# MIGHTEE: the nature of the radio-loud AGN population

I. H. Whittam,1,2 M. J. Jarvis,1,2 C. L. Hale,3 M. Prescott,2,4 L. K.
Morabito,5,6 I. Heywood,1,7 N. J. Adams,8 J. Afonso,9,10 Fangxia An,4 Y.
Ao,11,12 R. A. Bowler,8 J. D. Collier,13,14,15 R. P. Deane,16,17 J.
Delhaize,18 B. Frank,19,13,18 M. Glowacki,20,4 P. W. Hatfield,1 N. Maddox,21
L. Marchetti,18,22 A. M. Matthews,23 I. Prandoni,22 S.
Randriamampandry,24,25,26 Z. Randriamanakoto,24,26 D. J. B. Smith,27 A. R.
Taylor,18,13,2 N. L. Thomas,5,6 and M. Vaccari4,13,22
1Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road,
Oxford, OX1 3RH, UK
2 Department of Physics and Astronomy, University of the Western Cape, Robert
Sobukwe Road, Bellville 7535, South Africa
3 School of Physics and Astronomy, Institute for Astronomy, University of
Edinburgh, Royal Observatory, Blackford Hill, EH9 3HJ Edinburgh, UK
4 Inter-University Institute for Data Astronomy, University of the Western
Cape, Robert Sobukwe Road, 7535 Bellville, South Africa
5 Centre for Extragalactic Astronomy, Department of Physics, Durham
University, Durham, DH1 3LE, UK
6 Institute for Computational Cosmology, Department of Physics, Durham
University, Durham, DH1 3LE, UK
7Department of Physics and Electronics, Rhodes University, PO Box 94,
Grahamstown, 6140, South Africa
8 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,
Manchester, UK
9Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, OAL,
Tapada da Ajuda, PT1349-018 Lisboa, Portugal
10Departamento de Física, Faculdade de Ciências, Universidade de Lisboa,
Edifício C8, Campo Grande, PT1749-016 Lisbon, Portugal
11 Purple Mountain Observatory and Key Laboratory for Radio Astronomy, Chinese
Academy of Sciences, Nanjing, China
12 School of Astronomy and Space Science, University of Science and Technology
of China, Hefei, China
13 The Inter-University Institute for Data Intensive Astronomy, Department of
Astronomy, University of Cape Town, Private Bag X3, Rondebosch, 7701, South
Africa
14 School of Science, Western Sydney University, Locked Bag 1797, Penrith, NSW
2751, Australia
15 CSIRO Astronomy and Space Science, PO Box 1130, Bentley, WA, 6102,
Australia
16 Wits Centre for Astrophysics, School of Physics, University of the
Witwatersrand, 1 Jan Smuts Avenue, 2000, Johannesburg, South Africa
17Department of Physics, University of Pretoria, Hatfield, Pretoria, 0028,
South Africa
18 Department of Astronomy, University of Cape Town, Private Bag X3,
Rondebosch 7701, South Africa
19 South African Radio Astronomy Observatory, 2 Fir Street, Observatory, 7925,
South Africa
20 International Centre for Radio Astronomy Research, Curtin University,
Bentley, WA 6102, Australia
21 University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität,
Scheinerstr. 1, 81679 Munich, Germany
22 INAF - Istituto di Radioastronomia, via Gobetti 101, 40129 Bologna, Italy
23 The Observatories of the Carnegie Institution for Science, 813 Santa
Barbara Street, Pasadena, CA 91101, USA
24 South African Astronomical Observatory, P.O. Box 9, Observatory 7935, South
Africa
25 Southern African Large Telescope, P.O. Box 9, Observatory 7935, Cape Town,
South Africa
26 Department of Physics, University of Antananarivo, P.O. Box 906,
Antananarivo, Madagascar
27 Centre for Astrophysics Research, University of Hertfordshire, College
Lane, Hatfield, AL10 9AB, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We study the nature of the faint radio source population detected in the
MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) Early
Science data in the COSMOS field, focusing on the properties of the radio-loud
active galactic nuclei (AGN). Using the extensive multi-wavelength data
available in the field, we are able to classify 88 per cent of the 5223 radio
sources in the field with host galaxy identifications as AGN (35 per cent) or
star-forming galaxies (54 per cent). We select a sample of radio-loud AGN with
redshifts out to $z\sim 6$ and radio luminosities
$10^{20}<\textrm{L}_{1.4~{}\textrm{GHz}}/\textrm{W Hz}^{-1}<10^{27}$ and
classify them as high-excitation and low-excitation radio galaxies (HERGs and
LERGs). The classification catalogue is released with this work. We find no
significant difference in the host galaxy properties of the HERGs and LERGs in
our sample. In contrast to previous work, we find that the HERGs and LERGs
have very similar Eddington-scaled accretion rates; in particular we identify
a population of very slowly accreting AGN that are formally classified as
HERGs at these low radio luminosities, where separating into HERGs and LERGs
possibly becomes redundant. We investigate how black hole mass affects jet
power, and find that a black hole mass $\gtrsim 10^{7.8}~{}\textrm{M}_{\odot}$
is required to power a jet with mechanical power greater than the radiative
luminosity of the AGN ($L_{\textrm{mech}}/L_{\textrm{bol}}>1$). We discuss
that both a high black hole mass and black hole spin may be necessary to
launch and sustain a dominant radio jet.

###### keywords:

surveys – catalogues – Galaxies – galaxies: active – radio continuum: galaxies

††pubyear: 2022††pagerange: MIGHTEE: the nature of the radio-loud AGN
population–B

##  1 Introduction

Radio-loud Active Galactic Nuclei (RLAGN) are thought to play an important
role in galaxy evolution, regulating star-formation in massive galaxies.
Accretion of matter onto the supermassive black hole (SMBH) at the centre of
the galaxy can power relativistic jets (highly collimated beams of plasma)
which produce synchrotron emission visible with radio telescopes. RLAGN have
been widely studied over several decades, and they display a range of
different properties, with linear sizes ranging from pc to several Mpc and
radio powers spanning many orders of magnitude from $\sim 10^{19}$ W/Hz up to
$\sim 10^{29}$ W/Hz at 1.4 GHz (see reviews by de Zotti et al. 2010; Heckman &
Best 2014; Hardcastle & Croston 2020).

There is mounting evidence that there are two fundamentally different classes
of radio-loud AGN; one class which display the typical signatures of efficient
accretion such as an accretion disk and a dusty torus, and a second class
which appear to be lacking these structures and emit most of their energy as a
powerful radio jet (e.g. Laing et al. 1994; Merloni & Heinz 2007; Hardcastle,
Evans, & Croston 2009). The first class are referred to as high-excitation
radio galaxies (HERGs, due to the high-excitation lines visible in their
optical spectra), cold-mode sources, quasar mode or radiatively efficient
sources. The second class are called low-excitation radio galaxies (LERGs),
hot mode sources, radio mode sources, or radiatively inefficient sources.

In studies conducted to date, LERGs tend to be hosted by massive galaxies,
often at the centre of a group or cluster (Burns, 1990; Best et al., 2007),
which mostly contain older stars (e.g. Smolčić 2009; Herbert et al. 2010).
HERGs, however, are more likely to be found in less massive galaxies with a
younger stellar population (Best & Heckman, 2012). There is evidence that
HERGs show rapid cosmological evolution in their space density, while LERGs
show little or no evolution out to $z\sim 1$ (Clewley & Jarvis, 2004; Best et
al., 2014; Pracy et al., 2016; Prescott et al., 2016) and may display strong
negative evolution at higher redshifts (Williams et al., 2018).

Initially, it was believed that there was a direct link between the HERG and
LERG classes and the Fanaroff and Riley morphological classifications (FRI and
II classes, Fanaroff & Riley 1974), with most HERGs displaying edge-brightened
FRII morphologies and most LERGs appearing as centre-brightened FRI sources
(e.g. Jackson & Rawlings 1997). However, the existence of FRI HERGs (Blundell
& Rawlings, 2001) and FRII LERGs (e.g. Hine & Longair 1979; Willott et al.
1999; Croston, Ineson, & Hardcastle 2018 ) contradicts this scenario, and work
by Gendre et al. (2013) and Mingo et al. (2022) shows that the link between
accretion mode and morphology is very indirect. There is also evidence that
HERGs seem to be more dominated by radio emission from their cores than LERGs
(Whittam et al., 2016).

It had been proposed that there is a direct relationship between the accretion
mode and the source of fuel available, with HERGs accreting efficiently from
sources of cold gas, while LERGs accrete inefficiently from the hot gas halo
(Hardcastle, Evans, & Croston, 2007). More recent work, however, has argued
that Eddington-scaled accretion rate is the key driver of the difference
between HERGs and LERGs, rather than the source of the material being accreted
(e.g. Best & Heckman 2012; Best et al. 2014; Hardcastle 2018; Hardcastle &
Croston 2020). It is therefore important that we fully understand the
Eddington-scaled accretion rates of different AGN classes as we probe lower
radio powers and higher redshifts.

In the scenario building up in the literature, there has been thought to be a
dichotomy in accretion rates between the HERG and LERG classes; HERGs accrete
efficiently at $\gtrsim 1$ per cent of their Eddington accretion rate, while
LERGs accrete much more slowly at $\lesssim 1$ per cent of Eddington, with
almost no overlap in the accretion rates of the two classes (Best & Heckman,
2012; Mingo et al., 2014). The current understanding is that this is because
the two classes are a result of two fundamentally distinct accretion modes
(Best et al., 2005; Hardcastle, Evans, & Croston, 2006). HERGs are thought to
accrete cold gas efficiently via an optically thick, geometrically thin
accretion disc (e.g. Shakura & Sunyaev 1973), while LERGs accrete from a hot
gas reservoir (e.g. Janssen et al. 2012; Yuan & Narayan 2014; Hardcastle,
Evans, & Croston 2007) relatively slowly via an advection-dominated accretion
flow (Narayan & Yi, 1995; Quataert, 2003).

However, recent work by Whittam et al. (2018) using radio galaxies selected
from a Karl G. Jansky Very Large Array (VLA) survey of Stripe-82 (Heywood et
al., 2016) has suggested that the dichotomy in accretion rates of HERGs and
LERGs may not be as clear cut as previously thought; Whittam et al. find a
significant overlap in the accretion rates of the two classes. The Whittam et
al. study probes lower radio luminosities than the Best & Heckman (2012) work
(see Fig. 1) and the Mingo et al. (2014) study; this may be the reason for the
larger overlap in accretion rates, but Whittam et al. do not have the
statistics at lower luminosities to confirm this trend.

This suggests that the current leading model where there are two distinct
accretion modes, which equate to different feedback processes (see review by
Fabian 2012), does not tell the full story, and instead galaxies may display a
more continuous range of accretion rates and associated properties. This has
important implications for our understanding of galaxy evolution and how AGN
processes affect star-formation in a galaxy (e.g. Cattaneo et al. 2009;
Hardcastle & Croston 2020). However, further research at lower radio
luminosities is required to confirm this, which is the aim of this work.

The MeerKAT International Tiered GHz Extragalactic Exploration (MIGHTEE,
Jarvis et al. 2016) survey is a large survey project currently underway with
the MeerKAT radio telescope (Jonas, 2009). When complete, MIGHTEE will cover
20 square degrees across four different fields (COSMOS, XMM-LSS, ELAIS-S1 and
E-CDFS) to a depth of $\sim 2~{}\muup$Jy/beam rms at 1.28 GHz. The unique
combination of depth over a significant area combined with excellent multi-
wavelength coverage means that the MIGHTEE survey has the potential to provide
a significant step forward in our understanding of galaxy evolution. In
particular, the MIGHTEE survey allows us to study the accretion rates of a
large sample of AGN across a range of radio powers and redshifts. In this
paper we use MIGHTEE Early Science observations in the COSMOS field (Heywood
et al., 2022) to probe the nature of the apparently faint radio source
population, focusing on the properties of radio-loud AGN.

This paper is laid out as follows: in Section 2 we describe the MIGHTEE radio
data used in this work, and the ancillary multi-wavelength data used is
outlined in Section 3. In Section 4 we explain the scheme used to classify the
MIGHTEE radio sources. We then use this sample to explore the properties of
radio-loud AGN in Section 5; first we discuss the host galaxy properties of
different types of radio-loud AGN, next we investigate the accretion rates of
these classes, then we explore the host galaxy properties as a function of
accretion rate and finally we discuss the relationship between AGN power and
black hole mass. The implications of these results are discussed in Section 6,
and our conclusions are presented in Section 7.

Throughout this paper the following values for the cosmological parameters are
used: $H_{0}=70~{}{\rm km\,s}^{-1}~{}\rm Mpc^{-1}$, $\Omegaup_{\rm M}=0.3$ and
$\Omegaup_{\Lambdaup}=0.7$. Unless stated all magnitudes are AB magnitudes. We
use the following convention for radio spectral index, $\alpha$:
$S\propto\nu^{-\alpha}$, for a source with flux density $S$ and frequency
$\nu$.

##  2 Radio data - the MIGHTEE survey

The MIGHTEE Early Science radio continuum data release consists of one
pointing in the COSMOS field, covering $\sim 1.6~{}\textrm{deg}^{2}$, and
three overlapping pointings in the XMM-LSS field, covering $\sim
3.5~{}\textrm{deg}^{2}$. In this work, we restrict our analysis to the central
part of the COSMOS Early Science image, with a diameter of 1.04 degrees, as
this is the region over which multi-wavelength counterparts for the radio
sources have been identified (see Section 3.2 and Prescott et al., in prep).
These observations consist of a single field of view with the MeerKAT
telescope centred on RA 10h00m28.6s, Dec +02d12m21s. The observations were
taken with the L-band receiver (bandwidth 900 - 1670 MHz) between 2018 and
2020 and include 17.45 hours on source. For full details of the observations
and data reduction we refer the reader to Heywood et al. (2022).

The MIGHTEE Early Science data contains two versions of the data processed
with different Briggs (1995) robust weighting values; the first uses Briggs’
robustness parameter = 0.0 and is optimised for sensitivity, but has lower
resolution. The second image uses robust = -1.2 which down-weights the short
baselines in the core resulting in a higher resolution, but this comes at the
expense of sensitivity. In this paper we use the maximum-sensitivity (robust =
0.0) image, which has a circular synthesised beam full-width half maximum
(FWHM) diameter of 8.6 arcsec and a thermal noise of 1.7 $\muup$Jy/beam.
However, due to confusion noise the effective rms noise in the centre of the
image is $\sim 4~{}\muup$Jy/beam (Heywood et al., 2022).

Source finding was carried out using the Python Blob Detector and Source
Finder (PyBDSF; Mohan & Rafferty 2015) using the default source extract
parameters, see Heywood et al. (2022) for further details. Our initial sample
contains 6263 radio sources with $S_{1.28~{}\textrm{GHz}}>20~{}\muup$Jy in the
central part of the COSMOS field111Note that components which make up part of
an extended radio source are grouped together as part of the cross-matching
process described in Section 3.2. As mentioned, the full MIGHTEE Early Science
data released by Heywood et al. covers a larger area of the COSMOS field as
well as the XMM-LSS field, so contains a much larger number of sources, but
here we are limited to the region over which the multi-wavelength counterparts
for the radio sources have been identified to date.

Due to the wide bandwidth of the MeerKAT L-band receivers used for the MIGHTEE
observations ($900-1670$ MHz) and the varying response of the primary beam
with frequency (together with other factors such as flagging of the raw data),
the effective frequency of the MIGHTEE data varies across the image. This is
discussed in detail in Heywood et al. (2022). In order to have measurements at
a constant frequency and to aid comparisons with other work, we scale the
MIGHTEE flux densities and radio luminosities to 1.4 GHz using the effective
frequency map released with Heywood et al., assuming a spectral index of 0.7.
All radio luminosities are k-corrected assuming the same spectral index.

Figure 1: 1.4-GHz radio luminosity and redshift of the MIGHTEE Early Science
multi-wavelength cross-matched sample presented by Prescott et al. (in prep)
and studied in this work (red), along with the samples studied by Best &
Heckman (2012) (black) and Whittam et al. (2018) (blue).

Due to the depth of the radio data used to select the sample studied in this
paper, together with the quality of the ancillary data (see Section 3) we are
able to probe lower radio luminosities and higher redshifts than previous
studies of the accretion rates of radio-loud AGN, such as Best & Heckman
(2012) and Whittam et al. (2018). This is illustrated by Fig. 1 which shows
the radio luminosity and redshift distribution probed by this work compared to
those of two previous studies. As can been seen in the figure, there is almost
no overlap in the parameter space probed by the MIGHTEE sample and the Best &
Heckman (2012) study. This demonstrates the unique power of the MIGHTEE survey
to probe low-powered radio galaxies across cosmic time, which therefore has
potential to provide a new insight into AGN activity.

##  3 Multi-wavelength data

###  3.1 Optical and near-infrared

This work makes use of the extensive optical and near-infrared data in the
COSMOS field compiled by Bowler et al. (2020), (see also Adams et al. 2020,
2021). Briefly, this contains near-infrared imaging in the $YJHK_{s}$ band
from the fourth data release (DR4) of the UltraVISTA survey (McCracken et al.,
2012), optical data in $grizy$ filters from Hyper Suprime-Cam Subaru Strategic
Program DR1 (HSC SSP; Tanaka et al. 2017) along with data from two HSC narrow-
band filters at 8160 and 9210 Å, deeper optical imaging in the $u^{*}griz$
filters from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS), and
deep $z^{\prime}$-band imaging from Subaru/Suprime-Cam (Furusawa et al.,
2016). Additionally, mid-infrared data from the _Spitzer_ Infrared Array
Camera (IRAC) at 3.6 and 4.5 $\muup$m is included. This combines shallower
imaging from the _Spitzer_ Large-Area Survey with the HSC (SPLASH; Steinhardt
et al. 2014) with deeper data from the _Spitzer_ Matching Survey of the
UltraVISTA ultra-deep Stripes survey (SMUVS; Ashby et al. 2018) and the
_Spitzer_ Extended Deep Survey (SEDS; Ashby et al. 2013). Full details of the
catalogue creation are given in Bowler et al. (2020).

Additionally, this work makes use of the high-resolution _Hubble Space
Telesope (HST)_ Advanced Camera for Surveys (ACS) $I$-band image, further
details of these data are given in Scoville et al. (2007).

###  3.2 Cross-matching

The procedure used to identify the host galaxy of each radio source is
described in detail in Prescott et al. (in prep) and summarised briefly here.
Overlays displaying the MIGHTEE radio contours and the higher-resolution
Smolčić et al. (2017a) VLA-COSMOS 3 GHz radio contours on top of the
UltraVISTA $K_{s}$-band images were produced for each MIGHTEE radio component
in the early science low resolution Level 0 catalogue (described in Heywood et
al.). Although less sensitive for a typical radio source with a spectral index
of 0.7 (median rms is $S_{3~{}\textrm{GHz}}\sim 2.3~{}\muup$Jy/beam), the
higher-resolution (0.78 arcsec) VLA-COSMOS 3 GHz data are useful when
identifying the correct host galaxy for the radio sources.

Prescott et al. (in prep) use an updated version of the Xmatchit code
(described in Prescott et al. 2018) to quickly display the overlays for each
radio component. These were examined by eye by three separate people to
identify the most likely host galaxy for each radio component. Any sources
where the three classifiers did not agree were examined again by a committee.
In total, we have identified the host galaxy for 5223 out of 6262 (83 per
cent) radio sources. The 1039 unmatched radio sources are a combination of
sources which lie in masked regions close to bright sources in the
$K_{s}$-band image (208 sources), sources which are too confused for us to be
able to identify the correct host ID (i.e. where two or more individual
sources with separate host galaxies are blended together in the radio image;
693 sources), sources where there is no host galaxy visible in the UltraVISTA
$K_{s}$-band image (126 sources), and sources which appear to be artefacts in
the radio image (12 sources; note that these do not appear in the MIGHTEE
Early Science Level 1 catalogue released by Heywood et al. where artefacts
have been removed). This is discussed further in Prescott et al. (in prep).
This sample of 5223 sources is the focus of the remainder of this paper.

###  3.3 Mid and far-infrared

In addition to the data from the two shorter-wavelength _Spitzer_ IRAC bands
included in the Bowler et al. (2020) compilation described in Section 3.1, we
use data from the 5.8 and 8.0 $\muup$m bands from the SPLASH survey, accessed
from Laigle et al. (2016).

Far-infrared data were obtained from the _Herschel_ Extra-galactic Legacy
Project (HELP; Shirley et al. 2021). We use data at 24 $\muup$m from the
Multiband Imaging Photometer (MIPS, Rieke et al. 2004) instrument on the
_Spitzer_ Space Telescope, 100 and 160 $\muup$m from the Photodetector Array
Camera and Spectrometer (PACS, Poglitsch et al. 2010) on _Herschel_ and 250,
350 and 500 $\muup$m from the Spectral and Photometric Imaging Receiver
(SPIRE, Griffin et al. 2010), also on _Herschel_. Photometry was obtained
using xid\+ (Hurley et al., 2017), a probabilistic de-blender developed for
the HELP project. This utilises prior information from the four _Spitzer_ IRAC
bands, which have a higher resolution than the _Herschel_ data, and applies a
Bayesian approach to extract photometry from the _Herschel_ maps.

The HELP far-infrared catalogues were combined with the cross-matched
catalogue (Section 3.2) by matching to the position of the host galaxy using a
match radius of 1 arcsec. 4540 out of 5223 radio sources are detected in the
MIPS and PACS data, and 4957 in the SPIRE data.

###  3.4 X-ray

Deep X-ray imaging is available across the COSMOS field from the _Chandra_
COSMOS-Legacy project, which combines 1.8 Ms of data from the C-COSMOS survey
(Elvis et al., 2009) with 2.8 Ms of more recent _Chandra_ ACIS-I observations
(Civano et al., 2015) in the 0.5 - 10 keV energy band. The optical and
infrared counterparts to the _Chandra_ COSMOS-Legacy survey are presented in
Marchesi et al. (2016); we use this catalogue to identify X-ray counterparts
to the MIGHTEE radio sources via the positions of the optical host galaxies. A
total of 572 out of 5223 radio sources are detected in the X-ray observations.

###  3.5 VLBI

Very long baseline interferometry (VLBI) observations of the COSMOS field were
carried out by Herrera Ruiz et al. (2017) using the Very Long Baseline Array
(VLBA). The observations have a median resolution of $16.2\times
7.3~{}\textrm{mas}^{2}$ and a central frequency of 1.54 GHz. We matched the
VLBA catalogue to the MIGHTEE catalogue described in this work using the
positions of the optical host galaxies and a match radius of 1 arcsec. A total
of 255 MIGHTEE sources are detected in the VLBA catalogue.

###  3.6 Redshifts

Spectroscopic redshifts are available for a number of sources in the field
from the following observing campaigns; the Deep Imaging Multi-Object
Spectrograph (DEIMOS) 10K survey (Hasinger et al., 2018), the Fiber Multi-
Object Spectrograph (FMOS) survey (Silverman et al., 2015), the PRIsm MUlti-
object Survey (PRIMUS, Coil et al. 2011; Cool et al. 2013), the zCOSMOS survey
(Lilly et al., 2009), the 3D-HST survey (Skelton et al., 2014; Momcheva et
al., 2016)222The redshifts from the latter four surveys were compiled by the
HSC team and are available here: https://hsc-
release.mtk.nao.ac.jp/doc/index.php/dr1_specz/., the Sloan Digital Sky Survey
14th data release (SDSS DR14; Abolfathi et al. 2018) and the Large Early
Galaxy Astrophysics Census (LEGA-C) program (van der Wel et al., 2016;
Straatman et al., 2018). In total 2427 (46 per cent) of the sources in our
sample have a spectroscopic redshift available.

For the remaining sources we use photometric redshifts derived from the
excellent optical and near-infrared photometry available in the COSMOS field
(see Section 3.1). Briefly, the photometric redshifts are calculated using a
hierarchical Bayesian combination (as per Duncan et al. 2018) of two different
approaches; the more traditional template fitting, and a machine learning
approach. The template fitting is carried out using the LePhare Spectral
Energy Distribution (SED) fitting code (Arnouts & Ilbert, 2011) set up as
described in Adams et al. (2021), and the machine learning using the GPz
algorithm (Almosallam et al., 2016; Almosallam, Jarvis, & Roberts, 2016) set
up as described in Hatfield et al. (2020). For further details of this process
we refer the reader to Hatfield et al. (submitted).

Optical spectral line measurements are available for the 92 sources with SDSS
spectra and the 80 sources with spectra from LEGA-C, and are used in this
work. The procedures used to obtain the emission line fluxes for the SDSS
sources are described in Thomas et al. (2013).

###  3.7 AGNfitter

We use the SED fitting code AGNfitter to investigate the properties of the AGN
in the sample. AGNfitter is a fully Bayesian SED-fitted code and is described
in Calistro Rivera et al. (2016). It uses a library of theoretical, empirical
and semi-empirical models to characterise the nuclear and host galaxy emission
simultaneously. The SED is separated into four components; two arise from the
AGN and two from the host galaxy. Following the nomenclature of Calistro
Rivera et al., the AGN emission comprises of a UV/optical accretion disk
component (BB) and a hot dust torus component (TO). The host galaxy emission
components are stellar emission (GA) and reprocessed light from dust (SB).

Figure 2: Example of multiple SEDs taken from the posterior from AGNfitter.
The black points show the photometry and associated uncertainties. The purple
lines show different realisations of the AGN torus component (TO), the blue
lines are the AGN accretion disk component (BB), the yellow lines are the
stellar emission (GA) and the green lines are the reprocessed stellar light
from dust (SB). The red lines are the total SED. The red circles are the
simulated measurements derived by convolving the filter profile with the fit
SED.

We used a total of 24 bands ranging from the far-infrared to the optical as
described in Sections 3.1 and 3.3. Due to the well-known problem with SED-
fitting using different wavebands with (potentially) different systematic
uncertainties, we set any uncertainties which were $<10$ per cent to 10 per
cent. The redshift for each source is fixed to the best available value, as
described in Section 3.6. We achieved a good fit (quantified by log likelihood
values $>-100$) for 4969 out of 5223 sources. An example SED is shown in Fig.
2.

We use the results of the AGNfitter SED-fitting to estimate the accretion rate
of the AGN in our sample, as described in Section 5.2. The code also produces
estimates of the host galaxy’s stellar mass and star-formation rate, which are
used in the analysis. We compared the stellar masses derived by AGNfitter to
those estimated by the LePhare SED-fitting code (see Adams et al. 2021), and
found that the stellar masses from the two SED-fitting codes are generally in
good agreement; we therefore use those from AGNfitter in this work, but using
the values from LePhare instead does not change any of the conclusions in this
paper.

##  4 Source classification

The classifications in this work are based on five different criteria, which
are described in the following sub-sections. These are: radio excess (Section
4.1), mid-infrared colour cuts (Section 4.2), optical morphology (Section
4.3), X-ray luminosity (Section 4.4) and VLBI detection (Section 4.5). These
different selection criteria identify different AGN properties; the mid-
infrared colour cut identifies objects with a dusty AGN torus, the optical
morphology criterion selects optical quasars and the X-ray cut identifies AGN
with accretion-related X-ray emission. These are all signatures of quasar-like
AGN. The two radio criteria, however, identify sources with radio-AGN
activity. This is discussed further in Section 4.6, where the five criteria
are combined to give the overall classification scheme.

These classifications are released publicly with this work, details of the
catalogue are given in Appendix A. The classifications are compared to
classifications from optical spectra in Section 4.7 and to classifications
from the VLA-COSMOS 3-GHz Large Project (Smolčić et al., 2017a, b) which
covers the same field in Section 4.8.

We note that Williams et al. (2018) use information from AGNfitter SED fitting
to classify the sources in the LOFAR-Bootës sample as HERGs and LERGs. We
tested using this classification scheme and found that it was not appropriate
for the fainter sources in our sample, for details see Appendix B.

###  4.1 Radio-excess AGN

We make use of the infrared – radio correlation to identify sources with
significantly more radio emission than would be expected from star-formation
alone. The infrared – radio correlation can be quantified by the parameter
$q_{\text{IR}}$, which is defined as the logarithmic ratio of the infrared and
radio luminosities:

$q_{\text{IR}}=\text{log}_{10}\frac{L_{\text{IR}}~{}[\text{W}]\,/\,3.75\times
10^{12}~{}[\text{Hz}]}{L_{1.4~{}\text{GHz}}~{}[\text{W Hz}^{-1}]}$ (1)

where $L_{\text{IR}}$ is the total infrared luminosity between 8 - 1000
$\muup$m, estimated by AGNfitter. This is divided by the central frequency of
$3.75\times 10^{12}~{}\text{Hz}$ (80 $\muup$m) so that $q_{\text{IR}}$ is a
dimensionless quantity.

We use the stellar mass and redshift dependent infrared-radio correlation
(IRRC) from Delvecchio et al. (2021) to identify sources which display a radio
excess above what would be expected from star-formation. Delvecchio et al.
(2021) use the MIGHTEE Early Science data, as well as data from the VLA-COSMOS
3 GHz Large Project (Smolčić et al., 2017a) to investigate how the infrared-
radio correlation evolves with stellar mass and redshift simultaneously.
Following Delvecchio et al. and Williams et al. (2018), we consider any source
which lies more than 0.43 dex below the best fit correlation given by equation
5 in their paper as having a radio excess (this is equivalent to 2 $\sigma$,
where $\sigma$ is the intrinsic scatter in the relation). We note that
adopting this cut may result in a small number of SFG being misclassified as
radio-excess AGN, but using a less-aggressive cut would result in the opposite
problem, where radio-excess AGN are missed and classified as radio quiet.
Delvecchio et al. tested a number of different cuts to separate radio-AGN and
star-forming populations, and found the $2\sigma$ threshold used here to be
the best compromise, with contamination from SFG only around 3 - 4 per cent.

Fig. 3 shows $q_{\text{IR}}$ as a function of redshift and stellar mass, with
the Delvecchio et al. IRRC relation and radio excess cut shown. Using this
criterion, 1332 MIGHTEE sources are classified as having a radio excess, and
3590 are classified as not having a radio excess. A further 301 sources are
unable to be classified, as AGNfitter gives a poor fit (with log likelihood
$<-100$) so we are unable to place a reliable constraint on their total
infrared luminosity.

Figure 3: $q_{\text{IR}}$ as a function of redshift (top) and stellar mass
(bottom). We use the mass- and redshift-dependent IRRC from Delvecchio et al.
(2021) to identify sources with a radio excess. This correlation (black solid
line), along with the cut used (black dotted line), are shown at a fixed
stellar mass (log${}_{10}(\textrm{M/M}_{\odot})=10.5$) and redshift ($z=1$) in
the top and bottom panels respectively. Sources classified as radio-excess AGN
are shown as red points, while the rest of the sample studied in this paper
are shown as blue points. As the full mass- and redshift-dependent relation is
used to classify the sources, several of the classified sources appear
scattered above or below the classification line; this is because they are at
a different mass or redshift to the one for which the relation is shown.
Sources with a poor fit from AGNfitter are marked by squares.

###  4.2 Mid-infrared AGN

Galaxies which display power-law emission from an AGN torus can be identified
using a mid-infrared colour-colour diagram. We use the region on a
$S_{8.0~{}\muup\textrm{m}}/S_{4.5~{}\muup\textrm{m}}$ vs
$S_{5.8~{}\muup\textrm{m}}/S_{3.6~{}\muup\textrm{m}}$ diagram defined by
Donley et al. (2012), and classify any galaxy lying in this region as a mid-
infrared AGN.

Figure 4: Mid-infrared colour-colour diagram showing sources with detections
in all four bands (subscripts on axis labels are band wavelengths in
$\muup$m). Sources lying inside the Donley et al. (2012) AGN region, shown as
a black dashed line, are classified as Donley mid-infrared AGN (orange
points). Sources which cannot lie inside this region, taking into account the
uncertainties on the flux densities, are classified as ‘not Donley mid-
infrared AGN’ (blue points).

Sources which are found outside the Donley et al. AGN region, and which,
taking into account the quoted $1\sigma$ uncertainties on the flux density
measurements in all four bands, are not within $1\sigma$ of the boundary of
the AGN region, are classified as ‘not Donley mid-infrared AGN’. Additionally,
3$\sigma$ upper limits are calculated for sources which are not detected at
5.8 and/or 8.0 $\muup$m. Taking into account these limits, sources which could
not lie inside the Donley et al. AGN region are also classified as ‘not Donley
mid-infrared AGN’. These sources are shown on a mid-infrared colour-colour
diagram in Fig. 4. We note that the Donley et al. region was designed to
select a clean AGN sample at the expense of completeness, so lying outside
this region does not guarantee that a source is not an AGN. While using a
larger selection region would improve completeness of our mid-infrared AGN
sample, it would also contaminate the sample with a number of misclassified
star-forming galaxies.

In total, 273 sources are classified as Donley mid-infrared AGN, and 4542 are
‘not Donley mid-infrared AGN’. A further 409 sources are unable to be
classified, either because they are undetected in one or more bands and the
relevant flux density limits make it uncertain whether or not they lie inside
the Donley et al. AGN region, or because they lie close to the boundary and
the flux error bars could take them inside the region. Of the 273 sources
identified as AGN in the mid-infrared, 61 also have a radio excess.

###  4.3 Optical point-like AGN

Sources which display a point-like morphology in optical imaging can be
classified as AGN, since emission from the nucleus outshines the emission from
the host galaxy. To investigate the optical morphology of the MIGHTEE sources,
we use the _HST_ ACS $I$-band image (Scoville et al., 2007), with a resolution
of 0.09" FWHM. We classify any source with Class_star$>=0.9$, which is
therefore point-like in the image, as an optical point-like AGN. Sources
detected in the ACS $I$-band image with Class_star$<0.9$ are classified as
‘not optical point-like AGN’. This gives 157 optical point-like AGN and 4540
not optical point-like AGN. A further 526 sources are unable to be classified
as they are not detected in the ACS image. Of the 157 sources which are point-
like in the optical image, 71 are identified as mid-infrared AGN in Section
4.2 and 36 are classified as radio-excess AGN in Section 4.1.

###  4.4 X-ray AGN

X-ray observations can be used to identify AGN, as some of the brightest AGN
display characteristic accretion related X-ray emission. Using the X-ray data
described in Section 3.4, we consider a source to be an X-ray AGN if its rest-
frame (0.5 – 10 keV) X-ray luminosity $L_{X}>10^{42}~{}\text{erg s}^{-1}$
(Szokoly et al., 2004). The X-ray luminosities are K-corrected assuming an
X-ray spectral index of $\Gamma=1.4$, and no obscuration correction is applied
(see Marchesi et al. 2016 for details). If a source is not detected in the
X-ray and has $z<0.5$, we are able to place an upper limit on its X-ray
luminosity such that $L_{X}<10^{42}~{}\text{erg s}^{-1}$, so these sources are
classified as ‘not X-ray AGN’. Undetected sources with redshifts $>0.5$ could
have X-ray luminosities greater than this cutoff, so they are not classified.
This gives 519 X-ray AGN, 1084 ‘not X-ray AGN’ and 3620 unclassified sources
which lie at $z>0.5$. Of the 519 X-ray AGN, 213 are identified as radio-excess
AGN in Section 4.1, 154 are classified as mid-infrared AGN in Section 4.2 and
94 display a point-like morphology in the optical (Section 4.3).

###  4.5 VLBI AGN

We use the VLBI observations of the COSMOS field described in Section 3.5 to
identify AGN. In order to be detectable in the VLBI observations, a source
must have a brightness temperature above $10^{6}$ K (Herrera Ruiz et al.,
2017). However, at frequencies $\sim 1$ GHz the brightness temperature of
normal galaxies does not exceed $10^{5}$ K (Condon, 1992), so in order to have
a brightness temperature high enough to be detected by the VLBA observations,
a source must have AGN activity. We therefore classify the 255 MIGHTEE sources
detected in the VLBA observations as VLBA AGN. Of these, 216 are classified as
radio-excess AGN using the infrared – radio correlation as described above, 26
do not display a radio excess and 13 are unable to be classified using the
IRRC (due to poor constraints on their infrared luminosity).

###  4.6 Overall classifications

Figure 5: A mid-infrared colour-colour diagram (subscripts on axis labels are
band wavelengths in $\muup$m). Sources lying inside the Donley et al. (2012)
AGN region, shown as a black dashed line, are classified as mid-infrared AGN.
Sources classified as AGN using other criteria are marked in red. Top left:
optical point-like AGN (point-like in the optical; Section 4.3), top right:
X-ray AGN (Section 4.4), bottom left: radio-excess AGN (Section 4.1), bottom
right: VLBA AGN (Section 4.5).

We have five indicators of AGN emission (radio excess, mid-infrared colours,
optical morphology, X-ray power and compact radio emission detected by the
VLBA), as described in the previous sections and summarised in Table 1. These
criteria are compared in Fig. 5, which shows mid-infrared colour-colour
diagrams with sources classified as AGN using the four other AGN criteria
plotted separately. This shows that the X-ray, radio, optical point-like and
VLBA-detected AGN generally lie in the expected regions on this diagram; the
optical point-like AGN are generally found along the power-law wedge defined
by Donley et al. (2012) (shown by the black dashed line in Fig. 5), although
there is considerable scatter outside this region. Many of the X-ray AGN are
found in the Donley et al. AGN region, although a large number of them lie
along the extension of this power law to the bottom left. The radio-excess AGN
are concentrated in the bottom left part of the distribution, in the region
where ‘red and dead’ host galaxies are likely to be found, as expected.
Reassuringly, there are very few AGN of any type in the region generally
occupied by SFGs (i.e. the left ‘bunny ear’ region with
log${}_{10}(S_{8.0}/S_{4.5})\gtrsim 0.2$ and
$-0.5\lesssim\textrm{log}_{10}(S_{8.0}/S_{4.5})\lesssim 0.0$). The cluster of
radio-excess AGN found in the bottom left part of the diagram are mainly
LERGs, as expected. Note that we do not necessarily expect agreement between
the different AGN diagnostics, as any given AGN may only display one or two
indicators of AGN activity.

For the overall classifications, we classify a source as an AGN if it meets
any one (or more) of the five AGN criteria. Sources which we can securely
classify as not being an AGN using all five criteria are classified as star-
forming galaxies. Because the X-ray criterion limits us to only classifying
sources with redshifts $<0.5$ in this way, we introduce the additional
classification of ‘probable SFG’ for sources which have redshifts $>0.5$ so
are unable fulfil the ‘not X-ray AGN’ criteria, but which are classified as
‘not AGN’ using the other four criteria.

Additionally, we classify the radio excess AGN as high-excitation and low-
excitation radio galaxies (HERGs and LERGs) in a similar way to Whittam et al.
(2016). HERGs generally display typical AGN signatures across the
electromagnetic spectrum, while LERGs typically lack the usual AGN apparatus
(e.g. accretion disk, dusty torus). This means that while LERGs are radio
loud, they do not display AGN characteristics in other parts of the
electromagnetic spectrum. Therefore, we classify radio excess sources which
are classified as an AGN using at least one of the following other diagnostics
as HERGs: optical morphology, mid-infrared colours or X-ray power. Sources
which have a radio excess and are securely classified as ‘not AGN’ using the
remaining three criteria are classified as LERGs. Due to the X-ray limit, this
restricts us to sources with $z<0.5$. Therefore, in a similar way as for the
SFGs, we define a ‘probable LERG’ class - any radio excess source with $z>0.5$
which is securely classified as not being an AGN in the optical and mid-
infrared is considered a ‘probable LERG’. Radio-loud AGN which are not
classified as a HERG, LERG or probable LERG are referred to as ‘unclassified
RLAGN’; these are radio-loud AGN which do not meet the HERG criteria (i.e.
they are not identified as AGN using the X-ray, mid-infrared or optical
morphology data) but are not securely classified as ‘not AGN’ using all the
relevant criteria so are not able to be classified as LERGs or probable LERGs.
Sources which do not have a radio excess but which fulfil one of the other
three AGN criteria are classified as radio-quiet AGN; 417 sources fit these
criteria. Note that in order to be classified as either radio loud or radio
quiet a source must not have a poor fit with AGNfitter (quantified by log
likelihood $<-100$) so that we are able to place a reliable constraint on its
total infrared luminosity. This means that a small number of AGN (57) are not
classified as either radio loud or radio quiet. These classifications are
summarised in Table 2. Fig. 6 shows the proportion of different source types
as a function of radio flux density and redshift.

Figure 6: Top: proportion of sources with a host galaxy identification that
are classified as AGN and SFG as a function of radio flux density. The red
solid line shows the AGN, the solid blue line shows the SFG and probable SFG
combined, the dotted blue line shows the sources securely classified as SFG
only, and the dashed black line shows the unclassified sources. Bottom:
proportion of radio-excess AGN which are HERGs (red solid line), LERGs (blue
dashed line), probable LERGs (black dotted line) and unclassified RLAGN (cyan
dot-dashed line) as a function of redshift. The grey dashed line is at
$z=0.5$, the redshift beyond which we cannot securely classify LERGs so adopt
the ‘probable LERG’ classification instead. Table 1: Number of sources
classified as AGN, not robust AGN, and unclassified using the criteria
outlined in Section 4. The ‘not robust AGN’ column refers to sources which are
securely identified as not having radio excess, have an X-ray luminosity
$<10^{42}\textrm{erg \, s}^{-1}$, lie outside the Donley AGN selection region
on a mid-infrared colour-colour diagram, are extended in the optical or are
not detected by the VLBA observations respectively.

AGN criteria | AGN | Not robust AGN | Unclassified
---|---|---|---
Radio excess AGN | 1332 | 3590 | 301
Donley mid-infrared AGN | 273 | 4541 | 409
Optical point-like AGN | 157 | 4540 | 526
X-ray AGN | 519 | 10841 | 3620
VLBA AGN | 255 | 4968 |

1 Limited to sources with $z<0.5$ (see text).

Table 2: Summary of the number of sources in each of the classes described in Section 4.6. Overall class | Number of sources
---|---
AGN | 1806
SFG | 766
Probable SFG | 2040
Unclassified | 611
Total RLAGN | 1332
HERG | 249
LERG | 150
Probable LERG | 782
Unclassified RLAGN | 151
Radio quiet AGN | 417
Total number of sources | 5223

The catalogue containing these classifications is known as the Level 3
catalogue and is released with this work; the columns in this catalogue are
described in Appendix A and the full catalogue is available as supplementary
material.

###  4.7 Comparison with optical spectra

Table 3: Classifications using the scheme outlined in Section 4.6 for the 82 sources in our sample with SDSS spectra. BPT class |  | Classifications from this work
---|---|---
(from SDSS) | Total | AGN | SFG | Prob. SFG | Unclass.
Star-forming | 28 | 5 | 22 | 0 | 1
Composite | 22 | 9 | 13 | 0 | 0
Seyfert | 10 | 9 | 1 | 0 | 0
Seyfert/LINER | 1 | 1 | 0 | 0 | 0
LINER | 21 | 15 | 5 | 0 | 1

In our sample, 82 sources have a Baldwin, Philips and Terlevich (BPT; Baldwin,
Phillips, & Terlevich 1981) diagram classification from SDSS. These
classifications are compared to those using the scheme described in Section
4.6 in Table 3. The classifications are broadly in agreement, with a few
discrepancies. Notably, 5 sources which are found in the star-forming region
of the BPT diagram are classified as AGN using the scheme described in this
paper. All 5 of these sources have a radio excess but do not display any other
signatures of AGN activity. This demonstrates that classifications are not
always clear-cut when dealing with faint populations (in both the radio and
multi-wavelength data).

Table 4: Comparison between the classification of HERGs and LERGs used in this paper and those using [Oiii] equivalent width measurements from optical spectra. | Total | HERG | LERG | Prob. LERG | Unclass.
---|---|---|---|---|---
Spec. HERG | 6 | 3 | 0 | 3 | 0
Spec. LERG | 33 | 6 | 15 | 12 | 0
Figure 7: [Oiii] equivalent width for sources in our sample with line
measurements available from the SDSS or LEGA-C surveys. Sources classified as
HERGs (red solid line), LERGs (blue dashed line) and probable LERGs (cyan
dotted line) using the criteria in Section 4.6 shown separately.

The equivalent width of the [Oiii] line at 5007 Å is often used in the
literature to separate HERGs and LERGs, for example by Laing et al. (1994);
Jackson & Rawlings (1997); Tadhunter et al. (1998); Ching et al. (2017);
Prescott et al. (2018). Where [Oiii] line measurements are available, we
classify sources with [Oiii] equivalent width $>5$ Å as HERGs, and those with
values $<5$ Å as LERGs. 42 radio excess sources in our sample have an [Oiii]
equivalent width measurement available, from either SDSS or LEGA-C, so are
able to be classified in this way.

The classifications using [Oiii] equivalent width are compared to those
derived from the criteria in Section 4.6 in Table 4 and Fig. 7. While the
classifications using [Oiii] equivalent width are broadly in agreement with
those used in this work, six sources with [Oiii] equivalent width $<5$ Å are
classified as HERGs. All six sources have X-ray luminosities $>10^{42}$ erg/s,
indicating that there is AGN-accretion related X-ray emission, which is
characteristic of HERGs. Again, this shows that source classifications are not
always clear-cut, and depend on the criteria used. In another example, Mingo
et al. (2014) found seven sources in their sample of very bright radio
galaxies ($S_{2.7~{}\textrm{GHz}}>2$ Jy) that were classified as LERGs based
on their optical spectra but which showed signs of being radiatively efficient
at other wavelengths.

###  4.8 Comparison with VLA-COSMOS 3 GHz Large Project

The VLA-COSMOS 3 GHz Large Project (Smolčić et al. 2017a; hereafter VLA-
COSMOS) surveyed 2 deg2 of the COSMOS field at 3 GHz with median rms of 2.3
$\muup$Jy/beam and a resolution of 0.75 arcsec. They use a combination of mid-
infrared colours, rest-frame optical colours, X-ray emission, radio excess,
SED fitting and _Herschel_ detections to classify the radio sources detected
in their observations (full details are given in Smolčić et al. 2017b). As
many of these sources also appear in our catalogue, in this section we compare
their classifications to the classification scheme described in this work.
While there are some similarities in the classification schemes employed by
the two studies, there are some notable differences; for example, our work
utilises the high-resolution _HST_ data while the VLA-COSMOS study uses rest-
frame optical colours, and the two studies use different SED-fitting codes and
different radio-excess definitions.

Figure 8: 1.4-GHz integrated flux density from MIGHTEE for the MIGHTEE Early
Science cross-matched sample considered in this work (cyan), and the sub-
sample of these sources which are also in the VLA-COSMOS 3 GHz multi-
wavelength sample (black). Measured flux densities are scaled to 1.4-GHz using
the effective frequency map and assuming a spectral index of 0.7.

There are 3386 sources with multi-wavelength identifications in both the
MIGHTEE catalogue and the VLA-COSMOS catalogue (matched using optical
positions and match radius of 1 arcsec). The total MIGHTEE radio flux
densities of these sources are shown in Fig. 8. There are 2975 sources with
source type classifications available in both the VLA-COSMOS catalogue and
this work, the classifications of these sources are compared in Table 5. Here
we have combined the sources classified as SFG and probable SFG in this work
in one column, as this is approximately comparable to the VLA-COSMOS ‘SFG’
class, and listed the sources classified as SFG using our criteria in another
column. We have also combined our LERG and probable LERG classes in this table
to ease comparison. The redshift values used by the two projects are not
necessarily the same as we utilise new spectroscopic redshifts available for
some sources, and have used updated photometry and a different method to
estimate the photometric redshifts (see Section 3.6 for details). Although the
redshift estimates for many of the sources are consistent, the values for 320
(12 per cent) of sources are outliers, where an outlier is defined as being
when $|z_{\textrm{MIGHTEE}}-z_{\textrm{VLA-
COSMOS}}|/(1+z_{\textrm{MIGHTEE}})>0.15$. The number of sources in each
category where the redshifts used by the two projects do not significantly
disagree (i.e. when $|z_{\textrm{MIGHTEE}}-z_{\textrm{VLA-
COSMOS}}|/(1+z_{\textrm{MIGHTEE}})<0.15$) are shown in brackets in Table 5. We
find no trend with the type of source and discrepant redshift.

76 per cent of the sources classified as AGN in this work are also classified
as AGN in VLA-COSMOS, while 89 percent of our SFG are classified as clean
SFG333The VLA-COSMOS team define a SFG class, which includes some sources with
a radio excess, and a ‘clean SFG’ class where these radio-excess sources are
removed. Here we compare to their ‘clean SFG’ class, as this is more
consistent with the definition of SFG used in this work, which excludes all
radio-excess sources. in their work. This demonstrates that there is broad
agreement between the two classification schemes. However, despite the
excellent photometric data utilised by both groups, there are some differences
evident in the classifications, highlighting the dependence on the exact
classification method used. For example, 288 sources which are classified as
AGN in our catalogue are identified as clean SFGs in the VLA-COSMOS catalogue.
The vast majority of the sources (260 out of 288) are identified as being AGN
in the radio only. While both classification schemes use the far-infrared-
radio correlation to identify sources with a radio excess, we use different
versions of the correlation. Smolčić et al. (2017b) use a redshift-dependent
relation based on Delvecchio et al. (2017) and Delhaize et al. (2017). In this
work, we use the updated Delvecchio et al. (2021) correlation, which is
dependent on stellar mass as well as redshift. We also employ a different cut
to identify radio-excess AGN; following Delvecchio et al. (2021) and Williams
et al. (2018), we classify sources which lie more than $2\sigma$ from the IRRC
as having a radio-excess, where $\sigma$ is the instrinsic scatter on the
relation. Smolčić et al., however, use $3\sigma$ instead. This may well be
partly responsible for the higher number of radio AGN identified in our work.
Additionally, the compact configuration of MeerKAT means the telescope has
excellent sensitivity to low-surface brightness emission, meaning that it
picks up such extended emission from sources which may be missed by the VLA-
COSMOS observations. This issue is discussed in briefly Hale et al. (in prep)
and could be responsible for some radio excess AGN being identified in the
MIGHTEE observations and missed in the VLA survey.

This highlights the difficulties of classifying sources based on photometry
alone, and the sensitivity to different approaches.

Table 5: Comparison of sources classified in this work and the classifications
by the VLA-COSMOS team for sources which feature in both catalogues. The
numbers in brackets are the number of sources where the redshift values used
by each project agree within $|z_{\textrm{MIGHTEE}}-z_{\textrm{VLA-
COSMOS}}|/(1+z_{\textrm{MIGHTEE}})>0.15$. HLAGN and MLAGN are high and medium
luminosity AGN respectively, as classified by the VLA-COSMOS team. These can
be very approximately related to our HERG and LERG classes respectively. The
last row shows the percentage of sources in each MIGHTEE class classified as
the approximately equivalent class using the VLA classification scheme. For
these purposes, MIGHTEE AGN is compared to VLA AGN, MIGHTEE SFG & prob. SFG is
compared to VLA clean SFG in the second column, MIGHTEE SFG is also compared
to VLA clean SFG in the third column, MIGHTEE HERG is compared to VLA HLAGN,
and MIGHTEE LERG & prob. LERG is compared to VLA MLAGN. Note that the
classification methods are not identical so these classes are not directly
equivalent

. Sources classified as AGN and SFG by both classification schemes are shown
in bold to aid the reader.  VLA classes Classes in this work Total AGN SFG &
prob. SFG SFG HERG LERG & prob. LERG AGN 1075 (936) 200 (180) 27 (26) 201
(175) 457 (431) 1275 (1116) clean SFG 288 (239) 1288 (1196) 318 (315) 5 (3)
229 (202) 1576 (1435) HLAGN 598 (500) 102 (92) 18 (17) 198 (173) 51 (45) 700
(592) MLAGN 477 (436) 98 (88) 9 (9) 3 (2) 406 (386) 575 (524) Total 1408
(1207) 1567 (1448) 357 (353) 207 (179) 717 (659) 2975 (2655) % agree with VLA
class 76 (78) 82 (83) 89 (89) 96 (97) 57 (59)

##  5 Properties of the radio-loud AGN

###  5.1 Host galaxies of HERGs and LERGs

Figure 9: Radio luminosity as a function of redshift for the HERGs (red),
LERGs (blue), probable LERGs (black) and unclassified RLAGN (cyan) in this
sample. The large solid shapes show the median radio luminosity in each
redshift bin. The dotted line is at $z=0.5$, the redshift beyond which we are
unable to securely classify sources as LERGs due to the depth of the X-ray
data (see text), and instead adopt the probable LERG classification.

Fig. 9 shows the radio luminosity and redshift distribution of the HERGs and
LERGs in this sample. The median radio luminosities of the two classes of
radio galaxy are indistinguishable across the redshift range probed by this
sample ($0<z<5$).

The stellar masses and star-formation rates of HERGs and LERGs as a function
of redshift are shown in Fig. 10. These plots demonstrate that the HERGs and
LERGs in our sample are hosted by galaxies with very similar host galaxy
properties out to $z\sim 4$. The only exception is in the lowest redshift bin
(z < 0.4), where LERGs seem to be hosted by galaxies with higher stellar
masses than HERGs. This is in agreement with previous studies at higher radio
powers which overlap with this redshift bin (e.g. Best & Heckman 2012; Whittam
et al. 2018), which find a significant difference in the properties of
galaxies hosting these more powerful HERGs and LERGs. Our results demonstrate
that at lower radio powers and higher redshifts the host galaxies of HERGs and
LERGs are becoming indistinguishable.

While we are reasonably confident that all the sources in our HERG sample are
indeed HERGs, it is possible that some of the sources in our LERG and
‘probable LERG’ samples are HERGs where signs of efficient accretion have been
missed. In particular, the sources at $z>0.5$ classified as ‘probable LERGs’
could have accretion-related X-ray emission which is too faint to be detected
in the observations used in this work, and therefore should in reality be
classified as HERGs. In addition, the Donley et al. mid-infrared selection
used in this work is incomplete, so may have missed some mid-infrared HERGs.
These potentially misclassified HERGs could cause the distributions of the
host galaxy properties of the HERGs and LERGs to appear more similar than they
actually are. However, as the stellar mass and star-formation distributions of
the HERGs and probable LERGs are indistinguishable at $z>0.5$, adding a small
number of potentially misclassified probable LERGs into the HERG sample should
make little difference to the overall results.

The greyscale and the yellow points in Fig. 10 show the properties of the full
optical catalogue, plotted here to highlight possible selection effects. At
higher redshifts we can only detect more massive galaxies, but the median
stellar mass of the full population is at least an order of magnitude below
that for our radio galaxy sample across the full redshift range under
consideration here, so this should not affect our results. The host galaxies
of the radio galaxies are more massive than the general optically-selected
population, as expected. The stellar masses and star-formation rates shown in
this figure are estimated using the LePhare SED-fitting code by fixing the
redshift at the best available value for each source (see Section 3.6). We
show the LePhare galaxy properties in this figure, rather than those estimated
by AGNfitter used in the remainder of the paper, in order to be directly
comparable to the full optically-selected population also shown, for which
only the LePhare values are available. We note that plotting the AGNfitter
properties for our sample instead makes negligible difference to this plot,
and would not change any of the conclusions drawn from this figure.

Recent work by Kondapally et al. (2022) has uncovered a population of LERGs
hosted by star-forming (rather than quiescent) galaxies at higher redshifts
($z>1$), in contrast to previous work at lower redshifts which have found
LERGs are usually hosted by quiescent galaxies. This is consistent with the
result discussed here that HERGs, LERGs and probable-LERGs have very similar
star-formation rates. They also find that as the radio luminosity limit is
lowered, their sample contains more LERGs with lower stellar masses (at all
redshifts), compared to higher luminosities where LERGs tend to be hosted by
only the most massive galaxies. This is again consistent with the work
presented in this paper, where we find the host galaxy masses of HERGs and
LERGs to be very similar at $z>0.5$.

This is in good agreement with what is predicted by the Simba cosmological
hydrodynamical simulation (Davé et al., 2019). Thomas et al. (2021)
investigated the properties of radio-loud AGN in Simba, and found that HERG
and LERG hosts became increasingly similar as they probed lower radio powers,
which is supported by our results. However, although Thomas et al. (2021) find
HERG and LERG hosts in Simba have very similar stellar masses, they do find a
difference when looking at the most massive galaxies; all galaxies with
stellar masses $>2\times 10^{11}M_{\odot}$ host LERGs. This effect is not
evident in our MIGHTEE sample. Note however that the Thomas et al. study is at
$z=0$, while the sample selected from MIGHTEE covers a range of redshifts out
to $z=5$, which may well account for the differences seen. The properties of
MIGHTEE radio galaxies will be compared to an equivalent sample selected from
Simba in a future paper (Thomas et al., in prep).

There is tentative evidence that the HERGs in our sample are more likely to be
detected by the VLBA observations than the LERGs, suggesting that they may
have more compact radio emission: $25\pm 3$ per cent of HERGs in the sample
are detected in the VLBA catalogue, compared to $17\pm 3$ per cent of LERGs
and $15\pm 1$ per cent of probable LERGs. This supports the findings of
Whittam et al. (2016) that HERGs are more dominated by emission from their
cores than LERGs.

Figure 10: Stellar mass (top) and star formation rate (bottom) as a function
of redshift for the HERGs (red), LERGs (blue), probable LERGs (black) and
unclassified RLAGN (cyan) in this sample (small shapes). The greyscale shows
the distribution of galaxies in the full $K_{s}$-band selected optical/near-
infrared catalogue, the large yellow diamonds show the medians in each
redshift bin for this sample. The other large solid shapes show the median
stellar mass/star-formation rate for the different radio samples in each
redshift bin.Stellar masses and star-formation rates shown in this plot are
estimated from LePhare, rather than the AGNfitter values used in the rest of
this paper, see text for details.

###  5.2 Accretion Rates

Whittam et al. (2018) studied $\sim 1000$ radio galaxies selected from a VLA
survey of Stripe 82 (Heywood et al., 2016), and found significantly more
overlap in the accretion rates of the HERGs and LERGs than has been found in
previous studies (Best & Heckman, 2012; Mingo et al., 2014) at higher radio
luminosities. Here we extend this study to even lower radio luminosities using
the MIGHTEE Early Science data. For this section we limit the study to sources
with a good match only (flag $=$ 100 or 120, see Prescott et al. (in prep) for
further details), and sources with a good fit in AGNfitter (characterised by
log likelihood > -20) leaving a sample of 819 radio-loud AGN. We looked at the
SEDs of all sources excluded for having a poor fit to ensure they do not
represent e.g. a particular class of source. There are a variety of reasons
for poor fits, such as low signal to noise or scatter in the photometry, but
no pattern is evident.

Although we do not have line measurements from optical spectra for the
majority of the sources in the MIGHTEE sample, we are able to estimate the AGN
bolometric luminosity ($L_{\rm bol}$) from AGNfitter by integrating the best-
fit rest-frame direct AGN emission (the BB component) from 0.1 $\muup$m to 1
keV, and adding in the torus component (TO component).

The mechanical luminosity of the radio jet ($L_{\rm mech}$) was estimated from
the 1.4 GHz luminosity using the relationship from Cavagnolo et al. (2010),
$L_{\rm mech}=7.3\times
10^{36}(L_{1.4~{}\rm{GHz}}/10^{24}\rm{W~{}Hz^{-1}})^{0.7}$ W, assuming a
spectral index of 0.7, and taking into account the variation in effective
frequency across the MIGHTEE radio image to convert radio luminosities to rest
frame 1.4 GHz. This scaling relation was derived by studying the energies
associated with the cavities in hot X-ray gas evacuated by radio jets, and the
scatter is found to be around 0.7 dex (Cavagnolo et al., 2010). This scatter
may be partly due to variations in the particle content of radio jets.
Croston, Ineson, & Hardcastle (2018) studied the particle composition of radio
jets and found no systematic difference between HERGs and LERGs, suggesting
that any difference in radio luminosity observed between the two populations
translates (on average) to a difference in mechanical powers. The Cavagnolo et
al. (2010) relation used here is consistent with the Willott et al. (1999)
scaling relation if the ratio between non-radiating particles and relativistic
elections is assumed to be several tens of thousands (this is supported by
results in the literature, e.g. Dunn, Fabian, & Taylor 2005; Bîrzan et al.
2008). We note that the Cavagnolo et al. relation was derived for powerful
radio galaxies so may not be entirely applicable for the lower-powered radio
galaxies studied in this work, however we choose to use it to be consistent
with previous work (e.g. Best & Heckman 2012).

The black hole masses were estimated from stellar masses using the Häring &
Rix (2004) relation: $M_{\textrm{BH}}\sim 0.0014M_{\ast}$, which has a scatter
of $\sim 0.3$ dex. The Eddington limit for each source was then calculated as
follows: $L_{\textrm{Edd}}=1.3\times
10^{31}M_{\textrm{BH}}/M_{\odot}\textrm{W}$. The Eddington-scaled accretion
rate for each source was calculated as $\lambda=(L_{\rm bol}+L_{\rm
mech})/L_{\rm Edd}$. Although there is significant scatter on the scaling
relations used to estimate the accretion rates, as discussed, we do not expect
this to introduce a systematic effect. It is still informative to compare the
accretion rates estimated in this way for the different samples discussed in
this paper.

Figure 11: Distribution of Eddington-scaled accretion rates for HERGs (red
solid line), LERGs (blue dashed), probable LERGs (black dotted) and
unclassified radio-loud AGN (cyan dot-dashed). The top panel shows the
combined accretion rates estimated from the radiative and mechanical
luminosities, while the bottom panel shows the accretion rates considering
only the radiative luminosity.

The distribution of Eddington-scaled accretion rates for the HERGs, LERGs,
probable LERGs and unclassified radio-loud AGN are shown in Fig. 11. It is
clear that there is a significant overlap in the distribution of accretion
rates of the HERGs and the LERGs in this sample. It appears that the
unclassified radio-loud AGN have higher accretion rates than the sources
classified as HERGs and LERGs, however this is a selection effect. Sources are
unclassified when we do not have enough data to robustly classify them as
HERGs or LERGs, which is more likely to be the case at higher redshifts, as
can be seen from Fig. 6. At these higher redshifts (typically $z\gtrsim 2$),
we are only able to detect AGN with high accretion rates, resulting in the
unclassified sources we do detect having some of the highest accretion rates.
This effect can be seen more clearly in Fig. 12, which shows the Eddington
scaled accretion rates as a function of redshift.

Fig. 12 shows that although there is significant overlap in the accretion
rates of HERGs and LERGs, nearly all of the sources with high Eddington-scaled
accretion rates ($\gtrsim 0.1$) are HERGs or unclassified sources (compared to
the divide at $\sim 0.01$ found by past work). Previous studies of radio
galaxy accretion rates by Best & Heckman (2012) and Mingo et al. (2014) also
found that all of the LERGs have accretion rates < 0.01; the difference with
our sample is that as well as the efficiently-accreting HERGs, we are also
detecting significant numbers of HERGs with Eddington-scaled accretion rates
well below this value (between $10^{-3}$ and $10^{-2}$). This is due to the
fact that MIGHTEE allows us to probe lower luminosities and higher redshifts
than previous studies, as is illustrated by Fig. 1. Having said that, the
small number of sources with extremely low accretion rates, below $10^{-3}$ of
their Eddington rate, are all LERGs or probable LERGs.

Due to the small volume probed at low redshifts ($z<0.7$), MIGHTEE detects
very few of the rarer, powerful AGN which dominate both the Best & Heckman
(2012) and Whittam et al. (2018) samples at these redshifts. Our sample is
therefore lacking the efficiently accreting HERGs which constitute the bulk of
the HERG population in Best & Heckman (2012) and Whittam et al. (2018).

While the scaling relation used to estimate the mechanical luminosities in
this work is the same as that used by Best & Heckman (2012) and Whittam et al.
(2018), those two studies use L${}_{\textrm{[OIII]}}$ to estimate the AGN
bolometric luminosity, whereas we use the results from the SED fitting. While
we do not expect this to affect the results presented here, we note that the
bolometric luminosities may not be directly comparable with the work by Best &
Heckman (2012) and Whittam et al. (2018).

It is possible that misclassified sources could be somewhat responsible for
part of the overlap in accretion rates observed in our work. While we are
confident that sources classified as HERGs are indeed HERGs, it is possible
that some of the sources in our LERG and ‘probable LERG’ samples are actually
HERGs, where signs of efficient accretion have been missed. This is
particularly true for the ‘probable LERG’ class, where the limitations of the
X-ray data available mean we are unable to rule out accretion-related X-ray
emission. This means that some of the LERGs and probable-LERGs with high
Eddington-scaled accretion rates could be misclassified HERGs, but this does
not explain the slowly-accreting HERGs observed.

Figure 12: Eddington-scaled accretion rates as a function of redshift for the
different source classifications (HERGs = red pluses, LERGs = blue crosses,
probable LERGs = black circles and unclassified RLAGN = cyan circles). The top
panel shows accretion rates considering only the radiative luminosity, while
the bottom panel shows the combined radiative and mechanical luminosities.

Thomas et al. (2021) investigated the accretion rate of HERGs and LERGs in the
Simba simulation, which probes a similar volume to MIGHTEE and is therefore
comparable as it also does not contain the high luminosity sources found in
larger-area surveys. They found that the simulation predicts no obvious
difference in the Eddington fractions of the two classes at $z=0$. The results
from MIGHTEE are in agreement with this prediction, although the small sample
size at $z<0.1$ means that we cannot rule out other scenarios.

We have not included error bars on Figs. 12 and 13 to avoid cluttering the
figures, but note that the approximate size of the uncertainties can be seen
by the error bars in Fig. 14. In addition to the plotted uncertainties, there
is significant scatter on the scaling relations used to estimate the
mechanical luminosity (0.7 dex) and black hole mass (0.3 dex) in this work.
There is no evidence that this scatter will introduce a systematic effect, so
we do not expect this to affect the overall trends for the populations
discussed here. We also note that the mechanical luminosities and black hole
masses were estimated using the same scaling relations in Whittam et al.
(2018), where a difference in the accretion rates of the HERG and LERG samples
was observed, suggesting that the scatter in the scaling relations is not
responsible for the large overlap observed in this work.

###  5.3 Host galaxy properties as a function of accretion rate

Whittam et al. (2018) found that the radio-loud AGN host galaxy properties
varied continuously with accretion rate, with the most slowly accreting
sources being hosted by the most massive galaxies with the oldest stellar
population, while the sources accreting matter more rapidly have lower-mass
hosts and younger stellar populations. This is consistent with the idea that
the accretion rate of a galaxy is linked to the supply of cold gas, with the
sources which have a readily available gas supply having both high accretion
rates and young stellar populations.

Fig. 13 shows the host galaxy properties of the MIGHTEE radio-loud AGN as a
function of Eddington-scaled accretion rate. Sources are coloured according to
their redshift. This figure highlights a similar trend to that found by
Whittam et al. (2018); the sources accreting more efficiently (with higher
Eddington-scaled accretion rates) have higher star-formation rates and lower
stellar masses. Selection effects mean that we are only able to detect the
most slowly accreting sources (with Eddington-scaled accretion rate fractions
($<10^{-2}$) in the most massive galaxies (with stellar masses $\gtrsim
10^{10}\textrm{M}_{\odot}$ at $z\sim 0.5$). However, source with higher
accretion rates, which we are able to detect across the full range of stellar
masses, tend to be found in host galaxies with lower stellar masses. For
example, we find that none of galaxies that lie beyond the knee in the stellar
mass function at $\textrm{log}_{10}(\textrm{M}/\textrm{M}_{\odot})\sim 10.8$
have Eddington-scaled accretion rates in excess of 1.

We have seen that in the MIGHTEE sample HERGs and LERGs are hosted by very
similar galaxies (Section 5.1) and accretion rate is not a good predictor of
whether a source is a HERG or LERG (Section 5.2). It seems that the host
galaxy properties are more linked to the Eddington-scaled accretion rate than
HERG/LERG classification, raising the question as to whether or not the
HERG/LERG class is meaningful as we extend out parameter space to the lower
radio luminosity population.

Figure 13: Host galaxy properties of radio-loud AGN as a function of
Eddington-scaled accretion rate. The top panel shows stellar mass and the
bottom panels shows star-formation rate. The black dotted line in the top
panel shows the selection limit at $z=0.5$; at this redshift we can only
detect sources in the region above this line. The colour bar shows the
redshift of each source.

###  5.4 The relationship between AGN power and black hole mass

In order to avoid incompleteness over a large redshift range, we now split the
sample into redshift slices, and for each redshift range we consider only
sources with accretion rates where we know we are complete in that redshift
range. This selection is demonstrated by the red box in the left hand column
of Fig. 14. The remaining columns of Fig. 14 show how the bolometric and
mechanical luminosities of the sources in each redshift slice vary with
stellar mass. We find no correlation between bolometric luminosity and stellar
mass (the Pearson’s correlation coefficient $<|0.3|$ in all redshift bins out
to $z=4$), suggesting that the radiative power of these AGN is independent of
stellar mass. As there is a tight correlation between a galaxy’s stellar mass
and the mass of the supermassive black hole, this implies that the radiative
power of these radio-loud AGN is independent of the supermassive black hole
mass.

When we consider the mechanical power, as shown by the third column in Fig.
14, a trend becomes evident. While sources with low mechanical powers are
found in host galaxies with a range of stellar masses, higher powered jets are
only found in galaxies with stellar masses greater than
$10^{10.5}\textrm{M}_{\odot}$. As there is a tight correlation between a
galaxy’s stellar mass and the mass of the supermassive black hole, this
implies that a SMBH above a certain mass is required to launch a powerful jet.
Using the stellar mass - black hole mass relation of Häring & Rix (2004), the
stellar mass above which the galaxies in our sample appear to be able to
launch a powerful radio jet corresponds to a black hole mass of $\sim
10^{7.8}\textrm{M}_{\odot}$.

The jet power at which this switch between being hosted by galaxies with a
range of masses, to only being hosted by the most massive galaxies, increases
with redshift. In the lowest redshift bin ($0.25<z<0.5$) a large supermassive
black hole ($M_{\textrm{BH}}>10^{7.5}\textrm{M}_{\odot}$ is required to launch
jets with mechanical powers $>10^{36}$ erg/s, while at higher redshifts
($z>0.5$), black holes of this size are required to launch jets with
mechanical powers $>10^{37}$ erg/s, while less powerful jets are found in host
galaxies with a range of black hole masses. This may suggest that it is easier
to launch and sustain a powerful jet at higher redshifts, likely due to the
availability of gas to provide fuel for accretion. However, further data is
required to confirm this, as the sample studied here does not contain
similarly powerful sources at low redshifts, due to the small volume probed at
these redshifts.

The final column of Fig. 14 shows the ratio between the mechanical and
radiative powers of the radio-loud AGN in this sample as a function of stellar
mass/black hole mass. Across the redshift range, only galaxies with
supermassive black hole masses $\gtrsim 10^{8}\textrm{M}_{\odot}$ host AGN
with $L_{\textrm{mech}}/L_{\textrm{bol}}>1$. This suggests that a large black
hole mass is required to launch and maintain a radio jet that is powerful
relative to the radiative output. This is discussed further in the next
section.

Figure 14: Each row corresponds to a redshift and accretion-rate selected
sample, demonstrated by the red box in the figure in the first (left) column,
which shows the total accretion rate ($L_{\textrm{mech}}+L_{\textrm{bol}}$) as
a function of redshift. The top row shows sources with $0.2<z<0.5$ and
$1.2\times 10^{36}<(L_{\textrm{mech}}+L_{\textrm{bol}})/\textrm{W}<5\times
10^{37}$. The second row shows sources with $0.5<z<1.0$ and $5\times
10^{36}<(L_{\textrm{mech}}+L_{\textrm{bol}})/\textrm{W}<1\times 10^{38}$. The
third row shows sources with $1.0<z<1.5$ and $1\times
10^{37}<(L_{\textrm{mech}}+L_{\textrm{bol}})/\textrm{W}<2\times 10^{38}$. The
bottom row shows sources with $1.5<z<2.0$ and $2\times
10^{37}<(L_{\textrm{mech}}+L_{\textrm{bol}})/\textrm{W}<5\times 10^{38}$. The
second column shows stellar mass as a function of bolometric luminosity for
the sources selected in this way. The third column shows stellar mass /
supermassive black hole mass as a function of mechanical luminosity, and the
final (right-hand) column is the ratio
L${}_{\textrm{mech}}$/L${}_{\textrm{bol}}$.

##  6 Discussion

In the previous section we have investigated the properties of radio-loud AGN
with lower radio powers and at higher redshifts than have been studied by
previous work (see Fig. 1). In contrast to previous studies at higher radio
powers, we find very little difference in the host galaxy properties of HERGs
and LERGs (Section 5.1). We also find considerable overlap in the Eddington-
scaled accretion rates of the HERGs and LERGs; while the small number of
sources accreting very inefficiently (with Eddington-scaled accretion rates
$<10^{-3}$) are all LERGs, the accretion rates of the bulk of the population
of HERGs and LERGs are indistinguishable (Section 5.2). This is in contrast to
previous works which have found a dichotomy in the accretion rates of the two
classes (Best & Heckman, 2012; Mingo et al., 2014), due to the fact that the
MIGHTEE survey is probing higher redshifts and lower radio powers than
previous studies, so is detecting a significant population of slowly accreting
HERGs which were not detectable by previous work, together with the fact that
we are not sensitive to the rare, efficiently accreting HERGs at low redshifts
which dominated the previous samples. It is possible that source
misclassification could be partly responsible for the increased overlap in
accretion rates observed, as it is possible that some of the LERGs and
probable-LERGs in our sample with high Eddington-scaled accretion rates could
be misclassified HERGs. However, source misclassification is unlikely to be
responsible for inefficiently-accreting HERGs in our sample.

Taken together with the results of Whittam et al. (2018), who found a
difference in the accretion rates of the two classes but considerably more
overlap than had been found previously, these results suggest that as we probe
lower radio powers and higher redshifts, the HERG and LERG populations are
becoming increasingly similar, both in terms of Eddington-scaled accretion
rates and host galaxy properties.

Although there is no significant difference between the HERGs and LERGs in our
sample, there is a relationship between host galaxy properties and Eddington-
scaled accretion rate; the most-efficiently accreting sources are found in
galaxies with lower stellar masses and higher star-formation rates than the
sources with higher Eddington-scaled accretion rates (Section 5.3). This fits
in with the widely-accepted scenario that these sources contain a supply of
cold gas, which provides the necessary supply of fuel to both accrete
efficiently and form stars. What is noteable, however, is that this trend does
not seem to translate into HERG/LERG classification; many of the sources with
low Eddington-scaled accretion rates also have low star-formation rates
suggesting that they do not have a plentiful supply cold gas, but are
classified as HERGs. This means that despite accreting slowly they display at
least one characteristic usually associated with efficient accretion, such as
X-ray emission or the mid-infrared signature of a dusty torus. This implies
that as we reach lower radio powers and higher redshifts the situation becomes
less clear-cut than it is for more powerful radio galaxies in the local
universe.

Recent work by Kondapally et al. (2022) identified a population of LERGs
hosted by star-forming (rather than quiescent) galaxies at $z>0.5$, which they
suggest may be fuelled by cold gas, in a similar way to HERGs, rather than via
the hot gas mechanism which is typically thought to fuel LERGs in quiescent
galaxies. This again raises the question as to whether the distinction between
HERGs and LERGs is meaningful for this higher-redshift and lower-powered
population.

In Section 5.4 we found that while AGN with relatively weak radio jets
compared to the radiative emission from the nucleus (with
$L_{\textrm{mech}}/L_{\textrm{bol}}<1$) are found in galaxies with SMBH masses
across the full range found in our sample
($6<\textrm{log}_{10}(\textrm{M}_{\textrm{BH}}/\textrm{M}_{\odot})<8.5$), all
galaxies hosting jets with $L_{\textrm{mech}}/L_{\textrm{bol}}>1$ have black
hole masses $\gtrsim 10^{7.8}M_{\odot}$. This suggests that a large black hole
mass is required to launch and sustain a powerful radio jet. Our results show
that this holds out to at least $z\sim 2$. This is in agreement with McLure &
Jarvis (2004), who found that the radio-loudness of quasars is dependent on
black hole mass, with all the genuinely radio-loud quasars in their sample
having M${}_{\textrm{BH}}\geq 10^{8}\textrm{M}_{\odot}$. Herbert et al. (2011)
also found that radio luminosity scales with black hole mass. Baldi, Capetti,
& Massaro (2018) suggest that only when a supermassive black hole has both a
high mass and high spin is it able to sustain powerful radio jets for long
enough to produce an extended radio galaxy. This could explain why in our
sample a large black hole mass seems to be required to sustain a powerful
radio jet, but only a fraction of the radio-loud AGN which have large black
hole masses produce powerful jets.

The spin of a supermassive black hole depends on both the accretion and the
merger histories of the system. Major mergers are the main mechanism for
spinning-up black holes (Martínez-Sansigre & Rawlings, 2011), while chaotic
accretion reduces the spin of the central black hole. Galaxies with higher
masses are more likely to have undergone more mergers, and therefore have a
higher black hole spin. Supermassive black hole spin also evolves with
redshift; Martínez-Sansigre & Rawlings (2011) showed that galaxies at
$z\gtrsim 1$ are expected to have lower spins than those in the local
universe, where a significant fraction will have high spins.

Theoretical work suggests there is a connection between jet speed and black
hole spin (Blandford & Znajek, 1977; Thorne, Price, & MacDonald, 1986; Meier,
1999), where black holes with higher spin values are able to produce more
powerful relativistic jets. High spins may be required to launch a jet at all;
Maraschi et al. (2012) use general-relativistic magnetohydrodynamic (GRMHD)
simulations and gamma ray observations of blazars to argue SMBH spins $>0.5$
are required to launch a relativistic jet from a black hole. It has been
suggested that black hole spin could therefore be responsible for the radio
loud/radio quiet dichotomy, with AGN where the central SMBH is spinning faster
producing radio jets, while those with lower spins result in radio quiet AGN.
However, observational evidence for the connection between black hole spin and
the jet is inconclusive. Several studies support the idea that spin is
necessary for jet production (e.g. Narayan & McClintock 2012; Zhang, Zhang, &
Zhang 2016), while other studies of both X-ray binaries (Fender, Gallo, &
Russell, 2010) and AGN (van Velzen & Falcke, 2013) find no evidence for a
connection between black hole spin and jet power.

However while a high black hole spin may be necessary to produce a powerful
radio jet, it is not sufficient. Radio-quiet AGN with high spins have been
observed (e.g. Reynolds 2014), showing that not all AGN with high spin have a
jet. There are clearly other factors involved in launching and sustaining a
powerful radio jet, such as black hole mass, accretion rate, the fuel
available and magnetic fields.

It is also possible that black hole spin is one of the reasons for the
difference between the properties of HERGs and LERGs observed in this study
and those observed in previous studies. As previous studies are limited to
high radio luminosities, and therefore powerful radio jets, they may
preferentially select SMBHs with high spin. Additionally, these studies were
limited to lower redshifts, where SMBHs would have higher spins in this
scenario. The radio galaxies in this sample extend to lower radio luminosities
and higher redshifts, so may include SMBHs with lower spins as well as those
with high spins. This range of spin values could explain why we see a larger
range of jet powers and accretion efficiencies for HERGs and LERGs, resulting
in a larger overlap between the two populations.

##  7 Conclusions

In this work we have classified the radio sources in the MIGHTEE Early Science
data in the COSMOS field, allowing us to probe the faint radio source
population down to $S_{1.4~{}\textrm{GHz}}\sim 20~{}\muup$Jy, and used this
sample to investigate the nature of radio-excess AGN at both lower radio
powers and higher redshifts than previous studies. Making use of the extensive
multi-wavelength data in the COSMOS field, we identify 1806 AGN and 767 SFG,
with a further 2040 sources classified as ‘probable SFGs’. The radio-loud AGN
are further classified as high-excitation and low-excitation radio galaxies,
finding 249 HERGs, 150 LERGs and a further 782 ‘probable LERGs’. This
classification catalogue is released with this work.

We have used this sample to investigate the properties of radio-loud AGN with
$10^{20}<L/\textsc{W Hz}^{-1}<10^{27}$ out to $z\sim 5$, probing both lower
radio powers and higher redshifts than previous studies of radio galaxies. Our
main findings are:

  * •

We find no significant difference in the host galaxy properties of the HERGs
and LERGs in the MIGHTEE sample, except for the lowest redshift bin ($z<0.4$)
where LERGs are hosted by galaxies with higher stellar masses than HERGs.

  * •

There is considerable overlap in the accretion rates of the HERGs and LERGs in
our sample. This is in contrast to previous works which have found a dichotomy
in the accretion rates of the two classes (Best & Heckman, 2012; Mingo et al.,
2014), due to the fact that the MIGHTEE survey is probing both higher
redshifts and lower radio powers than previous studies.

  * •

Sources with higher Eddington-scaled accretion rates tend to be hosted by
galaxies with higher star-formation rates and smaller stellar masses.

  * •

As it is becoming increasingly hard to separate HERGs and LERGs into separate
populations at higher redshifts and lower radio powers, we suggest that this
classification may not be a helpful way to think about the radio galaxy
population, and instead one should consider how properties vary with
Eddington-scaled accretion rate.

  * •

A black hole mass $\gtrsim 10^{7.8}~{}\textrm{M}_{\odot}$ is required to power
a jet with $L_{\textrm{mech}}/L_{\textrm{bol}}>1$; we discuss that both a high
black hole mass and a high black hole spin may be necessary to launch and
sustain a radio jet with a high mechanical power relative to the radiative
output of the AGN.

## Acknowledgements

The authors thank the anonymous referee for their careful reading of the paper
and insightful comments which improved the quality of the manuscript. The
MeerKAT telescope is operated by the South African Radio Astronomy
Observatory, which is a facility of the National Research Foundation, an
agency of the Department of Science and Innovation. We acknowledge the use of
the ilifu cloud computing facility – www.ilifu.ac.za, a partnership between
the University of Cape Town, the University of the Western Cape, the
University of Stellenbosch, Sol Plaatje University, the Cape Peninsula
University of Technology and the South African Radio Astronomy Observatory.
The Ilifu facility is supported by contributions from the Inter-University
Institute for Data Intensive Astronomy (IDIA – a partnership between the
University of Cape Town, the University of Pretoria, the University of the
Western Cape and the South African Radio astronomy Observatory), the
Computational Biology division at UCT and the Data Intensive Research
Initiative of South Africa (DIRISA). The authors acknowledge the Centre for
High Performance Computing (CHPC), South Africa, for providing computational
resources to this research project. This work is based on data products from
observations made with ESO Telescopes at the La Silla Paranal Observatory
under ESO programme ID 179.A-2005 (Ultra-VISTA) and ID 179.A- 2006(VIDEO) and
on data products produced by CALET and the Cambridge Astronomy Survey Unit on
behalf of the Ultra-VISTA and VIDEO consortia. Based on observations obtained
with MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-
France-Hawaii Telescope (CFHT) which is operated by the National Research
Coun- cil (NRC) of Canada, the Institut National des Science de l’Univers of
the Centre National de la Recherche Scientifique (CNRS) of France, and the
University of Hawaii. This work is based in part on data products produced at
Terapix available at the Canadian Astronomy Data Centre as part of the Canada-
France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and
CNRS. The Hyper Suprime-Cam (HSC) collaboration includes the astronomical
communities of Japan and Taiwan, and Princeton University. The HSC
instrumentation and soft- ware were developed by the National Astronomical
Observatory of Japan (NAOJ), the Kavli Institute for the Physics and
Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High
Energy Accelerator Research Organization (KEK), the Academia Sinica Institute
for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University.
Funding was contributed by the FIRST program from Japanese Cabinet Office, the
Ministry of Education, Culture, Sports, Science and Technology (MEXT), the
Japan Society for the Promotion of Science (JSPS), Japan Science and
Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK,
ASIAA, and Princeton University. This research was funded in whole, or in
part, by the UK Science and Technology Facilities Council [ST/N000919/1]. For
the purpose of Open Access, the author has applied a CC BY public copyright
licence to any Author Accepted Manuscript version arising from this
submission. IHW, MJJ and PWH acknowledge generous support from the Hintze
Family Charitable Foundation through the Oxford Hintze Centre for
Astrophysical Surveys. IH and MJJ acknowledge support from the UK Science and
Technology Facilities Council [ST/N000919/1]. CLH acknowledges support from
the Leverhulme Trust through an Early Career Research Fellowship. NM
acknowledges the support of the LMU Faculty of Physics. NJA acknowledges
support from the European Research Council (ERC) Advanced Investigator Grant
EPOCHS (788113). MG was partially supported by the Australian Government
through the Australian Research Council’s Discovery Projects funding scheme
(DP210102103). LKM and NLT were supported by the Medical Research Council
[MR/T042842/1]. RB acknowledges support from an STFC Ernest Rutherford
Fellowship [grant number ST/T003596/1]. Y.A. acknowledges financial support by
NSFC grants 12173089 and 11933011. LM, IP and MV acknowledge financial support
from the Italian Ministry of Foreign Affairs and International Cooperation
(MAECI Grant Number ZA18GR02) and the South African Department of Science and
Innovation’s National Research Foundation (DSI-NRF Grant Number 113121) under
the ISARP RADIOSKY2020 Joint Research Scheme. DJBS acknowledges support from
the UK Science and Technology Facilities Council (STFC) under grant
[ST/V000624/1] JA acknowledges financial support from the Science and
Technology Foundation (FCT, Portugal) through research grants PTDC/FIS-
AST/29245/2017, UIDB/04434/2020 and UIDP/04434/2020. This research has made
use of NASA’s Astrophysics Data System. This research used Astropy, a
community-developed core Python package for Astronomy (Astropy Collaboration
et al., 2013, 2018). This work made use of the cubehelix colour scheme (Green,
2011). We also used Topcat (Taylor, 2005, 2011).

## Data Availability

The release of the MIGHTEE Early Science continuum data used for this work is
discussed in depth in Heywood et al. (2022), details of the data release and
how to access the data are provided there. The cross-matched catalogue and its
release is described in the work of Prescott et al. (in prep) and will be
released in accompaniment with their work. The catalogue presented in this
article is summarised in Appendix A and is published with this article as
supplementary material.

## References

  * Abolfathi et al. (2018) Abolfathi B., Aguado D. S., Aguilar G., Allende Prieto C., Almeida A., Ananna T. T., Anders F., et al., 2018, ApJS, 235, 42.
  * Adams et al. (2021) Adams N. J., Bowler R. A. A., Jarvis M. J., Häußler B., Lagos C. D. P., 2021, MNRAS, 506, 4933.
  * Adams et al. (2020) Adams N. J., Bowler R. A. A., Jarvis M. J., Häußler B., McLure R. J., Bunker A., Dunlop J. S., et al., 2020, MNRAS, 494, 1771.
  * Almosallam et al. (2016) Almosallam I. A., Lindsay S. N., Jarvis M. J., Roberts S. J., 2016, MNRAS, 455, 2387.
  * Almosallam, Jarvis, & Roberts (2016) Almosallam I. A., Jarvis M. J., Roberts S. J., 2016, MNRAS, 462, 726.
  * Arnouts & Ilbert (2011) Arnouts S., Ilbert O., 2011, ascl.soft. ascl:1108.009
  * Ashby et al. (2018) Ashby M. L. N., Caputi K. I., Cowley W., Deshmukh S., Dunlop J. S., Milvang-Jensen B., Fynbo J. P. U., et al., 2018, ApJS, 237, 39.
  * Ashby et al. (2013) Ashby M. L. N., Willner S. P., Fazio G. G., Huang J.-S., Arendt R., Barmby P., Barro G., et al., 2013, ApJ, 769, 80.
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille T. P., Tollerud E. J., Greenfield P., Droettboom M., Bray E., Aldcroft T., et al., 2013, A&A, 558, A33.
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan A. M., Sipőcz B. M., Günther H. M., Lim P. L., Crawford S. M., Conseil S., et al., 2018, AJ, 156, 123.
  * Baldi, Capetti, & Massaro (2018) Baldi R. D., Capetti A., Massaro F., 2018, A&A, 609, A1.
  * Baldwin, Phillips, & Terlevich (1981) Baldwin J. A., Phillips M. M., Terlevich R., 1981, PASP, 93, 5.
  * Best et al. (2014) Best P. N., Ker L. M., Simpson C., Rigby E. E., Sabater J., 2014, MNRAS, 445, 955.
  * Best & Heckman (2012) Best P. N., Heckman T. M., 2012, MNRAS, 421, 1569. doi:10.1111/j.1365-2966.2012.20414.x
  * Best et al. (2007) Best P. N., von der Linden A., Kauffmann G., Heckman T. M., Kaiser C. R., 2007, MNRAS, 379, 894.
  * Best et al. (2005) Best P. N., Kauffmann G., Heckman T. M., Brinchmann J., Charlot S., Ivezić Ž., White S. D. M., 2005, MNRAS, 362, 25.
  * Blandford & Znajek (1977) Blandford R. D., Znajek R. L., 1977, MNRAS, 179, 433.
  * Blundell & Rawlings (2001) Blundell K. M., Rawlings S., 2001, ApJL, 562, L5.
  * Bowler et al. (2020) Bowler R. A. A., Jarvis M. J., Dunlop J. S., McLure R. J., McLeod D. J., Adams N. J., Milvang-Jensen B., et al., 2020, MNRAS, 493, 2059.
  * Briggs (1995) Briggs D. S., 1995, AAS
  * Burns (1990) Burns J. O., 1990, AJ, 99, 14.
  * Bîrzan et al. (2008) Bîrzan L., McNamara B. R., Nulsen P. E. J., Carilli C. L., Wise M. W., 2008, ApJ, 686, 859.
  * Calistro Rivera et al. (2016) Calistro Rivera G., Lusso E., Hennawi J. F., Hogg D. W., 2016, ApJ, 833, 98. doi:10.3847/1538-4357/833/1/98
  * Cattaneo et al. (2009) Cattaneo A., Faber S. M., Binney J., Dekel A., Kormendy J., Mushotzky R., Babul A., et al., 2009, Natur, 460, 213.
  * Cavagnolo et al. (2010) Cavagnolo K. W., McNamara B. R., Nulsen P. E. J., Carilli C. L., Jones C., Bîrzan L., 2010, ApJ, 720, 1066.
  * Ching et al. (2017) Ching J. H. Y., Croom S. M., Sadler E. M., Robotham A. S. G., Brough S., Baldry I. K., Bland-Hawthorn J., et al., 2017, MNRAS, 469, 4584.
  * Civano et al. (2015) Civano F., Hickox R. C., Puccetti S., Comastri A., Mullaney J. R., Zappacosta L., LaMassa S. M., et al., 2015, ApJ, 808, 185.
  * Clewley & Jarvis (2004) Clewley L., Jarvis M. J., 2004, MNRAS, 352, 909.
  * Coil et al. (2011) Coil A. L., Blanton M. R., Burles S. M., Cool R. J., Eisenstein D. J., Moustakas J., Wong K. C., et al., 2011, ApJ, 741, 8.
  * Condon (1992) Condon J. J., 1992, ARA&A, 30, 575.
  * Cool et al. (2013) Cool R. J., Moustakas J., Blanton M. R., Burles S. M., Coil A. L., Eisenstein D. J., Wong K. C., et al., 2013, ApJ, 767, 118.
  * Croston, Ineson, & Hardcastle (2018) Croston J. H., Ineson J., Hardcastle M. J., 2018, MNRAS, 476, 1614.
  * Davé et al. (2019) Davé R., Anglés-Alcázar D., Narayanan D., Li Q., Rafieferantsoa M. H., Appleby S., 2019, MNRAS, 486, 2827.
  * de Zotti et al. (2010) de Zotti G., Massardi M., Negrello M., Wall J., 2010, A&ARv, 18, 1.
  * Delhaize et al. (2017) Delhaize J., Smolčić V., Delvecchio I., Novak M., Sargent M., Baran N., Magnelli B., et al., 2017, A&A, 602, A4.
  * Delvecchio et al. (2021) Delvecchio I., Daddi E., Sargent M. T., Jarvis M. J., Elbaz D., Jin S., Liu D., et al., 2021, A&A, 647, A123.
  * Delvecchio et al. (2017) Delvecchio I., Smolčić V., Zamorani G., Lagos C. D. P., Berta S., Delhaize J., Baran N., et al., 2017, A&A, 602, A3.
  * Donley et al. (2012) Donley J. L., Koekemoer A. M., Brusa M., Capak P., Cardamone C. N., Civano F., Ilbert O., et al., 2012, ApJ, 748, 142.
  * Duncan et al. (2018) Duncan K. J., Jarvis M. J., Brown M. J. I., Röttgering H. J. A., 2018, MNRAS, 477, 5177.
  * Dunn, Fabian, & Taylor (2005) Dunn R. J. H., Fabian A. C., Taylor G. B., 2005, MNRAS, 364, 1343.
  * Elvis et al. (2009) Elvis M., Civano F., Vignali C., Puccetti S., Fiore F., Cappelluti N., Aldcroft T. L., et al., 2009, ApJS, 184, 158.
  * Fabian (2012) Fabian A. C., 2012, ARA&A, 50, 455.
  * Fanaroff & Riley (1974) Fanaroff B. L., Riley J. M., 1974, MNRAS, 167, 31P.
  * Fender, Gallo, & Russell (2010) Fender R. P., Gallo E., Russell D., 2010, MNRAS, 406, 1425.
  * Furusawa et al. (2016) Furusawa H., Kashikawa N., Kobayashi M. A. R., Dunlop J. S., Shimasaku K., Takata T., Sekiguchi K., et al., 2016, ApJ, 822, 46.
  * Gendre et al. (2013) Gendre M. A., Best P. N., Wall J. V., Ker L. M., 2013, MNRAS, 430, 3086.
  * Green (2011) Green D. A., 2011, BASI, 39, 289
  * Griffin et al. (2010) Griffin M. J., Abergel A., Abreu A., Ade P. A. R., André P., Augueres J.-L., Babbedge T., et al., 2010, A&A, 518, L3.
  * Hardcastle, Evans, & Croston (2009) Hardcastle M. J., Evans D. A., Croston J. H., 2009, MNRAS, 396, 1929.
  * Hardcastle, Evans, & Croston (2006) Hardcastle M. J., Evans D. A., Croston J. H., 2006, MNRAS, 370, 1893.
  * Hardcastle, Evans, & Croston (2007) Hardcastle M. J., Evans D. A., Croston J. H., 2007, MNRAS, 376, 1849.
  * Hardcastle & Croston (2020) Hardcastle M. J., Croston J. H., 2020, NewAR, 88, 101539.
  * Hardcastle (2018) Hardcastle M., 2018, NatAs, 2, 273.
  * Hasinger et al. (2018) Hasinger G., Capak P., Salvato M., Barger A. J., Cowie L. L., Faisst A., Hemmati S., et al., 2018, ApJ, 858, 77.
  * Hatfield et al. (2020) Hatfield P. W., Almosallam I. A., Jarvis M. J., Adams N., Bowler R. A. A., Gomes Z., Roberts S. J., et al., 2020, MNRAS, 498, 5498.
  * Heckman & Best (2014) Heckman T. M., Best P. N., 2014, ARA&A, 52, 589.
  * Herbert et al. (2010) Herbert P. D., Jarvis M. J., Willott C. J., McLure R. J., Mitchell E., Rawlings S., Hill G. J., et al., 2010, MNRAS, 406, 1841.
  * Herbert et al. (2011) Herbert P. D., Jarvis M. J., Willott C. J., McLure R. J., Mitchell E., Rawlings S., Hill G. J., et al., 2011, MNRAS, 410, 1360.
  * Herrera Ruiz et al. (2017) Herrera Ruiz N., Middelberg E., Deller A., Norris R. P., Best P. N., Brisken W., Schinnerer E., et al., 2017, A&A, 607, A132.
  * Heywood et al. (2022) Heywood I., Jarvis M. J., Hale C. L., Whittam I. H., Bester H. L., Hugo B., Kenyon J. S., et al., 2022, MNRAS, 509, 2150.
  * Heywood et al. (2016) Heywood I., Jarvis M. J., Baker A. J., Bannister K. W., Carvalho C. S., Hardcastle M., Hilton M., et al., 2016, MNRAS, 460, 4433.
  * Hine & Longair (1979) Hine R. G., Longair M. S., 1979, MNRAS, 188, 111.
  * Hurley et al. (2017) Hurley P. D., Oliver S., Betancourt M., Clarke C., Cowley W. I., Duivenvoorden S., Farrah D., et al., 2017, MNRAS, 464, 885.
  * Häring & Rix (2004) Häring N., Rix H.-W., 2004, ApJL, 604, L89.
  * Jackson & Rawlings (1997) Jackson N., Rawlings S., 1997, MNRAS, 286, 241.
  * 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. (2016) Jarvis M., Taylor R., Agudo I., Allison J. R., Deane R. P., Frank B., Gupta N., et al., 2016, mks..conf, 6
  * Jonas (2009) Jonas J. L., 2009, IEEEP, 97, 1522.
  * Kondapally et al. (2022) Kondapally R., Best P. N., Cochrane R. K., Sabater J., Duncan K. J., Hardcastle M. J., Haskell P., et al., 2022, MNRAS, 513, 3742.
  * Laigle et al. (2016) Laigle C., McCracken H. J., Ilbert O., Hsieh B. C., Davidzon I., Capak P., Hasinger G., et al., 2016, ApJS, 224, 24.
  * Laing et al. (1994) Laing R. A., Jenkins C. R., Wall J. V., Unger S. W., 1994, ASPC, 54, 201
  * Lilly et al. (2009) Lilly S. J., Le Brun V., Maier C., Mainieri V., Mignoli M., Scodeggio M., Zamorani G., et al., 2009, ApJS, 184, 218.
  * Maraschi et al. (2012) Maraschi L., Colpi M., Ghisellini G., Perego A., Tavecchio F., 2012, JPhCS, 355, 012016.
  * Marchesi et al. (2016) Marchesi S., Civano F., Elvis M., Salvato M., Brusa M., Comastri A., Gilli R., et al., 2016, ApJ, 817, 34.
  * Martínez-Sansigre & Rawlings (2011) Martínez-Sansigre A., Rawlings S., 2011, MNRAS, 418, L84.
  * McCracken et al. (2012) McCracken H. J., Milvang-Jensen B., Dunlop J., Franx M., Fynbo J. P. U., Le Fèvre O., Holt J., et al., 2012, A&A, 544, A156.
  * McLure & Jarvis (2004) McLure R. J., Jarvis M. J., 2004, MNRAS, 353, L45.
  * Meier (1999) Meier D. L., 1999, ApJ, 522, 753.
  * Merloni & Heinz (2007) Merloni A., Heinz S., 2007, MNRAS, 381, 589.
  * Mingo et al. (2014) Mingo B., Hardcastle M. J., Croston J. H., Dicken D., Evans D. A., Morganti R., Tadhunter C., 2014, MNRAS, 440, 269.
  * Mingo et al. (2022) Mingo B., Croston J. H., Best P. N., Duncan K. J., Hardcastle M. J., Kondapally R., Prandoni I., et al., 2022, MNRAS, 511, 3250.
  * Mohan & Rafferty (2015) Mohan N., Rafferty D., 2015, ascl.soft. ascl:1502.007
  * Momcheva et al. (2016) Momcheva I. G., Brammer G. B., van Dokkum P. G., Skelton R. E., Whitaker K. E., Nelson E. J., Fumagalli M., et al., 2016, ApJS, 225, 27.
  * Narayan & McClintock (2012) Narayan R., McClintock J. E., 2012, MNRAS, 419, L69.
  * Narayan & Yi (1995) Narayan R., Yi I., 1995, ApJ, 452, 710.
  * Poglitsch et al. (2010) Poglitsch A., Waelkens C., Geis N., Feuchtgruber H., Vandenbussche B., Rodriguez L., Krause O., et al., 2010, A&A, 518, L2.
  * Pracy et al. (2016) Pracy M. B., Ching J. H. Y., Sadler E. M., Croom S. M., Baldry I. K., Bland-Hawthorn J., Brough S., et al., 2016, MNRAS, 460, 2.
  * Prescott et al. (2018) Prescott M., Whittam I. H., Jarvis M. J., McAlpine K., Richter L. L., Fine S., Mauch T., et al., 2018, MNRAS, 480, 707.
  * Prescott et al. (2016) Prescott M., Mauch T., Jarvis M. J., McAlpine K., Smith D. J. B., Fine S., Johnston R., et al., 2016, MNRAS, 457, 730.
  * Quataert (2003) Quataert E., 2003, ANS, 324, 435.
  * Reynolds (2014) Reynolds C. S., 2014, SSRv, 183, 277.
  * Rieke et al. (2004) Rieke G. H., Young E. T., Engelbracht C. W., Kelly D. M., Low F. J., Haller E. E., Beeman J. W., et al., 2004, ApJS, 154, 25.
  * Scoville et al. (2007) Scoville N., Abraham R. G., Aussel H., Barnes J. E., Benson A., Blain A. W., Calzetti D., et al., 2007, ApJS, 172, 38.
  * Shakura & Sunyaev (1973) Shakura N. I., Sunyaev R. A., 1973, A&A, 24, 337
  * Shirley et al. (2021) Shirley R., Duncan K., Campos Varillas M. C., Hurley P. D., Małek K., Roehlly Y., Smith M. W. L., et al., 2021, MNRAS, 507, 129.
  * Silverman et al. (2015) Silverman J. D., Kashino D., Sanders D., Kartaltepe J. S., Arimoto N., Renzini A., Rodighiero G., et al., 2015, ApJS, 220, 12.
  * Skelton et al. (2014) Skelton R. E., Whitaker K. E., Momcheva I. G., Brammer G. B., van Dokkum P. G., Labbé I., Franx M., et al., 2014, ApJS, 214, 24.
  * Smolčić (2009) Smolčić V., 2009, ApJL, 699, L43.
  * Smolčić et al. (2017a) Smolčić V., Novak M., Bondi M., Ciliegi P., Mooley K. P., Schinnerer E., Zamorani G., et al., 2017a, A&A, 602, A1.
  * Smolčić et al. (2017b) Smolčić V., Delvecchio I., Zamorani G., Baran N., Novak M., Delhaize J., Schinnerer E., et al., 2017b, A&A, 602, A2.
  * Steinhardt et al. (2014) Steinhardt C. L., Speagle J. S., Capak P., Silverman J. D., Carollo M., Dunlop J., Hashimoto Y., et al., 2014, ApJL, 791, L25.
  * Straatman et al. (2018) Straatman C. M. S., van der Wel A., Bezanson R., Pacifici C., Gallazzi A., Wu P.-F., Noeske K., et al., 2018, ApJS, 239, 27.
  * Szokoly et al. (2004) Szokoly G. P., Bergeron J., Hasinger G., Lehmann I., Kewley L., Mainieri V., Nonino M., et al., 2004, ApJS, 155, 271.
  * Tadhunter et al. (1998) Tadhunter C. N., Morganti R., Robinson A., Dickson R., Villar-Martin M., Fosbury R. A. E., 1998, MNRAS, 298, 1035.
  * Tanaka et al. (2017) Tanaka M., Hasinger G., Silverman J. D., Bickerton S., Furusawa H., Harikane Y., Hu E., et al., 2017, arXiv, arXiv:1706.00566
  * Taylor (2011) Taylor M., 2011, ascl.soft. ascl:1101.010
  * Taylor (2005) Taylor M. B., 2005, ASPC, 347, 29
  * Thomas et al. (2013) Thomas D., Steele O., Maraston C., Johansson J., Beifiori A., Pforr J., Strömbäck G., et al., 2013, MNRAS, 431, 1383.
  * Thomas et al. (2021) Thomas N., Davé R., Jarvis M. J., Anglés-Alcázar D., 2021, MNRAS, 503, 3492.
  * Thorne, Price, & MacDonald (1986) Thorne K. S., Price R. H., MacDonald D. A., 1986, bhmp.book
  * van der Wel et al. (2016) van der Wel A., Noeske K., Bezanson R., Pacifici C., Gallazzi A., Franx M., Muñoz-Mateos J. C., et al., 2016, ApJS, 223, 29.
  * van Velzen & Falcke (2013) van Velzen S., Falcke H., 2013, A&A, 557, L7.
  * Whittam et al. (2018) Whittam I. H., Prescott M., McAlpine K., Jarvis M. J., Heywood I., 2018, MNRAS, 480, 358.
  * Whittam et al. (2016) Whittam I. H., Riley J. M., Green D. A., Jarvis M. J., 2016, MNRAS, 462, 2122.
  * Williams et al. (2018) Williams W. L., Calistro Rivera G., Best P. N., Hardcastle M. J., Röttgering H. J. A., Duncan K. J., de Gasperin F., et al., 2018, MNRAS, 475, 3429.
  * Willott et al. (1999) Willott C. J., Rawlings S., Blundell K. M., Lacy M., 1999, MNRAS, 309, 1017.
  * Yuan & Narayan (2014) Yuan F., Narayan R., 2014, ARA&A, 52, 529.
  * Zhang, Zhang, & Zhang (2016) Zhang X., Zhang H.-. jing ., Zhang X., 2016, ChA&A, 40, 198.

##  Appendix A Structure of the Level-3 source classification catalogue

The Level-1 MIGHTEE Early Science catalogue of radio sources was released with
Heywood et al. (2022). The Level-2 catalogue contains information about the
multi-wavelength identifications for the Level-1 radio sources, and is
released with Prescott et al. (in prep). The source classifications described
in this work form the Level-3 catalogue, and are released here. The structure
of this catalogue is described below.

(0): Name: An IAU-style identifier of the form JHHMMSS.SS+/-DDMMSS.S, based on
the position of the host galaxy, as in Level-2.

(1): RA_Radio: The J2000 Right Ascension of the radio source in degrees. If
the source is multi-component radio source this is the Right Ascension
brightest component, as in Level-2.

(2): DEC_Radio: The J2000 Declination of the radio source in degrees. If this
is multiple component radio source it is the Declination brightest component,
as in Level-2.

(3): RA_host: The J2000 Right Ascension of the object in degrees from the
$K_{s}$-band selected multi-wavelength catalogue, as in Level-2.

(4): DEC_host: The J2000 Declination of the object in degrees from the
$K_{s}$-band selected multi-wavelength catalogue, as in Level-2.

(5): S_INT14: The total 1.4-GHz flux density of the radio sources in Jy. This
is scaled to 1.4-GHz from the measured frequency using the effective frequency
map and assuming a spectral index of 0.7.

(6): Redshift: The best available redshift value. This is a spectroscopic
redshift value if available, if not it is the photometric redshift from
Hatfield et al. (in prep). See Section 3.6. See column (8) for information
about the origin of the redshift value.

(7): Redshift_err: Uncertainty on the best available redshift value if
available. (-99 if not available – this is the case for some spectroscopic
redshifts.)

(8): Redshift_note: Note on the origin of the redshift (=‘photz’ if photoz is
used).

(9): L14: 1.4-GHz radio luminosity in W/Hz. Scaled to rest-frame 1.4 GHz
assuming a spectral index of 0.7.

(10): XAGN: boolean column, True if source is classified as an X-ray AGN, i.e.
has $L_{x}>10^{42}$ erg/s, see Section 4.4.

(11): notXAGN: boolean column, True if source is classified as not being an
X-ray AGN, i.e. has $L_{x}<10^{42}$ erg/s, see Section 4.4 (note that a source
must be positively identified as having $L_{x}<10^{42}$ erg/s, i.e. this is
not everything False in column (10)).

(12): RLAGN: boolean column, True if source is a radio-excess AGN, see Section
4.1.

(13): notRLAGN: boolean column, True if source does not have a radio excess,
see Section 4.1. (Note that a source must be positively identified as not
having a radio-excess, i.e. this is not everything False in column (12)).

(14): midIRAGN: Donley mid-infrared AGN, boolean column, True if source is
classified as a mid-infrared AGN, see Section 4.2.

(15): notmidIRAGN: not Donley mid-infrared AGN, boolean column, True if source
is classified as not being a mid-infrared AGN, see Section 4.2 (note that this
is not everything False in column (14)).

(16): optAGN: optical point-like AGN, boolean column, True if source is point-
like in the _ACS_ optical imaging, see Section 4.3.

(17): notoptAGN: not optical point-like AGN, boolean column, True if source is
resolved point-like in the _ACS_ optical imaging, see Section 4.3 (note that
this is not everything False in column (16)).

(18): VLBAAGN: boolean column, True if source is detected in the VLBA
observations, see Section 4.5. Note that everything False in this column is
not a VLBA AGN.

(19): AGN: overall AGN, boolean column, True if source is classified as an AGN
in the overall classifications, see Section 4.6.

(20): SFG: overall SFG, boolean column, True if source is classified as a SFG
in the overall classifications, see Section 4.6. (Limited to sources with
$z<0.5$, see text for details.)

(21): probSFG: probable SFG, boolean column, True if source is classified as a
probable SFG in the overall classifications, see Section 4.6. (Note that
sources with $z>0.5$ cannot be securely classified as SFG so will be
classified as probable SFG if appropriate, see text for details.)

(22): unclass: Unclassified sources, boolean column, True if source is not
able to be classified as an AGN, SFG or probable SFG.

(23): HERG: boolean column, True if source is classified as a HERG, see
Section 4.6.

(24): LERG: boolean column, True if source is classified as a LERG, see
Section 4.6. (Limited to sources with $z<0.5$, see text for details.)

(25): probLERG: Probable LERG, boolean column, True if source is classified as
a probable LERG, see Section 4.6. (Note that sources with $z\geq 0.5$ cannot
be securely classified as LERGs so will be classified as probable LERGs if
appropriate, see text for details.)

(26): RQAGN: radio-quiet AGN, boolean column, True if source is classified as
an AGN (column (19) is True) and is not radio loud (column (13) is True).

##  Appendix B Williams et al. (2018) classification scheme

Figure 15: AGN and SF fractions derived from AGNfitter in the same way as
Williams et al. (2018). They classify sources with $f_{\text{AGN}}>0.25$
(shown by the dotted line) as HERGs. The top panel shows sources classified as
SFG and AGN using our scheme, the middle panel shows sources classified as
HERGs and LERGs, the bottom panel shows sources with classifications from
optical spectra, using [Oiii] line measurements to classify HERGs and LERGs
(see Section 4.7 for details). Note that only sources with good AGNfitter fits
(log likelihood > -20) are shown.

Williams et al. (2018) use AGNfitter to classify sources detected in the LOFAR
Bootës field as HERGs and LERGs. Here we compare their classification scheme
to that used in this work. Williams et al. first select the radio-loud AGN
using a criteria similar to that described in Section 4.1. They then define
$f_{\text{AGN}}$ as:

$f_{\text{AGN}}=\frac{L_{\text{TO}}+L_{\text{BB}}}{L_{\text{TO}}+L_{\text{GA}}+L_{\text{BB}}}$
(2)

where $L$ are the luminosities of the different SED components from AGNfitter
described in Section 3.7; $L_{\text{TO}}$ is the luminosity from hot dust
torus component, $L_{\text{BB}}$ is due to the UV/optical accretion disk,
$L_{\text{GA}}$ is from the stellar emission and $L_{\text{SB}}$ is the
reprocessed light from dust (we use this nomenclature to be consistent with
Calistro Rivera et al. 2016; Williams et al. 2018). $f_{\text{AGN}}$ is
essentially the fraction of emission that is due to the AGN (i.e. the torus
and accretion disk components) compared to the total emission independent of
the mid-infrared star-forming component ($L_{\text{SB}}$).

Williams et al. also define:

$f_{\text{SF}}=\frac{L_{\text{SB}}}{L_{\text{SB}}+L_{\text{GA}}}$ (3)

which is the fraction due to the infrared starburst component compared to the
total galaxy component. $L_{\textrm{SB}}$ and $L_{\textrm{TO}}$ are calculated
over the wavelength range $1<\lambdaup/\muup\textrm{m}<30$, and
$L_{\textrm{BB}}$ and $L_{\textrm{GA}}$ are calculated over the wavelength
range $0.1<\lambdaup/\muup\textrm{m}<1$. Williams et al. classify sources with
$f_{\textrm{AGN}}>0.25$ as HERGs, and sources with AGN fractions below this
value as LERGs. The top panel of Fig. 15 shows $f_{\textrm{SF}}$ and
$f_{\textrm{AGN}}$ for sources classified as AGN, SFG and probable SFG in this
work. As expected, the SFG all have very high values of $f_{\text{SF}}$ (with
a very small number of exceptions). A significant fraction of the AGN also
have large $f_{\text{SF}}$ values; this is not necessarily unexpected, and
these AGN generally also have reasonably high values of $f_{\text{AGN}}$. The
middle panel of Fig. 15 shows HERGs, LERGs and probable LERGs classified in
this work, along with the $f_{\text{AGN}}=0.25$ HERG/LERG separation used by
Williams et al. The majority of the sources classified as HERGs in this work
have $f_{\text{AGN}}>0.25$, however so do a significant fraction of the LERGs
and probable LERGs. This suggests that while this cut may be a reasonable
method to select HERGs, the sample may be contaminated by a significant number
of LERGs. The bottom panel of Fig. 15 show the positions of sources in our
sample with spectroscopic classifications. While 17 of the 20 sources with
spectroscopic classifications with $f_{\text{AGN}}<0.25$ are LERGs, so are 3
out of the 6 sources with $f_{\text{AGN}}>0.25$. This again suggests that
while the majority of the sources with $f_{\text{AGN}}<0.25$ are indeed LERGs
(although 3 out of 20 are HERGs), there is some LERG contamination in the
sample found above this divide.