###### Abstract

We present a study of the radio variability of bright, $S_{1.4}\geq 100$ mJy,
high-redshift quasars at $z\geq 3$ on timescales up to 30–40 years. The study
involved simultaneous RATAN-600 measurements at frequencies of 2.3, 4.7, 8.2,
11.2, and 22.3 GHz in 2017–2020. In addition, data from the literature were
used. We have found that the variability index, $V_{S}$, which quantifies the
normalized difference between the maximum and minimum flux density while
accounting for measurement uncertainties, ranges from 0.02 to 0.96 for the
quasars. Approximately half of the objects in the sample exhibit a variability
index within the range of 0.25 to 0.50, comparable to that observed in blazars
at lower redshifts. The distribution of $V_{S}$ at 22.3 GHz is significantly
different from that at 2.3–11.2 GHz, which may be attributed to the fact that
a compact AGN core dominates at the source’s rest frame frequencies greater
than 45 GHz, leading to higher variability indices obtained at 22.3 GHz (the
$V_{S}$ distribution peaks around 0.4) compared to the lower frequencies (the
$V_{S}$ distribution at 2.3 and 4.7 GHz peaks around 0.1–0.2). Several source
groups with distinctive variability characteristics were found using cluster
analysis of quasars. We propose 7 new candidates for gigahertz peaked-spectrum
(GPS) sources and 5 new megahertz peaked-spectrum (MPS) sources based on their
spectrum shape and variability features. Only 6 out of 23 sources previously
reported as GPS demonstrate a low variability level typical of classical GPS
sources ($V_{S}<0.25$) at 4.7–22.3 GHz. When excluding the highly variable
peaked-spectrum blazars, we expect no more than 20% of the sources in the
sample to be GPS candidates and no more than 10% to be MPS candidates.

###### keywords:

active galaxies: high-redshift quasars; general radio continuum

12 3 25 Academic Editor: Luigina Feretti 2 April 2024 9 May 2024 10 May 2024
15 May 2024 https://doi.org/10.3390/galaxies12030025 High–redshift quasars at
$z\geq 3$: radio variability and MPS/GPS candidates High–redshift quasars at
$z\geq 3$ Yulia Sotnikova 1,2,3*, Alexander Mikhailov 1, Timur Mufakharov
1,2,3, Tao An 4,5, Dmitry Kudryavtsev 1, Marat Mingaliev 1,3,6, Roman
Udovitskiy 1, Anastasia Kudryashova 1, Vlad Stolyarov 1,7 and Tamara Semenova1
Yu. Sotnikova, A. Mikhailov and T. Mufakharov Sotnikova, Yu.; Mikhailov, A.;
Mufakharov, T. Correspondence<EMAIL_ADDRESS>
##  1 Introduction

Quasars (Schmidt, 1963) are highly variable celestial objects (Matthews and
Sandage, 1963) that emit radiation across the electromagnetic spectrum. In the
radio band, their variability (Dent, 1965; Kellermann and Pauliny-Toth, 1968)
is often attributed to the presence of outflows or jets that emanate from the
central region of a galaxy (Rees, 1970). These jets can exhibit a range of
behaviors, including propagating shocks (e.g., (Marscher and Gear, 1985;
Nyland et al., 2021)), precession (e.g., (Gergely and Biermann, 2009; Horton
et al., 2020)), bending (e.g., (Villata and Raiteri, 1999)), and interaction
with gas clouds (e.g., (Jarvis et al., 2019)). In addition, several other
phenomena may contribute to the observed flux density fluctuations in quasars,
such as accretion disk instabilities (e.g., (An et al., 2013; Wang et al.,
2014)), interstellar scintillation (e.g., (Walker, 1998; Koay et al., 2019)),
and lensing by the ionized structures (e.g., (Fiedler et al., 1987; Pushkarev
et al., 2013)).

Quasars at high redshifts play a crucial role in understanding the evolution
of galaxies and the influence of active galactic nuclei (AGNs) in shaping the
Universe. However, they are rarely detected in the radio band due to their
weak flux densities. These quasars typically exhibit either a steep, flat, or
peaked radio spectrum (De Breuck et al., 2000, 2006; Coppejans et al., 2016).
The peaked-spectrum sources are classified as high-frequency peakers (HFPs) as
well as megahertz and gigahertz peaked-spectrum (MPS and GPS) sources (O’Dea
et al., 1991; Coppejans et al., 2016; O’Dea and Saikia, 2021) based on the
location of the peak frequency in their radio spectra. The peaked-spectrum
(PS) sources represent an early stage in the radio source evolution, where
HFPs may evolve to GPSs, and some GPSs may further develop into extended
FRI/II radio galaxies (Fanti et al., 1990; Snellen et al., 2000; An and Baan,
2012). Some other GPS sources exhibit intermittent and short-lived radio
emission, offering insights into the dynamic nature of quasars and AGN
evolution (Readhead et al., 1996). Coppejans et al. (2015) proposed to search
for high-redshift ($z>2$) sources by identifying MPS sources that are compact
on scales of tens of milliarcseconds; though later Coppejans et al. (2017)
found a roughly equal proportion of flat, steep, and peaked radio spectra
among 30 quasars at $z>4.5$.

In a study of the radio spectra of over a hundred radio-loud $z\geq 3$
quasars, we found that almost half of the sample can be classified as PS
sources, either GPS or MPS (Sotnikova et al., 2021). A significant fraction of
PS sources in this sample are identified as blazars which are more easily
detectable due to the beamed emission from their jets compared to unbeamed
radio galaxies and AGNs. For blazar-type sources, beaming not only amplifies
the flux density but can also shift the peak frequencies to higher values,
contributing in certain cases to their classification as HFPs. Variability
serves as an important indicator to distinguish between blazars and unbeamed
PS sources. Genuine GPS sources exhibit low levels of variability (e.g.,
(Stanghellini et al., 1998; O’Dea, 1998; Stanghellini, 1999; Tornikoski et
al., 2009; Mingaliev et al., 2012, 2013; Sotnikova et al., 2019, 2021)), which
may be attributed to the expansion of the compact lobes. This expansion
usually does not change the shape of the spectrum, although the peak frequency
might shift (Dallacasa and Orienti, 2016). In contrast, blazars exhibit strong
and rapid flux variations in a wide range of timescales and frequencies, often
accompanied by changes in the spectrum shape, such as a peaked spectrum during
flaring activity (e.g., (Kovalev, 2005; Orienti et al., 2010; Sotnikova et
al., 2021)). By classifying GPS/MPS sources and blazars among high-redshift
radio sources, we can gain insights into the underlying physical mechanisms
that govern their formation and evolution, which may have profound
implications for our understanding of the early Universe. In this study we
determine the incidence of GPS and MPS sources in the early Universe and
assess the degree to which they are contaminated by blazars.

VLBI studies of high-redshift quasars reveal two major morphological patterns:
a core–jet structure, indicative of relativistic beaming of the jet, and a
compact double-lobed morphology, the so-called compact symmetric objects
(CSOs) with their jets lying on the plane of the sky and relativistic beaming
is not significant. Typically, quasars with the core–jet morphology have flat
radio spectra at gigahertz frequencies, while CSOs have peaked radio spectra,
small sizes ($<1$ kpc) and are classified as MPS/GPS sources (O’Dea et al.,
1991; Coppejans et al., 2016; O’Dea and Saikia, 2021)).

To identify blazars, GPS, and MPS sources, multi-frequency radio measurements
provide fundamental insights into the amplitude, time scale, and frequency
evolution of the flux density variability. The features of variability can be
used to identify blazar candidates as well as GPS and MPS sources. The aim of
this paper is to study the radio variability properties of bright quasars at
$z\geq 3$ on historical timescales of 30–40 yrs. We used the multi-frequency
RATAN-600 measurements obtained from 2017 to 2020 quasi-simultaneously at
frequencies of 2.3–22.3 GHz, complemented by available literature data.
Utilising the dataset compiled by Sotnikova et al. (2021), we present the
average variability parameters for the quasars, discuss flux density
variations for individual objects, and classify GPS/MPS sources according to
their long-term spectral behaviour.

##  2 Sample

The sample contains 101 quasars selected from the NRAO VLA Sky Survey (NVSS,
Condon et al., 1998) in the declination range from $-34^{\degree}$ to
$+49^{\degree}$ with the flux density $S_{1.4}\geq 100$ mJy and with redshifts
$z\geq 3$. The spectroscopic redshifts were obtained by cross-identification
in the National Aeronautics and Space Administration (NASA)/Infrared
Processing and Analysis Center (IPAC) Extragalactic Database (NED).111NED:
https://ned.ipac.caltech.edu Observations of the sample were conducted with
the RATAN-600 radio telescope during 2017–2020 at frequencies of 1.2, 2.3,
4.7, 8.2, 11.2, and 22.3 GHz quasi-simultaneously, within a 5–6 minute
interval. The flux densities were measured with a standard error of about
5–20% at 4.7, 8.2, 11.2 GHz and 10–35% at 1.2, 2.3, and 22.3 GHz (Sotnikova et
al., 2021). The parameters of the receivers are shown in Table 1. The
detection limit for a RATAN-600 single sector is approximately 5 mJy at 4.7
GHz (integration time is about 3s) under good conditions and at the average
antenna elevation angle (${\rm Dec}\sim 0^{\circ}$).

Table 1: RATAN-600 continuum radiometer parameters: the central frequency $f_{0}$, the bandwidth $\Delta f_{0}$, the detection limit for point sources per transit $\Delta F$, and the angular resolution, measured by the full width at half maximum (FWHM) along RA and Dec, calculated for the average angles. $f_{0}$ |  $\Delta f_{0}$ |  $\Delta F$ |  FWHMRA |  FWHMDec
---|---|---|---|---
(GHz) |  (GHz) |  (mJy/beam) |  (arcmin) |  (arcmin)
$22.3$ |  $2.5$ |  $50$ |  $0\hbox{$.\mkern-4.0mu^{\prime}$}17$ |  $1\hbox{$.\mkern-4.0mu^{\prime}$}6$
$11.2$ |  $1.4$ |  $15$ |  $0\hbox{$.\mkern-4.0mu^{\prime}$}34$ |  $3\hbox{$.\mkern-4.0mu^{\prime}$}2$
$8.2$ |  $1.0$ |  $10$ |  $0\hbox{$.\mkern-4.0mu^{\prime}$}47$ |  $4\hbox{$.\mkern-4.0mu^{\prime}$}4$
$4.7$ |  $0.6$ |  $8$ |  $0\hbox{$.\mkern-4.0mu^{\prime}$}81$ |  $7\hbox{$.\mkern-4.0mu^{\prime}$}6$
$2.3$ |  $0.08$ |  $40$ |  $1\hbox{$.\mkern-4.0mu^{\prime}$}71$ |  $15\hbox{$.\mkern-4.0mu^{\prime}$}8$
$1.2$ |  $0.08$ |  $200$ |  $3\hbox{$.\mkern-4.0mu^{\prime}$}07$ |  $27\hbox{$.\mkern-4.0mu^{\prime}$}2$

Our analysis of the radio spectra, which incorporate both the RATAN-600
measurements and the literature data, revealed that 47 out of 101 quasars
(46%) exhibit peaked radio spectra, while 24% have flat spectra,222Spectral
index estimated from the power law $S\sim\nu^{\alpha}$ and 15% have steep
ones. A small number of the sources have complex, upturn, or inverted spectra.
In this paper the spectral indices are used in terms of $\alpha_{\rm low}$ and
$\alpha_{\rm high}$ as they were defined in Sotnikova et al. (2021). For
peaked and upturn spectra, $\alpha_{\rm low}$ and $\alpha_{\rm high}$ are
determined lower and higher the frequency where the spectral slope changes its
sign from positive to negative or vice versa. For the rest of spectral types,
the low-frequency spectral index is calculated using decimetre-wavelength
measurements, such as Giant Metrewave Radio Telescope Sky Survey (TGSS, Intema
et al. (2017)), GaLactic and Extragalactic All-sky Murchison Widefield Array
(GLEAM, Hurley-Walker et al. (2017)), or Westerbork Northern Sky Survey
(WENSS, Rengelink et al. (1997)). The high-frequency spectral index is
estimated using centimetre catalogue data points. A spectrum is considered
flat if the spectral index is $-0.5\leq\alpha\leq 0$, and inverted if
$\alpha>0$. The spectrum is assumed to be complex for indeterminate shapes
with two or more maxima or minima. The spectrum is called steep or ultra-steep
for $-1.1<\alpha<-0.5$ and $\alpha\leq-1.1$ respectively.

The list of the sources and their characteristics are presented in Table
LABEL:TableA1: Col. 1 is the source name; Col. 2 is the redshift; Col. 3 is
the average RATAN-600 flux density at 4.7 GHz; Cols. 4–5 are the radio
morphology and its reference; Cols. 6–7 are the spectral indices, calculated
in Sotnikova et al. (2021); Col. 8 is the radio spectrum type; Col. 9 is the
blazar type; Col. 10 is the number of cluster. Forty-eight quasars in the
source list are classified as blazars according to the “Open Universe for
Blazars—Reference list
V2.0”.333https://openuniverse.asi.it/OU4Blazars/MasterListV2/, which includes
6077 blazars identified through radio, X-ray, and $\gamma$-ray surveys as well
as objects discovered based on their multi-frequency SED properties. This
database serves as the largest compilation of blazars to date (Giommi et al.,
2019). It contains the blazars from the Roma-BZCAT catalogue (Massaro et al.,
2015), the classification of which we used in our research. Most of the
quasars of the sample (88 of 101) have been observed using VLBI at 2, 5, 8, or
15 GHz, with the majority of them (66 of 88) exhibiting a core–jet morphology.

Compared to the sample in Sotnikova et al. (2021) we have excluded the source
J1600$+$0412 (87GB 155733.8$+$042120). J1600$+$0412 has $z=0.79$ in the latest
data release of the Sloan Digital Sky Survey (Albareti et al., 2015; Pâris et
al., 2018), but previously its redshift was miscalculated as $z=3.11$
(Afanas’ev et al., 2003).

There are six gravitationally lensed quasars in the sample.444marked by the
letter “a” in Table LABEL:TableA1 Their structure is unresolved by RATAN-600
because the maximum separations between them are in the range of
$0.54^{\second}-3.4^{\second}$ which is less than the angular resolution at
any RATAN-600 frequency. The notes for them are given in Appendix C.3.

###  2.1 The literature data

The literature data and their use in our study have been previously described
in detail in Sotnikova et al. (2021). The vast majority of the external radio
continuum measurements were obtained from the astrophysical CATalogs support
System (CATS database,555https://www.sao.ru/cats Verkhodanov et al. (2005,
2009)). These data allow us to estimate radio flux variability over a time
period of up to 30-40 years at the most representative observation frequency
of 4.7 GHz. The external data were adopted within 10% ranges of the RATAN-600
five frequencies. For example, at $\nu=4.7$ GHz we used all data within
$4.23$–$5.17$ GHz. The majority of the quasars (94/101) has more than 30 years
of observing coverage, and 78 out of 101 have more than 10 radio measurements
at 4.7 GHz (Table LABEL:TableA2). The median values of the number of
measurements (Nobs) and the years of observations at 4.7 and 22.3 GHz ($t$)
for the sample are 16/35 and 9/14 respectively (Table 2). In our study we
define the timescale of radio monitoring in the rest frame as $t_{\rm
rest}=t_{\rm obs}/(1+z)$; if not specified, the timescale is used in the
observer’s frame of reference.

Table 2:  The number of quasars (N) observed at 4.7 and 22.3 GHz with the median values of observed epochs Nobs and monitoring timescales in the observer’s ($t_{\rm obs}$) and source’s ($t_{\rm rest}$) frames of reference in years. Frequency |  N |  Nobs |  $t_{\rm obs}$ |  $t_{\rm rest}$
---|---|---|---|---
(GHz) |  |  |  (yrs) |  (yrs)
4.7 |  101 |  16 |  35 |  8
22.3 |  52 |  9 |  14 |  3

##  3 Multi–band radio variability

###  3.1 Variability estimates

In order to characterise the variability properties of the quasars at
different frequencies, we have computed the variability and modulation indices
and the fractional variability. The first and third characteristics take into
account measurement uncertainties, while the modulation index and the
fractional variability are less sensitive to outliers. The variability index
was calculated using the formula from Aller et al. (1992):

$V_{S}=\frac{(S_{\rm max}-\sigma_{S_{\rm max}})-(S_{\rm min}+\sigma_{S_{\rm
min}})}{(S_{\rm max}-\sigma_{S_{\rm max}})+(S_{\rm min}+\sigma_{S_{\rm
min}})}$ (1)

where $S_{\rm max}$ and $S_{\rm min}$ are the maximum and minimum flux
densities over all epochs of observations; $\sigma_{S_{\rm max}}$ and
$\sigma_{S_{\rm min}}$ are their errors. This formula prevents one from
overestimating the variability when there are observations with large
uncertainties in the data. We obtain a negative value of $V_{S}$ in the case
where the flux error is greater than the observed scatter in the data.

The modulation index, defined as the standard deviation of flux density
$\sigma_{S}$ divided by the mean flux density $\bar{S}$, was calculated as in
Kraus et al. (2003):

$M=\frac{\sigma_{S}}{\bar{S}}$ (2)

The fractional variability $F_{S}$ is defined as in Vaughan et al. (2003):

$F_{S}=\sqrt{\frac{V^{2}-\bar{\sigma}^{2}_{err}}{\bar{S}^{2}}}$ (3)

where $V^{2}$ is the variance, $\bar{S}$ is the mean flux density, and
$\sigma_{err}$ is the root mean square error. The uncertainty of $F_{S}$ is
determined as:

$\bigtriangleup
F_{S}=\sqrt{\left(\sqrt{\frac{1}{2N}}\frac{\bar{\sigma}^{2}_{err}}{F_{S}*\bar{S}^{2}}\right)^{2}+\left(\sqrt{\frac{\bar{\sigma}^{2}_{err}}{N}}\frac{1}{\bar{S}}\right)^{2}}$
(4)

where $N$ is the number of observations.

The distributions of the variability index, modulation index, and fractional
variability at 2.3–22.3 GHz are shown in Fig. 1. At 1.2 GHz we did not obtain
sufficient number of measurements to estimate variability. Table LABEL:TableA2
lists these parameters for each quasar, while their statistics are given in
Table 3. The negative variability indices have been excluded from the
calculation and distribution diagrams.

Light curves of the quasars obtained with RATAN-600 are presented in Appendix
D. For PS candidates we included additional RATAN-600 measurements of
2006–2017 from Mingaliev et al. (2012); Sotnikova et al. (2019). Their radio
spectra, compiled using both the RATAN-600 and CATS radio data, are also
presented in Appendix D.

The number of observing epochs Nobs and the timescale $t$ play a key role in
exploring AGN variability. Previous studies have known that variability tends
to increase with a greater number of observations, as sparser sampling may
lead to missed peaks of variability (Tornikoski et al., 2000; Nieppola et al.,
2007; Khabibullina et al., 2024). This finding is verified by our
observations, i.e., we found a correlation between Nobs and the variability
index at 4.7 GHz with Pearson’s $r=0.35$, p-val. $<10^{-3}$ (Fig. 2). The
observations of quasars in our sample are not homogeneous and differ in
timescales (see the parameters $t_{4.7}$ and N4.7 in Table LABEL:TableA2),
affecting the revealed variability level. The largest number of observations
at 4.7 GHz is N${}_{\rm obs}=187$ ($V_{S_{4.7}}=0.67$) for the blazar
J0646$+$4451.

We note that the distributions of $M$ and $F_{S}$ are similar (see Fig. 1).
Both these parameters are suitable for a large number of observations Nobs;
however, unlike the modulation index, the fractional variability takes
measurement errors into account. Therefore, the third parameter, $V_{S}$, can
be used for any number of observations. For these reasons, we will use the
variability index $V_{S}$ and the fractional variability $F_{S}$ in our
analysis, as these parameters can be effectively utilized regardless of the
number of observations. We note that we see in our sample a correlation
between variability index and fractional variability.

Figure 1: The variability (top row), modulation (middle row), and fractional
variability (bottom row) index distributions for the whole sample, peaked-
spectrum (PS) sources, and blazars.

Figure 2: The variability index $V_{S_{4.7}}$ versus the number of observations Nobs for the quasars. The size of the symbols is proportional to years of monitoring in the rest frame, we define three scales: $t_{\rm rest}\leq~{}5$, $5<t_{\rm rest}\leq 10$, and $t_{\rm rest}>10$ years. Bright quasars have been observed more frequently and for a longer period. Table 3:  The median, mean, maximum, and minimum values of the modulation index $M$, variability index $V_{S}$, and fractional variability $F_{S}$ calculated for different frequency bands (see text). |  N |  median |  mean |  min |  max
---|---|---|---|---|---
$M_{2.3}$ |  94 |  0.18 |  0.20$\pm$0.09 |  0.01 |  0.53
$V_{S_{2.3}}$ |  87 |  0.23 |  0.25$\pm$0.15 |  0.01 |  0.86
$F_{S_{2.3}}$ |  80 |  0.20 |  0.21$\pm$0.09 |  0.03 |  0.59
$M_{4.7}$ |  101 |  0.17 |  0.20$\pm$0.11 |  0.05 |  0.62
$V_{S_{4.7}}$ |  101 |  0.27 |  0.28$\pm$0.15 |  0.02 |  0.71
$F_{S_{4.7}}$ |  90 |  0.17 |  0.20$\pm$0.12 |  0.01 |  0.66
$M_{8.2}$ |  100 |  0.17 |  0.21$\pm$0.12 |  0.03 |  1.00
$V_{S_{8.2}}$ |  95 |  0.23 |  0.27$\pm$0.17 |  0.02 |  0.96
$F_{S_{8.2}}$ |  84 |  0.17 |  0.21$\pm$0.14 |  0.04 |  0.97
$M_{11.2}$ |  92 |  0.17 |  0.18$\pm$0.09 |  0.01 |  0.57
$V_{S_{11.2}}$ |  77 |  0.18 |  0.21$\pm$0.14 |  0.02 |  0.66
$F_{S_{11.2}}$ |  66 |  0.14 |  0.17$\pm$0.11 |  0.05 |  0.63
$M_{22.3}$ |  55 |  0.28 |  0.30$\pm$0.13 |  0.09 |  0.68
$V_{S_{22.3}}$ |  51 |  0.36 |  0.35$\pm$0.18 |  0.04 |  0.68
$F_{S_{22.3}}$ |  45 |  0.31 |  0.31$\pm$0.15 |  0.05 |  0.72

###  3.2 Refractive interstellar scintillation

The variability observed in this study can be caused by either intrinsic
(related to the source properties) or extrinsic factors arising from the
interaction of radio emission from a source with an inhomogeneous propagation
medium.

The flickers caused by scattering on the inhomogeneities of the interplanetary
medium have a characteristic timescale of the order of a second or less
(Morgan et al., 2018), so they are smoothed out during RATAN-600 observations
due to the relatively long scan time of 3–5 minutes during the source’s
transit. Similarly, for measurements at other radio telescopes, interplanetary
flickering is also insignificant, given the longer measurement times for
continuum flux density.

The scintillations caused by the propagation of radio waves in the
interstellar medium can have a diffractive and refractive character.
Diffractive scintillation is usually associated with an extremely compact
source, such as a pulsar or a fast radio burst. Additionally, observations
must be made in a narrow frequency band in order to resolve the fine-scale
structures responsible for the diffractive scintillation (Narayan, 1992). This
is because the scintillation pattern can be highly frequency-dependent. The
continuum radio measurements are carried out in a wide band (from hundreds of
MHz to several GHz); therefore, this type of flickering can not be detected in
our data.

Let’s focus on estimating the potential contribution of refractive
interstellar scintillations (RISS) to the variability at the RATAN-600
frequencies (1.2, 2.3, 4.7, 8.2, 11.2, and 22.3 GHz) for the sources from the
sample (in the declination range from $-34\degree$ to $+49\degree$). According
to Walker (1998), the transition frequency $\nu_{0}$ separating strong and
weak scattering modes lies in the range from 5 to 15 GHz for most quasars. We
will adopt these transition frequency values to estimate the modulation level
of the flux density $m$ and its timescale $t$. We used the following equations
in the weak mode (Walker, 1998):
$m=\left(\frac{\nu_{0}}{\nu}\right)^{17/12}\left(\frac{\theta_{F}}{\theta_{\rm
s}}\right)^{7/6}$, $t=\frac{1}{12}\sqrt{\frac{\nu_{0}}{\nu}}\frac{\theta_{\rm
s}}{\theta_{F}}$ (days), where
$\theta_{F}=\theta_{F0}\sqrt{\frac{\nu_{0}}{\nu}}$ is the size of the first
Fresnel zone at the frequency $\nu$, and $\theta_{\rm s}$ is the source’s
angular size. Equations in the strong mode are according to (Walker, 1998):
$m=\left(\frac{\nu}{\nu_{0}}\right)^{17/30}\left(\frac{\theta_{r}}{\theta_{\rm
s}}\right)^{7/6}$,
$t=\frac{1}{12}\left(\frac{\nu_{0}}{\nu}\right)^{\frac{11}{5}}\frac{\theta_{\rm
s}}{\theta_{r}}$ (days), where
$\theta_{r}=\theta_{F0}\left(\frac{\nu_{0}}{\nu}\right)^{\frac{11}{5}}$. We
estimated an angular size as $\theta_{\rm s}=5\times\theta_{\rm min}$, where
$\theta_{\rm min}=0.6\sqrt{S}/\nu$ is the minimum angular size for the
stationary source of synchrotron radiation (Kellermann and Owen, 1988), $S$ is
the flux density (in Jy) at the observer’s frequency (in GHz). We adopted
$S=100$ mJy, taking into account our sample selection criterion and
characteristic flux densities measured with RATAN-600. As a result we
calculate the flux density modulations and their typical timescales, as shown
in Table 4. We can conclude that for quasars far from the Galactic plane, the
modulation level is about 1 per cent, which is significantly lower than the
average values of the variability level for our sample. Therefore, RISS
contribute insignificantly to the overall variability for most of these
objects, except for a few individual cases where variability reaches $\leq 5$
per cent. For objects located close to the Galactic plane (the transitional
frequency around 15 GHz), RISS can make a significant contribution at low
frequencies of 1–2 GHz. However, at higher frequencies ($>5$ GHz), this
contribution is considerably smaller (again, for individual objects with a
level of variability of no more than 10%, the contribution of RISS is
significant but not decisive). Only three quasars in the sample are relatively
close to the Galactic plane, within the Galactic latitude
$-15^{\degree}<b<+15^{\degree}$: J0624$+$3856, J0733$+$0456, and
J2050$+$3127\. Their variability level at 2.3 GHz is in the range of 19–47%,
which may have a contribution from RISS but can not be explained only by it.

Thus, with the exception of a few specific objects, the contribution of
interstellar scintillation effects to the total variability of most quasars in
our sample is insignificant (see Table 4).

Table 4:  RISS modulation and its typical timescale estimates for RATAN-600 frequencies at the transitional frequencies of 5 and 15 GHz. The numbers of sources with the variability index and the fractional variability less than 5% and 10% are shown in the two last columns. Frequency |  Source’s size |  m (5 GHz) |  t (5 GHz) |  m (15 GHz) |  t (15 GHz) |  N, $var\leq 5\%$ |  N, $5\%<var\leq 10\%$
---|---|---|---|---|---|---|---
(GHz) |  (mas) |  (%) |  days |  (%) |  days |  $V_{S}/F_{S}$ |  $V_{S}/F_{S}$
2.3 |  0.41 |  2.1 |  8.6 |  8.5 |  17.2 |  4/1 |  10/4
4.7 |  0.20 |  1.2 |  4.2 |  4.7 |  8.4 |  6/3 |  4/14
8.2 |  0.12 |  0.7 |  2.4 |  2.9 |  4.8 |  6/3 |  6/10
11.2 |  0.08 |  0.6 |  1.8 |  2.3 |  3.5 |  11/7 |  9/9
22.3 |  0.04 |  0.3 |  0.9 |  1.3 |  1.8 |  4/1 |  4/1

###  3.3 Variability characteristics

We computed variability amplitudes at certain observing frequencies. They
correspond to different rest frame frequencies (Fig. 3, top), since the
sources span a large redshift range. Furthermore, the timescale of the
observations spans from about half a month to 7 years at 22.3 GHz and from 4
to 11 years at 4.7 GHz in the source’s rest frame (Fig. 3, bottom), and
consequently the median values of the variability timescale are 3 and 8 years
at observing frequencies of 22.3 and 4.7 GHz respectively (Table 2). We found
fairly wide scatter of the variability index throughout all the range of 9–130
GHz rest frame emission frequencies (Fig. 4). Those emission frequencies are
all associated with the dominating core component. There are no trends in the
$V_{S}$ to $\nu_{\rm rest}$ relation, confirmed by Pearson’s $r$=0.12
(p-val.=0.02).

Figure 3: The distribution of the observational frequencies converted to the
rest frame (top), and the distribution of the light curve durations in the
rest frame, $t_{\mathrm{rest}}$ in years (bottom).

Figure 4: The variability indices plotted relatively to the rest frame
frequencies. The outlier source is J0941$+$1145 with $V_{S}$ equal to 0.86 and
0.96.

We obtained the average variability level for the sample to be 0.20–0.30 at
five frequencies (Table 3). For all spectral types, the average variability is
higher at 22.3 GHz, up to $\sim 0.40$ (Table 5). Maximum variability is
observed in sources with flat, peaked, and complex spectra. Kolmogorov-Smirnov
test confirms that the $V_{S}$ and $F_{S}$ distributions are not significantly
different for the flat and peaked spectrum quasars.

We did not find a correlation between redshift and variability $V_{S}$ at 4.7
and 22.3 GHz. At redshifts greater than 3.5, we obtained the spread of
variability indices at 4.7 GHz almost comparable to that at smaller redshifts
(Fig. 5). But there are scarce statistics on both the number of the highest-
redshift quasars and the time scale of their radio monitoring. At 4.7 GHz ten
extremely distant ($z>4$) sources exhibit a wide range of variability on a
long time scale $t_{\rm rest}\sim 5$–10 yrs. The variability index varies from
0.12, which was obtained for the bright VLBI quasar (Krezinger et al., 2022)
J2134$-$0419 ($z=4.34$, Nobs=18, $t_{\rm rest}\sim$ 6 yrs), to 0.71 for the
peaked spectrum blazar J0525$-$3343 ($z=4.41$, Nobs=12, at $t_{\rm rest}\sim$
5.5 yrs) with an unresolved or slightly resolved core–jet structure in VLBI
images (Krezinger et al., 2022). The most distant blazar in the sample
($z=5.28$) J1026+2542 with a one-sided jet morphology (Frey et al., 2015) has
a well determined peaked spectrum and a variability index of 0.30 over $t_{\rm
rest}\sim 3.9$ yrs. However, even on a scale of 6–10 yrs in the rest frame
there are about 10% of quasars with $V_{S_{4.7}}<0.10$ (Fig. 6). Among them,
about one third are PS quasars.

Table 5: The mean values of $F_{S}$ and $V_{S}$ for quasars of different radio spectrum types, N is the number of spectra at each frequency. |  N2.3 |  $F_{S_{2.3}}$ |  N4.7 |  $F_{S_{4.7}}$ |  N8.2 |  $F_{S_{8.2}}$ |  N11.2 |  $F_{S_{11.2}}$ |  N22.3 | $F_{S_{22.3}}$
---|---|---|---|---|---|---|---|---|---|---
peaked |  41 |  0.19$\pm$0.08 |  43 |  0.19$\pm$0.12 |  41 |  0.18$\pm$0.10 |  31 |  0.18$\pm$0.09 |  23 | 0.28$\pm$0.13
flat |  20 |  0.22$\pm$0.09 |  22 |  0.20$\pm$0.11 |  22 |  0.21$\pm$0.19 |  20 |  0.14$\pm$0.09 |  10 | 0.38$\pm$0.17
steep |  9 |  0.20$\pm$0.04 |  10 |  0.21$\pm$0.12 |  1 |  0.50 |  4 |  0.35$\pm$0.19 |  7 | 0.17$\pm$0.13
inverted |  5 |  0.32$\pm$0.17 |  8 |  0.20$\pm$0.13 |  8 |  0.28$\pm$0.05 |  6 |  0.11$\pm$0.04 |  6 | 0.24$\pm$0.12
upturn |  1 |  0.46 |  2 |  0.24$\pm$0.11 |  2 |  0.38$\pm$0.38 |  1 |  0.17 |  2 | 0.29$\pm$0.09
complex |  4 |  0.16$\pm$0.03 |  5 |  0.18$\pm$0.08 |  4 |  0.21$\pm$0.09 |  4 |  0.17$\pm$0.09 |  3 | 0.32$\pm$0.17
|  N2.3 |  $V_{S_{2.3}}$ |  N4.7 |  $V_{S_{4.7}}$ |  N8.2 |  $V_{S_{8.2}}$ |  N11.2 |  $V_{S_{11.2}}$ |  N22.3 | $V_{S_{22.3}}$
peaked |  43 |  0.26$\pm$0.14 |  47 |  0.28$\pm$0.16 |  44 |  0.28$\pm$0.17 |  38 |  0.23$\pm$0.16 |  25 | 0.37$\pm$0.16
flat |  20 |  0.27$\pm$0.18 |  24 |  0.30$\pm$0.16 |  24 |  0.25$\pm$0.19 |  21 |  0.18$\pm$0.11 |  12 | 0.34$\pm$0.21
steep |  12 |  0.20$\pm$0.14 |  15 |  0.23$\pm$0.14 |  12 |  0.17$\pm$0.14 |  6 |  0.27$\pm$0.15 |  1 | 0.61
inverted |  7 |  0.26$\pm$0.16 |  8 |  0.26$\pm$0.13 |  8 |  0.36$\pm$0.08 |  6 |  0.18$\pm$0.13 |  8 | 0.23$\pm$0.17
upturn |  1 |  0.53 |  2 |  0.35$\pm$0.17 |  2 |  0.38$\pm$0.35 |  2 |  0.14$\pm$0.13 |  2 | 0.46$\pm$0.15
complex |  4 |  0.21$\pm$0.05 |  5 |  0.32$\pm$0.13 |  5 |  0.29$\pm$0.11 |  4 |  0.27$\pm$0.12 |  3 | 0.40$\pm$0.12

Figure 5:  The variability index $V_{S}$ at 4.7 (top) and 22.3 GHz (bottom)
versus redshift $z$ for blazars (orange circles) and non-blazars (blue
triangles). The size of the symbols is defined as in Fig. 2. The five well-
known blazars are tagged: J1026$+$2542 at $z=5.25$ (Sbarrato et al., 2012;
Frey et al., 2015); J1430$+$4204 at $z=4.71$ (Zhang et al., 2020);
J0324$-$2918 at $z=4.63$ (Hook et al., 2002); J0525$-$3343 at $z=4.41$ (Hook
and McMahon, 1998; Celotti and Ghisellini, 2008); J1028$-$0844 at $z=4.27$
(Zickgraf et al., 1997).

Figure 6: The $V_{S_{4.7}}$ and $V_{S_{22.3}}$ versus the rest frame timescale
$t_{\rm rest}$ for the PS and non-PS quasars (orange and blue triangles). The
symbol sizes are proportional to Nobs, they correspond to 10, 20, 50, 100, and
more number of observations. The dashed lines mark the 0.25 and 0.50
variability index levels.

For averaged spectra of the quasars measured over the entire historical time
period, we did not find a correlation between the variability at 2.3, 4.7,
8.2, 11.2 and 22.3 GHz ($V_{S}$, $F_{S}$) and the spectral indices
$\alpha_{\rm high}$ and $\alpha_{\rm low}$ in terms of Pearson and Spearman
correlation coefficients. Such correlation would be expected for AGNs due to
the fact that flat spectrum radio sources ($\alpha>-0.5$) are more variable
than the steep ones. Indeed, a strong correlation between the spectral index
and variability of bright AGNs has been found: for example, Fiedler et al.
(1987); Lazio et al. (2001). This lack of correlation is possibly due to the
prevalence of variable PS quasars with steep averaged spectra in the optically
thin emission part. In addition, the blazars make up at least half of the
sample and almost half of them have a peaked spectral shape (Sotnikova et al.,
2021). On a long time scale, these PS blazars demonstrate high radio
variability (0.25–0.75) near the peak frequency. In Fig. 7 the
“$\alpha$–$V_{S}$” plane is divided into four quadrants: steep-spectra with
$V_{S}>0.25$ and $<0.25$, flat-spectra with $V_{S}>0.25$ and $<0.25$. It is
clearly seen that PS quasars (orange and blue stars) make up the vast majority
in the steep-spectrum area with $V_{S}>0.25$. During a flare, the radio
spectra of some sources can exhibit characteristic spectrum evolution. In some
cases, the spectra move up while maintaining a peaked shape, while in the
others, they first move towards a flatter shape with increasing flux density
at high frequencies before moving to the steep-spectrum area after the flare,
when emission becomes optically thin.

An example illustrating this behaviour is the spectrum evolution of the PS
blazar J0646$+$4451 with $V_{S_{8.2}}=0.74$ and $\alpha_{\rm high}$=-0.62.
During the 17 years of RATAN-600 observations (Fig. 8), its spectral index
$\alpha_{\rm high}$ changed from $-1.51$ to $+0.35$, which corresponds to a
spectral index variability of 0.60. We estimated the variability of the
spectral index $V_{\alpha}$ using the same equation [1] in terms of the
$\alpha_{\nu}$ maximum and minimum values with their uncertainties. The blazar
had an ultra-steep spectrum ($\alpha=-1.51$) in March 2011 at the beginning of
its flux density decreasing at 2.3–22.3 GHz (orange spectrum), when radio
emission had become optically thin at the frequencies above 5 GHz after
several years of a relatively high state. There is a strong correlation
between $\alpha_{\rm high}$ and the flux density at 11.2 GHz, Pearson’s
$r=0.81$, p-val.$<10^{-3}$ (Fig. 8, top panel). Similar behavior is observed
in other PS blazars such as J2316$-$3349 and J0525$-$3343\. These spectral
evolution patterns are probably caused by changes in the physical conditions
in the source during a flare, such as variations in the magnetic field
strength or electron density, which affect the observed flux densities at
different frequencies.

We found significant correlation (Pearson’s $r>0.5$, p-val.$\ll 0.005$)
between the spectral index $\alpha_{\rm high}$ and the flux density
variability at 11.2 GHz for 15 of the most frequently observed (N $>10$)
quasars with $V_{S_{11.2}}>0.25$. This indicates that for these quasars,
changes in the spectral index are predominantly driven by variation in the
flux density at and above 11.2 GHz. Further studies are needed to investigate
the underlying physical processes driving the observed variability in these
quasars.

Figure 7: The variability indices $V_{S_{22.3}}$ (top) and $V_{S_{8.2}}$
(bottom) versus the high frequency spectral index $\alpha_{\rm high}$,
measured from the averaged historical spectra of the PS blazars and PS non-
blazars candidates (orange and blue stars) and the blazars/non-blazars with
another spectral types (orange and blue circles). The vertical dotted line
corresponds to the spectral index $\alpha=-0.5$, the horizontal line
corresponds to $V_{S}=0.25$. Some variable quasars with steep averaged radio
spectra are tagged.

Figure 8: The relation $\alpha_{\rm high}-S_{11.2}$ for the blazar
J0646$+$4451 is shown in the top panel. The spectral index $\alpha_{\rm high}$
evolution is presented in the middle panel. Corresponding RATAN-600 quasi-
simultaneous spectra are shown in the bottom panel (green color) together with
the literature data (grey color). The orange line corresponds to the ultra-
steep spectrum measured in 2011.

The estimates of AGN variability at different redshifts can be biased due to
the varying cosmological time dilation and different frequencies in the rest
frame. The poorly sampled light curves also strongly impact variability
estimates. Several factors, such as the time scale of monitoring $t_{\rm
rest}$, the frequency $\nu_{\rm rest}$, and the number of measurements Nobs
should be taken into account to compare variability at different $z$ (Vagnetti
et al., 2011, 2016). In order to search for patterns and tendencies by
localizing groups of similar objects in a multidimensional parameter space
(feature space) and investigating their statistical properties, we used two
independent methods of cluster analysis of the quasars (Appendix B). The first
uses PCA dimensionality reduction with k-means clustering, the second is based
on the self-organizing maps (Arthur and Vassilvitskii, 2007; Kohonen, 2001).
We chose the variability parameters at an observed frequency of 4.7 GHz, which
varies from 18 to 30 GHz in the rest frame. As a result, five quasar groups
were determined and their parameters described in Table 11, which allowed us
to compare the variability features within the clusters. An extremely highly
variable quasar group with median $V_{S_{4.7}}=0.48$ was found at the highest
redshifts, $z=4.3$–$5.3$, and they were observed as well at the shortest time
scales, the median $t_{\rm rest}=5.7$ yrs. The clustering algorithm also
determined a group of the most observed quasars with $N_{\rm obs}=24$–$187$.
These quasars are at intermediate $z\leq 3.9$ with long $t_{\rm rest}>7$ yrs.
It is interesting that these most monitored quasars do not generally show the
highest variability indices, which are nevertheless statistically higher than
those for low-variable cluster 2 and intermediate-variable cluster 1. It is
clearly seen that two factors impact the clustering result: the evolutionary
state of the objects and observational constraints, such as $N_{\rm obs}$ and
$t_{\rm rest}$.

##  4 Peaked-spectrum sources at high redshifts

Peaked spectrum quasars make up half of our sample Sotnikova et al. (2021). We
consider the source as PS when the spectral index changes its sign from
positive to negative in the average spectrum compiled with both the RATAN-600
and literature data. It is well known that only several per cent of genuine
GPS sources have been found in complete samples of bright AGNs spreading in a
wide range of redshifts: see, e.g., Torniainen et al. (2005, 2007); Mingaliev
et al. (2013); Sotnikova et al. (2019). It is commonly believed that the
mechanism which produces the absorption in the optically thick part in these
compact luminous objects is due to synchrotron self-absorption caused by the
high density of synchrotron-emitting electrons (Snellen et al., 1998).
Additionally, free-free absorption (FFA) has been suggested as a mechanism
that can produce the GHz-frequency turnover as well as the observed
anticorrelation between peak frequency and size in many of these sources
(Bicknell et al., 1997). Several explanations have been put forth to account
for the properties of the genuine GPS sources: they might be young radio
galaxies in the process of evolving into larger ones (Fanti et al., 1995; An
and Baan, 2012), or their compact nature could be a result of confinement
through interaction with a dense environment (van Breugel et al., 1984; Bai
and Lee, 2005; Labiano et al., 2006; Orienti et al., 2007; Dicken et al.,
2012), or the sources might be recurrent or intermittent sources (Baum et al.,
1990; Reynolds and Begelman, 1997; Stanghellini et al., 2005; An and Baan,
2012; Readhead et al., 2023).

While most scenarios are well applicable to the known GPS galaxies, the nature
of the GPS quasars has received limited attention in the literature. GPS
quasars are thought to be quite rare and challenging to identify due to strong
contamination from blazars. Compact beamed sources can exhibit temporarily
inverted radio spectra and may be easily disguised as GPS sources (Torniainen,
2008; Tornikoski et al., 2009). Study of the radio variability of PS quasars
on historical timescales allows one to detect genuine GPS and MPS quasars, to
estimate their fraction in the population of bright distant AGNs, and also to
check how the MPS method is effective in searching for high-redshift AGNs
(Coppejans et al., 2015, 2016).

To search for GPS/MPS sources, we employ the following common criteria: the
observed peak frequency $\nu_{\rm obs,peak}$ is less than 1 GHz for MPS
sources and from 1 up to 5 GHz for GPS sources; spectral indices of optically
thick $\alpha_{\rm thick}$ and thin $\alpha_{\rm thin}$ emission parts are
close to $+0.5$ and $-0.7$, respectively (for the peaked spectra they match
with $\alpha_{\rm low}$ and $\alpha_{\rm high}$, respectively); radio
variability does not exceed 25% on a long timescale, as GPS/MPS sources are
known as the least variable class of compact extragalactic radio sources
(O’Dea et al., 1990, 1991; de Vries et al., 1997; O’Dea, 1998; Edwards and
Tingay, 2004; O’Dea and Saikia, 2021). Another PS type is high frequency
peakers (HFPs), which are considered to be powerful and intrinsically compact
(<1 kpc) extragalactic radio sources with a spectral peak $\nu_{\rm peak,obs}$
above 5 GHz, representing the earliest stage of radio source evolution with
typical ages of a few hundred years (Fanti et al., 1995; Dallacasa et al.,
2002; Orienti, 2009). According to the criteria in Orienti et al. (2007);
Orienti and Dallacasa (2008), the HFPs lacking flux density variability and
with low fractional polarization (<1%) and intrinsically small linear sizes
(<1 kpc) are considered good candidates for young radio sources.

Table 6 presents the list of PS sources with their peak frequency, the width
of the radio spectra at the half maximum level (FWHM), and spectral type based
on (Sotnikova et al., 2021), radio morphology from the existing literature,
timescale of radio measurements, and the number of observing epochs.

The distributions of the parameters calculated for PS sources in this section
are shown in Fig. 9, and their mean values are listed in Table 7. When PS
blazars and non-blazars are considered separately, significant difference in
the spectral and variability parameters emerge, emphasizing the importance of
a careful approach in distinguishing intrinsically different sources that
happen to have a spectral peak in the MHz–GHz frequency range. As shown in
Table 7, PS blazars have their spectral peaks at higher frequencies and have
higher variations of flux densities. The distributions of variability
estimates at 2.3–22.3 GHz for the PS sources and blazars of the sample are
shown in Fig. 1 for comparison with the whole sample.

Table 6:  The peaked spectrum (PS) sources with their redshifts (Col. 2) and
peak frequencies from Sotnikova et al. (2021) calculated in the observer’s
frame of reference (Col. 3), radio spectrum width at half maximum (Col. 4),
timescale of radio measurements (in yrs) and the number of observing epochs at
4.7 GHz (Col. 5), variability index at 4.7 GHz (Col. 6), radio morphology and
its reference (Col. 7), blazar type from BZCAT (Massaro et al., 2015) (Col.
8), and PS type based on $\nu_{\rm peak,obs.}$ (Col. 9). Morphology
designations are the following: c—core, c+j—core with a jet, cso—compact
symmetric object, c+ext—compact structure with extension, E—core with small
extension, T—triple morphology.

NVSS name |  $z$ |  $\nu_{\rm peak,obs.}$ |  FWHM |  $t_{4.7}$/N4.7 |  $V_{S_{4.7}}$ |  Morph. |  Blazar |  Spectral
---|---|---|---|---|---|---|---|---
|  |  (GHz) |  dex |  |  |  |  type |  type
1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9
000657$+$141546 |  3.20 |  1.5 |  7.7 |  40/14 |  0.10 |  c+j (Paragi et al., 1999) |  |  GPS
004858$+$064005 |  3.58 |  3.9 |  1.5 |  36/25 |  0.25 |  cso (Zhang et al., 2022) |  |  GPS
010012$-$270851∗ |  3.52 |  1.4 |  1.7 |  31/10 |  0.17 |  c+j (Plavin et al., 2022) |  |  GPS
012100$-$280623 |  3.11 |  0.3 |  3.0 |  30/19 |  0.43 |  c+j (Plavin et al., 2022) |  FSRQ |  MPS
020346$+$113445a |  3.63 |  3.7 |  1.5 |  42/38 |  0.33 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
021435$+$015703∗ |  3.28 |  0.5 |  1.9 |  46/19 |  0.13 |  c+j (Plavin et al., 2022) |  |  MPS
023220$+$231756a |  3.42 |  0.5 |  2.0 |  33/13 |  0.29 |  c+j (Plavin et al., 2022) |  |  MPS
024611$+$182330 |  3.59 |  1.8 |  1.8 |  34/44 |  0.29 |  c+j (Paragi et al., 1999) |  FSRQ |  GPS
052506$-$334304 |  4.41 |  0.9 |  1.6 |  30/11 |  0.71 |  c+j (Krezinger et al., 2022) |  Uncert. |  MPS
053954$-$283956a |  3.10 |  7.0 |  1.8 |  43/66 |  0.59 |  c+j (Plavin et al., 2022) |  FSRQ |  HFP
062419$+$385648 |  3.46 |  0.3 |  2.5 |  46/68 |  0.30 |  c+j (Plavin et al., 2022) |  FSRQ |  MPS
064632$+$445116 |  3.39 |  17.3 |  1.5 |  47/187 |  0.67 |  c+j (Plavin et al., 2022) |  FSRQ |  HFP
073357$+$045614 |  3.10 |  5.8 |  1.8 |  40/35 |  0.37 |  c+j (Plavin et al., 2022) |  FSRQ |  HFP
075141$+$271631 |  3.20 |  0.2 |  1.5 |  42/13 |  0.04 |  |  |  MPS
075303$+$423130 |  3.59 |  0.9 |  1.5 |  34/23 |  0.12 |  cso (Zhang et al., 2022) |  |  MPS
083910$+$200208∗ |  3.30 |  1.8 |  2.0 |  35/16 |  0.29 |  c+j (Plavin et al., 2022) |  |  GPS
090549$+$041010∗ |  3.15 |  0.5 |  1.6 |  36/12 |  0.11 |  c+j (Paragi et al., 1999) |  |  MPS
093337$+$284532∗ |  3.42 |  1.7 |  1.5 |  34/17 |  0.25 |  E (Gobeille et al., 2014)b |  |  GPS
102623$+$254259 |  5.28 |  0.3 |  1.7 |  25/13 |  0.30 |  c+j (Krezinger et al., 2022) |  FSRQ |  MPS
104523$+$314232∗ |  3.23 |  0.9 |  2.3 |  34/10 |  0.11 |  c (Gobeille et al., 2014)b |  |  MPS
123055$-$113910 |  3.52 |  1.1 |  2.1 |  43/51 |  0.47 |  c+j (Zhang et al., 2022) |  FSRQ |  GPS
124209$+$372005 |  3.81 |  1.7 |  2.1 |  46/24 |  0.28 |  T (Gobeille et al., 2014)b |  |  GPS
130121$+$190421∗ |  3.10 |  1.7 |  1.9 |  35/13 |  0.05 |  c+j (Plavin et al., 2022) |  |  GPS
134022$+$375443 |  3.11 |  2.7 |  1.4 |  36/12 |  0.30 |  c+j (Paragi et al., 1999) |  |  GPS
135406$-$020603 |  3.70 |  2.6 |  1.8 |  38/60 |  0.24 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
135706$-$174402a |  3.14 |  1.8 |  1.7 |  38/19 |  0.28 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
140135$+$151325∗ |  3.23 |  1.3 |  2.0 |  33/11 |  0.36 |  |  |  GPS
140501$+$041536a |  3.20 |  8.3 |  2.1 |  43/26 |  0.25 |  c+j (Gobeille et al., 2014)b |  FSRQ |  HFP
141821$+$425020∗ |  3.45 |  0.9 |  1.5 |  34/4 |  0.02 |  |  |  MPS
142438$+$225600 |  3.62 |  3.3 |  1.5 |  42/29 |  0.14 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
144516$+$095835 |  3.55 |  1.3 |  1.6 |  41/76 |  0.15 |  c+j (Zhang et al., 2022) |  FSRQ |  GPS
150328$+$041949 |  3.66 |  5.6 |  1.5 |  39/8 |  0.10 |  c+ext (Paragi et al., 1999) |  |  HFP
152117$+$175601∗ |  3.06 |  3.5 |  1.4 |  40/13 |  0.32 |  c (Gobeille et al., 2014)b |  |  GPS
153815$+$001905 |  3.49 |  2.9 |  1.6 |  43/20 |  0.50 |  c+j (Plavin et al., 2022) |  |  GPS
155930$+$030447 |  3.89 |  4.5 |  1.7 |  37/63 |  0.41 |  T (Gobeille et al., 2014)b |  FSRQ |  GPS
160608$+$312447 |  4.56 |  2.5 |  1.5 |  37/26 |  0.28 |  cso (An et al., 2022) |  |  GPS
161637$+$045932 |  3.21 |  4.4 |  1.4 |  43/64 |  0.26 |  c+j (Gobeille et al., 2014)b |  FSRQ |  GPS
165844$-$073918a |  3.74 |  5.9 |  1.5 |  37/12 |  0.27 |  c+j (Plavin et al., 2022) |  FSRQ |  HFP
184057$+$390046 |  3.1 |  4.5 |  1.8 |  36/23 |  0.52 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
200324$-$325144 |  3.77 |  5.6 |  1.4 |  43/39 |  0.32 |  c+j (Plavin et al., 2022) |  FSRQ |  HFP
201918$+$112712∗ |  3.27 |  0.5 |  1.8 |  41/12 |  0.06 |  c+ext (Garrett et al., 1994) |  |  MPS
204257$-$222326 |  3.63 |  3.5 |  2.1 |  30/4 |  0.27 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
205051$+$312727 |  3.18 |  1.9 |  2.9 |  35/15 |  0.57 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS
212912$-$153840 |  3.26 |  6.8 |  1.5 |  37/54 |  0.16 |  c+j (Cheng et al., 2023) |  FSRQ |  HFP
224800$-$054117 |  3.29 |  0.4 |  3.3 |  30/13 |  0.22 |  c+j (Plavin et al., 2022) |  Uncert. |  MPS
231448$+$020150∗ |  4.11 |  1.7 |  2.1 |  40/20 |  0.20 |  c+j (Krezinger et al., 2022) |  |  GPS
231643$-$334912 |  3.10 |  3.9 |  1.3 |  31/18 |  0.18 |  c+j (Plavin et al., 2022) |  FSRQ |  GPS

a sources with two components in the radio spectrum. b VLA measurements. ∗ new
GPS/MPS candidates.

Table 7:  The mean values of the parameters for the PS source subsamples. |  N |  $\nu_{\rm peak,rest}$ |  $S_{\rm peak}$ |  FWHM |  $V_{S_{11.2}}$ |  $V_{S_{8.2}}$ | $V_{S_{4.7}}$
---|---|---|---|---|---|---|---
|  |  (GHz) |  (Jy) |  (dex) |  |  |
PS blazars |  25 |  $17.11\pm 15.82$ |  $0.94\pm 0.78$ |  $1.88\pm 0.53$ |  $0.32\pm 0.15$ |  $0.35\pm 0.16$ | $0.35\pm 0.16$
PS non-blazars |  22 |  $7.91\pm 6.12$ |  $0.41\pm 0.42$ |  $2.0\pm 1.3$ |  $0.12\pm 0.07$ |  $0.18\pm 0.12$ | $0.20\pm 0.12$
all |  47 |  $12.8\pm 13.1$ |  $0.69\pm 0.68$ |  $1.93\pm 0.96$ |  $0.23\pm 0.16$ |  $0.28\pm 0.17$ | $0.28\pm 0.16$

###  4.1 Rest frame peak frequency and FWHM

For the sources with a peaked radio spectrum, we estimated the rest frame peak
frequency $\nu_{\rm peak,rest}=\nu_{\rm peak,obs}(1+z)$, which ranges from 0.8
to 76 GHz. The redshift versus $\nu_{\rm peak,rest}$ relationship is shown in
Fig. 10, where we additionally plot PS sources at different redshifts from
other studies: the sample from Orienti and Dallacasa (2014) marked by cross
symbols, sources from Callingham et al. (2017) marked by star symbols, and
from Sotnikova et al. (2019) by grey circles. de Vries et al. (1997) found a
trend towards higher turnover frequencies at higher redshifts, but Fig. 10
shows a wide spread in the peak frequencies in our sample at redshifts $z$=3–5
and no evidence for correlation between them. Thus, sources with synchrotron
self-absorbed components around and even below 1 GHz in the rest frame occur
at high redshifts and at high radio luminosities.

We calculated the Full Width at Half Maximum (FWHM) for the PS sources in
units of decades of frequency (dex). For classical GPS sources, the parameter
FWHM $\sim 1$–1.5 dex, as has been found in O’Dea et al. (1990, 1991) and de
Vries et al. (1997) for a sample mostly represented by $z<3$ GPS sources (with
only 6 of 74 sources having $z>3$ in the latter study). Mingaliev et al.
(2013) compared the samples of GPS sources classified as galaxies and quasars
and found that the radio spectrum of GPS quasars is on average wider (FWHM
$\sim 1.6$) than that of the GPS galaxies (FWHM $\sim 1.4$). In our PS sample
sources, the FWHM varies from 1.3 to 7.7 dex with a mean value of $1.93\pm
0.96$ (Table 7).

Figure 9: The distributions of the parameters for PS sources. The observed and
rest frame peak frequencies are on top, and the flux densities at the peak
frequency and FWHMs are at the bottom.

Figure 10: Redshift versus rest frame peak frequency for 47 PS quasars from
the sample under investigation. The PS sources from Orienti and Dallacasa
(2014) are marked by grey triangles, from Callingham et al. (2017) by star
symbols, and from Sotnikova et al. (2019) by grey squares.

###  4.2 Spectral variability of identified HFP/GPS/MPS quasars

Blazars have the potential to contaminate GPS source samples since they
exhibit peaked radio spectra during their flaring states (O’Dea et al., 1986;
Kovalev, 2005; Planck Collaboration et al., 2011; Sotnikova et al., 2021). In
this section, we focus on the broadband long-term radio spectra of 23 quasars
previously classified as HFP, GPS, or MPS sources (O’Dea, 1990; O’Dea et al.,
1991; O’Dea, 1998; Marecki et al., 1999; Dallacasa et al., 2000; Tinti et al.,
2005; Mingaliev et al., 2013; Callingham et al., 2017; Mufakharov et al.,
2021). Their radio spectra and RATAN-600 light curves are presented in Figs.
21–22. The longest-term measurements, spanning up to 30–43 years, are
available at frequencies at 4.7, 11.2, and 22.3 GHz. They are listed in Table
8 with the information about their variability index at 11.2 and 22.3 GHz and
the historical period of observations.

Among the known HFP/GPS/MPS sources, six are not classified as blazars. Three
of these six sources (J0048$+$0640, J0751$+$2716, J0753$+$4231) have
relatively small variability indices $V_{S_{4.7}}=0.04$-$0.25$ and
$V_{S_{11.2}}=0.05$-$0.12$ over the timescales of 36–43 and 3–9 years,
respectively. Two of them have a compact symmetric morphology (Zhang et al.,
2022; An et al., 2022). J1606$+$3124 has been classified as a galaxy with a
radio structure similar to that of CSOs, and it may be the highest redshift
($z=4.56$) CSO galaxy discovered so far (An et al., 2022). We measured the
variability indices as 0.10–0.16 at 11.2 and 22.3 GHz and 0.28 at 4.7 GHz for
this source at a long timescale (37–43 yrs). The other two objects,
J1340$+$3754 and J1538$+$0019, have the variability indices
$V_{S_{4.7}}=0.30$–$0.50$ ($t=36$ and 43 yrs) and $V_{S_{11.2}}=0.03$–$0.27$
($t=5$ and 23 yrs).

Among seventeen GPS quasars in Table 8, which belong to the blazar population,
thirteen demonstrate high variability indices $V_{S_{22.3}}$ up to 0.67. Only
four blazars, namely J1424$+$2256, J1616$+$0459, J2248$-$0541, and
J2316$-$3349, have relatively low variability of less than 0.26 at 4.7 GHz and
less than 0.27 at 11.2 GHz. However, for J2248$-$0541 and J2316$-$3349, there
are no enough radio data to establish their variability reliably.

Thus, among previously reported 23 GPS, MPS, and HFP sources, seven quasars
demonstrate low radio variability ($V_{S}<0.27$) at 4.7–22.3 GHz, with four of
them being blazars. Only two GPS (J0048+0640, J1606+3124) and two MPS sources
(J0751+2716, J0753+4231) have variability attributes of young compact radio
sources. The description of 17 individual sources from this section that have
significant radio variability is presented in Appendix C.1.

Table 8:  The variability indices at 22.3 and 11.2 GHz of the earlier determined high-redshift HFP/GPS/MPS sources. The columns are the following: source name (Col. 1), timescale of radio measurements (in years) and the number of observing epochs at 22.3 and 11.2 GHz (Cols. 2–5), $V_{S_{22.3}}$ and $V_{S_{11.2}}$ (Cols. 6–7), blazar type according to BZCAT (Col. 8), references for the spectral classification (Col. 9), where [1]—Mingaliev et al. (2013); [2]—O’Dea et al. (1991); [3]—Coppejans et al. (2017); [4]—Dallacasa et al. (2000); [5]—Callingham et al. (2017); [6]—O’Dea (1990); [7]—Marecki et al. (1999). Name |  $t_{22.3}$ | N22.3 |  $t_{11.2}$ |  N11.2 |  $V_{S_{22.3}}$ |  $V_{S_{11.2}}$ | Blazar | Spectral
---|---|---|---|---|---|---|---|---
|  (yrs) |  |  (yrs) |  |  |  | type | type
1 |  2 | 3 |  4 |  5 |  6 |  7 | 8 | 9
J0048$+$0640 |  – | – |  7 |  17 |  – |  0.12 | – | GPS [1]
J0121$-$2806 |  7 | 18 |  5 |  14 |  0.41 |  0.20 | FSRQ | MPS [1]
J0203$+$1134 |  22 | 31 |  13 |  22 |  0.45 |  0.38 | FSRQ | GPS [2]
J0324$-$2918 |  15 | 15 |  5 |  16 |  0.39 |  0.14 | FSRQ | GPS [3]
J0646$+$4451 |  30 | 319 |  14 |  68 |  0.65 |  0.66 | FSRQ | HFP [2, 4]
J0751$+$2716 |  – | – |  3 |  9 |  – |  0.05 | – | MPS [5]
J0753$+$4231 |  – | – |  9 |  10 |  – |  0.09 | – | MPS [1]
J1230$-$1139 |  14 | 7 |  23 |  44 |  0.41 |  0.44 | FSRQ | GPS [1]
J1340$+$3754 |  – | – |  5 |  3 |  – |  0.03 | – | GPS [1]
J1354$-$0206 |  23 | 33 |  23 |  44 |  0.50 |  0.30 | FSRQ | GPS [2, 6]
J1357$-$1744 |  23 | 3 |  25 |  3 |  0.48 |  0.36 | FSRQ | GPS [2]
J1424$+$2256 |  22 | 18 |  14 |  14 |  0.10 |  0.16 | FSRQ | GPS [2, 4]
J1445$+$0958 |  23 | 27 |  42 |  33 |  0.67 |  0.57 | FSRQ | GPS [2, 6]
J1538$+$0019 |  23 | 10 |  23 |  9 |  0.38 |  0.27 | – | GPS [1]
J1559$+$0304 |  8 | 29 |  26 |  51 |  0.36 |  0.18 | FSRQ | GPS [5]
J1606$+$3124 |  43 | 22 |  41 |  15 |  0.10 |  0.16 | – | GPS [2]
J1616$+$0459 |  23 | 22 |  27 |  19 |  0.26 |  0.17 | FSRQ | HFP [2, 4, 6]
J1658$-$0739 |  10 | 9 |  12 |  6 |  0.33 |  0.13 | FSQR | GPS [2]
J1840$+$3900 |  20 | 13 |  13 |  10 |  0.52 |  0.45 | FSRQ | GPS [4, 7]
J2003$-$3251 |  15 | 36 |  13 |  8 |  0.42 |  0.15 | FSRQ | HFP [2]
J2129$-$1538 |  20 | 24 |  41 |  21 |  0.43 |  0.41 | FSRQ | HFP [2, 6]
J2248$-$0541 |  2 | 2 |  1 |  6 |  0.27 |  – | Uncert. | MPS [5]
J2316$-$3349 |  – | – |  7 |  13 |  – |  0.26 | FSRQ | GPS [1]

###  4.3 New GPS/MPS candidates

We found 12 new GPS/MPS candidates, which are marked with an asterisk symbol
in Table 6 and described in Appendix C.2. Seven of them, J0100$-$2708,
J0839$+$2002, J0933$+$2845, J1301$+$1904, J1401$+$1513, J1521$+$1756, and
J2314$+$0201, we consider as new GPS candidates. Five quasars, J0214$+$0157,
J0905$+$0410, J1045$+$3142, J1418$+$4250, and J2019$+$1127, we suggest as new
MPS candidates.

###  4.4 HFP candidates

There are 6 PS sources previously identified as HFP candidates (Table 6), with
a turnover peak at about 5 GHz or higher. If we consider the source’s rest
frame frequency, it is above 20 GHz. All of them are classified as blazars of
the FSRQ type in BZCAT and have high variability indices from 0.26 to 0.65 at
22.3 GHz according to our estimates. Four quasars, J0646$+$4451, J1616$+$0459,
J2003$-$3251, and J2129$-$1538, have been previously classified as HFPs
(Appendix C.1). For the remaining two quasars, J0733$+$0456 and J1503$+$0419,
we obtained the turnover frequency $\nu_{\rm peak,obs}$ equal to 5.8 and 5.6
GHz respectively (Sotnikova et al., 2021).

J0733$+$0456 was not previously considered as an HFP candidate. The
multifrequency data from the GLEAM survey at 72–231 MHz in 2013–2014 (Hurley-
Walker et al., 2017) and the RATAN-600 measurements in 2016–2020 made it
possible to classify the quasar as a PS source (Sotnikova et al., 2021) with a
high turnover frequency $\nu_{\rm peak,obs}=5.8$ GHz. The wide spectral peak
FWHM $=1.8$ reflects the high radio variability of the quasar at all the
considered frequencies ($V_{S}>0.30$).

J1503$+$0419, initially identified as an FSRQ in Healey et al. (2007),
exhibits a core and some extension in the VLA 5 GHz image. Later authors
Kimball et al. (2011) confirmed the presence of a lobe in the 1.4 GHz FIRST
survey image. However, when observed using VLBI, no discernible structure was
detected, as reported in Paragi et al. (1999). Unfortunately, there are very
little radio data. We measured a low variability index $V_{S}=0.10$ at 4.7 GHz
spanning a time period of $t_{4.7}=39$ years with a total of 8 observations.
The variability at 11.2 and 22.3 GHz can not be evaluated because the flux
density errors are larger than the observed scatter of the data, according to
the only two RATAN-600 observing epochs. The quasar was classified as a PS
source for the first time with an estimated peak frequency $\nu_{\rm
peak,obs}=5.6$ GHz and FWHM $=1.5$ Sotnikova et al. (2021).

Despite the presence of a peak above 5 GHz, we do not consider three quasars
as HFP candidates: J0539$-$2839, J1405$+$0415, and J1658$-$0739, since they
have two-component spectra or a strongly variable spectral shape with a wide
peak (Table 6, Table LABEL:TableA2).

Note that both the quasar J0257$+$4338 with a core–jet morphology (Gordon et
al., 2016) and the BL Lac blazar (D’Abrusco et al., 2014) or blazar of an
uncertain type in BZCAT with an unresolved core in VLBA images (Petrov et al.,
2006). J0525$-$2338 could hypothetically be considered as HFP candidates due
to their spectral shape, which has a hint of a possible peak near 8 and 20 GHz
(Sotnikova et al., 2021). The blazar J0525$-$2338 exhibits a rising spectrum
($\alpha_{\rm high}$=+0.60) and has the variability indices
$V_{S_{22.3}}=0.50$ and $V_{S_{11.2}}=0.36$. J0257$+$4338 is one of the most
distant quasars in the sample at $z=4.06$ (Amirkhanyan and Mikhailov, 2006)
with a variability level $V_{S_{8.2}}=0.45$. Its turnover frequency showed a
remarkable change from 2 GHz up to 8 GHz between 1990 and 2017, with a strong
increase in flux density from 0.13 Jy (Patnaik et al., 1992) up to 0.36 Jy.

##  5 Discussion

Studying the variability of quasars in the radio band is an approach to
understanding the astrophysical processes occurring in the sources. Long-term
(months, years, and decades) variability provides insights into the properties
of the jet, flaring activity, and interaction between the jet and the
surrounding medium, while short-term (from several hours to several days)
variability could provide information about the interstellar medium based on
the measurements of scintillations (Lovell et al., 2008). In our study, we
consider flux density variations at GHz frequencies over long periods of time
of a sample of high-redshift AGNs, which represent a superposition of the
aforementioned short-term events and long-term processes.

The redshift values range from 3.0 to 5.3 for the quasars in our sample, which
corresponds to a wide range of emission frequencies in the source’s reference
frame, from 9 to 130 GHz, and the rest frame time scales of monitoring from
several weeks to 11 years. Consequently, we can get the most general picture
of the dependence of the radio emission variability on the redshift and
frequency and on the time scale of monitoring.

The quasars that have showed a high level of variability but are not listed as
blazars could be considered as blazar candidates after checking their
morphology and other multi-band properties, thus usefully supplementing the
current lists of the known blazars in the “Open Universe for Blazars –
Reference list V2.0” and the Roma-BZCAT catalogue.

###  5.1 Variability properties

Estimates of the flux density variability show that the averaged variability
is higher at higher frequencies ($M_{22.3}=0.28$, $F_{S_{22.3}}=0.31$, and
$V_{S_{22.3}}=0.36$) with typical values of about 0.20–0.25 at other
frequencies. These values are comparable to those observed in blazars at any
redshift.

The distributions of $V_{S}$ and $F_{S}$ at 22.3 GHz are significantly
different from those at 2.3–11.2 GHz, which may be attributed to intrinsic
physical differences. At the source’s rest frequencies greater than 45 GHz
(i.e., $11.2\times(1+z)$, where $z\geq 3$), the radio emission from the
compact AGN core becomes more dominant, leading to a different variability
behavior (the $V_{S}$ distribution peaks around 0.4) compared to the lower
frequencies (the $V_{S}$ distribution peaks around 0.1–0.2). At frequencies
lower than 45 GHz, the variability may be mixed with variations from multiple
jet components, which can lead to smearing of the variability index.

Only the brightest peaked-spectrum sources can be detected at high redshifts
due to their steep radio spectrum above the peak frequencies. Compared to the
other sources in the sample, the PS sources are about two times brighter,
while the variability level is of the same order at all frequencies. The PS
sources are also found to be more variable than the AGNs with power-law
spectra at MHz frequencies in Chhetri et al. (2018) and Ross et al. (2021).
Some PS sources even demonstrate high amplitude variability of 100–2500% over
24 years at 1.5 GHz (Nyland et al., 2020). More than half of PS quasars in the
sample are blazars (25 out of 47), which affects the variability level of the
PS subsample.

We have not found a correlation between radio variability and redshift or the
spectral index; apparently, dense and long-term time series are required to
study such relationships more robustly. Comparing the variability of high-$z$
AGNs, the contribution of observational restrictions and different source
conditions in such a wide redshift range can not be easily distinguished for
our sample. We found several quasar groups with distinctive variability
features. The most interesting is a small highly variable group of quasars
located at redshifts of 4.3–5.3, notable by a shorter time scale of radio
monitoring, $t_{\rm rest}=4.0$–$6.7$ yrs, compared to the rest of the quasars
in the sample. One of the simple explanations is that the youngest quasars are
more compact, and as a consequence the variability time scale is shorter. This
can be confirmed by the recently reported relationship between variability
timescales and core sizes in Chih Hsu et al. (2023). On the other hand the
most bright sources can be detected at such high redshifts, and these bright
sources may be more variable on average. We should be careful making far-
reaching conclusions because only future long-term measurements can provide
evidence of the different properties of intrinsic variability.

###  5.2 Population of peaked spectrum sources at high redshifts

A comparison of radio spectra features and flux density variations of quasars
reveals that the peaked spectrum is a typical feature of blazars at redshifts
$z>3$, distinguishing them from the flat spectrum low-redshift blazars.
Obviously, only a small fraction of quasars can be associated with the so-
called classical GPS/MPS sources. The long-term radio data showed a
significant variability at GHz frequencies, up to 70 per cent, in the most
known GPS quasars (Section 4.2). Previous studies have mentioned the scarcity
of genuine GPS quasars (Cheng et al., 2023; Torniainen et al., 2005; O’Dea et
al., 1990), and we need long-term multifrequency observations to determine
their spectra reliably.

Because of the young age of HFPs, one could expect a larger proportion of them
at high redshifts compared to the intermediate ones. Previously, in Mingaliev
et al. (2013), we identified about 2% objects in the flux-density-complete
sample of GPS galaxies and quasars at lower redshifts (69% sources are at
$z\leq 2$) as HFP candidates. In our sample of high-redshift quasars, all 6
HFP candidates are FSRQ blazars, which exhibit high variability levels and
show a peaked spectrum shape occasionally, during a flare. These six quasars
are, on average, more variable, with the mean value of $V_{S_{22.3}}=0.43\pm
0.14$, compared to the whole sample ($V_{S_{22.3}}=0.35\pm 0.18$). Authors
Dallacasa et al. (2000) found that only 40% of the objects displayed all the
typical characteristics of young radio sources. Furthermore, all quasars in
the sample were excluded. So, to prevent contamination from selection and
boosting effects, authors Orienti and Dallacasa (2014) considered only
galaxies in their statistical analysis of HFP sources.

Three quasars with peaked radio spectra and a CSO-type morphology showed
relatively low variability levels at all the five frequencies we considered,
providing evidence in favor of them being bona-fide CSOs. These findings are
consistent with the estimates in Kiehlmann et al. (2023a, b), where they
correspond to $\sim 3$% of the sample.

It should be noted that for 12% of the objects there are no multifrequency and
long-term measurements, and our analysis is based on non-uniform sparse time
series. Only for about 10 quasars there are flux density measurements with
high cadence (N${}_{\rm obs}=40$–60) over a long time period. The strong
correlation between the number of observations and variability level confirms
the influence of the observational selection effect on the result.

##  6 Summary

In this study, we present the results of a multi-frequency radio variability
analysis of 101 bright radio quasars at $z\geq 3$ based on the RATAN-600
observations at 2.3–22.3 GHz conducted in 2017–2020 (Sotnikova et al., 2021),
as well as the information from the literature covering a time period of 30–40
years, which corresponds to a timescale of about ten years in the source’s
frame of reference. The main results are summarised as follows.

  1. 1.

The quasars show a wide spread of radio variability on any time scale of the
measurements. About half of the objects in the sample show a variability level
(25–50%) comparable to that of the blazars at low redshifts. Some quasars
demonstrate flux density variations of up to 60–90% at 8.2–22.3 GHz. The
median values of modulation index $M$, fractional variability $F_{S}$, and
variability index $V_{S}$ are about 0.20 at 2.3–8.2 GHz and are higher at 22.3
GHz (0.28–0.36). The proportion of sources with low variability of
$V_{S}<0.10$ varies from 8 to 20% at different frequencies.

  2. 2.

The distribution of the variability index is significantly different at 22.3
GHz compared to lower frequencies, demonstrating the peak at higher levels of
variability. This suggests that the emission from the compact core dominates
at higher frequencies, while at lower frequencies, the emission from jet
components could blend with the core emission, shifting the distribution peak
to lower values. In general, the variability we obtained at the range from
dozens to about a hundred GHz in the rest frame is attributed to the
dominating core component in quasars.

  3. 3.

Several quasar groups with distinctive variability characteristics were found.
Six highest-redshift quasars demonstrate average variability of about 0.50 and
at a shorter time scale than the others.

  4. 4.

Among the 23 GPS and MPS sources reported previously, only six objects show
low radio variability ($V_{S}<0.25$). We propose seven new candidates for GPS
sources (J0100$-$2708, J0839$+$2002, J0933$+$2845, J1301$+$1904, J1401$+$1513,
J1521$+$1756, and J2314$+$0201) and five new MPS candidates (J0214$+$0157,
J0905$+$0410, J1045$+$3142, J1418$+$4250, and J2019$+$1127) based on the
analysis of their spectral parameters and radio variability. We found that
about 18 and 9% of the sample of bright quasars at $z\geq 3$ are GPS and MPS
candidates, respectively.

  5. 5.

A peaked spectrum is a typical feature of blazars at high redshifts, and this
distinguishes them from the flat spectrum low-redshift blazars. The radio
variability exceeding more than 30% in high redshift PS sources is common for
blazars.

Conceptualization, Yu.S.; observations, Yu.S., A.M., T.M., T. S.; data
reduction, Yu.S., A.M., R.U., T. S.; methodology, Yu.S., A.M., T.M., D.K.,
V.S.; software, D.K., V.S.; writing—original draft preparation, Yu.S., A.M.,
T.M., D.K., A.K.; writing—review and editing, T.A., M.M.; funding acquisition,
Yu.S. All authors have read and agreed to the published version of the
manuscript.

Not applicable.

Not applicable.

This work is supported in the framework of the State project “Science” by the
Ministry of Science and Higher Education of the Russian Federation under the
contract 075-15-2024-541, and the National SKA Program of China
(2022SKA0120102, 2022SKA0130103).

The data underlying this article are available in the article. LABEL:TableA2
is distributed in the VizieR database.666https://cdsarc.cds.unistra.fr/viz-
bin/cat/J/other/Galax/12.25

###### Acknowledgements.

The observations were carried out with the RATAN-600 scientific facility. 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; the
CATS database, available on the Special Astrophysical Observatory website; the
SIMBAD database, operated at CDS, Strasbourg, France. This research has made
use of the VizieR catalogue access tool, CDS, Strasbourg, France. We thank the
anonymous referees for their comments and review of the manuscript. The
authors declare no conflict of interest. Abbreviations The following
abbreviations are used in this manuscript:
AGN | Active galactic nuclei
---|---
CSO | Compact symmetric object
FWHM | Full width at half maximum
GPS | Gigahertz peaked-spectrum
HFP | High-frequency peaker
MPS | Megahertz peaked-spectrum
PS | peaked radio spectrum
RISS | Refractive interstellar scintillation
yes

##  Appendix A Sample parameters

Table 9: The sample parameters: source name (Col. 1), redshift (Col. 2), average flux density at 4.7 GHz (Col. 3), radio structure (Col. 4) with references to the literature (Col. 5), spectral indices $\alpha_{\rm low}$ and $\alpha_{\rm high}$ (Cols. 6–7), radio spectrum type (Col. 8), blazar type from BZCAT (Col. 9), and number of cluster (Col. 10). Columns 3, 6–9 are adopted from Sotnikova et al. (2021). Morphology designations are the following: c – core, c+j – core with a jet, cso – compact symmetric object, c+ext – compact structure with extension, E – core with small extension, T – triple morphology. NVSS name | $z$ | $S_{4.7}$ | Morph. | Morph. | $\alpha_{\rm low}$ | $\alpha_{\rm high}$ | Spectral | Blazar | Cluster
---|---|---|---|---|---|---|---|---|---
|  | (Jy) | type | ref. |  |  | type | type |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
000108$+$191434 | 3.10 | $0.15\pm 0.01$ | c+j | 10 | $-0.87\pm 0.11$ | $+0.16\pm 0.01$ | upturn | FSRQ | 3
000657$+$141546 | 3.20 | $0.14\pm 0.01$ | c+j | 1 | $+0.02\pm 0.02$ | $-0.21\pm 0.01$ | peaked |  | 2
004858$+$064005 | 3.58 | $0.17\pm 0.01$ | cso | 8 | $+0.05\pm 0.03$ | $-0.95\pm 0.01$ | peaked |  | 1
010012$-$270852 | 3.52 | $0.12\pm 0.01$ | c+j | 10 | $+0.41\pm 0.04$ | $-0.47\pm 0.01$ | peaked |  | 1
012100$-$280623 | 3.11 | $0.17\pm 0.01$ | c+j | 10 | $+1.45\pm 0.15$ | $-0.08\pm 0.01$ | peaked | FSRQ | 3
013113$+$435812a | 3.12 | $0.03\pm 0.01$ | c+j | 2 | $-1.16\pm 0.02$ | $-0.12\pm 0.08$ | complex |  | 3
014844$+$421518 | 3.24 | $0.11\pm 0.01$ |  |  | $-0.27\pm 0.02$ | $+0.20\pm 0.01$ | upturn | FSRQ | 2
015106$+$251729 | 3.10 | $0.13\pm 0.01$ | c+j | 10 | $-0.05\pm 0.01$ | $-0.05\pm 0.01$ | flat |  | 3
020346$+$113445 | 3.63 | $0.65\pm 0.03$ | c+j | 10 | $+0.29\pm 0.01$ | $-0.51\pm 0.01$ | peaked∗ | FSRQ | 4
021435$+$015702 | 3.28 | $0.08\pm 0.01$ | c+j | 10 | $+0.34\pm 0.09$ | $-0.45\pm 0.01$ | peaked |  | 2
023220$+$231756 | 3.42 | $0.31\pm 0.02$ | c+j | 10 | $+0.87\pm 0.08$ | $-0.37\pm 0.01$ | peaked∗ |  | 1
024611$+$182330 | 3.59 | $0.17\pm 0.01$ | c+j | 1 | $+0.49\pm 0.02$ | $-0.35\pm 0.01$ | peaked | FSRQ | 4
025759$+$433836 | 4.06 | $0.31\pm 0.02$ | c+j | 5 | $+0.36\pm 0.01$ | $+0.04\pm 0.01$ | inverted |  | 1
032444$-$291821 | 4.63 | $0.15\pm 0.01$ | c+j | 5 | $+0.15\pm 0.01$ | $+0.15\pm 0.01$ | inverted | FSRQ | 0
033755$-$120404 | 3.44 | $0.29\pm 0.02$ | c+j | 10 | $-0.32\pm 0.01$ | $-0.27\pm 0.01$ | flat | FSRQ | 1
033900$-$013317 | 3.19 | $0.37\pm 0.02$ | c+j | 10 | $-0.03\pm 0.01$ | $-0.40\pm 0.01$ | flat | FSRQ | 2
035424$+$044107 | 3.26 | $0.39\pm 0.02$ | c+j | 10 | $+0.04\pm 0.02$ | $-0.36\pm 0.01$ | complex |  | 4
042457$+$080517 | 3.09 | $0.19\pm 0.01$ | c+j | 10 | $+0.11\pm 0.02$ | $+0.19\pm 0.01$ | inverted | FSRQ | 2
042835$+$173223 | 3.32 | $0.15\pm 0.01$ | c+j | 10 | $-0.09\pm 0.01$ | $-0.09\pm 0.01$ | flat | FSRQ | 4
052506$-$233810 | 3.1 | $0.74\pm 0.03$ | c+j | 10 | $+0.60\pm 0.01$ | $+0.34\pm 0.01$ | inverted | FSRQ | 4
052506$-$334304 | 4.41 | $0.40\pm 0.01$ | c+j | 5 | $+0.43\pm 0.02$ | $-0.96\pm 0.02$ | peaked | Uncert. | 0
053954$-$283956 | 3.10 | $0.99\pm 0.10$ | c+j | 10 | $+0.32\pm 0.01$ | $-0.32\pm 0.01$ | peaked∗ | FSRQ | 4
062419$+$385648 | 3.46 | $0.61\pm 0.03$ | c+j | 10 | $+0.40\pm 0.01$ | $-0.33\pm 0.01$ | peaked | FSRQ | 4
064632$+$445116 | 3.39 | $2.27\pm 0.10$ | c+j | 10 | $+0.52\pm 0.01$ | $-0.62\pm 0.01$ | peaked | FSRQ | 4
073357$+$045614 | 3.01 | $0.53\pm 0.03$ | c+j | 10 | $+0.39\pm 0.01$ | $-0.31\pm 0.01$ | peaked | FSRQ | 4
075141$+$271631a | 3.20 | $0.20\pm 0.01$ |  |  | $+1.02\pm 0.03$ | $-0.75\pm 0.01$ | peaked |  | 2
075303$+$423130 | 3.59 | $0.41\pm 0.02$ | cso | 8 | $+0.87\pm 0.04$ | $-0.61\pm 0.01$ | peaked |  | 1
083322$+$095941 | 3.75 | $0.09\pm 0.01$ | c+j | 1 | $-0.33\pm 0.01$ | $-0.33\pm 0.01$ | flat |  | 1
083910$+$200208 | 3.03 | $0.12\pm 0.01$ | c+j | 10 | $+0.36\pm 0.01$ | $-0.25\pm 0.01$ | peaked |  | 3
084715$+$383110 | 3.18 | $0.11\pm 0.01$ | c | 4c | $+0.07\pm 0.01$ | $+0.07\pm 0.01$ | inverted |  | 2
090549$+$041010 | 3.15 | $0.09\pm 0.01$ | c+j | 1 | $+0.57\pm 0.06$ | $-0.53\pm 0.01$ | peaked |  | 2
090915$+$035443 | 3.20 | $0.13\pm 0.01$ | c+j | 4,9 | $-0.35\pm 0.01$ | $-0.10\pm 0.01$ | flat |  | 3
091551$+$000712 | 3.07 | $0.21\pm 0.01$ | T | 4c | $-0.28\pm 0.01$ | $-0.28\pm 0.01$ | flat | FSRQ | 2
093337$+$284532 | 3.42 | $0.05\pm 0.01$ | E | 4c | $+0.17\pm 0.02$ | $-0.67\pm 0.01$ | peaked |  | 1
094113$+$114533 | 3.19 | $0.12\pm 0.01$ | c+j | 1 | $-0.51\pm 0.01$ | $-0.51\pm 0.01$ | flat |  | 3
101644$+$203746 | 3.11 | $0.55\pm 0.03$ | c+j | 1 | $-0.07\pm 0.01$ | $-0.52\pm 0.01$ | complex | FSRQ | 4
102010$+$104003 | 3.15 | $0.15\pm 0.01$ |  |  | $-0.63\pm 0.01$ | $-0.94\pm 0.01$ | steep |  | 2
102107$+$220921 | 4.26 | $0.12\pm 0.01$ | c+j | 5 | $-0.51\pm 0.01$ | $-0.17\pm 0.01$ | flat |  | 1
102623$+$254259 | 5.28 | $0.11\pm 0.01$ | c+j | 5 | $+0.11\pm 0.03$ | $-0.50\pm 0.01$ | peaked | FSRQ | 0
102645$+$365825 | 3.25 | $0.19\pm 0.01$ | c | 4c | $-0.08\pm 0.01$ | $-0.27\pm 0.01$ | flat |  | 3
102838$-$084438 | 4.27 | $0.10\pm 0.01$ | c+j | 5 | $-0.11\pm 0.01$ | $-0.11\pm 0.01$ | flat | FSRQ | 0
103626$+$132654 | 3.09 | $0.04\pm 0.01$ | T | 3 | $-0.89\pm 0.01$ | $-0.53\pm 0.01$ | steep |  | 3
104523$+$314232 | 3.23 | $0.08\pm 0.01$ | c | 4c | $+0.25\pm 0.03$ | $-0.56\pm 0.01$ | peaked |  | 2
110147$+$001038 | 3.69 | $0.06\pm 0.01$ | c | 4c | $-0.74\pm 0.01$ | $-0.78\pm 0.01$ | steep |  | 1
112500$+$333858 | 3.43 | $0.08\pm 0.01$ |  |  | $-0.78\pm 0.01$ | $-0.55\pm 0.01$ | steep |  | 2
112851$+$232616 | 3.04 | $0.10\pm 0.01$ | E | 4c | $-0.46\pm 0.01$ | $-0.46\pm 0.01$ | flat |  | 2
115016$+$433206 | 3.03 | $0.11\pm 0.01$ | c | 4c | $+0.01\pm 0.01$ | $+0.01\pm 0.01$ | inverted | FSRQ | 3
123055$-$113910 | 3.52 | $0.18\pm 0.01$ | c+j | 8 | $+0.34\pm 0.04$ | $-0.56\pm 0.01$ | peaked | FSRQ | 4
124209$+$372005 | 3.81 | $0.56\pm 0.02$ | T | 4c | $+0.26\pm 0.01$ | $-0.30\pm 0.01$ | peaked∗ |  | 4
130122$+$190421 | 3.10 | $0.08\pm 0.01$ | c+j | 10 | $+0.13\pm 0.01$ | $-0.68\pm 0.01$ | peaked |  | 2
134022$+$375443 | 3.11 | $0.30\pm 0.02$ | c+j | 1 | $+1.07\pm 0.01$ | $-1.02\pm 0.01$ | peaked |  | 3
135406$-$020603 | 3.70 | $0.70\pm 0.04$ | c+j | 10 | $+0.46\pm 0.01$ | $-0.35\pm 0.01$ | peaked | FSRQ | 4
135646$-$110130 | 3.01 | $0.23\pm 0.01$ | c+j | 10 | $+0.13\pm 0.01$ | $+0.13\pm 0.01$ | inverted | FSRQ | 2
135652$+$291817 | 3.24 | $0.05\pm 0.01$ | T | 4c | $-0.57\pm 0.01$ | $-0.57\pm 0.01$ | steep |  | 2
135706$-$174402 | 3.14 | $0.65\pm 0.04$ | c+j | 10 | $+0.28\pm 0.01$ | $-0.42\pm 0.01$ | peaked∗ | FSRQ | 4
140135$+$151325a | 3.23 | $0.04\pm 0.01$ |  |  | $+0.05\pm 0.01$ | $-0.78\pm 0.02$ | peaked |  | 3
140501$+$041536 | 3.20 | $0.73\pm 0.03$ | c+j | 4c | $+0.01\pm 0.01$ | $-0.43\pm 0.01$ | peaked∗ | FSRQ | 4
141152$+$430024 | 3.21 | $0.09\pm 0.01$ | c+j | 4c | $-0.21\pm 0.01$ | $-0.21\pm 0.01$ | flat |  | 2
141300$+$394745 | 3.71 | $0.05\pm 0.01$ |  |  | $-0.55\pm 0.01$ | $-0.44\pm 0.01$ | flat |  | 1
141318$+$450523 | 3.11 | $0.16\pm 0.01$ | c | 4c | $+0.04\pm 0.01$ | $+0.04\pm 0.01$ | inverted | FSRQ | 2
141821$+$425020 | 3.45 | $0.05\pm 0.01$ |  |  | $+0.32\pm 0.01$ | $-0.77\pm 0.01$ | peaked |  | 2
142107$-$064355 | 3.68 | $0.22\pm 0.01$ | c+j | 8 | $-0.65\pm 0.01$ | $-0.38\pm 0.01$ | complex | FSRQ | 1
142438$+$225600a | 3.62 | $0.61\pm 0.03$ | c+j | 10 | $+0.62\pm 0.01$ | $-0.59\pm 0.01$ | peaked | FSRQ | 4
143023$+$420436 | 4.71 | $0.12\pm 0.01$ | c+j | 5 | $-0.13\pm 0.01$ | $-0.13\pm 0.01$ | flat | FSRQ | 0
144516$+$095835 | 3.55 | $0.98\pm 0.04$ | c+j | 8 | $+0.68\pm 0.01$ | $-0.87\pm 0.01$ | peaked | FSRQ | 4
145722$+$051922 | 3.17 | $0.07\pm 0.01$ | c+j | 10 | $-0.30\pm 0.01$ | $-0.30\pm 0.01$ | flat |  | 2
145805$+$085529 | 3.06 | $0.06\pm 0.01$ |  |  | $-0.53\pm 0.01$ | $-0.87\pm 0.01$ | steep |  | 2
145927$+$325358 | 3.32 | $0.05\pm 0.01$ | complex | 4c | $-0.67\pm 0.01$ | $-0.85\pm 0.01$ | steep |  | 2
150328$+$041949 | 3.66 | $0.19\pm 0.01$ | c+extb | 1 | $+0.21\pm 0.01$ | $-0.29\pm 0.01$ | peaked |  | 2
152117$+$175601 | 3.06 | $0.13\pm 0.01$ | c | 4c | $+0.40\pm 0.03$ | $-0.87\pm 0.01$ | peaked |  | 3
152219$+$211957 | 3.22 | $0.08\pm 0.01$ |  |  | $-0.99\pm 0.01$ | $-1.04\pm 0.01$ | steep |  | 2
153815$+$001905 | 3.49 | $0.32\pm 0.02$ | c+j | 10 | $+0.38\pm 0.01$ | $-0.77\pm 0.01$ | peaked |  | 3
155930$+$030447 | 3.89 | $0.43\pm 0.02$ | T | 4c | $+0.11\pm 0.01$ | $-0.43\pm 0.01$ | peaked | FSRQ | 4
160608$+$312447 | 4.56 | $0.64\pm 0.03$ | cso | 6 | $+1.10\pm 0.02$ | $-0.57\pm 0.01$ | peaked |  | 0
161005$+$181143 | 3.11 | $0.07\pm 0.01$ | T | 4c | $-0.25\pm 0.01$ | $-0.79\pm 0.02$ | steep |  | 3
161637$+$045932 | 3.21 | $1.03\pm 0.04$ | c+j | 4c | $+0.64\pm 0.01$ | $-0.56\pm 0.01$ | peaked∗ | FSRQ | 4
163257$-$003321a | 3.42 | $0.15\pm 0.01$ | c+j | 10 | $-0.19\pm 0.01$ | $-0.19\pm 0.01$ | flat | FSRQ | 4
165519$+$324241 | 3.18 | $0.06\pm 0.01$ | c+j | 1 | $-0.80\pm 0.01$ | $-0.80\pm 0.01$ | steep |  | 2
165543$+$194847 | 3.26 | $0.11\pm 0.01$ | E | 4c | $-0.10\pm 0.01$ | $-0.36\pm 0.01$ | flat |  | 2
165844$-$073918 | 3.74 | $0.83\pm 0.03$ | c+j | 10 | $+0.16\pm 0.01$ | $-0.86\pm 0.01$ | peaked∗ | FSRQ | 1
171521$+$214534 | 4.01 | $0.16\pm 0.01$ | T | 5 | $-0.66\pm 0.01$ | $-0.66\pm 0.01$ | steep |  | 1
174020$+$350048 | 3.22 | $0.06\pm 0.01$ |  |  | $-0.69\pm 0.01$ | $-0.69\pm 0.01$ | steep |  | 2
184057$+$390046 | 3.1 | $0.18\pm 0.01$ | c+j | 10 | $+0.27\pm 0.01$ | $-0.32\pm 0.01$ | peaked | FSRQ | 3
193957$-$100241 | 3.78 | $0.59\pm 0.02$ | c+j | 8 | $-0.17\pm 0.01$ | $-0.73\pm 0.01$ | complex | FSRQ | 1
200324$-$325144 | 3.77 | $0.68\pm 0.03$ | c+j | 10 | $+0.40\pm 0.01$ | $-0.74\pm 0.01$ | peaked | FSRQ | 4
201918$+$112712a | 3.27 | $0.08\pm 0.01$ | c+ext | 7 | $+0.71\pm 0.01$ | $-0.84\pm 0.01$ | peaked |  | 2
204124$+$185502 | 3.05 | $0.17\pm 0.01$ |  |  | $-0.83\pm 0.01$ | $-0.83\pm 0.01$ | steep |  | 2
204257$-$222326 | 3.63 | $0.09\pm 0.01$ | c+j | 10 | $+0.13\pm 0.01$ | $-0.60\pm 0.02$ | peaked | FSRQ | 1
204310$+$125513 | 3.27 | $0.14\pm 0.02$ | c+j | 10 | $-0.18\pm 0.01$ | $-0.18\pm 0.01$ | flat | FSRQ | 3
205051$+$312727 | 3.18 | $0.57\pm 0.03$ | c+j | 10 | $+0.15\pm 0.01$ | $-0.39\pm 0.01$ | peaked | FSRQ | 3
212912$-$153841 | 3.26 | $1.46\pm 0.10$ | c+j | 11 | $+0.56\pm 0.01$ | $-0.61\pm 0.01$ | peaked∗ | FSRQ | 4
213412$-$041909 | 4.34 | $0.22\pm 0.01$ | c+j | 5 | $-0.31\pm 0.01$ | $-0.31\pm 0.01$ | flat |  | 1
221748$+$022011 | 3.57 | $0.32\pm 0.02$ | c+j | 10 | $-0.65\pm 0.01$ | $-0.52\pm 0.01$ | steep | FSRQ | 3
221935$-$271902 | 3.63 | $0.21\pm 0.01$ | c+j | 10 | $-0.14\pm 0.01$ | $-0.14\pm 0.01$ | flat | FSRQ | 1
222536$+$204014 | 3.56 | $0.13\pm 0.01$ | c+j | 10 | $-0.72\pm 0.01$ | $-0.72\pm 0.01$ | steep |  | 1
224800$-$054117 | 3.29 | $0.20\pm 0.01$ | c+j | 10 | $+0.02\pm 0.01$ | $-0.57\pm 0.01$ | peaked | Uncert. | 1
225153$+$221737 | 3.66 | $0.11\pm 0.01$ | c+j | 10 | $-0.36\pm 0.01$ | $-0.36\pm 0.01$ | flat | FSRQ | 4
231448$+$020150 | 4.11 | $0.07\pm 0.01$ | c+j | 5 | $+0.06\pm 0.01$ | $-0.53\pm 0.01$ | peaked |  | 1
231643$-$334912 | 3.1 | $0.48\pm 0.03$ | c+j | 10 | $+0.75\pm 0.02$ | $-1.58\pm 0.01$ | peaked | FSRQ | 2
232118$-$082721 | 3.16 | $0.18\pm 0.01$ | c+j | 10 | $-0.46\pm 0.01$ | $-0.17\pm 0.01$ | flat | FSRQ | 3
234451$+$343348 | 3.05 | $0.09\pm 0.01$ |  |  | $-0.50\pm 0.01$ | $-0.50\pm 0.01$ | flat |  | 2
a gravitationally lensed system. |
b also classified as core dominated with a lobe in Kimball et al. (2011). |
c VLA measurements. |
∗ sources with two components in the radio spectrum. |
5—Krezinger et al. (2022), 6—An et al. (2022), 7—Garrett et al. (1994), 8—Zhang et al. (2022), 9—Perger et al. (2021), |
10—Plavin et al. (2022), 11—Cheng et al. (2023). |
Table 9: continued. Table 10:  The variability, modulation and fractional variability indices for the sample. Columns 3–6 show the timescale (in year) at which we have estimated the variability and the number of measurements at 4.7 and 22.3 GHz. The table is available in the VizieR database at https://cdsarc.cds.unistra.fr/viz-bin/cat/J/other/Galax/12.25 Name | $z$ | $t_{\rm 4.7}$ | N4.7 | $t_{\rm 22.3}$ | N22.3 | $V_{S_{2.3}}$ | $M_{2.3}$ | $F_{2.3}$ | $V_{S_{4.7}}$ | $M_{4.7}$ | $F_{4.7}$ | $V_{S_{8.2}}$ | $M_{8.2}$ | $F_{8.2}$ | $V_{S_{11.2}}$ | $M_{11.2}$ | $F_{11.2}$ | $V_{S_{22.3}}$ | $M_{22.3}$ | $F_{22.3}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21
J0001$+$1914 | 3.10 | 35 | 21 | 3 | 9 | 0.53 | 0.42 | 0.46 | 0.47 | 0.31 | 0.31 | 0.63 | 0.64 | 0.65 | 0.23 | 0.17 | 0.17 | 0.57 | 0.34 | 0.35
J0006$+$1415 | 3.20 | 40 | 14 | – | – | 0.08 | 0.1 | 0.09 | 0.1 | 0.13 | 0.12 | 0.25 | 0.17 | 0.16 | 0.03 | 0.09 | – | – | – | –
J0048$+$0640 | 3.58 | 36 | 25 | – | – | 0.28 | 0.18 | 0.18 | 0.25 | 0.14 | 0.13 | 0.24 | 0.15 | 0.15 | 0.12 | 0.16 | 0.1 | – | – | –
J0100$-$2708 | 3.52 | 31 | 10 | – | – | 0.11 | 0.14 | 0.13 | 0.17 | 0.14 | 0.14 | 0.11 | 0.13 | 0.1 | 0.17 | 0.2 | 0.17 | – | – | –
J0121$-$2806 | 3.11 | 30 | 19 | 7 | 18 | 0.06 | 0.2 | 0.15 | 0.43 | 0.37 | 0.4 | 0.32 | 0.24 | 0.24 | 0.2 | 0.17 | 0.15 | 0.41 | 0.33 | 0.34
J0131$+$4358 | 3.12 | 34 | 12 | – | – | – | – | – | 0.37 | 0.22 | 0.22 | 0.3 | 0.27 | – | 0.17 | 0.28 | 0.1 | – | – | –
J0148$+$4215 | 3.24 | 34 | 14 | 3 | 8 | – | 0.07 | – | 0.23 | 0.17 | 0.16 | 0.14 | 0.12 | 0.11 | 0.05 | 0.1 | – | 0.36 | 0.25 | 0.22
J0151$+$2517 | 3.10 | 34 | 17 | 2 | 8 | 0.25 | 0.2 | 0.2 | 0.32 | 0.29 | 0.29 | 0.23 | 0.16 | 0.15 | 0.1 | 0.11 | 0.06 | 0.08 | 0.12 | –
J0203$+$1134 | 3.63 | 42 | 38 | 22 | 31 | 0.21 | 0.09 | 0.08 | 0.33 | 0.22 | 0.21 | 0.4 | 0.18 | 0.17 | 0.38 | 0.26 | 0.26 | 0.45 | 0.33 | 0.33
J0214$+$0157 | 3.28 | 36 | 19 | – | – | 0.23 | 0.21 | 0.2 | 0.13 | 0.12 | 0.08 | 0.23 | 0.21 | 0.21 | 0.03 | 0.16 | – | – | – | –
J0232$+$2317 | 3.42 | 33 | 13 | – | – | 0.2 | 0.2 | 0.22 | 0.29 | 0.19 | 0.19 | 0.21 | 0.15 | 0.14 | 0.08 | 0.17 | 0.12 | – | 0.11 | –
J0246$+$1823 | 3.59 | 34 | 44 | 2 | 5 | 0.34 | 0.26 | 0.27 | 0.29 | 0.17 | 0.08 | 0.25 | 0.15 | 0.15 | 0.29 | 0.2 | – | 0.31 | 0.33 | 0.34
J0257$+$4338 | 4.06 | 34 | 16 | 5 | 10 | 0.06 | 0.26 | 0.18 | 0.33 | 0.31 | 0.32 | 0.45 | 0.37 | 0.37 | 0.08 | 0.1 | 0.05 | 0.04 | 0.13 | 0.05
J0324$-$2918 | 4.63 | 30 | 19 | 15 | 15 | 0.08 | 0.08 | – | 0.44 | 0.43 | 0.45 | 0.41 | 0.25 | 0.25 | 0.14 | 0.16 | 0.13 | 0.39 | 0.4 | 0.39
J0337$-$1204 | 3.44 | 31 | 12 | 14 | 6 | 0.26 | 0.18 | 0.18 | 0.19 | 0.13 | 0.12 | 0.24 | 0.13 | 0.12 | 0.09 | 0.11 | 0.07 | 0.68 | 0.64 | 0.28
J0339$-$0133 | 3.19 |  $>$43 | 17 | 13 | 6 | 0.2 | 0.13 | 0.12 | 0.21 | 0.12 | 0.11 | 0.14 | 0.1 | 0.08 | 0.25 | 0.16 | 0.13 | 0.49 | 0.46 | 0.5
J0354$+$0441 | 3.26 | 40 | 31 | 22 | 13 | 0.18 | 0.15 | 0.14 | 0.27 | 0.13 | 0.11 | 0.22 | 0.18 | 0.17 | 0.17 | 0.15 | 0.12 | 0.54 | 0.47 | 0.47
J0424$+$0805 | 3.8 | 36 | 21 | 3 | 9 | 0.32 | 0.23 | 0.23 | 0.19 | 0.14 | 0.13 | 0.38 | 0.29 | 0.3 | 0.16 | 0.12 | 0.07 | 0.4 | 0.36 | 0.35
J0428$+$1732 | 3.32 | 30 | 56 | 5 | 17 | 0.38 | 0.27 | 0.28 | 0.33 | 0.16 | 0.14 | 0.22 | 0.19 | 0.19 | 0.22 | 0.13 | 0.07 | 0.46 | 0.34 | 0.32
J0525$-$2338 | 3.1 | 30 | 55 | 14 | 50 | 0.28 | 0.19 | – | 0.11 | 0.08 | 0.06 | 0.35 | 0.24 | 0.23 | 0.36 | 0.15 | 0.13 | 0.5 | 0.25 | 0.23
J0525$-$3343 | 4.41 | 30 | 18 | – | – | 0.29 | 0.3 | 0.36 | 0.71 | 0.62 | 0.66 | 0.3 | 0.25 | 0.18 | – | – | – | – | – | –
J0539$-$2839 | 3.10 |  $>$43 | 66 | 23 | 47 | 0.44 | 0.33 | 0.3 | 0.59 | 0.35 | 0.34 | 0.56 | 0.35 | 0.35 | 0.59 | 0.4 | 0.39 | 0.61 | 0.45 | 0.43
J0624$+$3856 | 3.46 | 46 | 68 | 23 | 47 | 0.4 | 0.35 | 0.35 | 0.3 | 0.18 | 0.18 | 0.43 | 0.2 | 0.19 | 0.26 | 0.21 | 0.18 | 0.35 | 0.27 | 0.2
J0646$+$4451 | 3.39 | 47 | 187 | 30 | 319 | 0.46 | 0.23 | 0.21 | 0.67 | 0.31 | 0.31 | 0.74 | 0.49 | 0.5 | 0.66 | 0.37 | 0.36 | 0.65 | 0.25 | 0.24
J0733$+$0456 | 3.1 | 40 | 35 | 4 | 15 | 0.47 | 0.21 | 0.21 | 0.37 | 0.24 | 0.24 | 0.48 | 0.36 | 0.37 | 0.29 | 0.21 | 0.18 | 0.44 | 0.27 | 0.24
J0751$+$2716 | 3.20 | 42 | 13 | – | – | 0.17 | 0.16 | 0.16 | 0.04 | 0.05 | – | 0.04 | 0.1 | 0.05 | 0.05 | 0.12 | – | – | – | –
J0753$+$4231 | 3.59 | 34 | 23 | 18 | 2 | 0.2 | 0.17 | 0.17 | 0.12 | 0.06 | 0.05 | 0.04 | 0.08 | 0.05 | 0.09 | 0.1 | 0.05 | – | 0.17 | –
J0833$+$0959 | 3.75 | 36 | 17 | – | – | – | 0.05 | – | 0.17 | 0.14 | 0.11 | 0.24 | 0.17 | 0.13 | – | 0.07 | – | – | – | –
J0839$+$2002 | 3.3 | 35 | 16 | 3 | 2 | 0.23 | 0.2 | 0.21 | 0.29 | 0.21 | 0.2 | 0.15 | 0.15 | 0.13 | 0.21 | 0.21 | 0.19 | 0.05 | 0.17 | –
J0847$+$3831 | 3.18 | 34 | 16 | 3 | 5 | 0.36 | 0.35 | 0.37 | 0.2 | 0.14 | 0.11 | 0.36 | 0.24 | 0.24 | – | 0.05 | – | 0.14 | 0.24 | 0.23
J0905$+$0410 | 3.15 | 36 | 12 | – | – | 0.17 | 0.19 | 0.23 | 0.11 | 0.12 | 0.06 | 0.17 | 0.2 | 0.21 | 0.04 | 0.15 | – | – | – | –
J0909$+$0354 | 3.20 | 37 | 18 | 2 | 2 | 0.15 | 0.18 | 0.19 | 0.5 | 0.29 | 0.29 | 0.36 | 0.23 | 0.23 | 0.26 | 0.22 | 0.22 | 0.05 | 0.18 | –
J0915$+$0007 | 3.7 | 42 | 19 | 3 | 7 | 0.27 | 0.23 | 0.19 | 0.23 | 0.15 | 0.14 | 0.08 | 0.11 | – | 0.05 | 0.1 | 0.05 | 0.61 | 0.68 | 0.72
J0933$+$2845 | 3.42 | 34 | 17 | – | – | 0.34 | 0.25 | 0.24 | 0.25 | 0.19 | 0.14 | 0.22 | 0.21 | 0.09 | 0.21 | 0.23 | – | – | – | –
J0941$+$1145 | 3.19 | 39 | 16 | 1 | 2 | 0.86 | 0.38 | 0.42 | 0.35 | 0.33 | 0.33 | 0.96 | 1 | 0.97 | 0.07 | 0.13 | 0.05 | – | 0.09 | –
J1016$+$2037 | 3.11 | 44 | 91 | 23 | 44 | 0.18 | 0.15 | 0.14 | 0.5 | 0.23 | 0.22 | 0.47 | 0.33 | 0.34 | 0.41 | 0.18 | 0.15 | 0.34 | 0.21 | 0.14
J1020$+$1040 | 3.15 | 42 | 11 | – | – | 0.18 | 0.17 | 0.17 | 0.09 | 0.08 | 0.06 | 0.23 | 0.17 | 0.15 | – | 0.06 | – | – | – | –
J1021$+$2209 | 4.23 | 35 | 12 | – | – | – | 0.06 | – | 0.18 | 0.13 | 0.11 | 0.13 | 0.16 | 0.15 | 0.09 | 0.13 | 0.1 | – | – | –
J1026$+$2542 | 5.28 | 25 | 13 | – | – | 0.12 | 0.12 | 0.12 | 0.3 | 0.15 | 0.14 | 0.2 | 0.17 | 0.17 | – | 0.08 | – | – | – | –
J1026$+$3658 | 3.25 | 35 | 11 | – | – | 0.05 | 0.08 | 0.07 | 0.4 | 0.3 | 0.31 | 0.43 | 0.3 | 0.32 | 0.02 | 0.08 | 0.05 | – | – | –
J1028$-$0844 | 4.27 | 31 | 49 | 4 | 5 | – | – | – | 0.56 | 0.35 | 0.31 | 0.15 | 0.15 | 0.14 | 0.23 | 0.31 | 0.33 | 0.25 | 0.3 | 0.31
J1036$+$1326 | 3.9 | 37 | 13 | – | – | – | – | – | 0.48 | 0.4 | 0.39 | 0.31 | 0.3 | 0.26 | 0.39 | 0.35 | 0.25 | – | – | –
J1045$+$3142 | 3.23 | 34 | 10 | – | – | 0.2 | 0.23 | 0.24 | 0.11 | 0.13 | 0.06 | 0.12 | 0.17 | 0.09 | – | 0.14 | – | – | – | –
J1101$+$0010 | 3.69 | 36 | 14 | – | – | 0 | 0.1 | – | 0.28 | 0.23 | 0.18 | 0.18 | 0.25 | 0.15 | 0.42 | 0.57 | 0.63 | – | – | –
J1125$+$3338 | 3.43 | 37 | 14 | – | – | 0.29 | 0.22 | 0.22 | 0.24 | 0.15 | 0.11 | 0.07 | 0.14 | – | – | 0.09 | – | – | – | –
J1128$+$2326 | 3.4 | 34 | 14 | – | – | 0.45 | 0.25 | 0.26 | 0.11 | 0.09 | 0.01 | 0.37 | 0.19 | 0.15 | – | 0.09 | – | – | – | –
J1150$+$4332 | 3.3 | 35 | 14 | 2 | 6 | 0.5 | 0.53 | 0.59 | 0.42 | 0.28 | 0.28 | 0.44 | 0.27 | 0.28 | 0.29 | 0.18 | 0.14 | 0.12 | 0.19 | 0.16
J1230$-$1139 | 3.52 |  $>$43 | 51 | 14 | 7 | 0.42 | 0.33 | 0.36 | 0.47 | 0.35 | 0.38 | 0.47 | 0.41 | 0.43 | 0.44 | 0.24 | 0.25 | 0.41 | 0.36 | 0.37
J1242$+$3720 | 3.81 | 46 | 24 | 21 | 13 | 0.18 | 0.15 | 0.12 | 0.28 | 0.21 | 0.21 | 0.29 | 0.18 | 0.19 | 0.19 | 0.14 | 0.12 | 0.14 | 0.17 | 0.11
J1301$+$1904 | 3.10 | 35 | 13 | – | – | 0.25 | 0.21 | 0.21 | 0.05 | 0.12 | - | – | 0.06 | – | – | 0.15 | – | – | – | –
J1340$+$3754 | 3.11 | 36 | 12 | – | – | 0.08 | 0.11 | 0.12 | 0.3 | 0.17 | 0.17 | 0.15 | 0.1 | 0.09 | 0.03 | 0.11 | – | – | – | –
J1354$-$0206 | 3.70 | 38 | 60 | 23 | 33 | 0.22 | 0.16 | 0.16 | 0.24 | 0.13 | 0.12 | 0.14 | 0.09 | 0.09 | 0.3 | 0.16 | 0.1 | 0.50 | 0.24 | –
J1356$-$1101 | 3.1 | 35 | 9 | – | – | 0.21 | 0.2 | 0.22 | 0.11 | 0.1 | 0.11 | 0.32 | 0.29 | 0.32 | – | – | – | 0.19 | 0.25 | –
J1356$+$2918 | 3.24 | 35 | 7 | – | – | – | – | – | 0.22 | 0.19 | 0.19 | 0.02 | 0.1 | 0.04 | – | – | – | – | – | –
J1357$-$1744 | 3.14 | 38 | 19 | 23 | 3 | 0.37 | 0.26 | 0.25 | 0.28 | 0.12 | 0.12 | 0.27 | 0.21 | 0.22 | 0.36 | 0.39 | 0.44 | 0.48 | 0.55 | 0.63
J1401$+$1513 | 3.23 | 33 | 11 | – | – | – | 0.03 | – | 0.36 | 0.28 | 0.28 | – | 0.14 | – | 0.09 | 0.27 | 0.18 | – | – | –
J1405$+$0415 | 3.20 |  $>$43 | 26 | 24 | 12 | 0.23 | 0.18 | 0.18 | 0.25 | 0.16 | 0.16 | 0.2 | 0.12 | 0.11 | 0.19 | 0.17 | 0.14 | 0.26 | 0.3 | 0.25
J1411$+$4300 | 3.21 | 34 | 10 | – | – | 0.08 | 0.16 | 0.17 | 0.05 | 0.06 | – | 0.13 | 0.15 | 0.12 | 0.13 | 0.17 | 0.14 | – | – | –
J1413$+$3947 | 4.12 | 34 | 10 | – | – | 0.22 | 0.27 | 0.29 | 0.12 | 0.14 | – | 0.03 | 0.15 | – | 0.15 | 0.26 | 0.2 | – | – | –
J1413$+$4505 | 3.11 | 34 | 8 | $<1$ | 2 | – | – | – | 0.27 | 0.16 | 0.16 | 0.19 | 0.19 | 0.21 | 0.03 | 0.13 | 0.11 | 0.09 | 0.24 | –
J1418$+$4250 | 3.45 | 34 | 4 | – | – | – | – | – | 0.02 | 0.08 | – | – | – | – | – | – | – | – | – | –
J1421$-$0643 | 3.68 | 30 | 6 | – | – | 0.19 | 0.18 | 0.2 | 0.3 | 0.23 | 0.26 | 0.21 | 0.16 | 0.17 | – | – | – | – | – | –
J1424$+$2256 | 3.62 | 42 | 29 | 22 | 18 | 0.47 | 0.14 | 0.14 | 0.14 | 0.12 | 0.11 | 0.66 | 0.21 | 0.17 | 0.16 | 0.16 | 0.14 | 0.1 | 0.28 | 0.17
J1430$+$4204 | 4.71 | 34 | 16 | 2 | 4 | 0.4 | 0.31 | 0.32 | 0.51 | 0.43 | 0.44 | 0.4 | 0.29 | 0.3 | 0.36 | 0.3 | 0.31 | 0.32 | 0.29 | 0.32
J1445$+$0958 | 3.55 | 41 | 76 | 23 | 27 | 0.15 | 0.1 | 0.08 | 0.15 | 0.1 | 0.09 | 0.26 | 0.17 | 0.15 | 0.57 | 0.26 | 0.26 | 0.67 | 0.4 | 0.38
J1457$+$0519 | 3.17 | 37 | 12 | – | – | 0.1 | 0.17 | 0.16 | 0.13 | 0.13 | 0.08 | 0.19 | 0.2 | 0.17 | 0.05 | 0.17 | 0.05 | – | – | –
J1458$+$0855 | 3.6 | 34 | 7 | – | – | – | 0.35 | – | 0.2 | 0.21 | – | – | 0.06 | – | – | – | – | – | – | –
J1459$+$3253 | 3.32 | 39 | 11 | – | – | 0.04 | 0.16 | – | 0.23 | 0.17 | 0.07 | 0.08 | 0.19 | – | – | 0.22 | – | – | – | –
J1503$+$0419 | 3.66 | 39 | 8 | – | – | 0.03 | 0.04 | 0.03 | 0.1 | 0.08 | 0.07 | 0.04 | 0.03 | – | – | 0.01 | – | – | – | –
J1521$+$1756 | 3.6 | 40 | 13 | – | – | 0.21 | 0.17 | – | 0.32 | 0.23 | 0.23 | 0.18 | 0.17 | – | 0.1 | 0.15 | 0.11 | – | – | –
J1522$+$2119 | 3.22 | 34 | 10 | – | – | 0.18 | 0.17 | 0.18 | 0.13 | 0.1 | – | 0.09 | 0.18 | – | – | 0.18 | – | – | – | –
J1538$+$0019 | 3.49 |  $>$43 | 20 | 23 | 10 | 0.39 | 0.34 | 0.35 | 0.5 | 0.36 | 0.36 | 0.58 | 0.37 | 0.38 | 0.27 | 0.2 | 0.19 | 0.38 | 0.28 | 0.12
J1559$+$0304 | 3.89 | 37 | 63 | 8 | 29 | 0.25 | 0.19 | 0.21 | 0.41 | 0.16 | 0.16 | 0.17 | 0.13 | 0.12 | 0.18 | 0.15 | 0.13 | 0.36 | 0.22 | 0.19
J1606$+$3124 | 4.56 | 37 | 26 | 43 | 22 | 0.3 | 0.16 | 0.15 | 0.28 | 0.18 | 0.19 | 0.22 | 0.15 | 0.15 | 0.16 | 0.13 | 0.12 | 0.1 | 0.15 | 0.07
J1610$+$1811 | 3.11 | 40 | 12 | – | – | 0.23 | 0.18 | 0.18 | 0.41 | 0.31 | 0.31 | 0.17 | 0.18 | 0.08 | – | 0.23 | – | – | – | –
J1616$+$0459 | 3.21 |  $>$43 | 64 | 23 | 22 | – | 0.13 | 0.12 | 0.26 | 0.13 | 0.12 | 0.42 | 0.15 | 0.13 | 0.17 | 0.1 | 0.09 | 0.26 | 0.25 | 0.21
J1632$-$0033 | 3.42 | 31 | 57 | 5 | 6 | 0.25 | 0.2 | 0.2 | 0.43 | 0.22 | 0.2 | 0.17 | 0.12 | 0.11 | 0.4 | 0.2 | 0.12 | 0.4 | 0.43 | 0.44
J1655$+$3242 | 3.18 | 34 | 12 | – | – | 0.24 | 0.22 | 0.21 | 0.04 | 0.12 | – | – | 0.09 | – | – | 0.12 | – | – | – | –
J1655$+$1948 | 3.26 | 34 | 15 | – | – | 0.28 | 0.26 | 0.26 | 0.24 | 0.19 | 0.18 | 0.27 | 0.16 | 0.14 | 0.12 | 0.17 | 0.11 | – | – | –
J1658$-$0739 | 3.74 | 37 | 12 | 10 | 9 | 0.22 | 0.16 | 0.16 | 0.27 | 0.21 | 0.21 | 0.33 | 0.27 | 0.28 | 0.13 | 0.12 | 0.05 | 0.33 | 0.35 | 0.32
J1715$+$2145 | 4.1 | 35 | 16 | – | – | 0.47 | 0.24 | 0.24 | 0.38 | 0.3 | 0.31 | 0.19 | 0.14 | 0.11 | – | 0.08 | – | – | 0.18 | –
J1740$+$3500 | 3.22 | 34 | 18 | – | – | 0.29 | 0.22 | 0.21 | 0.02 | 0.08 | – | – | 0.11 | – | 0.27 | 0.19 | – | – | – | –
J1840$+$3900 | 3.1 | 36 | 23 | 20 | 13 | 0.24 | 0.22 | 0.18 | 0.52 | 0.41 | 0.42 | 0.14 | 0.16 | 0.15 | 0.45 | 0.34 | 0.33 | 0.52 | 0.51 | 0.48
J1939$-$1002 | 3.78 | 30 | 17 | 23 | 4 | 0.28 | 0.19 | 0.15 | 0.15 | 0.09 | 0.09 | 0.25 | 0.14 | 0.15 | 0.33 | 0.28 | 0.29 | 0.33 | 0.33 | 0.36
J2003$-$3251 | 3.77 |  $>$43 | 39 | 15 | 36 | 0.53 | 0.32 | 0.18 | 0.32 | 0.2 | 0.2 | 0.44 | 0.15 | 0.14 | 0.15 | 0.16 | 0.13 | 0.42 | 0.31 | 0.31
J2019$+$1127 | 3.27 | 41 | 12 | – | – | 0.06 | 0.12 | – | 0.06 | 0.09 | 0.04 | 0.05 | 0.23 | – | – | – | – | – | – | –
J2041$+$1855 | 3.5 | 39 | 12 | – | – | 0.01 | 0.07 | – | 0.18 | 0.16 | 0.15 | 0.11 | 0.22 | – | 0.17 | 0.24 | 0.27 | – | – | –
J2042$-$2223 | 3.63 | 30 | 4 | – | – | 0.01 | 0.01 | – | 0.27 | 0.25 | – | 0.24 | 0.19 | 0.22 | – | – | – | – | – | –
J2043$+$1255 | 3.27 | 40 | 12 | – | – | – | – | – | 0.52 | 0.42 | 0.43 | 0.09 | 0.11 | 0.1 | – | 0.08 | – | – | – | –
J2050$+$3127 | 3.18 | 35 | 15 | 12 | 60 | 0.19 | 0.14 | 0.11 | 0.57 | 0.22 | 0.21 | 0.32 | 0.16 | 0.15 | 0.27 | 0.17 | 0.13 | 0.34 | 0.23 | 0.12
J2129$-$1538 | 3.26 | 37 | 54 | 20 | 24 | 0.19 | 0.15 | 0.12 | 0.16 | 0.11 | 0.1 | 0.34 | 0.26 | 0.25 | 0.41 | 0.22 | 0.21 | 0.43 | 0.27 | 0.25
J2134$-$0419 | 4.34 | 31 | 12 | 14 | 3 | 0.21 | 0.15 | 0.14 | 0.12 | 0.09 | 0.08 | 0.13 | 0.12 | 0.11 | 0.19 | 0.21 | 0.2 | 0.05 | 0.14 | 0.11
J2217$+$0220 | 3.57 | 42 | 25 | 22 | 14 | 0.28 | 0.29 | 0.28 | 0.46 | 0.34 | 0.34 | 0.54 | 0.42 | 0.43 | 0.34 | 0.24 | 0.23 | 0.61 | 0.52 | 0.5
J2219$-$2719 | 3.63 | 30 | 12 | 14 | 5 | 0.19 | 0.17 | 0.16 | 0.3 | 0.19 | 0.19 | 0.31 | 0.22 | 0.22 | 0.34 | 0.22 | 0.21 | 0.3 | 0.28 | 0.28
J2225$+$2040 | 3.56 | 34 | 12 | – | – | 0.18 | 0.13 | 0.13 | 0.13 | 0.07 | – | 0.06 | 0.1 | – | 0.02 | 0.18 | – | – | – | –
J2248$-$0541 | 3.29 | 30 | 13 | 2 | 2 | 0.36 | 0.27 | 0.28 | 0.22 | 0.14 | 0.14 | 0.14 | 0.1 | 0.08 | – | – | – | 0.27 | 0.35 | 0.42
J2251$+$2217 | 3.66 | 35 | 56 | – | – | 0.13 | 0.14 | 0.14 | 0.27 | 0.2 | 0.17 | 0.15 | 0.14 | 0.12 | 0.34 | 0.17 | 0.13 | – | – | –
J2314$+$0201 | 4.11 | 40 | 20 | – | – | – | 0.1 | – | 0.2 | 0.17 | 0.14 | 0.14 | 0.16 | 0.08 | 0.15 | 0.24 | 0.14 | – | – | –
J2316$-$3349 | 3.10 | 31 | 18 | – | – | 0.65 | 0.29 | 0.22 | 0.18 | 0.1 | 0.1 | 0.45 | 0.28 | 0.28 | 0.26 | 0.2 | 0.19 | – | – | –
J2321$-$0827 | 3.16 | 31 | 10 | 13 | 4 | 0.48 | 0.34 | 0.36 | 0.63 | 0.55 | 0.25 | 0.33 | 0.28 | 0.29 | 0.13 | 0.2 | 0.22 | 0.42 | 0.45 | 0.51
J2344$+$3433 | 3.5 | 35 | 15 | – | – | 0.28 | 0.23 | 0.23 | 0.24 | 0.22 | 0.2 | 0.33 | 0.36 | 0.36 | 0.18 | 0.19 | – | – | 0.2 | –
Table 10: continued.

##  Appendix B Cluster analysis of the quasars with PCA+k-means and Self
Organizing Maps

We have a number of parameters that can potentially influence the obtained
variability properties. They concern both the actual properties of the source,
like the emission frequency $\nu_{\rm rest}$ or redshift $z$, and the
characteristics connected with the observing process: the number of
observations Nobs and monitoring duration for the rest frame $t_{\rm rest}$.

Thus, the dependencies may be multiparametric. To search for possible
tendencies in this case, a technique of cluster analysis can be implemented.
The main idea is to localize groups of similar objects in a multidimensional
parameter space (feature space) and investigate their statistical properties.
The measure of similarity in our case is the feature space Euclidean distance.

Our data are most complete for the observed frequency of 4.7 GHz, therefore we
took the corresponding characteristics. The Kendall correlation matrix for the
considered parameters is shown in Fig. 11. We can see an analytical dependence
between $\nu_{\rm rest}$ and $z$ (${\rm corr}=1$), some correlation between
$\nu_{\rm rest}$ and $t_{\rm rest}$ (${\rm corr}=-0.41$), caused by their
mutual dependence on $z$, and a weak dependence between Nobs and $V_{S_{4.7}}$
(${\rm corr}=0.24$).

Figure 11: Correlation matrix with Kendall correlation coefficients

As $\nu_{\rm rest}$ and redshift $z$ are analytically connected, they actually
provide the same information about an object, so one of the characteristics
can be omitted, we chose $\nu_{\rm rest}$ for our analysis. As a result, we
end up with a quite simple 4D feature space of $V_{S_{4.7}}$, $t_{\rm rest}$,
$\nu_{\rm rest}$, and Nobs. For modelling we took $\log{\rm N}_{\rm obs}$ due
to very uneven distribution of this parameter.

The next step is dimensionality reduction using the standard primary component
analysis (PCA). In this way we reduce “the curse of dimensionality,” get rid
of correlation between feature space axes, and simplify visualization of the
results. Hereafter, we used the scikit-learn (Pedregosa et al., 2011) library
for our calculations. The explained variance along the primary components
after the scaling and PCA transformation is as follows: $\sim\\!52$%, 29%,
13%, 6%, thus we can drop the last component, saving 94% of information and
transforming our problem to the clustering in a 3D space of the first three
primary components.

The clustering has been performed using the k-means algorithm (Arthur and
Vassilvitskii, 2007). The optimal number of clusters, five, was estimated
based on the “elbow method” implemented in the Yellowbrick library (Bengfort
and Bilbro, 2019). The results are presented in Fig. 12. In the left panel one
can see the clusters found by the k-means algorithm directly in the primary
component (PC) space. For clarity, at right we show a 2D representation of the
same figure. It has been obtained using t-distributed stochastic neighbor
embedding (t-SNE) (van der Maaten and Hinton, 2008). Although the t-SNE
algorithm is strongly dependent on its “perplexity” hyperparameter, here we
have a fairly good separation of the clusters at its default value ($=\\!30$).
Notice that we did not perform a separate clustering in the 2D coordinates,
the cluster labels in the two panels are exactly the same, so the
visualization demonstrates good accordance between the PC clustering and its
t-SNE representation. The groups look more localized in the t-SNE coordinates.

Figure 12: Left: clusters in the primary component (PC) coordinates; right: 2D
t-SNE representation of the left panel.

Having the quasars marked with cluster labels, we can consider the difference
in the distributions of our characteristics within different clusters. The
distributions are shown in Fig. 13 as box plots. The box is the interquartile
range (IQR, 25th to 75th percentile, or Q1 to Q3), the median is shown as a
vertical line inside the box, the “whiskers” extend to show the rest of the
distribution, except for points that are determined as “outliers,” locating
beyond the median $\pm$ 1.5 IQR range, these outliers are shown by dots. The
numerical values are given in Table 11.

Figure 13: Distributions of the considered characteristics for different clusters. Each panel corresponds to a certain characteristic, the $y$-axes show the cluster ordinal numbers. The distributions are shown as box plots, see description in the text.  Table 11: Cluster characteristics Cluster |  N |  | Medians |  | Min–max values
---|---|---|---|---|---
|  |  |  $t_{\rm rest}$ (yr) |  $V_{S_{4.7}}$ |  $\nu_{\rm rest}$ (GHz) |  Nobs |  $z$ |  |  $t_{\rm rest}$ (yr) |  $V_{S_{4.7}}$ |  $\nu_{\rm rest}$ (GHz) |  Nobs |  $z$
0 |  6 |  |  5.7 |  0.48 |  26.3 |  21 |  4.6 |  |  4.0–6.7 |  0.28–0.71 |  24.8–29.5 |  15–48 |  4.3–5.3
1 |  21 |  |  7.0 |  0.22 |  22.0 |  13 |  3.7 |  |  5.8–7.9 |  0.12–0.38 |  20.2–25.1 |  4–24 |  3.3–4.3
2 |  31 |  |  8.4 |  0.13 |  19.7 |  12 |  3.2 |  |  7.6–10.3 |  0.02–0.27 |  18.8–21.9 |  4–21 |  3.0–3.7
3 |  20 |  |  8.7 |  0.42 |  19.3 |  14 |  3.1 |  |  7.3–9.9 |  0.29-0.63 |  18.9–21.5 |  10–24 |  3.0–3.6
4 |  23 |  |  9.1 |  0.29 |  20.8 |  55 |  3.4 |  |  6.9–10.7 |  0.11–0.67 |  18.8–23.0 |  24–187 |  3.0–3.9

Considering the $V_{S_{4.7}}$ panel in Fig. 13, we can separate out clusters 0
and 3 as the quasar groups with highest variability. Remarkably, these are
very different groups if we look at their other characteristics.

The six quasars of cluster 0 are the most distant objects ($z\geq 4.3$),
respectively with the highest emission frequencies $\nu_{\rm rest}\geq 24.8$
GHz and the shortest time of monitoring in the rest frame $t_{\rm rest}<7$
years, which, together with an ordinary number of observations N${}_{\rm
obs}=15$–$48$, does not prevent them to have prominent variability
$V_{S_{4.7}}=0.28$–$0.71$.

At the same time, quasars of cluster 3 with similar variability indices
$V_{S_{4.7}}=0.29$–$0.63$ are at the lowest redshifts in our sample, mostly
within $z=3.0$–$3.3$, and, correspondingly, with low $\nu_{\rm rest}$, mostly
less than 21 GHz. They have standard N${}_{\rm obs}=10$–$24$, but a
sufficiently long $t_{\rm rest}$ of 7–10 years.

Quasars of cluster 2 are very similar to those of cluster 3, except they have
the “opposite” lowest variability indices within the sample,
$V_{S_{4.7}}=0.02$–$0.27$.

Quasars of the “moderate” cluster 1 at intermediate redshifts $z=3.3$–$4.3$
show characteristics in between the values for clusters 0–3.

Ultimately, the clustering algorithm separated out a special group of the most
observed quasars with N${}_{\rm obs}=24$–$187$. These quasars are at close or
intermediate redshifts $z\leq 3.9$ with long $t_{\rm rest}$ greater 7 years
and low-to-intermediate $\nu_{\rm rest}\leq 23$ GHz. Noteworthy that these
most monitored quasars do not generally show the highest variability indices,
which are nevertheless statistically higher than those for low-variable
cluster 2 and intermediate-variable cluster 1.

These results were double-checked with another method which used the Self
Organizing Maps (SOM) to reduce the dimensionality of the input data set with
a subsequent cluster analysis with k-means.

A Self Organizing Map (Kohonen, 2001) is a type of the artificial neural
network that is trained using unsupervised learning. The aim of a SOM is to
transform the multi-dimensional input data set to a low-dimensional output
space (usually two-dimensional map), performing the dimensionality reduction.
This transformation is made adaptively in a topologically ordered fashion.

The SOM neurons are placed in the nodes of a 2D lattice and, after their
weights are randomly initialised, tuned to the input data vectors during
epochs of competitive learning. The number of the learning epochs depends on
the input data set, the size of the output map, the manner of updating the
neighboring neuron weights and usually varies between 10 and 100.

After such tuning, the weights of the output neurons on the lattice become
ordered, and it is possible to create a coordinate system on this lattice for
the input data that we analyze. Thus, the SOM makes a topological map of the
input vectors. We can consider these as non-linear generalisation of the PCA
method mentioned above.

Figure 14: Comparison of the PCA+k-means clustering (upper left panel) with 5
runs of the SOM training (other panels).

There are several SOM libraries available, and in the current analysis we used
the Python module somoclu777 https://github.com/peterwittek/somoclu (Wittek et
al., 2017). We chose a SOM map size of $200\times 320$ neurons, and the number
of learning epochs was 50. The same set of parameters ($V_{S_{4.7}}$, $t_{\rm
rest}$, $\nu_{\rm rest}$, and $\log{\rm N}_{\rm obs}$) was included into the
input vectors, forming a 4D-parameter space.

After the SOM algorithm had finished the learning stage, the k-means method
was used to perform the clustering, assuming 5 clusters. We can assign a
particular cluster number to the input data vector based on the nearest neuron
in the lattice, looking for the “winner” neuron, minimizing the squared
Euclidean distance between the input vector and the weight vector of the
lattice neuron. The input vector will belong to the same cluster as the
“winner” neuron.

A comparison of the SOM results with those of the PCA+k-means method, given in
Fig. 14 using the t-SNE conditional coordinates, shows that different runs of
SOM training can give somewhat different borders of the clusters, but their
general structure sustains. The Rand index, which is commonly used to compare
two clusterings, varies for our five SOM training runs from 0.86 to 1, showing
in one case a perfect match between the two methods.

Thus, we can state that the SOM results generally correspond to PCA+k-means
(with an accuracy of about 85% based on the Rand indices range). For our
analysis we chose the latter, as a more straightforward, unambiguous, and
interpretable approach, also well corresponding to t-SNE.

##  Appendix C Comments on individual sources

###  C.1 Identified HFP/GPS/MPS candidates which revealed significant radio
variability

J0121$-$2806 is an FSRQ classified as PS in Mingaliev et al. (2013). We
calculated that the spectral peak is at 0.3 GHz (Sotnikova et al., 2021). Due
to the absence of radio data at frequencies from 0.2 to 1.4 GHz, the spectral
maximum can not be determined reliably. The quasar demonstrates high flux
density variability with $V_{S_{4.7}}=0.43$ and $V_{S_{8.2}}=0.32$. The
spectral index $\alpha_{\rm thin}$ was changing from -0.70 to -0.08, remaining
almost flat in 2014–2020.

J0203$+$1134 is an FSRQ known as a GPS source with a peak frequency of about
17 GHz in the rest frame (O’Dea et al., 1991). The RATAN-600 observations
confirm the peaked spectral shape in the time period of 2006–2020. However,
occasionally it shows an inverted spectrum (e.g., in 2001) and has been
classified as having chaotic variability (Gorshkov et al., 2012). The
variability indices $V_{S_{4.7}}$ and $V_{S_{22.3}}$, which have been measured
at a historical scale of 20–40 years, are 0.33 and 0.45 respectively. The
broadband spectra are well described by two components, linear at the observer
frequencies of 0.07–0.5 GHz and convex at higher frequencies.

J0324$-$2918 was considered as a PS source in Coppejans et al. (2017), where
authors estimated a possible spectral turnover between 1.4 GHz and 7 GHz. The
uncertainty of positioning the peak was caused by the scatter of the observed
flux densities around 5 GHz, where the AT20G and PMN surveys contributed with
different resolutions and at different epochs of observations. In our study we
clarified the 2.3–22.3 GHz part of the spectrum as being inverted using quasi-
simultaneous RATAN-600 measurements. Thus we see that the radio spectrum of
J0324$-$2918 has a complex structure: below 1 GHz it has a peaked shape, but
above it is inverted. We obtained significant variability (up to 45%) for the
source during our monitoring, which is in agreement with the conclusion in
Coppejans et al. (2016) that its VLBI emission is Doppler-boosted.

J0646$+$4451 is one of the brightest high-redshift PS blazars. The object is
known as a high-frequency peaker (Dallacasa et al., 2000; Tinti et al., 2005)
and has for the first time been considered as a GPS source in O’Dea (1990).
The quasar has a spectral peak around 17–18 GHz in the observer’s frame of
reference (Torniainen et al., 2005; Sotnikova et al., 2021). Flux variations
are observed on both sides of the peak (Fig. 21), and the variability index
reaches 0.70 at 5–8 GHz. We observed variable peaked spectra for the blazar
during 2006–2011. In 2017–2021 the quasar had flat and even rising spectra,
i.e., the spectrum became optically thick at the high frequencies more than 10
GHz, with $\alpha_{\rm thick}=+0.22$ and $+0.35$ in April and August 2020. Its
RATAN light curves show a slow flux density decrease about 1.5–2 times, from 4
to 1.5–2 Jy, at 4.7–22.3 GHz in 2012–2020. The steepest radio spectrum
$\alpha_{\rm thin}=-1.58$ was observed in 2011, when the flux density started
decreasing at 2.3–22.3 GHz, and the spectrum became optically thin at
frequencies above 5 GHz after several years of a relatively high state.

J1230$-$1139 is an FSRQ and has been classified as a GPS candidate in
Mingaliev et al. (2013). Low frequency data are well represented by the GLEAM
and TGSS surveys. The VLBA observations show a large jet bending ($\sim
90\degree$) within 2 mas from one bright radio component at 8.4 GHz (Zhang et
al., 2022). We have found the variability indices at 4.7 and 22.3 GHz equal to
0.47 and 0.41 on timescales of $>$43 and 14 years respectively. The RATAN-600
observational data covers the period of 2015–2020. The overall number of
observations N${}_{\rm obs}=51$ at 4.7 GHz.

J1340$+$3754 is an FSRQ (Healey et al., 2007) at $z=3.11$ with a core–jet
morphology (Paragi et al., 1999). It has been classified as a GPS candidate in
Mingaliev et al. (2013). Extended monitoring revealed variability up to 30% at
our frequencies.

J1354$-$0206 is a known GPS source and a blazar (O’Dea, 1990; O’Dea et al.,
1991) with a core–jet morphology (Plavin et al., 2022). It demonstrated the
maximum variability at 22.3 GHz $V_{S_{22.3}}=0.50$ on a time scale of 23 yrs.

J1357$-$1744 is a known GPS (O’Dea et al., 1991) with a core–jet morphology
(Plavin et al., 2022). It shows quite high flux density variation both at high
and low frequencies ($V_{S_{2.3}}=0.37$ and $V_{S_{22.3}}=0.48$).

J1445$+$0958 at $z=3.55$ has been classified as a GPS source by O’Dea et al.
(1991) and is also an FSRQ with the core–jet type of radio morphology
(Gobeille et al., 2014; Zhang et al., 2022). The compiled spectrum has a well-
constrained absorbed part with $\alpha_{\rm thick}=+0.68$ ($0.01$). A high
variability index $V_{S_{22.3}}=0.67$ was calculated using 27 observing epochs
during a time period of about 20 years. At lower frequencies the variability
has a smaller amplitude, $V_{S}=0.15$ at 2.3 and 4.7 GHz.

The quasar J1538$+$0019 was classified as a GPS source in Mingaliev et al.
(2013). It has flux density variation at 2.3–22.3 GHz in the range
$V_{S}=0.27$–0.58 on a timescale of up to 40 years (Drinkwater et al., 1997;
Bennett et al., 1986). Its observed peak frequency shifted from 3 to 1 GHz
during 2015–2020.

J1559$+$0304 at $z=3.89$ with a compact core and a two-sided jet at 5 and 8.4
GHz (Gobeille et al., 2014) was classified as a PS source with the peak
between 72 MHz and 1.4 GHz by Callingham et al. (2017). We have obtained a
greater value of the spectral peak $\nu_{\rm peak,obs}=4.5$ GHz and the
variability index $V_{S_{22.3}}=0.36$ on a timescale of eight years. The
highest variability is observed near the spectral peak, historical 37-year
data show $V_{S_{4.7}}=0.41$ (N $=63$). The spectral shape seems to remain
convex during the RATAN observations in 2015–2020. But since the beginning of
2019, the flux density has started to increase slowly at 22.3–4.7 GHz.

J1606$+$3124 is a radio galaxy at $z=4.56$ with a peak in the radio spectrum
at $\nu_{\rm peak,obs}=2.5$ GHz. The radio properties of J1606$+$3124 studied
in An et al. (2022); Zhang et al. (2022) suggest that it is a young radio
source, the highest-redshift GPS galaxy known to date. The peak frequency in
the source’s rest frame corresponds to 13.9 GHz. A two-sided jet structure is
revealed by VLBI at 8.4 GHz.

J1616$+$0459, an FSRQ at $z=3.21$, was classified as a GPS and HFP source in
O’Dea (1990); O’Dea et al. (1991); Dallacasa et al. (2000). Analysing its
compiled radio spectrum, we estimated $\nu_{\rm peak,obs}=4.4$ GHz.The
variability index $V_{S_{4.7}}=0.26$ on a timescale of more than 40 years (N
$=64$), and $V_{S_{22.3}}=0.26$ on the 23-year timescale (N $=22$). The
highest variability was found at 8.2 GHz, $V_{S_{8.2}}=0.42$.

J1658$-$0739 is an FSRQ (Healey et al., 2007) at $z=3.74$ with a core–jet
morphology (Plavin et al., 2022). It has been introduced as a GPS candidate
with $\nu_{\rm obs,peak}=4.8$ GHz in (Edwards and Tingay, 2004) based on the
VLA and ATCA data, but our study revealed variability of 13–33%, which casts
doubt that J1658$-$0739 is a canonical GPS source. Also its radio spectrum
suggests the presence of another extended emission at lower frequencies,
turning up below 200 MHz.

The FSRQ blazar J1840$+$3900 at $z=3.1$ was classified as an HFP source in
several papers (Marecki et al., 1999; Dallacasa et al., 2000; Torniainen et
al., 2008), but the compiled radio spectra demonstrate a high level of
variability ($V_{S}\sim 0.52$) at 4.7 and 22.3 GHz on a timescale of 36 years.
The RATAN radio spectra had rising shapes in July 2006 and July 2014 at
4.7–22.3 GHz ($\alpha_{\rm thin}=+0.22$ and $+0.34$). We conclude that
J1840$+$3900 was misclassified as a GPS/HFP source.

The core–jet FSRQ blazar J2003$-$3251 at $z=3.77$ was classified as a GPS and
HFP candidate (O’Dea et al., 1991; de Vries et al., 1997). We determined its
spectral peak $\nu_{\rm peak,obs}=5.6$ GHz. The quasar had been demonstrating
moderate variability $V_{S_{22.3}}=0.25$ up to 2019. Since 2019 its flux
density has started to increase from 0.42 to 0.85 mJy at 22.3 GHz and from
0.50 to 0.61 at 11.2 GHz, and radio variability has reached 42% at 22.3 GHz.
Further long-term radio observations are required to determine its variability
properties.

The quasar J2129$-$1538 at $z=3.26$ is a bright FSRQ blazar, one of the first
known high-redshift GPS sources (O’Dea, 1990; O’Dea et al., 1991). The quasar
was studied as an HFP candidate in Jeong et al. (2016), where its variability
was estimated over 1.5 years of observations (4–6 epochs) with modulation
indices of 9 and 22.5% at 22 and 43 GHz respectively; its radio spectrum was
reported as steep ($\alpha_{22-43\rm GHz}=-0.52$). Cheng et al. (2023)
reported typical well-aligned core–jet structure for J2129$-$1538 at 8, 15 and
43 GHz radio images. The RATAN-600 observations were made in 2012–2020 and
showed slow flux density rising at 4.7–22.3 GHz since 2017. The spectral index
$\alpha_{\rm thin}$ was changing from $-0.04$ up to $-0.83$ (by 88%). We
estimated its variability index to be 43% at 22.3 GHz using data of 20-years-
long observations.

Thus, as we have shown above, longer time periods of monitoring of blazars are
likely to reveal higher flux density variations.

###  C.2 New GPS/MPS candidates

The quasar J0006$+$1415 has a structure with an extended component of 10 mas
from the core (Paragi et al., 1999). Its radio spectrum at hundreds of MHz is
presented by the TGSS and mostly by the GLEAM measurements, which demonstrate
quite a scatter of flux densities, e.g., at 130–170 MHz the variations of flux
density reaches 100% (110–220 mJy). Considering that, in some states its radio
spectrum could be flat or steep. We obtained the low level of variability
indices, 0.03–0.25 at 2.3–11.2 GHz. However, the spectral indices $\alpha_{\rm
thick}=+0.02$ and $\alpha_{\rm thin}=-0.21$ make the spectrum close to flat,
with FWHM $=7.7$, and barely corresponding to the canonical GPS spectrum.

The quasar J0100$-$2708 with a core–jet angular structure (Plavin et al.,
2022) has not much information about its radio continuum properties in the
literature. It has a clear peaked shape (FWHM $=1.7$) in the radio spectra,
where the optically thin part, with $\alpha_{\rm thin}=-0.47\pm 0.01$, is
represented by seven epochs of RATAN-600 observations. The optically thick
part mostly consists of the GLEAM data ($\alpha_{\rm thick}=+0.41\pm 0.01$).
Both modulation and variability indices do not exceed a value of 0.20 at
2.3–11.2 GHz.

For J0214$+$0157 the GLEAM and TGSS data for the optically thick part together
with the RATAN-600 data for the optically thin part show a peaked spectrum
(FWHM $=1.9$) with $\nu_{\rm peak,obs}=0.5$ GHz. We note a significant scatter
in the measured flux densities (0.01–0.26 Jy) below 100 MHz, and $V_{S}=0.23$
at 2.3 GHz. At the frequencies 4.7–11.2 the variability index equals
0.03–0.23. Due to moderate radio variability and the spectral shape, we
suggest J0214$+$0157 as a new MPS candidate.

The core–jet (Krezinger et al., 2022) PS blazar of an uncertain type
J0525$-$3343 at $z=4.41$ has a spectral peak $\nu_{\rm peak,obs}=0.9$ GHz and
could be considered as an MPS candidate with the spectral indices $\alpha_{\rm
thick}=+0.43\pm 0.02$ and $\alpha_{\rm thin}=-0.96\pm 0.02$. But its radio
variability reaches 29–71 per cent at 2.3, 4.7, and 8.2 GHz on a time scale of
30 years. The highest variability is found at 4.7 GHz, the maximum flux
density S${}_{\rm max}=0.21$ Jy was measured in 1990 in the Parkes-MIT-NRAO
(PMN) survey at 4.85 GHz (Wright et al., 1996). In the NVSS survey at 1.4 GHz,
carried out several years later (Condon et al., 1998), the flux density is
0.188 mJy, which gives a rising non-simultaneous spectrum.

The megahertz-peaked spectrum core–jet blazar J0624$+$3856 (Plavin et al.,
2022) has a spectral peak $\nu_{\rm peak,obs}=0.3$ GHz and FWHM $=2.5$ dex.
The highest variability $V_{S}=0.43$ is found at 8.2 GHz on a timescale of 30
years.

We consider J0839$+$2002 as a new GPS candidate despite some deviation from
the criteria of genuine GPS sources. The low-frequency spectral part is poorly
represented by a single TGSS measurement at 150 MHz (Intema et al., 2017). The
averaged spectral indices of the optically thick and thin parts are $+0.36\pm
0.01$ and $-0.25\pm 0.01$. The variability indices are 0.05, 0.21, 0.15, and
0.29 at 22.3, 11.2, 8.2, and 4.7 GHz respectively.

The core–jet quasar J0905$+$0410 was detected in X-rays (Brinkmann et al.,
1995), its radio structure has an extension of 10 mas (Paragi et al., 1999).
Its radio spectrum has a clear peak around $\nu_{\rm obs}\sim 0.5$ GHz with
the spectral indices $\alpha_{\rm thick}=+0.57\pm 0.06$ and $\alpha_{\rm
thin}=-0.53\pm 0.01$. The variation of flux densities is $V_{S}=0.04$–$0.17$
at 2.3–11.2 GHz (Table LABEL:TableA2). We suggest J0905$+$0410 as the second
new MPS candidate in the sample.

The next new GPS candidate J0933$+$2845 with narrow absorption lines (Muñoz et
al., 2003) is detected in X-rays, but its structure is unresolved (Snios et
al., 2021); in the radio band it has an extended structure (Gobeille et al.,
2014). Its radio spectrum has a clear peak at $\nu_{\rm peak,obs}\sim 1.7$
GHz. There is a lack of measurements for the optically thick part
($\alpha_{\rm thick}=+0.17\pm 0.02$), we rely on only one measurement point at
150 MHz from the TGSS. At frequencies higher than 2.3 GHz we calculated flux
densities variability in the range $V_{S}=0.21$–$0.34$.

The source J1045$+$3142 is classified as having an unresolved core morphology
(Gobeille et al., 2014) and features a clear peak in its radio spectrum at 0.9
GHz with moderate variability at 2.3 and 8.2 GHz. We suggest the quasar as a
new MPS candidate, although the optically thick spectral part ($\alpha_{\rm
thick}=+0.25\pm 0.03$) is represented by only three radio measurements
(Rengelink et al., 1997; Riley et al., 1999; Intema et al., 2017).

For the core–jet quasar J1301$+$1904 we calculated moderate and negligible
variabilities at frequencies of 2.3, 4.7, 8.2, and 11.2 GHz (Table
LABEL:TableA2) and a peaked spectrum with $\nu_{\rm peak,obs}\sim 1.7$ GHz.
The low-frequency spectral part is represented by only single measurement at
150 MHz (TGSS) with $\alpha_{\rm thin}=+0.13\pm 0.01$.

A new GPS candidate J1401$+$1513 has the optically thick spectral part close
to flat, $\alpha_{\rm thick}=+0.05\pm 0.01$, and the variability indices are
0.09 and 0.36 at 11.2 and 4.7 GHz ($t_{4.7}=33$ years). The low-frequency
spectral part, poorly represented by a single TGSS measurement, should be
determined more precisely.

The PS blazar (Healey et al., 2007) J1405$+$0415 has a compact core and a
resolved jet extending to 18 mas (Liu and Zhang, 2002; Yang et al., 2006;
Dodson et al., 2008). Its radio spectrum is composed of several components:
steep below 1 GHz, curved with a peak between 1 and 10 GHz, steep from 10 to
110 GHz, and inverted above 110 GHz. The quasar has moderate variability
indices ranging from 0.19 to 0.26 at the radio frequencies.

A new MPS candidate J1418$+$4250 has $\nu_{\rm peak,obs}\sim 0.9$ GHz, two
measurements below the peak (325 and 408 MHz), and measurements at five
frequencies above it. More long-term observations would be complementary, both
for peak frequency clarification and variability estimation. To estimate the
variability for the time being, we used a frequency of 4.7 GHz and obtained
$V_{S_{4.7}}=0.02$ on a timescale of 34 years, based however only on three
measurements of Green Bank in April and October 1987 (4.85 GHz) and RATAN-600
in July 2020 (4.7 GHz). The flux density varies insignificantly from 0.047 and
0.048 Jy to 0.054 Jy, which is within the measurement uncertainties
(0.006–0.009 Jy).

The new GPS candidate J1521$+$1756 has a spectral peak at 3.5 GHz, the
variability indices are 0.10, 0.18, and 0.32 at 11.2, 8.2, and 4.7 GHz on a
timescale $t_{4.7}=40$ years (Table LABEL:TableA2). The VLA images at 1.4 GHz
show an unresolved core morphology (Gobeille et al., 2014).

The quasar J2019$+$1127 should be treated carefully because it is associated
with the gravitationally lensed system MG B2016$+$112 consisting of three
components (Lawrence et al., 1984): a doubly imaged core and a counter–jet
quadruply imaged at higher resolution (More et al., 2009). The lensed radio
images of the object can not be resolved by RATAN-600. Its radio spectrum has
a complex structure below the peak frequency, caused either by the several
emission components or by the variability of the source.

J2314$+$0201 is a new GPS source of X-ray emission (Wu et al., 2013; Zhu et
al., 2019). We estimated the variability indices
$V_{S_{4.7-11.2}}=0.14$–$0.20$. Its radio spectrum has a peak, however there
is a lack of measurements in the optically thick spectral part, and we rely
only on one measurement point at 150 MHz from the TGSS.

###  C.3 Gravitationally lensed quasars

The lensing galaxy at $z=1.145$ (Lagattuta et al., 2010) creates four images
of the quasar J0131$+$4358 with a maximum image separation of $0.54^{\second}$
(Phillips et al., 2000). The quasar J0751$+$2716 is lensed by a galaxy at
$z=0.35$ (Tonry and Kochanek, 1999) into four images separated by
$0.8^{\second}$ (Lehar et al., 1997). J1401$+$1513 is a unique sextuple system
with a maximum angular separation between the quasar images of about
$1.7^{\second}$, the lensing group of three galaxies are located at $z\sim 1$
(Rusin et al., 2001). The quadruple images of J1424$+$2256, created by a
lensing galaxy at $z=0.34$ (Tonry, 1998), have a maximum separation of
$1.3^{\second}$ (Patnaik et al., 1992; Mao and Schneider, 1998). The lensing
galaxy located at $z=1.165$ (Ofek et al., 2006) creates a triple image of
J1632$-$0033 separated by about $1.5^{\second}$, according to the VLA
observations at 43 GHz (Winn et al., 2002, 2004). J2019$+$1127 is a narrow-
line Seyfert 1 galaxy, reviewed in Section 4.3 as a new MPS candidate. The
separation between three of its components is $3.4^{\second}$ (Lawrence et
al., 1984). Based on our results, the radio variability properties of the
lensed quasars show no peculiarities compared to other quasars.

##  Appendix D Light curves and radio spectra

Figure 15: The RATAN-600 light curves, the measurements at 22.3 GHz are
colored by orange, at 11.2 GHz by magenta, at 8.2 GHz by green, at 4.7 GHz by
blue.

Figure 16: The RATAN-600 light curves, the measurements at 22.3 GHz are
colored by orange, at 11.2 GHz by magenta, at 8.2 GHz by green, at 4.7 GHz by
blue.

Figure 17: The RATAN-600 light curves, the measurements at 22.3 GHz are
colored by orange, at 11.2 GHz by magenta, at 8.2 GHz by green, at 4.7 GHz by
blue.

Figure 18: The RATAN-600 light curves, the measurements at 22.3 GHz are
colored by orange, at 11.2 GHz by magenta, at 8.2 GHz by green, at 4.7 GHz by
blue.

Figure 19: The RATAN-600 light curves, the measurements at 22.3 GHz are