# Hard-X-ray-selected Active Galactic Nuclei – II. Spectral Energy
Distributions in the 5-45 GHz domain

Francesca Panessa1, Elia Chiaraluce2, Gabriele Bruni1, Daniele Dallacasa3,4,
Ari Laor5, Ranieri D. Baldi4, Ehud Behar5, Ian McHardy6, Francesco
Tombesi7,8,9,10,11, Fausto Vagnetti1,7

1 INAF – Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del
Cavaliere 100, I-00133 Roma, Italy
2 AKKA Technologies Italia srl, via Tiburtina 1072/1074, 00156 Roma, Italy
3 DiFA – Dipartimento di Fisica e Astronomia, Università di Bologna, via P.
Gobetti 93/2, I-40129 Bologna, Italy
4 INAF – Istituto di Radioastronomia, via Piero Gobetti 101, I-40129 Bologna,
Italy
5 Physics Department, The Technion, 32000, Haifa, Israel
6 School of Physics and Astronomy, University of Southampton, Southampton,
SO17 1BJ, UK
7 Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca
Scientifica 1, I-00133 Roma, Italy
8 INAF – Astronomical Observatory of Rome, Via Frascati 33, I-00078 Monte
Porzio Catone, Italy
9 Department of Astronomy, University of Maryland, College Park MD 20742, USA
10 X-ray Astrophysics Laboratory, NASA/Goddard Space Flight Center, Greenbelt,
MD 20771, USA
11 INFN – Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma,
Italy Contact<EMAIL_ADDRESS>
###### Abstract

A wide-frequency radio study of Active Galactic Nuclei (AGN) is crucial to
evaluate the intervening radiative mechanisms responsible for the observed
emission and relate them with the underlying accretion physics. We present
wide frequency (5-45 GHz), high-sensitivity (few
$\mathrm{{\mu}Jy\,beam^{-1}}$), (sub)-kpc JVLA observations of a sample of 30
nearby ($0.003\,\leq\,z\,\leq\,0.3$) AGN detected by INTEGRAL/IBIS at hard-X-
ray. We find a high detection fraction of radio emission at all frequencies,
i.e. $\geq$ 95 per cent at 5, 10 and 15 GHz and $\geq$ 80 per cent at 22 and
45 GHz. Two sources out of 30 remain undetected at our high sensitivities. The
nuclear radio morphology is predominantly compact, sometimes accompanied by
extended jet-like structures, or more complex features. The radio Spectral
Energy Distributions (SEDs) of the radio cores appear either as single or as a
broken power-law, a minority of them exhibits a peaked component. The spectral
slopes are either flat/inverted or steep, up to a break/peak or over the whole
range. The sample mean SED shows a flat slope up to 15 GHz which steepens
between 15 and 22 GHz and becomes again flat above 22 GHz. Significant radio-
X-ray correlations are observed at all frequencies. About half of the sample
features extended emission, clearly resolved by the JVLA, indicating low-power
jets or large scale outflows. The unresolved cores, which often dominate the
radio power, may be of jet, outflow, and/or coronal origin, depending on the
observed frequency.

###### keywords:

galaxies: active –galaxies: nuclei – galaxies: jets – galaxies: Seyfert –
black hole physics – radio continuum: galaxies

††pubyear: ††pagerange: Hard-X-ray-selected Active Galactic Nuclei – II.
Spectral Energy Distributions in the 5-45 GHz domain–LABEL:lastpage

##  1 Introduction

The connection between the accretion and ejection physics in Active Galactic
Nuclei (AGN) has been one of the hot topics of extragalactic astrophysics
since the first discoveries of active galaxies. The existence of scaling
relations involving the black-hole mass and fundamental quantities related to
the host galaxy (e.g. Kormendy & Richstone, 1995; Magorrian et al., 1998;
Ferrarese & Merritt, 2000; Gültekin et al., 2009) suggests that the AGN
ejection activity and host galaxy evolution are entangled. Indeed, the
mechanical kinetic energy ejected by the jet is believed to be one source of
AGN feedback into the host galaxy (Morganti, 2017). A connection between the
accretion and the ejection phenomena, with analogous properties to AGN, has
been observed in other accreting systems like black-hole X-ray binaries, XRB
(e.g. Falcke et al., 2004), coronally-active stars (e.g. Laor & Behar, 2008;
Raginski & Laor, 2016), young stellar objects (e.g. Price et al., 2003;
Ferreira & Deguiran, 2013), cataclysmic variables (e.g. Körding et al., 2008),
ultra–luminous X-ray sources (e.g. Mezcua et al., 2013) and tidal disruption
events (e.g. Zubovas, 2019), suggesting a common underlying physics.

Historically, AGN has been divided between Radio-Loud (RL) and Radio-Quiet
(RQ)111The RL/RQ definition is based on the value of the ratio of optical-to-
radio fluxes $R_{O}=\log{\frac{f{(4400{\mathring{A}}})}{f{(6\,cm)}}}$
(Kellermann et al., 1989). A similar definition has been proposed considering
the radio-to-X-ray luminosities:
$\mathrm{R_{X}=\log{({L_{R}(6\,cm)}/{L_{2-10\,keV}})}}$, with -4.5 as dividing
threshold between RQ and RL (e.g. Terashima & Wilson, 2003; Panessa et al.,
2006). However, the radio-loudness definition strongly depends on the observed
frequency, on the region size from where the radio flux is measured, and the
boundaries between RL and RQ AGN may also depend on the accretion rate and
luminosity of the source Panessa et al. (2007). Padovani (2016) proposed a
more physically meaningful dichotomy between ’jetted’ and ’non-jetted’
sources, where ’jetted’ sources are those exhibiting a clear signature of a
relativistic jet. In this work we refer to RQ AGN in the sense of ’non-jetted’
sources. There is emerging evidence that RQ AGN are not radio-silent, as in
these objects we do observe radio emission in a variety of shapes, scales and
strengths, with sources exhibiting outflowing and jet-like features, sub-
relativistics, less powerful, less collimated and on smaller scales with
respect to those of powerful RL AGN (e.g. Nagar et al., 2002), see Panessa et
al. (2019) for a review.

Previous works focusing on the cm spectral range of the RQ population at
arcsec resolution generally reported moderately-to-high detection fractions,
i.e. 70 - 90 per cent (e.g. van der Hulst et al., 1981; Kukula et al., 1995;
Roy et al., 1998; Nagar et al., 1999; Thean et al., 2000). More recently,
Smith et al. (2016, 2020) found a high detection fraction ($\sim$96 per cent)
for a sample of hard-X-ray selected AGN from Swift/BAT at 22 GHz with a
$\sim$1 arcsec resolution.
The morphology of the radio emission on arcsec scales is predominantly
compact, either unresolved or marginally resolved. However, a number of
sources exhibit extended structures, linear features, double/triple
components, core plus jet like features as well as diffuse emission, on
spatial scales ranging from $\sim$kpc (e.g. Ulvestad et al., 1981; Kukula et
al., 1998; Leipski et al., 2006) down to few hundreds of pc (e.g. Kukula et
al., 1995; Schmitt et al., 2001; Thean et al., 2001).
Previous studies of the spectral shape of RQ AGN were mainly performed at
frequencies $\leq$15 GHz, usually adopting a two-frequencies approach, which
only gives a limited information on the overall shape due to the limited
frequency coverage (e.g. Kellermann et al., 1989; Kukula et al., 1998; Chen et
al., 2022). Only few works have adopted a multi-frequency approach to study
the spectral shape of RQ AGN, but still limited to the frequency range
$\nu\,\leq$15 GHz (e.g. Antonucci & Barvainis, 1988; Barvainis et al., 1996;
Kukula et al., 1998; Barvainis et al., 2005). These works have led to the
finding that most sources show only steep spectra, however a number of them
(roughly 40-50 per cent) exhibit flat/inverted spectra in the cm/sub-cm range
(e.g. Antonucci & Barvainis, 1988; Kukula et al., 1995; Barvainis et al.,
1996; Kukula et al., 1998; Barvainis et al., 2005; Laor et al., 2019;
Chiaraluce et al., 2019).

In a number of sources the flat/inverted slope is found to dominate only at
higher frequencies ($\geq$ few GHz), i.e. an excess emission is found with
respect to the extrapolation from lower frequencies. This trend has been first
reported as a ”high-frequency excess” up to 2 cm by Antonucci & Barvainis
(1988); Barvainis et al. (1996), and then as a mm-excess, up to $\sim$ 100
GHz, by Laor & Behar (2008); Behar et al. (2015, 2018). Several radiative
processes have been invoked to explain the evidence of flat/inverted cm/sub-cm
spectra in RQ AGN, both thermal and non-thermal, like optically-thick
synchrotron emission from a compact source, either the base of the jet (e.g.
Falcke et al., 1995; Wilson & Colbert, 1995; Baldi et al., 2021a, 2022) or a
magnetically-heated corona (e.g. Laor & Behar, 2008; Raginski & Laor, 2016),
thermal free-free emission from nuclear sources at
$\mathrm{T_{B}\,\sim\,10^{6}\,K}$ and $\mathrm{T_{B}\,\sim\,10^{4}\,K}$
emission from NLR or starburst (e.g. Antonucci & Barvainis, 1988; Barvainis et
al., 1996; Padovani et al., 2011; Condon et al., 2013).

The evidence of steep spectra in RQ AGN has been explained invoking
synchrotron or free-free emission in the optically-thin regime from disk or
circumnuclear starburst regions, on host-galaxy scale but also down to few
hundreds pc (e.g. Barvainis et al., 1996; Padovani et al., 2011; Condon et
al., 2013; Zakamska et al., 2016); optically-thin synchrotron from AGN-driven
outflows, usually on few kpc scale (e.g. Mundell et al., 2000; Jiang et al.,
2010; Zakamska & Greene, 2014; Laor et al., 2019); or optically-thin
synchrotron emission from plasma blobs in a sub-relativistic jet, usually
associated to a linear morphology and on scales as small as hundreds of pc
(e.g. Barvainis et al., 1996; Kukula et al., 1999; Laor et al., 2019).

As additional research channel, the study of correlations between the X-ray
luminosity, considered a proxy for the accretion power, and the radio one,
measuring the strength of ejection phenomena, has allowed to test different
physical scenarios, such as radiatively efficient versus inefficient regimes
(e.g. Merloni et al., 2003; Falcke et al., 2004; Coriat et al., 2011; Dong et
al., 2014; Dong & Wu, 2015), or the so-called coronal models (e.g. Laor &
Behar, 2008; Raginski & Laor, 2016).

This work is a completion of the results presented in Chiaraluce et al.
(2020), which we hereafter refer to as Paper I. Here, we present the results
from new Jansky Very Large Array (JVLA) multi-frequency observations and
Spectral Energy Distributions (SEDs) for a sample of hard-X-ray selected AGN,
in a wide range of frequencies, 5 - 45 GHz, with a high sensitivity, few
${\mu}Jy$/beam, and at a resolution of $\sim\,$ arcsec, i.e. spatial scales
$\leq$kpc.

In this paper we use the $\Lambda$-CDM with the following cosmological
parameters: Ho=67.4 km s-1 Mpc-1, $\Omega_{m}$=0.315 and
$\Omega_{\Lambda}$=0.685 (Aghanim et al., 2018).

##  2 The sample

The starting point of our project is the volume limited sample of 89 hard-X-
ray selected AGN observed by INTEGRAL/IBIS and presented in Malizia et al.
(2009). We selected only the sources conveniently observable with the JVLA
between 5 and 45 GHz, i.e. north of DEC -30 deg, and we considered only
Seyfert galaxies, criteria which reduce the sample to 44 objects (hereafter
’parent’ sample). The characteristics of this sample have been extensively
presented in Paper I, and are here briefly retrieved.

This hard-X-ray selected sample has several advantages: i) the hard-X-ray
selection makes it relatively free of selection biases, e.g. absorption (see
discussion in Ho & Ulvestad, 2001, and Paper I); ii) it comprises moderate-to-
high luminosity objects, with 41.5$\mathrm{\,\leq\,\log{L_{2-10\,keV}}}$
$(erg\,s^{-1}$)$\,\leq\,$44.5; iii) the accretion rates are relatively high:
-2.5$\mathrm{\,\leq\,\log{L_{Bol}}}$/${L_{Edd}}\,\leq$-0.5 (central panel of
Fig. 1); iv) it covers a wide range of radio luminosities (Fig. 2), with the
bulk of the population made of RQ AGN (Fig. 3).

Table 1: List of sources together with observations information. Columns: (1)
Target name; (2) and (3) Right ascension and declination (J2000) from Malizia
et al. (2009); (4) Seyfert type; (5) Redshift; (6), (7), (8), (9) and (10), C,
X, Ku, K and Q band projects, respectively. For the archival data we use the
following notation: VLA project (month/year) [VLA configuration].

|  |  |  |  | Observations
---|---|---|---|---|---
Target | RA | DEC | Seyfert | z | C | X | Ku | K | Q
| (J2000) | (J2000) | Type |  | (5 GHz) | (10 GHz) | (15 GHz) | (22 GHz) | (45 GHz)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
IGR J00333+6122 | 00:33:18.41 | +61.27.43.10 | S1.5 | 0.105 | $\cdots$ | $\cdots$ | $\cdots$ | 18B-163 | 18B-163
NGC 788 | 02:01:06.40 |  $-$06:48:56.0 | S2 | 0.0136 | AW0126 (02/85) [A] | AM384 (12/92) [A] | $\cdots$ | 18B-163 | 18B-163
NGC 1068 | 02:42:40.71 |  $-$00:00:47.8 | S2 | 0.0038 | BG066 (04/99) [B] | AZ0053 (04/92) [C] | AW0085 (01/84) [B] | 18B-163 | 18B-163
QSO B0241+62 | 02:44:40.71 | +62.28.06.5 | S1 | 0.044 | AM0124 (06/86) [B/A] | AS644 (11/98) [C] | AS0786 (04/04) [C] | 18B-163 | 18B-163
NGC 1142 | 02:55:12.19 |  $-$00.11.02.3 | S2 | 0.0288 | 12A-066 (06/12) [B] |  AP233 (06/91) [A] AP212 (04/92) [B] | AJ105 (05/84) [B] | 18B-163 | 18B-163
B3 0309+411B | 03:13:01.96 | +41.20.01.2 | S1 | 0.136 | BT0007 (05/94) [A/B] | BM0074 (04/97) [B] | $\cdots$ | 18B-163 | 18B-163
NGC 1275 | 03:19:48.16 | +41.30.42.1 | S2 | 0.0175 | $\cdots$ | $\cdots$ | $\cdots$ | 18B-163 | 18B-163
LEDA 168563 | 04:52::04.85 | +49.32.43.7 | S1 | 0.029 | $\cdots$ | $\cdots$ | $\cdots$ | 18B-163 | 18B-163
4U 0517+17 | 05:10:45.51 | +16.29.55.8 | S1.5 | 0.0179 | $\cdots$ | $\cdots$ | $\cdots$ | 18B-163 | 18B-163
MCG+08-11-11 | 05:54:53.61 | +46.26.21.6 | S1.5 | 0.0205 | ULVE (03/82) [A] | AB0973 (11/04) [A] | AU0018 (11/83) [A] | 18B-163 | 18B-163
Mkn 3 | 06:15:36.36 | +71.02.15.1 | S2 | 0.0135 |  AW0258 (08/90) [A] GK0011 (02/94) [B] |  AW0278 (09/91) [A] BM0124 (06/00) [B] | AP0142 (09/87) [A] | 18B-163 | 18B-163
Mkn 6 | 06:52:12.25 | +74.25.37.5 | S1.5 | 0.0188 |  AB0740 (07/95) [A] AB0740 (11/95) [B] AB0740 (05/95) [D] | AW0278 (09/91) [A] | AP0142 (10/87) [A] | 18B-163 | 18B-163
NGC 4151 | 12:10:32.58 | +39:24:20.6 | S1.5 | 0.0033 | $\cdots$ | $\cdots$ | $\cdots$ | 18B-163 | 18B-163
Mkn 50 | 12:23:24.14 | +02.40.44.8 | S1 | 0.0234 | 19A-018 | 19A-018 | 19A-018 | $\cdots$ | $\cdots$
NGC 4388 | 12:25:46.75 | +12.39.43.5 | S2 | 0.0084 | 19A-018 | 19A-018 | 19A-018 | 18B-163 | 18B-163
LEDA 170194 | 12:39:06.32 | -16.10.47.8 | S2 | 0.036 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
NGC 4593 | 12:39:39.42 | -05.20.39.3 | S1 | 0.009 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
IGR J13091+1137 | 13:09:05.60 | +11.38.02.9 | S2 | 0.0251 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
NGC 5252 | 13:38:16.00 | +04.32.32.5 | S2 | 0.023 | 19A-018 | 19A-018 | 19A-018 | 18B-163 | 18B-163
NGC 5506 | 14:13:14.87 | -03.12.26.9 | S1.9 | 0.0062 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
IGR J16385-2057 | 16:38:30.91 | -20.55.24.6 | NLS1 | 0.0269 | $\cdots$ | $\cdots$ | $\cdots$ | 20A-066 | 20A-066
IGR J16426+6536 | 16:43:04.70 | +65:32:50.9 | NLS1 | 0.323 | $\cdots$ | $\cdots$ | $\cdots$ |  18B-163 20A-066 |  18B-163 20A-066
IGR J17513-2011 | 17:51:13.62 | -20.12.14.6 | S1.9 | 0.047 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
IGR J18027-1455 | 18:02:45.50 | -14.54.32.0 | S1 | 0.035 | $\cdots$ | $\cdots$ | $\cdots$ | 20A-066 | 20A-066
IGR J18259-0706 | 18:25:57.58 | +07.10.22.8 | S1 | 0.037 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
2E 1853.7+1534 | 18:56:01.28 | +15.38.05.7 | S1 | 0.084 | $\cdots$ | $\cdots$ | $\cdots$ | 20A-066 | 20A-066
IGR J20186+4043 | 20:18:38.73 | +40.40.59.9 | S2 | 0.0144 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
4C +74.26 | 20:42:37.30 | +75.08.02.4 | S1 | 0.104 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
IGR J23308+7120 | 23:30:37.28 | +71.22.46.0 | S2 | 0.037 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066
IGR J23524+5842 | 23:52:22.11 | +58.45.30.7 | S2 | 0.164 | 19A-018 | 19A-018 | 19A-018 | 20A-066 | 20A-066

Table 2: Luminosities and radio loudness parameters: Columns: (1) Target name;
(2) 2-10 keV X-ray luminosity Malizia et al. (2009); (3) 20-100 keV X-ray
luminosity from Malizia et al. (2009); (4) Bolometric luminosity; (5)
Eddington ratio; (6) Optical radio-loudness parameter (Kellermann et al.,
1989); (7) X-ray radio-loudness at 5 GHz; (8) X-ray radio-loudness at 22 GHz;
(9) X-ray radio-loudness at 45 GHz.

Name | log($L_{2-10~{}keV}$) | log($L_{20-100~{}keV}$) | log($L_{Bol}$) | log($L_{Bol}/L_{Edd}$) | log($R_{O}$) | log($R_{X}^{5~{}GHz}$) | log($R_{X}^{22~{}GHz}$) | log($R_{X}^{45~{}GHz}$)
---|---|---|---|---|---|---|---|---
| (erg/s) | (erg/s) | (erg/s) |  |  |  |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
IGR J00333+6122 | 44.19 | 44.44 | 44.80 | -1.84 | 1.90 | -4.42 | -4.64 | -4.71
NGC 788 | 42.86 | 43.29 | 43.55 | -2.06 | -1.04 | -5.42 | -5.01 | -4.9
NGC 1068 | 42.95 | 43.35 | 43.36 | -1.95 | 0.04 | -3.92 | -4.11 | -4.06
QSO B0241+62 | 43.87 | 44.41 | 44.39 | -1.80 | 0.70 | -3.06 | -1.91 | -1.60
NGC 1142 | 43.82 | 43.96 | 45.23 | -2.27 | 0.08 | -5.25 | -4.88 | -4.76
B3 0309+411B | 45.04 | 44.99 | $\cdots$ | $\cdots$ | 3.28 | -3.00 | -1.96 | -1.67
NGC 1275 | 42.89 | 43.38 | 44.32 | -2.28 | 2.99 | -0.96 | -0.35 | -0.16
LEDA 168563 | 43.9 | 44.04 | 44.33 | -1.77 | 1.50 | -4.70 | -4.80 | -4.80
4U 0517+17 | 43.23 | 43.62 | 43.44 | -1.66 | $\cdots$ | -5.27 | -4.75 | -4.40
MCG+08-11-11 | 43.69 | 43.74 | 43.90 | -1.65 | 1.27 | -4.25 | -4.29 | -3.98
Mkn 3 | 44.17 | 43.79 | 44.77 | -2.03 | 1.03 | -4.79 | -5.03 | -4.98
Mkn 6 | 43.27 | 43.57 | 44.27 | -1.96 | 1.17 | -3.93 | -3.40 | -3.31
NGC 4151 | 43.05 | 43.16 | 43.89 | -1.91 | 0.60 | -5.41 | -4.84 | -4.73
Mkn 50 | 43.05 | 43.2 | 43.66 | -1.84 | -1.02 | -5.53 | $\cdots$ | $\cdots$
NGC 4388 | 43 | 43.54 | 43.16 | -1.80 | -0.80 | -4.94 | -5.05 | -4.83
LEDA 170194 | 43.48 | 44.22 | 44.76 | -2.24 | 0.30 | -4.42 | -3.67 | -3.20
NGC 4593 | 42.8 | 43.09 | 43.12 | -1.72 | -1.86 | -5.63 | -4.95 | -4.49
IGR J13091+1137 | 43.44 | 43.77 | 44.44 | -2.16 | -0.90 | -5.49 | -5.17 | -5.08
NGC 5252 | 43.72 | 43.71 | 44.89 | -2.21 | 0.60 | -4.71 | -4.39 | -4.60
NGC 5506 | 42.83 | 42.85 | 42.96 | -1.79 | 0.90 | -3.91 | -3.85 | -3.77
IGR J16385-2057 | 43.02 | 43.39 | 43.26 | -1.67 | $\cdots$ | $\cdots$ | -4.37 | -4.32
IGR J16426+6536 | $\cdots$ | 45.97 | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$
IGR J17513-2011 | 43.4 | 44.1 | 43.09 | -1.01 | $\cdots$ | -4.75 | -4.29 | -3.89
IGR J18027-1455 | 43.23 | 44.04 | 43.83 | -1.83 | $\cdots$ | $\cdots$ |  $<$-5.46 |  $<$-4.97
IGR J18259-0706 | 43.19 | 43.66 | $\cdots$ | $\cdots$ | $\cdots$ | -4.99 | -4.65 | -4.37
2E 1853.7+1534 | 44.25 | 44.56 | 44.55 | -1.70 | $\cdots$ | $\cdots$ | -5.64 |  $<$-5.17
IGR J20186+4043 | 42.57 | 42.98 | $\cdots$ | $\cdots$ | -0.67 | -4.72 | -4.62 | -4.60
4C +74.26 | 44.75 | 45.04 | 45.76 | -1.96 | 1.92 | -3.20 | -2.54 | -2.45
IGR J23308+7120 | 42.8 | 43.55 | $\cdots$ | $\cdots$ | -0.44 | -5.16 |  $<$-5.11 |  $<$-4.28
IGR J23524+5842 | 44.41 | 44.85 | $\cdots$ | $\cdots$ | 1.12 | -5.04 | -5.22 |  $<$-4.67

Figure 1: Histogram showing the distribution of redshift (from Malizia et al.,
2009, left panel). Eddington ratio ($L_{Bol}/L_{Edd}$. centre panel) and
radio-loudness parameter (from quantities tabulated in Panessa et al., 2015,
right panel) for the parent sample (DEC $>$ -30 deg, semi-filled histogram)
and for the sources considered in this work (green), i.e. having at least two
SED data points. The blue, vertical dashed line is the R${}_{X}\,=\,$-4.5
limit of Terashima & Wilson (2003).

##  3 Radio observations and data reduction

In the present work we couple our high-frequencies radio data at 22 and 45 GHz
(JVLA-C configuration, project 18B-163, $\sim$1 and 0.5
${}^{\prime\prime}\,$resolution, respectively) already published in Paper I,
to lower frequencies (5, 10 and 15 GHz, i.e., C, X and Ku bands respectively)
proprietary data obtained in JVLA-B configuration (project: 19A-018). The more
extended configuration at lower frequencies guarantees us a matched resolution
with high frequencies data, a crucial point in order to build physically
meaningful SEDs: at 5, 10 and 15 GHz the expected resolution is $\sim$1, 0.6
and 0.4${}^{\prime\prime}\,$. Moreover, we complemented the high-frequency
observations at 22 and 45 GHz with new ones obtained in the same configuration
(project 20A-066).

Finally, we searched in the VLA archive low-frequency data for the objects for
which our own proprietary data were not available (i.e. NGC 788, NGC 1068, QSO
B0241+62, NGC 1142, B3 0309+411B, MCG +08-11-11, Mkn 3 and Mkn 6). When
available, we selected observations in the same configurations (VLA-B), when
not we considered other available configurations (mostly A), and in order to
match the resolution a tapering has been applied (next Section).

The above strategy translates into 30 objects out of 44 with at least two SED
data points. In Table 1 we summarise the characteristics of the sample
together with information on the observations and the corresponding projects:
9 sources have only two SED data points; one source (Mkn 50) has three SED
data points; two sources have four data points (NGC 788 and B3 0309+411B), the
majority of sources (18 out of 30) have 5 SED data points.

In Fig. 1 we plot a histogram of the distribution of the relevant physical
quantities of sources in this work, i.e redshift, Eddington ratio and X-ray
radio-loudness ($\mathrm{R_{X}=\log{({L_{R}(6\,cm)}/{L_{2-10\,keV}})}}$), as
compared to the whole sample of 44 source north DEC $\geq$ -30 deg. A
Kolmogorov-Smirnov test comparing the two distributions results, in all cases,
in a P$\sim$0.99, so the null hypothesis that the two samples are drawn from
the same parent population cannot be rejected. This would suggest that the
physical conclusions which can be drawn from the sources considered in this
work are likely representative of the whole sample.

The project 19A-018 has been observed in the period February - May 2019, the
project 20A-066 in the period February - May 2020. The characteristics of
observations for the high-frequency project 20A-066 are the same of 18B-163,
presented in Section 3 of Paper I, and we refer to that section for the
details. Sources in 19A-018 were observed at 5, 10 and 15 GHz for a minimum of
1 min to a maximum of 5 min. We applied phase calibration, bracketing targets
with suitable sources within a radius of 10 deg. The scans of the absolute
flux density scale calibrator has been performed once per scheduling block,
typically at the beginning or end of it, and, at a given frequency, it is
observed for no less than 2min30s.

The data calibration and reduction procedure for the proprietary JVLA data has
been performed with the calibration pipeline within the Common Astronomy
Software Application (casa 5.4.1 version222https://casa.nrao.edu, McMullin et
al., 2007). After calibration, the plots were inspected for residual RFI. For
the image reconstruction, the tclean task in casa has been used, applying the
Högbom (1974) deconvolver. We produced full resolution maps considering as
initial weighting the Briggs (1995) one with robustness parameter equal to
0.5, which ensures a balance between resolution and sensitivity. However, in
order to have X and Ku maps at a matched resolution with respect to C band, we
produced naturally-weighted tapered maps, in order to give more weight to the
short baselines and have an approximately equal UV coverage.

The typical RMS achieved is $\sim 10-40\,$${\rm\mu}$Jy beam-1, in agreement
with proprietary post-upgrade JVLA data (see Table 3 in Supplementary
material). For the archival VLA data, the reduction has been performed with
the Astronomical Image Processing System AIPS in the 31DEC20
version333http://www.aips.nrao.edu, following standard procedures. The imaging
procedure has been conducted via the task imagr. In all cases,
self–calibration has been performed for all the sources strong enough to
provide enough flux density for the model.

For both the proprietary JVLA data and the archival VLA ones, the image
analysis has been performed via the casa task imfit. Based on the source
morphology, single/multiple Gaussian fit on the image plane has been
performed. A comparison of the flux densities of calibrators for the
proprietary JVLA data with tabulated values in Perley & Butler (2017) led to
the estimation of a $\sim$5 per cent error in the flux calibration; for the
archival data a more conservative 10 per cent has been adopted. The
uncertainties in the final flux density measurements are affected by fitting
errors from imfit, and flux calibration error, which are added in quadrature
and adopted as the error measurements. In the case of components with a
resolved morphology, the error associated with the flux determination is given
by the formula
${\sigma_{S}}=\sqrt{N\times{(rms)^{2}}+({A_{s}}{\times}S)^{2}}$, where N is
the number of beam areas covered by a source of flux density S, and $A_{S}$
takes into account the uncertainty in the absolute flux density scale
(0.05$-$0.1, see Ho & Ulvestad, 2001).

In Table 1 we report the source coordinates taken from Malizia et al. (2009).
In a number of sources the above positions display a significant offset from
the derived radio ones (the latter reported in Table 3 in Supplementary
material). For this reason, we performed a careful cross-check with all
available positions (from optical, X-ray, IR, etc observations) in
literature444With the NASA NED and SIMBAD databases. for each source, in order
to determine the likely core component. In the maps, the white (or black)
crosses represent the original optical coordinates as in Malizia et al.
(2009), as quoted in Table 1, that were adopted during the scheduling of our
observations and therefore are their phase centres. In Table 2 in
Supplementary material we report the integrated and peak radio luminosities of
the core component at all frequencies and in Table 3 in Supplementary material
we report the derived parameters from the imaging analysis. The complete set
of maps for the entire sample is available on the project’s
website555https://sites.google.com/inaf.it/hxagn/radio-images, while a
representative image for each source, together with its SED, is reported in
Figure 2 in Supplementary material. In Table 2 we report the X-ray (2-10 keV
and 10-100 keV) and bolometric luminosities and the corresponding Eddington
ratios (as detailed in Paper I). The optical radio-loudness parameter
(Kellermann et al., 1989) and the X-ray radio-loudness parameter (Terashima &
Wilson, 2003) is calculated using the radio luminosities at 5, 22 and 45 GHz.

##  4 Results

###  4.1 Detection rates, radio luminosities and radio loudness

We find high detection rates of radio emission at all frequencies, with
detection fractions which decrease with frequency, i.e. 21/21, 21/21, 19/19,
26/29 and 24/29 at 5, 10, 15, 22 and 45 GHz, respectively, which translate
into rates of 96$\pm$8, 96$\pm$8, 95$\pm$8, 87$\pm$12 and 81$\pm$14,
respectively666Due to the limited statistics of the sample, in order to
estimate the detection fractions and associated uncertainties we used the
Laplace point estimate formula (Laplace 1812) and the Adjusted Wald method
(e.g. Sauro & Lewis, 2005)..

Figure 2: Histogram showing the distribution of core radio luminosities
$\mathrm{\log{{\nu}L_{\nu}}}$ at the different frequencies for sources in the
sample.

In Fig. 2 we show the distribution of core radio luminosities for the sources
in the sample at different frequencies. The bulk of sources has core radio
luminosities in the range
37$\mathrm{\,\leq\,\log{\,\nu\,L_{\nu}(erg\,s^{-1}})\,\leq\,}$40, well below
the values observed in radio galaxies (i.e.,
$\mathrm{\log{\,\nu\,L_{\nu}(erg\,s^{-1}})>}$42, Zirbel & Baum (1995)).

In Fig. 3 we show the distribution of radio-loudness parameters of the core
component at different frequencies. The fraction of radio sources which can be
classified as RL is 30 and 33 per cent considering the classical radio
loudness parameter and the X-ray one at 5 GHz, respectively (Terashima &
Wilson, 2003). However, given the low radio luminosities and the caveats
associated to the definition of a boundary in the radio-loudness parameter, we
consider as RQ AGN the majority of the sources in our sample, except for the
three most powerful radio emitters already mentioned in Paper I, i.e. QSO
B0241+62, B3 0309+411B and NGC 1275, and the giant radio galaxy 4C +74.26
(e.g. Bruni et al., 2020, and references therein), resulting in $\sim$ 13% of
RL AGN in the sample. This fraction of RL AGN is consistent with what already
observed so far in hard X-ray selected samples (e.g. Bassani et al., 2016, and
references therein).

Figure 3: Histogram showing the distribution of radio loudness for the sources
in the sample based on different definitions, i.e. Kellermann et al. (1989)
(first panel, from left, 9/30 classify as RL); Terashima & Wilson (2003) at 5
GHz (second panel, 10/30 classify as RL), 22 GHz (third panel) and at 45 GHz
(fourth panel). The vertical lines denote the RQ/RL limit depending on the
definition.

###  4.2 Undetected sources

Two sources out of 30 were not detected by our observations, i.e. IGR
J16426+6536 and IGR J18027-1455, and for both only observations at 22 and 45
GHz were available. For both we give 3$\times\,\sigma$ upper limits of
$\sim\,$0.1 and $\sim\,$0.15 ${\rm m}$Jy beam-1 at 22 and 45 GHz,
respectively, which result, in the case of IGR J18027-1455, in upper limits on
the radio luminosities of $\mathrm{\log{L_{R}\,(erg\,s^{-1})}\,\sim}$ 37.8 and
38.3 (upper limits on the radio powers of
$\mathrm{L_{\nu}(W\,Hz^{-1})\,\sim\,3\times 10^{20}}$ and
$\mathrm{L_{\nu}(W\,Hz^{-1})\,\sim\,4.5\times 10^{20}}$ at 22 and 45 GHz,
respectively). The derived upper limits on the X-ray radio-loudness parameter
are of -5.4 and -4.9 at the two frequencies, respectively, placing these
sources at the very-low-power end of the radio-loudness distribution. The
source IGR J16426+6536 benefits from observations in two epochs, one in
November 2018 and presented in Paper I, and one in June 2020, presented here.
In both cases the source is undetected at a similar flux limit (see Table 3 in
Supplementary material), variability at 17 months scales can therefore be
ruled out. Deeper observations, achievable with longer integration times,
would be required to confirm the radio-silent nature of these sources.

Figure 4: Radio maps of sources considered as an example for the four
morphological types adopted in Section 4.3: top-left, IGR J17513-2011
(morphological class A); top-right, IGR J23524+5842 (morphological class B);
bottom-left, LEDA 170194 (morphological class C); bottom-right, NGC 1142
(morphological class D). For space reasons, only the 5-GHz (C-band) maps are
shown. For each source we also show the corresponding SED, in which we
indicate the core and all the other emitting components (if present). The SED
and morphology for the remaining sources are shown in Figure 2 in
Supplementary material.

###  4.3 Morphology

We divided the morphology of the sources in the sample into four main classes,
adapting the classification in Baldi et al. (2021b), considering both full
array and tapered radio maps. In Table 3, we report the morphological
classification (column 2) for each source and in Fig. 4 we report an examples
of each of the four morphological classes:

  * •

core or core+jet/lobe (A): sources with a single core component, either
resolved or marginally resolved, sometimes with a small-scale protrusion
(either one-sided or two-sided); 17/30 sources belong to this class (e.g.,
IGRJ 17513-2011).

  * •

one-sided jet (B): sources with an extended asymmetric jet, which is possibly
resolved into several emitting components at higher resolutions; 7/30 sources
are in this class (e.g., IGRJ 23524+5842).

  * •

triple (C) sources exhibiting a triple morphology, interpreted as the radio
core plus symmetric jet/lobes (one source: LEDA 170194).

  * •

jet+complex (D): sources with a complex structure, with multiple components,
either compact, diffuse and/or extended; three sources fall in this
classification, i.e. NGC 1068, NGC 1142 and NGC 5506. Note that the D
classification corresponds to the E classification in Baldi et al. (2021b).

The morphological study for the sources across the cm-wave range reveals a
prevalence of compact components, either unresolved or marginally-resolved,
with nearly a half of the sample sources exhibiting jet-like structures, as
well as triple and more complex ones that extend up to kpc scales. We note
that the morphological classification depends on the distance of the source,
i.e., for high z sources structures below the kpc scales are not resolved.
However the majority of the sample sources are located in the nearby Universe,
allowing us to map projected linear sizes of hundreds of pc (e.g. the nearest
source is NGC 4593, $\sim$ 190 pc). On the other hand, high z objects (z$>$
0.1) in our sample are mostly radio galaxies (e.g. 3C+74.26, $\sim$ 2 kpc)
with a known morphology. The classification also depends on the selected
frequency. As an example, MCG+08-11-11 appears as a core plus a one sided jet-
like feature in our maps at matched resolution of $\sim$1 arcsec, however, in
the full resolution image, the core is resolved into 3 components, the central
one being the core (e.g. Ulvestad & Wilson, 1986). Indeed, sources with
extended emission are best detected at low frequencies for a combination of
effects. The surface brightness is enhanced by the steep spectrum and for a
given JVLA configuration, the beam is larger, increasing the sensitivity to
low surface brightness emission.

###  4.4 Radio spectral energy distributions

Table 3: The two-frequency spectral indices (and associated uncertainties) for the sources and the multiple components, when present. The frequency pairs considered are 5-10 GHz, 10-15 GHz, 15-22 GHz, 22-45 GHz; for NGC 788 and B3 0309+411B we report the 10-22 GHz spectral index, due to the lack of 15 GHz data. We also indicate the morphological classification based on the four classes. Name | Radio | Component | $\alpha_{5-10}$ | $\alpha_{10-15}$ | $\alpha_{15-22}$ | $\alpha_{22-45}$ | $\alpha_{10-22}$
---|---|---|---|---|---|---|---
| morph |  |  |  |  |  |
IGR J00333+6122 | A | core | $\cdots$ |  |  |  1.2 $\pm$ 0.4 |
NGC 788 | A | core |  0.8 $\pm$ 0.2 | $\cdots$ | $\cdots$ |  0.4 $\pm$ 0.3 |  -0.05$\pm$0.20
NGC 1068 |  | a |  0.65 $\pm$ 0.13 |  1.64 $\pm$ 0.13 |  0.69 $\pm$ 0.17 |  0.9 $\pm$ 0.1 |
| D | b(core) |  0.49 $\pm$ 0.13 |  1.59 $\pm$ 0.13 |  1.1 $\pm$ 0.2 |  0.8 $\pm$ 0.1 |
|  | d | $\cdots$ | $\cdots$ |  0.62 $\pm$ 0.18 |  0.47 $\pm$ 0.01 |
|  | sw | $\cdots$ | $\cdots$ |  -0.24 $\pm$ 0.19 |  0.14 $\pm$ 0.10 |
QSO B0241+62 | B | core |  -0.86 $\pm$ 0.13 |  -1.34 $\pm$ 0.12 |  0.252 $\pm$ 0.180 |  0.3 $\pm$ 0.1 |
|  | blob |  0.57 $\pm$ 0.13 |  2.4 $\pm$ 0.2 | $\cdots$ | $\cdots$ |
NGC 1142 | D | east | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ |
|  | a1 |  2.45 $\pm$ 0.18 |  -0.18 $\pm$ 0.18 |  1.28 $\pm$ 0.25 |  0.9 $\pm$ 0.3 |
|  | a2 |  1.72 $\pm$ 0.17 |  -0.24 $\pm$ 0.16 |  1.83 $\pm$ 0.23 |  1.4 $\pm$ 0.1 |
|  | b(core) |  0.04 $\pm$ 0.17 |  -0.17 $\pm$ 0.15 |  1.26 $\pm$ 0.21 |  0.5 $\pm$ 0.1 |
|  | d |  1.11 $\pm$ 0.18 |  1.03 $\pm$ 0.12 |  0.73 $\pm$ 0.22 | $\cdots$ |
B3 0309+411B | B | core |  -0.38 $\pm$ 0.13 | $\cdots$ | $\cdots$ |  0.06 $\pm$ 0.10 |  -0.7$\pm$0.1
|  | nw |  0.11 $\pm$ 0.13 | $\cdots$ | $\cdots$ | $\cdots$ |
NGC 1275 | A | core | $\cdots$ | $\cdots$ | $\cdots$ |  0.4 $\pm$ 0.1 |
LEDA 168563 | A | core | $\cdots$ | $\cdots$ | $\cdots$ |  1.07 $\pm$ 0.12 |
4U 0517+17 | A | core | $\cdots$ | $\cdots$ | $\cdots$ |  -0.09 $\pm$ 0.11 |
MCG+08-11-11 | B/C | core |  1.07 $\pm$ 0.13 |  1.1 $\pm$ 0.1 |  0.14 $\pm$ 0.19 |  0.7 $\pm$ 0.1 |
|  | jet |  2.23 $\pm$ 0.13 |  2.5 $\pm$ 0.5 |  -3.2 $\pm$ 0.9 |  1.1 $\pm$ 0.4 |
Mkn 3 |  | west |  1.31 $\pm$ 0.13 |  0.77 $\pm$ 0.12 |  1.8 $\pm$ 0.3 |  1.2 $\pm$ 0.1 |
| B | east(core) |  1.41 $\pm$ 0.13 |  0.35 $\pm$ 0.10 |  1.3 $\pm$ 0.1 |  0.87 $\pm$ 0.09 |
Mkn 6 |  | N |  0.98 $\pm$ 0.07 |  1.13 $\pm$ 0.10 | $\cdots$ | $\cdots$ |
| B/C/D | S(core) |  0.91 $\pm$ 0.07 |  1.0 $\pm$ 0.1 | $\cdots$ | $\cdots$ |
|  | Ext-EW |  2.6 $\pm$ 0.1 | $\cdots$ | $\cdots$ | $\cdots$ |
NGC 4151 | A | core | $\cdots$ | $\cdots$ | $\cdots$ |  0.7 $\pm$ 0.1 |
Mkn 50 | A | core |  -0.06 $\pm$ 0.20 |  0.03 $\pm$ 0.23 | $\cdots$ | $\cdots$ |
NGC 4388 | B(core) | NE |  0.9 $\pm$ 0.1 |  0.8 $\pm$ 0.2 |  1.08 $\pm$ 0.20 |  0.27 $\pm$ 0.11 |
|  | SW |  0.8 $\pm$ 0.1 |  0.47 $\pm$ 0.18 |  1.45 $\pm$ 0.22 |  1.6 $\pm$ 0.3 |
|  | North |  1.11 $\pm$ 0.13 |  5.4 $\pm$ 0.1 | $\cdots$ | $\cdots$ |
LEDA 170194 | C | Core |  -0.09 $\pm$ 0.14 |  0.42 $\pm$ 0.17 |  -0.21 $\pm$ 0.14 |  -0.8 $\pm$ 0.4 |
|  | SW |  0.14 $\pm$ 0.24 |  1.9 $\pm$ 0.4 | $\cdots$ | $\cdots$ |
|  | NE |  0.7 $\pm$ 0.5 |  2.0 $\pm$ 0.9 | $\cdots$ | $\cdots$ |
NGC 4593 | A | core |  -1.01 $\pm$ 0.15 |  -0.23 $\pm$ 0.16 |  0.77 $\pm$ 0.18 |  -0.54 $\pm$ 0.12 |
IGR J13091+1137 | A | core |  -0.57 $\pm$ 0.16 |  -0.51 $\pm$ 0.19 |  2.6 $\pm$ 0.2 |  0.7 $\pm$ 0.4 |
NGC 5252 | A | core |  0.04 $\pm$ 0.11 |  0.61 $\pm$ 0.17 |  0.28 $\pm$ 0.20 |  1.7 $\pm$ 0.1 |
NGC 5506 | D | core |  0.95 $\pm$ 0.15 |  0.78 $\pm$ 0.11 |  1.1 $\pm$ 0.2 |  0.76 $\pm$ 0.11 |
IGR J16385-2057 | A | core | $\cdots$ | $\cdots$ | $\cdots$ |  0.74 $\pm$ 0.25 |
IGR J17513-2011 | A | core |  -0.004 $\pm$ 0.140 |  -0.13 $\pm$ 0.18 |  0.9 $\pm$ 0.2 |  -0.40 $\pm$ 0.14 |
IGR J18259-0706 | A | core |  0.86 $\pm$ 0.14 |  0.8 $\pm$ 0.2 |  -0.6 $\pm$ 0.4 |  0.07 $\pm$ 0.30 |
2E 1853.7+1534 | A | core | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ |
IGR J20186+4043 | A | core |  0.87 $\pm$ 0.14 |  0.44 $\pm$ 0.17 |  1.3 $\pm$ 0.2 |  0.9 $\pm$ 0.3 |
4C +74.26 | A | core |  -0.15 $\pm$ 0.09 |  0.003 $\pm$ 0.200 |  0.24 $\pm$ 0.20 |  0.7 $\pm$ 0.1 |
IGR J23308+7120 | A | core |  0.64 $\pm$ 0.30 |  -0.4 $\pm$ 0.4 | $\cdots$ | $\cdots$ |
IGR J23524+5842 | B | core |  -0.6 $\pm$ 0.2 |  0.65 $\pm$ 0.20 |  4.63 $\pm$ 0.34 | $\cdots$ |
|  | NE |  1.33 $\pm$ 0.40 |  1.8 $\pm$ 0.7 | $\cdots$ | $\cdots$ |
Figure 5: Histogram showing the distribution of two-bands spectral indices
($S_{\nu}^{I}\,\propto\,{\nu}^{-\alpha}$) for the core components of sources
in this work; i.e. $\alpha_{5\,-\,10}$, $\alpha_{10\,-\,15}$,
$\alpha_{15\,-\,22}$ and $\alpha_{22\,-\,45}$ from left to right. The region
with $\alpha\,<\,0$ and delimited by the red dashed line represents the
’inverted’ regime; the region with $0<\,\alpha\,<\,0.5$ between the red dashed
and the blue dot-dashed lines represents the ’flat’ regime; the region with
with $\alpha\,>\,0.5$ and delimited by the blue dot-dashed line represents the
’steep’ regime, according to the adopted definitions.

With the present observations, spanning the 5 - 45 GHz interval, we can build
spectral energy distributions in the cm/sub-cm range at a matched resolution
($\sim$ arcsec) and sensitivity (a few ${\rm\mu}$Jy beam-1) for a
statistically relevant sample. In this way it is possible to characterise the
wide-frequency emission for the emitting components, both nuclear and extra-
nuclear, and interpret them in light of models invoked for emission in RQ
objects.
The definition of the spectral index used in this work is
$S_{\nu}^{I}\,\propto\,\nu^{-\alpha}$, where $S_{\nu}^{I}$ is the integrated
flux density. The uncertainties associated with the spectral indices has been
estimated as
$\sqrt{{{(\sigma_{f_{1}}/S_{f_{1}})}^{2}}+{{(\sigma_{f_{2}}/S_{f_{2}})^{2}}}}/ln({f_{2}/f_{1}})$,
where $\sigma_{f_{1,2}}$ and $S_{f_{1,2}}$ are the uncertainties on the flux
density and the flux density at the two frequencies (Ho & Ulvestad, 2001),
which are the central frequencies of the K and Q bands (therefore the flux
densities are the mean across the bandwidth). We define a steep spectrum as
having $\alpha$ $\geq$ 0.5, and a flat one as having $\alpha$ $<$ 0.5, as in
(Panessa & Giroletti, 2013). We define a spectrum as inverted if $\alpha$ $<$
0.

In order to characterise the spectral shape of the core components, we adopted
the classification presented in Barvainis et al. (1996), (see also Scheuer &
Williams (1968)), i.e. single power-law (S) spectra, for which a simple power-
law fit is sufficient, concave (C+) and convex (C-) spectra, for which the
spectrum can be fitted by a quadratic polynomial, and complex spectra (CPX),
which do not fit in none of the above cases. Based on the evidence in the
sample, we add an extra class, the spectra for which a broken power-law (BPL)
fit represents well the data.
In Table 4 we report the results of the SED fitting, first for the broken
power-law sources, then for the convex sources and finally for the single
power-law ones. In Fig. 2 in Supplementary material we show the spectral flux
and energy distributions of sources across the frequency range covered by our
observations (sources are ordered as in Table 4), while in Fig. 5 we show the
distribution of two-frequency spectral indices for the core components of
sources in the sample for the frequency pairs 5-10 GHz, 10-15 GHz, 15-22 GHz
and 22-45 GHz. The relative fraction of sources in the different classes is
the following: 67% of single power-law spectra (e.g. left panels of Fig. 4),
14% of convex spectra (e.g. top-right panel of Fig. 4), 19% of broken power-
law spectra (e.g. bottom-left panel of Fig. 4), none of concave nor complex
spectra. However, cases which have been classified as convex, i.e. NGC 4593
and IGR J13091+1137, could be classified in the complex class as well (see
next sections). In this classifications we excluded the sources with less than
2 frequency points (6/30 with two data points, 1/30 with one and 2/30
undetected).
The extra-nuclear components, when present, generally exhibit steep spectra.

Table 4: Results of the SED fitting for the sources in the sample. Columns: (1) Target name; (2) Component; (3) classification of core SED; (4) Spectral index from linear fit to all points; (5) Break frequency (in GHz) in case of broken power-law fit or peak in case of log-parabola fit; (6) Spectral index at $\nu\leq\nu_{B}$ (before break or peak); (7) Spectral index at $\nu\geq\nu_{B}$ (after break or peak). We show first the sources for which the core can be fitted by a broken power law, then those for which we performed a log-parabolic fit, finally the sources for which the core can be fitted by a single power-law. The sources for which only two data points or less were available (6/30) are omitted. Target | Comp | SED class | $\alpha_{All}$ | $\nu_{Break/Peak}$ | $\alpha(\nu\leq\nu_{Break/Peak})$ | $\alpha(\nu\geq\nu_{Break/Peak})$
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
NGC 5252 | Core | BPL | - |  $\sim$10 |  -0.04$\pm$0.11 |  +0.56$\pm$0.12
IGR J18259-0706 | Core | BPL | - |  $\sim$15 |  0.77$\pm$0.03 |  0.03$\pm$0.09
QSO B0241+62 | Core | BPL | - |  $\sim$15 |  -1.12$\pm$0.15 |  0.31$\pm$0.03
| Blob | - | - |  $\sim$10 |  0.57$\pm$0.13 |  2.4$\pm$0.2
NGC 1142 | d | - |  +0.97$\pm$0.04 | - | - | -
| East | - |  +0.76$\pm$0.09 | - | - | -
| A1 | - |  +0.94$\pm$0.11 | - | - | -
| A2 | - |  +1.25$\pm$0.25 | - | - | -
| b (Core) | BPL | - |  $\sim$15 |  -0.09$\pm$0.05 |  +0.74$\pm$0.11
NGC 4593 | Core | C- | - |  $\sim$15 |  -1.01$\pm$0.15 |  +0.8$\pm$0.2
| Excess | - |  -0.54$\pm$0.12 | - | - | -
IGR J13091+1137 | Core | C- | - |  $\sim$10 |  -0.57$\pm$0.16 |  +2.6$\pm$0.2
| Excess | - |  +0.7$\pm$0.4 | - | - | -
IGR J23524+5842 | Core | C- | - |  $\sim$9 |  -0.57$\pm$0.17 |  +4.6$\pm$0.3
| North | - |  1.78$\pm$0.02 | - | - | -
Mkn 50 | Core | S |  -0.02$\pm$0.02 | - | - | -
NGC 5506 | Core | S |  +0.85$\pm$0.02 | - | - | -
IGR J17513-2011 | Core | S |  +0.01$\pm$0.08 | - | - | -
IGR J20186+4043 | Core | S |  +0.90$\pm$0.03 | - | - | -
MGC+08-11-11 | Core | S |  +0.78$\pm$0.09 | - | - | -
| Jet | - | - | - | - | -
LEDA 170194 | Core | S |  -0.10$\pm$0.08 | - | - | -
| SW | - |  |  $\sim$10 |  +0.14$\pm$0.24 |  1.9$\pm$0.4
| NE | - |  |  $\sim$10 |  0.7$\pm$0.5 |  2.0$\pm$0.9
Mkn 3 | West | S |  1.22$\pm$0.07 | - | - | -
| East (Core) | - |  0.88$\pm$0.06 | - | - | -
Mkn 6 | North | - |  +1.24$\pm$0.05 | - | - | -
| South (Core) | S |  +0.92$\pm$0.04 | - | - | -
NGC 1068 | d | - |  +0.81$\pm$0.16 | - | - | -
| a | - |  +1.00$\pm$0.08 | - | - | -
| b (Core) | S |  +1.04$\pm$0.09 | - | - | -
| SW | - | - | - | - | -
NGC 788 | Core | S |  +0.19$\pm$0.06 | - | - | -
4C +74.26 | Core | S |  +0.23$\pm$0.13 | - | - | -
B3 0309+411B | Core | S |  -0.4$\pm$0.1 | - | - | -
IGR J23308+7120 | Core | S |  +0.21$\pm$0.30 | - | - | -
NGC 4388 | NE (Core) | S |  0.67$\pm$0.09 | - | - | -
| SW | - | - |  $\sim$15 |  +0.68$\pm$0.08 |  +1.53$\pm$0.01

##  5 Discussion

###  5.1 Detection rates of radio emission

The detection rates of radio emission we find here are generally higher with
respect to values reported in literature for surveys of Seyfert galaxies,
especially at lower frequencies, typical percentages 70$-$90 (e.g. van der
Hulst et al., 1981; Antonucci & Barvainis, 1988; Kellermann et al., 1989;
Ulvestad & Wilson, 1989; Kukula et al., 1995; Roy et al., 1998; Nagar et al.,
1999; Thean et al., 2000; Smith et al., 2020; Silpa et al., 2020; Sebastian et
al., 2020; Nyland et al., 2020; Baldi et al., 2021b). However, a comparison
with these works is not straightforward for several reasons: i) the different
selection criteria on which the various samples are based, which may led to
selection biases; ii) the different resolution of the observations, which may
result in comparison of different components because of the mismatch in the
spatial scale; iii) the different frequency coverage, as at different
frequencies emission from different components is expected to dominate, and
the spectral shape may change; iv) the different sensitivity, as pre-upgrade
observations (like the ones concerning work cited before) were characterised
by higher RMS with respect to post-upgrade observations777The post-upgrade VLA
can reach 4 ${\rm\mu}$Jy beam-1 (1-$\sigma$, in 1 hour) continuum sensitivity
at most bands, one order of magnitude lower than pre-upgrade VLA (e.g. van
Moorsel, 2014) (like the ones presented here), which translates into different
flux limits and therefore different detection rates. A proper comparison,
although only at higher frequencies, can be carried out with the 22 GHz,
1-arcsec characterisation of SWIFT/BAT hard-X-ray selected AGN made by Smith
et al. (2016, 2020), in which they report a high ($\sim$ 96/100) detection
rate, compatible with our estimate within the uncertainty at the same
frequency.

As reported in Paper I, the detection rate of radio emission at high
frequencies is larger than what has been reported in recent studies about mm
emission in a handful of RQ AGN (e.g. Behar et al., 2015, 2018). Moreover, if
we compare with the results obtained for LLAGN only, then our detection rates
are larger not only at the higher frequencies (e.g. Doi et al., 2011), but
also at the lower ones (see for comparison e.g. Ho & Ulvestad, 2001; Saikia et
al., 2018; Chiaraluce et al., 2019).

###  5.2 Morphology

According to the morphological classification presented in the previous
section, we find a prevalence of compact sources, either unresolved/slightly
resolved (17/28,$\,\sim$61 per cent), with the remaining sources exhibiting
jet-like features, as well as triple and more complex morphologies.

Previous surveys on Seyfert galaxies have found morphologies in similar
proportions, in which however the relative fraction depends on the frequency
band, as the detection fraction of extended structures is higher at low
frequencies, while the fraction of compact ones increases at higher
frequencies (e.g. Ulvestad et al., 1981; van der Hulst et al., 1981; Kukula et
al., 1998; Nagar et al., 1999; Leipski et al., 2006; Baldi et al., 2018,
2021a). Gallimore et al. (2006) found that, for a sample of Seyfert galaxies
observed at 5 GHz with compact (D) configuration of the VLA (therefore lower
angular resolution $\sim$15-20 arcsec) the fraction of sources exhibiting
kiloparsec-scale radio structures (KSRs) is significantly higher ($\sim$45 per
cent). They suggest that the lower fraction of extended sources found in a
number of works (e.g. Ulvestad & Wilson, 1989; Kukula et al., 1995; Schmitt et
al., 2001; Thean et al., 2001) may be due to the high resolution, which
resolves out the extended, low-surface brightness, steep-spectrum emission,
with the KSRs being likely associated to the nuclear AGN jet activity. For our
sources presented here, it is not possible to rule out that in a number of
them low-surface brightness emission, may be present as well.

In Smith et al. (2016, 2020), a compact component in all the detected sources
is found. In more than a half (55/96) of the sample, this is the only
component (either unresolved or slightly resolved), in agreement with our
findings, while in 11/96 sources jet-like structures on sub-kpc to kpc scales
are present. However, they find a significant number of sources (30/96) with a
diffuse morphology (i.e. extended but non-linear), which they attribute to
nuclear star formation.

###  5.3 Radio nuclear spectral energy distribution

The radio spectral slope in RQ AGN is likely the result of the combination of
different emitting components dominating at different frequencies. Star-
formation typically produces a synchrotron steep spectrum in the 1-10 GHz
regime, while a compact core is characterized by a flat or inverted spectrum
(Chen et al., 2022). An AGN wind/outflow and an extended jet produce an
optically-thin synchrotron steep spectrum (Panessa et al., 2019).

In our sample, we find a prevalence of single power-law spectra, with the
number of flat spectra equal to the number of steep spectra. If we include
also single power-law sources with only two data points, then the flat spectra
are 9 while the steep ones are 11.

In Fig. 6 we have plotted the mean spectral energy distribution obtained by
calculating the mean of the slopes of the cores between two frequencies from
Table 3 represented in Fν in arbitrary units. The average trend is that of a
nearly flat slope that steepens with increasing frequency, a major steepening
is observed between 15 and 22 GHz. It is interesting to note that between 22
and 45 GHz the slope flattens again. This suggests that the core emission is
generally optically thick below 15 GHz, in agreement with the results
presented in (Laor et al., 2019) for quasars with a similar range of Eddington
ratios. It becomes optically thin above 15 GHz and between 22 and 45 GHz it
becomes optically thick again. If we assume that the emission is produced by
synchrotron, the size of the emitting region at 15 GHz is smaller than the
broad line region size (from eq.22 in Laor & Behar (2008)). At higher
frequencies, another emitting source should be even smaller, as higher
frequency emission originates at smaller radii, and the flat spectrum can be
the result of the the emissivity integrated over the emitting volume. An
increased radio emission is indeed expected if the observed ’mm-excess’
component is extrapolated down to 45 GHz (Laor & Behar, 2008; Behar et al.,
2018).

Figure 6: Mean nuclear Spectral Energy Distribution in Fν between 5 and 45 GHz
obtained by calculating the mean of the two frequencies spectral slopes of the
cores reported in Table 3 and plotted in arbitrary units.

###  5.4 Radio - X-ray correlations

It has been found that both XRB and AGN follow tight X-ray versus radio
luminosity correlations, with two different tracks, i.e. one characterised by
a slope of $\sim$ 0.8 and followed by low-hard state XRB and low-luminosity
AGN (LLAGN, e.g. Gallo et al., 2003; Salvato et al., 2004; Panessa et al.,
2007; Chiaraluce et al., 2019), and one characterised by a slope of $\sim$ 1.4
and followed by ’outliers’ XRB and bright RQ AGN (e.g. Coriat et al., 2011;
Panessa et al., 2015; Dong et al., 2014). The scaling with the black-hole mass
has led to the formulation of the ’fundamental’ plane of black-hole activity
(e.g. Merloni et al., 2003; Bonchi et al., 2013; Dong et al., 2014), and to
theories unifying the accretion-ejection physics of XRB and AGN (e.g. Körding
et al., 2006). Typically, a flat slope of $\sim$ 0.8 is associated to
radiatively-inefficient accretion flows (e.g. Falcke et al., 2004; Coriat et
al., 2011; Dong & Wu, 2015), while a steep slope of $\sim$ 1.4 is associated
to radiatively-efficient accretion flows (e.g. Coriat et al., 2011; Gallo et
al., 2012; Fender & Gallo, 2014; Dong et al., 2014; Qiao & Liu, 2015).

In Table 5 we summarise the results of the correlations between the peak radio
luminosities of the core components and the X-ray ones. In Fig. 7 we show the
plots of the corresponding correlations (left panel). Since in 22 and 45 GHz
bands censored data in the peak radio luminosities were present, in order to
estimate the slopes we used the EM algorithm in the Astronomy Survival
Analysis software package ASURV Rev 1.2 (Isobe et al., 1990; Lavalley et al.,
1992), which implements the methods presented in Isobe et al. (1986).

In order to strengthen the validity of the radio versus X-ray correlation, we
have checked the significance of the corresponding flux-flux correlations. In
Table 1 in Supplementary material we report the statistical values associated
to flux-flux relations, and they are plotted in Fig. 1 in Supplementary
material. The radio versus 2-10 keV flux-flux relations are strong
($\mathrm{r\,\sim\,0.6-0.8}$) and significant ($\mathrm{P\,\leq\,10^{-3}}$),
while in the case in which 20-100 keV fluxes are considered the significance
is lower ($\sim\,10^{-2}$).

The slopes of the luminosity-luminosity relations at all frequencies (blue
dashed lines in the plots), except at 10 GHz, are compatible with the slope of
1.4 found in the case of radiatively efficient sources, with high correlations
coefficients and significance at 5 and 15 GHz, while at 22 and 45 GHz, where
upper limits are present, the correlations are weaker and the significance is
lower (order $\sim\,10^{-3}$).
In Fig. 7, the well known powerful radio sources previously mentioned occupy a
different locus. For this reason we investigated the same correlations
excluding the ’Offset’ sources (red dot-dashed lines). The slopes obtained in
this case tend to be flatter with respect to the previous case, with values in
the range 0.6 - 1.2 and, although the correlations are strong ($r\sim$ 0.6 -
0.8), the significance of the relations is lower, i.e. $\sim 10^{-3}$. This is
expected, as the powerful radio sources occupy the high-luminosity region of
the plane with the result of driving the overall relation (e.g. Hardcastle et
al., 2009).

We investigated also the existence of correlations between the peak radio
luminosity and hard-X-ray (i.e. 20-100 keV) one (right panel of Fig. 7),
finding strong correlations ($\rho\,=\,$0.5-0.7) with slopes in the range
1.3-2, with a high significance (order of $\sim\,10^{-3}-10^{-4}$). When the
’offset’ sources are excluded, in analogy with radio-X-ray correlations, the
slope flatten ($\sim\,0.6-1.1$) and, although strong ($\rho\,=\,$0.8-0.6), the
significance is lower ($\sim\,10^{-2}$).

|
---|---
Figure 7: Plots of the correlations between peak radio luminosities of the
core components and X-ray (2-10 keV, left panel) and hard-X-ray (20-100 keV,
right panel) ones. From top to bottom: 5, 10, 15, 22 and 45 GHz bands. The
solid black line is the ${L_{R}}/{L_{X}}\,\sim\,10^{-5}$ relation; the dashed
blue line represents a regression considering all the data, the red dot-dashed
line represents a regression discarding the offset sources (i.e. QSO B0241+62,
B3 0309+411B, NGC 1275 and 4C +74.26, see the text). In the case of 22 and 45
GHz bands, since upper limits were present, the regression lines are
calculated from a EM algorithm.

The slopes of the radio-X-ray luminosity correlations are compatible with 1.4
found by Panessa et al. (2015) using the complete sample of 79 hard X-ray
selected Seyferts and 1.4 GHz data ($\sim$ 10% of RL sources are present in
their sample). However, the radio observations in Panessa et al. (2015) are at
1.4 GHz and have a resolution of $\sim$45 arcsec, much larger than ours.
Therefore, the flux densities and luminosities considered for the relation may
be contaminated by contribution from extended, off-nuclear component, which
may be not directly AGN-related. Moreover, they consider all the 79 Seyferts
in the sample of Malizia et al. (2009), including several powerful radio
sources. Our slopes are also consistent with the findings presented in Dong et
al. (2014) for a sample of bright RQ AGN with similar properties (i.e.
Eddington ratios larger than 1 per cent and relatively low redshift, z $\leq$
0.3), compatible with a radiatively-efficient accretion regime as postulated
in AGN-XRB unification theories. However, when powerful radio sources are
excluded, the slopes become flatter. The peak of the distribution of Eddington
ratios of the sources in our work is in the range between -2.25 and -1.5,
while that of Dong et al. (2014), is in the range between -1 and -0.5. Our
result would suggest that when intermediate accretion regimes are considered,
the slope of the relation flattens, with values which are intermediate between
the 0.8 slope for the very-low accretion regimes and the slope of 1.4 for
higher accretion regimes.

With these observations we can test if the sources follow the empirical
$\mathrm{{L_{R}}/{L_{X}}\,\sim\,10^{-5}}$ relation valid for coronally-active
stars. The finding that also bright RQ AGN follow the relation has been
interpreted in light of models in which both radio and X-ray would come from a
hot corona (e.g. Laor & Behar, 2008). In the left panel of Fig. 7 the solid
black line represents the above relation. We find that at 5 and 10 GHz the
sources, except for the offset ones, roughly follow the relation, but at
higher frequencies (15, 22 and 45 GHz) their peak radio luminosities tend to
be systematically above the relation. In order to quantify this effect, we
calculated mean values of the quantity $\log{L_{R}/L_{X}}$ for the non-offset
sources888The offset sources, as expected, are characterised by
$\log{L_{R}/L_{X}},\,\geq\,-3$, considering different radio luminosities, with
the KMESTM routine in the ASURV package999The routine KMESTM gives the Kaplan-
Meier estimator for the distribution function of a randomly censored sample.
The mean values are -4.9$\pm$0.1 at 5 GHz, -4.8$\pm$0.1 at 10 GHz,
-4.6$\pm$0.1 at 15 Ghz, -4.8$\pm$0.1 at 22 GHz and -4.5$\pm$0.1 at 45
GHz101010In the case in which the smallest value is an upper limit the mean
may suffer from statistical biases, for details see the ASURV documentation.,
with an increase of $\mathrm{\log{L_{R}/L_{X}}}$ ratio with frequency. We note
that the $\mathrm{\log{L_{R}/L_{X}}}$ relation has been found considering the
5 GHz luminosity (e.g. Laor & Behar, 2008), while Behar et al. (2018) found
that when high frequencies (i.e. at $\sim$ 100 GHz) are considered, the
relation rather follow a $\sim$ $10^{-4}$ trend. Indeed, we find that as the
frequency increases, the sources tend to cluster in this intermediate regime.

Table 5: Results of the correlation between peak radio luminosities of the
core components and the 2-10 keV luminosities, for all the sample and
excluding the offset sources. Associated flux-flux correlations are also
reported. Columns: (1) the relation; (2) sample considered; (3) the slope of
the relation (log-log); (4) the intercept; (5) Spearmnan’s rank correlation
coefficient; (6) probability of the null hypothesis that null hypothesis is
that two sets of data are uncorrelated; (7) Kendall’s tau; (8) probability of
the null hypothesis.
(*) For K and Q bands, since upper limits in the dependent variables were present, the reported values are from the EM regression algorithm, the Spearman’s rho and the Generalised Kendall’s tau calculated in the ASURV package. Relation | Sample | m | q | $\rho$ | P-value | $\tau$ | P-value
---|---|---|---|---|---|---|---
|  | (slope) | (intercept) | (Spearman) | (Spearman) | (Kendall’s) | (Kendall’s)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
${\log{L_{5\,GHz}^{peak}}}-{\log{L_{2-10\,keV}}}$ | All |  1.63$\pm$0.23 |  -32$\pm$10 | 0.8 |  9$\times 10^{-6}$ | 0.64 |  5$\times 10^{-5}$
| RQ |  1.05$\pm$0.25 |  -7$\pm$11 | 0.7 |  1$\times 10^{-3}$ | 0.5 |  2$\times 10^{-3}$
${\log{F_{5\,GHz}^{peak}}}-{\log{F_{2-10\,keV}}}$ | All |  1.33$\pm$0.42 |  -4$\pm$5 | 0.6 |  7$\times 10^{-3}$ | 0.4 |  6$\times 10^{-3}$
| RQ |  1.33$\pm$0.40 |  -4$\pm$5 | 0.6 |  7$\times 10^{-3}$ | 0.4 |  7$\times 10^{-3}$
${\log{L_{10\,GHz}^{peak}}}-{\log{L_{2-10\,keV}}}$ | All |  1.77$\pm$0.24 |  -38$\pm$10 | 0.7 |  2$\times 10^{-4}$ | 0.6 |  3$\times 10^{-4}$
| RQ |  1.16$\pm$0.25 |  -12$\pm$11 | 0.6 |  1$\times 10^{-2}$ | 0.4 |  1$\times 10^{-2}$
${\log{F_{10\,GHz}^{peak}}}-{\log{F_{2-10\,keV}}}$ | All |  1.36$\pm$0.42 |  -3$\pm$5 | 0.64 |  2$\times 10^{-3}$ | 0.5 |  3$\times 10^{-3}$
| RQ |  1.37$\pm$0.40 |  -3$\pm$5 | 0.6 |  2$\times 10^{-3}$ | 0.5 |  3$\times 10^{-3}$
${\log{L_{15\,GHz}^{peak}}}-{\log{L_{2-10\,keV}}}$ | All |  1.55$\pm$0.30 |  -29$\pm$11 | 0.8 |  2$\times 10^{-5}$ | 0.6 |  1$\times 10^{-4}$
| RQ |  1.07$\pm$0.20 |  -8$\pm$9 | 0.76 |  3$\times 10^{-4}$ | 0.6 |  1$\times 10^{-3}$
${\log{F_{15\,GHz}^{peak}}}-{\log{F_{2-10\,keV}}}$ | All |  1.16$\pm$0.40 |  -5$\pm$5 | 0.6 |  7$\times 10^{-3}$ | 0.4 |  9$\times 10^{-3}$
| RQ |  1.15$\pm$0.44 |  -5.4$\pm$4.9 | 0.6 |  7$\times 10^{-3}$ | 0.43 |  9$\times 10^{-3}$
${\log{L_{22\,GHz}^{peak}}}-{\log{L_{2-10\,keV}}}^{*}$ | All |  1.4$\pm$0.4 |  -23$\pm$17 | 0.64 |  1$\times 10^{-3}$ |  z$\sim$3.5 |  4$\times 10^{-4}$
| RQ |  0.81$\pm$0.21 |  3.6$\pm$9.0 | 0.7 |  1.4$\times 10^{-3}$ |  z$\sim$3.2 |  1.5$\times 10^{-3}$
${\log{F_{22\,GHz}^{peak}}}-{\log{F_{2-10\,keV}}}^{*}$ | All |  1.4$\pm$0.5 |  -3$\pm$5 | 0.6 |  2$\times 10^{-3}$ |  z$\sim$3.2 |  1$\times 10^{-3}$
| RQ |  1.05$\pm$0.30 |  -6.8$\pm$3.0 | 0.6 |  5$\times 10^{-3}$ |  z$\sim$3.17 |  1.5$\times 10^{-3}$
${\log{L_{45\,GHz}^{peak}}}-{\log{L_{2-10\,keV}}}^{*}$ | All |  1.33$\pm$0.40 |  -18$\pm$17 | 0.6 |  3$\times 10^{-3}$ |  z$\sim$3.4 |  7$\times 10^{-4}$
| RQ |  0.71$\pm$0.2 |  8$\pm$8 | 0.6 |  6$\times 10^{-3}$ |  z$\sim$3.04 |  2$\times 10^{-3}$
${\log{F_{45\,GHz}^{peak}}}-{\log{F_{2-10\,keV}}}^{*}$ | All |  1.4$\pm$0.5 |  -3$\pm$6 | 0.6 |  2$\times 10^{-3}$ |  z$\sim$3.3 |  1$\times 10^{-3}$
| RQ |  1.0$\pm$0.3 |  -7.4$\pm$3.0 | 0.6 |  4$\times 10^{-3}$ |  z$\sim$3.23 |  1$\times 10^{-3}$

There is still no definite explanation for the observed functional form of
relation and care should be taken when deriving physical conclusions based on
them. Indeed, several works reported that different slopes are found when
considering different classes of objects, i.e. only RL sources (Wang et al.,
2006), Giga-Hertz Peaked and Compact Steep Spectrum sources (GPS and CSS, e.g.
Fan & Bai, 2016), Narrow-Line Seyfert 1 (NLS1, e.g. Yao et al., 2018), and
blazars (Zhang et al., 2018). Magnetically dominated coronae may explain the
observed relations in RQ AGN (e.g. Laor & Behar, 2008, and references
therein). Alternatively, an interpretation in terms of a coupling of inflow
and outflow as in XRBs may apply (e.g. Carotenuto et al., 2021, and references
therein).

##  6 Clues on the origin of nuclear radio emission

Four sources in our sample are well known powerful radio emitters QSO
B0241+62, B3 0309+411B, NGC 1275 and 4C +74.26. Their radio properties are
consistent with the jet activity already reported by previous studies (e.g.
Hutchings et al., 1982; de Bruyn, 1989; Pedlar et al., 1990; Ho & Ulvestad,
2001; Healey et al., 2007; Lister et al., 2019; Bruni et al., 2020).

The remaining sources (26/30) can be classified as RQ considering their radio
properties. Two of them are undetected (IGR J16426+6536 and IGR J18027-1455)
and one of them (2E 1853.7+1534) has been detected at 22 GHz (only 22 and 45
GHz observation were available) resulting in a diffuse component that maybe
consistent with jet/outflow or starburst emission.

Steep spectra are found in 11/30 sources. Five of them, namely NGC 1068,
MCG+08-11-11, Mkn 3, Mkn 6 and NGC 4388, exhibit resolved, jet-like structure,
sometimes coupled to more complex features. For these sources, the origin of
observed radio emission is compatible with optically-thin synchrotron emission
from a sub-relativistic jet. This in agreement with previous studies reporting
aligned structures on mas scales, high-brightness temperature
($\mathrm{\gg\,10^{8}\,K}$) and flat spectrum for the mas cores (e.g. Kukula
et al., 1996, 1999; Lal et al., 2004). However, in NGC 1068 and NGC 4388,
while a jet is observed at kpc and sub-kpc scales, mas scales observations
revealed low brightness temperature cores ($\mathrm{\sim\,10^{5}\,K}$),
compatible with thermal free-free emission from the inner torus (e.g.
Gallimore et al., 1996; Kukula et al., 1999; Mundell et al., 2000; Giroletti &
Panessa, 2009). Six sources, namely NGC 4151, IGR J00333+6122, LEDA 168563,
NGC 5506, IGR J1638-2057 and IGR J20186+4043, exhibit a compact morphology and
a steep spectrum. In this case, the observed radio emission may be due to
optically-thin emission from a sub-relativistic jet which is unresolved by our
observations, as already observed in NGC 4151 and NGC 5506 (e.g. Pedlar et
al., 1993; Mundell et al., 2003; Middelberg et al., 2004; Ulvestad et al.,
2005). Radio emission from star formation may instead occur at larger (a few
kpc) scales (e.g. Padovani et al., 2011; Condon et al., 2013). For the
remaining sources optically-thin synchrotron emission from disc winds can not
be ruled out and higher resolution observations are needed.
Three sources, namely IGR J23524+5842, NGC 4593 and IGR J13091+1137, exhibit
peaked spectra in the GHz range. The source IGR J23524+5842 exhibits a core
coupled to a one-sided lobe, and its radio emission likely comes from a jet;
for the other two this hypothesis can not be confirmed, as they are compact
and the SED exhibits an additional component at high frequencies.
Two more sources, namely NGC 5252 and NGC 1142, exhibit cores with flat
spectra up to a break (at $\sim$10 and $\sim$15 GHz, respectively). This
emission is likely due to a jet, the subsequent spectral decline is probably
marking the transition to the optically-thin regime. In the former, the non-
thermal origin of radio emission has been confirmed by VLBI studies (e.g.
Mundell et al., 2000), while in the latter this scenario cannot be confirmed.
The extra-nuclear radio emission of NGC 1142 is of star formation origin and
it is discussed in a dedicated section in Appendix A.
Finally, seven sources, namely NGC 788, 4U 0517+17, Mkn 50, LEDA 170194, IGR
J17513-2011, IGR J18259-0706 and IGR J23308+7120, exhibit compact flat-
spectrum cores. In addition to the flat core, LEDA 170194 shows a steep-
spectrum two-sided jet extending over $\sim$2 kpc.
The observed radio sources above exhibit flat spectra up to 45 GHz (with the
exception of IGR J23308+7120, which is flat up to 15 GHz and undetected at 22
and 45 GHz). This may be due to optically-thick synchrotron emission from a
compact jet. However, flat radio spectra extending up to high frequencies, may
also be due to synchrotron radio emission from a magnetically-heated corona
(e.g. Laor & Behar, 2008). In the so-called coronal models, the corona is a
radially-stratified plasma, both in the magnetic field and number density of
relativistic electrons, in either a spherical or disc geometry. Each plasma
shell emits as optically-thick synchrotron radiation, but variations in the
opacity from one shell to another produce different turnover frequencies, such
that external shells dominate low frequencies, while inner ones dominate the
high frequency range. The result is an overall flat radio spectrum (e.g.
Raginski & Laor, 2016). One difference between the compact jet and coronal
emission scenario is that in the former a break in the spectral slope (due to
the optically-thick/optically-thin transition) is expected at relatively low
frequencies (a few tens of GHz), while the compactness of the corona can
result in flat spectra up to $\sim$ 300 GHz (e.g. Laor & Behar, 2008; Raginski
& Laor, 2016). This suggests that, with the resolution and frequency coverage
of our observations, the external layers of the corona are eventually sampled.

In order to put more stringent constraints to the origin of radio emission in
these sources VLBI observations will be fundamental. Indeed, it will be
possible to determine the mas size of the sources, as a size smaller than
$\sim$pc rules out star-formation or an AGN wind interacting with the
interstellar medium. Moreover, it will also exclude free-free emission, as a
brightness temperature much larger than $\mathrm{\sim\,10^{6}\,K}$ is
compatible only with non-thermal emission (e.g. Condon & Ransom, 2016).
Finally, variability studies can constrain the size of the emitting regions
and therefore discriminate between star formation and non-thermal emission,
like the base of a jet or a corona, expected to vary on relatively small
timescales (e.g. Barvainis et al., 2005; Baldi et al., 2015; Panessa et al.,
2022).

##  7 Conclusions

In this paper we presented wide-band (5 - 45 GHz), high-sensitivity (a few
$\mathrm{{\mu}Jy\,beam^{-1}}$), sub-arcsec (1-0.4${}^{\prime\prime}\,$) JVLA
observations for a sample of 30 nearby ($0.003\,\leq\,z\,\leq\,0.3$) and
moderately accreting ($\mathrm{-2.5\,\leq\,\log{L/L_{Edd}}\,\leq\,-0.5}$)
hard-X-ray selected AGN. The observations allow to characterise the sub-kpc
scale radio properties of the sample and build wide-band SEDs, with the final
aim of investigating the origin of radio emission. Below we summarise our main
findings:

  * •

We find a high detection fraction of radio emission at all frequencies, that
decreases with frequency (21/21, 21/21, 19/19, 26/29 and 24/29, i.e. 96, 96,
95, 87 and 81 per cent at 5, 10, 15, 22 and 45 GHz, respectively). These
values occupy the high tail of the distribution of the detection rates
reported in literature for RQ AGN, typically around 70 - 90 per cent.

  * •

The radio luminosities of the detected sources are in the range between 37
$\,\leq\,\log{L_{R}(erg\,s^{-1}})\,\leq$ 40\. Four sources are known powerful
radio emitters and indeed show larger luminosities $\geq$ 41 (in log units).

  * •

Two sources (observed only at 22 and 45 GHz) have not been detected. The upper
limits on their flux densities are $\sim$0.15 and 0.1
$\mathrm{mJy\,beam^{-1}}$. One of them, IGR J16426+6536, has been observed
twice, $\sim$17 months apart, in both cases it is undetected. The upper limits
on radio luminosities imply values of the X-ray radio-loudness $R_{X}\,<-$4.5,
at the very-low-power tail of radio-loudness distribution, possibly hinting to
a ’radio-silent’ nature.

  * •

The morphology of the sources varies with the selected frequency, where
extended emission dominates the lower frequencies. Overall, the majority of
them are compact, characterised by a core component (17/30). The remaining
sources exhibit either one-sided (7/30) or two sided (1/30) jets. Three
sources exhibit a complex morphology.

  * •

The SED of the sources can be classified into three categories: single power-
law spectra (14/30), convex spectra (3/30) and broken power law spectra
(4/30). For 6/30 sources only 2 SED data points (at 22 and 45 GHz) are
available, while for one source only one data point is available. We derive a
mean radio spectral energy distribution of the cores.

  * •

We find a significant radio-X-ray correlation at all frequencies. When the
four powerful radio emitters are excluded, the slopes of the correlation range
between $\mathrm{m=0.7-1.2}$. This range is intermediate between the slope of
1.4 found for high luminosity AGN and the slope of 0.8 found for LLAGN, in
agreement with the intermediate accretion rates and luminosities covered by
the sample considered here.

  * •

Our sources roughly follow the empirical Gudel-Benz relation, with a
transition from the $\mathrm{10^{-5}}$ to the $\mathrm{10^{-4}}$ relation at
higher frequencies (i.e. 15, 22 and 45 GHz), suggesting a possible
contribution to both radio and X-ray from a hot corona. The four powerful
radio emitters significantly depart from the relation, as expected.

The combination of morphology, SED shape and (when available) VLBI information
from the literature allows to formulate possible scenarios for the radiative
mechanisms responsible for the radio emission: i) $\sim$13% of the sample is
RL; ii) $\sim$37% of the sample has steep spectra compatible with optically-
thin synchrotron from a jet, which is unresolved in compact cores. In
$\sim$13% of them, optically-thin synchrotron from disc winds can not be ruled
out; iii) flat spectrum sources are generally compact (except for LEDA 170194
which exhibits a two-sided jet), indicating a possible optically-thick
synchrotron emission from a compact jet and/or a hot corona ($\sim$30%); iv)
in $\sim$30% of the sample, peaked core spectra are found (in one case showing
a one-sided jet morphology) again suggesting a possible jet scenario.

This work is part of a large project aiming at investigating the origin of
radio emission through high-resolution, high-sensitivity, multi epoch, wide-
band radio observations. Our volume limited, well characterized hard X-ray
sample is perfectly suited to push over this effort by exploiting the
unprecedented capabilities of the Square Kilometer Arrays (SKA) pathfinders
and precursors.

## Acknowledgements

We acknowledge the anonymous referee for her/his valuable suggestions and
comments that have improved the quality of our manuscript. The authors would
like to thank the NRAO helpdesk staff for the help in the data reduction. The
National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. EC acknowledges the National Institute of Astrophysics (INAF) and the
University of Rome – Tor Vergata for the PhD scholarship in the XXXIII PhD
cycle for the period December 2017 - December 2020. GB and FP acknowledge
financial support under the INTEGRAL ASI-INAF agreement 2019-35-HH.0. Part of
the data reduction has been performed by EC at the DiFA - University of
Bologna and the Istituto di Radioastronomia in the period January - March
2020, a visit funded by the Bando Fondi Ricerca 2019 of the INAF-IAPS. FP
acknowledges support from a grant PRIN-INAF SKA-CTA 2016. AL was supported by
the Israel Science Foundation (grant no. 1008/18). E.B. is supported by a
Center of Excellence of the Israeli Science Foundation (grant No. 2752/19).
IMcH thanks STFC for support under grant ST/R000638/1. FT acknowledges support
by the Programma per Giovani Ricercatori - anno 2014 Rita Levi Montalcini.
This research made use of APLpy, an open-source plotting package for Python
(Robitaille & Bressert, 2012).

## Data Availability

The data underlying this article were accessed from NRAO
(https://science.nrao.edu/). The derived data generated in this research will
be shared on reasonable request to the corresponding author.

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##  Appendix A NGC 1142

NGC 1142 is a massive spiral galaxy and is part of an interacting system Arp
118, in which the companion is the massive elliptical galaxy NGC 1143,
$\sim$40 arcsec far away in the NW direction ($\sim$24 kpc). It is most
probably the result of a collisional encounter (e.g. Joy & Ghigo 1988).

Its radio map exhibits a complex morphology, with a central component, named
B, where the core is believed to reside, plus additional extra-nuclear
components on scales of $\sim$10 kpc (total extension). At 5, 10 and 15 GHz, a
southern ridge of radio emission extending on approximately the same spatial
scale is visible. At 22 GHz 6 components are detected plus a southern ridge,
namely East, A1, A2, C, B and D. In the 45 GHz naturally-weighted map only
three components are detected, namely A1, A2 and B. This is due to a combined
effect of the steep spectrum of the off-nuclear components and the lower
sensitivity at 45 GHz with respect to 22 GHz. At 5 GHz (archival post-upgrade
JVLA observations) the East component is blended with A1, while the C
component is not detected. At 10 and 15 GHz the significance of the detection
of the off-nuclear components is lower. This is due to a combined effect of
the steep spectrum and the higher RMS in these bands with respect to 5 and 22
GHz maps (archival VLA observations were of lower sensitivity before the
upgrade). The observed morphology is compatible with previous radio studies at
comparable resolution (e.g. Joy & Ghigo 1988; Condon et al. 1990; Thean et al.
2000), although an additional component, C, is detected with a high
significance at 22 GHz.

The present observations at matched resolution, although with slightly
different sensitivities, allow to build for the first time the SED for all the
detected components. The core (component B) exhibit a spectrum which is
flat/inverted up to to a break occurring at $\sim$15 GHz, with a steep decline
after it (see Table 4). This likely originates from the base of a jet,
However, due to the missing information at the mas scale, it is not possible
to rule out a possible thermal origin.

The extra-nuclear components are characterised by steep spectra in cm/sub-cm
range, with spectral indices in the range 0.7-1.3 (see Table 4 and bottom-
right panel of Fig. 4). These values, together with the observed morphology,
are compatible with radio emission from star formation (e.g. Condon 1992;
Panessa et al. 2019). This source is part of the Calar Alto Legacy Integral
Field spectroscopy Area (CALIFA) survey (Sánchez et al. 2012) which covers the
range of 3700 - 7000 angstrom with a 3.7 arcsec resolution.

In Fig. 8 we show over-plots of 22 GHz contours with optical emission lines
images corresponding to different lines, i.e. NII, OII, H$\alpha$ and
H${\beta}$ (the corresponding wavelengths of each optical map are indicated on
top). These lines may trace recent star formation (e.g. Calzetti et al. 2007).
From Fig. 8 it is possible to make the following considerations: i) the
component B, the nucleus, is always optically bright, as expected; ii) the
component D is bright in all emission lines; iii) the southern ridge is bright
in NII, OII and H$\alpha$, it is weak in H$\beta$; iv) the triple group
East/A1/A2 is bright in OII, it is weak in H$\alpha,\beta$ and NII.

The above considerations are suggesting that the radio emission from the
extra-nuclear steep spectrum components, coinciding with spikes in optical
emission lines maps, is indeed synchrotron radiation from regions of intense
star formation, as first proposed by Joy & Ghigo (1988). Previous works
support this interpretation and have found that the component D indeed
coincides with a giant HII region (e.g. Hippelein 1989); the southern ridge is
part of the ring of the disk galaxy which is stripped in an elliptical
geometry because of encounter with the companion galaxy, which has produced an
enhancement in the molecular gas density, as traced by CO(1-0) observations
(Gao et al. 1997, e.g.). In this scenario, the coincidence of star forming
regions traced by optical and radio observations with regions of increased gas
density is supported by dynamical models (e.g. Lamb et al. 1998). While the
interpretation of the origin of steep-spectrum radio emission of the extra-
nuclear components D and southern ridge fits with the above picture, that of
triple East/A1/A2 is not straightforward, as it appears weak in emission lines
(except for OII) and it is spatially coincident with a gap in the molecular
gas CO(1-0) (Gao et al. 1997). Interpretations for the origin of this radio
emission comprise emission from SNR in molecular gas clouds with low density
(e.g. Gao et al. 1997), radio emission from star formation triggered by the
temporary enhanced density in the impact locus (e.g. Lamb et al. 1998) or
emission from cosmic rays from star formation and supernovae explosions (e.g.
Appleton et al. 2003).

Figure 8: Maps for NGC 1142 in which we overplot our proprietary K-band
contours to CALIFA emission lines maps at different wavelengths, comprising
OII, H$\beta$, H$\alpha$ and NII. In each map, the wavelength corresponding to
the optical emission line image is indicated (in angstroms).