# The PG-RQS survey. Building the radio spectral distribution of radio-quiet
quasars. I. The 45-GHz data.

R. D. Baldi1,2, A. Laor3, E. Behar3, A. Horesh4, F. Panessa5, I. McHardy2, A.
Kimball6
1 INAF - Istituto di Radioastronomia, Via P. Gobetti 101, I-40129 Bologna,
Italy;
2 School of Physics and Astronomy, University of Southampton, Southampton,
SO17 1BJ, UK;
3 Department of Physics, Technion 32000, Haifa 32000, Israel
4 Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904,
Israel
5 INAF - Istituto di Astrofisica e Planetologia Spaziali, via Fosso del
Cavaliere 100, I-00133 Roma, Italy.
6 National Radio Astronomy Observatory, 1003 Lopezville Rd, Socorro, NM 87801,
USA E-mail<EMAIL_ADDRESS>
###### Abstract

The origin of the radio emission in radio-quiet quasars (RQQs) remains
unclear. Radio emission may be produced by a scaled-down version of the
relativistic jets observed in radio-loud (RL) AGN, an AGN-driven wind, the
accretion disc corona, AGN photon-ionisation of ambient gas (free-free
emission), or star formation (SF). Here, we report a pilot study, part of a
radio survey (‘PG-RQS’) aiming at exploring the spectral distributions of the
71 Palomar-Green (PG) RQQs: high angular resolution observations ($\sim$50
mas) at 45 GHz (7 mm) with the Karl G. Jansky Very Large Array of 15 sources.
Sub-mJy radio cores are detected in 13 sources on a typical scale of $\sim$100
pc, which excludes significant contribution from galaxy-scale SF. For 9
sources the 45-GHz luminosity is above the lower frequency ($\sim$1–10 GHz)
spectral extrapolation, indicating the emergence of an additional flatter-
spectrum compact component at high frequencies. The X-ray luminosity and black
hole (BH) mass, correlate more tightly with the 45-GHz luminosity than the
5-GHz. The 45 GHz-based radio-loudness increases with decreasing Eddington
ratio and increasing BH mass MBH. These results suggest that the 45-GHz
emission from PG RQQs nuclei originates from the innermost region of the core,
probably from the accretion disc corona. Increasing contributions to 45-GHz
emission from a jet at higher MBH and lower Eddington ratios and from a disc
wind at large Eddington ratios are still consistent with our results. Future
full radio spectral coverage of the sample will help us investigating the
different physical mechanisms in place in RQQ cores.

###### keywords:

Galaxies: active – Galaxies: nuclei – galaxies: jets – radio continuum:
galaxies – X-rays: galaxies

††pagerange: The PG-RQS survey. Building the radio spectral distribution of
radio-quiet quasars. I. The 45-GHz data.–The PG-RQS survey. Building the radio
spectral distribution of radio-quiet quasars. I. The 45-GHz data.††pubyear:
2018

##  1 Introduction

The origin of the radio emission in Radio-loud Active Galactic Nuclei (RL AGN)
is clear, luminous relativistic jets of magnetised plasma, which can extend
far out, on the host galaxy scale and beyond. Conversely, radio-quiet (RQ) AGN
are associated with radio emission which is typically $10^{3}$ times weaker
(as defined by Kellermann et al., 1989), in smaller structures (kpc-pc scale,
e.g. Blundell et al. 1996; Nagar et al. 1999; Ulvestad et al. 2005a; Gallimore
et al. 2006) with sub-relativistic velocities (e.g. Middelberg et al. 2004;
Ulvestad et al. 2005b) compared to RL AGN. The reduced sizes and low
brightness of the radio emission of RQ AGN create a major challenge for
detailed studies, in sharp contrast with the thoroughly studied RL AGN. The
fewer radio studies of RQ AGN (e.g. Barvainis & Antonucci 1989; Kellermann et
al. 1994; Barvainis et al. 1996; Kukula et al. 1998; Ulvestad et al. 2005a;
Leipski et al. 2006; Padovani et al. 2011; Doi et al. 2011; Zakamska et al.
2016; Jarvis et al. 2019; Smith et al. 2020b; Fawcett et al. 2020; Nyland et
al. 2020; Jarvis et al. 2021; Baldi et al. 2021a) generally lead to mixed
results. This encourages to keep investigating it, as it indicates that the
origin of the radio emission in RQ AGN is still an open question. If a number
of different processes are indeed involved, then the radio band can be used to
probe a range of physical processes, rather than being heavily dominated by a
single process, as occurs in RL AGN (see Panessa et al. 2019; Blandford et al.
2019 for reviews). From large scale to small scale: i) host galaxy star
formation could account for the observed FIR-to-radio emission observed in
active and non active galaxies (Condon et al., 2013; Zakamska et al., 2016);
ii) an AGN-driven wind is expected to shock the interstellar gas, leading to
particle acceleration and radio synchrotron emission, which may reach the
observed flux level (Jiang et al., 2010); iii) the intense radiation of the
AGN photo-ionizes large volumes of ambient gas, as supported by the strength
of the narrow and broad line emission observed in type-1 AGN, leading to
thermal free-free emission in the radio band (Baskin & Laor, 2021); iv) a
scaled-down jet, physically similar to the one in RL AGN, but much fainter,
less energetic and slower (Barvainis et al., 1996; Gallimore et al., 2006;
Talbot et al., 2021); v) a tight radio/X-ray luminosity relation for AGN
($\sim$10-5, Laor & Behar 2008) similar to coronally active stars (Güdel &
Benz, 1993; Güdel et al., 2002) suggests that coronal emission from magnetic
activity above the accretion disc (Field & Rogers, 1993; Gallimore et al.,
1997) may produce the observed radio emission.

High resolution and high sensitivity radio observations are fundamental to
determine the physical mechanism which produces the radio emission in RQ AGN.
The detection of a low-brightness radio core at the center of the radio
structures, where the supermassive black hole (BH) resides, requires
observations which can resolve the optically-thick synchrotron source, whose
size scales as $\nu^{-5/4}$ $L^{1/2}$ (e.g. Laor & Behar 2008; Inoue & Doi
2018). Therefore, radio observations at higher-frequencies, which probe the
emission on smaller scales, are required. Nevertheless, since the typical
radio spectra of RQ AGN are steep in the cm-band, the detection rate could
benefit from observations at intermediate radio frequencies, between the cm
and mm bands. In particular, in the band, 2–0.6 cm (15-50 GHz), the probed
physical scale of the radio-emitting region in nearby AGN is $\sim$0.01 pc,
which is an order of magnitude smaller than the optically-thick 5-GHz emission
region.

As opposed to observations at 1.4-8.5 GHz, higher frequency observations of RQ
AGN in the range 15-50 GHz are scarce. In the last decade, more efforts have
been spent towards studying the radio emission from RQ AGN moving gradually
from cm band to shorter wavelengths (e.g., Doi et al. 2005; Murphy et al.
2010; Park et al. 2013; Inoue & Doi 2014; Behar et al. 2015; Smith et al.
2016; Behar et al. 2018; Ricci et al. 2019; Smith et al. 2020a).

Figure 1: Distribution of the [O III] line, optical (4400 Å), X-ray (2-10
keV), bolometric luminosities (in erg s-1) and BH masses (in M⊙) of the whole
PG RQQ sample (71 objects). The filled histograms represent the distribution
of the 15 PG RQQs studied in this work. The KS tests confirm that the 15
sources are representative of the entire PG RQQ sample.

Radio observations at the cm-band with sub-mJy sensitivity and sub-arcsecond
resolution have found extended emission on kpc scale or compact unresolved
emission in the majority of RQ AGN (e.g., Nagar et al. 2002; Giroletti &
Panessa 2009; Panessa & Giroletti 2013; Maini et al. 2016; Baldi et al. 2018;
Chiaraluce et al. 2019; Baldi et al. 2021a). The flat or even inverted
spectrum observed at higher radio frequencies indicates a compact optically-
thick source (Doi et al., 2005, 2011; Behar et al., 2015, 2018), superimposed
on the steep-spectrum which originates from more extended optically-thin
structures that dominate at lower frequencies. Such a flat-spectrum core is
usually identified as the base of a possible jet or outflow, and may be
located in the X-ray corona (Markoff et al., 2005). To explore the nature of
the radio core, the identification of such a component, resolved with high
resolution observations, may help us to carry on an unbiased comparison with
the well-studied cores of RL AGN. On one hand, empirical relations between the
radio core luminosity and global properties of the AGN/galaxy have been found
for RL AGN (e.g. radio vs BH or galaxy mass, colour, SF, Eddington ratio, see
Heckman & Best 2014). On the other hand, for RQ AGN a similar study is limited
because a few studies on arcsec- and mas-scale radio emission have led to
conflicting or inconclusive results (e.g. the presence or not of a radio-MBH
relation, e.g. Lacy et al. 2001; McLure & Jarvis 2004; Bian et al. 2008;
Panessa & Giroletti 2013; Baldi et al. 2021b). Therefore, dedicated high-
resolution radio observations on large samples of RQ AGN are needed to resolve
their cores, and enable us to perform an impartial comparison with RL AGN and
their radio-based empirical relations.

Quasars, being luminous AGN, are perfect settings to explore the different
mechanisms of radio emission. Searching for a connection between
accretion/ejection properties and the radio emission in RQQs is, thus, the
goal of our PG-RQS (Palomar-Green Radio-Quiet SED) survey by building up the
radio (from MHz to mm band) spectral energy distributions of the 71 Palomar-
Green (PG) RQQs from the 87 Palomar Bright Quasar Survey at $z<0.5$ (Schmidt &
Green, 1983; Boroson & Green, 1992). The PG survey was the first large solid
angle (10,000 square degrees) complete quasar survey, selected to be blue and
point-like, and it remains the largest complete survey of optically bright
quasars at $B<$ 16, and therefore has no radio selection biases. It therefore
provides an unbiased view of the distribution of radio emission properties of
RQ AGN. The PG RQQ sample represents the most extensively studied sample of
type-1 AGN and, thus, the cornerstone for quasar studies in the last decades:
including, e.g. the overall SED (Neugebauer et al., 1987; Sanders et al.,
1989), radio continuum and imaging (Kellermann et al., 1989, 1994; Miller et
al., 1993), infrared photometry (Haas et al., 2003; Shi et al., 2014; Petric
et al., 2015), optical spectroscopy (Boroson & Green, 1992), optical
polarisation (Berriman et al., 1990), UV spectroscopy (Baskin & Laor, 2005),
soft X-ray spectroscopy (Brandt et al., 2000), and radio spectral indices
(Laor et al., 2019). From these studies, various fundamental properties were
derived, such as MBH (from broad H$\beta$ emission line widths, Kaspi et al.
2000; Vestergaard & Peterson 2006, and from stellar velocity dispersions,
Tremaine et al. 2002), accretion rates and radiative efficiencies (Davis &
Laor, 2011), and numerous other observed properties. This sample revealed
various interesting trends, such as the eigenvector 1 (EV1) set of emission
line correlations (Boroson & Green, 1992), the MBH – bulge mass relation in
AGN (Laor, 1998), and the MBH – radio loudness relation (Laor, 2000). In
conclusion, for its optical selection and its large multi-band coverage, the
PG RQQs represents an ideal sample to search for radio-based empirical
relations in the RQ regime. Although characterised by relatively high
accretion rates (in Eddington units), the extreme conditions of the accretion
and ejection of the PG RQQs could help in the identification of the origin of
the radio emission among the different physical mechanisms. Precisely, in this
work we present the results from a pilot study of 15 PG RQQs observed at 45
GHz with the Karl G. Jansky Very Large Array (VLA).

This paper is organised as follows. In Sect. 2 we present the project, the PG
sample, and the observations. Sect. 3 shows the main radio properties of the
sample and we seek for multi-band correlations in Sect 3.1. A comparison of
the results with RLQs is in Sect. 3.2 to highlight the similarities and
differences with the radio properties of RQQs, which we discuss in Sect 4. We
elaborate the final interpretation of the results based on the different radio
production processes in RQQs in Sect. 4.1 and on the comparison with X-ray
Binary systems in Sect. 4.2. We draw our conclusions in Sect 5.

Table 1: VLA A-array 45-GHz properties of the observed 15 PG RQQs.

PG name | alternative | z | size | Fcore | Ftot | rms | uvtaper | $F_{uvtaper}$ | P${}_{45~{}{\rm GHz}}$
---|---|---|---|---|---|---|---|---|---
| name |  | pc | mJy beam-1 | mJy | mJy beam-1 | k$\lambda$ | mJy beam-1 | erg s-1
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
PG 0003+199 | MRK 335 | 0.0258 | 52 | 0.50$\pm$0.04 | 0.60 | 0.036 | 300 | 0.82$\pm$0.08 | 38.52
PG 0026+129 |  | 0.1420 | 251 | 0.20$\pm$0.04 | 0.21 | 0.037 | 300 | 0.53$\pm$0.11 | 39.71
PG 0049+171 | MRK1148 | 0.0640 | 124 | 0.63$\pm$0.05 | 0.64 | 0.040 | 300 | 0.81$\pm$0.10 | 39.46
PG 0050+124 | UGC 545 | 0.0589 | 115 |  $<$0.15 |  | 0.051 | 500 | 0.30$\pm$0.08 | 39.06
PG 0052+251 |  | 0.1544 | 270 | 0.37$\pm$0.04 | 0.37 | 0.035 | 300 | 0.62$\pm$0.08 | 40.05
PG 0157+001 | MRK 1014 | 0.1631 | 282 | 0.48$\pm$0.06 | 0.52 | 0.058 | 300 | 0.55$\pm$0.11 | 40.22
PG 0844+349 |  | 0.0640 | 124 |  $<$0.06 |  | 0.020 | 300 |  $<$0.19 |  $<$38.46
PG 1001+054 |  | 0.1611 | 279 |  $<$0.06 |  | 0.019 | 250 | 0.13$\pm$0.04 | 39.65
PG 1048+342 |  | 0.1670 | 288 | 0.17$\pm$0.03 | 0.24 | 0.033 | 300 | 0.41$\pm$0.12 | 39.80
PG 1049-005 |  | 0.3599 | 508 |  $<$0.11 |  | 0.035 | 600 | 0.25$\pm$0.07 | 40.72
PG 1114+445 |  | 0.1439 | 254 | 0.13$\pm$0.02 | 0.16 | 0.025 | 600 | 0.17$\pm$0.05 | 39.54
PG 1149-110 |  | 0.0490 | 96 | 0.30$\pm$0.03 | 0.36 | 0.032 | 600 | 0.31$\pm$0.06 | 38.93
PG 1229+204 | MRK 771 | 0.0630 | 122 | 0.27$\pm$0.03 | 0.27 | 0.028 | 300 | 0.36$\pm$0.08 | 39.12
PG 1259+593 | SBS 1259+593 | 0.4778 | 602 |  $<$0.09 |  | 0.029 | 300 |  $<$0.24 |  $<$40.57
PG 1310-108 | II SZ 010 | 0.0343 | 69 | 0.19$\pm$0.03 | 0.24 | 0.039 | 300 | 0.38$\pm$0.07 | 38.42

Column description: (1)-(2) PG source name and alternative name; (3) redshift;
(4) physical size of 100 mas; (5)–(6) 45-GHz peak flux densities (mJy beam-1,
derived from CASA ‘imfit’ task) and total flux densities (mJy) from full-
resolution maps; (7) rms (mJy beam-1); (8) $uv$taper scale parameter; (9)
45-GHz peak flux density measured in low-resolution map (mJy beam-1); (10)
45-GHz core luminosity (erg s-1) from Fcore . Upper limits are evaluated at
3$\sigma$ level.

PG0003+199PG0026+129PG0049+171

PG0050+124PG0052+251PG0157+001

PG0084+349PG1001+054PG1048+342

PG1049-005PG1114+445PG1149-110

PG1229+204PG1259+593PG1310-108

Figure 2: The A-array VLA 45-GHz maps of the 15 PG RQQs in full resolution
(40-80 mas), except for PG 0050+124,PG 1001+054, PG 1049-005 for which we
present the $uv$-tapered map where the core emission is detected at a lower
resolution ($<$0.5 arcsec). Two objects, PG 0844+349 and PG 1259+593, are not
detected. The map properties (beam and contour levels) are presented in Table
2. Table 2: Parameters of the JVLA 45-GHz maps (Fig. 2).

PG name | beam | PA | contour levels
---|---|---|---
PG 0003+199 | 0.069$\times$0.049 | -60.6 | 0.09.5$\times$(-1,1,2,3,4)
PG 0026+129 | 0.064$\times$0.056 | 87.3 | 0.080$\times$(-1,1,2,2.4)
PG 0049+171 | 0.090$\times$0.053 | -54.3 | 0.085$\times$(-1,1,2,4,6)
PG 0050+124 | 0.35$\times$0.27 | -44.5 | 0.25$\times$(-1,1,2,2.5)
PG 0052+251 | 0.074$\times$0.052 | -71.5 | 0.080$\times$(-1,1,2,4)
PG 0157+001 | 0.10$\times$0.073 | -28.5 | 0.10$\times$(-1,1,2,4)
PG 0844+349 | 0.062$\times$0.048 | -83.4 | 0.047$\times$(-1,1)
PG 1001+054 | 0.53$\times$0.47 | -75.6 | 0.050$\times$(-1,1,2,2.5)
PG 1048+342 | 0.054$\times$0.040 | 67.2 | 0.077$\times$(-1,1,1.5,2)
PG 1049-005 | 0.27$\times$0.22 | 28.2 | 0.12$\times$(-1,1,1.5,2)
PG 1114+445 | 0.057$\times$0.048 | 82.2 | 0.055$\times$(-1,1,1.5,2)
PG 1149-110 | 0.083$\times$0.058 | -41.2 | 0.075$\times$(-1,1,2,4)
PG 1229+204 | 0.068$\times$0.049 | -82.7 | 0.065$\times$(-1,1,2,4)
PG 1259+593 | 0.061$\times$0.050 | 48.5 | 0.070$\times$(-1,1)
PG 1310-108 | 0.070$\times$0.054 | 5.3 | 0.065$\times$(-1,1,2,2.8)

Column description: (1) source name; (2) FWHM of the elliptical Gaussian
restoring beam (in arcsec) of the maps presented in Fig. 2; (3) PA of the
restoring beam (degree); (4) radio contour levels (mJy beam-1).

##  2 Sample and Observations

In this work we report the A-array VLA observations for a sub-sample of 15
objects (see Table 1), randomly selected from the whole 71 RQ PG quasars at
z$<$0.5 (Boroson & Green, 1992). The PG sample covers AGN over a wide range of
intrinsic properties, on a wide interval of bolometric luminosities LBol
$\sim$1043-1046 erg s-1 and with a MBH ranging from a few 106 M⊙ to a few 109
M⊙. The wealth of additional information available for this sample allows to
explore possible relations between the 45 GHz emission and other emission and
absorption properties, which are known to be related (e.g. Boroson & Green
1992).

Figure 1 depicts the distributions of the main AGN luminosity estimates ([O
III] emission line L${}_{\rm[O~{}III]}$, 4400 Å optical Lo, 2-10 keV X-ray LX,
bolometric luminosities111Bolometric luminosities of the PG QSOs are
calculated via broad-band (optical, UV and X-ray) SED modeling by Davis & Laor
(2011). Lbol and BH masses MBH taken from Boroson & Green (1992), Laor & Behar
(2008) and Davis & Laor (2011) for all 71 PG RQQs. The solid histograms show
the distributions of such parameters for the 15 PG RQQs studied here. We test
if our pilot sample is consistent with the hypothesis that it is randomly
drawn from the distribution of the whole sample using the Kolmogorov–Smirnov
test (KS test). The KS-test probability for each distribution is $>$90 per
cent and confirm that 15 targets are representative of the entire PG RQQ
sample.

This pilot observations of 15 PG RQQs at 45 GHz with the VLA is the first of a
series of studies, part of the PG-RQS survey, aiming at exploring the PG RQQs
at high and low radio frequencies with different radio arrays and angular
resolutions: at arcsec resolution with GMRT and LOFAR in the MHz regime to
milli-arcsec resolution with very-long baselined interferometry (VLBI)
observations (such as VLBA and eMERLIN), and including high frequency
observations with VLA (1–45 GHz) and with ALMA (85–500 GHz). An accurate
determination of the broad-band SEDs of PG RQQs will allow us to probe the
radial distribution of the radio emission at different scales (set by the band
frequency and resolution), and constraints possible emission mechanisms.

The VLA observations of the pilot sample presented in this work were carried
out in Q-band with 8-GHz bandwidth with exposure times of 12 minutes on source
between October 2016 and January 2017 (project 16B-126). Flux and phase
calibrator were observed, respectively, at the beginning of each scan (4 min)
and in cycles with the target (6 min).

We used the CASA pipeline to calibrate the visibility data, including the
flagging process. After obtaining the phase and amplitude solution using the
calibrators, we applied them to the target source using standard procedures.
Eventually, we inverted and cleaned with natural weight the visibility data to
obtain the final images with an angular resolution of $\sim$40-80 mas and a
typical rms of $\sim$0.02 mJy beam-1 at 45 GHz. To extract the flux densities
and uncertainties from the radio maps, we used ‘imfit’, part of the CASA
‘viewer’, which fits two-dimensional Gaussians to an intensity distribution on
a region selected interactively on the map. To possibly increase the chance of
detecting the core and extended emission, we also reduced the map resolution
by using different values of the `UVTAPER` parameter in the `IMAGR` task,
ranging between 600 k$\lambda$ to 250 k$\lambda$ for all the sources. This
parameter specifies the width of the Gaussian function in the $uv$-plane to
down-weight long-baseline data points. Smaller units of this parameter
correspond to a shallower angular resolution, i.e. a larger beam size, up to a
factor $\sim$10 larger than those reached in full resolution (i.e.
$\sim$0.3-0.5 arcsec).

Table 3: VLA peak flux densities in mJy of the 15 observed PG RQQs from 1.4 to
15 GHz taken from VLA archive and literature.

| Array-A VLA flux densities | B-C-D VLA flux densities
---|---|---
Frequency: | 1.4GHz | 5 GHz | 8.5 GHz | 1.4GHz | 5 GHz | 8.5 GHz | 15 GHz
Resolution: | 1$\aas@@fstack{\prime\prime}$3 | 0$\aas@@fstack{\prime\prime}$33 | 0$\aas@@fstack{\prime\prime}$20 |  |  |  |
Object | $F_{\nu}$ | $F_{\nu}$ | $F_{\nu}$ | $F_{\nu}$ | $F_{\nu}$ | $F_{\nu}$ | $F_{\nu}$
PG 0003+199 | 6.74$\pm$0.11a | 3.03$\pm$0.10b | 2.05$\pm$0.1c | 7.3$\pm$0.5f | 3.92$\pm$0.1b | 2.23$\pm$0.25g |
3.49$\pm$0.05e | 3.58$\pm$0.1e |
PG 0026+129 | 2.4$\pm$0.7d | 0.20$\pm$0.06b | 0.17$\pm$0.05e | 7.1$\pm$0.5f | 5.10$\pm$0.1b | 2.37$\pm$0.06e |
PG 0049+171 | 0.44$\pm$0.12a | 0.66$\pm$0.10b |  |  $<$2.5f | 0.64$\pm$0.10b | 0.66$\pm$0.10g |
PG 0050+124 | 5.1$\pm$0.4d | 1.80$\pm$0.10b | 0.9$\pm$0.2d | 6.22$\pm$0.35h | 2.60$\pm$0.11b |  | 1.06$\pm$0.32h
2.4$\pm$0.3d |
PG 0052+251 | 1.1$\pm$0.4d | 0.42$\pm$0.10b | 0.7$\pm$0.1d | 1.59$\pm$0.14a | 0.74$\pm$0.10b |  |
0.58$\pm$0.03e | 0.61$\pm$0.03e |  |
PG 0157+001 |  | 5.58$\pm$0.06b | 2.98$\pm$0.03e | 22.5$\pm$0.8h | 7.88$\pm$0.26h | 4.23$\pm$0.03e | 2.04$\pm$0.32h
PG 0844+349 |  |  $<$0.25b |  |  $<$0.38i | 0.31$\pm$0.06b |  |
PG 1001+054 |  |  $<$0.25b |  |  $<$2.5f | 0.80$\pm$0.1b | 0.64$\pm$0.3a |
PG 1048+342 |  |  |  |  $<$0.42i |  $<$0.19b |  $<$0.12a |
PG 1049-005 |  | 0.22$\pm$0.03e |  | 0.82$\pm$14i | 0.48$\pm$0.03b | 0.37$\pm$0.07a |
PG 1114+445 |  | 0.20$\pm$0.06b |  | 0.71$\pm$0.12i | 0.22$\pm$0.06b |  |
PG 1149-110 | 3.1$\pm$0.8d | 1.20$\pm$0.20d | 1.3$\pm$0.1d | 9.7$\pm$0.6f | 2.60$\pm$0.1b | 0.54$\pm$0.02a |
1.08$\pm$0.06e | 0.99$\pm$0.04a | 1.94$\pm$0.1e |
1.0$\pm$0.1b |  |  |
PG 1229+204 |  | 0.30$\pm$0.06b |  | 2.8$\pm$0.4f | 0.67$\pm$0.1b |  |
PG 1259+593 |  |  $<$0.25b |  |  $<$0.45i |  $<$0.3a |  |
PG 1310-108 |  |  $<$0.25b |  |  $<$2.5f | 0.26$\pm$0.06b |  $<$0.15a |

Upper limits are evaluated at 3$\sigma$ level. References: $a$ map obtained
from the image VLA archive, $b$ Kellermann et al. (1989), $c$ Kukula et al.
(1995); $d$ Kukula et al. (1998); $e$ Leipski et al. (2006); $f$ Condon et al.
(1998); $g$ Barvainis et al. (2005); $h$ Barvainis & Antonucci (1989); $i$
Becker et al. (1995).

##  3 Results

Figure 3: A compilation of the overall 1.4–45 GHz SED of the 15 PG RQQs
presented in this work based on VLA data. Filled points mark the highest
resolution, A array, data, and the crosses measurements at lower resolutions
(B-C-D arrays). The dot-dashed line shows the spectral slope for the VLA low-
resolution data, while the dashed line represents the spectral properties of
the unresolved core component at VLA high resolution. The corresponding values
reported on the plot are the spectral indices derived by fitting the censored
data. Figure 4: Radio flux densities at 5 and 45 GHz (in logarithmic scale)
normalised by the optical 4400Å flux density (i.e ratio between the radio and
optical flux densities) for the RQQs which are detected in Q-band. At the top-
right corner, we draw the typical error bar on the y-axis, $\sim$0.2-0.3. The
plot shows that RQQs tend to have steeper radio spectra because of brighter 5
GHz emission relative to the optical, rather than dimmer 45 GHz emission.

In the full-resolution maps we detect radio emission from the central
unresolved core in 10 sources with a flux density of the order of $\sim$0.1
mJy beam-1, reaching a S/N $\sim$ 3-5 (see Table 1). Reducing the angular
resolution by up to a factor $\sim$10 with `UVTAPER` allows us to detect three
additional objects, PG 0050+124,PG 1001+054, and PG 1049-005. However, two
objects, PG 0844+349 and PG 1259+593, remain undetected. In conclusion, we
detect a 45-GHz radio core in 13 out of 15 sources (86 $\pm$ 7 per cent of our
sample).

Figure 2 presents the full-resolution radio images at 45 GHz of our sample.
For the sources not detected in full resolution, we display the $uv$-tapered
images. Most of the targets appear unresolved or slightly resolved at the full
resolution on 50-100 mas (Table 2) which corresponds to a few hundred pc
(Table 1). The ratio between total and peak flux densities for these sources
is close to unity, suggesting their structure is unresolved. Four sources (PG
0049+171, PG 0050+124, PG 0157+001 and PG 1114+445) show a marginal elongation
of the radio core emission. The $uv$-tapered maps do not show any significant
evidence of extended emission in any of the targets of the sample.

Figure 5: The relation between the radio core luminosities at 5 and 45 GHz
(erg s-1) and the X-ray (2-10 keV), optical, bolometric and [O III] line
luminosities (erg s-1) for the 15 PG RQQs. The value in the upper part of each
panel expresses the rms scatter of the relation (assuming the upper-limits as
detections) and the generalised Kendall’s $\tau$ test probability (P) of a
fortuitous correlation. Note that the relations with P${}_{45~{}{\rm GHz}}$
are generally tighter, and the tightest relation is with LX. The outlier PG
1001+054 with L${}_{\rm X}<10^{43}$ erg s-1 is known to be significantly X-ray
absorbed (Schartel et al., 2005), and was not considered in fitting the
X-ray–radio relations. Table 4: Radio spectral indices of the PG 15 RQQs

name | 1 comp | 2 comp | S/F | $\alpha_{5-45\rm{GHz}}$
---|---|---|---|---
PG 0003+199 | -0.77$\pm$0.06 |  | $S$ | -0.83
PG 0026+129 | -0.54$\pm$0.26 | 0.02$\pm$0.07 | $S+F$ | 0.20
PG 0049+171 | 0.0$\pm$0.2 | 0.09$\pm$0.09 | $F$ | 0.25
PG 0050+124 | -0.74$\pm$0.04 | -0.82$\pm$0.09 | $S$ | -0.90
PG 0052+251 | -0.68$\pm$0.13 | -0.26$\pm$0.12 | $S+F$ | -0.26
PG 0157+001 | -0.98$\pm$0.09 | -1.11$\pm$0.02 | $S$ | -0.91
PG 0844+349 | -0.16 | -0.63 | $S$ |  $<$-0.32
PG 1001+054 | -0.85$\pm$0.20 | -0.37 | $S+F$ | -0.71
PG 1048+342 | 0.04 |  | $F$ |  $>$0.25
PG 1049-005 | -0.44$\pm$0.01 | -0.09$\pm$0.30 | $F$ | -0.04
PG 1114+445 | -0.92$\pm$0.20 | -0.18$\pm$0.20 | $S+F$ | -0.06
PG 1149-110 | -1.5$\pm$0.3 | -0.65$\pm$0.06 | $S$ | -0.86
PG 1229+204 | -1.1$\pm$0.1 | -0.11$\pm$0.10 | $S+F$ | -0.14
PG 1259+593 | -0.43 |  | ? |
PG 1310-108 | -1.6 | -0.13 | $F$ | -0.17

Column description: (1) PG source name; (2)-(3) spectral slopes of the first
and second radio components, estimated respectively typically at lower
frequencies ($\lesssim$5 GHz) and lower resolution (VLA B-C-D array), and
higher radio frequencies ($\gtrsim$5 GHz) and higher resolution (VLA A array)
(see Fig. 3); (4) general radio SED dominance: $S$ for steep-spectrum
component, $F$ for flat-spectrum component; $S+F$ combination of a steep- and
flat-spectrum component; (5) spectral indices between 5 and 45 GHz, with
typical errors of 30 per cent.

With the final goal of deriving the radio cm-wavelengths SEDs, we search in
the literature and VLA image
archive222https://archive.nrao.edu/archive/archiveimage.html for radio data
below 45 GHz, both at the highest resolution with A array, and at the lower
resolution with B-C-D arrays (see Table 3 and references therein). Figure 3
displays the radio SEDs of the 15 objects in the frequency range 1.4 – 45 GHz.
Filled points mark the highest resolution A array data, and the crosses
represent the measurements at lower resolutions. There is a rich variety of
spectral shapes ($F_{\nu}\sim\nu^{\alpha}$) across the 1–45 GHz band (Tab. 4).
We define the broad-band spectral class of the sources, based on the both the
A-array and the lower resolution VLA data available for the targets:

  * •

steep (S): if the radio SED is characterised by a steep spectral index
($\alpha<$ -0.5) in both high and low resolution data: PG 0003+199, PG
0050+124, PG 0157+001, PG 1149-110. We also include PG 0844+349 into this
category because with only one detection (at low resolution at 5 GHz) the
estimated spectral slope can be considered as upper limit.

  * •

flat or slightly inverted (F): if the radio SED is characterised by a flat
spectral index (0.1 $>\alpha>$ -0.5) in both high and low resolution data (or
only in high resolution if the low resolution data do not provide detections):
PG 0049+171, PG 1048+342, PG 1049-005, and PG 1310-108.

  * •

a broken power-law (S+F): the combination of steeper lower-frequency spectrum
and a flatter higher-frequency spectrum at either low or high resolution data:
PG 0026+129, PG 0052+251, PG 1001+054, PG 1114+445, and PG 1229+204.

We abstain from the spectral classification of PG 1259+593 because of the lack
of detections from the available radio data. Note that these radio SEDs do not
account for radio core variability, which is known to be present by as much as
a factor of 2-3 (Falcke et al., 2001; Barvainis et al., 2005; Mundell et al.,
2009; Baldi et al., 2015; Behar et al., 2020; Nyland et al., 2020), nor the
different angular resolutions ranging from 1.3 to 0.40 arcsec with A-array
observations in different bands.

The radio SEDs presented in Fig. 3 suggest that the typical radio spectrum of
PG RQQs consists of a combination of at least two components333The spectral
slopes are obtained by fitting the censored radio data in Fig. 3. In case of
the presence of non-detections, the spectral slope are rough estimates,
measured by assuming upper limits as detections for simplicity., a steep-
spectrum component which dominates at low frequencies and low resolution, and
a flat-spectrum component (typically unresolved) which emerges at high
resolution and at high frequencies (Tab. 4). At least for 9 sources a flat-
spectrum radio component emerges at high radio frequencies. Is this because
one component is brighter, or because the other component is weaker, relative
to the emission in other bands?

Figure 4 shows the 5–45 GHz spectra of the detected PG RQQs normalised by the
flux densities in the optical band from Kellermann et al. (1989) at 4400 Å (a
proxy of radio loudness). The plot shows that, the spectral steepness of the
RQQs is due to the brighter 5-GHz core component, rather than a dimmer 45-GHz
component. In turn, the flattening of the RQQ spectra is the result of the
weakening of the steep-spectrum component. This results would suggest that
steep-spectrum objects have an additional mechanism which produces optically
thin emission, which adds to the flat-spectrum optically thick emission that
most of objects have.

###  3.1 Multi-band correlations

As higher-energy photons are expected to originate from inner regions of the
nucleus (accretion disc, jet base, etc), early studies revealed that radio
properties in RQQs are linked to the accretion/ejection activity, derived from
high-energy bands (e.g., optical, X-ray, Boroson & Green 1992; Laor & Behar
2008). In addition, it has been recently found the radio spectral slopes of
RQQs can also depend on several AGN parameters, which in turn are linearly
combined in the EV1 diagram (see Laor et al. 2019 and references therein).

To derive possible meaningful correlations between the 45-GHz emission with
that in other lower-frequency VLA bands, we calculate the Q-band luminosities,
$\nu L_{\nu}$ ($\equiv P_{45~{}{\rm GHz}}$) in units of erg s-1), which covers
the range $\sim 38.4<\log L_{45~{}{\rm GHz}}<40.7$. We also use the core
luminosity densities at 5 GHz, $\nu L_{\nu}$ ($\equiv P_{5~{}{\rm GHz}}$ from
Kellermann et al. (1989) which covers the range $\sim 37.6<\log P_{5~{}{\rm
GHz}}<40.1$. Note that although we always use the A-configuration for both the
Q band and the C band observations for the following radio luminosity plots
(unless explicitly expressed), the Q band resolution is 40-80 mas versus
$\sim$0.3 arcsec in the C band, due to the factor 9 drop in frequency. Thus,
if the radio emission is extended, the derived slope between the two bands
will be steeper than the intrinsic core slope. In this scenario, since
extended radio emission is almost always characterised by an optically-thin
steep power-law, this possible bias will not change the character of the
45-GHz emission. This aperture bias does not work in the opposite direction,
and an observed flat spectrum is inevitably flat (or even flatter if it is
contaminated by a steep component) and must therefore originate from an
optically thick compact source. An intrinsic compact source will remain
unresolved in both bands, and the measured slope will be unaffected by the
different resolutions.

Figure 5 depicts the correlations of P${}_{5~{}{\rm GHz}}$ (left panel) and
P${}_{45~{}{\rm GHz}}$ (right panel) with the typical calorimeters of AGN
strength: the X-ray (2-10 keV) luminosity $L_{\rm X}$, the optical luminosity
$L_{\rm o}$, the bolometric luminosity $L_{\rm bol}$ and the [O III] line
luminosities $L_{\rm[O~{}III]}$. Since several upper-limits are present in the
datasets, the statistical significance of each correlation is measured by
using a censored statistical analysis (ASURV444ASURV package has been used
within the PyRAF software (Science Software Branch at STScI, 2012).; Lavalley
et al. 1992) which takes into account the presence of upper limits. We used
the `schmittbin` task (Schmitt, 1985) to calculate the associated linear
regression coefficients for two sets of variables. Effectively, we carried out
this procedure twice, obtaining two linear regressions: first, we consider the
former quantity as the independent variable and the latter as the dependent
one and second switching the roles of the variables. The best fit is
represented by the bisector of these two regression lines. This followed the
suggestion of Isobe et al. (1990) that considers such a method preferable for
problems that require a symmetrical treatment of the two variables. To
estimate the quality of the linear regression, we used the generalised
Kendall’s $\tau$ test (Kendall, 1983) (task `bhkmethod`) valid for sample
smaller than 30 targets as in our case and the associated probability that the
correlation is fortuitous. We have also measured the (maximum) rms of the
correlations, by assuming that censored data are detections. Table 5 provides
the statistical parameters, slope and intercepts of the linear regressions we
evaluate in this work.

Table 5: Statistical censored analysis of the tested correlations for RQQs and
RLQs.

$X$ | $Y$ | Fig. | sample | Stat | $\rho_{XY}$ | $P_{\rho_{XY}}$ | rms | Slope | Intercept
---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
$\log P_{5~{}{\rm GHz}}$ | $\log L_{\rm X}$ | 5 | RQQ | K | 0.857 | 0.0285 | 0.184 | 0.58$\pm$0.24 | 21.6$\pm$8.1
$\log P_{45~{}{\rm GHz}}$ | $\log L_{\rm X}$ | 5 | RQQ | K | 1.209 | 0.0011 | 0.117 | 0.60$\pm$0.20 | 20.5$\pm$7.6
$\log P_{5~{}{\rm GHz}}$ | $\log L_{\rm o}$ | 5 | RQQ | K | 0.933 | 0.0052 | 0.182 | 0.91$\pm$0.29 | 9.4$\pm$8.9
$\log P_{45~{}{\rm GHz}}$ | $\log L_{\rm o}$ | 5 | RQQ | K | 1.009 | 0.0046 | 0.172 | 0.90$\pm$0.29 | 9.0$\pm$6.1
$\log P_{5~{}{\rm GHz}}$ | $\log L_{\rm bol}$ | 5 | RQQ | K | 0.743 | 0.0260 | 0.233 | 0.97$\pm$0.32 | 7.8$\pm$9.1
$\log P_{45~{}{\rm GHz}}$ | $\log L_{\rm bol}$ | 5 | RQQ | K | 0.933 | 0.0081 | 0.168 | 0.99$\pm$0.34 | 6.7$\pm$9.5
$\log P_{5~{}{\rm GHz}}$ | $\log L_{\rm[O~{}III]}$ | 5 | RQQ | K | 0.705 | 0.0436 | 0.250 | 0.816$\pm$0.25 | 11.4$\pm$13.6
$\log P_{45~{}{\rm GHz}}$ | $\log L_{\rm[O~{}III]}$ | 5 | RQQ | K | 1.276 | 0.0003 | 0.238 | 0.811$\pm$0.19 | 11.0$\pm$12.5
$\log M_{\rm BH}$ | $\log P_{5~{}{\rm GHz}}$ | 7 | RQQ | K | 0.5902 | 0.0746 | 0.469 | 1.17$\pm$0.35 | 29.7$\pm$19.1
$\log M_{\rm BH}$ | $\log P_{45~{}{\rm GHz}}$ | 7 | RQQ | K | 1.0095 | 0.0023 | 0.297 | 1.17$\pm$0.28 | 30.3$\pm$33.7
$\log M_{\rm BH}$ | $\log P_{5~{}{\rm GHz}}$ | 7 | RLQ | P | 0.576 | 0.066 |  |  |
$\log M_{\rm BH}$ | $\log P_{45~{}{\rm GHz}}$ | 7 | RLQ | K | 0.2167 | 0.5352 |  |  |
$\log H\beta\,\,FWHM$ | $\alpha_{5-45~{}{\rm GHz}}$ | 8 | RQQ | K | 0.8791 | 0.0258 |  |  |
$\log H\beta\,\,FWHM$ | $\alpha_{5-45~{}{\rm GHz}}$ | 8 | RLQ | K | -0.850 | 0.0215 |  |  |
$\log L/L_{\rm Edd}$ | $\alpha_{5-45~{}{\rm GHz}}$ | 8 | RQQ | K | -0.593 | 0.132 |  |  |
$\log L/L_{\rm Edd}$ | $\alpha_{5-45~{}{\rm GHz}}$ | 8 | RLQ | K | 0.0167 | 0.964 |  |  |
$\log M_{\rm BH}$ | $\alpha_{5-45~{}{\rm GHz}}$ | 8 | RQQ | K | 0.725 | 0.0655 |  |  |
$\log M_{\rm BH}$ | $\alpha_{5-45~{}{\rm GHz}}$ | 8 | RLQ | K | -0.567 | 0.125 |  |  |
$\log L/L_{\rm Edd}$ | $\log P_{45~{}{\rm GHz}}/L_{\rm o}$ | 9 | RQQ | K | -0.991 | 0.0093 | 0.245 | -0.90$\pm$0.36 | -5.5$\pm$4.1
$\log L/L_{\rm Edd}$ | $\log P_{45~{}{\rm GHz}}/L_{\rm o}$ | 9 | RLQ | K | 0.0381 | 0.903 |  |  |
$\log M_{\rm BH}$ | $\log P_{45~{}{\rm GHz}}/L_{\rm X}$ | 9 | RQQ | K | 0.7619 | 0.0078 | 0.322 | 0.90$\pm$0.37 | -11.7$\pm$7.2
$\log M_{\rm BH}$ | $\log P_{45~{}{\rm GHz}}/L_{\rm X}$ | 9 | RLQ | K | -0.350 | 0.3387 |  |  |

Column description: (1)-(2) the two variables of the considered relation; (3)
Figure; (4) sample (RQQ or RLQ) for the tested correlation. (5)–(6)–(7) the
statistical analysis used for the given sub-sample to calculate the associated
linear regression coefficient $\rho_{\rm XY}$ and the probability that there
is no correlation $P_{\rho_{XY}}$: $K$ for the censored generalised Kendall’s
$\tau$ correlation coefficient and $P$ for the Pearson correlation coefficient
for a fully detected data set; (8) the rms scatter of the linear regression;
(9)–(10) the slope and the intercept of the best fits with their 1-$\sigma$
errors.

Figure 5 shows that P${}_{45~{}{\rm GHz}}$ presents a tighter correlations
with $L_{\rm X},L_{\rm opt},L_{\rm bol}$ and $L_{\rm[OIII]}$ compared to those
with P${}_{5~{}{\rm GHz}}$. A clear outlier from the X-ray–radio regressions
is PG 1001+054, which is known to be significantly X-ray absorbed (Schartel et
al., 2005). Therefore we excluded this target in the statistical analysis.
From all correlations presented in Fig. 5, the tightest fit is P${}_{45~{}{\rm
GHz}}$-$L_{\rm X}$ (rms = 0.117) and the most statistically significant one is
P${}_{45~{}{\rm GHz}}$– $L_{\rm[O~{}III]}$ (P = 0.0003). The strength of these
two relations is remarkable, given the fact that the X-ray and optical nuclei
are generally more variable (variability amplitudes, typically, of a factor of
several, up to $\sim$50, e.g. Markowitz & Edelson 2004; Paolillo et al. 2004;
Guainazzi et al. 2004; Saez et al. 2012; Lanzuisi et al. 2014) than those
detected in the radio-band (variability amplitudes of a factor of few, e.g.
Barvainis et al. 2005; Mundell et al. 2009).

###  3.2 Comparison with PG radio-loud quasars

The PG quasar sample (Boroson & Green, 1992) also includes 16 RL AGN. Below we
compare their 45 GHz properties with those of the PG RQQs to search for
significant similarities and differences between the two quasar samples. This
aims at investigating the nature of the radio emission in RQQs in relation to
the well-studied relativistic collimated jet emission of RL AGN.

We obtain 45-GHz VLA observations in A and B configuration for 8 RLQs from the
literature (see Table 6). For the remaining 8 sources, the 45 GHz flux
densities are roughly estimated by a power-law extrapolation of their radio
spectra (taken from the NASA/IPAC Extragalactic Database555NED,
http://ned.ipac.caltech.edu) from lower frequencies666This method is supported
by the fact that all the RLQs are Fanaroff-Riley type-II radio galaxies, which
have powerful extended steep-spectrum jets which dominate the entire broadband
radio SED. As a counter-check, the 45-GHz VLA luminosities of the 8 RLQs take
from literature are consistent with the values extrapolated from the data from
NED within the scatter of the power-law relation.. The typical spectral
coverage is from 74 MHz to 8.5 GHz and in some cases up to the 31.4 GHz. The
typical error bars on the 45-GHz flux densities for those sources is estimated
as a factor 2 of the measurements ($\sim$0.3 in logarithmic scale).

Figure 6 compares L${}_{45~{}{\rm GHz}}$ versus L${}_{5~{}{\rm GHz}}$ (erg s-1
Hz-1) of the PG RLQs and RQQs. The RLQs are typically $\sim 1000$ times
brighter than the RQQs at both 5 GHz and at 45 GHz. The scatter of the
relation between log L${}_{45~{}{\rm GHz}}$ and log L${}_{5~{}{\rm GHz}}$ of
the PG RQQs ($\sigma$=0.29) is smaller than that for that RLQs
($\sigma$=0.41). This may result from enhanced core variability and
orientation-dependent Doppler beaming or from the spectral extrapolation
scatter, valid for RLQs.

Table 6: Radio properties of the PG RLQ sample.

PG name | alternative | Fcore | $P_{45~{}{\rm GHz}}$
---|---|---|---
PG 0007+106 | MRK 1501 | 2.6$\pm$1.0a,b,c Jy | 43.32
PG 1226+023 | 3C 273 | 26.9$\pm$10.8a Jy | 44.89
PG 1302-102 | PKS 1302-102 | 0.59$\pm$0.07a,d Jy | 43.78
PG 1545+210 | 3C 323.1 |  $<$2.6a mJy |  $<$42.27
PG 1704+608 | 3C 351 |  $<$2.2a mJy |  $<$42.61
PG 2209+184 | II Zw 171 | 37.6$\pm$17.2a mJy | 41.25
PG 1103-006 | PKS 1106-0052 | 67.65$\pm$14.4e mJy | 43.27
PG 1512+370 | 4C +37.43 | 15.0f mJy | 42.47
PG 0003+158 | PKS 0003+15 | 56 mJy | 43.25
PG 1004+130 | 4C +13.41 | 79 mJy | 42.76
PG 1048-090 | 3C 246 | 148 mJy | 43.40
PG 1100+772 | 3C 249.1 | 110 mJy | 43.16
PG 1309+355 |  | 25 mJy | 42.00
PG 1425+267 | B2 1425+26 | 25 mJy | 42.68
PG 2251+113 | 4C +11.72 | 79 mJy | 43.06
PG 2308+098 | 4C +09.72 | 34 mJy | 42.99

Column description: (1)-(2) PG source name and alternative name; (3)–(4) radio
core flux densites and luminosities (erg s-1) obtained from Q-band radio maps
(upper list) and extrapolated by fitting the radio SED taken from NED (lower
list) (See Sect 3.2 for details); references: $a$ NVAS (NRAO VLA Archive
Survey), $b$ Gu et al. (2009), $c$ Lanyi et al. (2010), $d$ Perley &
Meisenheimer (2017), $e$ Sajina et al. (2011), $f$ Bolton et al. (2004); (4)
45-GHz core luminosity (erg s-1). The typical error of the core flux densities
of RLQs derived from their radio SED is approximately a factor $\sim$2 of the
measurements.

Since the BH mass has been found to be a crucial quantity for modeling and
interpreting observations in the framework of jet launching mechanism of RL
AGN (Blandford & Znajek, 1977; Cattaneo & Best, 2009), here we compare the
radio luminosities of the PG quasars with MBH. Fig. 7 shows the dependence of
$P_{45~{}{\rm GHz}}$ and $P_{\rm 5GHz}$ on MBH for the RL and RQ PG quasars.
The RQQs show a strikingly tight linear correlations, (P=0.0023 for
P${}_{45~{}{\rm GHz}}$) with a smaller scatter at 45 GHz than at 5 GHz, in the
form P${}_{45~{}{\rm GHz}}\propto M_{\rm BH}^{1.17}$, which is consistent
within the errors with the slope of the MBH-radio correlation established for
nearby RQ AGN observed with eMERLIN (Baldi et al., 2021b). For RLQs the radio-
BH relations have significantly larger scatter and are not statistically
significant, with $P$ values of only $\gtrsim$0.07. Apart from possible large
systematic errors due to the SED-extrapolated 45-GHz emission, the most
plausible physical reason of a larger scatter for the RLQ relation than that
of RQQs is the higher variability amplitude of RLQs due to Doppler boosting.

Figure 6: The 5-GHz radio core luminosities vs the 45-GHz luminosity (erg s-1
Hz-1). The filled points are the 15 RQQs, the empty points are the RLQs with
available VLA Q-band data and the crossed empty circles are the RLQs with the
45-GHz flux densities extrapolated from their radio spectra. The RLQs are
typically $\sim 1000$ more luminous than the RQQs at both 5 GHz and 45 GHz.
The dotted lines are drawn to visualise a scatter of a factor of 10. The
scatter of RQQs ($\sigma$=0.29) is smaller than that of RLQs ($\sigma$=0.41).

To derive the spectral slopes between the C and Q bands
(F${}_{\rm\nu}\sim\nu^{\alpha}$), we used the $uv$-tapered Q-band core flux
densities which are extracted from the images with a resolution comparable
with the C band data, $\sim$0.3-0.5 arcsec. The $\alpha_{5-45\rm{GHz}}$ values
range between -1 and 0.3 (Tab. 4, with typical errors of 30 per cent), a
narrower interval than the spectral indices derived at lower radio
frequencies, 5-8.5 GHz (Laor et al., 2019). We compared the 5–45 GHz indices
with the parameters of the EV1 set of correlations (Boroson & Green, 1992),
i.e., H$\beta$ FWHM, Eddington ratio L/LEdd, and MBH, in analogy to the
analysis done by Laor et al. (2019) (Fig. 8, left panels). We fit the censored
data, and the derived relations between the radio slopes and the three
quantities for the RQQs appear to be statistically weak (with probabilities of
fortuitous correlations higher than 0.02, see Tab 5). General trends have been
found: the radio slope generally seems to flatten for larger H$\beta$ width,
smaller L/LEdd and higher MBH, similarly to what was seen by Laor et al.
(2019), but with lower statistical significance. For a comparison with RLQs,
we analogously fit their censored $\alpha_{5-45\rm{GHz}}$ and EV1 quantities
(Fig. 8, right panels). The statistics of the regressions are even lower than
those of RQQs, but we can conclude that RLQs generally display opposite trends
to the ones obtained with RQQs, which could slightly strengthen the different
radio physical properties of RQQs and RLQs. The statistically strongest
relation (P $\sim$ 0.02) is $\alpha_{5-45\rm{GHz}}$ – H$\beta$ FWHM, where
RQQs and RLQs clearly reveal opposite regressions.

Figure 7: MBH (in M⊙) vs. P${}_{5~{}{\rm GHz}}$ (upper panel) and vs.
P${}_{45~{}{\rm GHz}}$ (lower panel) in units of erg s-1. The filled points
are the 15 RQQs, the empty points are the RLQs with available VLA Q band data
and the crossed empty circles are the RLQ with the 45-GHz flux densities
extrapolated from their radio spectra. The value of the generalised Kendall’s
$\tau$ test probability (P) for the RQQ relation and its rms is provided in
each panel. Note the tight relation of P${}_{45~{}{\rm GHz}}$ and MBH valid
for RQQs. Figure 8: The radio spectral index derived between 5 and 45 GHz as
function of the H$\beta$ FWHM (km s-1), L/LEdd and MBH (M⊙). The left panels
show the 15 PG RQQs, whereas the right panels show the 16 PG RLQs. The filled
points are the PG RQQs, while the empty points are the PG RLQs. Those with
crosses are the PG RLQs whose 45-GHz radio luminosities have been estimated by
fitting their radio SED. The value in the lower left corner of each panel
expresses the generalised Kendall’s $\tau$ test probability (P) of a
fortuitous correlation and its rms. The strongest trends are with the H$\beta$
FWHM, but are opposite in RQQs and RQQs, suggesting different emission
mechanisms.

As the radio loudness has been related to the accretion properties and BH mass
in the past (e.g. Nelson 2000; Ho 2008; Best et al. 2005; Heckman & Best 2014;
Chang et al. 2021), we also investigate the 45 GHz-based radio loudness of the
PG quasars, measured as P${}_{45~{}{\rm GHz}}$/Lo and P${}_{45~{}{\rm
GHz}}$/LX, respectively as function of L/LEdd and MBH (Fig. 9). We find a
tight P${}_{45~{}{\rm GHz}}$/Lo – L/LEdd correlation (left panel, P= 0.0093,
rms= 0.245), where the RQQs become quieter with increasing L/LEdd. At
$L/L_{\rm Edd}\gtrsim$ 0.3, which is roughly the value when the spectral
indices steepen, $\lesssim$0 (Fig. 8), we get that P${}_{45~{}{\rm
GHz}}$/L${}_{\rm o}<10^{-5}$, the typical value expected for the corona disc
emission. In addition we also find that P${}_{45~{}{\rm GHz}}$/LX is linearly
correlated with MBH (P=0.0078, rms=0.322): RQQs become louder with increasing
MBH. Since 45-GHz luminosities have been found to correlate with the optical
and X-ray luminosities (despite not with a slope of unity), the dependence of
these luminosity ratios with L/LEdd and BH mass highlights a second-order
effect in the radio emission production in RQQs. A larger sample of RQQs would
still be necessary to confirm this result. Conversely, RLQs do not show
statistically significant correlations. However we can note that at M${}_{\rm
BH}>10^{9}$ M⊙ all PG quasars become RL, and their P45GHz/LX jumps by a factor
of $\sim 30$, compared to the RQQs of our sample777The standard 5 GHz-to-
optical radio-loudness parameter drops by a factor of $\sim$1000 from RLQs and
RQQs at M${}_{\rm BH}\sim$ 109 M⊙..

Figure 9: Left panel: radio loudness estimated as ratio between 45-GHz and
optical luminosities versus L/LEdd. Right panel: radio loudness estimated as
ratio between 45-GHz and 2-10 keV X-ray luminosities versus MBH (M⊙). The
filled points are the PG RQQs, while the empty points are the PG RLQs. Those
with crosses are the PG RLQs whose 45-GHz radio luminosities have been
estimated by fitting their radio SED. The value in the lower part of each
panel expresses the rms and the generalised Kendall’s $\tau$ test probability
(P) of a fortuitous correlation for the RQQs. Note that the 45 GHz-based
radio-loudness decreases with increasing L/LEdd, while the X-ray based radio-
loudness increases towards higher MBH, with a jump by a factor of $\sim$30 at
$M_{\rm BH}>10^{9}$ M⊙, where all the PG quasars become RL.

##  4 Discussion

The overall 1.4 – 45 GHz spectra of the 15 PG RQQs studied here indicate that
two main components shape the SEDs of most of the sources: a steep-spectrum
and a flat-spectrum component which dominates, respectively, at low and high
radio frequencies. The 45-GHz emission is generally dominated by the latter,
which in some objects extends down to 5 GHz (at least in 9 sources), in
particular in high resolution observations. A flat-spectrum core suggests an
optically thick source, which implies a physically compact source with a size
$\sim$0.001$-$0.02 pc (e.g. eq. 22 in Laor & Behar 2008).

A compact source which characterises the 45-GHz emission, is also supported by
two further results from this study. In fact, most of our sources are
unresolved, i.e should be smaller than $\sim 50$ mas, which corresponds to
physical sizes smaller than $\sim 50-100$ pc. Only in two objects (PG 0844+349
and PG 1259+593) an unresolved core is not detected. These two sources also
lack of further detections at high resolution and at lower radio frequencies,
thus giving a coarse charaterisation of their radio spectra.

The other indirect evidence for the general compact nature of the 45 GHz
emission comes from the tight correlation of $P_{45~{}{\rm GHz}}$ with the
direct AGN luminosities $L_{\rm X},L_{\rm o},L_{\rm bol}$ and
$L_{\rm[O~{}III]}$, in particular when compared with the somewhat-weaker
correlations of $P_{\rm 5GHz}$ with these quantities. This result is notable
given the $\sim 20-30$ years time span between the 45 GHz and the earlier
optical and X-ray observations, and is similar to previous studies that have
found striking radio–X-ray correlations at even smaller radio scales and at
lower luminosities (e.g Panessa & Giroletti 2013; Panessa et al. 2015). As it
occurs at longer cm-band wavelengths, the 5 GHz luminosity may depend more on
the host galaxy properties, if it is produced e.g. by an AGN-driven wind which
shocks the host interstellar medium (ISM), or nuclear star formation (e.g.
Zakamska et al. 2016; Mancuso et al. 2017; Richards et al. 2021). Instead, at
higher radio frequencies, at 45 GHz in our case, the radio emission may
originate from an inner physical region at the accretion disc scale, e.g. from
coronal disc emission, or a weak jet (e.g. Chiaraluce et al. 2020; Smith et
al. 2020b, see Sect. 4.1 for the discussion on the radio origin), and is set
by the AGN properties.

The genuine compact nature of the 45 GHz emission of the PG RQQs which clearly
show spectral flattening at high frequencies, could be tested using VLBI
observations. A few available VLBI studies of RQ AGN (e.g. Blundell & Beasley
1998; Ulvestad et al. 2005b; Doi et al. 2013) reveal a mas-scale ($\sim pc$)
flat-spectrum compact source, which extrapolates well to the observed higher
radio-frequency emission (Laor et al., 2019). Future VLBI observations of the
PG RQQs, part of our survey, will confirm their compactness.

Although not statistically very robust, the suggested relations between
$\alpha_{\rm 5-45}$ and the H$\beta$ FWHM, L/LEdd and MBH are consistent with
the results found by Laor et al. (2019) for the PG quasars by using radio
slopes at 5–8.5 GHz. The most significant relation is the the steepening of
the radio slopes of RQQs with L/L${}_{\rm Edd}>0.3$ and low H$\beta$ widths.
This Eddington ratio limit can be interpreted at the condition of a
radiatively efficient accretion disc, required to launch a radiation pressure
driven wind, which then shocks the host ISM and produces a steep-spectrum
extended synchrotron source (King et al., 2013; Zakamska & Greene, 2014; Nims
et al., 2015). Conversely, the dependence on H$\beta$ FWHM is not simply
interpretable as a orientation effect, as a flatter spectra would be expected
in a polar view. The weaker correlations found here than the ones found with
$\alpha_{\rm 5-8.5}$ (Laor et al., 2019) may result from the fact that
$\alpha_{\rm 5-45}$ is more an estimate of the relative contributions of the
steep and flat sources. In contrast, the radio slope at 5-8.5 GHz, is a more
physical estimate of the nuclear properties and likely a more accurate measure
of the outflow characteristics.

A remarkable result of this study is the presence of unprecedentedly tight
correlation between the 45-GHz radio luminosity and the BH mass for our
sample, with a dependence similar to what has been found for local low-
luminosity RQ AGN, but with a larger scatter (Baldi et al., 2021b). The
connection between the mas-scale radio properties (luminosity, spectral slope,
radio loudness) and the BH mass for our sample suggests that the latter should
play an important role at setting the mechanism of radio production in RQQs
(in jet and wind scenarios). In addition, the radio loudness parameter has
been found to increase with BH mass and decrease with the Eddington ratio,
consistent with previous studies (e.g. Ho 2002; Merloni et al. 2003; Nagar et
al. 2005; Sikora et al. 2007; Gürkan et al. 2019; Chiaraluce et al. 2020).
However, in support of a distinct origin of the radio emission between RLQs
and RQQs is the different (even opposite) trends with radio slopes and BH
mass. Therefore, even in the same quasar regime (at high Eddington ratios),
the radio outflow of RQQs must differ in terms of its driving mechanism
compared to the strong jet observed in RLQs.

Based on the statistical significance of the tested correlations, the 45-GHz
emission in PG RQQs is mainly driven by the X-ray radiation and the BH mass.
The X-ray emitting corona coincide with the jet base for RLQs (Markoff et al.,
2005) and with the physical region where 45-GHz emission is produced, more
internal than the 5-GHz core, for RQQs (Laor & Behar, 2008). The similarity of
the 45-GHz emitting region of RLQs and RQQs would possibly suggest that the
corona is playing an important role in the radio emission production in
quasars and the properties of such a corona could account for the transition
from a relativistic jet in case of RLQs to a sub-relativistic outflow in case
of RQQs at high radio frequencies.

###  4.1 Origin of the 45-GHz emission in RQQs

Here we explore the various possible scenarios of radio-emitting physical
mechanisms (see Panessa et al. 2019), which may account for the results we
find in this work.

  * •

Star formation. A compact nuclear starburst could be scarcely consistent with
the flat-spectrum unresolved cores we find. High star formation (SF) rate is
generally expected at high accretion-rate AGN, as expected in a quasar regime
(Sani et al., 2010). At 45 GHz, in this scenario the radio emission could
primarily powered by free-free emission from discrete H II regions on sub-kpc
scale, making it an excellent tracer of massive SF (Murphy et al., 2018). The
expected SF rate estimated in this radio band is $\sim$0.6–60 $M_{\odot}$ yr-1
(equation 15 from Murphy et al. 2011, assuming electron temperature of 104 K
and a flat-spectrum non-thermal component), which is not far from what has
been found in luminous quasar hosts (Jarvis et al., 2020; Shangguan et al.,
2020) but is generally considered insufficient to explain the observed radio
emission from quasars by an order of magnitude (Zakamska & Greene, 2014;
Zakamska et al., 2016). Nevertheless, the morphological compactness of the
radio emission and the multi-band correlations of the radio luminosities with
AGN parameters (MBH, $L_{\rm bol}$, L/LEdd) argue against SF as the origin of
the high-frequency radio emission in PG RQQs.

  * •

Disc wind. An AGN-driven wind interacting with the ISM and the consequent
shock acceleration can cause synchrotron emission (see models from Jiang et
al. 2010; Nims et al. 2015). The optically-thin radio emission is expected
from an outflowing plasma from a standard accretion disc (Shakura & Sunyaev,
1973) with high radiation pressure, generally related to a high L/LEdd. Such
scenario would explain the relation between steep spectral slopes and the high
L/LEdd and large bolometric luminosities. A faster wind being accelerated by
higher continuum-scattering (i.e. higher Eddington ratio, Gofford et al. 2015)
will produce stronger shocks which will accelerate more electrons, resulting
in higher radio luminosities. The most luminous radio sources would
approximately lie on the relation between the radio luminosity and the [O III]
line width established by Zakamska & Greene (2014)888To be consistent with the
line width – $L_{\rm 1.4GHz}$ relation introduced by Zakamska & Greene (2014)
for obscured quasars, we derive the velocity width containing 90 per cent of
[O III] line, by assuming the conservative scenario where line is blueshifted
and [O III] and H$\beta$ widths are similar (H$\beta$ are slightly [8 per
cent] systematically narrower than [O III] on average, Zakamska & Greene
2014). In addition, we derive the 1.4-GHz luminosities from our measurements,
assuming a flat-spectrum synchrotron component with a slope of 0.5. Therefore,
this method with several assumptions provides an approximate estimate of the
radio emission from a disc wind model for our sample., interpreted as
synchrotron radio emission form a quasar-driven winds propagating into the ISM
of the host galaxy. A steep radio spectra would be consistent with synchrotron
emission from a diffuse disc wind on the scale of the galaxy. Moreover, the
radio production based on this mechanism is not predicted to depend directly
on MBH, in contrast with our results. In conclusion, we cannot fully rule out
the possibility that the 45-GHz radio luminosities of the high-Eddington
luminous PG RQQs have a significant contribution from a disc wind.

  * •

Jet. An uncollimated sub-relativistic jet, whose power is scaled down with
respect to the jets in RLQs, is another possible scenario. As already
discussed by Laor et al. (2019), an orientation dependence of the radio
properties similar to that interpreted for the RLQ unification scheme would
lead to an opposite relation between the observed spectral slope and the
H$\beta$ width: in the case of a type-1 AGN by definition, low inclination
would tend to show smaller line widths and flatter radio spectra (an
isotropically-emitting outflow could still be possible). The observed MBH
correlation with the radio luminosity and radio-loudness is consistent with
the idea of a jet lunching mechanism by extracting energy from a spinning
supermassive BH, specifically the Blandford-Znajek process (Blandford &
Znajek, 1977). A large BH masses and low Eddington ratios a core-brightened
jet component is possibly emerging in the radio band, in agreement with what
has been found for local Seyferts Baldi et al. (2021b). However, we do not
find any continuity of the radio properties between the RQQs and the RLQs of
the sample999It is still not clear whether a bimodal or continuous radio-
loudness distribution of RQ and RL AGN would be distinct in the radio
properties of the two classes (in terms of e.g. kinetic luminosity, size,
speeds) (e.g., Kellermann et al. 1989; Cirasuolo et al. 2003; Ho 2008;
Macfarlane et al. 2021), excluding any possible result bias due to the
incompleteness of the sample or because they come from the same original PG
sample. Furthermore, the RLQs reveal a hint of reverse trends to the radio-
based correlations shown by RQQs, suggesting different driving mechanisms of
radio production.

  * •

Coronal wind. A magnetically-active corona linked to an accretion disc can
produce synchrotron radio emission from the accelerated relativistic electrons
produced by magnetic reconnection (Laor & Behar, 2008; Raginski & Laor, 2016).
A dependence of the radio production on the X-ray power, produced by the
cooling electrons, and the Eddington ratio is expected. In fact the high-
frequency radio emission tightly correlates with high-energy nuclear
component, suggesting a causal common emitting region, i.e. corona. The
observed radio to X-ray luminosity ratio agrees with the 10-5 ratio found for
the analogous active coronae in cool active stars (Güdel & Benz, 1993). Highly
active coronae, associated with high L/LEdd, are able to produce extended
radio emission with an optically-thin bubble emerging from the outflowing
corona similar to a Coronal Mass Ejection. At higher X-ray luminosities, the
height of the corona would increase (Alston et al., 2020) with a higher
probability of outflowing. At low L/LEdd, the radio emission is only related
to the flat-spectrum self-absorbed emission emanated by an unresolved corona.
When the Compton scattering is the dominant cooling mechanism, the
luminosities from the corona should follow $\propto$ MBH (Taam et al., 2008;
Liu & Liu, 2009), consistent with the present results at 45 GHz.

Based on our result, the most probable scenarios to account for the radio
properties of PG RQQs is that their radio cores originate from non-thermal
relativistic electrons likely accelerated in an active corona, where intense
magnetic reconnection events occur. However, a possible increment of the
emission contribution from a weak jet, as the BH mass increases, cannot be
ruled out, similarly to the jet power dependence on MBH observed in RL AGN
(Liu et al., 2006), although the role of such a quantity in characterising the
RQ AGN properties is still controversial (e.g., Boroson 2002; Metcalf &
Magliocchetti 2006; Gürkan et al. 2019; Macfarlane et al. 2021; Baldi et al.
2021b). In our case, this interpretation will accommodate the flat-spectrum
cores we observe at low L/LEdd and large BH masses. In addition, the most
luminous quasars at high Eddington ratios could have an important contribution
in the radio band from disc winds. In fact, when the AGN disc is able to drive
strong winds due to high radiation pressure, optically-thin intense steep-
spectrum radio emission can be emanated either by the accretion disc itself or
from the outflowing corona. The absence of such outflowing component at low
L/LEdd is due to the decreasing of the radiation pressure and thus its
relative radio contribution, which make the flat-spectrum core emerges over
the steep-spectrum component. Nevertheless, it appear clear that a nuclear
star-forming core does not appear to reconcile with our results and with a
general interpretation of the radio emission in type-1 QSOs (Zakamska et al.,
2016).

###  4.2 Comparison with X-ray Binary Systems

Since jets are observed across all types of active BHs, it is interesting to
ask whether there are any similarities between the radio properties of the
RQQs and those of X-ray binary systems (XRBs) and hence whether RQQs
correspond to any particular X-ray ’state’ of XRBs. Fender et al. (2004)
provide a full description of the change of radio luminosity with ’state’. In
the low/hard X-ray state where, very broadly, the accretion rate is low or
only moderate and the accretion is probably radiatively inefficient, there is
steady and relatively powerful radio emission from a jet, with radio and X-ray
luminosities being well correlated (e.g. Corbel et al. 2013). Although not the
only possible interpretation, the correlations shown in Fig. 5 are quite
consistent with such a scenario. At very high accretion rates, i.e. the soft
X-ray state where the accretion is radiatively efficient, there is no
detectable radio emission. For example, the persistent soft-state XRB
4U1957+11 (Maccarone et al., 2020) is undetected in radio maps with noise
level of 1.07 $\mu$Jy/beam, whilst at a 2-20 keV X-ray flux of 10-9 erg cm-2
s-1. The radio/X-ray ratio for the present PG RQQs is 10-5 far greater than
value for XRBs.

Part of the increased radio emission in RQQs with respect to XRBs may be due
to the BH mass dependency in core-dominated jets. Heinz & Sunyaev (2003) argue
that AGN should be 3 – 4 orders of magnitude more radio loud than XRBs.
However, with radio flux densities 3 or 4 orders of magnitude above the upper
limit for 4U1957+11, and X-ray fluxes about 2 orders of magnitude less than
that of 4U1957+11, the PG RQQs are still at least 1-2 orders of magnitude more
radio loud than expected if they were soft state XRBs, even taking account of
the mass dependency. Consequently, RQQs are probably not simply soft-state
systems (see Davis & Tchekhovskoy 2020).

The increase of radio luminosity with BH mass seen in our sample is consistent
with at least a contribution from a compact jet in the radio emission in a
hard-state scenario. Conversely, a decrease in radio luminosity with
increasing accretion rate is not consistent with a jet scenario (Heinz &
Sunyaev, 2003), at least if the RQQs remain in the hard state. However, the
variation of radio luminosity with accretion rate and BH mass in RQQs,
differently from XRB states, likely indicates a complexity of different
accretion-ejection modes (e.g. Fernández-Ontiveros & Muñoz-Darias 2021; Baldi
et al. 2021b) and that at least two sources of radio emission co-exist for
RQQs.

##  5 Conclusions

This initial study (15 targets) of a comprehensive radio survey of the PG RQQs
(71 objects), named PG-RQS, reveals the following main results.

  1. 1.

The 45-GHz emission is detected in 13 out of 15 PG RQQs, is generally
unresolved, implying a source smaller than typically 50-100 pc.

  2. 2.

The high frequency emission in PG RQQs is generally characterised by a flat
spectrum component, that indicates a compact optically thick source.

  3. 3.

The 45-GHz luminosity is tightly correlated with the AGN nuclear strength
(X-ray, optical, [O III], bolometric luminosities), suggesting an origin at
the accretion disc scale. The 45-GHz luminosity is also correlated with BH
mass.

  4. 4.

The radio spectral properties of RQQs marginally correlate with AGN
parameters: a flat-spectrum core emerges at low Eddington ratios, large BH
masses and small H$\beta$ widths.

  5. 5.

The 45 GHz-based radio loudness decreases with increasing Eddington ratio and
decreasing BH mass.

The most plausible scenario to account for the general properties of the
compact 45-GHz cores detected in our sample is synchrotron emission from a
magnetically active X-ray coronae. However, at high Eddington ratios and large
BH masses a radio-emission contribution from a disc wind and weak jet,
respectively, cannot be ruled out. These preliminary intriguing results need
to be verified by extending this study to the complete sample of the 71 PG
RQQs, which will help us to improve the statistical significance of the weak
regressions found in this work. Further studies, within the PG-RQS survey, at
higher resolution using the VLBI technique, together with an expanded spectral
coverage from low frequencies using GMRT and LOFAR observatories, to the mm
and sub-mm regime using ALMA, will likely allow to determine the range of
radio emission mechanism in RQ AGN, and shed new light on a host of physical
processes from star formation on kpc scale down to the coronal structure on
milli-pc scale. The future step will be the advent of SKA, which will survey
vast numbers of local RQ active galaxies with $\mu$Jy-sensitivity at low and
intermediate radio frequencies (Orienti et al., 2015), providing the
cornerstone of our understanding of radio emission across a wide range of
galaxy types and accretion properties.

## Acknowledgments

We thank the anonymous referee for his/her helpful comments to improve the
manuscript. A.H. acknowledges support by the I-Core Program of the Planning
and Budgeting Committee and the Israel Science Foundation, and support by ISF
grant 647/18. This research was supported by Grant No. 2018154 from the United
States-Israel Binational Science Foundation (BSF). A.L. acknowledges support
by the Israel Science Foundation (grant no. 1008/18). E.B. is funded by a
Center of Excellence of THE ISRAEL SCIENCE FOUNDATION (grant No. 2752/19).
I.M. acknowledges support from STFC under ST/R000638/1. The National Radio
Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.

## Data availability

The radio data used in this work have been obtained by the VLA. The
uncalibrated dataset is public and available from the VLA data archive
(project 16B-126). Calibrated image products are available upon reasonable
request to the corresponding author.

## References

  * Alston et al. (2020) Alston W. N., et al., 2020, Nature Astronomy, 4, 597
  * Baldi et al. (2015) Baldi R. D., Behar E., Laor A., Horesh A., 2015, MNRAS, 454, 4277
  * Baldi et al. (2018) Baldi R. D., et al., 2018, MNRAS, 476, 3478
  * Baldi et al. (2021a) Baldi R. D., et al., 2021a, MNRAS, 500, 4749
  * Baldi et al. (2021b) Baldi R. D., et al., 2021b, MNRAS, 508, 2019
  * Barvainis & Antonucci (1989) Barvainis R., Antonucci R., 1989, ApJS, 70, 257
  * Barvainis et al. (1996) Barvainis R., Lonsdale C., Antonucci R., 1996, AJ, 111, 1431
  * Barvainis et al. (2005) Barvainis R., Lehár J., Birkinshaw M., Falcke H., Blundell K. M., 2005, ApJ, 618, 108
  * Baskin & Laor (2005) Baskin A., Laor A., 2005, MNRAS, 356, 1029
  * Baskin & Laor (2021) Baskin A., Laor A., 2021, MNRAS
  * Becker et al. (1995) Becker R. H., White R. L., Helfand D. J., 1995, ApJ, 450, 559
  * Behar et al. (2015) Behar E., Baldi R. D., Laor A., Horesh A., Stevens J., Tzioumis T., 2015, MNRAS, 451, 5036
  * Behar et al. (2018) Behar E., Vogel S., Baldi R. D., Smith K. L., Mushotzky R. F., 2018, MNRAS, 478, 399
  * Behar et al. (2020) Behar E., et al., 2020, MNRAS, 491, 3523
  * Berriman et al. (1990) Berriman G., Schmidt G. D., West S. C., Stockman H. S., 1990, ApJS, 74, 869
  * Best et al. (2005) Best P. N., Kauffmann G., Heckman T. M., Brinchmann J., Charlot S., Ivezić Ž., White S. D. M., 2005, MNRAS, 362, 25
  * Bian et al. (2008) Bian W.-H., Chen Y.-M., Hu C., Huang K., Xu Y., 2008, Chinese J. Astron. Astrophys., 8, 522
  * Blandford & Znajek (1977) Blandford R. D., Znajek R. L., 1977, MNRAS, 179, 433
  * Blandford et al. (2019) Blandford R., Meier D., Readhead A., 2019, ARA&A, 57, 467
  * Blundell & Beasley (1998) Blundell K. M., Beasley A. J., 1998, MNRAS, 299, 165
  * Blundell et al. (1996) Blundell K. M., Beasley A. J., Lacy M., Garrington S. T., 1996, ApJ, 468, L91
  * Bolton et al. (2004) Bolton R. C., et al., 2004, MNRAS, 354, 485
  * Boroson (2002) Boroson T. A., 2002, ApJ, 565, 78
  * Boroson & Green (1992) Boroson T. A., Green R. F., 1992, ApJS, 80, 109
  * Brandt et al. (2000) Brandt W. N., Laor A., Wills B. J., 2000, ApJ, 528, 637
  * Cattaneo & Best (2009) Cattaneo A., Best P. N., 2009, MNRAS, 395, 518
  * Chang et al. (2021) Chang N., Xie F. G., Liu X., Ho L. C., Dong A. J., Han Z. H., Wang X., 2021, MNRAS, 503, 1987
  * Chiaraluce et al. (2019) Chiaraluce E., Bruni G., Panessa F., Giroletti M., Orienti M., Rampadarath H., Vagnetti F., Tombesi F., 2019, MNRAS, 485, 3185
  * Chiaraluce et al. (2020) Chiaraluce E., Panessa F., Bruni G., Baldi R. D., Behar E., Vagnetti F., Tombesi F., McHardy I., 2020, MNRAS, 495, 3943
  * Cirasuolo et al. (2003) Cirasuolo M., Celotti A., Magliocchetti M., Danese L., 2003, MNRAS, 346, 447
  * Condon et al. (1998) Condon J. J., Cotton W. D., Greisen E. W., Yin Q. F., Perley R. A., Taylor G. B., Broderick J. J., 1998, AJ, 115, 1693
  * Condon et al. (2013) Condon J. J., Kellermann K. I., Kimball A. E., Ivezić Ž., Perley R. A., 2013, ApJ, 768, 37
  * Corbel et al. (2013) Corbel S., Coriat M., Brocksopp C., Tzioumis A. K., Fender R. P., Tomsick J. A., Buxton M. M., Bailyn C. D., 2013, MNRAS, 428, 2500
  * Davis & Laor (2011) Davis S. W., Laor A., 2011, ApJ, 728, 98
  * Davis & Tchekhovskoy (2020) Davis S. W., Tchekhovskoy A., 2020, ARA&A, 58, 407
  * Doi et al. (2005) Doi A., Kameno S., Kohno K., Nakanishi K., Inoue M., 2005, MNRAS, 363, 692
  * Doi et al. (2011) Doi A., Nakanishi K., Nagai H., Kohno K., Kameno S., 2011, AJ, 142, 167
  * Doi et al. (2013) Doi A., Asada K., Fujisawa K., Nagai H., Hagiwara Y., Wajima K., Inoue M., 2013, ApJ, 765, 69
  * Falcke et al. (2001) Falcke H., Lehár J., Barvainis R., Nagar N. M., Wilson A. S., 2001, in Probing the Physics of Active Galactic Nuclei. p. 265 (arXiv:astro-ph/0009457)
  * Fawcett et al. (2020) Fawcett V. A., Alexander D. M., Rosario D. J., Klindt L., Fotopoulou S., Lusso E., Morabito L. K., Calistro Rivera G., 2020, MNRAS, 494, 4802
  * Fender et al. (2004) Fender R. P., Belloni T. M., Gallo E., 2004, MNRAS, 355, 1105
  * Fernández-Ontiveros & Muñoz-Darias (2021) Fernández-Ontiveros J. A., Muñoz-Darias T., 2021, MNRAS, 504, 5726
  * Field & Rogers (1993) Field G. B., Rogers R. D., 1993, ApJ, 403, 94
  * Gallimore et al. (1997) Gallimore J. F., Baum S. A., O’Dea C. P., 1997, Nature, 388, 852
  * Gallimore et al. (2006) Gallimore J. F., Axon D. J., O’Dea C. P., Baum S. A., Pedlar A., 2006, AJ, 132, 546
  * Giroletti & Panessa (2009) Giroletti M., Panessa F., 2009, ApJ, 706, L260
  * Gofford et al. (2015) Gofford J., Reeves J. N., McLaughlin D. E., Braito V., Turner T. J., Tombesi F., Cappi M., 2015, MNRAS, 451, 4169
  * Gu et al. (2009) Gu M., Cao X., Jiang D. R., 2009, MNRAS, 396, 984
  * Guainazzi et al. (2004) Guainazzi M., Jimenez-Bailon E., Piconcelli E., 2004, arXiv e-prints, pp astro–ph/0409438
  * Güdel & Benz (1993) Güdel M., Benz A. O., 1993, ApJ, 405, L63
  * Güdel et al. (2002) Güdel M., Audard M., Smith K. W., Behar E., Beasley A. J., Mewe R., 2002, ApJ, 577, 371
  * Gürkan et al. (2019) Gürkan G., et al., 2019, A&A, 622, A11
  * Haas et al. (2003) Haas M., et al., 2003, A&A, 402, 87
  * Heckman & Best (2014) Heckman T. M., Best P. N., 2014, ARA&A, 52, 589
  * Heinz & Sunyaev (2003) Heinz S., Sunyaev R. A., 2003, MNRAS, 343, L59
  * Ho (2002) Ho L. C., 2002, ApJ, 564, 120
  * Ho (2008) Ho L. C., 2008, ARA&A, 46, 475
  * Inoue & Doi (2014) Inoue Y., Doi A., 2014, PASJ, 66, L8
  * Inoue & Doi (2018) Inoue Y., Doi A., 2018, ApJ, 869, 114
  * Isobe et al. (1990) Isobe T., Feigelson E. D., Akritas M. G., Babu G. J., 1990, ApJ, 364, 104
  * Jarvis et al. (2019) Jarvis M. E., et al., 2019, MNRAS, 485, 2710
  * Jarvis et al. (2020) Jarvis M. E., et al., 2020, MNRAS, 498, 1560
  * Jarvis et al. (2021) Jarvis M. E., et al., 2021, MNRAS, 503, 1780
  * Jiang et al. (2010) Jiang Y.-F., Ciotti L., Ostriker J. P., Spitkovsky A., 2010, ApJ, 711, 125
  * Kaspi et al. (2000) Kaspi S., Smith P. S., Netzer H., Maoz D., Jannuzi B. T., Giveon U., 2000, ApJ, 533, 631
  * Kellermann et al. (1989) Kellermann K. I., Sramek R., Schmidt M., Shaffer D. B., Green R., 1989, AJ, 98, 1195
  * Kellermann et al. (1994) Kellermann K. I., Sramek R. A., Schmidt M., Green R. F., Shaffer D. B., 1994, AJ, 108, 1163
  * Kendall (1983) Kendall M., 1983, A New Measure of Rank Correlation. Vol. 30, Biometrika
  * King et al. (2013) King A. L., et al., 2013, ApJ, 762, 103
  * Kukula et al. (1995) Kukula M. J., Pedlar A., Baum S. A., O’Dea C. P., 1995, MNRAS, 276, 1262
  * Kukula et al. (1998) Kukula M. J., Dunlop J. S., Hughes D. H., Rawlings S., 1998, MNRAS, 297, 366
  * Lacy et al. (2001) Lacy M., Laurent-Muehleisen S. A., Ridgway S. E., Becker R. H., White R. L., 2001, ApJ, 551, L17
  * Lanyi et al. (2010) Lanyi G. E., et al., 2010, AJ, 139, 1695
  * Lanzuisi et al. (2014) Lanzuisi G., et al., 2014, ApJ, 781, 105
  * Laor (1998) Laor A., 1998, ApJ, 505, L83
  * Laor (2000) Laor A., 2000, ApJ, 543, L111
  * Laor & Behar (2008) Laor A., Behar E., 2008, MNRAS, 390, 847
  * Laor et al. (2019) Laor A., Baldi R. D., Behar E., 2019, MNRAS, 482, 5513
  * Lavalley et al. (1992) Lavalley M., Isobe T., Feigelson E., 1992, in Worrall D. M., Biemesderfer C., Barnes J., eds, Astronomical Society of the Pacific Conference Series Vol. 25, Astronomical Data Analysis Software and Systems I. pp 245–+
  * Leipski et al. (2006) Leipski C., Falcke H., Bennert N., Hüttemeister S., 2006, A&A, 455, 161
  * Liu & Liu (2009) Liu J.-Y., Liu B.-F., 2009, Research in Astronomy and Astrophysics, 9, 966
  * Liu et al. (2006) Liu Y., Jiang D. R., Gu M. F., 2006, ApJ, 637, 669
  * Maccarone et al. (2020) Maccarone T. J., Osler A., Miller-Jones J. C. A., Atri P., Russell D. M., Meier D. L., McHardy I. M., Longa-Peña P. A., 2020, MNRAS, 498, L40
  * Macfarlane et al. (2021) Macfarlane C., et al., 2021, MNRAS, 506, 5888
  * Maini et al. (2016) Maini A., Prandoni I., Norris R. P., Giovannini G., Spitler L. R., 2016, A&A, 589, L3
  * Mancuso et al. (2017) Mancuso C., et al., 2017, ApJ, 842, 95
  * Markoff et al. (2005) Markoff S., Nowak M. A., Wilms J., 2005, ApJ, 635, 1203
  * Markowitz & Edelson (2004) Markowitz A., Edelson R., 2004, ApJ, 617, 939
  * McLure & Jarvis (2004) McLure R. J., Jarvis M. J., 2004, MNRAS, 353, L45
  * Merloni et al. (2003) Merloni A., Heinz S., di Matteo T., 2003, MNRAS, 345, 1057
  * Metcalf & Magliocchetti (2006) Metcalf R. B., Magliocchetti M., 2006, MNRAS, 365, 101
  * Middelberg et al. (2004) Middelberg E., et al., 2004, A&A, 417, 925
  * Miller et al. (1993) Miller P., Rawlings S., Saunders R., 1993, MNRAS, 263, 425
  * Mundell et al. (2009) Mundell C. G., Ferruit P., Nagar N., Wilson A. S., 2009, ApJ, 703, 802
  * Murphy et al. (2010) Murphy T., et al., 2010, MNRAS, 402, 2403
  * Murphy et al. (2011) Murphy E. J., et al., 2011, ApJ, 737, 67
  * Murphy et al. (2018) Murphy E. J., Dong D., Momjian E., Linden S., Kennicutt R. C. J., Meier D. S., Schinnerer E., Turner J. L., 2018, ApJS, 234, 24
  * Nagar et al. (1999) Nagar N. M., Wilson A. S., Mulchaey J. S., Gallimore J. F., 1999, ApJS, 120, 209
  * Nagar et al. (2002) Nagar N. M., Falcke H., Wilson A. S., Ulvestad J. S., 2002, A&A, 392, 53
  * Nagar et al. (2005) Nagar N. M., Falcke H., Wilson A. S., 2005, A&A, 435, 521
  * Nelson (2000) Nelson C. H., 2000, ApJ, 544, L91
  * Neugebauer et al. (1987) Neugebauer G., Green R. F., Matthews K., Schmidt M., Soifer B. T., Bennett J., 1987, ApJS, 63, 615
  * Nims et al. (2015) Nims J., Quataert E., Faucher-Giguère C.-A., 2015, MNRAS, 447, 3612
  * Nyland et al. (2020) Nyland K., et al., 2020, ApJ, 905, 74
  * Orienti et al. (2015) Orienti M., D’Ammando F., Giroletti M., Giovannini G., Panessa F., 2015, in Advancing Astrophysics with the Square Kilometre Array (AASKA14). p. 87 (arXiv:1412.5846)
  * Padovani et al. (2011) Padovani P., Miller N., Kellermann K. I., Mainieri V., Rosati P., Tozzi P., 2011, ApJ, 740, 20
  * Panessa & Giroletti (2013) Panessa F., Giroletti M., 2013, MNRAS, 432, 1138
  * Panessa et al. (2015) Panessa F., et al., 2015, MNRAS, 447, 1289
  * Panessa et al. (2019) Panessa F., Baldi R. D., Laor A., Padovani P., Behar E., McHardy I., 2019, Nature Astronomy,
  * Paolillo et al. (2004) Paolillo M., Schreier E. J., Giacconi R., Koekemoer A. M., Grogin N. A., 2004, ApJ, 611, 93
  * Park et al. (2013) Park S., Sohn B. W., Yi S. K., 2013, A&A, 560, A80
  * Perley & Meisenheimer (2017) Perley R. A., Meisenheimer K., 2017, A&A, 601, A35
  * Petric et al. (2015) Petric A. O., Ho L. C., Flagey N. J. M., Scoville N. Z., 2015, ApJS, 219, 22
  * Raginski & Laor (2016) Raginski I., Laor A., 2016, MNRAS, 459, 2082
  * Ricci et al. (2019) Ricci R., Prandoni I., De Ruiter H. R., Parma P., 2019, A&A, 621, A19
  * Richards et al. (2021) Richards G. T., McCaffrey T. V., Kimball A., Rankine A. L., Matthews J. H., Hewett P. C., Rivera A. B., 2021, arXiv e-prints, p. arXiv:2106.07783
  * Saez et al. (2012) Saez C., Brandt W. N., Gallagher S. C., Bauer F. E., Garmire G. P., 2012, ApJ, 759, 42
  * Sajina et al. (2011) Sajina A., Partridge B., Evans T., Stefl S., Vechik N., Myers S., Dicker S., Korngut P., 2011, ApJ, 732, 45
  * Sanders et al. (1989) Sanders D. B., Phinney E. S., Neugebauer G., Soifer B. T., Matthews K., 1989, ApJ, 347, 29
  * Sani et al. (2010) Sani E., Lutz D., Risaliti G., Netzer H., Gallo L. C., Trakhtenbrot B., Sturm E., Boller T., 2010, MNRAS, 403, 1246
  * Schartel et al. (2005) Schartel N., Rodríguez-Pascual P. M., Santos-Lleó M., Clavel J., Guainazzi M., Jiménez-Bailón E., Piconcelli E., 2005, A&A, 433, 455
  * Schmidt & Green (1983) Schmidt M., Green R. F., 1983, ApJ, 269, 352
  * Schmitt (1985) Schmitt J. H. M. M., 1985, ApJ, 293, 178
  * Science Software Branch at STScI (2012) Science Software Branch at STScI 2012, PyRAF: Python alternative for IRAF (ascl:1207.011)
  * Shakura & Sunyaev (1973) Shakura N. I., Sunyaev R. A., 1973, A&A, 24, 337
  * Shangguan et al. (2020) Shangguan J., Ho L. C., Bauer F. E., Wang R., Treister E., 2020, ApJ, 899, 112
  * Shi et al. (2014) Shi Y., Rieke G. H., Ogle P. M., Su K. Y. L., Balog Z., 2014, ApJS, 214, 23
  * Sikora et al. (2007) Sikora M., Stawarz Ł., Lasota J.-P., 2007, ApJ, 658, 815
  * Smith et al. (2016) Smith K. L., Mushotzky R. F., Vogel S., Shimizu T. T., Miller N., 2016, ApJ, 832, 163
  * Smith et al. (2020a) Smith K. L., et al., 2020a, MNRAS, p. 3237
  * Smith et al. (2020b) Smith K. L., Koss M., Mushotzky R., Wong O. I., Shimizu T. T., Ricci C., Ricci F., 2020b, ApJ, 904, 83
  * Taam et al. (2008) Taam R. E., Liu B. F., Meyer F., Meyer-Hofmeister E., 2008, ApJ, 688, 527
  * Talbot et al. (2021) Talbot R. Y., Sijacki D., Bourne M. A., 2021, arXiv e-prints, p. arXiv:2111.01801
  * Tremaine et al. (2002) Tremaine S., et al., 2002, ApJ, 574, 740
  * Ulvestad et al. (2005a) Ulvestad J. S., Wong D. S., Taylor G. B., Gallimore J. F., Mundell C. G., 2005a, AJ, 130, 936
  * Ulvestad et al. (2005b) Ulvestad J. S., Antonucci R. R. J., Barvainis R., 2005b, ApJ, 621, 123
  * Vestergaard & Peterson (2006) Vestergaard M., Peterson B. M., 2006, ApJ, 641, 689
  * Zakamska & Greene (2014) Zakamska N. L., Greene J. E., 2014, MNRAS, 442, 784
  * Zakamska et al. (2016) Zakamska N. L., et al., 2016, MNRAS, 455, 4191