11institutetext: Anton Pannekoek Institute for Astronomy, University of
Amsterdam, P.O. Box 94249, 1090 GE Amsterdam, Nederland 22institutetext:
ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4,
Dwingeloo, 7991 PD, The Netherlands 33institutetext: Kapteyn Astronomical
Institute, University of Groningen, PO Box 72, 97200 AB, Groningen, The
Netherlands 44institutetext: Caltech/IPAC, 1200 E. California Boulevard,
Pasadena, CA 91125, USA 55institutetext: Center for Gravitation, Cosmology,
and Astrophysics, Department of Physics, University of Wisconsin-Milwaukee, PO
Box 413, Milwaukee, WI, 53201, USA 66institutetext: Leiden Observatory, Leiden
University, PO Box 9513, 2300 RA, Leiden, The Netherlands

# A LOFAR sample of luminous compact sources coincident with nearby dwarf
galaxies††thanks: Tables 1 and 3 are available in electronic form at the CDS
via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via
https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/XXX/XXX

D. Vohl , Email<EMAIL_ADDRESS>H. K. Vedantham 2233 J. W. T. Hessels 1122
C. G. Bassa 22 D. O. Cook 44 D. L. Kaplan 55 T. W. Shimwell 2266 C. Zhang 55

The vast majority of extragalactic compact continuum radio sources are
associated with star formation or jets from (super)massive black holes and, as
such, are more likely to be found in association with starburst galaxies or
early-type galaxies. Two new populations of radio sources were recently
identified: (a) compact and persistent sources (PRSs) associated with fast
radio bursts (FRBs) in dwarf galaxies and (b) compact sources in dwarf
galaxies that could belong to the long-sought population of intermediate-mass
black holes. Despite the interesting aspects of these newly found sources, the
current sample size is small, limiting scrutiny of the underlying population.
Here, we present a search for compact radio sources coincident with dwarf
galaxies. We search the LOFAR Two-meter Sky Survey (LoTSS), the most sensitive
low-frequency (144 MHz central frequency) large-area survey for optically thin
synchrotron emission to date. Exploiting the high spatial resolution
($6\arcsec$) and low astrometric uncertainty ($\sim
0\,\aas@@fstack{\prime\prime}2$) of the LoTSS, we match its compact sources to
the compiled sample of dwarf galaxies in the Census of the Local Universe, an
H$\upalpha$ survey with the Palomar Observatory 48 inch Samuel Oschin
Telescope. We identify 29 over-luminous compact radio sources, evaluate the
probability of chance alignment within the sample, investigate the potential
nature of these sources, and evaluate their volumetric density and volumetric
rate. While optical line-ratio diagnostics on the nebular lines from the host
galaxies support a star-formation origin rather than an AGN origin, future
high-angular-resolution radio data are necessary to ascertain the origin of
the radio sources. We discuss planned strategies to differentiate between
candidate FRB hosts and intermediate-mass black holes.

###### Key Words.:

stars: neutron – stars: black holes– galaxies: dwarf – radio continuum:
general

##  1 Introduction

FRB 20121102A was the first fast radio burst (FRB) source found to repeat
(Spitler et al., 2016). Its repetitive nature rules out progenitor models
related to cataclysmic explosions for at least a fraction of all FRBs. FRB
20121102A was also the first FRB source to be precisely localized to a host
galaxy (Chatterjee et al., 2017) from a coordinated observing campaign between
the Karl G. Jansky Very Large Array (VLA) and the 305m William E. Gordon
Telescope at the Arecibo Observatory. The host galaxy is a low-mass, low-
metallicity dwarf at a redshift of $z=0.19273\pm 0.0008$ (Tendulkar et al.,
2017), and as such has the characteristics of a typical host to long gamma-ray
bursts and super-luminous supernovae. These simple facts suggest that the
mechanism driving FRBs may be linked to these latter phenomena. Moreover, FRB
20121102A was the first FRB found to be co-located with a persistent radio
source (PRS; Chatterjee et al., 2017), with a luminosity of
$L_{\mathrm{radio}}\sim 10^{39}\,\mathrm{erg\,s^{-1}}$, which is more 50 times
what would be expected from star formation activity alone.

Very long baseline interferometry (VLBI) observations with the European VLBI
Network (EVN) showed that the FRB and the PRS are located within $\lesssim
40\,{\rm pc}$ (transverse distance) of one another (Marcote et al., 2017),
strongly connecting the two. Optical and far-infrared observations using the
Hubble Space Telescope revealed that the FRB/PRS location is slightly offset
from the centroid of a star formation knot within the host (Bassa et al.,
2017). The PRS has a flat spectral index, that is,
$S_{\nu}\propto\nu^{\alpha}$, with $\alpha\sim-0.07\pm 0.03$ below 10 GHz
(Resmi et al., 2021), and with a possible turnover at lower frequencies,
estimated as $\alpha\sim 0.3$ between 433 MHz and 1.4 GHz by Mondal et al.
(2020). The spectral energy distribution (SED) derived from multiwavelength
measurements and upper limits matches that of the Crab nebula, though with
orders-of-magnitude higher luminosity. Finally, bursts from FRB 20121102A have
a high and variable Faraday rotation measure (RM; Michilli et al., 2018), and
the dispersion measure (DM) also shows secular changes (Hessels et al., 2019;
Platts et al., 2021).

These measurements combined make a plausible case for an FRB engine that is a
young, highly magnetized neutron star embedded in an expanding supernova
remnant and powering a pulsar wind nebula (PWN; Murase et al., 2016; Margalit
& Metzger, 2018) or magnetar wind nebula Margalit & Metzger (MWN; 2018); Zhao
& Wang (MWN; 2021). Another plausible explanation is that the FRB engine is
within the vicinity of a massive black hole, which in turn creates the PRS. In
this context, the FRB source may be a neutron star near a black hole, or may
even be a black hole jet. Other authors have suggested that an accreting
compact object engine (e.g., ultra-luminous X-ray sources accreting at highly
super-Eddington rates) could explain the PRS (Chen et al., 2022; Sridhar &
Metzger, 2022). There is only one other known repeating FRB co-localized to a
PRS (Niu et al., 2022). Like FRB 20121102A, FRB 20190520B is hosted in a star-
forming dwarf galaxy, with a large $\mathrm{DM}_{\mathrm{host}}$ contribution,
a high repetition rate, and its associated PRS has a shallow spectral index
($\alpha=-0.41\pm 0.04$).

Given these two cases of FRB/PRS connection, it seems that PRSs represent an
important aspect of some FRBs, even if their nature remains mysterious. If
PRSs are wind nebulae, a limited lifespan during which they can be detected
($\sim$few centuries; Gaensler & Slane, 2006) could explain why only a subset
of FRBs have a PRS counterpart. Considering a sample of 15 localized FRBs with
radio sensitivity limits that could allow the detection of a PRS (including
six repeating FRBs), Law et al. (2022) estimated that PRS occurrence could be
as high as 20% for repeating FRBs given that 2 out of the 6 repeating FRBs in
their sample are associated to a PRS. Furthermore, given that most FRBs with
meaningful PRS limits would also limit PRS emission out to $z\approx 0.4$, a
distance that includes a similar number of repeating and nonrepeating FRBs
—supporting the argument that PRS emission from repeaters and nonrepeaters is
equally well-constrained— these authors estimate that PRS detectability in
repeating FRBs is not strongly biased by distance.

Separately, Reines et al. (2020) identified a sample of compact radio sources
associated with dwarf galaxies and suggested that they may be the long-sought
population of intermediate-mass black holes (IMBHs, ${\rm\sim
10^{2}-10^{5}\,M_{\odot}}$; Greene et al., 2020) predicted to reside in dwarf
galaxies (e.g., McConnell & Ma, 2013; Reines & Volonteri, 2015). Furthermore,
the compact radio sample presented by Reines et al. (2020) has been shown to
share many similarities with the PRS associated with FRB 20121102A, with radio
luminosities, SEDs, light curves, ratios of radio-to-optical flux, and spatial
offsets between the radio source and the host optical center being consistent
with arising from the same population (Eftekhari et al., 2020).

Follow-up observations of the 13 dwarf galaxies with likely accreting IMBHs
from Reines et al. (2020) with the Very Long Baseline Array (VLBA) led to four
source detections at milliarcsecond (mas) resolution. These four sources have
the largest offset from their host centroid in the sample, which suggests that
they are all likely background AGNs (Sargent et al., 2022). Two sources among
the VLBA nondetections are associated with spectroscopically confirmed AGNs
that are consistent with being located at their galaxy photocenter. Sargent et
al. also re-examined the radio–star formation relationship and found that a
star-formation origin cannot be ruled out for approximately 5 out of the 9
VLBA nondetections. These authors conclude that these sources are either the
posited wandering accreting massive black hole scenario, or simply background
AGN.

While the existence of wandering black holes has yet to be definitively proven
(IMBHs in dwarf galaxies have a much shallower gravitational potential than in
more massive galaxies that could in theory allow for off-nuclear location),
the well-documented case of FRB 20121102A nevertheless highlights that such
off-nuclear compact radio emission can occur, even within a star forming
region within the host galaxy. Although the connection between IMBHs, PRSs,
and FRBs remains unclear —most FRB models prefer a magnetar progenitor (e.g.,
see discussion in Eftekhari et al., 2020)— over-luminous compact radio sources
(OCRs) in dwarf galaxies are an interesting radio source population in their
own right.

To improve our understanding of PRSs and their potential connection to the FRB
and/or IMBH phenomena (e.g., constrain FRB progenitor models), it is
imperative to increase the known sample size (Vohl et al., 2023). Here, we
present a targeted search for compact radio sources coincident with dwarf
galaxies using the LOFAR Two-Meter Sky Survey (LoTSS) second data release
(DR2; Shimwell et al., 2022) — the most sensitive large-area survey for
optically thin synchrotron emission to date— as our radio reference catalogue,
and the Palomar Observatory 48 inch Samuel Oschin Telescope ‘Census of the
Local Universe’ (CLU; Cook et al., 2019) as our optical reference catalogue.

The article is organized as follows: in §2 we describe our candidate selection
methodology and discuss chance alignment probability. In §3 we discuss the
selected candidates, and complement the information available for our sample
with ancillary survey data at various wavelengths. In §4 we discuss the
potential nature of these sources and our plans for future work, and in §5 we
close with a summary.

##  2 Candidate selection

###  2.1 Sample description

LoTSS DR2 comprizes 4,396,228 radio sources spanning over 5600 deg2 of the
northern sky. LoTSS operates at a central frequency of 144 MHz with 48 MHz of
bandwidth ($120-168$ MHz). The survey has a $\sim
6\arcsec\times({\small\frac{144\,\rm{MHz}}{v}})$ angular resolution and a
median root mean square (rms) sensitivity of about $80\,\rm{\upmu Jy/beam}$.
Furthermore, with a $0\,\aas@@fstack{\prime\prime}2$ astrometric
uncertainty111Namely, the uncertainty tying the LoTSS radio frame to the
PanSTARRS (PS1; Chambers et al., 2016) frame, along with the formal error to
evaluate the source centroid, given by $\frac{6\arcsec}{\rm{S/N}}$, where S/N
is the signal-to-noise ratio. For $\gtrsim$mJy level sources detected at
$\gtrsim 10\sigma$, the latter is dominant. We refer the reader to Shimwell et
al. (2022) for further details about astrometry in LoTSS DR2. for sources
brighter than 20 mJy —which is comparable to optical surveys— and a 90% point
source completeness for sources $\geq 0.8$ mJy/beam, LoTSS DR2 represents an
excellent catalogue for our study.

We cross-match LoTSS DR2 to the CLU-compiled catalogue, a compilation of all
known galaxies out to 200 Mpc (Cook et al., 2019). CLU-compiled is an
extension to the CLU photometric survey carried out with four narrow-band
H$\upalpha$ filters corresponding to redshifts up to $z=0.0471$. CLU-compiled
is a compilation from existing galaxy databases (NASA/IPAC Extragalactic
Database (NED, https://ned.ipac.caltech.edu), Hyperleda, http://leda.univ-
lyon1.fr, Extragalactic Distance Database http://edd.ifa.hawaii.edu, the Sloan
Digital Sky Survey DR12, the 2dF Galaxy Redshift Survey, and The Arecibo
Legacy Fast ALFA (ALFALFA)) and is designed to provide the most complete list
of galaxies with measured distances in the LIGO sensitivity volume. The
compiled catalogue comprizes 271,867 sources, of which 95,047 fall within the
LoTSS DR2 footprint. For brevity, we use the terms CLU and CLU-compiled
interchangeably throughout the paper. Distances based on Tully–Fischer methods
were favored over kinematic (i.e., redshift) distances; however, the majority
of the distances are based on redshift information. For cases where neither
Tully-Fischer nor redshift was available, a distance based on the H$\upalpha$
filters is provided.

In addition to distances, CLU-compiled also contains compiled photometric
information. In particular, sources have been cross-matched to within 4″ with:
(i) Sloan Digital Sky Survey (SDSS) data release 12 (Alam et al., 2015) for
optical fluxes; (ii) GALEX all-sky (Martin et al., 2005; Bianchi et al., 2014)
for far- and near-ultraviolet (FUV, NUV) Kron fluxes (Kron, 1980); and (iii)
Wide-field Infrared Survey Explorer (WISE; Wright et al., 2010) for mid-
infrared fluxes. Additionally, CLU-compiled aggregates these ancillary data to
cull contaminants (i.e., bright stars, high-redshift sources with emission
lines shifted to within the CLU H$\upalpha$ bands) and measure several
physical properties of galaxies such as their stellar mass and star formation
rate (SFR).

We select sources in the mass range corresponding to dwarf galaxies
($10^{7}\leq M_{*}/M_{\odot}\leq 3\times 10^{9}$), leaving 31,190 sources. We
finally keep only galaxies with a valid SFR measurement, leaving 18,159
galaxies that form our parent sample. With regards to the LoTSS DR2 catalogue,
we select sources with a peak brightness of $\geq 0.8$ mJy/beam, for a total
of 2,622,903 sources. Furthermore, we constrain the matched sample to reject
extended sources using the $R_{99.9}$ compactness criterion (see Shimwell et
al., 2022, Equation 2), where the ratio of the natural logarithm of the
integrated flux density ($S_{I}$) to peak brightness ($S_{P}$) is less than or
equal to the envelope that encompasses the 99.9 percentile of the
$S_{I}/S_{P}$ distribution, leaving 2,275,400 sources. Finally, we limit our
source selection to those fitted with a single Gaussian component by the
source finder pyBDSF (Mohan & Rafferty, 2015), which was used to produce the
LoTSS source catalogue, leaving 2,051,534 sources.

###  2.2 Cross-matching and filtering

We aim to identify OCRs dwelling in dwarf galaxies with luminosity exceeding
the contribution expected from star formation alone. To find these, we cross-
matched our subset of LoTSS and CLU sources (§ 2.1) using a radius of
$(6+\epsilon)\arcsec$ (the angular resolution of LoTSS, with $\epsilon$ being
the astrometric uncertainty for a given source), yielding 708 matches. We then
rejected all sources that lie within three standard deviations of the radio
luminosity versus star formation rate (L–SFR) relationship presented by Gürkan
et al. (2018)222For consistency with Gürkan et al. (2018), throughout this
paper, we use a concordance cosmology with $H_{0}=70\,{\rm
km\,s^{-1}\,Mpc^{-1}}$, $\Omega_{m}=0.3$, and $\Omega_{\Lambda}=0.7$.. This
yields just 32 sources. It is worth noting that Smith et al. (2021)
highlighted a dependence of the L–SFR relation on stellar mass, with galaxies
at $\sim 10^{9.5}\,M_{*}/M_{\odot}$ following the relation from Gürkan et al.
(2018), while those at lower masses tend to have a lower luminosity for a
fixed SFR. Therefore, given the L-SFR mass dependence and that the stellar
mass–metallicity relation indicates a trend where galaxy metallicity increases
with increasing stellar mass (e.g., Curti et al., 2020), our sample selected
above the $3\sigma$ threshold should be considered as a lower limit, and
outliers are not simply due to low metallicity in their host galaxies.

We verify that redshift values listed in CLU match those of other measurements
listed in the NED, because redshifted emission lines other than H$\upalpha$
could fall within the CLU filter and masquerade as H$\upalpha$. Indeed,
objects with incorrectly attributed redshifts will be over-represented in our
sample, which is selected based on nonadherence to the L–SFR relationship.
Among the 32 sources, we find that three objects have redshifts that are
inconsistent with the median redshift from the NED. We therefore remove these
from our sample, leaving 29 candidates. From these, 11 out of the 29 sources
have spectra available in the NED. Next, we check IR magnitudes for any
obvious AGNs by evaluating sources whose WISE colors fall within the AGN
region prescribed by Jarrett et al. (2011, Eq. 1), represented in Figure 1.
Two candidates fall within this AGN region, leaving 27 sources to be further
scrutinized.

We depict the candidate selection on the L–SFR plane in Figure 2. We discuss
the distribution of matched galaxies (including all galaxy masses) along the
L–SFR plane in Appendix A. Candidates are summarized in Table 1, and are
investigated further in the following sections. Astrometric uncertainties
provided by LoTSS were taken into account during cross-matching. Therefore,
while a projected offset of $7\arcsec$ is listed for ILT J125944.53+275800.9,
the lower limit on its offset taking into account the radio astrometric
uncertainties on right ascension and declination is
$5\,\aas@@fstack{\prime\prime}4$.

Table 1: Properties of selected candidates.

Source name | Host name | Projected offset | $z$ | $S$ | $\log L$ | $\log{\rm SFR}$ | $\sigma$ | $\alpha$ | $R_{g}$
---|---|---|---|---|---|---|---|---|---
(ILT J) |  | (arcsec) | (pc) |  | (mJy) | (${\rm W/Hz}$) | (${\rm M_{\odot}/yr}$) |  |  |
003532.36+303008.0 | CLU J003532.3+303008 | $0.7\pm 0.1$ | $165$ |  $0.0121\pm 0.01196$ (n) | $11.89\pm 0.35$ | $21.6$ | $-1.02\pm-2.16$ | $3.85$ | $-0.56$ | $1.93$
125915.34+274604.2 | SSTSL2 J125915.27+274604.1 | $0.8\pm 0.4$ | $321$ |  $0.0211$ (k) | $2.57\pm 0.28$ | $21.4$ | $-1.29\pm-1.63$ | $4.56$ | – | –
231715.38+184339.0 | 2MASX J23171540+1843385 | $0.8\pm 0.7$ | $355$ |  $0.0409\pm 0.00034$ (m) | $2.57\pm 0.50$ | $22.0$ | $-0.98\pm-1.45$ | $6.09$ | – | $0.13$
021835.45+262040.9 | LAMOST J021835.51+262040.7 | $0.9\pm 0.3$ | $57$ |  $0.0033$ (k) | $6.55\pm 0.44$ | $20.2$ | $-2.32\pm-3.35$ | $3.79$ | $-0.53$ | $0.63$
075257.15+401026.3 | UGC 04068 | $0.9\pm 0.2$ | $133$ |  0.0412$\pm$0.00010 (m) | $7.37\pm 0.35$ | $22.5$ | $-1.64\pm-2.40$ | $13.37$ | $-0.54$ | –
165252.24+391151.7 | CLU J165252.32+391152.0 | $1.0\pm 0.8$ | $540$ |  $0.0272\pm 0.00700$ (k) | $1.83\pm 0.38$ | $21.5$ | $-1.00\pm-1.48$ | $3.08$ | – | $0.53$
162244.56+321259.3 | 2MASS J16224461+3213007 | $1.0\pm 0.1$ | $451$ |  0.0221$\pm$0.00009 (k) | $8.06\pm 0.18$ | $22.0$ | $-0.75\pm-1.56$ | $4.29$ | $-0.63$ | $0.50$
153943.52+592730.7 | CLU J153943.44+592729.8 | $1.1\pm 0.2$ | $883$ |  $0.0411\pm 0.00695$ (k) | $3.06\pm 0.17$ | $22.1$ | $-0.55\pm-1.23$ | $3.72$ | – | $0.52$
015915.79+242500.6 | KUG 0156+241 | $1.2\pm 0.5$ | $128$ |  $0.0130\pm 0.00003$ (m) | $4.30\pm 0.43$ | $21.2$ | $-1.35\pm-2.73$ | $3.69$ | $-0.01$ | $0.04$
131858.22+332859.9 | CLU J131858.32+332859.8 | $1.3\pm 0.4$ | $74$ |  $0.0029\pm 0.00285$ (k) | $1.58\pm 0.19$ | $19.5$ | $-3.01\pm-3.56$ | $3.77$ | – | $0.51$
161439.00+545334.8 | CLU J161439.12+545334.0 | $1.3\pm 1.1$ | $76$ |  $0.0029\pm 0.00285$ (k) | $1.03\pm 0.25$ | $19.3$ | $-3.32\pm-3.74$ | $4.69$ | – | $0.47$
142859.42+331005.2 | 2MASX J14285953+3310067 | $1.5\pm 0.8$ | $863$ |  0.0291$\pm$0.00009 (k) | $1.97\pm 0.29$ | $21.6$ | $-1.00\pm-1.42$ | $3.68$ | – | $0.08$
140549.55+365943.9 | CLU J140549.44+365944.5 | $1.5\pm 0.3$ | $86$ |  $0.0029\pm 0.00285$ (k) | $2.66\pm 0.21$ | $19.7$ | $-2.74\pm-3.50$ | $3.40$ | – | $0.73$
121407.57+423829.2 | KISSR 1246 | $1.8\pm 0.1$ | $675$ |  $0.0181\pm 0.00280$ (k) | $2.86\pm 0.11$ | $21.3$ | $-1.28\pm-1.84$ | $3.90$ | – | $1.06$
163850.81+352901.0 | CLU J163850.64+352900.9 | $2.0\pm 0.7$ | $118$ |  0.0029$\pm$0.00285 (k) | $2.15\pm 0.34$ | $19.6$ | $-2.99\pm-3.47$ | $4.48$ | – | $0.30$
110704.14+391812.3 | CLU J110704.32+391811.8 | $2.2\pm 0.4$ | $127$ |  $0.0029\pm 0.00285$ (k) | $2.51\pm 0.25$ | $19.7$ | $-2.79\pm-3.46$ | $3.61$ | – | $0.34$
143050.99+410642.6 | SDSS J143051.12+410640.8 | $2.4\pm 0.2$ | $1632$ |  0.0342$\pm$0.00011 (k) | $2.71\pm 0.18$ | $21.9$ | $-0.66\pm-1.41$ | $3.12$ | – | $0.41$
220737.01+231516.0 | CLU J220737.20+231515.8 | $2.6\pm 0.1$ | $154$ |  $0.0029\pm 0.00285$ (k) | $12.19\pm 0.33$ | $20.3$ | $-2.30\pm-3.27$ | $4.56$ | – | $1.39$
090406.54+530314.6 | SDSS J090406.38+530311.8 | $3.1\pm 0.0$ | $2410$ |  0.0386$\pm$0.00007 (k) | $6.69\pm 0.13$ | $22.4$ | $-0.43\pm-1.23$ | $4.74$ | $0.18$ | –
023058.18+232412.6 | CLU J023058.15+232409.3 | $3.3\pm 0.6$ | $191$ |  $0.0029\pm 0.00285$ (k) | $11.49\pm 1.31$ | $20.3$ | $-2.35\pm-3.39$ | $4.73$ | $-0.66$ | $0.97$
140524.35+613358.7 | 2MASS J14052457+6134020 | $3.3\pm 0.0$ | $386$ |  0.0057$\pm$0.00001 (k) | $22.37\pm 0.13$ | $21.2$ | $-1.88\pm-2.80$ | $7.23$ | $-0.88$ | $0.55$
130022.42+281451.7 | 2MASS J13002220+2814499 | $3.7\pm 0.8$ | $2002$ |  0.0266 (k) | $1.47\pm 0.33$ | $21.4$ | $-1.12\pm-1.69$ | $3.17$ | – | $-0.04$
122250.31+681434.2 | SDSS J122249.71+681431.8 | $3.9\pm 0.1$ | $2630$ |  0.0332$\pm$0.00005 (k) | $2.79\pm 0.15$ | $21.8$ | $-0.71\pm-1.34$ | $3.37$ | – | $0.43$
091333.83+300056.9 | 2MASX J09133387+3000514 | $5.5\pm 0.4$ | $2281$ |  0.0204$\pm$0.00002 (k) | $5.89\pm 0.49$ | $21.7$ | $-0.88\pm-1.66$ | $3.88$ | $-0.97$ | $-0.10$
113634.77+592533.3 | SBS 1133+597 | $5.6\pm 0.0$ | $1182$ |  0.0104$\pm$0.00011 (k) | $12.82\pm 0.12$ | $21.5$ | $-1.30\pm-2.15$ | $5.08$ | $-0.96$ | $0.15$
125940.18+275123.5 | 2MASX J12594007+2751177 | $5.8\pm 0.0$ | $1491$ |  0.0127$\pm$0.00004 (k) | $22.34\pm 0.20$ | $21.9$ | $-1.69\pm-2.27$ | $10.28$ | $-1.00$ | $0.39$
125944.53+275800.9 | SDSS J125944.76+275807.1 | $7.0\pm 1.6$ | $4670$ |  $0.0329\pm 0.00025$ (k) | $2.38\pm 0.56$ | $21.8$ | $-0.87\pm-1.44$ | $4.02$ | – | –
161111.24+360401.0 | CLU J161111.2+360400 | $0.3\pm 0.1$ | $75$ |  $0.0121\pm 0.01196$ (n) | $8.45\pm 0.17$ | $21.4$ | $-1.10\pm-2.30$ | $3.49$ | $-0.79$ | $1.15$
143037.30+352053.3 | SDSS J143037.09+352052.8 | $2.6\pm 0.6$ | $2036$ |  $0.0390\pm 0.00000$ (k) | $1.18\pm 0.21$ | $21.6$ | $-0.92\pm-1.29$ | $3.35$ | – | $1.64$

  * •

Columns: Source name in LoTSS DR2; host galaxy name in CLU; projected offset
between the radio source and H$\upalpha$ source coordinates in arcsec, and
corresponding transverse distance in parsec; redshift ($z$), with distance
method indicated in parentheses: (k) kinematic; (m) median (redshift-
independent), (n) narrowband (H$\upalpha$); star formation rate ($\log{\rm
SFR}$); radio luminosity at 144 MHz ($\log L$); standard deviation ($\sigma$)
above the L-SFR relation; radio spectral index ($\alpha$; §3.2); radio
loudness $R_{g}$ (§4). Sources with spectral line measurements in SDSS table
galSpecLine (§3.1; Tremonti et al., 2004; Brinchmann et al., 2004) have their
redshifts marked in bold. Candidates below and above an offset value of
$(2+\epsilon)\arcsec$ are demarcated with a solid line, with $\epsilon$ being
the LoTSS astrometric uncertainty. The third (bottom) section includes
candidates in the AGN region of Figure 1.

Figure 1: WISE color–color plot. Photometric ratios in magnitude (mag) between
three IR bands (W1${\,\rm{}_{3.4\upmu\\\ m}}$, W2${\,\rm{}_{4.6\upmu\\\ m}}$,
W3${\,\rm{}_{12\upmu\\\ m}}$, with W1-W2, W2-W3). Black markers correspond to
dwarf galaxies matched to a compact radio source with luminosity exceeding
$3\sigma$ in the L–SFR relation. Gray-filled markers indicate dwarf galaxies
matched to a radio source. We demarcate the two sources falling within the AGN
region (Jarrett et al., 2011) marked by dashed lines within our sample as
being classified. Figure 2: Candidate selection via the L–SFR relation. Gray-
filled markers indicate compact radio sources matched to dwarf galaxies
matched. Black filled circles correspond to our final selection of OCRs
matched to a dwarf galaxy with luminosity exceeding $3\sigma$ (dashed line) on
the L–SFR relation by Gürkan et al. (2018, and the solid line) shows those
with validated redshift. The uncertainty on luminosity is below the marker
size. Orange markers are sources within the AGN region in Figure 1. As a
reference, we show PRS luminosity and the SFR of the host for both FRB
20121102A (Tendulkar et al., 2021; Law et al., 2022) and FRB 20190520B (Niu et
al., 2022), with luminosity measurements scaled to 144 MHz using $\alpha$ from
Resmi et al. (2021, evaluated between 2 MHz and 10 GHz,) and from Niu et al.
(2022, evaluated between 1.5 and 5.5 GHz), respectively. We also show the
transient source VT 1137+0337 using values from Dong & Hallinan (2023).
Finally, we show Reines et al. (2020) galaxies (J0909+5655, J1136+2643,
J1220+3020) matched in CLU for which SFR information is available, with
luminosity scaled to 144 MHz using $\alpha$ values fitted between 1.4 GHz and
9 GHz by Eftekhari et al. (2020). The large scatter in luminosity is discussed
in §2.3 and Appendix A.

###  2.3 Chance alignment probability

We begin by evaluating the likelihood of matching a galaxy and a background
radio source by coincidence due to chance alignment following the two methods
described by Reines et al. (2020). Firstly, we estimate the cumulative number
of compact radio source counts per steradian $N(S_{min})$ with 144 MHz flux
densities greater than $S_{min}=0.8\,\rm{mJy}$, taking into account only
compact sources based on pyBDSF single-component cases and the $R_{99.9}$
compactness criterion. Multiplying $N(S_{min})\approx 2,051,534\,{\rm
steradian}^{-1}$ by the area confined in a $6\arcsec$ radius circle gives
$N_{bk,gal}=0.0032$, the expected number of background sources for a given
galaxy. Across our entire parent sample of 18,159 dwarf galaxies, we expect
$N_{bk,samp}\approx 58\pm\sqrt{58}\approx 58\pm 8$ background sources (where
the error is computed for Poisson statistics). We therefore expect
$N_{bk,samp}$ to be present in our original 708 matches, or about 0.8%.
Performing a similar analysis using a cross-matching radius of $2\arcsec$
leads to $N_{bk,samp}\approx 6\pm 2$ background sources (with an original
number of matches of 573 using a $2\arcsec$ cut), or about $1\%$. Considering
that outliers caused by a false association should be evenly distributed above
and below the L–SFR relation (Figure 2), it is likely that nearly all
candidates below the $(2+\epsilon)\arcsec$ mark and about half of the
candidates above this threshold are true associations.

Secondly, we perform an empirical estimate of the expected number of false
associations using the data. We cross-match each source in the CLU subsample
to its nearest neighbor in LoTSS, up to a maximal matching radius of
$40\arcsec$. Figure 3 shows the observed offset distribution. The offset
probability histogram for chance associations should be equal to zero at an
offset of zero and rise linearly for small offsets (blue solid line in Figure
3). The observed distribution is minimal at a matching radius of $6\arcsec$,
beyond which the number of sources per offset, $N(d_{\rm{off}})$, increases
linearly as $N(d_{\rm{off}})=3.1d_{\rm{off}}$, with offset $d_{\rm{off}}$ in
units of arcsec. The total estimated number of background sources with offsets
of less than $6\arcsec$ is found by integrating $N(d_{\rm{off}})$ from
$N(d_{\rm{off}}=0\arcsec$ to $5\arcsec$, which gives $N_{bk,samp}\approx 64\pm
8$ sources. This is consistent with our calculation above using known radio
source counts. Here again, putting a cut at $2\arcsec$ (pink vertical line)
leads to $N_{bk,samp}\approx 9\pm 3$, which is also consistent within errors
with the analytical method.

Figure 3: Observed offset distribution after cross-matching CLU and LoTSS
surveys, using a match radius of $40\arcsec$. We select our target galaxies to
have offsets of $2\arcsec$ (pink vertical dashed line) and $6\arcsec$ (blue
vertical dashed line). The blue solid line shows the expected number of chance
alignments with background sources as a function of offset.

From these two analyses, it is unclear whether outliers on the L–SFR relation
found in §2 are caused by chance alignment, where two unrelated sources lead
to an incorrect luminosity calculation (e.g., a radio source is assigned an
incorrect redshift). To resolve this issue, we performed Monte Carlo
simulations. We repeated all cross-matching and outlier selection steps (as
described in §2.1 and §2.2) after randomly shifting spatial coordinates for
all sources within the LoTSS set in each Monte-Carlo run. For both cases,
using $2\arcsec$ and $6\arcsec$ as the cross-matching radius limit, we
performed 1000 realizations of the process, selecting spatial shifts from a
uniform distribution of $[-10,10]$ arcmin, keeping track of the number of
outliers at each realization.

Cumulative distributions summarising each Monte Carlo simulation are shown in
Figure 4. At $6\arcsec$, for the entire sample of CLU, on average, it is
common to find 10 matches (median) above the $3\sigma$ mark of the L–SFR
relation by chance, and is unlikely to find 27 by chance ($p\ll 10^{-4}$). At
a $2\arcsec$ cutoff, it is common to get two matches by chance, and highly
unlikely to find 16. Given our 16 matches selected below
$(2+\epsilon)\arcsec$, we expect a false-positive fraction of 0.125. The
remaining 11 sources with offsets between $(2+\epsilon)-(6+\epsilon)\arcsec$
may be chance alignments.

Figure 4: Cumulative distributions from 1000 Monte Carlo realizations of
matches exceeding $3\sigma$ on the L–SFR relation from Gürkan et al. (2018).
Top panel: $6\arcsec$ matching radius; bottom panel: $2\arcsec$ matching
radius.

While this does not mean that candidates with a projected offset of greater
than $2\arcsec$ are necessarily chance alignments —for example, a small
transverse distance may indicate a true association—, assessing whether or not
they are real associations remains difficult with the currently available
data. For this reason, we demarcate candidates below and above
$(2+\epsilon)\arcsec$ in Table 1 and the following sections with a black line.
Nevertheless, we show in the following section that nearly all candidates—both
below and above this demarcation—fall within the optical footprint of their
respective matched galaxies.

Finally, the redshift distribution of the selected candidates listed in Table
1 is vastly different from that of all dwarf galaxies from CLU in the LoTSS
field (Figure 5). A two-sample Kolmogorov-Smirnov (KS) test between these two
distributions lends a $p$-value of $1.08\times 10^{-5}$, indicating the
selected candidates do not simply track the redshift distribution of the whole
CLU dwarf galaxy sample.

Figure 5: Redshift distributions of selected candidates listed in Table 1
(gray) and for all dwarf galaxies from CLU in the LoTSS field (black). A two-
sample KS test between these two distributions gives a $p$-value of $\ll
0.005$.

##  3 Candidates

The final candidate list includes 27 sources, with 16 having a projected
offset of lower than $(2+\epsilon)\arcsec$. Composite images for each
candidate in ascending order of offset are presented in Figure 6 (offset
$\lesssim 2\arcsec$) and Figure 7 ($\gtrsim 2\arcsec$ and OCRs within the AGN
region of Figure 1), and candidates are detailed in Table 1. Given that all
H$\upalpha$ filters used by CLU fall within the frequency range covered by the
PanSTARRS (PS1; Chambers et al., 2016; Flewelling et al., 2020) r filter, we
use PS1 to generate image cutouts around the coordinates of our candidates.
The central coordinates of the matched objects from LoTSS and CLU are
indicated by black crosses and plus symbols, respectively.

All candidates shown in Figure 6 and most candidates in Figure 7 fall well
within the galaxy contours. ILT J125940.18+275123.5 falls within the low-
surface-brightness regions of its host galaxy, while the associated host
galaxy of ILT J125940.18+275123.5 (candidate with largest offset) is of
extremely low surface density, and likely a chance alignment (further
discussed in Appendix B). SDSS J143037.09+352052.8 (matched to the AGN
candidate ILT 143037.30+352053.3) is also extremely faint in the PS1 r filter
image and may also be a chance alignment. However, data from the JVO
Subaru/Suprime-Cam (Aihara et al., 2019) show the radio source to be within
the galaxy (Appendix B).

We note that galaxies 2MASS J13002220+2814499 (ILT J130022.42+281451.7), SDSS
J125944.76+275807.1 (ILT J125944.53+275800.9), 2MASX J12594007+2751177 (ILT
J125940.18+275123.5), and SSTSL2 J125915.27+274604.1 (ILT J125915.34+274604.2)
are part of the cluster of galaxies ACO 1656 (Appendix C). Similarly, 2MASX
J23171540+1843385 (ILT J231715.38+184339.0) is part of the compact group of
galaxies HCG 94. Finally, the Simbad
service333http://simbad.cds.unistra.fr/simbad indicates 2MASX
J09133387+3000514 (ILT J091333.83+300056.9) as having a 75% probability of
being a hierarchical member of the galaxy cluster HCG 37.

In the following subsections, we investigate the possible nature of the
candidates by considering complementary information in ancillary surveys; for
example, optical spectra and flux density measurements at other radio
wavelengths.

|  |  |
---|---|---|---
|  |  |
|  |  |
|  |  |
Figure 6:  Over-luminous compact radio sources with a projected offset of less
than $(2+\epsilon)\arcsec$. Each panel indicates the source name from LoTSS
and the host galaxy name above a PS1 R filter image in logarithmic gray scale.
Contours indicate optical data from PS1 (Chambers et al., 2016; Flewelling et
al., 2020) at $\mu+[1,2,...,10]\sigma$ levels, with $\mu$ and $\sigma$ being
the median and standard deviation, respectively. The black crosses and plus
symbols ($\times$, +) indicate the central coordinates of matched objects from
LoTSS and CLU, respectively. LoTSS astrometric uncertainty is marked as a
yellow box. Where available in the CLU catalog, we indicate a yellow ellipse
corresponding to the H$\upalpha$ detection isophote (D25). For each panel, in
the top left, we indicate the spatial offset ($\arcsec$) between the $\times$
and + markers as a white bar, along with corresponding transverse distance
(pc). Top right: LoTSS radio flux at 144 MHz in mJy, with uncertainty on the
last digit in parenthesis, host galaxy stellar mass (${\rm M^{\rm host}_{*}}$)
in ${\rm M_{\odot}}$, and redshift ($z$), with distance method indicated in
parentheses. Here, (k) means kinematic, (m) median (redshift-independent), and
(n) narrowband (H$\upalpha$). Where available, we indicate the spectral index
($\alpha$; Figure 9; §3.2) and the location of the SDSS spectroscopic fiber as
a filled yellow circle (Figure 8; §3.1, §9). Bottom left: White circles
indicate the LoTSS $6\arcsec$ beam, noting that the restoring beam used in
DDFacet (Tasse et al., 2018) for each image product type is kept constant over
the data release region and that all image products are made with a
$uv$-minimum of 100 m with the $uv$-maximum varied to provide images at
different resolutions; the highest resolution $6\arcsec$ images use baselines
up to 120 km (i.e., all LOFAR stations within the Netherlands).

|  |  |
---|---|---|---
|  |  |

|  |
---|---|---

|
---|---

Figure 7:  Over-luminous compact radio sources with projected offset greater
than $(2+\epsilon)\arcsec$. OCRs within the AGN region in Figure 1 are shown
below demarcation lines. See Figure 6 for component descriptions.

###  3.1 Main source of ionization in host galaxies

A useful tool for distinguishing between galaxies with different prevailing
photo-ionization sources is the family of emission line ratio diagnostic
diagrams introduced by Baldwin, Phillips, & Terlevich (1981, hereafter, BPT)
in which the source location is determined by a pair of low-ionization,
emission-line intensity ratios. We searched archival data444Data from: SDSS
(Abdurro’uf et al., 2022) DR 17, CALIFA (Calar Alto Legacy Integral Field
Area; González Delgado et al., 2015) survey, and LAMOST (Large Sky Area Multi-
Object Fibre Spectroscopic Telescope; Guo et al., 2022) survey. for optical
spectra to within $6\arcsec$ of the CLU coordinates. In SDSS, we found 11
matches within our candidates, and 483 out of the total 708 matched dwarf
galaxies. However, it is worth noting that $\sim 40$% of nearby radio-loud
AGNs are too gas poor and optically inactive to be detected via optical line
ratio (Geréb et al., 2015). Furthermore, low-luminosity dwarf galaxies with
low metallicities —particularly those with high star formation rates— are
susceptible to contamination from stellar processes that can potentially hide
AGN indicators (Reines et al., 2013; Molina et al., 2021). Using the
normalized emission line measurements from the MPA-JHU555A collaboration of
researchers from the Max Planck Institute for Astrophysics (MPA) and the Johns
Hopkins University (JHU). spectroscopic reanalysis666Values are taken from the
table galSpecLine. A table description is available at this url (last visited
7 September 2022). (Tremonti et al., 2004; Brinchmann et al., 2004), we
evaluated the ratios of measured line fluxes (Table 2) for $\rm{[O{\sc
III}]/H\upbeta}$ against ${\rm[N{\sc II}]/H\upalpha}$ and ${\rm[S{\sc
II}]/H\upalpha}$. We show the results in Figure 8.

Figure 8: BPT diagrams for sources with SDSS spectra showing the main source of ionization. Green and black markers correspond to sources with projected separation of less than or greater than $(2+\epsilon)\arcsec$, respectively. Gray circles are all “compact radio source-dwarf galaxy” matches with spectral line information in SDSS. Markers with a colored inner circle (colors other than black) occupy interesting parts of parameter space and are discussed in §4. The galaxy marked with a white inner circle lies above the gray line in the ${\rm S{\sc II}/H\upalpha}$ panel, while being well within the star formation range in the ${\rm[N{\sc II}]/H\upalpha}$ panel. Blue and pink inner circles fall within the composite region in the ${\rm[N{\sc II}]/H\upalpha}$ panel, where we can expect a contribution from both star formation ($H{\sc II}$ regions) and AGN activity. Finally, the galaxy marked by a cyan inner circle was classified as an AGN candidate by Truebenbach & Darling (2017) by selecting sources detected in the AllWISE and FIRST catalogs but not detected in 2MASS or SDSS DR7 and DR9.  Table 2: Emission line ratio measurements for host galaxies observed by SDSS. Source name | Host name | $\log\leavevmode\nobreak\ [{\rm N{\sc II}]/H}\upalpha$ | $\log\leavevmode\nobreak\ [{\rm O{\sc II}I]/H}\upbeta$ | $\log\leavevmode\nobreak\ [{\rm S{\sc II}]/H}\upalpha$ | $\alpha$ | $R_{g}$
---|---|---|---|---|---|---
ILT J075257.15+401026.3 | UGC 04068 | $-0.143(129)$ | $-0.017(052)$ | $-0.371(115)$ | $-0.54$ | –
ILT J162244.56+321259.3 | 2MASS J16224461+3213007 | $-0.777(311)$ | $0.073(050)$ | $-0.366(111)$ | $-0.63$ | $0.50$
ILT J142859.42+331005.2 | 2MASX J14285953+3310067 | $-0.500(179)$ | $-0.316(005)$ | $-0.260(170)$ | – | $0.08$
ILT J143050.99+410642.6 | SDSS J143051.12+410640.8 | $-0.946(158)$ | $0.127(044)$ | $-0.331(210)$ | – | $0.41$
ILT J090406.54+530314.6 | SDSS J090406.38+530311.8 | $-1.120(148)$ | $0.469(147)$ | $-0.483(159)$ | $0.18$ | –
ILT J140524.35+613358.7 | 2MASS J14052457+6134020 | $-1.254(837)$ | $0.538(426)$ | $-0.895(491)$ | $-0.88$ | $0.55$
ILT J122250.31+681434.2 | SDSS J122249.71+681431.8 | $-0.960(283)$ | $0.360(123)$ | $-0.592(091)$ | – | $0.43$
ILT J113634.77+592533.3 | SBS 1133+597 | $-0.651(474)$ | $-0.024(005)$ | $-0.565(235)$ | $-0.96$ | $0.15$
ILT J125940.18+275123.5 | 2MASX J12594007+2751177 | $-0.190(234)$ | $0.049(211)$ | $-1.510(505)$ | $-1.00$ | $0.39$

###  3.2 Spectral indices in the radio band

A radio continuum spectrum dominated by nonthermal synchrotron emission has a
characteristic power-law slope, $S_{v}\propto v^{\alpha}$. To evaluate the
spectral index $\alpha$ of our candidates, we cross-matched other radio
surveys to within a $6\arcsec$ radius from our source center. In particular,
we searched the Rapid ASKAP Continuum Survey (RACS; McConnell et al., 2020,
1.25 GHz), the Faint Images of the Radio Sky at Twenty centimeters survey
(FIRST; Becker et al., 1995, 1.4 GHz), the NRAO VLA Sky Survey (NVSS; Condon
et al., 1998, 1.4 GHz), and the Very Large Array Sky Survey (VLASS; Lacy et
al., 2020, 3 GHz). The coverage of each survey can be found in Appendix F.

We find a total of 12 matches among the 29 source candidates. Spatial coverage
by the various surveys is discussed in Appendix F. Table 3 lists the
multifrequency flux measurements used to evaluate spectral indices ($\alpha$),
following the order of sources in Table 1. Figure 9 presents for each matched
source a radio spectrum and best model from fitting a single power law to flux
measurements including uncertainties (dashed line), with corresponding
$\alpha$. The resulting spectral indices range between $0.2\pm 0.01$ and
$-1.0\pm 0.10$.

It is worth noting that if our sources are partially resolved by some surveys
then our spectral index estimates will be systematically biased. The beam
sizes of LoTSS (6″) and FIRST (5″) are comparable, while the beam of VLASS is
slightly smaller ($\sim$3″), and is larger in both NVSS and and RACS
($\sim$15″). We checked whether or not the sources were point-like by
comparing the peak flux density to the integrated flux density in RACS, VLASS
and LoTSS (NVSS does not provide peak flux information) in Fig. 10. In most
cases, flux ratios in FIRST, RACS and VLASS point toward compactness, with
median ratios of 1.0, 0.8, and 0.8, respectively (with a minimal ratio of 0.6,
0.6, and 0.8; and a maximal ratio of 1.7, 1.0, and 0.9). Despite the point-
source-like nature of our candidates, we caution the reader that the possible
presence of diffuse synchrotron emission from the host galaxy could have
biased our flux estimates. This effect is especially apparent at very large
beam size ratios (e.g., Venkattu et al., 2023). Unfortunately, we do not yet
have VLBI detection of our sources to test this hypothesis: we cross-matched
the candidates with the Radio Fundamental Catalog777http://astrogeo.org/rfc/,
last visited 27 June 2023. and mJIVE-20 (Deller & Middelberg, 2014)—two VLBI
datasets—, but found no matches.

Table 3: Fluxes for candidates matched in at least one ancillary radio survey.

Source name | $S_{\rm LoTSS}$ | $S_{\rm RACS}$ | $S_{\rm FIRST}$ | $S_{\rm NVSS}$ | $S_{\rm VLASS}$ | $\alpha$ | $\alpha_{\rm HF}$
---|---|---|---|---|---|---|---
(ILT J) | (mJy) | (mJy) | (mJy) | (mJy) | (mJy) |  |
003532.36+303008.0 | $11.89\pm 0.35$ | – | – | $3.90\pm 0.50$ | $1.99\pm 0.28$ | $-0.6\pm 0.04$ | $-0.9\pm 0.25$
021835.45+262040.9 | $6.55\pm 0.44$ | $2.07\pm 0.86$ | – | – | – | $-0.5\pm 0.19$ | –
075257.15+401026.3 | $7.37\pm 0.35$ | – | $2.14\pm 0.15$ | – | [$0.50\pm 0.05$] | $-0.5\pm 0.04$ | [$-1.9\pm 0.13$]
162244.56+321259.3 | $8.06\pm 0.18$ | – | $1.81\pm 0.15$ | $2.70\pm 0.40$ | [$1.20\pm 0.05$] | $-0.6\pm 0.03$ | [$-0.8\pm 0.05$]
015915.79+242500.6 | $4.30\pm 0.43$ | $4.18\pm 1.13$ | – | – | – | $-0.0\pm 0.13$ | –
090406.54+530314.6 | $6.69\pm 0.13$ | – | $12.65\pm 0.15$ | $15.30\pm 0.90$ | $9.52\pm 0.23$ | $0.2\pm 0.01$ | $-0.4\pm 0.03$
023058.18+232412.6 | $11.49\pm 1.31$ | $3.51\pm 0.89$ | – | $2.40\pm 0.40$ | – | $-0.7\pm 0.08$ | –
140524.35+613358.7 | $22.37\pm 0.13$ | – | $3.11\pm 0.14$ | – | $1.08\pm 0.24$ | $-0.9\pm 0.02$ | $-1.4\pm 0.30$
091333.83+300056.9 | $5.89\pm 0.49$ | – | $0.65\pm 0.13$ | – | – | $-1.0\pm 0.10$ | –
113634.77+592533.3 | $12.82\pm 0.12$ | – | $1.44\pm 0.20$ | – | – | $-1.0\pm 0.06$ | –
125940.18+275123.5 | $22.34\pm 0.20$ | $5.83\pm 1.38$ | $2.09\pm 0.18$ | $3.00\pm 0.40$ | – | $-1.0\pm 0.03$ | –
161111.24+360401.0 | $8.45\pm 0.17$ | – | $1.41\pm 0.14$ | – | [$0.50\pm 0.05$] | $-0.8\pm 0.04$ | [$-1.4\pm 0.18$]

  * •

Measurements from LoTSS, RACS, VLA FIRST, NVSS, and VLASS at 144 MHz, 1.25
GHz, 1.4 GHz, 1.4 GHz, and 3 GHz, respectively. Values in square parentheses
are estimated based on cutout image from CIRADA Image Cutout Web Service. Only
spectral indices in brackets include estimates from CIRADA Cutouts.

Figure 9: Radio spectra of candidates matched in one or more of the RACS,
FIRST, NVSS, and VLASS surveys, with central frequencies of 1.25 GHz, 1.4 GHz,
1.4 GHz, and 3 GHz, respectively. LoTSS observes at a central frequency of 144
MHz. The source name in LoTSS is indicated for each candidate. Black markers
show flux measurements with uncertainties (small enough not to be visible),
and the dashed blue lines show the best power-law fit over all frequencies,
with power-law index $\alpha$ also indicated. Where applicable, a gray dashed
line shows the best power-law fit at higher frequencies (${\rm\sim 1-3}$ GHz.
Figure 10: Comparing peak flux ($S_{p}$) and integrated flux ($S_{i}$, Tables
1 and 3) measurements in the various surveys. Gray lines in the upper panel
indicate a 1:1 ratio. In the lower panel, the solid and dashed blue lines
indicate the median and mean of each ratio distribution, respectively. NVSS
does not provide peak flux information.

###  3.3  X-ray and gamma ray bands

We searched the ancillary data from the Chandra and XMM-Newton (namely Chandra
Source Catalog Release 2.0, XMM-EPIC, and XMM-EPIC-STACK) which we query via
the astroquery (v0.4.6) ESA Sky module, and the Burst Alert Spectroscopic
Survey (BASS; Koss et al., 2017) to within 15″. Chandra SC2 observed 7 out of
the 29 candidates, and XMM-Newton only 2. The only match (found in Chandra
SC2) corresponds to the source 2CXO J125943.4+275802. The X-ray source covers
the cluster of galaxies ACO 1656 mentioned in §3, and can be attributed to
free-free emission (bremsstrahlung) at the cluster scale, and therefore not
directly attributable to our compact source. It is worth noting that X-ray
observations toward FRB 20121102A have not yet been constraining (Chatterjee
et al., 2017; Marcote et al., 2017). Similarly, we search the Fermi 4FGL
second data release to within 6 arcmin for gamma-ray emission (also with
astroquery.esasky). All candidate fields have been observed; we did not find
any match.

We find it difficult to interpret the X-ray nondetections using the
fundamental plane of BH activity, that is, the empirical correlation between
the continuum X-ray, radio emission, and mass of an accreting black hole
(Gültekin et al., 2019). Firstly, the 6″spatial resolution data from LoTSS can
only provide upper limits as it is not possible to isolate the nuclear core
flux with good point-source sensitivity (which would require subarcsecond
spatial resolution). Furthermore, LoTSS and any X-ray data mentioned in this
section were not obtained simultaneously, and the timescale for variations in
flux would be short for IMBHs, that is, scaling with the size of the “event
horizon” and therefore with the black hole mass.

We obtained flux upper limits in the hard state for both Chandra (accessed
with CSCview888https://cxc.harvard.edu/csc/gui/intro.html, last accessed 18
July 2023., using values in the 2–7 keV range) and XMM-Newton (accessed with
flix999https://www.ledas.ac.uk/flix/flix.html, last accessed 18 July 2023. for
XMM-Newton in the 2–10 keV range). We evaluate the upper limits using the
prescription from Gültekin et al. (2019), which typically uses radio flux at 5
GHz, and X-ray flux at 2–10 keV. We scale radio flux to 5 GHz using either
$\alpha=-0.7$ or using spectral indices from Table 3 where available. Results
are listed in Table 4, with estimated BH mass limits ranging from below $\sim
10^{7}\,{\rm M_{\odot}}$ to $\sim 10^{8}\,{\rm M_{\odot}}$. Given the reasons
highlighted above, we advise the reader to use these upper limits with
caution.

Table 4: BH mass upper limits estimated from radio flux and X-ray flux limits.

Source name | M∗,host | Lr | Lx,XMM | Lx,Chandra | M${}_{\mathbin{\vbox{\hbox{\scalebox{0.5}{$\bullet$}}}},{\rm XMM}}$ | M${}_{\mathbin{\vbox{\hbox{\scalebox{0.5}{$\bullet$}}}},{\rm Chandra}}$
---|---|---|---|---|---|---
(ILT J) | (${\rm M_{\odot}}$) | (${\rm erg\,s^{-1}}$) | (${\rm erg\,s^{-1}}$) | (${\rm erg\,s^{-1}}$) | (${\rm M_{\odot}}$) | (${\rm M_{\odot}}$)
153943.52+592730.7 | $2.0\times 10^{9}$ | $5.0\times 10^{37}$ | $<3.0\times 10^{41}$ | – | $<2.2\times 10^{7}$ | –
125940.18+275123.5 | $1.4\times 10^{9}$ | $3.4\times 10^{37}$ | $<3.5\times 10^{40}$ | $<1.1\times 10^{39}$ | $<5.2\times 10^{7}$ | $<4.0\times 10^{8}$
125915.34+274604.2 | $8.2\times 10^{8}$ | $1.1\times 10^{37}$ | – | $<1.3\times 10^{40}$ | – | $<2.6\times 10^{7}$
125944.53+275800.9 | $2.7\times 10^{8}$ | $2.5\times 10^{37}$ | – | $<7.2\times 10^{39}$ | – | $<9.4\times 10^{7}$
142859.42+331005.2 | $2.7\times 10^{9}$ | $1.6\times 10^{37}$ | – | $<2.2\times 10^{40}$ | – | $<3.0\times 10^{7}$
091333.83+300056.9 | $1.7\times 10^{9}$ | $2.3\times 10^{37}$ | – | $<2.9\times 10^{39}$ | – | $<1.5\times 10^{8}$
231715.38+184339.0 | $2.3\times 10^{9}$ | $4.1\times 10^{37}$ | – | $<6.9\times 10^{39}$ | – | $<1.7\times 10^{8}$
143037.30+352053.3 | $6.3\times 10^{8}$ | $1.7\times 10^{37}$ | – | $<2.6\times 10^{40}$ | – | $<3.0\times 10^{7}$

  * •

Radio luminosity from LoTSS are scaled to 5 GHz, X-ray data from XMM-Newton
(2–10 keV) and Chandra (2–7 keV).

##  4 Discussion

###  4.1 Cause of radio emission

We here investigate what can be ascertained about the potential progenitors of
our selected candidates given emission line ratios and spectral index
measurements presented in §3. Markers below and to the left of the solid and
dashed gray lines in Figure 8 indicate that the emission lines are due to star
formation and not to AGN activity (Kewley et al., 2001; Kauffmann et al.,
2003). Measurement uncertainties cannot definitively rule out an AGN
contribution in three cases. For galaxies falling within the star formation
region of this parameter space, ionising flux is primarily provided by hot,
massive, young stars and associated supernovae surrounded by HII regions
(Zajaček et al., 2019).

A few cases occupy interesting regions of parameter space. ILT
J090406.54+530314.6 (white inner circles) sits above the gray line in the
${\rm S{\sc II}/H\upalpha}$ panel, while sitting well within the star
formation range in the ${\rm[N{\sc II}]/H\upalpha}$ panel. ILT
J075257.15+401026.3 (blue inner circles) and ILT J125940.18+275123.5 (pink
inner circles) fall within the composite region between models from Kewley et
al. (2001) and Kauffmann et al. (2003) in the ${\rm[N{\sc II}]/H\upalpha}$
panel. For these, we can expect a contribution from both star formation (HII
regions) and AGN activity.

Similarly, the galaxy UGC 04068, which hosts ILT J075257.15+401026.3 has been
classified as an AGN by Véron-Cetty & Véron (2010), while the classification
based on the SDSS spectrum is simply “galaxy” (rather than other considered
classes in SDSS nomenclature, such as QSO). There is a bright star located
near the centroid of the galaxy (slightly leftward in Figure 6) that may
impact the overall flux observed in the spectrum, especially given the
location of the SDSS spectrograph fiber (pink circle) almost exactly between
the galaxy centroid and that of the bright star. It is also the only case
within the candidates where the CLU catalog contains a fitted H$\upalpha$ D25
measurement. CLU J163850.64+352900.9 and 2MASX J09133387+3000514 are
unclassified in SDSS, while all other matches are classified as galaxies.

Finally, we note that ILT J113634.77+592533.3 (cyan inner circles) was
classified as an AGN candidate by Truebenbach & Darling (2017) by selecting
sources detected in the AllWISE and FIRST catalogs, but not detected in 2MASS
or SDSS DR7 and DR9. However, we note that the source may be matched to the
galaxy SBS 1133+597, which has been observed by SDSS and for which the BPT
diagram rather indicates that the driving source of ionization in the galaxy
can be attributed to star formation.

The value of $\alpha$ helps distinguish between optically thin and optically
thick emission mechanisms. We note that flux measurements from the archival
surveys we used span several decades of observations, with FIRST and NVSS
being the oldest, and RACS, VLASS and LoTSS being contemporaneous but not
simultaneous. Using archival data spanning many decades comes with the caveat
that measurements may be affected by time-dependent phenomena like
scintillation or source evolution. In cases where radio emission is powered by
an AGN, variability at various timescales (from days to years) can be expected
with potential flux variations of the order of 100 mJy at GHz frequencies, and
in rare cases varying by factors of several in flux density over timescales
measured in decades (Nyland et al., 2020). Almost no variability is expected
from star formation on the timescale covered by our data.

The range of spectral indices covered by various source types is known to
differ. Pulsars have spectral indices of $\lesssim-1.2$ (Bates et al., 2013).
Given the range of values of our candidates, they are unlikely to be pulsars.
Moreover, we can assume that if an OCR (detected by LoTSS/FIRST/NVSS) is a
radio pulsar, it would have to be Galactic, and would therefore be an
unrelated foreground object in a chance alignment with the background galaxy
as LoTSS should not be sensitive to extragalactic pulsars. Supernova remnants
tend to have spectral indices ranging between $-0.1$ and $-0.8$ (Kothes et
al., 2006; Alvarez et al., 2001). Six of our candidates fall within this
range, including five cases with offset below $(2+\epsilon)\arcsec$. Planck
Collaboration et al. (2011) showed that the spectral indices of AGNs at low
frequencies ($1.1-\leq 70$ GHz) are fairly flat, with an average of $-0.06$.
Their distribution is narrow, with 91% of the indices being in the range
$\alpha\in[$-0.5$,0.5]$. However, a few sources have remarkably steep spectra
$\leq-0.8$, while others have inverted spectra ($\alpha=0.86$). Although our
spectral indices are calculated at lower frequencies than these (where
possible, we also computed the spectral index at higher frequency between
$1.4-3$ GHz), they all fall within this broad range.

Comparing spectral indices between 4.85 and 10.45 GHz from a distribution of
radio sources with optical counterparts, Zajaček et al. (2019) showed that the
ionization potential of sources with an inverted radio spectrum
($\alpha>-0.4$) is weaker than that of sources with a steep radio spectrum
($\alpha<-0.7$). In particular, simultaneous two-point $\alpha$ measurement at
4.85 and 10.45 GHz at Effelsberg highlighted that decreasing spectral indices
from steep to flat ($-0.7<\alpha<-0.4$) to inverted leads to a decrease in
typical line ratios (BPT diagram), particularly ${\rm[O{\sc III}]/H\upbeta}$.

Zajaček et al. (2019) considered radio loudness $R_{g}$ in addition to
$\alpha$ and ionization ratio in order to highlight three distinct classes of
radio emitters resulting from recurrent nuclear jet activity distributed along
the transition from Seyfert to LINER sources in the optical diagnostic, namely
sources with: (class 1) steep $\alpha$, high ionization ratio, and high radio
loudness; (class 2) flat $\alpha$, lower ionization ratio, and intermediate
radio loudness; and (class 3) inverted $\alpha$, low ionization ratio, and low
radio loudness.

To compare our results to those of Zajaček et al. (2019), we computed $R_{g}$
using the flux density from LoTSS, $F_{144}$. We converted $F_{144}$ into the
$AB_{\nu}$ radio magnitude system of Oke & Gunn (1983), according to Ivezić et
al. (2002): $m_{1.4}=-2.5\log{F_{1.4}/3631\,{\rm Jy}}$, in which the zero
point 3631 Jy does not depend on wavelength, and scaled the fluxes from 144
MHz to 1.4 GHz using either our fitted spectral indices or $\alpha=-0.7$
otherwise. Subsequently, the radio loudness can be calculated as the ratio of
the radio flux density to the optical flux density, $R_{g}\equiv\log{F_{\rm
radio}/F_{\rm optical}}=0.4(g-m_{144})$, with $g$ corresponding to the
magnitude in the optical $g$-band. We use SDSS magnitudes in the g band where
available, and g-band Kron magnitudes from PS1 where available otherwise.

We list values of $R_{g}$ in Table 1. For our whole set of candidates, $R_{g}$
ranges between 0.05 and 2.48, with mean, median, and standard deviation of
1.21, 1.16, and 0.48, respectively. Sources for which we can evaluate $R_{g}$
and emission line ratio between ${\rm[O{\sc III}]}$ and ${\rm H\upbeta}$ are
shown in the upper panel of Figure 11, displaying $\alpha$ where possible
using the color map101010We note that the point with $\alpha\sim-0.6$ shown in
pink is calculated using detections at all available frequencies, and that its
equivalent at higher frequencies corresponds to $-0.88$, as shown in Table 3.
and in gray otherwise. In addition, we show distributions of $R_{g}$ (central
panel) and $\alpha$ (lower panel) for candidates with and without available
optical spectra in gray and black, respectively. In the lower panel, we mark
the regions defined by Eckart et al. (1986) separating steep ($\alpha<-0.7$,
class 1), flat ($-0.7\leq\alpha\leq-0.4$, class 2), and inverted
($\alpha>-0.4$, class 3) spectrum sources in blue, green and pink,
respectively, in order to reflect the distributions of the spectral index for
samples of radio-loud galaxies in the range of ${\rm 1.6-5\,GHz}$ —regions of
parameter space also used to classify sources by Zajaček et al. (2019).

The region occupied in the emission line ratio–loudness plane by our matched
sources corresponds to that of sources classified as class 3 by Zajaček et al.
(2019, e.g., their Figure 12), though with much lower $R_{g}$ (the lower bound
on $R_{g}$ used by Zajaček et al. being $\sim 0.7$). The sample used by these
latter authors covered supermassive black holes ($\rm>10^{5}\,M_{\odot}$),
explaining the loudness discrepancy where dwarf galaxies could be hosting
IMBHs instead. Their spectral index distribution (black, lower panel) rather
points toward class 1 or 2, even when considering $\alpha$ evaluated at higher
frequencies ($1.4-3$ GHz; orange dotted border showing sources with associated
spectrum; blue border showing all cases matched at high frequencies).
Unfortunately, given that only four sources shown in the top panel of Figure
11 were matched in other surveys to evaluate a spectral index, these results
provide only small number statistics. Nevertheless, the initial information
they carry points toward a mismatch between the primarily AGN-related source
studied by Zajaček et al. (2019), which mainly fall along the demarcation line
between Seyfert and LINER, and our candidates primarily located well within
the star formation region of the BPT diagram, which strengthens our hypothesis
that the OCRs in our sample are not AGNs. Follow-up observations at higher
frequencies similar to those observed by Zajaček et al. would allow this
tension to be further scrutinized.

Figure 11: Comparing radio loudness $R_{g}$, emission line ratio ${\rm[O{\sc
III}]/H\upbeta,}$ and spectral index, where available. From the sample of 26
$R_{g}$ values (Table 1), 7 also have ${\rm[O{\sc III}]/H\upbeta}$ values
available (Table 2, alias T2; black bars in central panel), and 9 have fitted
$\alpha$ values (Table 3, alias T3). HF indicates spectral indices fitted
between 1.4 and 3 GHz. Class 1, 2, and 3 (c1, c2, c3) as defined by Eckart et
al. (1986). Unfilled histograms in middle and lower panels represent all
available “compact radio source-dwarf galaxy” matches below 3$\sigma$ on the
L–SFR relation.

###  4.2 Volumetric density and rate of over-luminous compact radio sources

The CLU catalog consists of galaxies selected to be within 200 Mpc and is
complete to a flux limit of $10^{-14}\,$erg s-1 cm-2. This limit corresponds
to a dust-unobscured star formation rate of $\approx 1$ M⊙ yr-1 (Cook et al.,
2019). The 200 Mpc distance is small enough for us to assume a Euclidean
geometry in our volume density calculations. Based on the 29 sources in Table
1, we can summarily compute a lower limit of $856\pm 150$ sources Gpc-3
($1\sigma$ Poisson bounds in parentheses) for compact radio sources (on
arcsecond-scales) above 0.8 mJy at 144 MHz that deviate by more than $3\sigma$
from the radio–SFR relationship. The limit is preliminary because VLBI
observations are necessary to conclusively rule out a star-formation origin
for our sources.

We can compare this rate to that suggested by Law et al. (2022) for persistent
radio sources associated with FRB progenitors. These latter authors compute a
volume density of $50-10,000$ Gpc-3 for sources with a 1.4 GHz radio
luminosity of greater than $10^{29}\,$ ergs s-1 Hz-1. A separate volume
density computed by Ofek (2017) is close to the upper end of the density
computed by Law et al. (2022). A source of $10^{29}$ erg s-1 Hz-1 luminosity
placed at our survey horizon of 200 Mpc would have a flux density of 2.2 mJy.
Given our survey completeness of 0.8 mJy, such a source would be detected in
our survey if it was optically thin or if it had an inverted spectrum with a
spectral index shallower than $\approx 0.4$ (i.e., a relatively flat
spectrum). However, our survey is also sensitive to closer sources with much
lower flux densities.

To account for this, we assumed that the FRB-related PRS sources follow a
Schechter luminosity function (Schechter, 1976) with an exponent of $-1$ and a
cut-off luminosity that is ten times the Law et al. (2022) normalization point
of $10^{29}$ erg s-1 Hz-1. We also assumed that the sources have a flat
spectrum and computed the number of sources that would likely exceed the 0.9
mJy completeness limit of our survey. We then numerically computed the
expected number of detectable sources within a 200 Mpc horizon. For the
$50-10,000$ Gpc-3 range specified in Law et al. (2022), we expect to detect
$0.3-58$ sources, which is consistent with our yield of 28 candidates. Values
of cut-off luminosity in excess of $10^{30.5}\,$erg s-1 Hz-1 are necessary to
create a tension between our yield and the Law et al. (2022) rates. While the
consistency is encouraging, we caution against drawing firm conclusions
because of the unknown FRB beaming fraction on which the Law et al. (2022)
estimate is based, along with the disparate selection filters applied in the
analysis of these latter authors and ours.

###  4.3 Star formation versus active (intermediate-mass) black holes

Condon et al. (2019) evaluated the luminosity functions for sources whose
radio emission is dominated by star formation and AGN, respectively. After
scaling the luminosity of our candidates to 1.4 GHz using either the spectral
indices evaluated in §3.2 or $\alpha\approx-0.7$ for typical synchrotron
spectra of optically thin radio sources for the remaining sources, we find
luminosity values ranging between $10^{17.9}$ and $10^{22.7}$
$\mathrm{W\,Hz^{-1}}$, with a median of $10^{19.9}$ $\mathrm{W\,Hz^{-1}}$.
Compared to the luminosity functions for star formation and AGN of Condon et
al. (2019), the radio emission from our candidates is more likely attributable
to star formation.

A critical step towards establishing the candidates presented in previous
sections as potential FRB hosts is to conclusively determine the compactness
of these sources. To this end, we obtained time on the European VLBI network
(EVN) and e-MERLIN to observe the most likely candidates. Compactness in LoTSS
images only ensures a brightness temperature of $\gtrsim 10^{4}\,{\rm K}$,
which is insufficient to rule out unusually radio-bright star formation as the
cause of the radio emission. Moreover, our sources may have a significant
component of their radio flux attributed to star formation with the rest in a
compact source component. VLBI at $\lesssim 10\,$mas resolution is therefore
the best observational technique to totally eliminate (i.e., resolve out) the
star-formation component and establish the presence of a compact source.
Furthermore, including the e-MERLIN array should allow us to distinguish
between compact and star-formation components, if present. In addition, we are
in the process of reimaging the archival LoTSS radio data on these sources
while including the international stations from LOFAR. The resulting images
should have a resolution of about $0\aas@@fstack{\prime\prime}25$ (LOFAR-VLBI;
Morabito et al., 2022). These higher-angular-resolution images should inform
us about the following possible outcomes.

If a target were not detected at very high resolution then it would confirm
the star-formation hypothesis. This would be a rather unusual conclusion as
the selected targets all violate the radio–SFR relationship, and so a
nondetection at very high resolution would cast doubt on the canonical radio-
AGN selection technique that is widely used (Davis et al., 2022). It is
possible that AGN-related flux is present on intermediate scales of a few
hundred milliarcseconds, which are inaccessible to the EVN, but should be
accessible by the intermediate scale of e-MERLIN. Moreover, in such a case,
AGN-related flux should also be detectable with LOFAR long-baseline data.

The detection of a core–jet structure would confirm the AGN-like IMBH
hypothesis. Although the radio detection of black-hole jet candidates in dwarf
galaxies based on the procedure mentioned in §2 is now becoming feasible
(Davis et al., 2022), confirmatory VLBI detection of the jet (or structure
thereof) is rare (Paragi et al., 2014; Yang et al., 2020; Eftekhari et al.,
2020). As such, confirmation of the AGN hypothesis will have interesting
scientific consequences for studies of feedback in dwarf galaxies.

If an unresolved point is detected, although it would rule out the star-
formation hypothesis, both the PWN and unresolved AGN would remain
plausible—even if the source proves to be slightly ($\ll 1\arcsec$) offset
from the optical stellar light centroid. Based on the known properties of
starburst galaxies, a detection on EVN long baselines should exclude star
formation as the cause of the bulk of the radio emission (Condon et al.,
1991). Here, a path forward would be to follow-up such sources to model their
broad-band SED (e.g., with optical spectroscopy directly on-source to search
for canonical AGN signatures, and with radio observations at C, X, and K
bands) in order to decipher between the PWN and AGN hypotheses.

###  4.4 Future search for FRBs

Finally, we also plan to search these targets for millisecond-duration bursts
with the 25 meter Westerbork Synthesis Radio Telescope. Starting with the
hypothesis that some are similar in nature to currently known PRSs, we can
expect these to be repeating FRB sources. Furthermore, given the periodic
activity of some FRBs, such as FRB 20121102A (Cruces et al., 2021; Rajwade et
al., 2020) and FRB 20180916B (Chime/Frb Collaboration et al., 2020), it is
plausible that a subset of our candidates could also display on/off phases of
FRB emission.

##  5 Summary

In this paper, we present a targeted search for OCRs coincident with dwarf
galaxies up to $z\lesssim 0.05$.

  1. 1.

We identified candidate compact sources with luminosity exceeding $3\sigma$
relative to the L–SFR relation (Gürkan et al., 2018).

  2. 2.

Through ancillary surveys, we investigated the possible nature of the
candidates.

  3. 3.

Emission line ratios from SDSS spectra show the main source of ionization in
the host galaxies where the candidates are located is likely star formation,
and not AGN activity.

  4. 4.

Spectral indices suggest that our candidates could be SNRs or AGNs—although,
the combination of $\alpha$ with emission line ratios and radio loudness
provides evidence that we may be observing sources other than typical AGNs.

  5. 5.

A comparison to the luminosity functions for star formation and AGN of Condon
et al. (2019) indicates that radio emission from our candidates is more likely
attributable to star formation.

  6. 6.

We derive a preliminary lower limit of $856\pm 150$ sources Gpc-3 ($1\sigma$
Poisson bounds in parentheses) for compact radio sources (on arcsecond-scales)
above 0.8 mJy at 144 MHz that deviate by more than $3\sigma$ from the
radio–SFR relationship.

  7. 7.

For the $50-10,000$ Gpc-3 range specified in Law et al. (2022), we expect to
detect $0.3-58$ sources within the 200 Mpc horizon of our optical parent
sample, which is consistent with our yield of 28 candidates.

Follow-up high-angular-resolution imaging should allow us to further describe
these outlying radio sources. Furthermore, searching these sources for high-
time-resolution bursts may inform us about the FRB progenitor. If only a
subsample of our candidates turn out to be active sources of persistent radio
emission associated to FRBs, as is the case for those presented by Chatterjee
et al. (2017) and Niu et al. (2022), it would be possible to evaluate whether
or not these are indeed calorimeters allowing us to estimate the energy output
of the central FRB engine.

We end by noting that due to the unprecedented sensitivity of LoTSS to
optically thin synchrotron sources in a wide-angle survey, we have been able
to select interesting radio sources in dwarf galaxies. The proposed VLBI
observations are a crucial step toward the discovery of a new population of
either wind nebulae or black holes in nearby dwarf galaxies—both outcomes
being scientifically interesting.

###### Acknowledgements.

This work was carried out in part through funding from the European Open
Science Cloud (EOSC) Future, an EU-funded H2020 project. DV thanks Benito
Marcote, Shivani Bhandari, Kenzie Nimmo, and Betsey Adams for valuable
discussions. We thank our referee for constructive comments. LOFAR is the Low
Frequency Array designed and constructed by ASTRON. It has observing, data
processing, and data storage facilities in several countries, which are owned
by various parties (each with their own funding sources), and which are
collectively operated by the ILT foundation under a joint scientific policy.
The ILT resources have benefited from the following recent major funding
sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans, France;
BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of
Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The
Science and Technology Facilities Council, UK; Ministry of Science and Higher
Education, Poland; The Istituto Nazionale di Astrofisica (INAF), Italy. The
Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made
possible through contributions by the Institute for Astronomy, the University
of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
participating institutes, the Max Planck Institute for Astronomy, Heidelberg
and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns
Hopkins University, Durham University, the University of Edinburgh, the
Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics,
the Las Cumbres Observatory Global Telescope Network Incorporated, the
National Central University of Taiwan, the Space Telescope Science Institute,
the National Aeronautics and Space Administration under Grant No. NNX08AR22G
issued through the Planetary Science Division of the NASA Science Mission
Directorate, the National Science Foundation Grant No. AST-1238877, the
University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos
National Laboratory, and the Gordon and Betty Moore Foundation. This research
has made use of the VLASS QLimage cutout server at URL cutouts.cirada.ca,
operated by the Canadian Initiative for Radio Astronomy Data Analysis
(CIRADA). CIRADA is funded by a grant from the Canada Foundation for
Innovation 2017 Innovation Fund (Project 35999), as well as by the Provinces
of Ontario, British Columbia, Alberta, Manitoba and Quebec, in collaboration
with the National Research Council of Canada, the US National Radio Astronomy
Observatory and Australia’s Commonwealth Scientific and Industrial Research
Organisation. This research is based in part on data collected at Subaru
Telescope, which is operated by the National Astronomical Observatory of
Japan. We are honored and grateful for the opportunity of observing the
Universe from Maunakea, which has the cultural, historical and natural
significance in Hawaii. Part of the data are retrieved from the JVO portal
(http://jvo.nao.ac.jp/portal) operated by the NAOJ. Software: Astropy (Astropy
Collaboration et al., 2013, 2018, 2022), Astroquery (Ginsburg et al., 2019),
(Robitaille & Bressert, 2012), Aladin (Boch et al., 2011), Topcat (Taylor,
2011), askap_surveys111111https://github.com/askap-vast/askap_surveys, last
visited 10 July 2023. (David Kaplan and Andrew O’Brien (UW-Milwaukee)),
matchmaker (Vohl, 2023). The custom code used to generate these results is
publicly available at https://doi.org/10.5281/zenodo.10018524.

## References

  * Abdurro’uf et al. (2022) Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35
  * Aihara et al. (2019) Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, PASJ, 71, 114
  * Alam et al. (2015) Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12
  * Alvarez et al. (2001) Alvarez, H., Aparici, J., May, J., & Reich, P. 2001, A&A, 372, 636
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33
  * Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5
  * Bassa et al. (2017) Bassa, C. G., Tendulkar, S. P., Adams, E. A. K., et al. 2017, ApJ, 843, L8
  * Bates et al. (2013) Bates, S. D., Lorimer, D. R., & Verbiest, J. P. W. 2013, MNRAS, 431, 1352
  * Becker et al. (1995) Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559
  * Bianchi et al. (2014) Bianchi, L., Conti, A., & Shiao, B. 2014, Advances in Space Research, 53, 900
  * Boch et al. (2011) Boch, T., Oberto, A., Fernique, P., & Bonnarel, F. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 442, Astronomical Data Analysis Software and Systems XX, ed. I. N. Evans, A. Accomazzi, D. J. Mink, & A. H. Rots, 683
  * Bonnarel et al. (2000) Bonnarel, F., Fernique, P., Bienaymé, O., et al. 2000, A&AS, 143, 33
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chatterjee et al. (2017) Chatterjee, S., Law, C. J., Wharton, R. S., et al. 2017, Nature, 541, 58
  * Chen et al. (2022) Chen, G., Ravi, V., & Hallinan, G. W. 2022, arXiv e-prints, arXiv:2201.00999
  * Chime/Frb Collaboration et al. (2020) Chime/Frb Collaboration, Amiri, M., Andersen, B. C., et al. 2020, Nature, 582, 351
  * Condon et al. (1998) Condon, J. J., Cotton, W. D., Greisen, E. W., et al. 1998, AJ, 115, 1693
  * Condon et al. (1991) Condon, J. J., Huang, Z. P., Yin, Q. F., & Thuan, T. X. 1991, ApJ, 378, 65
  * Condon et al. (2019) Condon, J. J., Matthews, A. M., & Broderick, J. J. 2019, ApJ, 872, 148
  * Cook et al. (2019) Cook, D. O., Kasliwal, M. M., Van Sistine, A., et al. 2019, ApJ, 880, 7
  * Cruces et al. (2021) Cruces, M., Spitler, L. G., Scholz, P., et al. 2021, MNRAS, 500, 448
  * Curti et al. (2020) Curti, M., Mannucci, F., Cresci, G., & Maiolino, R. 2020, MNRAS, 491, 944
  * Davis et al. (2022) Davis, F., Kaviraj, S., Hardcastle, M. J., et al. 2022, MNRAS, 511, 4109
  * Deller & Middelberg (2014) Deller, A. T. & Middelberg, E. 2014, AJ, 147, 14
  * Dong & Hallinan (2023) Dong, D. Z. & Hallinan, G. 2023, ApJ, 948, 119
  * Eckart et al. (1986) Eckart, A., Witzel, A., Biermann, P., et al. 1986, A&A, 168, 17
  * Eftekhari et al. (2020) Eftekhari, T., Berger, E., Margalit, B., Metzger, B. D., & Williams, P. K. G. 2020, ApJ, 895, 98
  * Flewelling et al. (2020) Flewelling, H. A., Magnier, E. A., Chambers, K. C., et al. 2020, ApJS, 251, 7
  * Gaensler & Slane (2006) Gaensler, B. M. & Slane, P. O. 2006, ARA&A, 44, 17
  * Geréb et al. (2015) Geréb, K., Morganti, R., Oosterloo, T. A., Hoppmann, L., & Staveley-Smith, L. 2015, A&A, 580, A43
  * Ginsburg et al. (2019) Ginsburg, A., Sipőcz, B. M., Brasseur, C. E., et al. 2019, AJ, 157, 98
  * González Delgado et al. (2015) González Delgado, R. M., García-Benito, R., Pérez, E., et al. 2015, A&A, 581, A103
  * Greene et al. (2020) Greene, J. E., Strader, J., & Ho, L. C. 2020, ARA&A, 58, 257
  * Gültekin et al. (2019) Gültekin, K., King, A. L., Cackett, E. M., et al. 2019, ApJ, 871, 80
  * Guo et al. (2022) Guo, Y., Liu, C., Wang, L., et al. 2022, VizieR Online Data Catalog, J/A+A/667/A44
  * Gürkan et al. (2018) Gürkan, G., Hardcastle, M. J., Smith, D. J. B., et al. 2018, MNRAS, 475, 3010
  * Hessels et al. (2019) Hessels, J. W. T., Spitler, L. G., Seymour, A. D., et al. 2019, ApJ, 876, L23
  * Ivezić et al. (2002) Ivezić, Ž., Menou, K., Knapp, G. R., et al. 2002, AJ, 124, 2364
  * Jarrett et al. (2011) Jarrett, T. H., Cohen, M., Masci, F., et al. 2011, ApJ, 735, 112
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055
  * Kewley et al. (2001) Kewley, L. J., Dopita, M. A., Sutherland, R. S., Heisler, C. A., & Trevena, J. 2001, ApJ, 556, 121
  * Koss et al. (2017) Koss, M., Trakhtenbrot, B., Ricci, C., et al. 2017, ApJ, 850, 74
  * Kothes et al. (2006) Kothes, R., Fedotov, K., Foster, T. J., & Uyanıker, B. 2006, A&A, 457, 1081
  * Kron (1980) Kron, R. G. 1980, ApJS, 43, 305
  * Lacy et al. (2020) Lacy, M., Baum, S. A., Chandler, C. J., et al. 2020, PASP, 132, 035001
  * Law et al. (2022) Law, C. J., Connor, L., & Aggarwal, K. 2022, ApJ, 927, 55
  * Marcote et al. (2017) Marcote, B., Paragi, Z., Hessels, J. W. T., et al. 2017, ApJ, 834, L8
  * Margalit & Metzger (2018) Margalit, B. & Metzger, B. D. 2018, ApJ, 868, L4
  * Martin et al. (2005) Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJ, 619, L1
  * McConnell et al. (2020) McConnell, D., Hale, C. L., Lenc, E., et al. 2020, PASA, 37, e048
  * McConnell & Ma (2013) McConnell, N. J. & Ma, C.-P. 2013, ApJ, 764, 184
  * Michilli et al. (2018) Michilli, D., Seymour, A., Hessels, J. W. T., et al. 2018, Nature, 553, 182
  * Mohan & Rafferty (2015) Mohan, N. & Rafferty, D. 2015, PyBDSF: Python Blob Detection and Source Finder, Astrophysics Source Code Library, record ascl:1502.007
  * Molina et al. (2021) Molina, M., Reines, A. E., Greene, J. E., Darling, J., & Condon, J. J. 2021, ApJ, 910, 5
  * Mondal et al. (2020) Mondal, S., Bera, A., Chandra, P., & Das, B. 2020, MNRAS, 498, 3863
  * Morabito et al. (2022) Morabito, L. K., Jackson, N. J., Mooney, S., et al. 2022, A&A, 658, A1
  * Murase et al. (2016) Murase, K., Kashiyama, K., & Mészáros, P. 2016, MNRAS, 461, 1498
  * Niu et al. (2022) Niu, C. H., Aggarwal, K., Li, D., et al. 2022, Nature, 606, 873
  * Nyland et al. (2020) Nyland, K., Dong, D., Hallinan, G., et al. 2020, in American Astronomical Society Meeting Abstracts, Vol. 235, American Astronomical Society Meeting Abstracts #235, 129.01
  * Ofek (2017) Ofek, E. O. 2017, ApJ, 846, 44
  * Oke & Gunn (1983) Oke, J. B. & Gunn, J. E. 1983, ApJ, 266, 713
  * Paragi et al. (2014) Paragi, Z., Frey, S., Kaaret, P., et al. 2014, ApJ, 791, 2
  * Planck Collaboration et al. (2011) Planck Collaboration, Aatrokoski, J., Ade, P. A. R., et al. 2011, A&A, 536, A15
  * Platts et al. (2021) Platts, E., Caleb, M., Stappers, B. W., et al. 2021, MNRAS, 505, 3041
  * Rajwade et al. (2020) Rajwade, K. M., Mickaliger, M. B., Stappers, B. W., et al. 2020, MNRAS, 495, 3551
  * Reines et al. (2020) Reines, A. E., Condon, J. J., Darling, J., & Greene, J. E. 2020, ApJ, 888, 36
  * Reines et al. (2013) Reines, A. E., Greene, J. E., & Geha, M. 2013, ApJ, 775, 116
  * Reines & Volonteri (2015) Reines, A. E. & Volonteri, M. 2015, ApJ, 813, 82
  * Resmi et al. (2021) Resmi, L., Vink, J., & Ishwara-Chandra, C. H. 2021, A&A, 655, A102
  * Robitaille & Bressert (2012) Robitaille, T. & Bressert, E. 2012, APLpy: Astronomical Plotting Library in Python, Astrophysics Source Code Library, record ascl:1208.017
  * Sargent et al. (2022) Sargent, A. J., Johnson, M. C., Reines, A. E., et al. 2022, ApJ, 933, 160
  * Schechter (1976) Schechter, P. 1976, ApJ, 203, 297
  * Shimwell et al. (2022) Shimwell, T. W., Hardcastle, M. J., Tasse, C., et al. 2022, A&A, 659, A1
  * Smith et al. (2021) Smith, D. J. B., Haskell, P., Gürkan, G., et al. 2021, A&A, 648, A6
  * Spitler et al. (2016) Spitler, L. G., Scholz, P., Hessels, J. W. T., et al. 2016, Nature, 531, 202
  * Sridhar & Metzger (2022) Sridhar, N. & Metzger, B. D. 2022, ApJ, 937, 5
  * Tasse et al. (2018) Tasse, C., Hugo, B., Mirmont, M., et al. 2018, A&A, 611, A87
  * Taylor (2011) Taylor, M. 2011, TOPCAT: Tool for OPerations on Catalogues And Tables, Astrophysics Source Code Library, record ascl:1101.010
  * Tendulkar et al. (2017) Tendulkar, S. P., Bassa, C. G., Cordes, J. M., et al. 2017, ApJ, 834, L7
  * Tendulkar et al. (2021) Tendulkar, S. P., Gil de Paz, A., Kirichenko, A. Y., et al. 2021, ApJ, 908, L12
  * Tremonti et al. (2004) Tremonti, C. A., Heckman, T. M., Kauffmann, G., et al. 2004, ApJ, 613, 898
  * Truebenbach & Darling (2017) Truebenbach, A. E. & Darling, J. 2017, MNRAS, 468, 196
  * Venkattu et al. (2023) Venkattu, D., Lundqvist, P., Pérez-Torres, M., et al. 2023, arXiv e-prints, arXiv:2307.02365
  * Véron-Cetty & Véron (2010) Véron-Cetty, M. P. & Véron, P. 2010, A&A, 518, A10
  * Vohl (2023) Vohl, D. 2023, matchmaker, Zenodo. DOI:10.5281/zenodo.7986693
  * Vohl et al. (2023) Vohl, D., Vedantham, H. . K., Hessels, J. W. T., & Bassa, C. G. 2023, arXiv e-prints, arXiv:2303.11967
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * Yang et al. (2020) Yang, J., Gurvits, L. I., Paragi, Z., et al. 2020, MNRAS, 495, L71
  * Zajaček et al. (2019) Zajaček, M., Busch, G., Valencia-S., M., et al. 2019, A&A, 630, A83
  * Zhao & Wang (2021) Zhao, Z. Y. & Wang, F. Y. 2021, ApJ, 923, L17

##  Appendix A The obtained L–SFR distribution

The zero point on the L–SFR relation from Gürkan et al. (2018) was obtained on
more massive ($\sim 10^{8.5}$–$10^{1}1\,M_{\odot}$) galaxies than our dwarf
sample. In figure 12, we show that the zero point corresponds to the peak of
the distribution when matching compact radio sources to all galaxy masses
available within CLU using a $6\arcsec$ matching radius. The peak of the
distribution of matched dwarf galaxies falls just below the zero point.
Objects below $-10\sigma$ (14 dwarf galaxies) have redshifts below 0.002,
except two extra cases at higher masses that have redshifts of 0.003 and
0.027, respectively.

Figure 12:  Matched compact radio objects along the L–SFR plane. Gray-filled
bins indicate cases matched to dwarf galaxies. Gray border bins indicate cases
matched to galaxies at all masses available in CLU. Blue bins indicate OCRs.
Very low-luminosity cases encountered in Figure 2 are further investigated in
Figure 13.  Figure 13: Compact radio objects matched to dwarf galaxies (left)
and all galaxies (right) along the L–SFR plane as a function of redshift and
offset. Very low-luminosity cases encountered in Figure 2 all have redshifts
below 0.002.

##  Appendix B 2MASX J12594007+2751177 and SDSS J143037.09+352052.8

The dwarf galaxy 2MASX J12594007+2751177 was shown to be of very low surface
density in PS1 (Figure 7). To better highlight the environment in which this
galaxy resides, Figure 16 shows the same field as observed by PS1 in r filter
(right) as shown previously, and a JVO Subaru/Suprime-Cam (Aihara et al. 2019)
composite image (left) using all filters—where 2MASX J12594007+2751177 is
apparent. Green markers (x, +) show the location of the LoTSS and CLU
detections, respectively. The Subaru Suprime-Cam image strengthens the
hypothesis that 2MASX J12594007+2751177 and ILTJ125944.53+275800.9 are
unrelated.

Figure 14: Environment around 2MASX J12594007+2751177 as observed by PS1 in r
filter (right, Figure 7), and JVO Subaru/Suprime-Cam composite image (left)
using all filters—where 2MASX J12594007+2751177 (pink markers) is apparent.
Green markers ($\times$, +) show the location of the LoTSS and CLU detections,
respectively. Figure generated with Aladin Desktop (Bonnarel et al. 2000).

Finally, the AGN candidate ILT 143037.30+352053.3 was matched to the host
galaxy SDSS J143037.09+352052.8. SDSS J143037.09+352052.8 is not resolved in
PS1 r filter shown in Figure 7. We found a JVO Subaru/Suprime-Cam image for
this field, which indicates that the radio source is within the optical
footprint of the host, which we show in Figure 15.

Figure 15: Environment around SDSS J143037.09+352052.8 as observed by PS1 in r
filter (right, Figure 7), and JVO Subaru/Suprime-Cam composite image (left)
using all filters—where SDSS J143037.09+352052.8 (pink markers) is apparent.
Green markers ($\times$, +) show the location of the LoTSS and CLU detections,
respectively.

##  Appendix C ACO 1656

We note in §3 that four of our selected compact radio sources fall within
galaxies that are members of the cluster of galaxies ACO 1656. These are
galaxies and respective matched radio sources (Table 1) are 2MASS
J13002220+2814499 (ILTJ130022.42+281451.7), SDSS J125944.76+275807.1
(ILTJ125944.53+275800.9), 2MASX J12594007+2751177 (ILTJ125940.18 +275123.5),
and SSTSL2 J125915.27+274604.1 (ILTJ125915.34+274604.2). We show the position
of these galaxies along with the central coordinate of ACO 1656 in Figure 16,
which displays a PS1 composite image of the z and g filters, as plotted in
Aladin Desktop (Bonnarel et al. 2000).

Figure 16: Cluster of galaxies ACO 1656 (pink markers), and four dwarf
galaxies matched to compact radio sources (pink squares).

##  Appendix D Host properties

In Table 1, a number of physical properties are listed, including luminosity
of the compact radio source, as well as redshift and star formation rate of
the host galaxy. Here, we also present the distribution relative to stellar
mass and specific star formation rate (sSFR, the star formation rate
normalized by the stellar mass) in Figure 18. Similarly, Figure 18 shows SFR
and sSFR in relation to stellar mass. Here, we note that none of our
candidates reach the same level of SFR as the host galaxies from FRB 20121102A
(Tendulkar et al. 2017) and FRB 20190520B (Niu et al. 2022), with FRB
20190520B being within range. The host galaxy of FRB 20121102A stands out with
respect of its sSFR compared to the rest of the data points. The host galaxies
of the IMBH candidates studied by Reines et al. fall within the SFR and sSFR
ranges of our candidates. We note that two out of the three galaxies matched
to CLU in our study correspond to unresolved radio sources (J0909+5655,
J1136+2643) in Sargent et al. (2022). We performed two-sample KS tests between
the respective candidates distributions to that of the background sample
(“compact radio sources-dwarf galaxy” matches below 3$\sigma$ on the L–SFR
relation) for stellar mass, SFR, and sSFR that yield $p$-values of 0.2, 0.8,
and 0.4 respectively, and are therefore consistent with being drawn from the
same population.

Figure 17: Distribution of host stellar mass (left panel), SFR (middle panel),
and sSFR (right panel) for candidates listed in Table 1. Gray bars indicate
values for all “compact radio source-dwarf galaxy” matches below 3$\sigma$ on
the L–SFR relation.  Figure 18: Host stellar mass as a function of SFR and
sSFR for our candidates. We also indicate values for FRB 20121102A, FRB
20190520B, and Reines et al. (2020) sources from Figure 2. Gray markers
indicate all “compact radio source-dwarf galaxy” matches below 3$\sigma$ on
the L–SFR relation.

##  Appendix E Radio luminosity versus ${\sc OI}/{\rm H\upalpha}$

Reines et al. (2020) showed that the relation between the emission line ratio
$[{\sc OI}]_{\lambda 3600}/{\rm H\upalpha}$ and the luminosity at 9 GHz could
be used to separate radio emission from radio AGN and star formation. We used
the spectral indices fitted in §3.2 (and the canonical $\alpha=-0.7$
otherwise) to scale the luminosity of our sources to 9 GHz for sources with
spectral line measurements available in SDSS. We show the results in Figure
19. Most of our sources fill the gap region found in Figure 10 of Reines et
al. (2020) that divides radio emission consistent with star formation and
radio AGN. We note that, despite the fact that scaling flux from 144 MHz to 9
GHz remains an approximation, typically 10% of the flux being resolved out at
higher frequencies would only marginally affect the luminosity of sources
plotted here.

As mentioned in Appendix D, galaxies J0909+5655 and J1136+2643 were matched to
CLU, with both radio source being unresolved by the VLBA (Sargent et al.
2022). The remaining match (J1220+3020, $L_{\rm 144\,MHz}\sim 5\times
10^{21}\,{\rm W\,Hz^{-1}}$) is one of Reines’ sources with optical
spectroscopic signature (obtained with targeted observation at the location of
the radio source with GMOS-N/IFU) consistent with accreting IMBH, via the AGN
coronal line [Fe X] and enhanced [O I] emission coincident with the radio
source (Molina et al. 2021; Sargent et al. 2022). We do not detect these
sources in LoTSS, despite two of them being within the DR2 footprint.

The two VLBA detections at 144 MHz-scaled luminosity from Reines et al. (2020)
using spectral indices by Eftekhari et al. (2020) yield $\sim 1.39\times
10^{22}$ and $\sim 2.47\times 10^{22}\,{\rm W}\,{\rm Hz^{-1}}$. It is
therefore plausible that a fraction of the radio luminosity reported for our
candidates could be attributed to an unresolved compact component. However,
our scaling from 9 GHz to 144 MHz should be seen as an informed approximation,
and radio luminosity values presented in Figure 19 should be regarded as
order-of-magnitude estimates.

Figure 19:  Black markers indicate values where the luminosity was scaled to 9
GHz with spectral indices obtained in §3.2, while gray markers were scaled
using the canonical $\alpha=-0.7$ for synchrotron spectra of optically thin
radio sources.

##  Appendix F Spatial coverage of ancillary surveys

In this section, we evaluate the spatial coverage of radio surveys used in
§3.2. Figure 20 shows multiorder coverage (MOC) maps for each of these
surveys, seen as subdivided cells. Each survey is color coded and described in
the figure caption. In addition, we overplot our candidates using yellow ‘+’
markers. We note that seven sources have not been observed by FIRST and nine
have been observed by RACS (Figure 9). All other sources could have been
observed by the remaining surveys. Finally, we also show coverage for SDSS
DR12 (§3.1), as well as Chandra SC2, XMM-Newton EPIC, and Fermi 4FGL (§3.3).

Figure 20: Coverage maps of surveys searched in §3. Source candidates
discussed in this paper are shown as white circles.