High-Redshift Quasars at z ≥ 3: Radio Variability and MPS/GPS Candidates

Abstract

We present a study of the radio variability of bright, $S_{1.4}\ge 100$ mJy, high-redshift quasars at $z\ge 3$ on timescales of up to 30–40 yrs. The study involved simultaneous RATAN-600 measurements at the 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 from 0.25 to 0.50, which is 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 the cluster analysis of quasars. We propose seven new candidates for gigahertz-peaked spectrum (GPS) sources and five new megahertz-peaked spectrum (MPS) sources based on their spectrum shape and variability features. Only 6 out of the 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.

1. Introduction

Quasars [1] are highly variable celestial objects [2] that emit radiation across the electromagnetic spectrum. In the radio band, their variability [3,4] is often attributed to the presence of outflows or jets that emanate from the central region of a galaxy [5]. These jets can exhibit a range of behaviors, including propagating shocks (e.g., [6,7]), precession (e.g., [8,9]), bending (e.g., [10]), and interaction with gas clouds (e.g., [11]). In addition, several other phenomena may contribute to the observed flux density fluctuations in quasars, such as accretion disk instabilities (e.g., [12,13]), interstellar scintillation (e.g., [14,15]), and lensing by the ionized structures (e.g., [16,17]).

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 [18,19,20]. The peaked-spectrum sources are classified as high-frequency peakers (HFPs) as well as megahertz- and gigahertz-peaked spectrum (MPS and GPS) sources [21,22,23] 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 [24,25,26]. Some other GPS sources exhibit intermittent and short-lived radio emission, offering insights into the dynamic nature of quasars and AGN evolution [27]. Coppejans et al. [28] proposed to search for high-redshift ($z>2$) sources by identifying the MPS sources that are compact on scales of tens of milliarcseconds; though later Coppejans et al. [29] 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 $z\ge 3$ quasars, we found that almost half of the sample can be classified as PS sources, either GPS or MPS [30]. 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., [31,32,33,34,35,36,37,38]), 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 [39]. 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., [38,40,41]). 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.

The VLBI studies of high-redshift quasars reveal two major morphological patterns: a core-jet structure, indicative of the 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 [21,22,23]).

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 $z\ge 3$ 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 the available literature data. Utilising the dataset compiled by Sotnikova et al. [30], 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 [42]) in the declination range from −34° to +49° with the flux density $S_{1.4}\ge 100$ mJy and with redshifts $z\ge 3$. 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).1 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 min 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 [30]. The parameters of the receivers are shown in

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.

${\mathit{f}}_0$	$\mathbf{\Delta }{\mathit{f}}_0$	$\mathbf{\Delta }\mathit{F}$	FWHMRA	FWHMDec
(GHz)	(GHz)	(mJy/beam)	(arcmin)	(arcmin)
$22.3$	$2.5$	50	$0.\prime 17$	$1.\prime 6$
$11.2$	$1.4$	15	$0.\prime 34$	$3.\prime 2$
$8.2$	$1.0$	10	$0.\prime 47$	$4.\prime 4$
$4.7$	$0.6$	8	$0.\prime 81$	$7.\prime 6$
$2.3$	$0.08$	40	$1.\prime 71$	$15.\prime 8$
$1.2$	$0.08$	200	$3.\prime 07$	$27.\prime 2$

. The detection limit for a RATAN-600 single sector is approximately 5 mJy at 4.7 GHz (integration time is about 3 s) under good conditions and at the average antenna elevation angle ($\mathrm{Dec}$∼$0^{\circ }$).

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,2 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 ${\alpha }_{\mathrm{low}}$ and ${\alpha }_{\mathrm{high}}$ as they were defined in [30]. For peaked and upturn spectra, ${\alpha }_{\mathrm{low}}$ and ${\alpha }_{\mathrm{high}}$ 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 the spectral types, the low-frequency spectral index is calculated using decimetre-wavelength measurements, such as Giant Metrewave Radio Telescope Sky Survey (TGSS [43]), GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM [44]), or Westerbork Northern Sky Survey (WENSS [45]). The high-frequency spectral index is estimated using centimetre catalogue data points. A spectrum is considered flat if the spectral index is $-0.5\le \alpha \le 0$, 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 $\alpha \le -1.1$, respectively.

The list of the sources and their characteristics are presented in

Table A1. 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 ${\alpha }_{\mathrm{low}}$ and ${\alpha }_{\mathrm{high}}$ (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 [30]. 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	${\mathit{S}}_{4.7}$	Morph.	Morph.	${\mathit{\alpha }}_{\mathbf{low}}$	${\mathit{\alpha }}_{\mathbf{high}}$	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+435812 a	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+271631 a	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	4 c	$+0.07\pm 0.01$	$+0.07\pm 0.01$	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	4 c	$-0.28\pm 0.01$	$-0.28\pm 0.01$	flat	FSRQ	2
093337+284532	3.42	$0.05\pm 0.01$	E	4 c	$+0.17\pm 0.02$	$-0.67\pm 0.01$	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	4 c	$-0.08\pm 0.01$	$-0.27\pm 0.01$	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	4 c	$+0.25\pm 0.03$	$-0.56\pm 0.01$	peaked		2
110147+001038	3.69	$0.06\pm 0.01$	c	4 c	$-0.74\pm 0.01$	$-0.78\pm 0.01$	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	4 c	$-0.46\pm 0.01$	$-0.46\pm 0.01$	flat		2
115016+433206	3.03	$0.11\pm 0.01$	c	4 c	$+0.01\pm 0.01$	$+0.01\pm 0.01$	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	4 c	$+0.26\pm 0.01$	$-0.30\pm 0.01$	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	4 c	$-0.57\pm 0.01$	$-0.57\pm 0.01$	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+151325 a	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	4 c	$+0.01\pm 0.01$	$-0.43\pm 0.01$	peaked *	FSRQ	4
141152+430024	3.21	$0.09\pm 0.01$	c+j	4 c	$-0.21\pm 0.01$	$-0.21\pm 0.01$	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	4 c	$+0.04\pm 0.01$	$+0.04\pm 0.01$	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+225600 a	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	4 c	$-0.67\pm 0.01$	$-0.85\pm 0.01$	steep		2
150328+041949	3.66	$0.19\pm 0.01$	c+ext b	1	$+0.21\pm 0.01$	$-0.29\pm 0.01$	peaked		2
152117+175601	3.06	$0.13\pm 0.01$	c	4 c	$+0.40\pm 0.03$	$-0.87\pm 0.01$	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	4 c	$+0.11\pm 0.01$	$-0.43\pm 0.01$	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	4 c	$-0.25\pm 0.01$	$-0.79\pm 0.02$	steep		3
161637+045932	3.21	$1.03\pm 0.04$	c+j	4 c	$+0.64\pm 0.01$	$-0.56\pm 0.01$	peaked *	FSRQ	4
163257−003321 a	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	4 c	$-0.10\pm 0.01$	$-0.36\pm 0.01$	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+112712 a	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 [116]. ^c VLA measurements. * sources with two components in the radio spectrum. 5—[62], 6—[102], 7—[103], 8—[99], 9—[129], 10—[100], 11—[104].

: 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 [30]; 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”,3 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 [46]. It contains the blazars from the Roma-BZCAT catalogue [47], 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 [30], we have excluded the source J1600+0412 (87 GB 155733.8+042120). J1600+0412 has $z=0.79$ in the latest data release of the Sloan Digital Sky Survey [48,49], but, previously, its redshift was miscalculated as $z=3.11$ [50].

There are six gravitationally lensed quasars in the sample.4 Their structure is unresolved by RATAN-600 because the maximum separations between them are in the range of 0.54″–3.4″, which is less than the angular resolution at any RATAN-600 frequency. The notes for them are given in Appendix C.3.

The Literature Data

The literature data and their use in our study have been previously described in detail in [30]. The vast majority of the external radio continuum measurements were obtained from the astrophysical CATalogs support System (CATS database,5 [51,52]). These data allow us to estimate the radio flux variability over a time period of up to 30–40 yrs 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 yrs of observing coverage, and 78 out of 101 have more than 10 radio measurements at 4.7 GHz (

Table A2. 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.

Name	z	${\mathit{t}}_{4.7}$	N4.7	${\mathit{t}}_{22.3}$	N22.3	${\mathit{V}}_{{\mathit{S}}_{2.3}}$	${\mathit{M}}_{2.3}$	${\mathit{F}}_{2.3}$	${\mathit{V}}_{{\mathit{S}}_{4.7}}$	${\mathit{M}}_{4.7}$	${\mathit{F}}_{4.7}$	${\mathit{V}}_{{\mathit{S}}_{8.2}}$	${\mathit{M}}_{8.2}$	${\mathit{F}}_{8.2}$	${\mathit{V}}_{{\mathit{S}}_{11.2}}$	${\mathit{M}}_{11.2}$	${\mathit{F}}_{11.2}$	${\mathit{V}}_{{\mathit{S}}_{22.3}}$	${\mathit{M}}_{22.3}$	${\mathit{F}}_{22.3}$
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	–

). The median values of the number of measurements (N_obs) 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. The number of quasars (N) observed at 4.7 and 22.3 GHz with the median values of observed epochs N_obs and monitoring timescales in the observer’s ($t_{\mathrm{obs}}$) and source’s ($t_{\mathrm{rest}}$) frames of reference in yrs.

Frequency	N	Nobs	${\mathit{t}}_{\mathbf{obs}}$	${\mathit{t}}_{\mathbf{rest}}$
(GHz)			(yrs)	(yrs)
4.7	101	16	35	8
22.3	52	9	14	3

). In our study, we define the timescale of radio monitoring in the rest frame as $t_{\mathrm{rest}}=t_{\mathrm{obs}}/(1+z)$; if not specified, the timescale is used in the observer’s frame of reference.

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 [53]:

$$V_S=\frac{(S_{\max }-{\sigma }_{S_{\max }})-(S_{\min }+{\sigma }_{S_{\min }})}{(S_{\max }-{\sigma }_{S_{\max }})+(S_{\min }+{\sigma }_{S_{\min }})}$$

(1)

where $S_{\max }$ and $S_{\min }$ are the maximum and minimum flux densities over all epochs of observations; ${\sigma }_{S_{\max }}$ and ${\sigma }_{S_{\min }}$ 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 $\overline{S}$, was calculated as in [54]:

$$M=\frac{{\sigma }_S}{\overline{S}}$$

(2)

The fractional variability $F_S$ is defined as in [55]:

$$F_S=\sqrt{\frac{V^2-{\overline{\sigma }}_{err}^2}{{\overline{S}}^2}}$$

(3)

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

$$△F_S=\sqrt{{\left(\sqrt{\frac{1}{2N}}\frac{{\overline{\sigma }}_{err}^2}{F_S\ast {\overline{S}}^2}\right)}^2+{\left(\sqrt{\frac{{\overline{\sigma }}_{err}^2}{N}}\frac{1}{\overline{S}}\right)}^2}$$

(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 Figure 1. At 1.2 GHz, we did not obtain a sufficient number of measurements to estimate the variability. Table A2 lists these parameters for each quasar, while their statistics are given in

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 ± 0.09	0.01	0.53
$V_{S_{2.3}}$	87	0.23	0.25 ± 0.15	0.01	0.86
$F_{S_{2.3}}$	80	0.20	0.21± 0.09	0.03	0.59
$M_{4.7}$	101	0.17	0.20 ± 0.11	0.05	0.62
$V_{S_{4.7}}$	101	0.27	0.28 ± 0.15	0.02	0.71
$F_{S_{4.7}}$	90	0.17	0.20 ± 0.12	0.01	0.66
$M_{8.2}$	100	0.17	0.21 ± 0.12	0.03	1.00
$V_{S_{8.2}}$	95	0.23	0.27 ± 0.17	0.02	0.96
$F_{S_{8.2}}$	84	0.17	0.21 ± 0.14	0.04	0.97
$M_{11.2}$	92	0.17	0.18 ± 0.09	0.01	0.57
$V_{S_{11.2}}$	77	0.18	0.21 ± 0.14	0.02	0.66
$F_{S_{11.2}}$	66	0.14	0.17 ± 0.11	0.05	0.63
$M_{22.3}$	55	0.28	0.30 ± 0.13	0.09	0.68
$V_{S_{22.3}}$	51	0.36	0.35 ± 0.18	0.04	0.68
$F_{S_{22.3}}$	45	0.31	0.31 ± 0.15	0.05	0.72

. The negative variability indices have been excluded from the calculation and distribution diagrams.

The light curves of the quasars obtained with RATAN-600 are presented in Appendix D. For the PS candidates, we included additional RATAN-600 measurements of 2006–2017 from [35,37]. Their radio spectra, compiled using both the RATAN-600 and CATS radio data, are also presented in Appendix D.

The number of observing epochs N_obs and the timescale t play a key role in exploring the 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 [56,57,58]. This finding is verified by our observations, i.e., we found a correlation between N_obs and the variability index at 4.7 GHz with Pearson’s $r=0.35$, p-value $<{10}^{-3}$ (Figure 2). The observations of quasars in our sample are not homogeneous and differ in timescales (see the parameters $t_{4.7}$ and N_4.7 in Table A2), affecting the revealed variability level. The largest number of observations at 4.7 GHz is N_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 Figure 1). Both these parameters are suitable for a large number of observations N_obs; 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 the variability index and fractional variability.

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 emissions 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 [59], so they are smoothed out during RATAN-600 observations due to the relatively long scan time of 3–5 min 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 [60]. 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 us 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° to +49°). According to [14], the transition frequency ${\nu }_0$ separating the 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 [14]: $m={\left(\frac{{\nu }_0}{\nu }\right)}^{17/12}{\left(\frac{{\theta }_F}{{\theta }_{\mathrm{s}}}\right)}^{7/6}$, $t=\frac{1}{12}\sqrt{\frac{{\nu }_0}{\nu }}\frac{{\theta }_{\mathrm{s}}}{{\theta }_F}$ (days), where ${\theta }_F={\theta }_{F0}\sqrt{\frac{{\nu }_0}{\nu }}$ is the size of the first Fresnel zone at the frequency $\nu$, and ${\theta }_{\mathrm{s}}$ is the source’s angular size. Equations in the strong mode are according to [14]: $m={\left(\frac{\nu }{{\nu }_0}\right)}^{17/30}{\left(\frac{{\theta }_r}{{\theta }_{\mathrm{s}}}\right)}^{7/6}$, $t=\frac{1}{12}{\left(\frac{{\nu }_0}{\nu }\right)}^{\frac{11}{5}}\frac{{\theta }_{\mathrm{s}}}{{\theta }_r}$ (days), where ${\theta }_r={\theta }_{F0}{\left(\frac{{\nu }_0}{\nu }\right)}^{\frac{11}{5}}$. We estimated an angular size as ${\theta }_{\mathrm{s}}=5\times {\theta }_{\min }$, where ${\theta }_{\min }=0.6\sqrt{S}/\nu$ is the minimum angular size for the stationary source of synchrotron radiation [61], 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. RISS modulation and its typical timescale estimates for RATAN-600 frequencies at the transitional frequencies of between 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, $\mathit{var}\le 5\%$	N, $5\%<\mathit{var}\le 10\%$
(GHz)	(mas)	(%)	days	(%)	days	${\mathit{V}}_{\mathit{S}}/{\mathit{F}}_{\mathit{S}}$	${\mathit{V}}_{\mathit{S}}/{\mathit{F}}_{\mathit{S}}$
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

. 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 contributes insignificantly to the overall variability for most of these objects, except for a few individual cases where the variability reaches ≤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° < b < +15°: 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).

3.3. Variability Characteristics

We computed the variability amplitudes at certain observing frequencies. They correspond to different rest frame frequencies (Figure 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 (Figure 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 a fairly wide scatter of the variability index throughout all the range of 9–130 GHz rest frame emission frequencies (Figure 4). Those emission frequencies are all associated with the dominating core component. There are no trends in the $V_S$ to ${\nu }_{\mathrm{rest}}$ relation, confirmed by Pearson’s r = 0.12 (p-value = 0.02).

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 ∼0.40 (

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	${\mathit{F}}_{{\mathit{S}}_{2.3}}$	N4.7	${\mathit{F}}_{{\mathit{S}}_{4.7}}$	N8.2	${\mathit{F}}_{{\mathit{S}}_{8.2}}$	N11.2	${\mathit{F}}_{{\mathit{S}}_{11.2}}$	N22.3	${\mathit{F}}_{{\mathit{S}}_{22.3}}$
peaked	41	0.19 ± 0.08	43	0.19 ± 0.12	41	0.18 ± 0.10	31	0.18 ± 0.09	23	0.28 ± 0.13
flat	20	0.22 ± 0.09	22	0.20 ± 0.11	22	0.21 ± 0.19	20	0.14 ± 0.09	10	0.38 ± 0.17
steep	9	0.20 ± 0.04	10	0.21 ± 0.12	1	0.50	4	0.35 ± 0.19	7	0.17 ± 0.13
inverted	5	0.32 ± 0.17	8	0.20 ± 0.13	8	0.28 ± 0.05	6	0.11 ± 0.04	6	0.24 ± 0.12
upturn	1	0.46	2	0.24 ± 0.11	2	0.38 ± 0.38	1	0.17	2	0.29 ± 0.09
complex	4	0.16 ± 0.03	5	0.18 ± 0.08	4	0.21 ± 0.09	4	0.17 ± 0.09	3	0.32 ± 0.17
	N2.3	${\mathit{V}}_{{\mathit{S}}_{\mathbf{2}.\mathbf{3}}}$	N4.7	${\mathit{V}}_{{\mathit{S}}_{\mathbf{4}.\mathbf{7}}}$	N8.2	${\mathit{V}}_{{\mathit{S}}_{\mathbf{8}.\mathbf{2}}}$	N11.2	${\mathit{V}}_{{\mathit{S}}_{\mathbf{11}.\mathbf{2}}}$	N22.3	${\mathit{V}}_{{\mathit{S}}_{\mathbf{22}.\mathbf{3}}}$
peaked	43	0.26 ± 0.14	47	0.28 ± 0.16	44	0.28 ± 0.17	38	0.23 ± 0.16	25	0.37 ± 0.16
flat	20	0.27 ± 0.18	24	0.30 ± 0.16	24	0.25 ± 0.19	21	0.18 ± 0.11	12	0.34 ± 0.21
steep	12	0.20 ± 0.14	15	0.23 ± 0.14	12	0.17 ± 0.14	6	0.27 ± 0.15	1	0.61
inverted	7	0.26 ± 0.16	8	0.26 ± 0.13	8	0.36 ± 0.08	6	0.18 ± 0.13	8	0.23 ± 0.17
upturn	1	0.53	2	0.35 ± 0.17	2	0.38 ± 0.35	2	0.14 ± 0.13	2	0.46 ± 0.15
complex	4	0.21 ± 0.05	5	0.32 ± 0.13	5	0.29 ± 0.11	4	0.27 ± 0.12	3	0.40 ± 0.12

). The maximum variability is observed in sources with flat, peaked, and complex spectra. The 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, which are almost comparable to that at smaller redshifts (Figure 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 of $t_{\mathrm{rest}}$∼5–10 yrs. The variability index varies from 0.12, which was obtained for the bright VLBI quasar [62] J2134−0419 ($z=4.34$, N_obs = 18, $t_{\mathrm{rest}}$∼6 yrs), to 0.71 for the peaked spectrum blazar J0525−3343 ($z=4.41$, N_obs = 12, at $t_{\mathrm{rest}}$∼5.5 yrs) with an unresolved or slightly resolved core-jet structure in VLBI images [62]. The most distant blazar in the sample ($z=5.28$), J1026+2542 with a one-sided jet morphology [63], has a well-determined peaked spectrum and a variability index of 0.30 over $t_{\mathrm{rest}}$∼$3.9$ yrs. However, even on a scale of 6–10 yrs in the rest frame there are about 10% of quasars with $V_{S_{4.7}}<0.10$ (Figure 6). Among them, about one third are PS quasars.

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 ${\alpha }_{\mathrm{high}}$ and ${\alpha }_{\mathrm{low}}$ in terms of the Pearson and Spearman correlation coefficients. Such a 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, [70,71]. 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 [30]. On a long time scale, these PS blazars demonstrate high radio variability (0.25–0.75) near the peak frequency. In Figure 7, the “$\alpha$–$V_S$” plane is divided into four quadrants: steep spectra with $V_S>0.25$ and <0.25, and 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 an increasing flux density at high frequencies before moving to the steep spectrum area after the flare, when the 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 ${\alpha }_{\mathrm{high}}$ = −0.62. During the 17 years of RATAN-600 observations (Figure 8), its spectral index ${\alpha }_{\mathrm{high}}$ 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 ${\alpha }_{\mathrm{high}}$ and the flux density at 11.2 GHz, Pearson’s $r=0.81$, p-value $<{10}^{-3}$ (Figure 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 a significant correlation (Pearson’s $r>0.5$, p-value ≪ 0.005) between the spectral index ${\alpha }_{\mathrm{high}}$ 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, the changes in the spectral index are predominantly driven by a 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.

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 $t_{\mathrm{rest}}$, the frequency ${\nu }_{\mathrm{rest}}$, and the number of measurements N_obs should be taken into account to compare variability at different z [72,73]. 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 the PCA dimensionality reduction with k-means clustering, the second is based on the self-organizing maps [74,75]. 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 A3. Cluster characteristics.

Cluster	N	Medians					Min–Max Values
		${\mathit{t}}_{\mathrm{rest}}$ (yr)	${\mathit{V}}_{{\mathit{S}}_{\mathbf{4}.\mathbf{7}}}$	${\mathit{\nu }}_{\mathrm{rest}}$ (GHz)	Nobs	$\mathit{z}$	${\mathit{t}}_{\mathrm{rest}}$ (yr)	${\mathit{V}}_{{\mathit{S}}_{\mathbf{4}.\mathbf{7}}}$	${\mathit{\nu }}_{\mathrm{rest}}$ (GHz)	Nobs	$\mathit{z}$
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

, 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 $t_{\mathrm{rest}}=5.7$ yrs. The clustering algorithm also determined a group of the most observed quasars with $N_{\mathrm{obs}}=24$–187. These quasars are at intermediate $z\le 3.9$ with long $t_{\mathrm{rest}}>7$ 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 $N_{\mathrm{obs}}$ and $t_{\mathrm{rest}}$.

4. Peaked-Spectrum Sources at High Redshifts

Peaked spectrum quasars make up half of our sample Sotnikova et al. [30]. 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 the 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., [36,37,76,77]. It is commonly believed that the mechanism that 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 [78]. 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 [79]. 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 [26,80], or their compact nature could be a result of confinement through interaction with a dense environment [81,82,83,84,85], or the sources might be recurrent or intermittent sources [26,86,87,88,89].

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 [34,90]. The 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 [22,28].

To search for GPS/MPS sources, we employ the following common criteria: the observed peak frequency ${\nu }_{\mathrm{obs},\mathrm{peak}}$ is less than 1 GHz for MPS sources and from 1 up to 5 GHz for GPS sources; spectral indices of optically thick ${\alpha }_{\mathrm{thick}}$ and thin ${\alpha }_{\mathrm{thin}}$ emission parts are close to $+0.5$ and $-0.7$, respectively (for the peaked spectra they match with ${\alpha }_{\mathrm{low}}$ and ${\alpha }_{\mathrm{high}}$, 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 [21,23,32,91,92,93]. 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 ${\nu }_{\mathrm{peak},\mathrm{obs}}$ above 5 GHz, representing the earliest stage of radio source evolution with typical ages of a few hundred years [80,94,95]. According to the criteria in [96,97], 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. The peaked spectrum (PS) sources with their redshifts (Col. 2) and peak frequencies from Sotnikova et al. [30] 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 [47] (Col. 8), and PS type based on ${\nu }_{\mathrm{peak},\mathrm{obs}.}$ (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, and T—triple morphology.

NVSS Name	z	${\mathit{\nu }}_{\mathbf{peak},\mathbf{obs}.}$	FWHM	${\mathit{t}}_{4.7}$/N4.7	${\mathit{V}}_{{\mathit{S}}_{4.7}}$	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 [98]		GPS
004858+064005	3.58	3.9	1.5	36/25	0.25	cso [99]		GPS
010012−270851 *	3.52	1.4	1.7	31/10	0.17	c+j [100]		GPS
012100−280623	3.11	0.3	3.0	30/19	0.43	c+j [100]	FSRQ	MPS
020346+113445 a	3.63	3.7	1.5	42/38	0.33	c+j [100]	FSRQ	GPS
021435+015703 *	3.28	0.5	1.9	46/19	0.13	c+j [100]		MPS
023220+231756 a	3.42	0.5	2.0	33/13	0.29	c+j [100]		MPS
024611+182330	3.59	1.8	1.8	34/44	0.29	c+j [98]	FSRQ	GPS
052506−334304	4.41	0.9	1.6	30/11	0.71	c+j [62]	Uncert.	MPS
053954−283956 a	3.10	7.0	1.8	43/66	0.59	c+j [100]	FSRQ	HFP
062419+385648	3.46	0.3	2.5	46/68	0.30	c+j [100]	FSRQ	MPS
064632+445116	3.39	17.3	1.5	47/187	0.67	c+j [100]	FSRQ	HFP
073357+045614	3.10	5.8	1.8	40/35	0.37	c+j [100]	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 [99]		MPS
083910+200208 *	3.30	1.8	2.0	35/16	0.29	c+j [100]		GPS
090549+041010 *	3.15	0.5	1.6	36/12	0.11	c+j [98]		MPS
093337+284532 *	3.42	1.7	1.5	34/17	0.25	E [101] b		GPS
102623+254259	5.28	0.3	1.7	25/13	0.30	c+j [62]	FSRQ	MPS
104523+314232 *	3.23	0.9	2.3	34/10	0.11	c [101] b		MPS
123055−113910	3.52	1.1	2.1	43/51	0.47	c+j [99]	FSRQ	GPS
124209+372005	3.81	1.7	2.1	46/24	0.28	T [101] b		GPS
130121+190421 *	3.10	1.7	1.9	35/13	0.05	c+j [100]		GPS
134022+375443	3.11	2.7	1.4	36/12	0.30	c+j [98]		GPS
135406−020603	3.70	2.6	1.8	38/60	0.24	c+j [100]	FSRQ	GPS
135706−174402 a	3.14	1.8	1.7	38/19	0.28	c+j [100]	FSRQ	GPS
140135+151325 *	3.23	1.3	2.0	33/11	0.36			GPS
140501+041536 a	3.20	8.3	2.1	43/26	0.25	c+j [101] 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 [100]	FSRQ	GPS
144516+095835	3.55	1.3	1.6	41/76	0.15	c+j [99]	FSRQ	GPS
150328+041949	3.66	5.6	1.5	39/8	0.10	c+ext [98]		HFP
152117+175601 *	3.06	3.5	1.4	40/13	0.32	c [101] b		GPS
153815+001905	3.49	2.9	1.6	43/20	0.50	c+j [100]		GPS
155930+030447	3.89	4.5	1.7	37/63	0.41	T [101] b	FSRQ	GPS
160608+312447	4.56	2.5	1.5	37/26	0.28	cso [102]		GPS
161637+045932	3.21	4.4	1.4	43/64	0.26	c+j [101] b	FSRQ	GPS
165844−073918 a	3.74	5.9	1.5	37/12	0.27	c+j [100]	FSRQ	HFP
184057+390046	3.1	4.5	1.8	36/23	0.52	c+j [100]	FSRQ	GPS
200324−325144	3.77	5.6	1.4	43/39	0.32	c+j [100]	FSRQ	HFP
201918+112712 *	3.27	0.5	1.8	41/12	0.06	c+ext [103]		MPS
204257−222326	3.63	3.5	2.1	30/4	0.27	c+j [100]	FSRQ	GPS
205051+312727	3.18	1.9	2.9	35/15	0.57	c+j [100]	FSRQ	GPS
212912−153840	3.26	6.8	1.5	37/54	0.16	c+j [104]	FSRQ	HFP
224800−054117	3.29	0.4	3.3	30/13	0.22	c+j [100]	Uncert.	MPS
231448+020150 *	4.11	1.7	2.1	40/20	0.20	c+j [62]		GPS
231643−334912	3.10	3.9	1.3	31/18	0.18	c+j [100]	FSRQ	GPS

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

presents the list of PS sources with their peak frequency, the width of the radio spectra at the half maximum level (FWHM), and a spectral type based on [30], 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 Figure 9, and their mean values are listed in

Table 7. The mean values of the parameters for the PS source subsamples.

	N	${\mathit{\nu }}_{\mathbf{peak},\mathbf{rest}}$	${\mathit{S}}_{\mathbf{peak}}$	FWHM	${\mathit{V}}_{{\mathit{S}}_{11.2}}$	${\mathit{V}}_{{\mathit{S}}_{8.2}}$	${\mathit{V}}_{{\mathit{S}}_{4.7}}$
		(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	$12.8\pm 13.1$	$0.69\pm 0.68$	$1.93\pm 0.96$	$0.23\pm 0.16$	$0.28\pm 0.17$	$0.28\pm 0.16$

. 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 in 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 Figure 1 for comparison with the whole sample.

4.1. Rest Frame Peak Frequency and FWHM

For the sources with a peaked radio spectrum, we estimated the rest frame peak frequency ${\nu }_{\mathrm{peak},\mathrm{rest}}={\nu }_{\mathrm{peak},\mathrm{obs}}(1+z)$, which ranges from 0.8 to 76 GHz. The redshift versus ${\nu }_{\mathrm{peak},\mathrm{rest}}$ relationship is shown in Figure 10, where we additionally plot PS sources at different redshifts from other studies: the sample from [105] marked by cross symbols, sources from [106] marked by star symbols, and from [37] by grey circles. [92] found a trend towards higher turnover frequencies at higher redshifts, but Figure 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∼1–1.5 dex, as has been found in [21,107] and [92] for a sample mostly represented by $z<3$ GPS sources (with only 6 of 74 sources having $z>3$ in the latter study). [36] 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∼1.6) than that of the GPS galaxies (FWHM∼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).

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 [38,40,108,109]. In this section, we focus on the broadband long-term radio spectra of 23 quasars previously classified as HFP, GPS, or MPS sources [21,32,36,106,110,111,112,113,114]. Their radio spectra and RATAN-600 light curves are presented in Figure A11 and Figure A12. The longest-term measurements, spanning up to 30–43 yrs, are available at frequencies at 4.7, 11.2, and 22.3 GHz. They are listed in

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 yrs) 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. [36]; [2]—O’Dea et al. [21]; [3]—Coppejans et al. [29]; [4]—Dallacasa et al. [112]; [5]—Callingham et al. [106]; [6]—O’Dea [110]; [7]—[111].

Name	${\mathit{t}}_{22.3}$	N22.3	${\mathit{t}}_{11.2}$	N11.2	${\mathit{V}}_{{\mathit{S}}_{22.3}}$	${\mathit{V}}_{{\mathit{S}}_{11.2}}$	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]

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 yrs, respectively. Two of them have a compact symmetric morphology [99,102]. 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 [102]. 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 the 17 GPS quasars in Table 8, which belong to the blazar population, 13 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 a 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 not enough radio data to establish their variability reliably.

Thus, among the previously reported 23 GPS, MPS, and HFP sources, 7 quasars demonstrate low radio variability ($V_S<0.27$) at 4.7–22.3 GHz, with 4 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 the 17 individual sources from this section that have significant radio variability is presented in Appendix C.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 six 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 ${\nu }_{\mathrm{peak},\mathrm{obs}}$ equal to 5.8 and 5.6 GHz, respectively [30].

J0733+0456 was not previously considered as an HFP candidate. The multifrequency data from the GLEAM survey at 72–231 MHz in 2013–2014 [44] and the RATAN-600 measurements in 2016–2020 made it possible to classify the quasar as a PS source [30] with a high turnover frequency ${\nu }_{\mathrm{peak},\mathrm{obs}}=5.8$ 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 [115], exhibits a core and some extension in the VLA 5 GHz image. Later authors [116] 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 [98]. 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 $t_{4.7}=39$ yrs 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 ${\nu }_{\mathrm{peak},\mathrm{obs}}=5.6$ GHz and FWHM $=1.5$ [30].

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 and Table A2).

Note that both the quasar J0257+4338 with a core-jet morphology [117] and the BL Lac blazar [118] or blazar of an uncertain type in BZCAT with an unresolved core in VLBA images [119]. J0525−2338 could hypothetically be considered as an HFP candidates due to their spectral shape, which has a hint of a possible peak near 8 and 20 GHz [30]. The blazar J0525−2338 exhibits a rising spectrum (${\alpha }_{\mathrm{high}}$ = +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 $z=4.06$ [120] 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 [121] 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 [122]. In our study, we consider the 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 yrs. Consequently, we can obtain 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 that 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

The 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 $z\ge 3$), 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 [123,124]. Some PS sources even demonstrate the high amplitude variability of 100–2500% over 24 yrs at 1.5 GHz [125]. 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 the 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, $t_{\mathrm{rest}}=4.0$–$6.7$ 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 [126]. 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 the radio spectra features and flux density variations in 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 [76,91,104], 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 [36], we identified about 2% objects in the flux-density-complete sample of GPS galaxies and quasars at lower redshifts (69% sources are at $z\le 2$) as HFP candidates. In our sample of high-redshift quasars, all six 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 [112] found that only 40% of the objects displayed all the typical characteristics of young radio sources. Furthermore, all the quasars in the sample were excluded. So, to prevent contamination from selection and boosting effects, authors [105] 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 [127,128], where they correspond to ∼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 a high cadence (N_obs = 40–60) over a long time period. The strong correlation between the number of observations and the 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 $z\ge 3$ based on the RATAN-600 observations at 2.3–22.3 GHz conducted in 2017–2020 [30], as well as the information from the literature covering a time period of 30–40 yrs, which corresponds to a timescale of about 10 yrs in the source’s frame of reference. The main results are summarised as follows.

• 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 the modulation index M, the fractional variability $F_S$, and the 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 a low variability of $V_S<0.10$ varies from 8 to 20% at different frequencies;
• 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;
• Several quasar groups with distinctive variability characteristics were found. The six highest-redshift quasars demonstrate an average variability of about 0.50 and at a shorter time scale than the others;
• Among the 23 GPS and MPS sources reported previously, only 6 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 $z\ge 3$ are GPS and MPS candidates, respectively;
• 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.