# LeMMINGs. III. The e-MERLIN Legacy Survey of the Palomar sample. Exploring
the origin of nuclear radio emission in active and inactive galaxies through
the [O iii] – radio connection.

R.D. Baldi1,2, D.R.A. Williams3, R.J. Beswick3, I. McHardy2, B.T. Dullo4, J.H.
Knapen5,6, L. Zanisi2, M.K. Argo3,7, S. Aalto8, A. Alberdi9, W.A. Baan10, G.J.
Bendo3,11, D.M. Fenech12, D.A. Green13, H.-R. Klöckner14, E. Körding15, T.J.
Maccarone16, J.M. Marcaide17, I. Mutie18,3, F. Panessa19, M.A. Pérez-Torres9,
C. Romero-Cañizales20, D.J. Saikia21, P. Saikia22, F. Shankar2, R.E. Spencer3,
I.R. Stevens23, P. Uttley24, E. Brinks25, S. Corbel26,27, I. Martí-Vidal28,
C.G. Mundell29, M. Pahari30, M.J. Ward31<EMAIL_ADDRESS>
###### Abstract

What determines the nuclear radio emission in local galaxies? To address this
question, we combine optical [O iii] line emission, robust black hole (BH)
mass estimates, and high-resolution e-MERLIN 1.5-GHz data, from the LeMMINGs
survey, of a statistically-complete sample of 280 nearby, optically active
(LINER and Seyfert) and inactive (Hii and Absorption line galaxies [ALG])
galaxies. Using [O iii] luminosity ($L_{\rm[\text{O\,{iii}}]}$) as a proxy for
the accretion power, local galaxies follow distinct sequences in the
optical–radio planes of BH activity, which suggest different origins of the
nuclear radio emission for the optical classes. The 1.5-GHz radio luminosity
of their parsec-scale cores ($L_{\rm core}$) is found to scale with BH mass
($M_{\rm BH}$) and [O iii] luminosity. Below $M_{\rm BH}\sim$106.5 M⊙, stellar
processes from non-jetted Hii galaxies dominate with $L_{\rm core}\propto
M_{\rm BH}^{0.61\pm 0.33}$ and $L_{\rm core}\propto
L_{\rm[\text{O\,{iii}}]}^{0.79\pm 0.30}$. Above $M_{\rm BH}\sim$106.5 M⊙,
accretion-driven processes dominate with $L_{\rm core}\propto M_{\rm
BH}^{1.5-1.65}$ and $L_{\rm core}\propto L_{\rm[\text{O\,{iii}}]}^{0.99-1.31}$
for active galaxies: radio-quiet/loud LINERs, Seyferts and jetted Hii galaxies
always display (although low) signatures of radio-emitting BH activity, with
$L_{\rm 1.5\,GHz}\gtrsim$1019.8 W Hz-1 and $M_{\rm BH}\gtrsim 10^{7}$ M⊙, on a
broad range of Eddington-scaled accretion rates ($\dot{m}$). Radio-quiet and
radio-loud LINERs are powered by low-$\dot{m}$ discs launching sub-
relativistic and relativistic jets, respectively. Low-power slow jets and
disc/corona winds from moderately high to high-$\dot{m}$ discs account for the
compact and edge-brightened jets of Seyferts, respectively. Jetted Hii
galaxies may host weakly active BHs. Fuel-starved BHs and recurrent activity
account for ALG properties. In conclusion, specific accretion-ejection states
of active BHs determine the radio production and the optical classification of
local active galaxies.

###### keywords:

galaxies: active – galaxies: jet – galaxies: nuclei – galaxies: star formation
– radio continuum: galaxies

††pubyear: 2020††pagerange: LeMMINGs. III. The e-MERLIN Legacy Survey of the
Palomar sample. Exploring the origin of nuclear radio emission in active and
inactive galaxies through the [O iii] – radio connection.–A

##  1 Introduction

Supermassive black holes (SMBHs) are expected to reside at the centre of all
massive galaxies (e.g. Aller & Richstone 2002; Marconi et al. 2004; Shankar et
al. 2004). The accretion on to SMBHs in Active Galactic Nuclei (AGN) provides
a major power source in the Universe and is believed to regulate the evolution
of galaxies, by injecting energy and momentum (‘feedback’, Fabian 2012). Such
feedback sets the reciprocal relation between the observed properties of SMBHs
(e.g. central velocity dispersion $\sigma$ as a proxy of BH mass) and their
host bulges (e.g. Magorrian et al. 1998; Gebhardt et al. 2000; Häring & Rix
2004). Much of our understanding of AGN phenomena (feeding and feedback) comes
from the study of bright, powerful active SMBHs that have accreted primarily
during typical active periods of the order of a few 108 yr in a radiatively
efficient mode, as Seyfert nuclei and QSOs (Marconi et al., 2004; Shankar et
al., 2004; Cao, 2007). During such a phase, a geometrically thin, optically
thick, standard accretion disc (SAD, Shakura & Sunyaev 1973), characterised by
a high radiative efficiency mode (mass-to-energy conversion efficiency of
$\epsilon\sim$0.1, e.g. Shankar et al. 2020), is needed both to reproduce the
currently observed SMBH space density and large-scale environment and to solve
the Soltan argument (Soltan, 1982).

However, the vast majority of SMBHs in the local Universe are in a quiescent
state or, unless activity has been seen in some band, of extremely-low nuclear
outputs (e.g. Huchra & Burg 1992; Filho et al. 2006; Ho 2008): the latter are
regarded to host a low-luminosity AGN (LLAGN, traditionally defined as having
H$\alpha$ luminosities $\leq$ 1040 erg s-1, Ho et al. 1997a). Unfortunately,
the weakness of the radiative signals from low-activity SMBHs make their study
difficult. Problems include: i) confusion with brighter, non-AGN components,
ii) obscuration and, iii) selection effects.

The scarcity of deep multi-band studies for large samples of LLAGN means that
understanding SMBH activity in the low luminosity regime is currently limited.
Theories indicate that LLAGN are characterized by a low accretion rate
($\dot{m}$) and/or low radiative efficiency (Ho, 1999; Panessa et al., 2007).
In models of radiatively inefficient accretion flows (RIAFs; Narayan & Yi
1994, 1995; Yuan et al. 2012b, a; White et al. 2020), the kinetic energy is
either advected with the gas into the SMBH, or channelled into an outflow. The
magnetic field combined with ‘puffed-up’ geometrically thick structures could
provide a plausible mechanism for collimating axial outflows, accounting for a
large fraction of observed jets in LLAGN (Maoz, 2007; Mezcua & Prieto, 2014).

Probably the most common manifestation of LLAGN appears in the form of low-
ionisation nuclear emission-line regions (LINERs; Heckman 1980), which are
detected in the nuclei of a large fraction of nearby galaxies (Ho et al.,
1997b; Kauffmann et al., 2003). The current picture of LINERs is a ‘mixed bag’
of objects, with some photoionized by stars, some by AGN, and some perhaps
excited by shocks (Allen et al., 2008; Sarzi et al., 2010; Capetti & Baldi,
2011; Singh et al., 2013). By assuming an active BH origin of the LINER
population (or a part of it), the transition from the Seyfert to LINER regime
corresponds to a decrease in the Eddington ratio (defined as the ratio between
the bolometric AGN luminosity and the Eddington luminosity, $L_{\rm
Bol}$/$L_{\rm Edd}$) (Ho, 2008; Kewley et al., 2006), accompanied by a
hardening of the ionizing spectrum. At the extremely low end of the Eddington
luminosity, active SMBHs with low $\dot{m}$ and low radiative efficiency can
even be hidden at the centre of (apparently) inactive galaxies, where star
formation (SF) outshines the faint active nucleus.

Table 1: Radio and optical properties of the LeMMINGs (Palomar) sample.

Name |  Hubble | class | $\sigma$ | log $M_{\rm BH}$ | log $L_{\rm[\text{O\,{iii}}]}$ | log Edd | det | morph | log $L_{\rm core}$ | log $L_{\rm Total}$
---|---|---|---|---|---|---|---|---|---|---
|  | BPT | km s-1 | M⊙ | erg s-1 | ratio |  |  | erg s-1 | erg s-1
(1) |  (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
NGC 7817 |  SAbc | H | 66.7 | 6.21 | 39.29 |  $-$1.51 | U | $-$ |  $<$35.64 | $-$
IC 10 |  IBm? | H | 35.5 | 5.11 | 37.13 |  $-$2.57 | U | $-$ |  $<$32.91 | $-$
NGC 147 |  dE5 pec | ALG | 22 | 4.28 | $-$ | $-$ | U | $-$ |  $<$32.39 | $-$
NGC 185 |  dE3 pec | L | 19.9 | 4.10 | 34.63 |  $-$4.06 | U | $-$ |  $<$32.33 | $-$
NGC 205 |  dE5 pec | ALG | 23.3 | 4.34∗ | $-$ | $-$ | U | $-$ |  $<$32.36 | $-$

Column description: (1) source name; (2) morphological galaxy type taken from
RC3 (de Vaucouleurs et al., 1991); (3) optical spectroscopic classification
based on BPT diagrams and from the literature. H=Hii, S=Seyfert, L=LINER, and
ALG=Absorption line galaxy. ‘j H’ marks the jetted Hii galaxies and ‘RL’
identifies the RL AGN; (4) stellar velocity dispersion $\sigma$
($\rm{\,km\,s}^{-1}$) from Ho et al. (2009); (5) logarithm of BH mass
($M_{\odot}$) determined from $\sigma$ (Tremaine et al., 2002) or from direct
BH mass measurements (galaxies marked with ∗, van den Bosch 2016) ; (6)
logarithm of [O iii] luminosities from Ho et al. (1997a) or from the
literature (non corrected for extinction, see Paper II for references); (7)
logarithm of Eddington ratio ($L_{\rm Bol}$/$L_{\rm Edd}$); (8) radio
detection status: ‘I’ = detected and core identified; ‘U’ = undetected; ‘unI’
= detected but core unidentified; ‘I+unI’ = detected and core identified with
additional unknown source(s) in the field; (9) radio morphological class: A =
core/core–jet; B = one-sided jet; C = triple; D = doubled-lobed ; E = complex;
(10)–(11) logarithm of radio core and total luminosities at 1.5 GHz (erg s-1).
To convert the radio luminosities in erg s-1 to W Hz-1 at 1.5 GHz, an amount
of +16.18 should be subtracted from log $L_{\rm core}$ and log $L_{\rm
Total}$. The full table is available as supplementary material.

Understanding the physics of the accretion/ejection of matter in low-
luminosity regimes is important for a variety of reasons. First, the steep
local AGN luminosity function shows that LLAGN outnumber the QSO population by
a few orders of magnitudes at $z<0.3$ (Heckman & Best, 2014; Saikia et al.,
2018b). The large abundance of local LLAGN indicates that such a population
represents the common mode of SMBH accretion at low redshifts and gives a
snapshot of the ordinary relation between the SMBH and its host. Second, the
identification of the LLAGN population would help to constrain the occupation
fraction of active SMBH in galaxies. Such a quantity is unknown at low stellar
masses $<$109-10 M⊙ (Greene, 2012; Gallo & Sesana, 2019), and is crucial for
establishing the BH mass density function and to calibrate the prescriptions
for SMBH–galaxy growth of semi-analytical and numerical models (Shankar, 2009;
Barausse et al., 2017). Third, the discovery of large cavities of hot gas that
have been formed in the intra-cluster medium typically by jets from LLAGN in
massive elliptical galaxies (e.g. Dunn & Fabian 2006; Werner et al. 2019),
indicates that jet-mode feedback is a crucial aspect of the low-luminosity
stage of SMBH activity (Heinz et al., 2007; Fabian, 2012).

In the last decades, the preferred method for finding active SMBHs was by
X-ray selection, but even the deepest current observations cannot probe the
heavily absorbed sources (e.g. the Chandra Deep Fields, Alexander et al.
2003). High-resolution radio observations (providing quantities such as, e.g.,
Spectral Energy Distribution [SED] or brightness temperature [$T_{\rm B}$])
offer complementary, direct views of BH accretion even in dusty environments,
and can detect AGN at $\dot{m}$ below those detectable in other wave-bands

In active galaxies, apart from stellar processes, a plethora of radio-emitting
mechanisms associated with SMBH accretion can compete (see Panessa et al. 2019
for a review). Relativistic or sub-relativistic jets which accelerate
particles (Padovani, 2016; Blandford et al., 2019), disc winds which shock and
sweep the interstellar medium (ISM) (Zakamska & Greene, 2014) and outflowing
magnetically-active coronae (Laor & Behar, 2008), are the main astrophysical
phenomena which can account for cm/mm-wavelength radiation in the pc-scale
regions of AGN. The combination of radio and optical data can provide more
robust diagnostics to separate SF and AGN components (see e.g. Best et al.
2005b; Smolčić et al. 2008; Kauffmann et al. 2008; Best & Heckman 2012;
Radcliffe et al. 2018; Muxlow et al. 2020) and break the degeneracy among all
the possible radio-emitting physical processes: the goal of this work.

Jets111The term ‘jet’ indicates outflow of ejected plasma that becomes
collimated (unlike a wind), which transports outwards mass, energy and angular
momentum. The bulk speed can generally be relativistic, leading to a radio-
loud AGN, or sub-relativistic, corresponding to a radio-quiet one., generally
seen in radio, but sometimes in other bands as well (e.g. in the optical, as
in M 87, Perlman et al. 1999) are an unambiguous indicator of nuclear activity
seen in LLAGN (e.g. Körding et al. 2006). The increasing evidence of finding
jets associated with LLAGN compared to the high-luminosity AGN is supported by
sparse radio studies of LLAGN and QSOs (e.g. Kukula et al. 1999; Nagar et al.
2000; Mezcua & Prieto 2014; Padovani 2016), although a few studies have found
contradictory results (e.g. Jiang et al. 2007; Macfarlane et al. 2021). This
result can be generalised by the fact that the radio loudness, i.e. the ratio
between the radio and the optical emission associated with the active SMBH,
increases at lower bolometric luminosities and at low Eddington ratios (Ho,
2002, 2008; Kozieł-Wierzbowska et al., 2017; Laor et al., 2019). The presence
of a link between the SMBH capability of emanating bright jets and their AGN
multi-band nuclear properties (bolometric luminosities, Eddington ratios,
etc.) has been interpreted in the light of different accretion modes. Among
active galaxies, RIAF discs and large SMBHs ($>$108 M⊙) are generally more
efficient at accelerating particles to relativistic velocities than SAD and
small SMBHs (Meier, 2001; Nemmen et al., 2007; Begelman, 2012; McKinney et
al., 2012). All these favourable conditions are generally met in LLAGN, which
despite weak optical nuclei, display a broad variety of radio properties, from
flat-spectrum cores to steep-spectrum kpc-scale jets (Nagar et al., 2000).

Since jets are observed across all types of active BHs (Galactic BHs, X-ray
binaries [XRBs], and AGN), it is still under debate whether the accretion–jet
symbiosis is scale-invariant, regardless of the accretion mode in, e.g., the
so-called ‘Fundamental Plane of BH activity’ (Merloni et al., 2003; Falcke et
al., 2004; Plotkin et al., 2012; Bonchi et al., 2013; Gültekin et al., 2019).
This 3D plane (radio luminosity $L_{\rm radio}$, X-ray luminosity $L_{\rm X}$
and BH mass $M_{\rm BH}$) is believed to unify all active BHs at different
mass scales, indicating common physical mechanisms in accretion and jet
production among all accreting compact objects. Historically, in analogy with
the states in XRBs, LINERs are thought to be the hard-state equivalent of an
XRB, where the radiation is produced inefficiently and the jet is dominating
over the disc emission ($L_{\rm X}$ $\propto\dot{m}^{2}$, e.g. Esin et al.
1997), while Seyfert galaxies are thought to be the equivalent of
high-$\dot{m}$ XRBs ($L_{\rm X}$ $\propto\dot{m}$, e.g. Fender et al. 2003),
where jets are never seen222Dark decaying jets have been rarely seen in
particular transitional stages of the soft state (e.g. Rushton et al. 2012;
Drappeau et al. 2017).. However, recently there is compelling evidence that
the AGN optical classifications are not likely to map in a 1-to-1 manner to
the spectral states observed from accreting stellar mass BHs and a growing
list of disc observational constraints of XRBs challenge its application to
AGN (see review from Davis & Tchekhovskoy 2020). For AGN, the $\dot{m}$ break
between LINERs and Seyferts is typically at about $10^{-3}$, while for the
XRBs hard states are typically seen below 2 per cent of $L_{\rm Edd}$
(Maccarone, 2003; Vahdat Motlagh et al., 2019), and soft states are typically
seen above that level. A few Seyfert galaxies also show evidence of Fourier
power spectra with similar characteristics to those of hard-state XRBs
(Markowitz et al., 2003; Vaughan et al., 2005) and (low-luminosity) Seyferts
often show jetted structures (e.g. Kukula et al. 1995; Thean et al. 2000;
Giroletti & Panessa 2009; Kharb et al. 2017), differently from soft-state
XRBs.

To have a less biased view of the properties of SMBH accretion and the
SMBH–host link at low masses, an accurate census of the accretion and jet
properties is needed. This requirement is satisfied by the LeMMINGs (Legacy
e-MERLIN Multi-band Imaging of Nearby Galaxy Sample)
survey333http://www.e-MERLIN.ac.uk/legacy/projects/lemmings.html (Beswick et
al., 2014). It consists of 1.5-GHz observations (and upcoming 5-GHz
observations) of 280 nearby galaxies from the Palomar sample, which is usually
considered to be one of the best selected and most complete samples of nearby
galaxies. The two data releases (Baldi et al. 2018, Paper I, and Baldi et al.
2021, Paper II) represent the deepest 1.5-GHz survey of local ($<$110 Mpc)
active and inactive galaxies at milli-arcsecond resolution and $\upmu$Jy
sensitivity with the e-MERLIN array. Only partial conclusions on the optical-
radio connection have been already drawn in Paper I because of incompleteness
of the sample. The full coverage of the [O iii]-line optical and radio data in
this work allows to exploit the statistical completeness of the sample to
investigate the origin of the radio cores in local galaxies.

In Section 2 we present the LeMMINGs project and the radio and optical [O iii]
properties of the sample. We show the optical–radio diagnostics to explore the
nature of the radio emission for each optical class in Section 3. In Section 4
we discuss the results and focus on each optical class. We revise the radio
properties of the LLAGN population and draw our conclusions about disc–jet
coupling in LLAGN and SMBH-host connection in nearby galaxies in Section 5. A
supplementary section A focuses on the BH mass function of local galaxies.

##  2 The Survey and the sample

The LeMMINGs sample represents a subset of 280 galaxies from the Revised
Shapley-Ames Catalog of Bright Galaxies and the Second Reference Catalogue of
Bright Galaxies (Sandage & Tammann, 1981) (details in Papers I and II). The
sample is taken from the optical spectroscopic Palomar survey (Ho et al.,
1997a), selecting only targets with $\delta$ $>$20∘, to be accessible to the
e-MERLIN array. The sample is optically selected ($B_{\rm T}<$ 12.5 mag), so
has no radio bias, and a median distance of 20 Mpc. Based on the updated
optical emission-line diagnostic diagrams (BPT, Baldwin et al. 1981; Kewley et
al. 2006; Buttiglione et al. 2010), the sample has been classified into Hii,
Seyfert, LINER and Absorption Line Galaxies (ALG) (see Papers I and II). The
galaxies for which the active SMBH is the main photoionising source are
Seyferts (18/280) and LINERs (94/280). The inactive galaxies are represented
by Hii galaxies (140/280) where star forming regions populated by massive
young stars mainly photoionise the surrounding gas, and ALG (28/280), which
are optically inactive galaxies and do not show evident emission lines and are
typically in early-type hosts.

e-MERLIN observations at L band (1.2–1.7 GHz) of the 280 Palomar galaxies are
presented in Papers I and II. An angular resolution of $\lesssim$200 mas and
high sensitivity ($1\sigma\sim 0.8\,$mJy beam-1) enabled the detection of
radio emission at pc scale of 44.6 per cent (125/280) of the sample. We
detected the radio cores444We define core as the unresolved central component
of the radio source, which pinpoints the location of a putative SMBH, and may
represent a jet base, an unresolved disc-driven emission or a nuclear stellar
cluster (NSC). with typical radio sizes of $\lesssim$100 pc and radio core
luminosities, $L_{\rm core}$, in the range $\sim$1034–1040 erg s-1 (Table 1).
For 106 of the 125 detected sources we identified the radio core within the
structure, co-spatial with the optical galaxy centre: 56/94 LINERs, 12/18
Seyferts, 5/28 ALGs and 33/140 Hii galaxies. Conversely for the remaining 19
‘unidentified’ sources, the detected radio emission was not associated with
the central optical nucleus. We resolved parsec-scale radio structures with a
broad variety of morphologies (Tab. 1): core/core–jet (class A, the most
common), one-sided jet (class B), triple sources (class C), double-lobed
(class D), and complex shapes (class E) with extents of $\sim$3–6600 pc. There
are 31 sources with clear jets (class B, C and D), which are referred to as
‘jetted’ galaxies. LINERs and Seyferts are the most luminous sources, whereas
Hii galaxies are the least. LINERs show elongated core-brightened radio
structures while Seyferts reveal the highest fraction of symmetric
morphologies. The majority of the 33 radio-detected Hii galaxies have single
radio core or complex extended structures, but seven of them show clear jets.
ALGs exhibit on average the most luminous radio structures, similar to that of
LINERs.

When considering the galaxy morphological types, most of the sources are late-
type galaxies (LTGs, from Sa to Sd, $\sim$71 per cent), with a smaller
fraction of elliptical and lenticulars (E and S0, early-type galaxies [ETGs]).
In terms of BH masses, we derive the values using the stellar velocity
dispersions $\sigma$ measured from optical spectra (mostly from Ho et al.
2009, see Table 1) and the empirical $M_{\rm BH}$–$\sigma$ relation from
Tremaine et al. (2002), analogous to what was done in Paper I. For 36 sources,
we use direct SMBH measurements (derived from stellar and gas dynamics, mega-
masers, or reverberation mapping) available from the $M_{\rm BH}$ compilation
of van den Bosch (2016). Our sample of 280 galaxies harbours BHs with 104
$\lesssim$ $M_{\rm BH}$ $\lesssim$ 109 M⊙. As a test, we also derive the BH
masses using the $M_{\rm BH}$–$\sigma$ relation from van den Bosch (2016),
which is based on a larger sample of BH masses than the one from Tremaine et
al. (2002). The two relations agree with each other within 0.3 dex, for
intermediate BH masses, $\sim$106–108 M⊙, but differ at higher BH masses
within 0.5 dex and at lower BH masses within 1 dex. This scatter defines the
errors on the $M_{\rm BH}$ measurements. LINERs, Seyferts and ALGs typically
host SMBHs with masses $\gtrsim$107 M⊙, while Hii galaxies have typically
lower BH masses.

###  2.1 [O iii] emission line

The [O iii] emission line is an optical forbidden $\lambda$5007 Å transition,
produced by gas photoionisation by a strong radiation field either from an
active SMBH or star-forming region. In the case of an AGN, because of its high
energy ionisation level, [O iii] emission is extended from several kpc on
galaxy scale down to the innermost central region on pc scale, in the so-
called ‘narrow-line region’ (NLR) (Kewley et al., 2019). Despite being
slightly dependent on the AGN orientation and obscuration (e.g. Risaliti et
al. 2011; Bisogni et al. 2017), [O iii] line luminosity,
$L_{\rm[\text{O\,{iii}}]}$, is a good (but not ideal) indicator of the
bolometric AGN luminosity ($L_{\rm Bol}$ = 3500$\times
L_{\rm[\text{O\,{iii}}]}$, Heckman et al. 2004 for LLAGN). Since the line
emitting region can extend up to several kpc, the main caveat of the [O iii]
line is the contribution from other ionising sources, such as shocks and
purely stellar processes (Binette et al., 1994; Dickson et al., 1995; Dopita
et al., 1997), which could result in an overestimate of the SMBH accretion
power. Conversely, if the kpc-scale NLR extends beyond the spectroscopic slit
used by Ho et al. (1995) (1–2 arcsec, from a few pc to $\sim$1 kpc for our
sample), this may lead to an underestimate of the AGN bolometric luminosity.

Figure 1: The Eddington ratio (ratio between the bolometric AGN luminosity,
$L_{\rm Bol}$ = 3500 $\times\,L_{\rm[\text{O\,{iii}}]}$, Heckman et al. 2004
for LLAGN and the Eddington luminosity) for the LeMMINGs sample with the [O
iii] line detected: Hii, LINER, and Seyfert galaxies. The filled histogram
identifies the radio detected sources.

For the LeMMINGs sample, we collect the [O iii] luminosities (Tab. 1, not
corrected for extinction) from the Palomar optical survey (Ho et al., 1997a)
and from the most recent surveys/observations (see Papers I and II for more
details). In our sample, Seyferts, LINERs and Hii galaxies have mean [O iii]
luminosities of 5.0$\times$1039, 3.5$\times$1038, and 1.5$\times$1038 erg s-1,
respectively. For the vast majority of ALGs, upper limits on [O iii]
luminosities are not available.

Despite some caveats on $L_{\rm[\text{O\,{iii}}]}$ as an indicator of AGN
strength (e.g. Lamastra et al. 2009; Netzer 2009, particularly at low
luminosities), we can also calculate the Eddington ratio, $L_{\rm
Bol}$/$L_{\rm Edd}$, a gauge of the accretion rate, $\dot{m}$ (listed in Table
1 and shown in Figure 1 for our sample). The Eddington ratios of LINERs and
Seyferts are generally below and above 10-3, respectively, the typical
threshold used to separate between low and high $\dot{m}$ on to the SMBHs
(Best & Heckman, 2012). For Hii galaxies, in the conservative scenario that
their line emission is powered by the AGN, we note that, although less
luminous in line emission, they have intermediate Eddington ratios between
LINERs and Seyferts because their BH masses are typically lower than those of
active galaxies.

Since optical emission lines (e.g. H$\alpha$ and [O iii]) can be caused by
hot, young massive stars in star-forming regions, we can also assume a stellar
origin of the line emission: $L_{\rm[\text{O\,{iii}}]}$ can thus be used as a
SF rate (SFR) estimator, SFR (M⊙/yr) = 7.9$\times$10-42
$L_{\rm[\text{O\,{iii}}]}$ (erg s-1) following Kennicutt (1998) and adopting
log([O iii]/H$\alpha$) = 0.0$\pm$0.5, Moustakas et al. 2006; Suzuki et al.
2016).

###  2.2 Radio loudness

The investigation of the nature of the radio emission in the LeMMINGs galaxies
would benefit from a separation between radio-loud (RL) and radio-quiet (RQ)
AGN. For the former (i.e. radio galaxies, RGs) the relativistic jets are the
main power source; for the latter different mechanisms (SF, sub-relativistic
jets, and disc/corona winds) are likely to produce radio continuum (Panessa et
al., 2019). Accordingly, we have used the ratio $L_{\rm
core}/L_{\rm[\text{O\,{iii}}]}$ defined as the spectroscopic radio loudness
parameter (Capetti & Balmaverde, 2006) based on local ellipticals. In general
Seyfert galaxies and RQ AGN show a larger excess of line-emission (at a given
radio-core luminosity) than those of RL objects, i.e. $L_{\rm
radio}$/$L_{\rm[\text{O\,{iii}}]}<$ 10-2 (Capetti & Balmaverde, 2007;
Ishibashi et al., 2014). Since the LeMMINGs sample contains a more
heterogeneous mixture of early and late type galaxies than the sample used by
Capetti & Balmaverde (2006), and RL AGN are known to be associated with the
most massive BHs555More than 80 per cent of the local AGN with $M_{\rm BH}$ ¿
107.7 M⊙ and with 150-MHz radio luminosities $>$ 1021 W Hz-1 are RL (Sabater
et al., 2019). (Chiaberge & Marconi, 2011), we select the RL galaxies (black
circles, Fig. 2) based on these two conditions: $L_{\rm
core}$/$L_{\rm[\text{O\,{iii}}]}>$ 10-2 and $M_{\rm BH}$ > 107.7 M⊙ (in
agreement with local RL LLAGN, Baldi & Capetti 2010). The selected RL AGN in
the LeMMINGs sample are thus 18 LINERs and one jetted Hii galaxy (see Tab. 1).

The radio loudness is known to increase with $M_{\rm BH}$ (Fig. 2, see Nelson
2000; Best et al. 2005b), and the presence of a bimodal, dichotomous or
continuous distribution of radio loudness between RQ and RL AGN is still
controversial (e.g. Kellermann et al. 1989; Cirasuolo et al. 2003). In fact,
we note that other possible RL candidates (mostly LINERs) are close to our
RL/RQ selection boundary. A clean RQ/RL separation simply based on the radio-
loudness parameter and BH mass is not possible, as a detailed radio study of
the jet with very-long baseline interferometers (VLBI) would be needed (see
Giovannini 2003, 2004). Therefore, our criteria select the most bona fide RL
AGN of the sample. Furthermore, the radio loudness is also known to inversely
correlate with the Eddington ratio (Ho, 2008; Yang et al., 2020). However,
since in our case both quantities are derived from the [O iii] luminosities
(i.e. the spectroscopic radio loudness $\propto L_{\rm[\text{O\,{iii}}]}^{-1}$
and Eddington ratio $\propto L_{\rm[\text{O\,{iii}}]}$), an inverse
correlation between these two quantities is hence expected.

##  3 The optical–radio connection and the origin of the radio emission

BPT diagrams attribute the optical emission lines of LINERs and Seyferts to
photoionisation from AGN activity, whereas for Hii galaxies the line
ionisation is most likely due to SF processes. The paucity of studies on the
nuclear emission of ALGs casts doubts on the nature of this class of sources.
However, the origin of the radio emission associated with an optical nucleus
for each class is controversial, since several processes compete (Panessa et
al., 2019). The [O iii] line emission taken from the Palomar spectroscopic
survey is extracted from a more extended nuclear region than the sub-arcsec
radio emission detected by our e-MERLIN survey. A direct spatial comparison
between the optical and radio emitting regions is therefore not possible in
this work. Consequently, a possible mismatch between the spatial distributions
of the radio and optical regions could lead to a misinterpretation of the
origin of the radio emission, e.g. genuine AGN-driven nucleus in a Hii galaxy.
Fortunately, forthcoming studies with integral-field spectroscopy (e.g. from
the MaNGA survey, Bundy et al. 2015) on local radio-emitting galaxies (e.g.
Roy et al. 2021, Mulcahey et al in prep.) and with HST photometry on the
LeMMINGs sample itself (Dullo et al. in prep.) will clarify this point.

In analogy to Paper I for a sub-sample (103 objects), we here carefully study
the connection between the radio emission down to $\sim$50 pc and the sub-kpc
[O iii] emission, weighing the role of $M_{\rm BH}$, for the entire LeMMINGs
sample. Specifically, we explore the $L_{\rm
core}$–$L_{\rm[\text{O\,{iii}}]}$–$M_{\rm BH}$ relation to investigate the
origin of nuclear radio emission in active and inactive galaxies.

###  3.1 Radio properties versus BH mass

Hints to possibly identify the genuine AGN origin of the nuclear emission come
from two quantities: the BH mass and the radio luminosity. The former is often
used as an indicator of BH activity as active nuclei are preferentially
associated with massive systems (e.g., Chiaberge & Marconi 2011). The latter
roughly establishes the likelihood of the source being radio-jet dominated, a
sign of an active SMBH (Cattaneo & Best, 2009). Both quantities are connected
in active nuclei, as AGN tend to become more radio powerful (e.g. radio
louder) at larger $M_{\rm BH}$ (e.g. Best et al. 2005b).

Figure 2: The spectroscopic radio-loudness parameter $L_{\rm
core}/L_{\rm[\text{O\,{iii}}]}$ as a function of $M_{\rm BH}$ (in M⊙) for our
sample. The area limited by the dashed line encloses the RL AGN (black
circles), selected to have $L_{\rm core}$/$L_{\rm[\text{O\,{iii}}]}>$ 10-2 and
$M_{\rm BH}>$ 107.7 M⊙. The symbols and colour codes are described in the
legend: LINERs as blue up-pointing triangles, Seyferts as red diamonds, and
Hii galaxies as orange squares. The filled (empty) symbols are the radio
detected (non-detected with 3$\sigma$ upper limits) radio sources. The plus
signs identify the jetted Hii galaxies. We also include six 3C/FR Is (pale-
blue down-pointing triangles) to highlight the locus of RL AGN. Figure 3: In
the upper plot, the histograms of the entire sample (solid line) and of radio-
detected sources (dashed line) in bins of BH mass. In the lower panel, 1.5-GHz
core luminosities ($L_{\rm core}$ in erg s-1) as a function of the BH masses
(in M⊙) for the sample, divided per optical class (symbol and colour coded as
in the legend, analogous to Fig.2). The filled symbols refer to the detected
radio sources, while the empty symbols refer to non-detected radio sources
(3$\sigma$ upper limits). The unidentified sources (detected but the radio
core has not been identified) are the empty symbols with radio 3$\sigma$ upper
limits. The jetted Hii galaxies show an additional plus sign. The dotted line
represents the linear correlation found for RL AGN (marked by black circles)
and 3C/FR Is, the dashed line for active and jetted (ALG and Hii) galaxies for
$M_{\rm BH}$ $\gtrsim$ 106.5 M⊙ and the solid line for the non-jetted Hii
galaxies for $M_{\rm BH}$ $\lesssim$106.5 M⊙ (see Sect. 3.1 for details and
Table 2 for the best-fit parameters using censored-data statistics). In the
bottom-right corner we show the typical error bars associated with the data
points. Figure 4: Histograms of the fraction of radio detected galaxies in the
LeMMINGs sample in $M_{\rm BH}$ bins. The solid-line histogram considers the
entire sample, while the blue dashed line is the distribution of only the
active galaxies (LINER, Seyferts and jetted ALG and Hii galaxies). The two
dashed lines represent the best fit for two distributions (Tab. 2 for the best
fit parameters). Figure 5: The total 1.5-GHz luminosity ($L_{\rm Total}$ in
erg s-1) as a function of the BH masses (M⊙) for the LeMMINGs sample, divided
per radio morphological class A, B, C, D, and E (symbol and colour coded
according to the legend). Table 2: Statistical censored analysis of radio-
optical correlations of the full LeMMINGs sample presented as a function of
galaxy type.

$X$ | $Y$ | Fig. | sub-sample | Stat | $\rho_{XY}$ | $P_{\rho_{XY}}$ | $\rho_{XY,D}$ | Slope | Intercept
---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
$\log M_{\rm BH}$ | $\log L_{\rm core}$ | 3 | active galaxies | S | 0.549 |  $<$0.0001 | 0.526 | 1.65$\pm$0.25 | 23.0$\pm$8.1
$\log M_{\rm BH}$ | $\log L_{\rm core}$ | 3 | non-jetted Hii | S | 0.575 | 0.0003 | 0.541 | 0.61$\pm$0.33 | 31.2$\pm$8.7
$\log M_{\rm BH}$ | $\log L_{\rm core}$ | 3 | RL AGN + 3C/FR I | P | 0.526 | 0.00069 | 0.496 | 1.52$\pm$0.31 | 25.1$\pm$4.1
$\log$ $M_{\rm BH}$ | $f_{d}$ | 4 | all ($M_{\rm BH}>10^{6.5}$ M⊙) | P | 0.951 | 0.00098 | $-$ | 0.22$\pm$0.03 | -1.11$\pm$0.24
$\log$ $M_{\rm BH}$ | $f_{d}$ | 4 | active gal. ($M_{\rm BH}>10^{6.5}$ M⊙) | P | 0.925 | 0.0028 | $-$ | 0.15$\pm$0.03 | -0.45$\pm$0.21
$\log L_{\rm[\text{O\,{iii}}]}$ | $\log L_{\rm core}$ | 6 | Seyferts | K | 1.190 | 0.0002 | 0.920 | 0.99$\pm$0.20 | -3.5$\pm$5.5
$\log L_{\rm[\text{O\,{iii}}]}$ | $\log L_{\rm core}$ | 6 | RL AGN + 3C/FR I | P | 0.876 | 9.4$\times$10-9 | 0.840 | 1.31$\pm$0.18 | -13.1$\pm$7.0
$\log L_{\rm[\text{O\,{iii}}]}$ | $\log L_{\rm core}$ | 6 | RQ LINERs | S | 0.579 |  $<$0.0001 | 0.542 | 1.21$\pm$0.28 | -11.1$\pm$6.4
$\log L_{\rm[\text{O\,{iii}}]}$ | $\log L_{\rm core}$ | 6 | non-jetted Hii | S | 0.347 |  $<$0.0001 | 0.323 | 0.79$\pm$0.30 | 5.0$\pm$10.2
$\log$ Eddington ratio | $\log L_{\rm core}$ | 7 | Seyfert | K | 0.591 | 0.0149 | 0.582 | 0.98$\pm$0.36 | 37.6$\pm$13.4
0.83 $\log L_{\rm[\text{O\,{iii}}]}$ \+ 0.82 $M_{\rm BH}$ | $\log L_{\rm core}$ | 8 | Seyferts | K | 1.072 | 0.0007 | $-$ | 0.84$\pm$0.21 | 3.3$\pm$10.2
0.83 $\log L_{\rm[\text{O\,{iii}}]}$ \+ 0.82 $M_{\rm BH}$ | $\log L_{\rm core}$ | 8 | RL AGN + 3C/FR I | P | 0.886 | 3.8$\times$10-9 | $-$ | 1.20$\pm$0.15 | -9.1$\pm$6.1
0.83 $\log L_{\rm[\text{O\,{iii}}]}$ \+ 0.82 $M_{\rm BH}$ | $\log L_{\rm core}$ | 8 | RQ LINERs | S | 0.543 |  $<$0.0001 | $-$ | 0.83$\pm$0.19 | 4.0$\pm$9.5
0.83 $\log L_{\rm[\text{O\,{iii}}]}$ \+ 0.82 $M_{\rm BH}$ | $\log L_{\rm core}$ | 8 | non-jetted Hii | S | 0.426 |  $<$0.0001 | $-$ | 0.60$\pm$0.25 | 13.0$\pm$12.9

Column description: (1)-(2) the two variables of the considered relation; (3)
Figure; (4) the sub-sample of galaxies for the tested correlation. ‘Active
galaxies’ include AGN (LINER and Seyferts) and jetted (ALG and Hii) galaxies;
(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 $P_{\rho_{XY}}$: $S$ for the censored
generalised Spearman’s correlation coefficient (for $>$30 objects), $K$ for
the censored generalised Kendall’s $\tau$ correlation coefficient (for $<$30
objects) and $P$ for the Pearson correlation coefficient for fully a detected
data set; (8) censored partial rank correlation coefficient between X and Y
adjusting for the target distance D; (9)-(10) the slope and the intercept of
the best fits with their 1-$\sigma$ errors.

The distribution of radio-detected galaxies as a function of BH mass in the
LeMMINGs sample is shown in Figure 3 (upper panel) and it is clear that the
detection fraction increases with $M_{\rm BH}$ (a closer look in Fig. 4).
Similarly, a positive trend between the radio core luminosities, $L_{\rm
core}$, and $M_{\rm BH}$ is also observed (lower panel, Fig. 3). In analogy to
Paper I, for the objects with $M_{\rm BH}\gtrsim 10^{6.5}$ M⊙, a clear
sequence includes all active and jetted galaxies, despite the large scatter.
However, below 106.5 M⊙, which mostly includes Hii galaxies, a flatter
correlation emerges. Interestingly, the small sub-group of jetted Hii galaxies
have $M_{\rm BH}\gtrsim 10^{6.5}$ M⊙ and generally follow the sequence of the
active galaxies.

In order to assess the presence of correlations, we performed a statistical
censored analysis (ASURV package; Feigelson & Nelson 1985; Lavalley et al.
1992) which takes into account upper limits. We used the `schmittbin` task
(Schmitt, 1985) to calculate the associated linear regression coefficients for
two sets of variables. The best fit is represented by the bisector of the two
regression lines obtained by switching the $x$ and $y$ axes as dependent and
independent variables. In order to estimate the quality of the linear
regression, for small data sets ($N<30$) we also derived the generalised
Kendall’s $\tau$ correlation coefficient (Kendall, 1938) between the two
variables, using the `bhkmethod` task. Otherwise for larger samples, we used
the Spearman’s rank order correlation coefficient, using the `spearman` task
(Akritas, 1989). To measure the linear correlation between two fully detected
sets of data, we estimate the Pearson correlation coefficient $r$ (Pearson,
1895). We also test the possible influence of the sample distance D in driving
the established correlations, estimating the censored partial rank coefficient
$\rho_{\rm XY,D}$ (Akritas & Siebert, 1996). Table 2 reports the parameters of
the statistical analysis of the correlations we analyse hereafter in this
work.

We fit the linear (in a $\log$-$\log$ plot, hereafter) radio–$M_{\rm BH}$
correlation by including all the active galaxies, i.e. those which show
characteristics of AGN activity in optical (emission line ratios) or radio
(presence of jets) bands: RQ/RL LINERs, Seyferts and jetted ALG and Hii
galaxies. For BH masses $\gtrsim$106.5 M⊙, we find $L_{\rm core}\propto M_{\rm
BH}^{1.65\pm 0.25}$ with a Spearman’s correlation coefficient of 0.549. This
value shows the likelihood of the two quantities not correlating as less than
1$\times$10-4 (Tab. 2).

In contrast, the non-jetted Hii galaxies tend to fall on another radio–$M_{\rm
BH}$ sequence with $M_{\rm BH}\lesssim$106.5 M⊙. Indeed, their relation
clearly flattens with respect to that of active galaxies as $L_{\rm
core}\propto M_{\rm BH}^{0.61\pm 0.33}$ with a chance (Spearman’s $\rho$ =
0.575) probability of correlation of 3$\times$10-4 (Tab. 2). The two incident
radio–$M_{\rm BH}$ relations valid for star-forming and active galaxies
strengthen the scenario of a different origin of the radio emission: SF-driven
for non-jetted Hii galaxies and AGN-driven for active galaxies.

Figure 6: [O iii] line luminosity ($L_{\rm[\text{O\,{iii}}]}$ in erg s-1) vs
1.5-GHz core luminosities ($L_{\rm core}$ in erg s-1) for the LeMMINGs sample.
The different optical classes are coded (symbol and colour) according to the
legend of Fig 2. The jetted Hii galaxies show an additional plus sign. The
filled symbols refer to the detected radio sources, while the empty symbols
refer to non-detected radio sources (3$\sigma$ upper limits). The unidentified
sources (detected but the radio core has not been identified) are the empty
symbols with radio 3$\sigma$ upper limits. The dotted line represents the
linear correlation by fitting only the RL AGN (black circles) together with
the 3C/FR Is, the blue dashed line represents the fit by including RQ LINERs,
the red dashed line for Seyferts and the yellow triple-dot-dashed line for
non-jetted Hii galaxies (see Table 2 for best-fit parameters). The black bars
in the bottom-right corner indicate the typical errors for the data-points.

Paper I suggested that LINERs and low-power RGs are powered by a common
central engine, e.g. a RIAF disc with a coupled jet (Falcke et al., 2004;
Nemmen et al., 2014). Paper I compiled a sample of six Fanaroff & Riley type I
(FR I) RGs (i.e. 3C 66B, 3C 264, 3C 78, 3C 338, 3C274, and 3C 189, from the
Revised Third Cambridge Catalogue, 3C, Bennett 1962) at $z<$0.05 observed with
MERLIN at 1.5 GHz (see Table 4 in Paper I). In Figures 2 and 3, FR Is stand
out from the rest of the sources for their large radio luminosities and BH
masses, and thus higher radio loudness, and clearly extend the LINER
population to higher values. Therefore, we fit the mass-radio relation valid
for the whole RL AGN group (RL Palomar + FR I galaxies, dotted line in Fig.
3). We find $L_{\rm core}\propto M_{\rm BH}^{1.52\pm 0.31}$ with a Pearson
correlation coefficient of 0.526 and a two-sided no-correlation probability
significance of 6.9$\times$10-4.

Two different radio-$M_{\rm BH}$ sequences below and above $\sim$106.5 M⊙,
respectively, for star-forming and active galaxies have been thus validated,
also by excluding the distance effect in driving the correlations (as the
censored partial rank coefficients only marginally decrease, see Tab 2).
Therefore, now that the presence of a break at $M_{\rm BH}\sim$106.5 M⊙ has
been highlighted, we can focus on the fraction of radio detections, $f_{d}$,
as a function of $M_{\rm BH}$ for the entire LeMMINGs sample (Fig. 4). For
$M_{\rm BH}>$107.5 M⊙, this fraction is 50 per cent, reaching $>$75 per cent
in the last bins, $>$108.5 M⊙. Conversely, the fraction flattens at $\sim$20
per cent below $\sim$106.5 M⊙, where the SF was found to largely contribute in
our sample (Fig. 3). By considering only the sub-sample of active galaxies,
the fraction of radio detections is unexpectedly higher than that of the
entire sample in each BH mass bin. We also note that the $f_{d}$ reaches 100
per cent for active galaxies with $L_{\rm core}$ $\gtrsim$1036 erg s-1
($\gtrsim 10^{19.8}$ W Hz-1) and $M_{\rm BH}$ $\gtrsim$ 107 M⊙. We fit the two
detection fraction distributions as a function of BH mass for $M_{\rm
BH}>$106.5 M⊙ to avoid both the SF flattening and a single AGN case (Seyfert
NGC 4395666The active galaxy with the lowest $M_{\rm BH}$ of the sample,
3.7$\times$104 M⊙). The best fits (see statistical parameters in Tab. 2) are
$f_{d}$ $\propto M_{\rm BH}^{0.22\pm 0.03}$ and $\propto M_{\rm BH}^{0.15\pm
0.03}$, respectively, for the whole LeMMINGs sample and for the active
galaxies.

All of the radio morphological classes are represented along the radio (both
$L_{\rm core}$ and $f_{d}$) $-$ $M_{\rm BH}$ sequence. The total integrated
radio luminosity, $L_{\rm Total}$, also broadly increases with the BH mass
(Fig. 5). There is no overall trend which links a specific radio morphological
classification to a given range of radio luminosities. The fraction of targets
assigned to class B, C, D and E (e.g. clear jetted structures or complex)
typically increases with $L_{\rm Total}$/$M_{\rm BH}$ because of their large
extended, and sometimes diffuse, radio emission. Core/core–jet structures
(class A) are observed across a slightly broader $M_{\rm BH}$ and $L_{\rm
Total}$ range than the other classes. A similar effect has been also noted in
the $L_{\rm core}$–$M_{\rm BH}$ plot. This could be the consequence of two
effects: the preference for faint sources to appear as single cores and a
Doppler boosted flux in the case of aligned sources. However, the latter
scenario, i.e. a core boosting, is expected to marginally affect our results
at 1.5 GHz in the sub-mJy regime (only for RL AGN, see e.g. blazar-like heart
of NGC 1275, Walker et al. 1994).

###  3.2 Radio properties versus [O iii] luminosity

The comparison between radio and optical properties of galaxies is a powerful
tool to explore the nature of their nuclear emission. The [O iii] luminosity
represents a robust upper limit (unless there is strong dust extinction) to
any bolometric emission from an accretion disc in the case of an AGN (Lamastra
et al., 2009) (or from stellar emission in the case of an Hii galaxy,
Moustakas et al. 2006). The radio emission efficiency, i.e. the fraction of
the radio emission produced with respect to the AGN (or SF) bolometric
luminosity, offers a good diagnostic to investigate the nature of the nuclei.

The radio core luminosity as a function of [O iii] luminosity is shown in
Figure 6 for the LeMMINGs sample (without ALGs which lack optical
counterparts, but including NGC 5982 with a $L_{\rm[\text{O\,{iii}}]}$ upper
limit). The three optical classifications (LINER, Seyfert, Hii galaxy) tend to
cluster in different regions of the [O iii]–radio diagram, despite a large
overlap, similarly to what has been noted in the analogous plot for a smaller
sub-sample in Paper I. Seyferts are up to 100 times more luminous in the [O
iii] emission line compared with LINERs for a given $L_{\rm core}$, or
equivalently have 100 times less luminous radio cores. The Hii galaxies have
the lowest radio and [O iii] luminosities, whilst the LINERs have intermediate
values. Analogously to Paper I, we report that the LINERs appear to broadly
follow a linear trend in the [O iii]-radio plot. Similarly to Fig. 3, the
relation formed by Hii galaxies shows a break with respect to that valid for
active galaxies at lower luminosities. Compared to the results from Paper I,
we note that Seyferts show a distinct relation with respect to the other
classes. The current complete sample allows us to derive more robust relations
by using the censored data analysis (see Table 2) than those obtained in Paper
I.

First, Seyfert galaxies clearly show a striking linear correlation in the form
$L_{\rm core}$$\propto L_{\rm[\text{O\,{iii}}]}$0.99±0.20 with a (Kendall’s
$\rho$ = 1.190) probability of 0.0002 of being caused fortuitously. At higher
radio luminosities, RL AGN follow the 3C/FR Is on a steeper linear fit,
$L_{\rm core}$$\propto L_{\rm[\text{O\,{iii}}]}$1.31±0.18 (Pearson’s P value =
9.4$\times$10-9). RQ LINERs fill the gap between RL AGN and Seyferts with a
correlation almost parallel to the one found for RGs, i.e. $L_{\rm
core}$$\propto L_{\rm[\text{O\,{iii}}]}$1.21±0.28 (Spearman’s P value $<$
0.0001). At low powers, the sequence of non-jetted Hii galaxies clearly
flattens with respect to that formed by active galaxies, but with a broader
scatter, i.e. $L_{\rm[\text{O\,{iii}}]}$$\propto L_{\rm core}$0.79±0.30
(Spearman’s P value $<$ 0.0001). Once the distance dependence has been
considered, these optical-radio relations are still statistically valid,
because the censored partial rank coefficients are only slightly smaller than
the generalised correlation coefficients (see Tab. 2).

Beyond the optical classification, the sources with a core/core–jet or triple
structure tend to follow the correlation of the active galaxies, as they are
mostly classified as LINERs and Seyferts. Similarly, most of the ETGs also
follow the correlation of active galaxies. Conversely, we do not find any
statistically significant correlation between the Eddington ratios and $L_{\rm
core}$ for our sample (see Fig.7, probability of fortuitous correlations
$>$0.04). Nevertheless, we note for Seyferts: i) a mild positive trend where
$L_{\rm core}$ and Eddington ratio linearly increases with a slope
0.98$\pm$0.36 with a large scatter $\sim$1 dex (Kendall’s $\rho$ = 0.591 [
essentially unchanged correlation coefficient, if considering the distance
dependence] and probability of a null correlation 0.0149, Tab. 2]) and ii) the
jetted morphologies correspond to objects with higher Eddington rates.

Figure 7: Eddington ratio (whose bolometric luminosity is estimated from
$L_{\rm[\text{O\,{iii}}]}$, see Sect. 2.1) vs 1.5-GHz core luminosity (erg
s-1) only for active galaxies (LINER, Seyferts and jetted Hii galaxies, and no
ALGs for the lack of their optical counterparts). Symbols and colours,
described in the legend, are coded analogously to Fig.2. The dashed line
represents the best fit for Seyferts (by using censored-data statistics, see
Table 2).

###  3.3 The optical Fundamental plane of BH activity

Observational attempts at explaining the similarities between the X-ray and
radio properties of SMBHs and XRBs eventually culminated in the discovery of
the so-called ‘Fundamental Plane of Black Hole Activity’ (hereafter ‘FPBHA’
Merloni et al., 2003; Heinz & Sunyaev, 2003; Falcke et al., 2004). The FPBHA
is a 3D hyper-plane that correlates the radio luminosity with the X-ray
luminosity, scaled by the BH mass, and seems to hold for XRBs and active
SMBHs. By using a similar approach, Saikia et al. (2015) introduced a new
version of the FPBHA using the [O iii] luminosity as a tracer of the
accretion, instead of the X-ray luminosity and found an analogous correlation
for active BHs. The advantage of using the [O iii] line instead of the X-ray
data is the accessibility from the ground with reasonable resolution. Full
coverage of the optical and radio data for the entire LeMMINGs sample allows a
complete analysis of the Fundamental Plane (FP). New X-ray Chandra
observations and the X-ray-based FP of the LeMMINGs sample will be addressed
in forthcoming papers (Williams et al., in prep.)

Figure 8: The fundamental plane of BH activity (FPBHA) in the optical band for
the LeMMINGs sample with e-MERLIN data, i.e. $L_{\rm core}$ vs 0.83$\times$log
$L_{\rm[\text{O\,{iii}}]}$ \+ 0.82$\times$$\log$$M_{\rm BH}$ (1.5-GHz core and
[O iii] luminosities in erg s-1 and BH masses in M⊙) parameterised as
expressed by Saikia et al. (2015). Colour and symbols are explained in the
legend. The filled symbols refer to the detected radio sources, while the
empty symbols refer to non-detected radio sources (3$\sigma$ upper limits).
The unidentified sources are the empty symbols with radio 3$\sigma$ upper
limits. The dotted line represents the best fit for RL AGN (large black
circles) and 3C/FR Is, the blue dashed line represents the fit for RQ LINERs,
the red dot-dashed line for Seyferts and the yellow triple-dot-dashed line for
non-jetted Hii galaxies (see Table 2 for best fit parameters using censored-
data statistics). The black bars in the bottom-right corner indicate the
typical errors for the data-points.

Figure 8 depicts the optical FPBHA of the LeMMINGs galaxies, by using the same
parametrisation expressed by Saikia et al. (2015). Note that these authors
used 15-GHz VLA observations at a resolution of
$\sim$0$\aas@@fstack{\prime\prime}$13, comparable with that of our e-MERLIN
data. Yet, their observations are possibly less contaminated by SF and more
sensitive to the nuclear optically-thick radio emission than our 1.5-GHz
observations because of the higher radio frequency.

In Paper I, despite a limited number of sources, we noted that the active
galaxies appear to broadly follow a common correlation in the optical FP,
stretching their luminosities up to FR I RGs. Nevertheless, Paper I also noted
the three classes are slightly stratified within the FP scatter across the
radio luminosities, possibly reminiscent of the different accretion states for
each optical class. Here, thanks to the sample completeness, we are able to
recognise that different optical classes move separately along the plane.
LINERs still appear to follow the FR Is at lower luminosities. The RL (FR I,
Parma et al. 1986) jetted Hii, NGC 3665, lies on the RL AGN relation and the
rest of the jetted Hii galaxies agrees with the FPBHA of RQ LINERs. Seyferts,
on the other hand, seem to cover a different sequence in the plane because of
their lower radio core luminosities. Non-jetted star forming galaxies stand
out from the rest of the sample because of their smaller BH masses and lower
[O iii] and radio luminosities. Therefore, similar to the approach taken in
Paper I, we prefer to fit the FPBHA for the different classes, by using the
parametrisation introduced by Saikia et al. (2015) (in units of erg s-1 for
luminosities and M⊙ for BH masses)777We refrain from providing a new optical
FPBHA parametrisation independent of that of Saikia et al. because of the
presence of a large fraction of upper limits in radio and [O iii] data and the
fact that [O iii] luminosity is not an absolute estimator of the AGN activity.
We will dedicate an accurate analysis on the X-ray-based FPBHA, by using the
state-of-the-art censored-data statistics (Williams et al., in prep.).:

$\log L_{\rm core}=(0.83\,\ \log L_{\rm[\text{O\,{iii}}]}+0.82\,\,\log M_{\rm
BH})\,m+q$

where Saikia et al. found $m$ = 1.0 and $q$ = $-$3.08 for their sample. Table
2 collects all the statistical results obtained from fitting the FP for
different classes. Seyferts exhibit a tight linear correlation even evident to
the naked eye, with a slope of $m$=0.84$\pm$0.21. The generalised Kendall’s
$\tau$ coefficient of the Seyfert FP is 1.072 which indicates that two axis
quantities do not correlate with a probability of 0.0007. The whole LINER
population shows a large scatter in the FP. A better understanding of this
population is possible by separating RL and RQ LINERs, which follow different
tracks in Fig. 8: RL LINERs extend the FR Is to lower regimes, whereas RQ in
general tend towards the locus of Seyferts. We search for linear correlations
separately for the two LINER classes. For RL AGN (RL LINERs + FR Is), the fit
clearly appears steeper than the Seyfert plane, with a slope of
$m$=1.20$\pm$0.15 (Pearson’s P value = 3.8$\times$10-9). For the RQ LINERs,
the plane is statistically consistent with the one defined by Seyfert galaxies
but it extends to lower luminosities with a larger scatter, bridging the gap
between RL LINERs and Seyferts: $m$ = 0.83$\pm$0.19 with a (Spearman’s) P
value $<$0.0001. The non-jetted Hii galaxies break the generic FP of the
active galaxies with a flatter slope ($m$ = 0.60$\pm$0.25, Spearman’s P value
$<$0.0001) extending to the lowest luminosities and BH masses of the sample.

Although $L_{\rm core}$ has been found to correlate with both $M_{\rm BH}$ and
$L_{\rm[\text{O\,{iii}}]}$ for the LeMMINGs sample (Sect. 3.1 and 3.2), a
mutual dependence could stretch the optical FPs we observe. The scatters of
the FPs of the optical classes (FWHM $<$0.8 dex) are typically smaller than
the scatters of the relations defined for each class in the radio-$M_{\rm BH}$
and the radio-[O iii] planes (FWHM $<$1 dex). This suggests that the observed
FPs are not stretched by any particular dependence on one of the three
quantities ($L_{\rm core}$, $M_{\rm BH}$, $L_{\rm[\text{O\,{iii}}]}$) which
establish the plane, as it has been also confirmed by other studies (e.g.
Saikia et al. 2018a). Nevertheless, the large number of upper limits in the
radio and line measurements may undermine the reliability of the fitted FPs.
To test the accuracy of the established FPs, in the cases of non-detected
Seyfert and LINER galaxies in the radio band, if we assign a core luminosity
extrapolated by the $M_{\rm BH}$-$L_{\rm core}$ relation found for active
galaxies, the corresponding data-points would lie on the plane of their
corresponding class. Analogously, non-detected ALGs (in [O iii], but detected
in radio) would sit between RL and RQ LINERs. Conversely, non-jetted Hii
galaxies would follow the plane of the RQ LINERs if they had the core
luminosities assigned by the $M_{\rm BH}$-$L_{\rm core}$ relation valid for
AGN at their BH masses. This result reinforces the discrepancies of the
observed FPs and their physical meanings for the different optical classes. In
summary, star forming and active galaxies follow different FPs, as also
evident in the radio-[O iii] plane (Fig. 6), which are likely a consequence of
different origins of their radio emission in relation to their main source of
energy (stellar or BH accretion).

##  4 Discussion

The LeMMINGs survey has unveiled radio cores at the centre in around half of
our sample of local Palomar galaxies. Here we investigate the origin of the
nuclear 1.5-GHz emission and discuss the optical–radio association in the
context of physical models of disc–jet coupling888Disc–jet coupling refers to
the connection between the inflowing accretion mode and the outflowing mode,
in the form of e.g., jets, winds, or slow outflows (Panessa et al., 2019). and
SF for each optical class (see Table 3 for a simple summarising sketch, see
also Panessa et al. 2019).

###  4.1 LINERs

LINERs are amongst the most frequently detected and most luminous sources in
the LeMMINGs sample. They are mostly detected in ETGs and feature bright radio
cores and jets.

Near-infrared, optical and X-ray nuclear emission in LINERs has generally been
interpreted as related to an active SMBH (Terashima et al., 2002; Balmaverde
et al., 2006; González-Martín et al., 2006; Flohic et al., 2006; Kharb et al.,
2012), although reservations have been raised in the past (e.g., stellar-
dominated optical nuclei, Capetti 2011). In contrast, several pieces of
evidence convincingly argue in favour of an AGN origin of the radio emission
in LINERs. First, their high brightness temperatures measured with e-MERLIN
and VLBI ($T_{\rm B}>$107 K, Papers I and II, Falcke et al. 2000) suggest
synchrotron emission from (mildly to highly) relativistic jets. Second, core
luminosities for LINERs correlate with their BH masses up to the classical RL
regime with $M_{\rm BH}\sim 10^{9}M_{\odot}$, suggesting that the mass of the
SMBH plays a major role in the production of radio emission. Third, LINERs are
often associated with either symmetric or asymmetric pc/kpc-scale jets with
luminosities of $\sim$1036 erg s-1, similar to low-power RGs (Fanti et al.,
1987). Such morphologies and powers cannot easily be explained by SF, as the
latter resides in the sub-mJy regime below 1034 erg s-1 (Bonzini et al., 2013;
Mascoop et al., 2021). Fourth, the jets tend to be core-brightened, similar to
small FR Is (Capetti et al., 2017), suggesting that the jets are probably
collimated and launched relativistically on parsec scales, but rapidly slow
down along the jet propagation axis on kpc scales. These characteristics are
similar to what is seen and modelled in nearby low-luminosity RGs (Morganti et
al., 1987; Giovannini et al., 2005; Massaglia et al., 2016; Rossi et al.,
2020).

The analysis of LINERs in this work has led to rather different results
compared to what we found in Paper I, probably due to the inhomogeneous
population of LINERs in the latter. Here we identify two sub-classes, RL and
RQ. A group of eighteen RL LINERs have the lowest Eddington ratios
($\lesssim$10-4) and are the brightest sources of the sample. They typically
reveal core–jet and twin jet morphologies, reside in ETGs and extend the
relations of 3C/FR Is to low radio and [O iii] luminosities. The complementary
RQ group of LINERs have slightly higher accretion rates than the RLs
(Eddington ratios mostly $\sim$10-4–10-3) and form an intermediate
optical–radio relation between RL AGN and Seyferts.

Similarities in the correlations of RL LINERs and FR Is support the idea that
they likely share the same central engine, capable of launching relativistic
jets. The correlation between radio and optical (continuum) emission found for
FR Is is best explained as the result of a single emission process in the two
bands (i.e. non-thermal synchrotron emission from the base of the relativistic
jet, Chiaberge et al. 1999). Analogously, an [O iii]-radio correlation found
for FR Is and low-luminosity RL LINERs (Balmaverde & Capetti, 2006) suggests a
similar ionising central source. Therefore, this interpretation is plausibly
also valid for the RL LINERs in our sample, indicating that they represent the
scaled-down version of FR Is with lower luminosities and accretion rates, as
also reported in previous studies (Falcke et al., 2004; Allen et al., 2006;
Balmaverde et al., 2008). Multiple theoretical and analytical studies of FR Is
(e.g. Meier 2001; Begelman 2012; McKinney et al. 2012) suggest that they are
powered by a RIAF disc, usually as an advection-dominated accretion flow
(ADAF, see reviews by Narayan & Yi 1994; Narayan & McClintock 2008), which can
efficiently produce jets. As LINERs are usually radio-louder than the other
optical classes and similar to low-power RGs (Capetti & Balmaverde, 2006;
Kharb et al., 2012), a model of an ADAF disc with a low-power jet (jet-
dominated accretion flows, JDAF, Falcke et al. 2004) has been used as well to
describe the disc–jet coupling of LINER-like AGN.

Conversely, the RQ LINERs appear to deviate from the RL AGN correlations,
pointing to a different interpretation for their central engine. A possible
truncated disc with an optically thick disc at larger radii (Chen et al.,
1989; Maoz, 2007; Narayan & McClintock, 2008; Nemmen et al., 2014) could
represent an intermediate regime between the low-$\dot{m}$ JDAF model for RL
LINERs and high-$\dot{m}$ SAD models for luminous Seyferts. The accretion flow
may begin as a thin SAD but, at a certain transition radius, gradually
switches from a cold to a hot ADAF mode, resulting in composite
characteristics with weaker sub-relativistic jets and slightly higher
accretion rates. This result is broadly consistent with what has been found
for a general dual population of RL and RQ LINERs in the local Universe (e.g.,
Chiaberge et al. 2005; Balmaverde & Capetti 2006).

Table 3: Simplistic sketch of the origin of radio emission in relation to the
accretion modes in local galaxies.

class |  | radio |  $\dot{m}$ |  disc
---|---|---|---|---
RL LINER |  | relativistic jets |  $\lesssim 10^{-3}$ |  RIAF
RQ LINER |  | sub-relativistic jets |  $\lesssim 10^{-3}$ |  truncated thick disc
(RQ) Seyfert |  {220pt | sub-relativistic jets |  $\lesssim 10^{-2}$ |  JED/truncated slim disc
| disc/corona wind |  $\gtrsim 10^{-2}$ |  SAD
ALG |  | (sub-)relativistic jets |  $\lesssim 10^{-3}$ |  recurrent/starving RIAF
jetted H II | sub-relativistic jets and SF |  $\lesssim 10^{-3}$ |  RIAF?
non-jetted H II |  | SF |  |

Column description: (1) optical class; (2) radio properties: sub-/relativistic
jets, disc or magnetically-active corona wind, and SF; (3) Eddington-scaled
accretion rate $\dot{m}$; (4) disc mode (see Sect. 4.1–4.4 for details).

###  4.2 Seyferts

Seyfert galaxies show the highest radio detection fraction in the LeMMINGs
sample. Two thirds of the detected Seyferts are found in spiral galaxies and
one third in ETGs. The Seyferts with the highest Eddington ratios and BH
masses are the most luminous at 1.5 GHz, featuring edge-brightened radio
morphologies.

Seyfert nuclei lie in a different region of the optical–radio plane with
respect to RL LINERs and FR Is: for a similar radio luminosity, they show a
significant optical excess (2–3 dex). On the one hand, their optical line
excess is qualitatively similar to that observed in luminous type-I QSO, where
their high-energy output is interpreted as a result of thermal emission from a
radiatively efficient accretion disc (SAD, Panessa et al. 2006; Cappi et al.
2006; Singh et al. 2011). On the other hand, a large variety of radio
characteristics observed in local Seyferts (e.g. morphologies, radio SED in
relation to accretion properties, Laor et al. 2019) prevents a complete
comprehension of the origin of their radio emission (Panessa et al., 2019;
Silpa et al., 2020), although a non-thermal synchrotron origin for compact
cores in Seyferts has been clearly established (Kukula et al., 1999; Mundell
et al., 2000; Nagar et al., 2000; Ho & Ulvestad, 2001).

As a first approximation, the radio and optical properties observed in our
sample of Seyferts are consistent with the general properties of SADs: higher
accretion rates ($>$10-3 Eddington rate) and lower efficiency at launching and
collimating jets than ADAF-dominated LINERs. In fact, diffuse lobe-like radio
structures are observed more frequently in Seyferts than in LINERs in LeMMINGs
and in other samples of local Seyferts (e.g. Kukula et al. 1993, 1995;
Morganti et al. 1999; Kharb et al. 2006; Gallimore et al. 2006). These
lobes999We cannot fully rule out SF-driven super-winds as the cause of the
observed lobes in Seyferts (Pedlar et al., 1985; Heckman et al., 1993).
However, such a scenario is unlikely because these structures are primarily
observed in star forming galaxies at low radio luminosities ($<$1034 erg s-1),
where other than radio bubbles, extended SF in the galactic disc is observed.
have been interpreted as sub-relativistic outflows at the core, which inflate
bubbles and produce bow shocks in the ISM (Middelberg et al., 2004; Yuan &
Narayan, 2014).

To complete the puzzle, Seyferts are clearly radio-quieter than RQ LINERs,
suggesting a different disc–jet coupling. Their strikingly distinct
correlation between the radio core and disc luminosity, and the lack of
continuity between Seyferts and other AGN classes, rule out the possibility
that Seyfert jets are just the scaled-down versions of RG relativistic flows
(Talbot et al., 2021). Our study also reveals a moderate increase of the radio
luminosity and jetted structure fraction at higher Eddington ratios, which can
be interpreted as increasing jet luminosity with higher $\dot{m}$ ($P_{\rm
jet}$ = $\eta_{\rm jet}\dot{m}c^{2}$ where $\eta_{\rm jet}$ is the jet
production efficiency). This is different from the literature where there are
reports of a tendency of an increased jet production ($\eta_{\rm jet}$) as the
system goes fainter from QSOs to low-luminosity Seyferts (e.g. Trippe 2014;
Wójtowicz et al. 2020), which is consistent with the anti-correlation between
radio loudness and bolometric luminosity in AGN (e.g. Terashima & Wilson 2003;
Panessa et al. 2007; Ho 2008) and in XRB (Fender et al., 2009). Such an effect
could be caused by an incomplete separation between RQ and RL Seyferts and a
lack of angular resolution to resolve jets. Previous studies were based on
more heterogeneous samples of radio-emitting Seyferts/QSOs than our sample
which consists of a complete sample of resolved jetted RQ Seyferts. In fact,
recent studies (Rusinek et al. 2020; Chang et al. 2021) which separate RQ and
RL AGN, show a slight $\eta_{\rm jet}$ increment to small Eddington ratios for
RQ Seyferts, an effect that is enhanced by including RL Seyferts. Therefore,
considering a differential dependence on $\dot{m}$ for each radio-emitting
physical mechanism competing in the total radio production $\eta_{\rm radio}$
(= $\eta_{\rm jet}$ \+ $\eta_{\rm disc-wind}$ \+ $\eta_{\rm corona-wind}$)
could solve the tension (Laor et al., 2019). At low $\dot{m}$, a (core-
brightened) sub-relativistic jet ($\eta_{\rm jet}$ $>$ $\eta_{\rm disc-wind}$
\+ $\eta_{\rm corona-wind}$) might dominate over a (edge-brightened) radio-
emitting disc/corona wind, which, in turn, becomes important at high $\dot{m}$
($\eta_{\rm disc-wind}$ or $\eta_{\rm corona-wind}$ $>$ $\eta_{\rm jet}$) (see
Sect. 4.5 for discussion and comparison with XRBs). Such scenario would
account for both the heterogeneous radio properties of Seyferts and the
general tendency of low-luminosity Seyferts to expel more compact jets than
QSOs over a large range of Eddington ratios, covering the gap between two
extreme classes: almost-radio-silent high-$\dot{m}$ QSOs and jetted
low-$\dot{m}$ LINERs. In addition, the role of the BH parameters (e.g. mass,
spin) is to sustain and reinforce the jet/wind launch (Yang et al., 2021).

To accommodate the disc and radio similarities respectively with QSOs and
LINERs, several scenarios have been proposed within the large breadth of SAD
models. At small Eddington ratios, a solution could be the model of Jet
Emitting Discs (JED, Ferreira et al. 2010) which are much less dense than an
optically-thick disc and arise at larger magnetisation, where magneto-
centrifugally driven jets are launched (Ferreira, 1997). Another scenario is
the presence of a truncated slim disc whose inner radius, where the jet is
anchored, shrinks, by dragging higher poloidal magnetic flux strength closer
to a spinning SMBH. This condition favours the launch of strong radio outflows
(Tchekhovskoy et al., 2011), and leads to an increase of the jet Lorentz
factor $\Gamma_{\rm jet}$, similar to what is seen in the hard-state XRBs
(e.g. Fender et al. 2004). At higher Eddington ratios, a quasar-driven
uncollimated wind is favoured, able to shock the ISM and accelerate
relativistic electrons producing synchrotron radio emission (Faucher-Giguère &
Quataert, 2012; Zakamska & Greene, 2014). An alternative scenario is an
outflow of coronal plasma above the accretion disc, which slightly collimates
within a narrow nozzle near the SMBH and then fans out to form a diffuse radio
morphology (Donea & Biermann, 2002; Markoff et al., 2005; King et al., 2011;
Raginski & Laor, 2016).

###  4.3 Absorption line galaxies

The ALGs lack evidence of BH-accretion activity in the optical band but may
still conceal a weak AGN at their centres, since they show bright radio cores
and jets.

Apart from a few irregular/dwarf ALGs which are probably powered by stellar
processes (Paudel & Yoon, 2020), when detected in radio, ALGs appear
indistinguishable from LINERs: massive ETGs hosting SMBHs with masses
$\sim$108 M⊙ and core-brightened radio morphologies. In addition, the radio-
detected ALGs are potential RL AGN, since their optical counterparts are not
detected. This scenario is supported by a multi-band study of local line-less
RL AGN whose nuclei and hosts are similar to those of LINER-like RGs (Best et
al., 2005b; Baldi & Capetti, 2010), although at slightly higher luminosities
than those of LeMMINGs sample (1039–1041 erg s-1). The radio detection of ALGs
in this survey, and in previous studies, argue for the presence of an active
SMBH in at least a quarter of ALGs. In this scenario, the optically weak
characteristics of ALGs could also be reconciled with the picture of
low-$\dot{m}$ RGs, where nuclear conditions (i.e. low ionising source, poor
gas availability) do not favour optical emission from a compact NLR. This
picture has been observed in particularly faint FR Is (Buttiglione et al.,
2009) and relic RGs (Capetti et al., 2013).

Even under favourable conditions, local SMBHs are known to exhibit levels of
activity much lower than those expected from gas supplying rates onto the
galactic nuclei, and only a small fraction of silent SMBHs can turn into AGN.
Dynamic stability of gas reservoirs and particular conditions of magnetic
field loops, which trap stars and gas in orbits, could lead to a fuel-starved
SMBH (Inayoshi et al., 2020), thus resulting in ALGs. The problem of dormant
massive BHs has much been discussed in the last decades (e.g Fabian &
Canizares 1988; Kormendy & Ho 2001; Herpich et al. 2018) and the inactivity of
ALGs falls in this investigation.

Another possible interpretation of the apparent absence of nuclear activity in
ALGs is intermittent accretion (Czerny et al., 2009). For example, the
currently quiescent Sgr A* was recently found to have undergone a period of
activity a few million years ago, which created a radio outflow as a
consequence of an accretion event (Heywood et al., 2019). Around 30 per cent
of fading AGN have been found to feature jets (Esparza-Arredondo et al.,
2020). The large fraction of non-detected ALGs suggests that if they have
intermittent periods of accretion activity, they are short-lived (104–105
years, Reynolds & Begelman 1997). This is supported by estimates based on
their radio jet lengths (Papers I and II). Any intermittent activity could be
caused by occasional accretion events lasting a few Myr, where X-ray emitting
hot-gas atmosphere, typical of ETGs (Forman et al., 1985), feeds the
strangulated SMBH at a very low $\dot{m}$, and establishes a quasi-spherical
accretion regime which supports the jet launching (Ho, 2002; Allen et al.,
2006).

In summary, unfavourable nuclear conditions, SMBH dormancy and nuclear
recurrence can account for the optical and radio detections (or lack thereof)
in ALGs. However, once the accretion is set, the activity phases visible in
the two bands are not necessarily synchronised: the jet production can
possibly lag the disc activity by a few 102-104 yr (depending on $M_{\rm BH}$
and jet length and power) as expected by disc–jet evolution models (e.g.
Czerny et al. 2009).

###  4.4 Hii galaxies

The Hii galaxies are generally interpreted as SF-dominated nuclei, based on
the emission line ratios in BPT diagrams, but this does not preclude them from
having a weak AGN. Hii galaxies show mostly compact single cores and extended
complex structures.

The analysis of the full LeMMINGs sample confirm the results from Paper I: the
presence of a dual population of Hii galaxies, i.e. jetted and non-jetted,
which are probably related to different origins of the core emission. In
general, jetted Hii galaxies are found to have larger $M_{\rm BH}$
($\gtrsim$106.5 M⊙) than their non-jetted companions.

The vast majority of radio-detected Hii galaxies are non-jetted. They are less
[O iii] luminous by a factor $\sim$30 than active galaxies, and typically have
a large radio excess with respect to the [O iii]–radio correlation found for
LINERs at low $L_{\rm[\text{O\,{iii}}]}$. All these characteristics are
consistent with a scenario of a nuclear starburst on a scale of $<$1 kpc,
producing stellar emission at 1.5 GHz. To corroborate this picture of a
stellar origin, Paper I concluded that thermal/non-thermal and free-free radio
emission predicted from supernova (SN) progenitors, SN explosions and SN
remnants and Hii regions (Ulvestad et al., 1981; Condon, 1992) are sufficient
to account for radio luminosities of non-jetted Hii galaxies. In addition, a
population of SNe expected from high SFR ($\sim$30–50 M⊙ yr-1) might be able
to blow bubble-like super-winds (Weaver et al., 1977; Heckman et al., 2015),
which would match the extended irregular morphologies (E class) observed in
some sources.

In contrast, three aspects of the (seven) jetted Hii sources point to the
presence of an active SMBH, powering their radio emission: i) larger BH masses
than the non-jetted companions; ii) core-brightened and elongated radio
morphologies, ii) similar line-radio correlation and FPBHA to those found for
RQ/RL LINERs. As an example, the well-known FR I (NGC 3665, Parma et al. 1986)
belongs to this sub-sample. We conclude that it is likely that this population
of jetted Hii galaxies does host weak AGN, whose output is too dim to
significantly contribute to the optical emission, dominated by nuclear SF. The
possible LLAGN signatures found in jetted Hii galaxies are similar to those of
sub-Eddington LINERs (likely powered by a RIAF), rather than the efficiently
accreting Seyferts, and could represent the tip of the iceberg of a large
population of weakly-active sub-mJy star forming galaxies at low powers
(Padovani, 2016; Muxlow et al., 2020). Another scenario to account for their
radio-optical properties is the combination of both SF and an active BH in the
event of a jet shocking a dense ISM and triggering in-situ SF (Gaibler et al.,
2012; Dugan et al., 2014). The SF–AGN co-existence underlines the symbiotic
relationship between these two types of activity, particularly in LTGs (e.g.
Santini et al. 2012).

###  4.5 Low-luminosity AGN and disc–jet coupling

Almost half ($\sim$45 per cent) of the LeMMINGs galaxies are not radio silent,
but are characterized by low radio powers ($>$ 1017.6 W Hz-1). Our survey has
revealed that local galaxies can show evidence of weak AGN-driven activity, in
the form of sub-galactic jets (B, C, D classes) or optical line ratios (LINER
or Seyfert) down to $L_{\rm core}$ $\gtrsim$1018.7 W Hz-1. By binning the
sample by radio luminosity and BH mass, the fraction of radio detections
reaches 100 per cent for galaxies with $L_{\rm core}$ $\gtrsim$1019.8 W Hz-1
(twice than the survey sensitivity limit) and with $M_{\rm BH}$ $\gtrsim$ 107
M⊙, regardless of optical type. This limit represents the lowest luminosity
for which the most massive BHs hosted by local (Palomar) galaxies are ‘always’
switched on. This limit is lower than what has been obtained from previous
radio surveys, $\sim$1020–1021 W Hz-1 for the most massive galaxies (Mauch &
Sadler, 2007; Cattaneo & Best, 2009; Sabater et al., 2019).

Assuming that some (if not all) of the radio emission in LLAGN comes from
jets, the jet fraction is expected to increase with decreasing Eddington
ratios, and consequently the radio loudness should increase with increasing BH
mass (Ho, 2008). However, the jet/radio properties of nearby galaxies have
been shown to be more complicated than a simple bimodality (presence or lack
of jet in relation of low- or high-$\dot{m}$ disc), suggesting specific modes
of accretion and jet launching mechanisms for different optical AGN classes
(Best & Heckman, 2012; Hardcastle, 2018). The high sensitivity and resolution
of our survey casts light on the entanglement between radio/jet and
optical/disc properties in LLAGN. Further help in disentangling this
complexity comes from the comparison with the analogous disc–jet coupling
observed in XRBs (Remillard & McClintock, 2006; Fernández-Ontiveros & Muñoz-
Darias, 2021). Within the low/hard XRB state, there are indications that the
transition radius between an inner ADAF and an outer thin disc decreases with
increasing luminosity (Narayan, 2005) and a short-lived strong radio outburst
occurs where highly relativistic jets are launched (e.g., Fender et al. 2004).
Conversely, clear jets are never seen in high-soft XRBs, while our survey and
other studies demonstrate that their putative AGN-equivalent (low-luminosity)
Seyferts can produce jets as much as LINERs do. While jetted AGN and low/hard
XRBs clearly lie on the same FPBHA (Merloni et al., 2003; Falcke et al.,
2004), Gültekin et al. (2019), by including radio-active high/soft state XRBs,
cannot rule out that the latter and Seyferts are inconsistent with the FP made
up of low/hard state XRBs and LINERs. Furthermore, Fischer et al. (2021) has
recently shown that, Seyferts, once resolved with the VLBI on sub-parsec
scales, can have corresponding $L_{\rm core}$ upper limits that are
systematically below the predictions from the FPBHA. The tension with the
analogies between stellar mass BHs and active SMBHs probably rests on
attempting to use the optical class to set the association. The Eddington-
ratio argument could partially resolve this tension. For XRBs, sources are
almost entirely in hard states below 2 per cent of $L_{\rm Edd}$ (Maccarone,
2003; Vahdat Motlagh et al., 2019), while above that value both states are
present. For AGN classes, LINER and Seyfert distributions usually roughly
break up at 0.1 per cent of $L_{\rm Edd}$. Therefore, the global properties of
LINERs (e.g. low Eddington ratios; weak or strong, persistent radio jets; hard
X-ray spectra) make this class similar to hard-state XRBs. Conversely,
Seyferts show more heterogeneous radio and disc properties and consists of a
mixture of hard and soft states (Fernández-Ontiveros & Muñoz-Darias, 2021).
Low-$\dot{m}$ Seyferts (between 0.1 and 2 per cent of $L_{\rm Edd}$) could be
more similar to hard XRBs, able to launch compact jets, while the
high-$\dot{m}$ Seyferts are more similar to soft XRBs. However, as disclosed
in Sect. 4.2, the current status of results on Seyferts based on radio
observations reveals a higher level of complexity than this scenario. In fact,
we would expect a larger fraction of jetted structures at low $\dot{m}$,
similar to hard XRBs, which is opposite to what we observe in our sample, but
in agreement if we consider a larger population which includes luminous
Seyferts and QSOs. A possible explanation to this apparent contradiction is
that different physical mechanisms of radio production co-exist in Seyferts,
which makes the comparison with XRBs even more challenging. At higher
accretion rates ($\dot{m}\gtrsim 10^{-2}$), disc and corona wind are expected
to play an important role in the radio emission (Laor et al., 2019) and could
account for the observed tendency to display edge-brightened structures. At
lower $\dot{m}\lesssim 10^{-2}$, a sub-relativistic compact jet, more similar
to RQ LINERs, could dominate over the other radio-emitting physical processes
(Table 3).

Although (simultaneous) high-frequency radio (e.g. mm-band) and X-ray
observations would be ideal to isolate the pc-scale emission and its link to
the disc (see Bell et al. 2011; Behar et al. 2020), in our 1.5-GHz survey, we
observed a significant dependence of radio-optical properties (i.e. disc–jet
coupling) with $M_{\rm BH}$. The small range of stellar BH masses of XRBs does
not enable a straightforward comparison of radio models valid for XRBs with
the results from the LeMMINGs survey. Instead, this is possible for AGN in
general. In fact, AGN disc models predict different mass dependencies for the
radio emission. The similar slopes found for RL and RQ AGN ($L_{\rm
core}\propto M_{\rm BH}^{1.5-1.65}$) despite the large scatter, can be
interpreted as a single strong connection between the radio output and the BH
mass, regardless of the type of the radio product (i.e. relativistic or sub-
relativistic jets, winds, etc). In the observed range of $L_{\rm
core}$–$M_{\rm BH}$ slopes, a degeneracy of models exists: for jet-dominated
sources (e.g., JDAF, Falcke et al. 2004) $L_{\rm
radio}\propto\bar{a}^{2}M_{\rm BH}$ (where $\bar{a}$ is the BH spin), ADAF
models which predict radio emission $L_{\rm radio}$ $\propto$ $M_{\rm
BH}^{8/5}$ $\dot{m}^{6/5}$ (Yi & Boughn, 1999), while relativistic jets can be
described by the Blandford–Znajek (BZ, Blandford & Znajek 1977) process as
$L_{\rm radio}\propto\bar{a}^{2}M_{\rm BH}^{2}B^{2}$ (where $B$ is the
magnetic field). Across the different AGN classes, a large range of BH spins,
accretion rates and magnetic field strengths could account for the significant
but scattered relations we observe. The transition from RQ AGN (jetted Hii
galaxies, RQ LINERs and Seyferts) to RL AGN (RL LINERs and FR Is) could be
caused by an increment of BH or disc parameter values, which result in a boost
of the radio emission (Blandford et al., 2019; Chen et al., 2021).

The radio emission production in XRBs is related to accretion rate and high-
energy-band luminosity (from optical to X-ray, produced by physical processes
in disc and/or corona). Their jet contribution to the observed high-energy
flux is largely debatable (e.g. Fender 2001; Markoff et al. 2003). Despite the
problematic comparison between states of SMBHs and stellar BHs, radio and disc
emission models of XRBs could still help to understand the physical processes
involved in active SMBHs. For the jet-mode inefficient discs in XRBs, $L_{\rm
radio}$ $\propto$ $L_{\rm X}^{0.5-0.7}$, whereas for disc-dominated sources
$L_{\rm radio}$ $\propto$ $L_{\rm X}^{1.4}$ (see Coriat et al. 2011). In our
LeMMINGs sample, assuming that [O iii] is a good indicator of the bolometric
AGN power which scales with the X-ray output, LINERs show a steeper radio-disc
luminosity dependence ($L_{\rm core}\propto
L_{\rm[\text{O\,{iii}}]}^{1.2-1.3}$ for RL and RQ LINERs) than Seyferts
($L_{\rm core}$ $\propto L_{\rm[\text{O\,{iii}}]}$). This is opposite to the
equivalent relationship observed in hard/soft XRBs. Furthermore, the absence
of a clear dependence of the radio luminosity on Eddington ratios in LINERs
casts new light on a possible disparity between jetted accreting compact
objects, since hard-state XRBs show $L_{\rm radio}\propto\dot{m}^{1.4}$ (e.g.
Körding et al. 2006), unless $L_{\rm[\text{O\,{iii}}]}$ scales as $\dot{m}$
for LINERs (Netzer, 2009).

In the context of AGN models, for SAD-dominated sources the ratio $L_{\rm
radio}$/$L_{\rm X}\propto\eta_{\rm jet}\,\bar{a}^{2}$ (Yi & Boughn, 1999) is
expected to be constant and limited to a narrow range of values, as we find
for our Seyferts, if the $\bar{a}$ range is finite. Conversely, for LINERs,
that are powered by RIAF discs, the relation between bolometric AGN and jet
power is difficult to model because jet emission can dominate their entire SED
(Körding et al., 2008) and [O iii]-line contamination from jet photoionising
shocks can overpredict the bolometric AGN power (Capetti et al., 2005; Netzer,
2009). However, in a simplistic scenario of a disc origin of the radio
emission, ADAF discs would predict much shallower relations ($L_{\rm
core}\propto L_{\rm X}^{\alpha}$ with $\alpha<$0.6 depending on
bremsstrahlung-dominated and multiple Compton scattering regimes, Yi & Boughn
1998) than the observed slopes for LINERs (1.2-1.3). Furthermore, the observed
radio-[O iii] relation found for LINERs is even steeper (despite the large
scatter) than any previous relations between the kinetic jet power and the
bolometric AGN luminosities found for LINER-like RL AGN (slopes $<$1, e.g.
Capetti & Balmaverde 2006; Merloni & Heinz 2007; Baldi et al. 2019b).
Therefore, assuming that RL LINERs are the scaled-down version of RGs and
normalising the $L_{\rm radio}$/$L_{\rm X}$ comparison with previous studies
based on this assumption, the steeper slopes might be the consequence of a
closer view of jet launching mechanism even in RQ LINERs. The high sensitivity
and sub-arcsec resolution (crucially intermediate between VLA and VLBI)
provided by our survey allowed us to probe the parsec scale region near the
core where the jet is launched and reveal the relevant role of $\Gamma_{\rm
jet}$ and BH spin/mass in the jet production. These parameters could
eventually induce much steeper relations than those established with shallower
radio observations.

Although, the reliability of the [O iii]–X-ray conversion could affect this
comparison, the difference between AGN and XRBs is stark. In conclusion, the
apparent disparity between AGN and XRB states suggests that LLAGN show
different disc–jet couplings and more complicated mechanisms of radio
production than the XRBs (without considering transition phases). However, a
more detailed (radio/X-ray) study and comparison between LLAGN and XRBs is
needed and is not the goal of this work.

Another variable which can increase the scatter of the observed radio-optical
relations and complicate our comprehension of the disc–jet connection, is the
core variability. Radio flickering and transient events have been documented
in the nuclei of some LLAGN, particularly Seyferts (e.g. Wrobel 2000; Mundell
et al. 2009; Giannios & Metzger 2011; Baldi et al. 2015a; Mattila et al. 2018;
Williams et al. 2019; Nyland et al. 2020).

###  4.6 Black hole – host connection

The LeMMINGs survey detected nuclear radio activity from high- down to low-
mass galaxies ($L_{\rm bulge}\sim 10^{9}-10^{10.5}$ $L_{\odot}$, Nagar et al.
2005), which harbour SMBHs with masses $\gtrsim$106.5 M⊙. SF- and BH-driven
radio emission are the two main mechanisms responsible for the $\mu$Jy-level
radio core emission (Padovani et al., 2015) with several pieces of evidence
pointing to an increment of AGN contribution to radio emission as $M_{\rm BH}$
increases. In fact, the radio detection and jet fraction increase with BH mass
for $\gtrsim$106.5 M⊙ and the ‘bulgeness’ of the host (i.e. favouring ETGs,
see Paper II).

One of the main results of our survey is the presence of a break of the
empirical relations (radio, [O iii], $M_{\rm BH}$, optical FPBHA) between the
star forming and active galaxies at $\sim$106.5 M⊙ (conservatively, between
$\sim$106 and $\sim$107 M⊙). A BH mass of $\sim$106.5 M⊙ seems to represent
the turnover from a SF to an AGN regime as the BH mass increases. Such a break
corresponds to the $M_{\rm BH}$ which roughly separates the BH mass function
of local LTGs and ETGs (Davis et al., 2014; Greene et al., 2020), i.e. pseudo-
bulges and bulges (Yesuf et al., 2020) and SF- and AGN-dominated sources
respectively (see Kelly & Merloni 2012, Appendix A and Fig. 9). Both the
fraction of galaxies which host a radio AGN and the radio core powers
correlate with $M_{\rm BH}$ with different relations at the two sides of this
BH mass turnover. These relationships possibly agree with galaxy evolution
models which predict that high-mass galaxies evolve faster and host a radio-
AGN which suppresses SF more effectively than low-mass galaxies (Fabian,
2012), which instead form stars in the current Universe (e.g. Lapi et al.
2011; Behroozi et al. 2019). However, it is important to point out that such a
break could also be the consequence of an intrinsic $M_{\rm BH}$-$\sigma$
relation which flattens out at low BH masses (Mezcua, 2017; Shankar et al.,
2019).

Substantial progress in understanding the process of radio AGN phenomena in
the nearby Universe has recently been made by combining optical and radio
surveys to determine the statistical relationships between radio activity and
galaxy/BH mass. It has been found that the fraction of galaxies that host RL
AGN (with $L_{\rm radio}$ $>$ 1021 W Hz-1) is a strong function of stellar
mass $\propto M_{*}^{2.5}$ and BH mass $\propto M_{\rm BH}^{1.6}$ (Best et
al., 2005b; Mauch & Sadler, 2007; Sabater et al., 2019; Hardcastle et al.,
2019) with the most massive ETGs ‘always’ switched on at low radio powers
($\gtrsim 10^{21}$ W Hz-1). In our statistically-complete heterogeneous sample
of local galaxies, mostly consisting of LTGs, we find a flatter dependence
between the radio-AGN fraction $f_{d}$ and BH mass for the active galaxies,
($\propto M_{\rm BH}^{0.15}$), independent of the radio properties. The
different slopes between our work and previous studies could be ascribed to
three aspects: the higher angular resolution and higher sensitivity of our
survey, crucial to identifying jets, the identification of genuine ‘jetted’ RQ
AGN with respect to RL AGN, and a possible presence of a break in the radio
luminosity function at 1019.5–1020 W Hz-1 (Nagar et al., 2005). This results
in the inclusion of SMBHs with masses lower than those of standard RL AGN
($<$108 M⊙), which can often emanate low-power jets on sub-kpc scale, despite
their nominal radio-quietness definition, differently from the rarer powerful
RGs. This selection eventually induces a much shallower dependence with BH
mass. Janssen et al. (2012) also noted a shallower $f_{d}$-$M_{\rm BH}$
relation than previous studies, scaling as $\propto M_{*}^{1.5}$, for Seyfert-
like radio sources, that remains still steeper than what we found for RQ AGN.
Moreover, in our survey, we do not find a clear separation (within the large
scatter) between LINERs and Seyferts in the radio–$M_{\rm BH}$ plane. This
likely indicates that accretion rate, which largely differs between the two
classes, plays a more complicate role in the radio production, together with
BH mass/spin (see Sect. 4.5).

The observed correlation between $L_{\rm core}$ and BH mass or host type can
also be an indirect consequence of a more fundamental relationship between
radio luminosity and optical bulge luminosity (or mass) (Falcke et al., 2001;
Ho, 2002; Nagar et al., 2002): ETGs show larger radio luminosities than LTGs
(Laor, 2000; Decarli et al., 2007; Mauch & Sadler, 2007; Gallo et al., 2008).
The more massive elliptical galaxies or bulge-dominated systems are more
efficient at producing radio emission as they have larger SMBHs, and hence,
are more likely to be highly RL than spiral galaxies for $M_{\rm BH}>$108 M⊙
(Chiaberge & Marconi, 2011). The high bulge-to-disc ratio is achieved in more
evolved galaxies, where spheroids and pseudo-bulges dominate the central
gravitational well. At their centres the extended jets expelled from accreting
SMBHs can more easily plough through the more rarefied ISM than in discy
(spiral) galaxies. Furthermore, according to the spin and gap paradigm (e.g.
Moderski et al. 1998; Garofalo et al. 2010; Meier 2012), a higher BH spin and
a larger gap region between the inner edge of the accretion disc, typically
achieved in ETGs, can cause a larger magnetic flux accumulation on the SMBH,
and consequently a maximisation of the BF jet mechanism. Such a condition is
reached with retrograde accretion. Typically in LTG, a low-spinning SMBH and
prograde disc have been suggested to account for their limited jet production
compared to the different RL AGN classes, found commonly in ETGs (RQ AGN
against FR classes, see, e.g. Tchekhovskoy & McKinney 2012; Garofalo et al.
2014; Garofalo & Bishop 2020).

###  4.7 Star formation

Non-jetted Hii galaxies clearly depart from the AGN classes in the
optical–radio plane and FPBHA at low $L_{\rm core}$ and $M_{\rm BH}<$106.5 M⊙,
showing a clear break likely caused by the increased SF contributions to the
pc-scale radio emission. Such a sub-sample represents a much larger population
of low-luminosity star-forming galaxies, which dominate the local Universe at
$M_{\rm BH}<$106.5 M⊙ (Appendix A, Greene & Ho 2007; Greene et al. 2020),
where stellar processes are generally the main source of energy.

Assuming that non-jetted Hii galaxies are powered by SF, the relation between
radio luminosities in such galaxies and $M_{\rm BH}$ can be deciphered as a
link between thermal/non-thermal SF luminosity and BH mass, in the form
$L_{\rm SF}\propto M_{\rm BH}^{0.61}$, which has the largest scatter of the
observed linear regressions, due to the large uncertainties of $M_{\rm BH}$
estimates at low values and numerous radio non-detections. This unprecedented
relation is likely the result of the observed link found between SF indicators
such as radio, far-infrared, optical or line luminosities, and galaxy mass
(e.g. Mauch & Sadler 2007; Gürkan et al. 2018). Moreover, the SF contribution
in the radio band with respect to the AGN activity is expected to increase
with galaxy mass (Aird et al., 2019). In fact the observed correlation
suggests that the radio production due to SF broadly increases with BH mass,
as the latter quantity is approximately a constant proportion of the galaxy
mass (from a third down to a fifth in the lowest $M_{\rm BH}\sim$105 M⊙,
Häring & Rix 2004; Reines & Volonteri 2015; Martín-Navarro & Mezcua 2018),
i.e. the stellar content: more stars likely produce more radio emission. This
is consistent with the idea that SF, although mostly included in the disc
(Bluck et al., 2020) and known to scale with galaxy mass (Speagle et al.,
2014), would possibly also scale with $M_{\rm BH}$. More precisely, the
nuclear starburst is plausibly set by the available gas mass present in the
NSC ($M_{\rm NSC}$, Fernández-Ontiveros et al. 2009; Neumayer et al. 2020),
which scales with the galaxy dynamical mass ($M_{\rm NSC}\propto
M_{dyn}^{0.55}$, Scott & Graham 2013), which in turn respond to the SMBH
gravitational well (Cen, 2015; Pitchford et al., 2016). Such a sequence of
links eventually enacts the radio-$M_{\rm BH}$ and radio-optical relations
observed for star-forming galaxies, e.g setting the fraction of radio emission
with respect to the photoionising energy from young stellar populations and SN
products.

Using the [O iii] as a SF indicator (Suzuki et al., 2016), the observed
optical luminosities of non-jetted Hii galaxies can be interpreted by a SFR up
to 101.1±0.5 M⊙ yr-1 in a nuclear starburst. The [O iii]-radio correlation
valid for non-jetted Hii galaxies also represents an empirical method to
predict the nuclear radio emission in star forming galaxies based on the
ubiquitous [O iii] line data. The best fit approximately agrees with the [O
iii]–radio relation estimated from Herschel, LOFAR and VLA data ($L_{\rm
1.4~{}GHz}$ = [0.83$\pm$0.10] $\log$ $L_{\rm[\text{O\,{iii}}]}$ \+
[7.9$\pm$2.0], Best et al. 2005a; Gürkan et al. 2015, 2018), although our
observations are at a higher resolution than any previous study on large
samples of star forming galaxies.

##  5 Reviewing the radio properties of local galaxies

###  5.1 The LeMMINGs view

The 1.5-GHz LeMMINGs survey has revealed pc-scale cores and jet-like
structures in more than a third of local optically active and inactive Palomar
galaxies (Papers I and II). Such nuclei are part of a large population of
radio LLAGN and faint nuclear starbursts ($\gtrsim$1017.6 W Hz-1). This result
adds observational evidence that a large fraction of LLAGN (even RQ AGN)
feature low-power galactic-scale jets (Webster et al., 2021), which may have a
tremendous impact on their hosts by continuously injecting energy, a
fundamental ingredient for galaxy feedback (Morganti, 2017; Jarvis et al.,
2019; Hardcastle & Croston, 2020; Smith et al., 2020b; Venturi et al., 2021;
Jarvis et al., 2021), as supported by the state-of-the-art jet simulations
(Massaglia et al., 2016; Mukherjee et al., 2018, 2020).

In this work we have investigated the nature of the pc-scale nuclear radio
components of LINERs, Seyferts, ALG and Hii galaxies. The emission-line [O
iii] luminosity, available for the entire sample, gives the optical nuclear
counterpart of the 1.5-GHz cores we detected. The optical–radio connection and
the optical FPBHA (Saikia et al., 2015) probe the different physical processes
involved at the centre of galaxies. In these diagnostic diagrams we have found
that optical classes follow distinct tracks: this is indicative of different
physical processes responsible for the radio emission and broadly agrees with
previous multi-band studies of LLAGN and star-forming galaxies (e.g. Körding
et al. 2006; Vitale et al. 2015; Tadhunter 2016; Mancuso et al. 2017; Smith et
al. 2020a). Nonetheless, we have set more robust constraints on these trends
with respect to previous studies and Paper I, especially in the thus far
poorly explored regime of low luminosities and BH masses, by leveraging the
unprecedented completeness and depth of the LeMMINGs survey.

.

LINERs are divided into two classes: RQ and RL. The RL LINERs ($\sim$19 per
cent of LINERs) appear to represent the scaled-down version of FR Is at lower
radio and [O iii] luminosities and BH masses down to $\sim$107.5 M⊙. Our
results indicate that the class of RL LINERs belong to a large homogeneous
population of RL LLAGN ($<$ 1042 erg s-1), characterized by a broad and
continuous distribution of parameters of relativistic jets (e.g. sizes,
luminosities, $\Gamma_{\rm jet}$), powered by a sub-Eddington, RIAF-like disc,
and hosted in ETGs (Heckman & Best, 2014). This picture, in turn, suggests
that a common jet-launching mechanism operates in all RL LINERs which smoothly
connects low-power (sub)kpc-scale jetted LINERs to more powerful compact RGs
(named FR 0s, Baldi et al. 2015b) and full-fledged FR Is and FR IIs (Kharb et
al., 2014; Mingo et al., 2019; Grandi et al., 2021). Conversely, RQ LINERs
consist of a more heterogeneous population of LLAGN, which can reside in
either LTGs or ETGs. An intermediate disc between low-$\dot{m}$ ADAF and
high-$\dot{m}$ SAD may be consistent with the observed characteristics of RQ
LINERs, where radio emission is due to a low-power non-relativistic
uncollimated jet (Gallimore et al., 2006).

Seyfert nuclei radiate at a larger fraction of Eddington luminosity than
LINERs. The common picture is that Seyferts are powered by a radiatively
efficient SAD with higher accretion rates (Eddington ratios $\gtrsim$ 10-3)
than seen in LINERs. Nevertheless, Seyferts are not radio-silent at all, and
can show compact or edge-brightened jetted morphologies. In order to reconcile
their radio and optical properties, different disc–jet models, intermediate
between jetted LINERs and the ‘radio-silent’ near-Eddington QSOs (Balick &
Heckman, 1982; Liu et al., 2020) have been proposed. Low-$\dot{m}$ Seyferts
are possibly the scaled-down version of the so-called red QSOs, which have
intermediate radio loudness and have been found to have a higher incidence of
compact and extended radio morphologies than blue QSOs (e.g. Klindt et al.
2019; Rosario et al. 2020), which instead are more similar to high-$\dot{m}$
Seyferts. We conclude that the change of disc–jet coupling from low-power
Seyferts to powerful QSOs and the predominance of a specific radio-emitting
physical process may depend on different factors (Garofalo & Bishop, 2020):
the jet efficiency with respect to the disc- or corona-wind radio production
decreases with Eddington ratio and increases with BH mass, ‘bulgeness’ of the
host (favouring ETGs), and SMBH/disc spin.

Apart from a few irregular galaxies, the vast majority of ALGs are hosted by
massive ETGs with $M_{\rm BH}$ $>$ 107 M⊙, which lack of significant optical
emission from the nucleus. They have been interpreted as part of a large
population of evolved massive galaxies (Salucci et al., 1999), which
occasionally or recurrently go through periods of LINER-like low-$\dot{m}$
activity, during which they launch pc-scale jets. However, during this low-
activity phenomenon, the optical line nucleus remains quiescent due to the
combination of a low ionising radiation field produced by the disc (and jet)
and the rarefaction of cold gas to photoionise (Capetti et al., 2005).

A dual population of Hii galaxies has been found in our sample. On one hand,
the majority of the Hii galaxies are hosted in LTGs with $M_{\rm
BH}\lesssim$106.5 M⊙ and their optical–radio properties reconcile with a SF
origin. A SF rate of $\sim$10 M⊙ yr-1 in the central region can account for
their compact cores, with SN-driven winds (Heckman et al., 2015) or extended
Hii regions possibly causing their complex radio structures. On the other
hand, $\sim$5 per cent of Hii galaxies exhibit jet-like radio structures.
These sources follow the diagnostic optical–radio sequence of AGN-classed
sources with $M_{\rm BH}$ $\gtrsim$106.5 M⊙. The co-existence of a LINER-like
sub-Eddington accreting SMBH and a nuclear starburst, which are responsible
for the radio/jet and the optical properties, respectively, is the simplest
way to solve their puzzling nature (Padovani, 2016).

###  5.2 Conclusions

The LeMMINGs survey characterises radio activity (either from SF or AGN) from
a complete sample of local galaxies, by reaching a 100 per cent detection rate
for galaxies with $M_{\rm BH}$ $>$ 107 M⊙ down to luminosities $L_{\rm core}>$
1019.8 W Hz-1. This limit represents the lowest luminosity for which galaxies
appear to host a radio-active SMBH in the local Universe. The fraction of
radio-active galaxies scales as $\propto$$M_{\rm BH}^{0.15}$, a relation that
is flatter than what has been found in previous radio surveys (e.g. Best et
al. 2005b), probably because of higher angular resolution and the inclusion of
RQ AGN.

One of the main results of our survey is the presence of a break at $M_{\rm
BH}\sim 10^{6.5}$ M⊙ moving from the SF to AGN regime with increasing BH mass.
Such a $M_{\rm BH}$ value roughly separates the star-forming galaxy and
(LL)AGN populations in the local Universe. At larger BH masses, mostly in
ETGs, a link between SMBH activity and jet production is well established (e.g
Cen 2012; Heckman & Best 2014). In contrast, in less-massive (late-type)
galaxies, SF makes a proportionally larger contribution to radio luminosity
causing a flattening of the relations valid for AGN at lower $M_{\rm BH}$.

For galaxies with small BH masses, $\lesssim$106.5 M⊙, thermal/non-thermal
emission from stellar processes in star forming galaxies is the most plausible
scenario of the origin of their radio emission. An unprecedented empirical
relation between their nuclear radio emission and BH masses, $L_{\rm
core}\propto M_{\rm BH}^{0.61}$, has been inferred in our sample (although
with large scatter). This relation between the nuclear SF and the SMBH was
found as a result of the e-MERLIN array, able to resolve out smooth, extended
emission, and reveal the radio emission at the nuclear scale, where the
central starburst is more likely to respond to the influence of the central
SMBH.

The steepening of the empirical correlations found for galaxies with BH masses
$\gtrsim$106.5 M⊙ ($L_{\rm core}\propto$$M_{\rm BH}^{1.5-1.65}$ and radio-AGN
fraction $\propto$$M_{\rm BH}^{0.15}$) with respect to those at lower BH
masses (valid for star-forming galaxies) strongly invoke an active SMBH as the
main driver of their radio emission. The link between radio activity, SMBH
properties, and local conditions (e.g. host type, gas availability) appears
more complicated than the standard BH–disc bimodality deduced from galaxy–SMBH
models (Heckman & Best, 2014), or direct analogies with XRBs states (Remillard
& McClintock, 2006; Fender et al., 2009): low-$\dot{m}$/jet vs
high-$\dot{m}$/no-jet. As a first approximation, the Eddington-scaled
accretion rates ($\dot{m}$) of the sample correspond to two extreme radio and
host categories. The most massive and bulged galaxies, which are the radio
loudest with the (optically) faintest nuclei (LINERs, ALGs, and jetted Hii
galaxies), are powered by sub-Eddington ($\dot{m}\lesssim 10^{-3}$) RIAF-like
discs and launch the most core-brightened jets. In contrast, LTGs can host
high-$\dot{m}$ ($\dot{m}\gtrsim 10^{-3}$) standard disc and occasionally
support sub-relativistic edge-brightened jets. As a second-order
approximation, a closer inspection of the data reveal that optical
classifications do not simply map the accretion states and this can further
complicate the comparison with XRBs. Therefore, to break the degeneracy
between radio-loudness, accretion modes and host types, distinct disc–jet
couplings (accretion/ejection states) that are observed among the various
optical–radio classes (RL/RQ, LINER/Seyfert, SF/AGN-dominated) are required.
The connection between disc and jet is probably determined by a combination of
several factors (some not directly observable at present), including BH spin,
magnetic field strength, accretion rotation, gas supply, small and large-scale
environment, and host location within the environment (e.g. distance from
cluster centre). These parameters play a significant role in setting the
generic disc configuration (e.g. accretion mode, rate and radiative
efficiency) and the radio production mechanism (e.g. jet, outflow, wind) for
each optical/radio class. Variation of these factors could favour the increase
of the jet production efficiency and/or jet bulk speed (Lagos et al., 2009).
This picture would account for the continuous, rather than dichotomous, radio
properties observed in LLAGN which are characterised by a broad distribution
of sizes and luminosities of their extended radio emission, from weak RQ LINER
(even ALG) to RGs and from jetted low-power Seyferts to extremely-RQ
high-$\dot{m}$ QSOs (Brown et al., 2011; Kharb et al., 2014; Garofalo et al.,
2014; Baldi et al., 2019a; Garofalo & Singh, 2019). A time-dependent evolution
among different radio/optical states would add a further level of complexity
to this picture, probably in analogy to XRB intermediate states (Fernández-
Ontiveros & Muñoz-Darias, 2021). An exhaustive comparison between LLAGN and
XRBs will be addressed in a future work by using X-day data.

A complete census of the local SMBH population, offered by the forthcoming
deep follow-up 5-GHz e-MERLIN observations along with complete Chandra X-ray
and HST optical data, pushing to the rather unexplored regime of very low
luminosities, $\sim$1016 W Hz-1 (comparable to Sgr A*), will allow an unbiased
view of the multi-band SMBH activity of the local Universe and provide even
more robust constraints on disc–jet coupling in LLAGN.

## Acknowledgements

We thank the referee for her/his comments, which helped to improve the paper.
This research was supported by a Newton Fund project, DARA (Development in
Africa with Radio Astronomy), and awarded by the UK’s Science and Technology
Facilities Council (STFC) - grant reference ST/R001103/1. This research was
supported by European Commission Horizon 2020 Research and Innovation
Programme under grant agreement No. 730884 (JUMPING JIVE). FS acknowledges
support from a Leverhulme Trust Research Fellowship. J.H.K. acknowledges
support from the European Union’s Horizon 2020 research and innovation
programme under Marie Skłodowska-Curie grant agreement No 721463 to the
SUNDIAL ITN network, from the State Research Agency (AEI) of the Spanish
Ministry of Science and Innovation and the European Regional Development Fund
(FEDER) under the grant with reference PID2019-105602GB-I00, and from IAC
project P/300724, financed by the Ministry of Science and Innovation, through
the State Budget and by the Canary Islands Department of Economy, Knowledge
and Employment, through the Regional Budget of the Autonomous Community. IMV
thanks the Generalitat Valenciana (funding from the GenT Project
CIDEGENT/2018/021) and the MICINN (funding from the Research Project
PID2019-108995GB-C22). AA and MAPT acknowledge support from the Spanish MCIU
through grant PGC2018-098915-B-C21 and from the State Agency for Research of
the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the
Instituto de Astrofìsica de Andalucìa (SEV-2017-0709). B.T.D. acknowledges
financial support from grant “Ayudas para la realización de proyectos de I+D
para jóvenes doctores 2019.” funded by Comunidad de Madrid and Universidad
Complutense de Madrid under grant No. PR65/19-22417.’

## DATA AVAILABILITY

The data on which this paper is based are publicly available from the e-MERLIN
archive. Calibrated image products are available upon reasonable request to
the corresponding author. These, along with other LeMMINGs advanced survey
products, will be publicly hosted on upcoming project web-page which is being
developed (http://lemmingslegacy.pbworks.com).

## References

  * Abazajian et al. (2009) Abazajian K. N., et al., 2009, ApJS, 182, 543
  * Aird et al. (2019) Aird J., Coil A. L., Georgakakis A., 2019, MNRAS, 484, 4360
  * Akritas (1989) Akritas M., 1989, Aligned Rank Tests for Regression With Censored Data. Penn State Dept. of Statistics Technical Report, 1989
  * Akritas & Siebert (1996) Akritas M. G., Siebert J., 1996, MNRAS, 278, 919
  * Alexander et al. (2003) Alexander D. M., et al., 2003, AJ, 126, 539
  * Allen et al. (2006) Allen S. W., Dunn R. J. H., Fabian A. C., Taylor G. B., Reynolds C. S., 2006, MNRAS, 372, 21
  * Allen et al. (2008) Allen M. G., Groves B. A., Dopita M. A., Sutherland R. S., Kewley L. J., 2008, ApJS, 178, 20
  * Aller & Richstone (2002) Aller M. C., Richstone D., 2002, AJ, 124, 3035
  * Baldi & Capetti (2010) Baldi R. D., Capetti A., 2010, A&A, 519, A48
  * Baldi et al. (2015a) Baldi R. D., Behar E., Laor A., Horesh A., 2015a, MNRAS, 454, 4277
  * Baldi et al. (2015b) Baldi R. D., Capetti A., Giovannini G., 2015b, A&A, 576, A38
  * Baldi et al. (2018) Baldi R. D., et al., 2018, MNRAS, 476, 3478
  * Baldi et al. (2019a) Baldi R. D., Torresi E., Migliori G., Balmaverde B., 2019a, Galaxies, 7, 76
  * Baldi et al. (2019b) Baldi R. D., Rodríguez Zaurín J., Chiaberge M., Capetti A., Sparks W. B., McHardy I. M., 2019b, ApJ, 870, 53
  * Baldi et al. (2021) Baldi R. D., et al., 2021, MNRAS, 500, 4749
  * Baldwin et al. (1981) Baldwin J. A., Phillips M. M., Terlevich R., 1981, PASP, 93, 5
  * Balick & Heckman (1982) Balick B., Heckman T. M., 1982, ARA&A, 20, 431
  * Balmaverde & Capetti (2006) Balmaverde B., Capetti A., 2006, A&A, 447, 97
  * Balmaverde et al. (2006) Balmaverde B., Capetti A., Grandi P., 2006, A&A, 451, 35
  * Balmaverde et al. (2008) Balmaverde B., Baldi R. D., Capetti A., 2008, A&A, 486, 119
  * Barausse et al. (2017) Barausse E., Shankar F., Bernardi M., Dubois Y., Sheth R. K., 2017, MNRAS, 468, 4782
  * Begelman (2012) Begelman M. C., 2012, MNRAS, 420, 2912
  * Behar et al. (2020) Behar E., et al., 2020, MNRAS, 491, 3523
  * Behroozi et al. (2019) Behroozi P., Wechsler R. H., Hearin A. P., Conroy C., 2019, MNRAS, 488, 3143
  * Bell et al. (2011) Bell M. E., et al., 2011, MNRAS, 411, 402
  * Bennett (1962) Bennett A. S., 1962, Mem. RAS, 68, 163
  * Bernardi et al. (2003) Bernardi M., et al., 2003, AJ, 125, 1849
  * Best & Heckman (2012) Best P. N., Heckman T. M., 2012, MNRAS, 421, 1569
  * Best et al. (2005a) Best P. N., Kauffmann G., Heckman T. M., Ivezić Ž., 2005a, MNRAS, 362, 9
  * Best et al. (2005b) Best P. N., Kauffmann G., Heckman T. M., Brinchmann J., Charlot S., Ivezić Ž., White S. D. M., 2005b, MNRAS, 362, 25
  * Beswick et al. (2014) Beswick R., Argo M. K., Evans R., McHardy I., Williams D. R. A., Westcott J., 2014, in Proceedings of the 12th European VLBI Network Symposium and Users Meeting (EVN 2014). 7-10 October 2014. Cagliari, Italy. p. 10
  * Binette et al. (1994) Binette L., Magris C. G., Stasińska G., Bruzual A. G., 1994, A&A, 292, 13
  * Bisogni et al. (2017) Bisogni S., Marconi A., Risaliti G., 2017, MNRAS, 464, 385
  * 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
  * Bluck et al. (2020) Bluck A. F. L., et al., 2020, MNRAS, 499, 230
  * Bonchi et al. (2013) Bonchi A., La Franca F., Melini G., Bongiorno A., Fiore F., 2013, MNRAS, 429, 1970
  * Bonzini et al. (2013) Bonzini M., Padovani P., Mainieri V., Kellermann K. I., Miller N., Rosati P., Tozzi P., Vattakunnel S., 2013, MNRAS, 436, 3759
  * Brinchmann et al. (2004) Brinchmann J., Charlot S., White S. D. M., Tremonti C., Kauffmann G., Heckman T., Brinkmann J., 2004, MNRAS, 351, 1151
  * Brown et al. (2011) Brown M. J. I., Jannuzi B. T., Floyd D. J. E., Mould J. R., 2011, ApJ, 731, L41
  * Bundy et al. (2015) Bundy K., et al., 2015, ApJ, 798, 7
  * Buttiglione et al. (2009) Buttiglione S., Capetti A., Celotti A., Axon D. J., Chiaberge M., Macchetto F. D., Sparks W. B., 2009, A&A, 495, 1033
  * Buttiglione et al. (2010) Buttiglione S., Capetti A., Celotti A., Axon D. J., Chiaberge M., Macchetto F. D., Sparks W. B., 2010, A&A, 509, A6
  * Cao (2007) Cao X., 2007, ApJ, 659, 950
  * Capetti (2011) Capetti A., 2011, A&A, 535, A28
  * Capetti & Baldi (2011) Capetti A., Baldi R. D., 2011, A&A, 529, A126
  * Capetti & Balmaverde (2006) Capetti A., Balmaverde B., 2006, A&A, 453, 27
  * Capetti & Balmaverde (2007) Capetti A., Balmaverde B., 2007, A&A, 469, 75
  * Capetti et al. (2005) Capetti A., Verdoes Kleijn G. A., Chiaberge M., 2005, A&A, 439, 935
  * Capetti et al. (2013) Capetti A., Robinson A., Baldi R. D., Buttiglione S., Axon D. J., Celotti A., Chiaberge M., 2013, A&A, 551, A55
  * Capetti et al. (2017) Capetti A., Massaro F., Baldi R. D., 2017, A&A, 598, A49
  * Cappi et al. (2006) Cappi M., et al., 2006, A&A, 446, 459
  * Cattaneo & Best (2009) Cattaneo A., Best P. N., 2009, MNRAS, 395, 518
  * Cen (2012) Cen R., 2012, ApJ, 755, 28
  * Cen (2015) Cen R., 2015, ApJ, 805, L9
  * 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
  * Chen et al. (1989) Chen K., Halpern J. P., Filippenko A. V., 1989, ApJ, 339, 742
  * Chen et al. (2021) Chen Y., et al., 2021, ApJ, 913, 93
  * Chiaberge & Marconi (2011) Chiaberge M., Marconi A., 2011, MNRAS, 416, 917
  * Chiaberge et al. (1999) Chiaberge M., Capetti A., Celotti A., 1999, A&A, 349, 77
  * Chiaberge et al. (2005) Chiaberge M., Capetti A., Macchetto F. D., 2005, ApJ, 625, 716
  * Cirasuolo et al. (2003) Cirasuolo M., Magliocchetti M., Celotti A., Danese L., 2003, MNRAS, 341, 993
  * Condon (1992) Condon J. J., 1992, ARA&A, 30, 575
  * Coriat et al. (2011) Coriat M., et al., 2011, MNRAS, 414, 677
  * Czerny et al. (2009) Czerny B., Siemiginowska A., Janiuk A., Nikiel-Wroczyński B., Stawarz Ł., 2009, ApJ, 698, 840
  * Davis & Tchekhovskoy (2020) Davis S. W., Tchekhovskoy A., 2020, ARA&A, 58, 407
  * Davis et al. (2014) Davis B. L., et al., 2014, ApJ, 789, 124
  * Decarli et al. (2007) Decarli R., Gavazzi G., Arosio I., Cortese L., Boselli A., Bonfanti C., Colpi M., 2007, MNRAS, 381, 136
  * Dickson et al. (1995) Dickson R., Tadhunter C., Shaw M., Clark N., Morganti R., 1995, MNRAS, 273, L29
  * Donea & Biermann (2002) Donea A.-C., Biermann P. L., 2002, Publ. Astron. Soc. Australia, 19, 125
  * Dopita et al. (1997) Dopita M. A., Koratkar A. P., Allen M. G., Tsvetanov Z. I., Ford H. C., Bicknell G. V., Sutherland R. S., 1997, ApJ, 490, 202
  * Drappeau et al. (2017) Drappeau S., et al., 2017, MNRAS, 466, 4272
  * Dugan et al. (2014) Dugan Z., Bryan S., Gaibler V., Silk J., Haas M., 2014, ApJ, 796, 113
  * Dullo et al. (2020) Dullo B. T., Bouquin A. Y. K., Gil de Paz A., Knapen J. H., Gorgas J., 2020, ApJ, 898, 83
  * Dunn & Fabian (2006) Dunn R. J. H., Fabian A. C., 2006, MNRAS, 373, 959
  * Esin et al. (1997) Esin A. A., McClintock J. E., Narayan R., 1997, ApJ, 489, 865
  * Esparza-Arredondo et al. (2020) Esparza-Arredondo D., Osorio-Clavijo N., González-Martín O., Victoria-Ceballos C., Haro-Corzo S. A. R., Reyes-Amador O. U., López-Sánchez J., Pasetto A., 2020, ApJ, 905, 29
  * Fabian (2012) Fabian A. C., 2012, ARA&A, 50, 455
  * Fabian & Canizares (1988) Fabian A. C., Canizares C. R., 1988, Nature, 333, 829
  * Falcke et al. (2000) Falcke H., Nagar N. M., Wilson A. S., Ulvestad J. S., 2000, ApJ, 542, 197
  * Falcke et al. (2001) Falcke H., Nagar N. M., Wilson A. S., Ho L. C., Ulvestad J. S., 2001, in Kaper L., Heuvel E. P. J. V. D., Woudt P. A., eds, Black Holes in Binaries and Galactic Nuclei. Springer-Verlag, p. 218, doi:10.1007/10720995_45
  * Falcke et al. (2004) Falcke H., Körding E., Markoff S., 2004, A&A, 414, 895
  * Fanaroff & Riley (1974) Fanaroff B. L., Riley J. M., 1974, MNRAS, 167, 31P
  * Fanti et al. (1987) Fanti C., Fanti R., de Ruiter H. R., Parma P., 1987, A&AS, 69, 57
  * Faucher-Giguère & Quataert (2012) Faucher-Giguère C.-A., Quataert E., 2012, MNRAS, 425, 605
  * Feigelson & Nelson (1985) Feigelson E. D., Nelson P. I., 1985, ApJ, 293, 192
  * Fender (2001) Fender R. P., 2001, MNRAS, 322, 31
  * Fender et al. (2003) Fender R. P., Gallo E., Jonker P. G., 2003, MNRAS, 343, L99
  * Fender et al. (2004) Fender R. P., Belloni T. M., Gallo E., 2004, MNRAS, 355, 1105
  * Fender et al. (2009) Fender R. P., Homan J., Belloni T. M., 2009, MNRAS, 396, 1370
  * Fernández-Ontiveros & Muñoz-Darias (2021) Fernández-Ontiveros J. A., Muñoz-Darias T., 2021, MNRAS, 504, 5726
  * Fernández-Ontiveros et al. (2009) Fernández-Ontiveros J. A., Prieto M. A., Acosta-Pulido J. A., 2009, MNRAS, 392, L16
  * Ferreira (1997) Ferreira J., 1997, A&A, 319, 340
  * Ferreira et al. (2010) Ferreira J., Petrucci P. O., Murphy G., Zanni C., Henri G., 2010, Jet Emitting Discs: a New Accretion Flow Solution. p. 49
  * Filho et al. (2006) Filho M. E., Barthel P. D., Ho L. C., 2006, A&A, 451, 71
  * Fischer et al. (2021) Fischer T. C., et al., 2021, ApJ, 906, 88
  * Flohic et al. (2006) Flohic H. M. L. G., Eracleous M., Chartas G., Shields J. C., Moran E. C., 2006, ApJ, 647, 140
  * Forman et al. (1985) Forman W., Jones C., Tucker W., 1985, ApJ, 293, 102
  * Gaibler et al. (2012) Gaibler V., Khochfar S., Krause M., Silk J., 2012, MNRAS, 425, 438
  * Gallimore et al. (2006) Gallimore J. F., Axon D. J., O’Dea C. P., Baum S. A., Pedlar A., 2006, AJ, 132, 546
  * Gallo & Sesana (2019) Gallo E., Sesana A., 2019, ApJ, 883, L18
  * Gallo et al. (2008) Gallo E., Treu T., Jacob J., Woo J.-H., Marshall P. J., Antonucci R., 2008, ApJ, 680, 154
  * Garofalo & Bishop (2020) Garofalo D., Bishop K., 2020, PASP, 132, 114103
  * Garofalo & Singh (2019) Garofalo D., Singh C. B., 2019, ApJ, 871, 259
  * Garofalo et al. (2010) Garofalo D., Evans D. A., Sambruna R. M., 2010, MNRAS, 406, 975
  * Garofalo et al. (2014) Garofalo D., Kim M. I., Christian D. J., 2014, MNRAS, 442, 3097
  * Gebhardt et al. (2000) Gebhardt K., et al., 2000, ApJL, 539, L13
  * Giannios & Metzger (2011) Giannios D., Metzger B. D., 2011, MNRAS, 416, 2102
  * Giovannini (2003) Giovannini G., 2003, New Astron. Rev., 47, 551
  * Giovannini (2004) Giovannini G., 2004, Ap&SS, 293, 1
  * Giovannini et al. (2005) Giovannini G., Taylor G. B., Feretti L., Cotton W. D., Lara L., Venturi T., 2005, ApJ, 618, 635
  * Giroletti & Panessa (2009) Giroletti M., Panessa F., 2009, ApJ, 706, L260
  * González-Martín et al. (2006) González-Martín O., Masegosa J., Márquez I., Guerrero M. A., Dultzin-Hacyan D., 2006, A&A, 460, 45
  * Grandi et al. (2021) Grandi P., Torresi E., Macconi D., Boccardi B., Capetti A., 2021, ApJ, 911, 17
  * Greene (2012) Greene J. E., 2012, Nature Communications, 3, 1304
  * Greene & Ho (2007) Greene J. E., Ho L. C., 2007, ApJ, 667, 131
  * Greene et al. (2020) Greene J. E., Strader J., Ho L. C., 2020, ARA&A, 58, 257
  * Gültekin et al. (2019) Gültekin K., King A. L., Cackett E. M., Nyland K., Miller J. M., Di Matteo T., Markoff S., Rupen M. P., 2019, ApJ, 871, 80
  * Gürkan et al. (2015) Gürkan G., et al., 2015, MNRAS, 452, 3776
  * Gürkan et al. (2018) Gürkan G., et al., 2018, MNRAS, 475, 3010
  * Hardcastle (2018) Hardcastle M., 2018, Nature Astronomy, 2, 273
  * Hardcastle & Croston (2020) Hardcastle M., Croston J., 2020, New Astronomy Reviews, 88, 101539
  * Hardcastle et al. (2019) Hardcastle M. J., et al., 2019, A&A, 622, A12
  * Häring & Rix (2004) Häring N., Rix H.-W., 2004, ApJ, 604, L89
  * Heckman (1980) Heckman T. M., 1980, A&A, 500, 187
  * Heckman & Best (2014) Heckman T. M., Best P. N., 2014, ARA&A, 52, 589
  * Heckman et al. (1993) Heckman T. M., Lehnert M. D., Armus L., 1993, in Shull J. M., Thronson H. A., eds, Astrophysics and Space Science Library Vol. 188, The Environment and Evolution of Galaxies. p. 455, doi:10.1007/978-94-011-1882-8_25
  * Heckman et al. (2004) Heckman T. M., Kauffmann G., Brinchmann J., Charlot S., Tremonti C., White S. D. M., 2004, ApJ, 613, 109
  * Heckman et al. (2015) Heckman T. M., Alexandroff R. M., Borthakur S., Overzier R., Leitherer C., 2015, ApJ, 809, 147
  * Heinz & Sunyaev (2003) Heinz S., Sunyaev R. A., 2003, MNRAS, 343, L59
  * Heinz et al. (2007) Heinz S., Merloni A., Schwab J., 2007, ApJ, 658, L9
  * Herpich et al. (2018) Herpich F., Stasińska G., Mateus A., Vale Asari N., Cid Fernandes R., 2018, MNRAS, 481, 1774
  * Heywood et al. (2019) Heywood I., et al., 2019, Nature, 573, 235
  * Ho (1999) Ho L. C., 1999, ApJ, 516, 672
  * Ho (2002) Ho L. C., 2002, ApJ, 564, 120
  * Ho (2008) Ho L. C., 2008, ARA&A, 46, 475
  * Ho & Ulvestad (2001) Ho L. C., Ulvestad J. S., 2001, ApJS, 133, 77
  * Ho et al. (1995) Ho L. C., Filippenko A. V., Sargent W. L., 1995, ApJS, 98, 477
  * Ho et al. (1997a) Ho L. C., Filippenko A. V., Sargent W. L. W., 1997a, ApJS, 112, 315
  * Ho et al. (1997b) Ho L. C., Filippenko A. V., Sargent W. L. W., 1997b, ApJ, 487, 568
  * Ho et al. (2009) Ho L. C., Greene J. E., Filippenko A. V., Sargent W. L. W., 2009, ApJS, 183, 1
  * Huchra & Burg (1992) Huchra J., Burg R., 1992, ApJ, 393, 90
  * Inayoshi et al. (2020) Inayoshi K., Ichikawa K., Ho L. C., 2020, ApJ, 894, 141
  * Ishibashi et al. (2014) Ishibashi W., Auger M. W., Zhang D., Fabian A. C., 2014, MNRAS, 443, 1339
  * Janssen et al. (2012) Janssen R. M. J., Röttgering H. J. A., Best P. N., Brinchmann J., 2012, A&A, 541, A62
  * Jarvis et al. (2019) Jarvis M. E., et al., 2019, MNRAS, 485, 2710
  * Jarvis et al. (2021) Jarvis M. E., et al., 2021, MNRAS, 503, 1780
  * Jiang et al. (2007) Jiang L., Fan X., Ivezić Ž., Richards G. T., Schneider D. P., Strauss M. A., Kelly B. C., 2007, ApJ, 656, 680
  * Kauffmann et al. (2003) Kauffmann G., et al., 2003, MNRAS, 346, 1055
  * Kauffmann et al. (2008) Kauffmann G., Heckman T. M., Best P. N., 2008, MNRAS, 384, 953
  * Kellermann et al. (1989) Kellermann K. I., Sramek R., Schmidt M., Shaffer D. B., Green R., 1989, AJ, 98, 1195
  * Kelly & Merloni (2012) Kelly B. C., Merloni A., 2012, Advances in Astronomy, 2012, 970858
  * Kendall (1938) Kendall M., 1938, Biometrika, 30, 81
  * Kennicutt (1998) Kennicutt Jr. R. C., 1998, ARA&A, 36, 189
  * Kewley et al. (2006) Kewley L. J., Groves B., Kauffmann G., Heckman T., 2006, MNRAS, 372, 961
  * Kewley et al. (2019) Kewley L. J., Nicholls D. C., Sutherland R. S., 2019, ARA&A, 57, 511
  * Kharb et al. (2006) Kharb P., O’Dea C. P., Baum S. A., Colbert E. J. M., Xu C., 2006, ApJ, 652, 177
  * Kharb et al. (2012) Kharb P., et al., 2012, AJ, 143, 78
  * Kharb et al. (2014) Kharb P., O’Dea C. P., Baum S. A., Hardcastle M. J., Dicken D., Croston J. H., Mingo B., Noel-Storr J., 2014, MNRAS, 440, 2976
  * Kharb et al. (2017) Kharb P., Subramanian S., Vaddi S., Das M., Paragi Z., 2017, ApJ, 846, 12
  * King et al. (2011) King A. L., et al., 2011, ApJ, 729, 19
  * Klindt et al. (2019) Klindt L., Alexander D. M., Rosario D. J., Lusso E., Fotopoulou S., 2019, MNRAS, 488, 3109
  * Körding et al. (2006) Körding E. G., Fender R. P., Migliari S., 2006, MNRAS, 369, 1451
  * Körding et al. (2008) Körding E. G., Jester S., Fender R., 2008, MNRAS, 383, 277
  * Kormendy & Ho (2001) Kormendy J., Ho L., 2001, Supermassive Black Holes in Inactive Galaxies, doi:10.1888/0333750888/2635.
  * Kozieł-Wierzbowska et al. (2017) Kozieł-Wierzbowska D., Stasińska G., Vale Asari N., Sikora M., Goettems E., Wójtowicz A., 2017, Frontiers in Astronomy and Space Sciences, 4, 39
  * Kukula et al. (1993) Kukula M. J., Ghosh T., Pedlar A., Schilizzi R. T., Miley G. K., de Bruyn A. G., Saikia D. J., 1993, MNRAS, 264, 893
  * Kukula et al. (1995) Kukula M. J., Pedlar A., Baum S. A., O’Dea C. P., 1995, MNRAS, 276, 1262
  * Kukula et al. (1999) Kukula M. J., Ghosh T., Pedlar A., Schilizzi R. T., 1999, ApJ, 518, 117
  * Lagos et al. (2009) Lagos C. D. P., Padilla N. D., Cora S. A., 2009, MNRAS, 395, 625
  * Lamastra et al. (2009) Lamastra A., Bianchi S., Matt G., Perola G. C., Barcons X., Carrera F. J., 2009, A&A, 504, 73
  * 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
  * Lapi et al. (2011) Lapi A., et al., 2011, ApJ, 742, 24
  * Lavalley et al. (1992) Lavalley M., Isobe T., Feigelson E., 1992, ASURV: Astronomy Survival Analysis Package. Astronomical Society of the Pacific Conference Series, p. 245
  * Liu et al. (2020) Liu X., Chang N., Han Z., Wang X., 2020, Universe, 6, 68
  * Maccarone (2003) Maccarone T. J., 2003, A&A, 409, 697
  * Macfarlane et al. (2021) Macfarlane C., et al., 2021, MNRAS, 506, 5888
  * Magorrian et al. (1998) Magorrian J., et al., 1998, AJ, 115, 2285
  * Mancuso et al. (2017) Mancuso C., et al., 2017, ApJ, 842, 95
  * Maoz (2007) Maoz D., 2007, MNRAS, 377, 1696
  * Marconi et al. (2004) Marconi A., Risaliti G., Gilli R., Hunt L. K., Maiolino R., Salvati M., 2004, MNRAS, 351, 169
  * Markoff et al. (2003) Markoff S., Nowak M., Corbel S., Fender R., Falcke H., 2003, New Astron. Rev., 47, 491
  * Markoff et al. (2005) Markoff S., Nowak M. A., Wilms J., 2005, ApJ, 635, 1203
  * Markowitz et al. (2003) Markowitz A., et al., 2003, ApJ, 593, 96
  * Martín-Navarro & Mezcua (2018) Martín-Navarro I., Mezcua M., 2018, ApJ, 855, L20
  * Mascoop et al. (2021) Mascoop J. L., Anderson L. D., Wenger T. V., Makai Z., Armentrout W. P., Balser D. S., Bania T. M., 2021, ApJ, 910, 159
  * Massaglia et al. (2016) Massaglia S., Bodo G., Rossi P., Capetti S., Mignone A., 2016, A&A, 596, A12
  * Mattila et al. (2018) Mattila S., et al., 2018, Science, 361, 482
  * Mauch & Sadler (2007) Mauch T., Sadler E. M., 2007, MNRAS, 375, 931
  * McKinney et al. (2012) McKinney J. C., Tchekhovskoy A., Blandford R. D., 2012, MNRAS, 423, 3083
  * Meert et al. (2015) Meert A., Vikram V., Bernardi M., 2015, MNRAS, 446, 3943