatures exceeding
the $T_{\mathrm{b,eq}}\approx 5\times 10^{10}$ K equipartition limit
(Readhead, 1994). Blazars are traditionally divided into two main sub-classes,
flat-spectrum radio quasars (FSRQs) that show prominent optical and
ultraviolet emission lines in their spectra, and BL Lac objects with weak or
even no emission lines (e.g. Fossati et al., 1999; Massaro et al., 2015).
Since FSRQs are quite luminous in the optical, they can be detected from large
cosmological distances. Due to the lack of emission lines, the redshifts of BL
Lacs are often hard to determine, thus most of them with known redshifts are
at $z<2$ (Plotkin et al., 2008).

As the AGN jets propagate through the interstellar or intergalactic space,
they interact with the ambient medium, creating radio-emitting regions, i.e.
hotspots and lobes. Quasars with jet inclination angles $\theta>10\arcdeg$ are
often referred to as misaligned sources. These include objects like the
unbeamed versions of gigahertz-peaked spectrum (GPS) and compact steep-
spectrum (CSS) sources, and the symmetric ones are called compact symmetric
objects (CSOs) or medium symmetric objects (MSOs). They are found at $z>4$ as
well (e.g. Coppejans et al., 2017; Shao et al., 2022). In contrast to blazars,
the radio emission of these types of AGN is dominated by the outer regions of
the jet, while the ‘core’ emission coinciding with the optical position, due
to the absence of Doppler-boosting, often remains undetected (e.g., An & Baan,
2012; O’Dea & Saikia, 2021, and references therein). Characteristic features
of young misaligned sources are the extended kpc-scale radio emission,
symmetric radio structure, and steep radio spectrum. Non-variable and non-
Doppler-boosted emission is also a common feature. Young radio sources like
CSOs have concave-shape (peaked) continuum spectra, in addition to the
symmetric radio structure (e.g. Tremblay et al., 2016; Krezinger et al.,
2020).

To study the family of jetted high-redshift radio sources in detail, or to use
them for classical cosmological tests (e.g. Gurvits et al., 1999; Kellermann
et al., 1999), a comprehensive sample of radio quasars is needed. Furthermore,
it also has a critical importance in the building of a quasar luminosity
function (Haiman et al., 2004). As Volonteri et al. (2011) showed, at a given
redshift, for every blazar there must be hundreds of misaligned sources whose
jets point in a different direction. This number can be estimated as about
$2\Gamma^{2}$ (Ghisellini & Sbarrato, 2016), where $\Gamma$ denotes the bulk
Lorentz factor of the jet plasma, and blazars are defined as jetted sources
with viewing angles of $\theta<1/\Gamma$. Volonteri et al. (2011) compared the
number of high-redshift ($z>3$) radio-loud quasars derived by cross-matching
the Sloan Digital Sky Survey (SDSS, Schneider et al., 2010) and the Faint
Images of the Radio Sky at Twenty-Centimeters (FIRST, White et al., 1997)
surveys to the number of radio-loud quasars expected from the blazar
luminosity function at different redshifts. They found the observed number of
misaligned radio-loud quasars much smaller than that estimated based on the
blazar luminosity function. Every new high-redshift blazar discovered further
increases this apparent deficit, as each of them implies the existence of
hundreds of more sources with misaligned jets. Several scenarios were proposed
as a solution for this problem (e.g. Volonteri et al., 2011; Ghisellini &
Sbarrato, 2016). Volonteri et al. (2011) suggested that the difference might
be due to internal and external absorption mechanisms, lower bulk Lorentz
factors in jets in the early Universe, or observational effects arising from
survey sensitivity. At high redshift, the radio lobes are dimmed due to the
interaction of their electrons with photons of the cosmic microwave background
(Ghisellini et al., 2015). Compact hotspots would be less affected and thus
more easily detectable. Also, high-redshift galaxies may be heavily obscured
due to a dense bubble surrounding the central region of the AGN (Ghisellini &
Sbarrato, 2016), effectively reducing the number of misaligned jetted quasars
that can be identified optically. Only the most powerful jets are able to
penetrate this bubble, sweeping away most of the material along their path,
revealing the central engine to our telescopes.

In contrast to the arguments outlined above, flux density-limited samples
(e.g. Caccianiga et al., 2019; Lister et al., 2019) indicate that there is no
inconsistency between the number of blazars and misaligned radio AGN at all.
Their results suggest that the most luminous radio-loud quasars have a density
peak at higher redshifts ($z\sim 4$), while the less luminous population has
similar cosmological evolution to radio-quiet quasars with space density peak
at $z\approx 2$. Using a sample of $z<4$ quasars, Mao et al. (2017) arrived at
a similar conclusion. Both arguments above are in conflict with what Ajello et
al. (2009) found while investigating an X-ray selected sample of blazars. It
seems that radio and X-ray selections are sampling different classes of
objects with different cosmological behavior. However, Ighina et al. (2021)
found that the different blazar evolutions observed in radio and X-rays can be
explained by the inverse-Compton interaction of the relativistic electrons in
the jet and with the cosmic microwave background photons. This effect becomes
more important at higher redshifts, leading to the increase of the observed
X-ray-to-radio luminosity ratios with redshift.

Lister et al. (2019) argue that estimating the number of misaligned sources
with $\sim\Gamma^{2}$ is oversimplified because it does not account for the
observational biases caused by flux density-limited sampling. The distribution
of jet Lorentz factors has a broad peak between 5 and 15, then falls off
rapidly until $\Gamma\approx 50$. As a consequence, there is only a shallow
increase in the misaligned (parent) population of jetted sources above
$\Gamma\approx 15$. Low-$\Gamma$ jets require strong Doppler boosting and thus
very small viewing angles to be detectable. The underlying misaligned
population is therefore large. On the other hand, the relatively rare
high-$\Gamma$ jets enter more easily in the flux density-limited samples,
allowing for comparatively larger jet inclinations. Their parent population is
therefore smaller. The general trend with $\Gamma$ is in fact opposite to what
is expected from the $\sim\Gamma^{2}$ rule (Lister et al., 2019).

Furthermore, e.g. Coppejans et al. (2016) and Cao et al. (2017) found that AGN
may in some cases be mistakenly classified as blazar candidates based on X-ray
and low-resolution radio observations only. High-resolution imaging with very
long baseline interferometry (VLBI) revealed that some of these sources show
low-brightness-temperature radio cores, and extended structures with steep
radio spectrum on scales of $\sim 10-100$ milliarcsecond (mas) which are at
odds with the blazar classification.

Correctly identifying the blazars is critical for constructing the blazar
luminosity function at high redshifts. By offering the finest, mas-scale
angular resolution at cm wavelengths, observations of the known high-redshift
radio sources with VLBI are uniquely suited for distinguishing between
compact, high brightness temperature radio emission of blazars and the more
extended structures of misaligned jetted AGN. Multi-frequency radio
interferometric observations can distinguish between compact cores from
hotspots and more extended radio lobes, through the observed spectral
characteristics, morphological information, and and brightness temperatures.
Comparing the results of VLBI observations with lower-resolution radio images
and data obtained at different wavebands is also essential in the
classification process (Sbarrato, 2021).

Phase-referenced VLBI observations using well-known, nearby calibrator sources
also provide relative astrometric positions for the radio-emitting features,
accurate to mas level. The comparison of VLBI positions with the precise
optical astrometric data from the recent Early Data Release 3 (EDR3, Gaia
Collaboration et al., 2021) of the Gaia space mission (Gaia Collaboration et
al., 2016), if available, adds further relevant astrophysical information to
aid the source classification. While the optical position of an AGN marks the
location of the accretion disk in combination with the optical synchrotron
emission of the innermost sub-mas scale jet (Plavin et al., 2019), the VLBI
intensity peak pinpoints the brightest and most compact emission feature,
usually the self-absorbed base or the jet (i.e. the core), or maybe a shock
front (i.e. a hotspot in a lobe) in an extended radio source. Hence, a
significant offset between the radio and optical positions could be related to
the misaligned nature of the jet, while for blazars, no large positional
difference is expected. Long-term VLBI monitoring of resolved radio jets can
be used to measure component proper motion and to determine their physical and
geometric properties (e.g. Frey et al., 2015; Perger et al., 2018; Zhang et
al., 2020).

Despite the high value of VLBI imaging investigations, only a few dozens of
the known radio quasars at $z\geq 4$ have been studied with this technique to
date (see their list compiled in Table 1). Jets of distant radio quasars are
harder to detect, because the observed frequencies correspond to $(1+z)$ times
higher emitted frequencies in the rest frame of the sources, where the steep-
spectrum jets become intrinsically fainter. This way, prominent extended
features are less likely to be detected in high-redshift radio AGN (e.g.
Gurvits, 2000; Gurvits et al., 2015).

In this paper, we present VLBI observations of 13 high-redshift radio quasars
at $z>4$, which were carried out with the European VLBI Network (EVN) combined
with e-MERLIN (Multi-Element Radio-Linked Interferometer Network) antennas at
1.7 and 5 GHz frequencies from 2017 to 2020. We investigate the nature of
these sources using the newly-obtained VLBI data, combined with the available
radio spectral information and the recent Gaia EDR3 optical positions, where
available. In Section 2, we present the list of $z\geq 4$ radio quasars
previously imaged with VLBI, and describe our sample and the selection
process. We give detailed description on the EVN observations and data
reduction in Section 3. In Section 4, we present the results and the
properties derived for the new sample, which we discuss in Section 5.
Conclusions are given in Section 6. Throughout this paper, we assume a
standard flat $\Lambda$ Cold Dark Matter cosmology with $\Omega_{\rm m}=0.3$,
$\Omega_{\rm\Lambda}=0.7$, and $H_{0}=70$ km s-1 Mpc-1. We used the cosmology
calculator of Wright (2006) for determining projected linear sizes and
luminosity distances.

##  2 Sample Selection

According to the updated catalog of Perger et al. (2017), there are 56 sources
at $z\geq 4$ that were imaged with VLBI at least at one frequency band. Table
1 lists these high-redshift sources with literature references, and can be
considered as an update to table 5 of Coppejans et al. (2016). The observed
frequencies range from 1.4 to 43 GHz. We inspected the published radio images
to classify the mas-scale structure of the sources visually. The notations of
the simple morphological classes: C refers to sources with a single compact
component, J to sources having a core–jet type morphology, and E to sources
with extended radio structure on angular scales of a few tens of mas. In
addition to the morphological classification, sources are also categorized by
their total flux density radio continuum spectra, based on low-resolution
observations when sufficient data are available in the literature. The range
of available frequencies varies from source to source, but typically covers
$\sim 0.1-10$ GHz. We define three classes containing flat (f), steep (s) and
peaked (p) spectrum sources. However, we note that the multi-frequency
measurements may not have been necessarily simultaneous, and the frequency
coverage is inhomogeneous in the sample. Therefore this simple classification
is indicative only and not used in any quantitative analysis.

Table 1: List of the VLBI imaged radio quasars at $z\geq 4$ from the literature.  Name | $z$ |  $\nu$ (GHz) | Classification | VLBI reference
---|---|---|---|---
J001115.2$+$144601 | 4.96 | 1.7, 5 | C-f | 32
J003126.8$+$150740 | 4.29 | 4.3, 7.6 | C-f | 52
J010013.0$+$280225 | 6.33 | 1.5 | C-s | 36, 51
J012126.1$+$034706 | 4.13 | 2.3, 8.4 | C-s | 25
J012201.8$+$031002 | 4.00 | 4.3, 7.6 | C-f | 46
J013127.3$-$032100 | 5.18 | 1.7, 22, 43 | C-f | 29, 35
J021043.1$-$001818 | 4.65 | 1.7, 5 | C-f | 32
J025759.1$+$433836 | 4.07 | 2.3, 8.4, 8.6, 8.7 | J-f | 31
J030947.0$+$271757 | 6.10 | 1.5, 5, 8.4 | J-f | 42
J031147.0$+$050802 | 4.51 | 1.7, 2.3, 5 | E-s | 9, 27
J032444.3$-$291821 | 4.62 | 2.3, 8.6, 8.7, 22 | J-p | 12, 24, 32, 31
J052506.1$-$334306 | 4.42 | 4.3, 7.6 | J-f | 46
J081333.2$+$350811 | 4.92 | 1.6, 5 | E-s | 17
J083643.8$+$005453 | 5.80 | 1.6, 5 | C-s | 5, 11
J083946.2$+$511201 | 4.40 | 1.7, 5 | J-f | 33
J090630.7$+$693031 | 5.47 | 2.3, 8.4, 8.6, 8.7, 15, 22, 43 | C-p | 7, 9, 22, 32, 35, 39, 44
J091316.5$+$591921 | 5.12 | 1.4 | C-p | 8
J094004.8$+$052630 | 4.50 | 1.7, 5 | C-s | 32
J101335.0$+$281181 | 4.75 | 1.7, 5 | C-f | 32
J102107.5$+$220921 | 4.26 | 4.3, 7.6 | J-f | 46
J102623.6$+$254259 | 5.25 | 1.7, 4.8, 4.9, 5, 22, 43 | J-f | 12, 13, 26, 30, 35
J102838.8$-$084438 | 4.28 | 2.3, 8.7 | J-f | 9
J105320.4$-$001649 | 4.30 | 1.4 | C-f | 8
J112925.4$+$184624 | 6.82 | 1.5 | C-s | 48
J114657.8$+$403708 | 4.98 | 1.6, 5 | C-s | 17
J115502.9$-$310758 | 4.30 | 2.3, 8.6, 8.7, 22 | C-p | 4
J120523.1$-$074232 | 4.69 | 1.4 | E-f | 10
J123503.0$-$000331 | 4.69 | 1.4 | c-p | 8
J124230.6$+$542257 | 4.73 | 1.6, 5 | E-p | 17
J125359.3$-$405932 | 4.46 | 2.3, 4.3, 7.6, 8.6, 8.7 | C-s | 4
J131121.3$+$222738 | 4.61 | 1.7, 5 | C-f | 32
J140025.4$+$314910 | 4.64 | 1.7, 5 | C-f | 32
J142048.0$+$120546 | 4.03 | 1.5, 1.7, 5 | E-s | 33, 46, 49
J142738.5$+$331241 | 6.12 | 1.4, 1.6, 5 | E-s | 15, 16
J142952.1$+$544717 | 6.21 | 1.6, 5 | E-s | 19
J143023.7$+$420436 | 4.71 | 2.3, 4.8, 5, 8.3, 8.4, 8.6, 8.7, 15, 22 | J-f | 2 3, 6, 13, 18, 21 23, 24, 32, 43, 52
J145147.1$-$151220 | 4.76 | 4.3, 7.6 | C-s | 37
J145459.0$+$110928 | 4.93 | 1.7, 5 | C-f | 32
J151002.9$+$570243 | 4.31 | 2.3, 4.8, 5, 7.6, 8.3, 8.6, 8.7, 15 | J-p | 1, 3, 9, 13, 20, 21, 31, 46, 52
J153049.9$+$104931 | 5.72 | 1.7 | E-s | 41
J153533.9$+$025423 | 4.39 | 4.3, 7.6 | C-f | 52
J154823.9$+$333459 | 4.68 | 1.7, 5 | E-s | 32
Table 1: Continued

Name | $z$ |  $\nu$ (GHz) | Classification | VLBI reference
---|---|---|---|---
J160608.5$+$312446 | 4.56 | 2.3, 4.8, 5, 8.3, 8.4, 8.7, 22 | J-p | 3, 13, 31, 32, 34, 50
J161105.6$+$084435 | 4.55 | 1.6, 5 | C-f | 17
J162830.0$+$115403 | 4.47 | 1.7, 5 | C-s | 32
J165913.2$+$210115 | 4.83 | 1.6, 5 | J-p | 17
J171521.1$+$214534 | 4.01 | 2.3, 4.3, 7.6, 8.6, 8.7 | J-s | 21, 46
J172026.6$+$310431 | 4.62 | 1.7, 5 | C-f | 32
J195136.0$+$013442 | 4.11 | 2.3, 4.3, 7.6, 8.4, 8.6, 8.7 | C-p | 9, 31, 37
J210240.3$+$601510 | 4.58 | 2.3, 8.3, 8.6, 8.7 | J-p | 3, 14, 32, 39
J213412.0$-$041909 | 4.33 | 1.7, 4.3, 5, 7.6 | J-p | 33, 38, 46
J222032.6$+$002536 | 4.20 | 1.7, 5 | E-s | 33
J222843.5$+$011032 | 5.95 | 1.6 | J-p | 28
J224607.6$-$052635 | 4.60 | 1.4, 1.6 | C-s | 45
J231448.7$+$020151 | 4.11 | 4.3, 7.6 | J-f | 52
J232936.8$-$152014 | 5.84 | 1.6 | J-s | 40
J235758.6$+$140202 | 4.33 | 4.3, 7.6 | C-f | 52

Note. — Col. 1 – radio source name derived from J2000 right ascension and
declination; Col. 2 – redshift; Col. 3 – VLBI observing frequencies; Col. 4 –
mas-scale morphological classification (capital letters) and spectral
classification (small letters) based on low-resolution observations (see text
in Section 2); Col. 5 – VLBI references: 1: Frey et al. (1997); 2: Paragi et
al. (1999); 3: Beasley et al. (2002); 4: Fomalont et al. (2003); 5: Frey et
al. (2003); 6: Fey et al. (2004); 7: Romani et al. (2004); 8: Momjian et al.
(2004); 9: Petrov et al. (2005); 10: Momjian et al. (2005); 11: Frey et al.
(2005); 12: Petrov et al. (2006); 13: Helmboldt et al. (2007); 14: Petrov et
al. (2008); 15: Momjian et al. (2008); 16: Frey et al. (2008); 17: Frey et al.
(2010); 18: Veres et al. (2010); 19: Frey et al. (2011); 20: O’Sullivan et al.
(2011); 21: Pushkarev & Kovalev (2012); 22: Petrov et al. (2012b); 23: Cheung
et al. (2012); 24: Petrov et al. (2012a); 25: Petrov (2013); 26: Frey et al.
(2013); 27: Parijskij et al. (2014); 28: Cao et al. (2014); 29: Gabányi et al.
(2015); 30: Frey et al. (2015); 31: Gordon et al. (2016); 32: Coppejans et al.
(2016); 33: Cao et al. (2017); 34: Lee et al. (2017); 35: Zhang et al. (2017);
36: Wang et al. (2017); 37: Schinzel et al. (2017); 38: Perger et al. (2018);
39: Frey et al. (2018); 40: Momjian et al. (2018); 41: Gabányi et al. (2018);
42: Spingola et al. (2020); 43: Zhang et al. (2020); 44: An et al. (2020); 45:
Fan et al. (2020) 46: Petrov (2021); 47: Hunt et al. (2021); 48: Momjian et
al. (2021); 49: Gabányi et al. (2021); 50: An et al. (2022); 51: Liu et al.
(2022) 52: Astrogeo database (http://astrogeo.org/)

To increase the sample compiled in Table 1, we chose 13 high-redshift radio-
loud quasars from the list of Sbarrato et al. (2013) which contains 31 $z>4$
blazar candidates with radio loudness $R>100$. Their selection was based on
the catalog of Shen et al. (2011) who matched the SDSS Data Release 7 (DR7)
quasar list (Schneider et al., 2010) with radio sources from the FIRST survey
(White et al., 1997). Out of the 31 sources from the list of Sbarrato et al.
(2013), 15 were already imaged with VLBI. A careful inspection of the original
survey catalogs revealed that as many as 3 SDSS DR7 optical quasars (i.e.
about $10\%$) were mistakenly identified by Shen et al. (2011) with apparently
unrelated radio sources, due to the large matching radius they applied,
$30\arcsec$. In contrast, Ivezić et al. (2002) found that with just $3\arcsec$
radius, practically all true SDSS–FIRST matches are included. The three
misidentified objects in Shen et al. (2011) (SDSS J111856.15+370255.9, SDSS
J143003.96+144354.8, and SDSS J145212.86+023526.3) are in fact not radio-loud
high-redshift quasars.

At the time of initiating our VLBI observing project, the sample of these 13
new sources was as large as about one-third of all VLBI-imaged radio sources
above redshift 4. Even now, with new results in the literature published after
the start of our project, the increase due to our results is by more than
$25\%$ (cf. Table 1). Our target sources and their parameters are listed in
Table 2. Each of the targets can be found in the FIRST (White et al., 1997)
and the U.S. National Radio Astronomy Observatory (NRAO) VLA Sky Survey (NVSS,
Condon et al., 1998) catalogs. Each of them is detected also in the ongoing
Karl G. Jansky Very Large Array All Sky Survey (VLASS, Lacy et al., 2020;
Gordon et al., 2020). Their redshifts are within a narrow range of $4<z<4.5$,
thus they represent radio AGN that are at similar cosmological distances. Note
that J1307$+$1507 is blended in NVSS with a bright radio source seen within
$\sim 13\arcsec$ separation. Therefore we have to consider its flux density as
an upper limit in Table 2.

Out of the 13 sources chosen, we found 6 having X-ray measurements available
in the literature. All 6 are observed with Chandra (Weisskopf et al., 2002) in
various surveys (Bassett et al., 2004; Vignali et al., 2005; Wu et al., 2013b;
Zhu et al., 2019). One of them (J1309$+$5733) is also detected in the XMM-
Newton Slew Survey (Saxton et al., 2008).

Table 2: The $z>4$ radio quasar sample presented in this study.

Name | Source ID | $z$ | $S_{\mathrm{FIRST,1.4GHz}}$ | $S_{\mathrm{NVSS,1.4GHz}}$ | $S_{\mathrm{VLASS,2.7GHz}}$
---|---|---|---|---|---
|  |  | (mJy) | (mJy) | (mJy)
J030437.21$+$004653.5 | J0304$+$0046 | 4.31 | 21.0 (0.1) | 24.6 (0.8) | 14.63 (0.16)
J085111.59$+$142337.7 | J0851$+$1423 | 4.31 | 16.2 (0.1) | 12.3 (0.5) | 6.75 (0.21)
J091824.38$+$063653.3 | J0918$+$0636 | 4.19 | 26.5 (0.1) | 30.9 (1.0) | 41.18 (0.24)
J100645.58$+$462717.2 | J1006$+$4627 | 4.44 | 6.3 (0.4) | 6.3 (0.1) | 6.73 (0.24)
J103717.72$+$182303.0 | J1037$+$1823 | 4.05 | 13.7 (0.2) | 11.4 (0.5) | 7.89 (0.23)
J123142.17$+$381658.9 | J1231$+$3816 | 4.14 | 24.0 (0.1) | 25.7 (0.9) | 11.09 (0.20)
J130738.83$+$150752.0 | J1307$+$1507 | 4.11 | 3.9 (0.1) |  $<$16.2 (0.6) | 2.07 (0.22)
J130940.70$+$573309.9 | J1309$+$5733 | 4.27 | 11.3 (0.1) | 11.2 (0.9) | 11.07 (0.24)
J132512.49$+$112329.7 | J1325$+$1123 | 4.41 | 71.1 (0.1) | 81.4 (2.5) | 51.03 (0.26)
J141209.96$+$062406.9 | J1412$+$0624 | 4.47 | 43.5 (0.1) | 47.2 (1.5) | 25.98 (0.25)
J143413.05$+$162852.7 | J1434$+$1628 | 4.20 | 4.2 (0.1) | 5.0 (0.5) | 2.30 (0.29)
J152028.14$+$183556.1 | J1520$+$1835 | 4.12 | 6.9 (0.2) | 8.8 (0.5) | 2.54 (0.25)
J172007.19$+$602824.0 | J1720$+$6028 | 4.42 | 5.1 (0.2) | 6.6 (0.4) | 5.15 (0.17)

Note. — Col. 1 – radio source name derived from J2000 right ascension and
declination; Col. 2 – shortened source name used throughout this paper; Col. 3
– redshift; Col. 4 – FIRST 1.4 GHz flux density and its uncertainty; Col. 5 –
NVSS 1.4 GHz flux density and its uncertainty; Col. 6 – VLASS 2.7 GHz flux
density and its uncertainty.

##  3 Observations and Data Reduction

###  3.1 EVN Observations

The selected target sources were observed with the EVN in e-VLBI mode (e-EVN,
Szomoru et al., 2004) at two central frequencies, 1.66 and 4.99 GHz. In the
e-VLBI experiments, data from the radio telescopes were streamed to the
correlator through an optical fiber network in real time. The data were
processed at the SFXC software correlator (Keimpema et al., 2015) at the Joint
Institute for VLBI European Research Infrastructure Consortium (JIVE) in
Dwingeloo, The Netherlands.

The series of experiments started in 2017 December and ended in 2020 November,
under the project code EG102 (PI: K. Gabányi). A total of 12 observing
sessions (EG102A to EG102L) were scheduled. In addition to the elements of the
EVN, antennas of the e-MERLIN were occasionally also included in the observing
network. Table 3 contains the details of the EVN observations, including the
date, the frequency, the target sources with their corresponding phase-
reference calibrators, and the participating telescopes in each project
segment. The following radio telescopes participated in the various segments:
e-EVN: Jodrell Bank Mk2 (Jb, United Kingdom), Westerbork (Wb, The
Netherlands), Effelsberg (Ef, Germany), Medicina (Mc, Italy), Noto (Nt,
Italy), Sardinia (Sr, Italy), Onsala 25-m (O8, Sweden), Toruń (Tr, Poland),
Irbene 32-m (Ir, Latvia), Irbene 16-m (Ib, Latvia), Yebes (Ys, Spain), Svetloe
(Sv, Russia), Zelenchukskaya (Zc, Russia), Badary (Bd, Russia), Tianma (T6,
China), Sheshan (Sh, China), Kunming (Km, China), Hartebeesthoek (Hh, South
Africa); e-MERLIN (United Kingdom): Cambridge (Cm), Darnhall (Da), Defford
(De), Knockin (Kn), Pickmere (Pi).

The observations were performed in phase-reference mode (Beasley & Conway,
1995), by regularly nodding between the target sources and the corresponding
bright nearby calibrators (all within $\approx 2\arcdeg$ angular separation).
The same phase-reference calibrator was used at both frequencies for each
target source (Table 3).

Table 3: Details of the observations in the EVN project EG102. Project | Frequency | Observing date | Participating radio telescopes | Source ID | Total on-source | Datarate | Phase | Separation
---|---|---|---|---|---|---|---|---
segment |  $\nu$ (GHz) |  |  |  | time (min) | (Mbps) | calibrator | ($\arcdeg$)
A | 1.7 | 2017 Dec 14 | Jb, Wb, Ef, Mc, O8, T6, Tr, Hh, Ir | J0304$+$0046 | 198 | 1024 | J0301$+$0118 | 0.96
B | 5 | 2018 Jan 16 | Jb, Ef, Mc, Nt, O8, Sh, Tr, Hh, Ib | J0304$+$0046 | 108 | 2048 | J0301$+$0118 | 0.96
C | 5 | 2018 Apr 10 | Jb, Wb, Ef, Mc, Nt, O8, T6, Tr, Ys, Hh, Ib | J0918$+$0636 | 222 | 2048 | J0915$+$0745 | 1.31
D | 1.7 | 2018 May 17 | Jb, Wb, Ef, Mc, O8, T6, Tr, Hh, Ib, Sr | J0918$+$0636 | 270 | 1024 | J0915$+$0745 | 1.31
|  |  |  | J1309$+$5733 | 144 | 1024 | J1302$+$5748 | 0.95
E | 5 | 2018 Jun 19 | Jb, Wb, Ef, Mc, Nt, Tr, Ys, Hh, Ib, T6 | J1309$+$5733 | 198 | 1024 | J1302$+$5748 | 0.95
F | 1.7 | 2019 Jan 23 | Jb, Wb, Ef, Mc, O8, T6, Tr, Hh, Ir, Sr | J1307$+$1507 | 108 | 1024 | J1300$+$1417 | 1.88
|  |  |  | J1520$+$1835 | 138 | 1024 | J1521$+$1756 | 0.69
G | 5 | 2019 Feb 14 | Jb, Wb, Ef, Mc, Nt, O8, T6, Tr, Ys, Hh, Ib | J1307$+$1507 | 150 | 2048 | J1300$+$1417 | 1.88
|  |  |  | J1520$+$1835 | 126 | 2048 | J1521$+$1756 | 0.69
H | 5 | 2019 Mar 19 | Jb, Wb, Ef, Nt, Mc, O8, T6, Tr, Ys, Hh, Ib, | J1037$+$1823 | 102 | 2048 | J1045$+$1735 | 2.05
|  |  | Cm, Da, De, Kn, Pi | J1231$+$3816 | 132 | 2048 | J1228$+$370 | 1.31
|  |  |  | J1412$+$0624 | 132 | 2048 | J1410$+$0731 | 1.19
I | 5 | 2019 May 14 | Jb, Wb, Ef, Mc, Nt, O8, T6, Tr, Ys, Hh, Ir, | J0851$+$1423 | 96 | 2048 | J0858$+$1409 | 1.83
|  |  | Sv, Bd, Zc, Cm, Da, De, Kn, Pi | J1006$+$4627 | 144 | 2048 | J0958$+$4725 | 1.73
|  |  |  | J1325$+$1123 | 108 | 2048 | J1327$+$1223 | 1.19
J | 1.7 | 2020 Jun 23 | Jb, Wb, Ef, O8, T6, Hh, Ir, | J0851$+$1423 | 102 | 1024 | J0858$+$1409 | 1.83
|  |  | Cm, Da, De, Kn, Pi | J1037$+$1823 | 150 | 1024 | J1045$+$1735 | 2.05
|  |  |  | J1231$+$3816 | 108 | 1024 | J1228$+$3706 | 1.31
|  |  |  | J1412$+$0624 | 126 | 1024 | J1410$+$0731 | 1.19
|  |  |  | J1434$+$1628 | 192 | 1024 | J1428$+$1628 | 1.45
K | 1.7 | 2020 Oct 07 | Jb, Wb, Ef, Mc, Nt, O8, T6, Hh, Ir, | J1006$+$4627 | 132 | 1024 | J0958$+$4725 | 1.73
|  |  | Sr, Cm, Da, De, Kn, Pi | J1325$+$1123 | 180 | 1024 | J1327$+$1223 | 1.19
|  |  |  | J1720$+$6028 | 126 | 1024 | J1722$+$6105 | 0.70
L | 5 | 2020 Nov 18 | Jb, Wb, Ef, Mc, O8, T6, Tr, Ys, Hh, Ir, | J1434$+$1628 | 144 | 2048 | J1428$+$1628 | 1.45
|  |  | Sv, Zc, Bd, Km, Cm, Da, De, Kn, Pi | J1720$+$6028 | 144 | 2048 | J1722$+$6105 | 0.70

###  3.2 Data Reduction

The VLBI data were calibrated with the NRAO Astronomical Image Processing
System (aips) software package (Greisen, 2003), following the standard
procedure. After loading the raw correlated data, interferometric visibility
amplitudes were calibrated using the antenna gain curves and the system
temperatures measured at the telescopes (or nominal values if system
temperature measurements were unavailable). 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 corrected for radio telescopes
with azimuth–elevation mount. Then global fringe-fitting (Schwab & Cotton,
1983) was performed on the phase-reference calibrators and bright fringe-
finder sources also scheduled in the experiments. The calibrated visibility
data were exported to Difmap (Shepherd et al., 1994), where we carried out
hybrid mapping, including several iterations of the clean algorithm (Högbom,
1974) and phase-only self-calibration (Alef & Porcas, 1986). Then antenna-
based gain correction factors were determined for the different calibrator and
fringe-finder sources. If exceeding $\pm 5\%$, the median correction factors
were applied to the visibility amplitudes in aips, for all the calibrator and
the target sources. The clean model components of the calibrators produced in
Difmap were transferred to aips, as inputs for the repeated fringe-fitting of
the calibrator data, to improve phase solutions by taking the calibrator
source structure into account. Finally, the fringe-fit solutions obtained for
the phase-reference calibrators were interpolated to the target source data.
The calibrated visibility data of the target sources were then exported from
aips.

Difmap was used to produce the images of the target sources. We applied
natural weighting, with amplitude errors raised to the power of $-1$ (uvweight
$0,-1$) to reduce the image noise. For the typically weak (mJy-level) targets,
up to a few rounds of clean iterations were performed, without self-
calibration. Phase-only self-calibration was attempted for four sources only
(J0918+0636, J1325+1123, and J1412+0624 at both frequencies, J1309+5733 at 1.7
GHz only) which had flux densities exceeding 15 mJy in their compact
components. After reaching an insignificant peak-to-noise level (below $\sim
6$) in the residual images, a clean iteration involving $1000$ steps with a
small loop gain $(0.01)$ was applied to smooth the noise features in the final
images displayed in Figure 1. The image parameters are listed in Table 4.
Circular Gaussian brightness distribution model components were also fitted to
the visibility data (Pearson, 1995) in Difmap, to quantitatively characterize
sizes and flux densities (Table 5).

We note that the project segments EG102B (J0304$+$0046 at 5 GHz) and EG102C
(J0918$+$0636 at 5 GHz) observed in early 2018 were affected by a temporary
technical problem with the calibration control in the digital baseband
converters at the EVN stations (see also Ghirlanda et al., 2019). The
resulting loss of coherence prevented us from properly calibrating the
amplitudes and making reliable images and brightness distribution models of
these two sources at 5 GHz. However, they were clearly detected and their
phase-referenced positions could still be estimated (Table 4). Among the two
sources above, J0918$+$0636 was observed previously with the EVN at 5 GHz on
1999 Sep 23 (experiment code ES034A, PI: I.A.G. Snellen). The participating
seven radio observatories were Ef, Jb, Mc, Nt, O8, Hh, and the phased array of
the Westerbork Synthesis Radio Telescope with 13 antenna elements. The
observing time spent on J0918$+$0636 was 1.8 h. The observing setup and the
calibration process were similar to those reported for the experiment ES034B
(Perger et al., 2018). Here in Table 5 we present fitted Gaussian model
parameters derived for J0918$+$0636 from this archival EVN observation, to
supplement our EG102 data.

For weaker sources below 15 mJy flux density (i.e. those that were not self-
calibrated), the effect of coherence loss on the peak brightnesses and flux
densities (Martí-Vidal et al., 2010) has to be considered. To estimate the
level of coherence loss, we imaged and modeled the stronger sources with and
without performing phase self-calibration and found an average model flux
density difference of $25\%$. While the actual value may vary from source to
source because of different target–calibrator separations, network stations
and signal-to-noise ratios, this correction factor is consistent with
estimates found for other EVN experiments (e.g. Mosoni et al., 2006; Gabányi
et al., 2019). Therefore, we multiplied the fitted flux densities for the weak
sources by a factor of 1.25 and marked those values with an asterisk in Table
5.

Figure 1: EVN images at 1.7 and 5 GHz. The red cross indicates the Gaia
optical position with its uncertainty, where available. In cases where the red
crosses are too small, additional large red $\times$ symbol marks the
position. Its purpose is simply to guide the eye and the size has no special
meaning. The blue cross in the 1.7-GHz image denotes the 5-GHz VLBI position
with the uncertainties of the 1.7- and 5-GHz positional difference for sources
where the offset between the two VLBI radio positions is non-negligible. The
lowest contours are drawn at $\pm 3$ times the image noise. The positive
contours increase by a factor of 2. The restoring beam is shown in the bottom-
left corner. Table 4 contains the image parameters. Figure 1: $Continued$
Figure 1: $Continued$ Figure 1: $Continued$

##  4 Results

We present the naturally weighted clean images for each source in Figure 1,
listing the image parameters in Table 4. The parameters of the fitted Gaussian
model components are given in Table 5, with uncertainties calculated following
Fomalont (1999). An additional $5\%$ error was added in quadrature to the flux
densities, to account for the VLBI absolute amplitude calibration uncertainty
(e.g. An et al., 2012; Frey et al., 2015). Except for the two sources
(J0304$+$0046 and J0918$+$0636) missing reliable 5-GHz data, model parameters
are given at both frequencies.

The power-law spectral index $\alpha$ is defined as $S\propto\nu^{\alpha}$,
where $S$ is the modeled flux density and $\nu$ the frequency. The two-point
spectral indices were determined from flux density measurements at 1.7 and 5
GHz. VLBI spectral indices and their uncertainties are given in Col. 9 of
Table 5, except for the two quasars without 5-GHz flux densities. We note that
the measurements of the same target source at the two frequencies were
conducted with a typical time difference of $\sim 1$ month, however, reaching
up to $17$ months in some cases (Table 3). Hence, the calculated spectral
indices should be treated with caution as they are based on non-simultaneous
measurements, and some sources might be variable.

To check whether the sources are resolved by the interferometer, we calculated
the minimum resolvable size for each project segment following equation (2) in
Kovalev et al. (2005). We found that out of the 13 targets, four sources
(J0851$+$1423, J1037$+$1823, J1231$+$3816, and J1325$+$1123) are resolved and
three (J0918$+$0636, J1309$+$5733, and J1720$+$6028) are unresolved at both
frequency bands. The other six sources are unresolved by either of the 1.7- or
5-GHz EVN observations. Based on the derived model parameters and spectral
indices, we calculated the redshift-corrected brightness temperatures (Condon
et al., 1982)

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

and the monochromatic power (Hogg et al., 2002)

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

at both frequencies. Here $z$ is the redshift, $S_{\nu}$ the integrated flux
density of the core in Jy, $\theta$ the fitted circular Gaussian diameter
(full width at half-maximum, FWHM) in mas, $\nu$ the observing frequency in
GHz, $\alpha=\alpha_{1.7}^{5}$ the spectral index between the two measured
frequencies, 1.7 and 5 GHz, and $D_{\text{L}}$ the luminosity distance in Mpc.
For the sources with unresolved core components, we can only give a lower
limit to the brightness temperature, substituting the minimum resolvable
angular size in Equation (1).

The phase-referenced VLBI positions of the sources were obtained from the
5-GHz images using the aips task maxfit. The right ascension (RA) and
declination (Dec) values are presented in Cols. 2–3 of Table 4. The estimated
astrometric errors at 5 GHz are comparable to those of the Gaia optical
coordinates.

Table 4: VLBI image parameters and source positions.

ID | RAGaia (${}^{\mathrm{h~{}min~{}s}}$) | DecGaia (∘ ′ ′′) | $\nu$ | Restoring beam |  $1\sigma$ nosie
---|---|---|---|---|---
| RAVLBI,5GHz (${}^{\mathrm{h~{}min~{}s}}$) | DecVLBI,5GHz (∘ ′ ′′) | (GHz) | (mas$\times$mas) | (∘) | (mJy beam-1)
J0304$+$0046 | $-$ | $-$ | 5 | 2.5 $\times$ 1.4 | 86.2 | $-$
| 03 04 37.21595 (0.3) | 00 46 53.6159 (0.3) | 1.7 | 22.3 $\times$ 3.4 | 84.1 | 0.31
J0851$+$1423 | 08 51 11.59953 (0.9) | 14 23 37.7017 (0.4) | 5 | 1.8 $\times$ 0.9 | 7.6 | 0.06
| 08 51 11.59954 (0.6) | 14 23 37.7013 (0.6) | 1.7 | 4.3 $\times$ 2.9 | 12.5 | 0.07
J0918$+$0636 | 09 18 24.37998 (0.4) | 06 36 53.4111 (0.3) | 5 | 1.6 $\times$ 0.9 | 9.3 | $-$
| 09 18 24.37998 (0.4) | 06 36 53.4162 (0.6) | 1.7 | 18.1 $\times$ 2.9 | 89.5 | 0.39
J1006$+$4627 | 10 06 45.59650 (0.7) | 46 27 17.2828 (0.8) | 5 | 4.3 $\times$ 0.93 | 176.5 | 0.17
| 10 06 45.59633 (0.5) | 46 27 17.2833 (0.5) | 1.7 | 14.1$\times$ 3.6 | 0.8 | 0.10
J1037$+$1823 | 10 37 17.73037 (1.6) | 18 23 03.0931 (0.8) | 5 | 5.2 $\times$ 0.8 | 4.0 | 0.10
| 10 37 17.73040 (0.6) | 18 23 03.0918 (0.6) | 1.7 | 4.4 $\times$ 3.6 | 52.6 | 0.09
J1231$+$3816 | 12 31 42.17213 (0.5) | 38 16 59.0408 (0.4) | 5 | 5.2 $\times$ 0.9 | 0.2 | 0.08
| 12 31 42.17206 (0.4) | 38 16 59.0429 (0.4) | 1.7 | 19.9 $\times$ 3.9 | 84.6 | 0.08
J1307$+$1507 | 13 07 38.83415 (0.5) | 15 07 52.1226 (0.3) | 5 | 7.2 $\times$ 1.4 | 89.1 | 0.03
| 13 07 38.83423 (0.6) | 15 07 52.1223 (0.6) | 1.7 | 18.8 $\times$ 4.1 | 90 | 0.04
J1309$+$5733 | 13 09 40.68855 (0.3) | 57 33 09.9371 (0.3) | 5 | 2.4 $\times$ 0.6 | 12.9 | 0.21
| 13 09 40.68854 (0.3) | 57 33 09.9368 (0.3) | 1.7 | 23.8 $\times$ 20.8 | 98.9 | 0.13
J1325$+$1123 | 13 25 12.49327 (0.4) | 11 23 29.8380 (0.2) | 5 | 1.9 $\times$ 0.9 | 8.3 | 0.20
| 13 25 12.49322 (0.4) | 11 23 29.8389 (0.4) | 1.7 | 4.9 $\times$ 3.8 | 35.3 | 0.52
J1412$+$0624 | 14 12 09.96955 (0.7) | 06 24 06.8665 (0.5) | 5 | 1.6 $\times$ 0.9 | 11.7 | 0.06
| 14 12 09.96965 (0.4) | 06 24 06.8665 (0.6) | 1.7 | 19.8 $\times$ 3.8 | 83.2 | 0.13
J1434$+$1628 | 14 34 13.05469 (0.4) | 16 28 52.7346 (0.5) | 5 | 1.9 $\times$ 1.0 | 10.0 | 0.02
| 14 34 13.05461 (0.5) | 16 28 52.7350 (0.5) | 1.7 | 18.4 $\times$ 3.8 | 79.2 | 0.03
J1520$+$1835 | 15 20 28.14216 (0.3) | 18 35 56.1587 (0.3) | 5 | 7.4 $\times$ 1.4 | 88.3 | 0.03
| 15 20 28.14386 (0.4) | 18 35 56.1767 (0.3) | 1.7 | 4.5 $\times$ 3.9 | 45.0 | 0.06
J1720$+$6028 | 17 20 07.18399 (2.1) | 60 28 24.0118 (1.5) | 5 | 3.9 $\times$ 1.1 | 29.0 | 0.02
| 17 20 07.18368 (0.3) | 60 28 24.0128 (0.2) | 1.7 | 12.0 $\times$ 2.9 | 46.7 | 0.08

Note. — Col. 1 $-$ source designation; Col. 2–3 $-$ right ascension and
declination coordinates of the sources, the first line per source lists the
optical coordinates obtained by Gaia (where available), the second line per
source lists the VLBI 5-GHz position; Col. 4 $-$ observed frequency; Col. 5
$-$ elliptical Gaussian restoring beam half-power width; Col. 6 $-$ major axis
position angle of the restoring beam, measured from north through east; Col. 7
$-$ 1$\sigma$ image noise.

Table 5: Basic parameters and the derived physical properties of the sample of
$z>4$ radio sources in the EG102 experiment.

ID | $S_{\mathrm{VLBI,1.7~{}GHz}}$ | $S_{\mathrm{VLBI,5~{}GHz}}$ | $\theta_{\mathrm{1.7~{}GHz}}$ | $\theta_{\mathrm{5~{}GHz}}$ | $\alpha_{1.7}^{5}$ | $T_{\mathrm{b,1.7~{}GHz}}$ | $T_{\mathrm{b,5~{}GHz}}$ | $P_{\mathrm{1.7~{}GHz}}$ | $P_{\mathrm{5~{}GHz}}$
---|---|---|---|---|---|---|---|---|---
| (mJy) | (mJy) | (mas) | (mas) |  | ($10^{9}$ K) | ($10^{9}$ K) | ($10^{26}$ W Hz-1) | ($10^{26}$ W Hz-1)
J0304$+$0046 | 15.01* (2.32) | $-$ |  $<$ 4.78 | $-$ | $-$ |  $>$ 1.47 | $-$ | 5.20 (0.98)a | $-$
J0851$+$1423 | 4.94* (0.82) | 4.60* (0.67) | 4.24 (0.64) | 1.12 (0.15) |  $-0.12$ (0.19) | 0.62 (0.21) | 0.94 (0.28) | 2.10 (0.42) | 1.95 (0.35)
J0918$+$0636 | 38.53 (3.86) | 35.50† (2.18) |  $<$ 2.41 |  $<$ 0.71† |  $-0.08$ (0.11) |  $>$ 14.52 |  $>$ 17.85 | 14.62 (2.14) | 13.47 (1.66)
J1006$+$4627 | 8.78* (0.73) | 6.69* (0.53) |  $<$ 1.75 | 1.41 (0.08) |  $-0.25$ (0.11) |  $>$ 6.58 | 0.89 (0.13) | 4.90 (0.68) | 3.73 (0.51)
J1037$+$1823 | 7.38* (0.77) | 7.15* (1.05) | 2.44 (0.20) | 2.88 (0.38) |  $-0.05$ (0.29) | 2.64 (0.51) | 0.21 (0.07) | 2.54 (0.38) | 2.46 (0.71)
J1231$+$3816 | 8.91* (0.82) | 6.79* (0.72) | 4.91 (0.34) | 1.12 (0.11) |  $-0.25$ (0.13) | 0.80 (0.13) | 1.36 (0.27) | 4.41 (0.62) | 3.36 (0.52)
J1307$+$1507 | 2.69* (0.19) | 1.20* (0.14) | 9.95 (0.15) |  $<$ 1.14 |  $-0.76$ (0.14) | 0.06 (0.01) |  $>$ 0.23 | 2.98 (0.38) | 1.32 (0.21)
J1309$+$5733 | 22.30 (1.32) | 12.78* (1.52) |  $<$ 1.90 |  $<$ 0.40 |  $-0.52$ (0.15) |  $>$ 13.73 |  $>$ 21.03 | 18.10 (2.25) | 10.40 (1.71)
J1325$+$1123 | 62.70 (3.91) | 31.16 (1.86) | 0.76 (0.02) | 1.12 (0.03) |  $-0.61$ (0.09) | 248.00 (20.98) | 6.56 (0.55) | 63.40 (7.39) | 31.50 (3.91)
J1412$+$0624 | 18.80 (1.89) | 15.38 (0.85) |  $<$ 2.66 | 0.77 (0.02) |  $-0.18$ (0.10) |  $>$ 6.11 | 6.92 (0.47) | 9.44 (1.37) | 7.73 (0.95)
J1434$+$1628 | 1.99* (0.22) | 1.23* (0.12) |  $<$ 2.88 | 0.79 (0.06) |  $-0.44$ (0.15) |  $>$ 0.53 | 0.49 (0.09) | 1.38 (0.21) | 0.85 (0.12)
J1520$+$1835 | 4.80* (0.61) | 1.05* (0.17) | 2.95 (0.31) |  $<$ 1.44 |  $-1.42$ (0.21) | 1.19 (0.30) |  $>$ 0.13 | 15.68 (2.64) | 3.43 (0.67)
J1720$+$6028 | 7.25* (0.50) | 4.20* (0.23) |  $<$ 1.27 |  $<$ 0.29 |  $-0.51$ (0.08) |  $>$ 10.32 |  $>$ 13.68 | 6.15 (0.79) | 3.56 (0.44)

Note. — † based on archival data from experiment ES034A. a assuming 0 spectral
index. Col. 1 $-$ Source designation; Cols. 2-3 $-$ fitted 1.7- and 5-GHz EVN
flux densities and uncertainties; flux density values marked with * are
corrected for the $25\%$ coherence loss for deriving the physical parameters
(see Section 3.2); Cols. 4-5 $-$ fitted circular Gaussian component diameter
(FWHM) at 1.7 and 5 GHz, or upper limit equals to the minimum resolvable
angular size (Kovalev et al., 2005) for unresolved components; Col. 6 $-$
spectral index between 1.7 and 5 GHz; Cols. 7-8 $-$ brightness temperature and
its uncertainty at 1.7 and 5 GHz, or lower limit for unresolved components;
Cols. 9-10 $-$ monochromatic radio power and its uncertainty at 1.7 and 5 GHz.

##  5 Discussion

###  5.1 The Origin of the Radio Emission and Doppler-boosting

The brightness temperatures are $T_{\mathrm{b}}>10^{6}$ K for all sources,
indicating non-thermal radio emission related to AGN activity (Kewley et al.,
2000; Middelberg et al., 2011). As non-thermal emission could also originate
from supernova remnants or remnant complexes, sources have to meet a
monochromatic power limit for the radio emission to be considered as driven by
AGN activity (Alexandroff et al., 2012). As Magliocchetti et al. (2014)
showed, radio emission of sources at $z>2$ is powered by AGN if the 1.4-GHz
monochromatic powers exceed $4\times 10^{24}$ W Hz-1, while star formation is
the dominant process for objects with lower powers. The rest-frame 1.4-GHz
powers can be calculated according to Equation (2), where the
$S_{\mathrm{1.4\,GHz}}$ flux density values of the brightest components are
extrapolated from the 1.7- and 5-GHz values measured with VLBI, assuming
power-law spectra with the determined $\alpha_{1.7}^{5}$ spectral index (Table
5). All 13 sources exceed this limit. For the one with missing 5-GHz flux
density measurement (J0304+0046), we considered a broad range of possible
spectral indices, $-1\leq\alpha_{1.7}^{5}\leq 0$.

The brightness temperature of the sources (Table 5) can be used to determine
whether the emission is relativistically enhanced (Doppler-boosted). Readhead
(1994) estimated the theoretical value of the intrinsic brightness temperature
in case of the energy densities of the emitting plasma and the magnetic field
are in equipartition, and found $T_{\mathrm{b,eq}}\approx 5\times 10^{10}$ K.
By assuming equipartition condition in the sources, the intrinsic brightness
temperature is $T_{\mathrm{b,eq}}$, and the Doppler factor can be calculated
as

$\delta=\frac{T_{\mathrm{b}}}{T_{\mathrm{b,eq}}}.$ (3)

where $T_{\mathrm{b}}$ is the redshift-corrected (or source rest-frame)
brightness temperature derived from VLBI measurements at a given frequency. If
$\delta>1$, the radio emission is considered Doppler-boosted. Among the
sources examined, J1325$+$1123 is the only one with certainly Doppler-boosted
radio emission at 1.7 GHz. On the other hand, there are three sources
(J0851$+$1423, J1037$+$1823, and J1231$+$3816) where no indication of Doppler-
boosting is seen. For the remaining, not clearly resolved objects whose
brightness temperatures are lower limits at either of the frequency bands, the
data are insufficient to decide whether the radio emission is Doppler-enhanced
or not.

Doppler-boosting in AGN jets can be observed under very special conditions
only. Indeed, when there is no sign of Doppler-boosting (i.e. $\delta\leq 1$),
it is either because of the jet inclination angle is large and thus
relativistic beaming is not present, or the flux density is measured far away
from the peak frequency of the spectrum. In the latter case, it is possible
that the source would appear Doppler-boosted at other frequencies, closer to
the radio spectral peak (e.g. Readhead, 1994; Cheng et al., 2020).

###  5.2 Continuum Radio Spectra

Continuum radio spectra of the 13 sources are shown in Figure 2, both using
fitted compact component flux densities from our high-resolution EVN data, and
total flux densities from low-resolution measurements from the literature
(Table 6). VLBI data are available at two frequencies (except for J0304+0046
with only 1.7-GHz flux density), therefore we determined the two-point
spectral index $\alpha_{1.7}^{5}$ (Table 5) by assuming a power-law radio
spectrum. We note that although most of the EVN measurements of the same
target source at the two frequencies were conducted with a typical time
difference of $\sim 1$ month, in some cases up to $17$ months elapsed between
the two observations (Table 3), and in the case of J0918$+$0636, the time
difference is $\sim 20$ yr. Hence the calculated spectral indices for those
sources (especially for J0918$+$0636) should be treated with caution because
of possible long-term flux density variability.

Spectra with $\alpha<-0.5$ are called steep, with $-0.5\leq\alpha\leq 0$ flat,
and with $0<\alpha$ inverted. From the 12 quasars in our sample with spectral
indices characteristic to the compact VLBI-imaged structure, $5$ sources
($42\%$) have steep and $7$ ($58\%$) have flat spectra. Taking into account
the uncertainties of the spectral indices, there are 3 sources that could have
either flat or steep spectrum within the errors. Similarly, there are 3
sources with flat spectra which could be inverted within the uncertainties.
Similar flat-to-steep-spectrum ratio was found by Coppejans et al. (2016) in
their study of $z>4.5$ quasars. The two smaller samples of $z>4$ quasars of
Frey et al. (2010) and Cao et al. (2017) also have similar ratios, with
$50-50\%$ of objects with flat and steep spectra.

For the total flux density spectra also plotted in Figure 2, we collected
available single-dish and low-resolution radio interferometric observations
from the literature for all the sources in our sample. Since these quasars are
relatively faint and typically below the survey flux density thresholds, only
a handful of measurements were found for the majority of them. Fortunately,
the 1.4-GHz FIRST (White et al., 1997) and NVSS (Condon et al., 1998), and the
recent 2.7-GHz VLASS (Lacy et al., 2020; Gordon et al., 2020) surveys all have
observations for all of our sources. In NVSS, J1307$+$1507 is blended with a
nearby bright radio source, therefore, the corresponding spectral point is
marked as an upper limit in Figure 2. In addition to the surveys above, Table
6 contains the references where flux densities were collected from for our
sources.

Table 6: Total flux density data used to make Fig. 2 taken from the
literature.

ID | $\alpha$ | $S_{\mathrm{150~{}MHz}}$ | $S_{\mathrm{330~{}MHz}}$ | $S_{\mathrm{610~{}MHz}}$ | $S_{\mathrm{1.4~{}GHz}}$ | $S_{\mathrm{2.7~{}GHz}}$ | $S_{\mathrm{5~{}GHz}}$ | $S_{\mathrm{8.5~{}GHz}}$ | $S_{\mathrm{10.6~{}GHz}}$
---|---|---|---|---|---|---|---|---|---
|  | (mJy) | (mJy) | (mJy) | (mJy) | (mJy) | (mJy) | (mJy) | (mJy)
J0304$+$0046 |  $-$0.26 (0.10) |  36.2 (5.7)10 |  |  |  22.5 (0.1)3 |  14.63 (0.16)12 |  |  |
|  |  |  |  |  24.6 (0.8)4 |  |  |  |
J0851$+$1423 |  $-$0.87 (0.07) |  92.1 (12.6)10 |  |  |  16.2 (0.1)3 |  6.75 (0.21)12 |  |  |
|  |  |  |  |  12.3 (0.5)4 |  |  |  |
J0918$+$0636 | 0.07 (0.07) | 18.6 (4.8) |  |  |  26.5 (0.1)3 |  41.18 (0.24)12 |  38.57 |  25.6 (0.4)6 |  23.17
|  |  |  |  |  30.9 (1.0)4 |  |  26.6 (0.4)8 |  |
J1006$+$4627 |  $0.05$ (0.06) |  $<$ 11.7* |  |  |  6.3 (0.1)3 |  6.73 (0.24)12 |  |  |
|  |  |  |  |  6.4 (0.4)4 |  |  |  |
J1037$+$1823 |  $-0.78$ (0.05) |  $<$ 7.5* |  |  |  13.4 (0.2)3 |  7.89 (0.23)12 |  |  |
|  |  |  |  |  11.4 (0.5)4 |  |  |  |
J1231$+$3816 |  $-0.89$ (0.05) |  157.5 (16.9)10 |  77 (2.9)5 |  |  24.04 (0.13)3 |  11.09 (0.20)11 |  |  |
|  |  |  |  |  25.7 (0.9)4 |  |  |  |
J1307$+$1507 |  $-1.61$ (0.14) | 190.6 (6.3)* |  |  |  3.89 (0.13)3 |  2.07 (0.22)12 |  |  |
|  |  |  |  |  $<$ 16.2 (0.6)4 |  |  |  |
J1309$+$5733 |  $S_{0}=$ 13 (1) |  10.01 (2.43)11 |  |  |  11.33 (0.14)3 |  11.07(0.24)11 |  7.57 |  |  3.77
|  $\nu_{0}=$ 0.6 (0.1) |  $<$ 7.8* |  |  |  11.2 (0.9)4 |  |  |  |
J1325$+$1123 |  $S_{0}=$ 72 (17) | 29.2 (6.3) |  |  |  71.5 (0.1)3 |  51.03 (0.26)12 |  72 (12)1 |  42.6 (0.4)6 |
|  $\nu_{0}=$ 1.5 (0.2) |  |  |  |  81.4 (2.5)4 |  |  47.67 |  |
|  |  |  |  |  |  |  68 (10)2 |  |
J1412$+$0624 |  $-$0.42 (0.06) |  122.8 (16.2)10 |  |  |  43.5 (0.1)3 |  25.98 (0.25)12 |  23.0 (0.2)8 |  23.5 (0.4)6 |
|  |  |  |  |  47.2 (1.5)4 |  |  34 (6)7 |  |
J1434$+$1628 |  $-$1.12 (0.27) |  $<$ 11.4* |  |  |  4.21 (0.14)3 |  2.30 (0.29)12 |  |  |
|  |  |  |  |  5.0 (0.5)4 |  |  |  |
J1520$+$1835 |  $-$1.71 (0.31) |  $<$ 16.5* |  |  |  6.94 (0.15)3 |  2.54 (0.25)12 |  |  |
|  |  |  |  |  8.8 (0.5)4 |  |  |  |
J1720$+$6028 |  $-$0.20 (0.11) |  $<$ 9.9* |  |  6.93 (0.18)8 |  5.06 (0.15)3 |  5.15 (0.17)12 |  |  |
|  |  |  |  |  6.6 (0.4)4 |  |  |  |
|  |  |  |  |  6.01 (0.26)6 |  |  |  |

Note. — Col. 1 $-$ source designation; Col. 2 $-$ fitted spectral indices;
where log-parabolic function was fitted, we give the fitted values $S_{0}$ in
mJy and $\nu_{0}$ in GHz.; Col. 3–10 $-$ flux densities and their
uncertainties (where available) collected from the literature; numbers in the
upper indices are references for the flux density values. The symbol * marks
the TGSS $3\sigma$ upper limits. References: 1: Gregory & Condon (1991); 2:
Becker et al. (1991); 3: Becker et al. (1995); 4: Condon et al. (1998); 5; de
Bruyn et al. (2000); 6: Myers et al. (2003); 7: Holt et al. (2004); 8: Jackson
et al. (2007); 9: Garn et al. (2007); 10: Intema et al. (2017); 11: Shimwell
et al. (2017); 12: Gordon et al. (2020)

In most cases, we fitted the spectral data points with a power-law function,
similarly to the high-resolution case. However, for J1309$+$5733 and
J1325$+$1123, we found that the choice of a log-parabolic function

$\log S=a(\log\nu-\log~{}\nu_{0})^{2}+b$ (4)

resulted in a better fit (i.e. lower $\chi^{2}$ values) than using the power-
law. In Equation (4), $\nu_{0}$ is the frequency corresponding to the peak
flux density $S_{0}$, while $a$ and $b$ are numerical constants without any
physical meaning (e.g. Coppejans et al., 2017). The fitted spectral index
$\alpha$ (for the power-law cases), or the $\nu_{0}$ and $S_{0}$ values (for
the log-parabolic fits) are given in Col. 2 of Table 2 and as insets in the
spectrum plots (Figure 2).

To obtain low-frequency flux density points for our spectra, we analysed TGSS
Alternative Data Release 1 (Tata Institute of Fundamental Research Giant
Metrewave Radio Telescope Sky Survey, Intema et al., 2017) images, since all
of our sources are in its sky coverage. Four out of the 13 sources are listed
in the TGSS source catalogue. Caccianiga et al. (2019) found two other sources
of our sample (J0918$+$0636 and J1325$+$1123) in the TGSS images detected with
lower significance (at least $2\sigma$). For these two, and for another source
J1307$+$1507 that we found in the image but not in the TGSS source catalogue,
we fitted Gaussian brightness distribution models at the source positions with
the aips task jmfit using the corresponding TGSS tiles. For the remaining six
undetected objects, we consider the $3\sigma$ image noise (measured in the
close vicinity of the objects using the task imean) to derive an upper limit
to the flux density of an unresolved source (Table 6). This way we get
important constrains on the low-frequency end of the spectra, even if there is
no TGSS detection available.

Some of the sources whose spectrum is fitted with a power-law function might
in reality have a peaked spectrum as well, that is better described with a
log-parabolic function. However, because of the lack of low-frequency
measurements, parameters of such a fit would be poorly constrained. Indeed,
when low-frequency synchrotron emission is properly sampled, high-redshift
($z>5$) radio-loud quasars tend to show evidence for spectral turnover at
rest-frame frequencies $\sim 1-50$ GHz (Shao et al., 2022). Peaked continuum
radio spectra are also common for bright $z>3$ radio quasars (Sotnikova et
al., 2021).

Figure 2: Radio continuum spectra of the 13 sources in our EVN sample. Black:
total flux density data collected from the literature. Blue: compact component
flux densities observed with high resolution in this project.

###  5.3 Flux Density Variability

Our possibility to investigate flux density variability is limited because
there are generally no measurements available at the same frequencies and
angular resolutions, but at different observing epochs. However, all of our
sources have been detected in three VLA surveys (FIRST, NVSS, and VLASS),
albeit the NVSS flux density value for J1307$+$1507 can only be regarded as an
upper limit. We calculate flux density ratios from non-simultaneous
measurements (Table 7) and interpret them in the context of variability.

As discussed by Coppejans et al. (2016), the ratio between the FIRST and NVSS
flux densities ($S_{\mathrm{FIRST}}/S_{\mathrm{NVSS}}$) can be a variability
indicator. Both surveys were conducted at 1.4 GHz but at different epochs, and
in different configurations of the VLA. The B configuration used by FIRST
provided $\sim 5\arcsec$ angular resolution, while the most compact D
configuration used by NVSS led to $\sim 45\arcsec$ resolution. Following
Coppejans et al. (2016), we consider a source definitely variable if the FIRST
flux density exceeds the NVSS value by more than $10\%$. In our sample, there
are two such sources, J0851$+$1423 and J1037$+$1823 (Table 7). If
$S_{\mathrm{FIRST}}/S_{\mathrm{NVSS}}\ll 1$, it may be caused either by
variability or the presence of an emission region extended to $\sim 10\arcsec$
which remains unresolved in NVSS but becomes resolved in FIRST. In general,
any other source may as well be variable, even with
$S_{\mathrm{FIRST}}/S_{\mathrm{NVSS}}\approx 1$, just being unresolved and
having, accidentally, nearly equal flux densities at the two epochs when the
FIRST and NVSS measurements were made.

In a similar way, we can compare VLBI and VLA flux densities at the same
frequencies that were measured with substantially different angular
resolutions. Table 7 gives 1.4- and 2.7-GHz flux density ratios based on FIRST
and VLASS data, respectively. The VLBI values were calculated by extrapolating
(to 1.4 GHz) and interpolating (to 2.7 GHz) our EVN measurements made at 1.7
and 5 GHz, assuming a power-law radio spectrum in the GHz frequency range,
using spectral indices $\alpha_{1.7}^{5}$ calculated in Section 5.1 (Table 5).
For J0304+0046 and J0918$+$0636, i.e. the sources with single-frequency EVN
data available, we assumed here a zero spectral index. We repeat the
cautionary note that the EVN spectral index values may be affected by
variability since the measurements at the two frequencies were not
simultaneous. Also, if any of our objects is a GPS or megahertz peaked-
spectrum (MPS) source, their spectra are not necessarily well described by a
power-law function. However, the range where extrapolation and interpolation
are done is quite narrow in frequency. If
$S_{\mathrm{VLBI,1.4\,GHz}}/S_{\mathrm{FIRST}}>1.1$ or
$S_{\mathrm{VLBI,2.7\,GHz}}/S_{\mathrm{VLASS}}>1.1$, we consider the source
variable. If these ratios are below unity, the most likely explanation is that
a significant fraction of the total radio emission originates from an extended
region completely resolved with VLBI. However, variability cannot be ruled out
entirely in any of the sources.

In summary, we consider a source variable when at least one of the three flux
density ratios described above exceeds unity by more than 10%. By this
criterion, we find the following quasars definitely variable: J0851$+$1423,
J0918$+$0636, J1006$+$4627, J1037+1823, J1309$+$5733, and J1720$+$6028 (Table
7).

Table 7: Flux density ratios of the target sources.

ID | $S_{\mathrm{FIRST}}/S_{\mathrm{NVSS}}$ | $S_{\mathrm{VLBI,1.4\,GHz}}/S_{\mathrm{FIRST}}$ | $S_{\mathrm{VLBI,2.7\,GHz}}/S_{\mathrm{VLASS}}$
---|---|---|---
J0304$+$0046 | 0.85 (0.03) | 0.71∗ | 1.03∗
J0851$+$1423 | 1.32 (0.05) | 0.33 (0.03) | 0.74 (0.14)
J0918$+$0636 | 0.86 (0.03) | 1.45∗ | 0.94∗
J1006$+$4627 | 0.98 (0.06) | 1.47 (0.10) | 1.16 (0.07)
J1037$+$1823 | 1.20 (0.06) | 0.54 (0.06) | 0.92 (0.21)
J1231$+$3816 | 0.93 (0.03) | 0.39 (0.01) | 0.72 (0.04)
J1307$+$1507 | – | 0.80 (0.03) | 0.92 (0.12)
J1309$+$5733 | 1.01 (0.08) | 2.28 (0.02) | 1.62 (0.04)
J1325$+$1123 | 0.87 (0.03) | 1.09 (0.01) | 1.02 (0.01)
J1412$+$0624 | 0.92 (0.03) | 0.56 (0.01) | 0.83 (0.02)
J1434$+$1628 | 0.83 (0.09) | 0.52 (0.04) | 0.70 (0.17)
J1520$+$1835 | 0.78 (0.05) | 0.91 (0.03) | 0.98 (0.10)
J1720$+$6028 | 0.77 (0.03) | 1.57 (0.06) | 1.11 (0.05)

Note. — ∗ assuming 0 spectral index. Col. 1 $-$ Source designation; Col. 2 $-$
Ratio of 1.4-GHz FIRST and NVSS flux densities and its uncertainty; Col. 3 $-$
Ratio of the extrapolated 1.4-GHz VLBI and FIRST flux densities and its
uncertainty; Col. 4 $-$ Ratio of the interpolated 2.7-GHz VLBI and VLASS flux
densities and its uncertainty

###  5.4 Gaia Optical Positions

The coordinates from the recent Gaia (Gaia Collaboration et al., 2016) EDR3
catalog are the most accurate optical astrometric positions available (Gaia
Collaboration et al., 2021). The high sensitivity of Gaia enables the
detection of faint extragalactic sources as well, like the high-redshift AGN
in our sample. We checked the reliability of Gaia positions by comparing the
newest EDR3 solutions with those in the earlier data release (DR2, Gaia
Collaboration et al., 2018), and found that they are consistent within the
positional accuracy of the survey (from a few $\mu$as to a few mas, depending
on the actual object). Comparing the Gaia EDR3 optical coordinates with radio
positions of quasars obtained from our VLBI observations can help to reveal
additional information on the nature of these sources.

The VLBI radio position corresponds to the brightest compact region of the
jet, which may be either a synchrotron self-absorbed core or a compact hotspot
associated with a shock front between the jet and the surrounding medium. On
the other hand, the optical position is mostly determined by the location of
the accretion disk, which is in the closest vicinity of the central SMBH.
However, the preferred direction of occasional offsets between the radio and
optical AGN positions, up to a few mas, is found to statistically coincide
with the VLBI jet direction, suggesting the presence of strong pc-scale
optical jet emission in certain objects (Kovalev et al., 2017; Plavin et al.,
2019). In misaligned jetted sources like CSOs, the brightest features marking
the radio position are hotspots in the radio lobes, which appear further away
from the central object. Therefore, if a significant offset exceeding the
usual values found for beamed AGN is detected between the radio (VLBI) and
optical (Gaia) coordinates, it strongly suggests the misaligned nature of the
quasar. For faint radio sources, like the typical high-redshift quasars,
revealing a Gaia–VLBI positional mismatch could help constraining the class.

All but one of our sources (J0304$+$0046) have been observed with Gaia and
have EDR3 optical position available. The positional uncertainties in EDR3 are
below $1$ mas in most cases, except for J1037$+$1823 and J1720$+$6028, for
which the errors are somewhat higher, but still within $\sim 2$ mas. We
indicate Gaia positions in our VLBI images with red crosses, while 5-GHz VLBI
peak positions are also shown in the 1.7-GHz images (with blue crosses) when
the offset is non-negligible (Figure 1). Radio and optical positions are
listed in Table 4, along with their uncertainties. We consider a positional
offset significant if the optical position differs by more than
$3\sigma_{\mathrm{pos}}$ from the 5-GHz position. Here $\sigma_{\mathrm{pos}}$
is the uncertainty of the positional difference,
$\sigma_{\mathrm{pos}}=\sqrt{\sigma_{\mathrm{5\,GHz}}^{2}+\sigma_{\mathrm{Gaia}}^{2}}$,
where $\sigma_{\mathrm{5\,GHz}}$ is the uncertainty of the 5-GHz radio
coordinate and $\sigma_{\mathrm{Gaia}}$ refer to the uncertainty of the Gaia
optical coordinate. We tag a source with ‘Slight’ in Table 8 when the
radio–optical offset is between $(1-3)\times\sigma_{\mathrm{pos}}$. There are
a few sources where the 1.7- and 5-GHz radio positions do not agree. These are
indicated in Figure 1 and the notable individual cases are discussed in
Section 5.5.

###  5.5 Classification and Notes on Individual Sources

Here we attempt to classify the radio quasars in our sample as blazar or non-
blazar sources. We take various aspects into account, namely the radio
structure revealed by our EVN images (Section 4, Figure 1) and the fitted
brightness distribution model parameters (Table 5), the continuum radio
spectra (Section 5.2), the possible flux density variability (Section 5.3),
and the Gaia EDR3 optical coordinates (Section 5.4). We also checked in the
literature whether there are any available archival X-ray data for them. The
criteria we considered for the classification and the results are summarized
in Table 8. Two main classes are defined, FSRQs and steep-spectrum sources
(SS). Based on the measured brightness temperatures as well as the 1.4-GHz
monochromatic powers, the radio emission of all 13 sources originates from AGN
activity (Section 5.1). We also briefly comment on individual sources.

Table 8: Summary of the classification of the target sources.

ID | X-ray | Doppler-boosted | Total flux density | VLBI |  Variable | Radio–optical | Classification
---|---|---|---|---|---|---|---
|  |  | spectrum | spectrum |  | offset |
J0304$+$0046 | Yes | Possibly | Flat | – | Possibly | – | FSRQ?
J0851$+$1423 | No | No | Steep | Flat | Yes | No | SS
J0918$+$0636 | Yes | Possibly | Inverted | Flat | Yes | Yes | FSRQ
J1006$+$4627 | No | Possibly | Inverted | Flat | Yes | Slight | FSRQ
J1037$+$1823 | No | No | Steep | Flat | Yes | No | SS
J1231$+$3816 | Yes | No | Steep | Flat | Possibly | No | SS
J1307$+$1507 | No | Possibly | Steep | Steep | Possibly | No | SS
J1309$+$5733 | Yes | Possibly | Peaked | Steep | Yes | No | FSRQ
J1325$+$1123 | Yes | Yes | Peaked | Steep | Possibly | No | FSRQ
J1412$+$0624 | Yes | Possibly | Flat | Flat | Possibly | Slight | FSRQ
J1434$+$1628 | No | Possibly | Steep | Flat | Possibly | No | SS
J1520$+$1835 | No | Possibly | Steep | Steep | Possibly | Yes | SS (CSO)
J1720$+$6028 | No | Possibly | Flat | Steep | Yes | Slight | FSRQ

Note. — Col. 1 $-$ Source designation; Col. 2 $-$ X-ray detection; Col. 3$-$
Doppler boosting (‘Possibly’ means $T_{\rm b}$ is lower limit at either
frequency); Col. 4 $-$ Spectral classification based on the collected total
flux density data; Col. 5 $-$ Spectral classification based on the dual-
frequency EVN data; Col. 6 $-$ Source variability; Col. 7 $-$ Radio–optical
positional offset; Col. 8 $-$ Proposed classification; SS stands for steep
spectrum, the question mark indicates if contradictory properties are found
and discussed in Section 5.5

J0304$+$0046: This source has reliable EVN data only at 1.7 GHz. A single
compact component without any extended emission is present which could
indicate a blazar core, and the flat total flux density spectrum suggests an
FSRQ. However, in the absence of a Gaia optical position, a VLBI spectral
index, and a clear evidence for Doppler-boosted emission, we cannot classify
this object with complete certainty. Chandra X-ray measurement is presented in
Zhu et al. (2019) with a $1.8$ lower limit to the photon index in the interval
of 0.5$-$8 keV.

J0851$+$1423: At 5 GHz, we see an indication of an extended structure in the
northwest–southeast (NW–SE) direction. The faint NE feature might as well be a
noise peak at $\sim 5\sigma$. There is a $\sim 5$ mas offset (within
$3\sigma$) between the two radio positions. Based on the total flux density
spectrum, we classify this as a steep-spectrum source. However, as it seems to
be variable and its VLBI spectrum is flat, simultaneous sensitive multi-
frequency follow-up VLBI observations would be ideal to securely confirm the
nature of this source.

J0918$+$0636: This source, together with a few others from our sample, can be
found in a multi-wavelength study of Ighina et al. (2019). They gave an X-ray
photon index of $1.3\pm 0.4$ (between 0.5$-$10 keV) and derived a flat radio
spectrum. Their classification is uncertain. Note that both the total flux
density spectrum and the two-point VLBI spectrum (which is based on
measurements about two decades apart) are likely affected by variability. The
radio and optical coordinates have a significant offset of 5 mas in
declination. The calibrator J0915$+$0745 shows compact emission thus it cannot
explain the positional difference. The X-ray detection (Bassett et al., 2004)
strengthens the FSRQ classification.

J1006$+$4627: There is a slight radio–optical offset, about 3 mas in the jet
direction. The flux density upper limit at 150 MHz is consistent with the
inverted/flat continuum spectrum. Only an upper limit to the X-ray flux from
ROSAT data is available (Vignali et al., 2005).

J1037$+$1823: The total flux density spectum is steep based on the data points
in the GHz range, but considering the upper limit at 150 MHz, it seems that
the spectrum is in fact peaked. The VLBI position is different at the two
observed frequencies, with an offset of $\sim 6$ mas in the NW direction.
However, this value is still within $3\sigma$. A likely explanation is that
the phase-reference calibrator source (J1045$+$1735) has an extended jet
structure roughly in this direction, which may not be fully accounted for. The
agreement between the 5-GHz VLBI position and the Gaia position suggests that
the 5-GHz component coincides with the AGN core.

J1231$+$3816: This object is detected with Chandra (Zhu et al., 2019) with
derived photon index of $1.4\pm 0.3$ between 0.5$-$8 keV. We classify it as a
steep-spectrum source.

J1307$+$1507: The 1.7- and 5-GHz VLBI positions have $\sim 5$ mas ($2\sigma$)
offset in the N–S direction. The Gaia optical position agrees well with the
5-GHz VLBI position.

J1309$+$5733: The source is detected with the EVN at both frequencies but only
short baselines between five European antennas were available at 1.7 GHz.
Therefore, the angular resolution achieved is poorer than for other sources in
the sample (Figure 1). To characterize the total flux density spectrum, we
applied a log-parabolic function as, with a 150-MHz Low-Frequency Array
(LOFAR) measurement (Shimwell et al., 2017) included, it gave a better fit
than a simple power-law. The spectral peak is $(13\pm 1)$ mJy at $(600\pm
100)$ MHz. However, the VLBI flux densities are well above the total flux
density spectrum (Figure 2), suggesting high-amplitude variability. Based on
this, the peaked shape of the total flux density spectrum constructed from
non-simultaneous measurements may be caused by flux density variability, thus
we classify the source as FSRQ. This is also supported by the Chandra X-ray
measurement (Bassett et al., 2004) with photon index with $1.8\pm 0.5$
(between 0.5$-$8 keV) and the detection in the XMM-Newton Slew Survey (Saxton
et al., 2008).

J1325$+$1123: This is the second source where we fitted log-parabolic function
to the total flux density data. A spectrum has a peak of $(72\pm 17)$ mJy at
$(1.5\pm 0.2)$ GHz. The scatter of the flux density values suggests possible
variability. The two radio positions have $\sim 4$ mas offset ($<3\sigma$),
similarly to J1037$+$1823 and J1307$+$1507\. The location of the 5-GHz peak
falls in an extended part of the 1.7-GHz structure (Figure 1). In this case,
the calibrator (J1327$+$1223) does not have an extended jet. The source is
detected in X-rays with Chandra (Bassett et al., 2004). The photon index
between 0.5$-$10 keV is $1.5\pm 0.5$ as given by Ighina et al. (2019), who
found that the radio spectrum is peaked, similarly to our finding. Their
classification of this source is uncertain.

J1412$+$0624: This source is tentatively classified as FSRQ. However, there is
no clear evidence for Doppler-boosted emission. There is a slight
radio–optical positional offset, still within $<3\sigma_{\mathrm{pos}}$,
almost perpendicular to the structure seen in the 5-GHz image (Figure 1) which
shows somewhat spurious extended features around the central core. It has
Chandra X-ray detection (Wu et al., 2013b). The source may be a quasar with
jet inclination angle larger than that typical for blazars. Ighina et al.
(2019) gave an X-ray photon index of $1.6\pm 0.5$ between 0.5$-$10 keV, and
also found the radio spectrum flat. However, they were uncertain whether this
source was a blazar.

J1434$+$1628: It is the faintest source with the lowest radio powers in our
sample (Table 5). Similarly to J1037$+$1823, the 150-MHz flux density upper
limit suggests a peaked spectrum instead of the steep spectrum fitted to the
GHz data points. We found no strong evidence for the blazar nature so we
classify it as a misaligned radio source.

J1520$+$1835: Arguably, it is the most puzzling source in our sample, and one
of the faintest. Both the total flux density and VLBI spectra are ultra-steep
($\alpha<-1$). As in most other cases, however, low-frequency total flux
density measurements would better constrain the spectral fit. The TGSS upper
limit indeed suggests a peaked overall spectrum, in contrast to the steep
spectrum fitted to the high-frequency data points in the GHz range. The most
remarkable feature is that the Gaia optical position has a highly significant
offset with respect to the VLBI position which is coincident at both
frequencies. The angular separation between the optical and radio positions is
$\sim 30$ mas, which at the source redshift corresponds a projected linear
distance of $250$ pc. This alone suggests the presence of a CSO-like source
whose brighter (NE) hotspot is detected with the EVN but the radio emission of
the other lobe on the opposite (SW) side of the core is completely resolved
out. In the 1.7-GHz image of J1520$+$1835, while the radio brightness peak is
located at $(0,0)$ as for all other sources, the field is centered on the Gaia
position marked by a red cross (Figure 1). The core, also invisible in the
radio, is marked by the Gaia position. Another observed property seems to
support this scenario: it is not uncommon that a CSO component has extremely
steep VLBI spectrum in the optically thin regime (e.g. Wu et al., 2013a).

An alternative explanation is a positional mismatch. Certainly, we cannot
exclude the possibility that the radio and optical AGN are two different
background/foreground sources seen in projection. However, given the very
small angular separation, this possibility is extremely low. Therefore, we
suggest that J1520$+$1835 is a CSO candidate. The number of high-redshift CSOs
(and candidates) observed so far is extremely small (Frey et al., 2008; An et
al., 2022). Although limited observational data are available on this source,
we note that qualitatively, the suspected morphology on the angular scale of
tens of mas described above makes it similar to the low-redshift CSO quasar
PKS 1117$+$146 (Bondi et al., 1998). Sensitive follow-up e-MERLIN imaging
observations could be able to confirm the presence of the suspected emission
in the SW.

J1720$+$6028: The flux density upper limit at 150 MHz does not contradict with
the flat total flux density spectrum. The radio–optical positional offset is
$\sim 5$ mas in right ascension. However, the Gaia value has the highest
uncertainty among our targets, $\sim 2$ mas in both coordinates. The
radio–optical offset, taking the positional uncertainties into account, is
close to the jet direction. The optical position can be associated with the
fainter jet component seen in the 1.7-GHz image (Figure 1). All other
parameters of this source suggest that it is an FSRQ.

##  6 Summary

In this paper, we investigated 13 high-redshift ($4<z<4.5$) blazar candidates,
to reveal the nature of these radio sources. To this end, we performed a
series of dual-frequency (1.7 and 5 GHz) VLBI observations using the EVN and
e-MERLIN arrays. Based on these high-resolution observations and additional
low-resolution radio data obtained from the literature, we derived physical
properties such as the origin of the radio emission, flux density variability,
spectral indices, and the potential presence of Doppler-boosting in the jet.
The Gaia EDR3 optical coordinates were also collected for 12 of the 13 sources
in the sample. Moreover, we found X-ray detections in the literature for 6
sources. Based on the available information, we made an attempt to decide
whether our target sources belong to blazars or AGN with misaligned radio
jets. This sample increases the number of known VLBI-observed $z>4$ radio AGN
by about $25\%$.

All sources could be classified based on the observed and derived properties.
Out of the 13 radio sources studied, six objects (46%) turned out to be
blazars, with core–jet or compact core morphology. Six other sources (46%)
fall in the category of misaligned objects like steep-spectrum (GPS/MPS)
sources. Finally, one source (8%) is tentatively classified as blazar with
some uncertainty. Although it shows more characteristics of an FSRQ,
additional data are needed to confirm this classification. Previous studies of
high-redshift radio AGN (Coppejans et al., 2016; Cao et al., 2017) reached
similar conclusions for the blazar/non-blazar ratio in their sample. In this
new $z>4$ radio quasar sample, J1520$+$1835 appears as a potential CSO
candidate, based on the large offset of its VLBI radio and Gaia optical
positions. To confirm this, high-sensitivity follow-up VLBI and e-MERLIN
observations would be needed. Other sources are also good targets for follow-
up observations. However, none of them seems particularly promising for long-
term jet proper motion monitoring, as prominent jet structures are not
detected, in accordance with the expectation for highly redshifted steep-
spectrum radio features.

High-resolution VLBI observations are essential for studies of jetted AGN in
the early Universe. Combined with other data, e.g. precise Gaia optical
astrometry or X-ray observations of jet emission, VLBI data give us a useful
tool to classify $z>4$ objects. An important conclusion of this study, in
accordance with the earlier findings of Cao et al. (2017), is that a pre-
selection of blazar candidates based on their infrared, optical or X-ray
properties combined with the presence of strong radio emission detected with
low-resolution observations does not guarantee their true blazar nature, as
some of them turn out to be misaligned jetted sources.

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. The research leading to these
results has received funding from the European Commission Horizon 2020
Research and Innovation Programme under grant agreement No. 730562 (RadioNet).
We thank the Hungarian National Research, Development and Innovation Office
(OTKA K134213 and 2018-2.1.14-TÉT-CN-2018-00001) for support. H. M. C.
acknowledges support by the National Natural Science Foundation of China
(Grants No. U2031116 and U1731103). 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. This research has made use of
the VizieR catalog access tool, CDS, Strasbourg, France (DOI:
10.26093/cds/vizier). The original description of the VizieR service was
published in Ochsenbein et al. (2000).

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