# Finding LoTSS of hosts for GRBs: a search for galaxy - gamma-ray burst
coincidences at low frequencies with LOFAR

R. A. J. Eyles-Ferris1 and R. L. C. Starling1
1School of Physics and Astronomy, University of Leicester, University Road,
Leicester, LE1 7RH, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The LOFAR Two-Metre Sky Survey (LoTSS) is an invaluable new tool for
investigating the properties of sources at low frequencies and has helped to
open up the study of galaxy populations in this regime. In this work, we
perform a search for host galaxies of gamma-ray bursts (GRBs). We use the
relative density of sources in Data Release 2 of LoTSS to define the
probability of a chance alignment, $P_{\rm chance}$, and find 18 sources
corresponding to 17 GRBs which meet a $P_{\rm chance}$<1% criterion. We
examine the nature and properties of these radio sources using both LOFAR data
and broadband information, including their radio spectral index, star
formation rate estimates and any contributions from active galactic nucleus
emission. Assuming the radio emission is dominated by star formation, we find
that our sources show high star formation rates ($10^{1}$–$10^{3}$$M_{\odot}$
yr-1) compared with both a field galaxy sample and a sample of core-collapse
supernova hosts, and the majority of putative hosts are consistent with
ultraluminous infrared galaxy (ULIRG) classifications. As a result of our
analyses, we define a final sample of eight likely GRB host candidates in the
LoTSS DR2 survey.

###### keywords:

gamma-ray bursts – radio continuum: galaxies – surveys

††pubyear: 2023††pagerange: Finding LoTSS of hosts for GRBs: a search for
galaxy - gamma-ray burst coincidences at low frequencies with LOFAR–B

##  1 Introduction

The properties of gamma-ray bursts (GRBs) are the result of their progenitors
and therefore the environment in which they have evolved. The majority of GRBs
discovered to date are long GRBs, bursts in which 90% of the isotropic
equivalent energy is detected over a period longer than two seconds. These
GRBs are driven by the collapse of massive stars and hence are strongly
connected to star formation. As such, while GRBs are cosmological and are
found across redshifts up to 9.4 (Cucchiara et al., 2011), the peak of their
redshift distribution is also commensurate with the peak of star formation
($z\sim 2.2$, Evans et al., 2009; Fynbo et al., 2009; Jakobsson et al., 2012).
However, despite this strong connection, long GRBs are not unbiased tracers of
star formation (Levesque, 2014). Long GRBs have been found to be hosted in a
wide variety of galaxy types but there is evidence of a bias towards galaxies
with lower masses, high specific star formation and low metallicities (e.g.
Christensen et al., 2004; Savaglio et al., 2009; Lyman et al., 2017). These
environments are ideal for forming collapsars, the progenitors of long GRBs,
and other studies have suggested that higher metallicities actually suppress
collapsar formation (e.g. Yoon et al., 2006; Woosley & Bloom, 2006; Perley et
al., 2016). Short GRBs, where 90% of the isotropic equivalent energy is
detected over a period shorter than two seconds, have different progenitor
systems and are driven by compact binary mergers. They therefore display a
greater variety in their host galaxy properties and do not require active star
formation. There is also a minority of short GRBs that appear to lack hosts -
most likely due to natal kicks ejecting them from their original hosts and
resulting in offsets of tens of kiloparsecs (e.g. Tunnicliffe et al., 2014;
Mandhai et al., 2022; Fong et al., 2022).

It is therefore clear that a galaxy’s star formation rate (SFR) has a
significant impact on its likelihood to host long GRBs in particular. There
are several methods to measure SFR including at UV and optical wavelengths.
However, these methods are significantly affected by dust extinction in the
target galaxy. This extinction, and its effects on SFR measurements, is often
hard to constrain and leads to significant biases. Star formation also drives
radio emission, however, which is significantly less affected by dust
extinction. This therefore offers an opportunity for dust unbiased
measurements of long GRB hosts.

There are factors to consider when using radio data in this way, however.
While radio emission is a good tracker of star formation, a significant
proportion of extragalactic radio sources are active galactic nuclei (AGN).
AGN can also be a significant contaminant in sources that are also highly
starforming. It is therefore important to minimise AGN contamination to
accurately measure the properties of any galaxies identified. There is also
the possibility of lingering emission from any GRB afterglows further
contaminating the sample. This has occurred in other studies (e.g. Stanway et
al., 2014) although we do not expect it to be a contributor in here due to the
low frequency of the regime probed and the historic nature of the GRBs
investigated.

We also need to consider other biases inherent to such a survey. The
luminosity of the radio emission from star formation is strongly dependent on
the SFR. In a blind search for such sources, therefore, we may expect to only
detect galaxies with very elevated SFRs. While we expect long GRB hosts to
have high SFRs, it could be difficult to determine whether the hosts detected
via radio are representative of the entire population or comprise an outlying
subsample of extreme starforming galaxies. Alternatively, a large proportion
of long GRB hosts with lower, albeit still high, SFRs could remain undetected
and the search would be inherently incomplete. Due to star formation no longer
being necessary, compared to long GRB hosts, short GRB hosts are more likely
to be radio-quiet despite their lower mean redshift ($z\lesssim 1$, Klose et
al., 2019; Fong et al., 2022). This means a radio search is also unlikely to
detect them and lead to greater incompleteness across the broader GRB
population.

Radio searches for GRB hosts have proven to be productive in past studies,
however (e.g. Berger et al., 2003; Michałowski et al., 2012; Stanway et al.,
2014; Li et al., 2015; Perley et al., 2015, 2016; Klose et al., 2019). At GHz
frequencies, these galaxies typically have measured SFRs much higher than
those obtained through UV/optical methods (e.g. Christensen et al., 2004;
Michałowski et al., 2012). Long GRBs are also commonly hosted in powerful
luminous infrared galaxies (LIRGs) and ultra-luminous infrared galaxies
(ULIRGs) and the highly dusty nature of these galaxies means radio is the only
way to recover obscured star formation. In these cases, SFRs of hundreds to
over a thousand $M_{\odot}$ yr-1have been recovered (Perley et al., 2017;
Hsiao et al., 2020). The fraction of GRB hosts with such dust obscuration is
still unclear (e.g. Gatkine et al., 2020) and radio surveys offer a way to
constrain this further. While some of the differences between UV/optical SFRs
and radio SFRs have been attributed to afterglow or AGN contamination, it is
clear radio is a valuable tool to investigate these galaxies.

A new window into the low frequency behaviour of galaxies has recently opened
with the second Data Release of the LOFAR Two-metre Sky Survey (LoTSS DR2,
Shimwell et al., 2022). LoTSS DR2 covers 6335 square degrees in two regions
centred on 12h45m00s +44°30’00" (RA-13 region) and 1h00m00s +28°00’00" (RA-1
region), approximately 27% of the northern hemisphere. The frequency range is
significantly lower than most radio surveys at 120–168 MHz subdivided into
three 16 MHz wide bands, a regime almost entirely unprobed in studies of GRB
host galaxies. The survey achieves a resolution of 6" and RMS limits of 74
$\mu$Jy and 106 $\mu$Jy in the RA-13 and RA-1 regions respectively. This has
allowed 4.4 million sources to be detected, and in this paper, we investigate
these catalogues to identify associations between LoTSS sources and GRBs
detected with the X-ray Telescope (XRT, Burrows et al., 2005) on board the
Neil Gehrels Swift Observatory (Swift, Gehrels et al., 2004). These GRBs are
extremely well localised to within $\leq$ 2 arcsec 90% of the time (Evans et
al., 2009), ideal for crossmatching to LoTSS DR2.

In Section 2, we present our crossmatching method and initial associations. We
further discuss our method in Section 3, focussing on any selection biases and
its completeness. The properties of our matches are investigated and presented
in Section 4 and these are combined with our discussion of our methodology to
produce a final sample of GRB associations in 5. Finally, we summarise in
Section 6.

Throughout this paper, we give errors to 1-$\sigma$ and adopt a flat
$\Lambda$CDM cosmology with $H_{0}=71$ km s-1 Mpc-1, $\Omega_{m}=0.27$ and
$\Omega_{\Lambda}=0.73$.

##  2 Associating GRBs and possible hosts

###  2.1 Crossmatching

Our sample of GRBs was taken from the live Swift-XRT GRB
Catalogue111https://www.swift.ac.uk/xrt_live_cat/ (Evans et al., 2009) hosted
by the UK Swift Science Data Centre (UKSSDC) up to 15 July 2022. This
consisted of 1489 GRBs and we found 280 of them (253 long GRBs and 27 short
GRBs) were located within the LoTSS DR2 footprint, defining the footprint as
the area within one degree of at least one LoTSS DR2 source, as shown in
Figure 1. We note that two sources apparently within the LoTSS footprint are
excluded by this criterion but this is most likely due to blanked regions
within the footprint222see https://lofar-surveys.org/dr2_release.html. We
matched this sample to the lotss_dr2.main_sources table (Shimwell et al.,
2021), selecting all LoTSS sources within 10 times the 90% XRT error region
for each GRB. We then calculated the probability of chance alignment, $P_{\rm
chance}$, following the method of Tunnicliffe et al. (2014). In that work,
GRBs were matched to possible host galaxies in the Sloan Digital Sky Survey
(SDSS) by examining the correlation of flux and source density in a sample of
the SDSS. The $P_{\rm chance}$ of possible matches was then evaluated by
comparison with this overall population.

Figure 1: The coverage of LoTSS DR2 shown in grey. The image is focussed on
the RA-13 region and the RA-1 region is split. Red point and blue points
indicate long and short GRBs respectively within the LoTSS DR2 footprint while
purple points indicate GRBs of both types outside the footprint.

We generated 15,000 random points within the footprint of LoTSS DR2 and
measured the separations from these points to the nearest sources above
various total flux thresholds. We classified these sources by cross-matching
to the NASA/IPAC Extragalactic Database333https://ned.ipac.caltech.edu/ (NED)
and the Set of Identifications, Measurements and Bibliography for Astronomical
Data (SIMBAD, Wenger et al., 2000)
database444https://simbad.u-strasbg.fr/simbad/, assuming the LoTSS DR2 source
to correspond to the closest object within 20". These cross matches were then
used to select only galaxies from the sample and we found that the
relationship between the separations from the random points, $\delta x$, and
the flux of the galaxies, $F$, was reasonably well fit as

$\log(\delta x)=\alpha\log(F)+c$ (1)

where $\alpha=0.417\pm 0.002$ and $c=2.153\pm 0.005$. We also took a
comparison sample of field galaxies from this population, selecting sources
with SIMBAD galaxy counterparts with sufficiently low separations for their
$P_{\rm chance}$<1%. We further subdivided this into active and inactive
galaxies using their SIMBAD classifications. We refer to these samples later
in this paper as ActiveField and InactiveField, respectively.

We used this fit to define the percentile contours of the distribution and we
plot the 1st, 5th, 10th, 25th and 50th percentiles in Figure 2. For each
source matched to a GRB, $P_{\rm chance}$ was therefore determined by which
percentile contour the matched source lay on. We calculated these for all of
our matched sources and selected a threshold of $P_{\rm chance}$<1%. We found
that twelve long GRBs and one short GRB had at least one match meeting this
threshold, while a further four long GRBs had matches consistent with the
threshold when accounting for errors. We plot the flux density and separation
from the GRBs of our crossmatched sources in Figure 2 and summarise them in
Table 1. We also extracted images of each LoTSS source and the position of
their potential match from the full LoTSS mosaics and present them in Figure
6. All of the LoTSS sources are most likely galaxies, with the majority having
known counterparts in SIMBAD. Two GRBs, 050509B and 081025, were found to have
multiple matches. We discuss these sources further below. The 17 matched GRBs
represent 6.0% of the 280 GRBs within the footprint. For the two GRB types,
this breaks down into 16/253 or 6.3% of long GRBs and 1/27 or 3.8% of short
GRBs.

Figure 2: The correlation between separation and flux density for galaxies in
the LoTSS DR2 release. Grey indicates matches to 15,000 random points and the
black lines indicate the 1st, 5th, 10th, 25th and 50th percentile contours.
Matches to our CCSNe sample are plotted in gold and matches to long and short
GRBs are plotted in red and blue respectively. For the GRB matches, circles
indicate sources where $P_{\rm chance}$ is less than 1% and crosses indicate
sources where $P_{\rm chance}$ is consistent within errors of being less than
1%. The right hand panel zooms in to more clearly show our matches.

This method can lead to crossmatches at large angular separations, up to $\sim
35$". This is primarily due to the lower source density at higher flux density
limits and therefore greater separations are allowed. Such large separations
are possible. For instance, the formation of the compact binary progenitors of
short GRBs induces a significant kick velocity such that short GRBs can occur
a significant distance from their original hosts. For both short and long
GRBs, there are also the possibilities that the GRBs are occurring in the
outskirts of extended galaxies or that they are located at low redshifts where
a large angular separation does not translate to a large physical separation.
This latter case would also account for the high brightness of some putative
hosts but is also inconsistent with the observed gamma-ray fluence of several
of the bursts. Finally, there is also the possibility of the positional
accuracy playing a significant role.

Alternatively, many of the LoTSS sources are extended, consistent with their
galactic nature, and as such the separations may also be dependent on the
angular size of the host. We calculated the extent of each LoTSS source
towards the centre of the associated GRB’s XRT error region assuming the
source to be Gaussian in nature and include this in Table 1. Note that we used
the major and minor axes of the sources after deconvolution with the beam,
while the images in Figure 6 are derived from the raw mosaics. We also derived
the normalised separation, i.e. the separation divided by the extent. This has
previously been investigated at optical wavelengths by Blanchard et al.
(2016), who found that for long GRBs, the normalised separation was typically
$\lesssim$one but could range up to $\sim$nine in extreme cases. Our
normalised separations are generally somewhat larger than this but are not
incompatible within errors. However, there are a number of sources with
significantly larger separations, further reducing the likelihood of these
being accurate crossmatches.

####  2.1.1 GRBs with multiple matches

For our only short GRB, GRB 050509B, two separate LoTSS sources were
consistent with being matches according to our $P_{\rm chance}$ criterion. GRB
050509B is a relatively well studied short GRB and it is likely to have
occurred within a cluster (Barthelmy et al., 2005; Pedersen et al., 2005).
Multiple matches are therefore not surprising. While the afterglow was only
detected in X-rays, the GRB was sufficiently localised for Very Large
Telescope observations to confirm the likely host is 2MASX J12361286+285858026
(Hjorth et al., 2005b, a; Castro-Tirado et al., 2005), a large elliptical
galaxy with a UV-measured SFR of $<0.2$ $M_{\odot}$ yr-1 (Gehrels et al.,
2005). As shown in Figure 9, one of our matched sources, ILT
J123613.00+285902.9, is spatially consistent with this galaxy. The other LoTSS
source, ILT J123612.26+285929.2, is likely unrelated to GRB 050509B. However,
we still evaluate its properties as it could be part of the same cluster as
2MASX J12361286+285858026 and therefore coevolved with it.

Upon inspection of the LoTSS mosaics, we also found that the counterpart to
GRB 081025, ILT J162131.13+602837.1, appeared to be a double source, as shown
in Figure 6. From archival 2MASS images, we determined that it was two
distinct galaxies with insufficient angular separation to be resolved as
individual sources in the LoTSS pipeline. However, the pipeline also outputs
the separate Gaussians that make up each source and we were able to identify
the two Gaussians, here designated A and B, matching each component of ILT
J162131.13+602837.1, both of which individually met the $P_{\rm chance}$
threshold. We therefore treated these as separate sources in our analysis.

####  2.1.2 Redshifts and physical scales

The redshifts of our sample are important for both accurately measuring the
properties of the LoTSS sources but for our crossmatching process. Four of the
matched GRBs already had measured redshifts, two each from spectroscopy of
their afterglows and of their probable hosts. We identified further redshifts
from catalogue crossmatches comprising two from SIMBAD and five photometric
redshifts from SDSS. Of our 18 matches, therefore, we identify 12 possible
redshifts.

Based on these redshifts, we calculated both the physical separation of the
GRB from the LoTSS source and the apparent physical extent of the sources.
These values are also given in Table 1.

The separations are generally significantly higher than the typical results of
a $\sim$few kpc identified previously for long GRBs (e.g. Bloom et al., 2002;
Blanchard et al., 2016; Lyman et al., 2017). However, we note the previous
results are derived using optical data, and some differences might therefore
be expected, and that our separations typically have relatively large errors.
Nevertheless, the more extreme values are likely indicative of inaccuracies in
the crossmatching process.

On the other hand, the behaviour of short GRBs differs and a more significant
separation would often be expected. This is due to the nature of short GRBs,
the progenitors of which can be imparted a significant kick velocity through
their formation mechanism, and therefore have large separations from their
original host. Observationally, these separations are a few kpc greater than
those of long GRBs (e.g. Tunnicliffe et al., 2014; Fong et al., 2022). From
simulations, the distribution of separations could be expected to peak at
around 10 kpc and can reach to over 100 kpc (Mandhai et al., 2022). Our
matches to GRB 050509B are both consistent with this behaviour.

###  2.2 Core-collapse supernovae sample

To provide an additional comparison sample to our putative GRB hosts, we also
derived a sample of core-collapse supernovae (CCSNe) host candidates following
the same procedure. CCSNe are a well studied population of which long GRBs
could represent a subsample.

CCSNe are generally found at significantly lower redshifts than long GRBs and
typically belong to types Ib, Ic or II. In previous studies, there have been
found to be significant differences between hosts of CCSNe and long GRBs (e.g.
Levesque, 2014, and references therein), however, these differences have been
found to vary between types. For instance, long GRBs tend to be located within
UV bright regions of their hosts, consistent with high degrees of star
formation (e.g. Svensson et al., 2010). The resultant offset distribution is
more similar to Ib or Ic CCSNe than type II (Blanchard et al., 2016; Lyman et
al., 2017). Similarly, Ic and long GRBs both trace optical g-band emission
within their hosts with other CCSNe displaying weaker associations (Kelly et
al., 2008). For all CCSNe types, the luminosity and morphology distribution of
their hosts is also substantially different than for long GRBs. Fruchter et
al. (2006) found that CCSNe hosts tend to be both more luminous and more
regular than long GRB hostss. This supported by Svensson et al. (2010)’s
conclusion that CCSN hosts tend towards massive spirals. Compared to the low
metallicity nature of long GRB hosts, CCSN hosts are also typically much more
metal rich (e.g. Levesque et al., 2010).

We took the sample of the sadly defunct Open Supernova
catalogue555https://github.com/astrocatalogs/supernovae which includes events
up to April 8 2022, and selected all supernovae of suggested type Ib, Ic and
II. This resulted in 1162 CCSNe within the LoTSS DR2 footprint, which we
defined as above. We crossmatched these objects to LoTSS DR2 with a $P_{\rm
chance}$ threshold of 1% which resulted in 877 matches corresponding to 664
SNe, or 57.1% of the sample within the LoTSS DR2 footprint.

We found the low redshifts of the CCSNe population to have a significant
effect on the crossmatching process. Such nearby sources have correspondingly
high flux densities and the angular offsets of the supernovae from the LoTSS
sources were found to be significantly greater than those of the GRB sample,
in some cases $>100$". However, these angular offsets still correspond to
physical offsets of $\sim$tens of kpc or less. The nine times larger
proportion of CCSNe matches compared to GRB matches is therefore not
surprising.

The proximity of the CCSNe sample is also likely responsible for the large
number of supernovae with multiple LoTSS matches as many supernovae are close
enough for their hosts’ structure to be resolved. Such galaxies will be
detected as multiple sources in the LoTSS pipeline as the islands of flux are
sufficiently separated.

##  3 Selection effects and completeness

###  3.1 Selection biases

It is important to consider the biases inherent in a radio selection of host
galaxies. As most long GRBs are associated with star-forming galaxies, it
might be expected that radio emission from their hosts is dominated by the
synchrotron radiation associated with star formation but that the minimum SFR
probed will depend on the survey depth and galaxy redshift. Gürkan et al.
(2018) found the SFR, $\psi$, and luminosity at 150 MHz, $L_{150}$, to be
correlated as

$L_{150}=L_{1}\psi_{\rm G}^{\beta}$ (2)

where $L_{1}=10^{22.06\pm 0.01}$ W Hz-1 is the luminosity at 150 MHz of a
source with an SFR of 1 $M_{\odot}$ yr-1 and $\beta=1.07\pm 0.01$. Smith et
al. (2021) also derive SFRs for 150 MHz emission, finding a similar
prescription:

$\displaystyle\log L_{150}=$ $\displaystyle(0.90\pm 0.01)\log(\psi_{\rm
S}/M_{\odot}~{}{\rm yr}^{-1})+$ (3) $\displaystyle(0.33\pm 0.04)\log(M_{\rm
gal}/10^{10}M_{\odot})+22.22\pm 0.02$

for $L_{150}$ in W Hz-1. We note, however, that this method requires the mass
of the galaxy.

Equation 2 can therefore be used to evaluate these selection effects. We used
the grey field sources in Figure 2 to derive an approximate detection limit
for LoTSS DR2. We found that only 0.1% of sources have total flux densities
<0.30 mJy. We therefore take this to be an appropriate and relatively
conservative assumption for the detection limit. Using Equation 2, we derive
the SFR required to reach this flux density up to $z=3.5$ and plot it in
Figure 3.

Figure 3: The required SFR to reach 0.30 mJy at 150 MHz for a given redshift
(blue curve). The UV/optical derived SFRs for a sample taken from Wang et al.
(2020) and the live Swift-XRT GRB Catalogue (Evans et al., 2009) are overlaid
in red. Radio derived SFRs from Perley & Perley (2013), Stanway et al. (2014)
and Perley et al. (2015) are overlaid in purple. The inset zooms into GRBs
051022 and 100816A as they are coincidentally close and cannot be
distinguished in the full plot.

We also compare this function to a sample of long GRB hosts with SFRs
estimated through optical or UV methods. Such methods are significantly more
impacted by the effects of dust obscuration than radio methods and may
therefore result in underestimated SFRs. We would therefore expect radio
methods to favour both higher SFRs and lower redshfits. The sample is taken
from GRBs in both the catalogue of Wang et al. (2020) and the live Swift-XRT
GRB Catalogue (Evans et al., 2009). This yields 92 GRB hosts with no crossover
with our crossmatched sample, plotted in red in Figure 3. We also plot 12 long
GRB hosts with radio measured SFRs taken from Perley & Perley (2013), Stanway
et al. (2014) and Perley et al. (2015), noting that GRB 051022 is present in
both samples with measured SFRs consistent within errors. This comparison
demonstrates that radio detections are intrinsically biased towards hosts with
atypically high SFRs compared to the UV/optically measured sample. The
redshift distribution of sources we might expect to detect also differs from
the full population with a clear bias towards lower redshifts, probably due to
the SFRs required being significantly less extreme than for most of the
sample. We do note, however, that 6 of the 92 UV/optically derived SFRs do
reach the threshold. The radio emission of some putative hosts may also be
enhanced by components other than star formation. The most obvious source of
such contamination is likely to be AGN and we investigate this in Section 4.5.

###  3.2 Completeness

The sample of GRB hosts from Wang et al. (2020) also allow the completeness of
our methods to be evaluated. Of the 92 GRBs in the UV/optical sample, six
($\sim$6.5%) GRB hosts do appear to reach the threshold for detection. We also
found that two hosts, those of GRBs 051022 and GRB 100816A, lie within the
LoTSS DR2 footprint and have UV/optically derived SFRs of
$60.0^{+12.0}_{-36.2}$ $M_{\odot}$ yr-1 (Castro-Tirado et al., 2007; Svensson
et al., 2010; Krühler et al., 2015) and $58.0^{+51.0}_{-26.0}$ $M_{\odot}$
yr-1 (Krühler et al., 2015) respectively. GRB 051022 has also been observed at
5.227 GHz which yielded a slightly enhanced SFR of $74.0^{+20.0}_{-20.0}$
$M_{\odot}$ yr-1 (Perley & Perley, 2013). We therefore predict flux densities
at 144 MHz using Equation 2 of $0.30^{+0.18}_{-0.19}$ mJy for GRB 051022’s
counterpart and $0.29^{+0.28}_{-0.14}$ mJy for GRB 100816A’s. These values are
consistent with being below our estimated detection limit and no such
counterparts were identified in the LoTSS DR2 catalogues for either GRB.

To confirm these non-detections, we examined the mosaics at the positions of
these GRBs and for GRB 100816A, found no evidence of a source. In contrast, we
did identify a bright source approximately 16" away from GRB 051022, ILT
J235603.13+193633.0, as shown in Figure 10. This source was not previously
selected by our criteria, due to the well localised nature of GRB 051022 and
its XRT error region of 1.5". We note, however, that its $P_{\rm chance}$
would meet the 1% threshold.

We therefore examined the GRB Coordinates Network Circulars for GRB 051022 and
found Cameron & Frail (2005) reported two radio sources, a point source
coincident with the XRT error region and a previously reported optical source
(Castro-Tirado et al., 2005), and a large extended source to the North West of
the error region. Further observations indicated the point source to indeed be
the GRB afterglow (van der Horst et al., 2005; de Ugarte Postigo et al., 2005;
Rol et al., 2007). ILT J235603.13+193633.0 is, however, consistent with the
extended source and we therefore conclude it is unrelated to GRB 051022.

While we cannot directly measure the SFR of these two hosts, our non-
detections do constrain their behaviour somewhat. In particular, the galaxies’
radio SFRs cannot be significantly greater than those measured through
UV/optical methods. This is consistent with the work of Greiner et al. (2016),
who observed a sample of 11 long GRB hosts at 2.1 GHz and 3 GHz. No hosts were
detected and the limits were sufficient to establish that any radio detectable
star formation would be only be a factor of two to three greater than that
measured by UV/optical methods. While the redshifts of the two non-detected
sources are only constrained to $z\sim 0.8$, our results agree with Greiner et
al.’s conclusion that only a small fraction of the star formation in these
galaxies may be obscured by dust.

The non-detections provide weak constraints on the completeness of our method.
Although subject to small number statistics, they suggest that the fraction of
long GRB host candidates we might identify in LoTSS DR2 is $\lesssim$6.5%,
consistent with the 6.3% we find crossmatches for. As discussed in Section 3.1
and later, it is also plausible that our methods actually lead to spurious
associations and further evaluation and elimination of some host candidates
must be performed.

Table 1: A summary of the GRBs and crossmatches we identify in Section 2.1
ordered by GRB class and $P_{\rm chance}$. GRBs are classified as short (S)
and long (L) based on the standard observed $t_{90}=2$ s cutoff. Note that the
extent columns refer to the LoTSS source’s apparent extent from its centre
towards the GRB position rather than the maximum size of the source.

GRB | Class | LoTSS match | Redshift | Angular | Angular | Normalised | Physical | Physical | $P_{\rm chance}$
---|---|---|---|---|---|---|---|---|---
|  |  |  | separation (") | extent (") | separation | separation (kpc) | extent (kpc) | (%)
200716C | L | ILT J130402.61+293839.3 | $0.341^{1}$ | $2.20\pm 1.50$ | $2.05^{+0.11}_{-0.15}$ | $1.1^{+0.9}_{-0.7}$ | $10.6\pm 7.2$ | $9.87^{+0.55}_{-0.72}$ | $0.01^{+0.01}_{-0.01}$
201229A | L | ILT J140245.38+481150.7 | — | $1.91\pm 1.77$ | $0.75^{+0.70}_{-0.52}$ | $2.5^{+13.5}_{-2.5}$ | — | — | $0.02^{+0.07}_{-0.02}$
190211A | L | ILT J130635.93+415811.3 | — | $27.49\pm 3.51$ | $1.77^{+0.01}_{-0.01}$ | $15.5^{+2.1}_{-2.1}$ | — | — | $0.09^{+0.03}_{-0.02}$
060123 | L | ILT J115847.46+453050.9 | $0.562^{2}$ | $4.57\pm 3.60$ | $4.81^{+1.56}_{-1.94}$ | $1.0^{+1.9}_{-0.8}$ | $25.9\pm 20.5$ | $27.28^{+8.87}_{-11.01}$ | $0.15^{+0.52}_{-0.15}$
091130B | L | ILT J133235.11+340524.3 | $0.282^{3}$ | $7.10\pm 1.63$ | $1.08^{+0.46}_{-0.19}$ | $6.6^{+3.2}_{-3.0}$ | $30.0\pm 6.9$ | $4.58^{+1.95}_{-0.79}$ | $0.20^{+0.16}_{-0.09}$
110903A | L | ILT J130815.16+585857.2 | $0.311^{3}$ | $5.26\pm 2.38$ | $<0.36$ | $>8.0$ | $23.8\pm 10.8$ | $<1.61$ | $0.31^{+0.58}_{-0.23}$
081025 | L | ILT J162131.13+602837.1 A | — | $16.15\pm 5.49$ | $4.05^{+0.48}_{-0.42}$ | $4.0^{+2.0}_{-1.6}$ | — | — | $0.41^{+0.44}_{-0.25}$
150213B | L | ILT J165348.36+341126.2 | $0.704^{3}$ | $7.08\pm 2.73$ | $<0.74$ | $>5.9$ | $50.7\pm 19.6$ | $<5.27$ | $0.41^{+0.70}_{-0.29}$
220412A | L | ILT J081553.01+302035.9 | $0.402^{4}$ | $8.70\pm 2.92$ | $2.14^{+1.44}_{-0.78}$ | $4.1^{+4.5}_{-2.5}$ | $46.6\pm 15.7$ | $11.47^{+7.72}_{-4.16}$ | $0.42^{+0.58}_{-0.26}$
081025 | L | ILT J162131.13+602837.1 B | — | $27.89\pm 5.47$ | $5.86^{+0.52}_{-0.50}$ | $4.8^{+1.5}_{-1.2}$ | — | — | $0.68^{+0.33}_{-0.27}$
071020 | L | ILT J075839.09+325133.9 | $2.146^{5}$ | $8.41\pm 4.60$ | $<1.05$ | $>3.6$ | $70.7\pm 38.7$ | $<8.82$ | $0.74^{+1.57}_{-0.63}$
110521A | L | ILT J080031.58+454950.2 | — | $13.95\pm 2.61$ | $1.27^{+1.10}_{-0.47}$ | $11.0^{+9.7}_{-6.2}$ | — | — | $0.91^{+0.63}_{-0.44}$
060206 | L | ILT J133144.19+350305.6 | $4.050^{6}$ | $10.60\pm 2.17$ | $3.02^{+0.74}_{-1.17}$ | $3.5^{+3.4}_{-1.3}$ | $74.7\pm 15.3$ | $21.31^{+5.21}_{-8.23}$ | $0.92^{+0.69}_{-0.47}$
080507 | L | ILT J153442.14+562609.0 | — | $11.75\pm 3.66$ | $2.13^{+1.48}_{-1.26}$ | $5.5^{+12.2}_{-3.3}$ | — | — | $1.05^{+1.15}_{-0.67}$
140808A | L | ILT J144453.38+491305.9 | $3.290^{7}$ | $13.87\pm 3.78$ | $2.14^{+0.08}_{-0.81}$ | $6.5^{+6.8}_{-1.9}$ | $105.6\pm 28.8$ | $16.27^{+0.64}_{-6.15}$ | $1.11^{+0.89}_{-0.60}$
191101A | L | ILT J164720.21+434437.0 | $0.681^{8}$ | $13.13\pm 1.81$ | $0.46^{+1.07}_{-0.45}$ | $28.5^{+1470}_{-21.1}$ | $92.7\pm 12.8$ | $3.22^{+7.54}_{-3.18}$ | $1.29^{+0.62}_{-0.45}$
080916B | L | ILT J105437.13+690416.8 | — | $24.27\pm 6.64$ | $7.15^{+5.48}_{-4.09}$ | $3.4^{+6.7}_{-2.0}$ | — | — | $2.08^{+3.42}_{-1.26}$
050509B | S | ILT J123613.00+285902.9 | $0.225^{\rm 9}$ | $10.14\pm 5.62$ | $2.04^{+0.35}_{-0.33}$ | $5.0^{+4.2}_{-3.1}$ | $36.3\pm 20.1$ | $7.32^{+1.26}_{-1.17}$ | $0.11^{+0.15}_{-0.10}$
050509B | S | ILT J123612.26+285929.2 | $0.225^{\rm 9}$ | $32.64\pm 5.48$ | $2.99^{+0.14}_{-0.14}$ | $10.9^{+2.5}_{-2.2}$ | $116.9\pm 19.6$ | $10.71^{+0.50}_{-0.49}$ | $0.69^{+0.30}_{-0.25}$

  * •

Redshift sources: 1Giarratana et al. (2023); 2Berger et al. (2006); 3SDSS
Photoz table (Beck et al., 2016); 4Galaxy clusters optical catalogue from SDSS
DR6 (Szabo et al., 2011); 5Jakobsson et al. (2007); 6Prochaska et al. (2006);
7Gorosabel et al. (2014); 8SDSS Quasar Catalogue (Lyke et al., 2020);
9Prochaska et al. (2005).

##  4 Host properties

In this section, we examine the behaviour of our putative GRB hosts to assist
with classification and examine how their properties compare to galaxy
samples.

###  4.1 Counterparts in other radio surveys

To expand the frequency space for our putative hosts, we also performed
crossmatches to other radio surveys. This allows us to better examine the
spectral behaviour of the sources, in particular, allowing possible
identification and classification of any AGN activity.

We crossmatched our putative hosts to the Westerbork Northern Sky Survey
(WENSS, Rengelink et al., 1997), Faint Images of the Radio Sky at Twenty-
centimeters (FIRST, Becker et al., 1995; White et al., 1997; Helfand et al.,
2015), the NRAO Very Large Array Sky Survey (NVSS, Condon et al., 1998), Giant
Metrewave Radio Telescope (GMRT) 150 MHz Survey (Intema et al., 2017) and the
Very Large Array Sky Survey (VLASS, Gordon et al., 2021). This extended our
frequency regime to between 144 MHz and 3 GHz. We performed this crossmatch
using VizieR666https://doi.org/10.26093/cds/vizier, selecting the nearest
source in each table within 20" to maximise the number of plausible matches.
However, only five of our LoTSS sources had counterparts across these
catalogues, given in Table 2.

In addition to the results in the survey catalogues, the host of GRB 200716C
was also examined at radio wavelengths by Giarratana et al. (2023), who
identified flux densities in the archival data of these surveys. We include
their results when calculating the properties of this galaxy.

Table 2: The candidate counterparts to our putative hosts in other radio surveys. The name prefixes are given in the brackets. Sources are ordered by $P_{\rm chance}$ and GRB class. GRB | LoTSS match | WENSS | FIRST | NVSS | GMRT 150 MHz | VLASS
---|---|---|---|---|---|---
|  | (WENSS) | (FIRST) | (NVSS) | (TGSSADR) | (VLASS1QLCIR)
201229A | ILT J140245.38+481150.7 | — | J140245.4+481150 | — | — | —
190211A | ILT J130635.93+415811.3 | B1304.3+4214 | J130635.9+415811 | J130635+415812 | J130635.9+415812 | J130635.94+415811.3
220412A | ILT J081553.01+302035.9 | — | J081552.9+302036 | — | — | —
191101A | ILT J164720.21+434437.0 | — | — | J164721+434440 | — | —
050509B | ILT J123612.26+285929.2 | — | — | J123612+285930 | — | —

###  4.2 Radio Spectral behaviour

Table 3: The spectral indices and WISE colours and classifications of our putative hosts ordered by GRB class and $P_{\rm chance}$. We use the criteria of Mingo et al. (2016) and Mingo et al. (2019) to determine classification. *s indicate sources where the colours are not fully constrained or that have redshifts greater than one and therefore the classifications are not fully constrained; and $\dagger$s indicate sources suggested to be AGN in other studies. GRB | LoTSS match | $\alpha_{\rm LoTSS}$ | $\alpha_{\rm wide}$ | $W1-W2$ | $W2-W3$ | Implied WISE class
---|---|---|---|---|---|---
200716C | ILT J130402.61+293839.3 | $0.89\pm 0.25$ | $-0.65\pm 0.07$ | $0.13\pm 0.11$ | $2.93\pm 0.46$ | Star-forming
201229A | ILT J140245.38+481150.7 | $0.64\pm 2.73$ | $0.43\pm 0.07$ | $0.82\pm 0.30$ | $<3.65$ | ULIRG/AGN*$\dagger$
190211A | ILT J130635.93+415811.3 | $0.27\pm 0.18$ | $-0.56\pm 0.03$ | $0.53\pm 0.33$ | $<4.38$ | ULIRG/AGN*
060123 | ILT J115847.46+453050.9 | — | — | $0.04\pm 0.20$ | $4.23\pm 0.35$ | ULIRG
091130B | ILT J133235.11+340524.3 | $2.35\pm 1.59$ | — | $0.34\pm 0.08$ | $3.44\pm 0.19$ | ULIRG*
110903A | ILT J130815.16+585857.2 | — | — | $0.31\pm 0.14$ | $3.92\pm 0.26$ | ULIRG
081025 | ILT J162131.13+602837.1 A | $0.14\pm 1.24$ | — | $-0.29\pm 0.46$ | $<4.12$ | ULIRG*
150213B | ILT J165348.36+341126.2 | — | — | $0.10\pm 0.35$ | $<4.15$ | ULIRG*
220412A | ILT J081553.01+302035.9 | — | $0.02\pm 0.01$ | $0.14\pm 0.13$ | $<2.69$ | Star-forming*
081025 | ILT J162131.13+602837.1 B | $0.10\pm 1.08$ | — | $0.17\pm 0.06$ | $<1.03$ | Elliptical
071020 | ILT J075839.09+325133.9 | — | — | $0.32\pm 0.12$ | $3.51\pm 0.31$ | ULIRG*
110521A | ILT J080031.58+454950.2 | — | — | $0.62\pm 0.33$ | $<3.74$ | ULIRG/AGN*
060206 | ILT J133144.19+350305.6 | — | — | $0.28\pm 0.11$ | $2.66\pm 0.54$ | Star-forming
080507 | ILT J153442.14+562609.0 | — | — | $0.57\pm 0.14$ | $<3.13$ | AGN*
140808A | ILT J144453.38+491305.9 | — | — | $1.05\pm 0.28$ | $<4.04$ | ULIRG/AGN*
191101A | ILT J164720.21+434437.0 | — | $0.58\pm 0.31$ | $0.80\pm 0.13$ | $2.75\pm 0.12$ | AGN$\dagger$
080916B | ILT J105437.13+690416.8 | — | — | $0.42\pm 0.09$ | $4.13\pm 0.14$ | ULIRG*
050509B | ILT J123613.00+285902.9 | $-0.21\pm 0.24$ | — | $0.27\pm 0.06$ | $<1.29$ | Elliptical
050509B | ILT J123612.26+285929.2 | $0.27\pm 0.41$ | $-0.58\pm 0.18$ | $<0.91$ | $<3.87$ | ULIRG/AGN*

Following Shimwell et al. (2022), the LoTSS band can be divided into three 16
MHz wide bands centred at 128, 144 and 160 MHz. We downloaded the primary beam
corrected images for each of these bands and extracted the flux densities for
our putative hosts using the
PyBDSF777https://www.astron.nl/citt/pybdsf/index.html package, setting both
the thresh_pix and thresh_isl parameters to 3 (i.e. a detection significance
of 3-$\sigma$). The flux densities were then fitted with a power law model,
$F_{\nu}=k\nu^{\alpha}$, to derive spectral indices, given in Table 3 as
$\alpha_{\rm LoTSS}$. The varying significance of each source across the LoTSS
bandwidth means that the source was not necessarily detected in each band and
therefore we could only derive spectral indices for seven sources. We
attempted to increase this number by lowering the significance thresholds but
found that the resultant spectral indices were unphysically extreme, likely
indicative of noise being extracted rather than real sources. In general, we
found our values for $\alpha_{\rm LoTSS}$ to be poorly constrained, likely due
to large errors in the flux density measurements and the relatively narrow
frequency range. We note, however, that this is consistent with the findings
of Shimwell et al. (2022).

For the sources with counterparts at GHz frequencies, we refitted the power
law model but included both the flux densities given in those catalogues and
the flux density across the full LoTSS band centred at 144 MHz. The resulting
spectral indices are given in Table 3 as $\alpha_{\rm wide}$ and our sources’
fitted SEDs are shown in Figure 11.

For most sources with both $\alpha_{\rm LoTSS}$ and $\alpha_{\rm wide}$, we
found that both values for $\alpha$ are reasonably consistent. However, in the
cases of ILT J123612.26+285929.2 and ILT J130402.61+293839.3, the $\alpha_{\rm
LoTSS}$ and $\alpha_{\rm wide}$ indicate opposite behaviour for the spectrum.
In this case, as with other sources with both $\alpha_{\rm LoTSS}$ and
$\alpha_{\rm wide}$, we are inclined to trust $\alpha_{\rm wide}$ more due to
$\alpha_{\rm LoTSS}$ being poorly constrained, as mentioned above. It is also
plausible that the true SED has a more complex structure than the single power
law assumed and, for instance, $\alpha_{\rm LoTSS}$ and $\alpha_{\rm wide}$
capture separate parts of a broken power law. Measurements with the LOFAR low-
band antennas (LBA) may be useful in further constraining any spectral
turnover.

###  4.3 IR behaviour

Figure 4: The $W1-W2$ and $W2-W3$ colours of the closest AllWISE sources to
our putative host sample. Our CCSNe comparison sample is plotted in gold. Red
points indicate putative GRB hosts with AGN indicators either from literature
or from their spectral indices while blue points indicate sources with no
other traces of AGN activity. A $\blacktriangleleft$ indicates an upper limit
in $W2-W3$ and the triple arrow indicates $W1-W2$ is an upper limit and
$W2-W3$ is unconstrained. Open points indicate sources with a separation >5"
between the AllWISE and the LoTSS source.

We also examined the infrared colours of the galaxies in the Wide-field
Infrared Survey Explorer (WISE) bands. These colours are widely used to assist
with classifying galaxies and help evaluate any AGN activity. We matched our
sources to the closest objects in the AllWISE catalogue (Cutri et al., 2021)
finding that all such matches had a $P_{\rm chance}$<1%. We used the criteria
of Mingo et al. (2016) and Mingo et al. (2019), to broadly classify galaxies
into AGN, luminous IR galaxies (LIRGs), ultra-luminous IR galaxies (ULIRGs),
star-forming and elliptical classes. We tabulate the $W1-W2$ and $W2-W3$
colours in Table 3 and plot them in Figure 4.

We also derived WISE colours for the CCSNe sample, also shown in Figure 4. We
found that all types of CCSNe follow similar behaviour with no significant
differences between them. This behaviour is also compatible with the
distribution exhibited by our GRB host candidates although the sources matched
to GRBs are more likely to have colours consistent with AGN activity. We
further examine such activity in the following section.

According to our criteria, both the GRB and CCNSe samples are dominated by
ULIRGs. While it might be expected that a greater proportion of each sample
would be star-forming galaxies, LIRGs and ULIRGs are common radio-selected
hosts for these transients (e.g. Perley et al., 2015). The nature of these
galaxies enhances star formation, with the star formation efficiency increased
by a factor of 2 – 3 compared to the general galaxy population. During an
extreme starburst, this enhancement can reach up to an order of magnitude
(Graciá-Carpio et al., 2008; García-Burillo et al., 2012). Other radio studies
of GRB hosts have found them to be consistent with LIRGs or ULIRGs and
identified high SFRs of order 50 – 200 $M_{\odot}$ yr-1 (Perley et al., 2015).
These galaxies were also found to be significantly lower luminosity relative
to their SFRs than field galaxies, a result consistent with other studies
(e.g. Levesque, 2014; Perley et al., 2016; Lyman et al., 2017). This is
compatible with the suggestion that there is a metallicity bias or cutoff in
long GRB hosts. These high SFRs and low metallicities are ideal for creating
an environment rich with collapsars, the progenitors of both long GRBs and
CCSNe. There could also be systematic reasons why ULIRGs are so dominant. It
is likely that our criteria over simplify the complex behaviour of the
galaxies and therefore neglect the significant overlap between different
classifications. In addition, as discussed in Section 3.1, there are
significant selection effects inherent to a radio search. This biases towards
selecting a different population of galaxies than optical surveys for
instance, and such a sample would be expected to include a greater proportion
of ULIRGs than the overall population of galaxies.

###  4.4 Star formation

Table 4: The masses and SFRs of our putative hosts. The masses are taken from
SDSS. The SFRs are calculated using the prescriptions of Gürkan et al.
($\psi_{\rm G}$, Equation 2), Smith et al. ($\psi_{\rm S}$, Equation 3) and
Bell ($\psi_{\rm B}$, Equation 5).

GRB | LoTSS match | Redshift | $\log(M_{\rm gal}/M_{\odot})$ | $\psi_{\rm G}$ | $\psi_{\rm S}$ | $\psi_{\rm B}$
---|---|---|---|---|---|---
|  |  |  | ($M_{\odot}$ yr-1) | ($M_{\odot}$ yr-1) | ($M_{\odot}$ yr-1)
200716C | ILT J130402.61+293839.3 | 0.341 | — | $111.1^{+11.9}_{-10.7}$ | — |  $167\pm 21.2$ / $338.3\pm 84.6$${\dagger}$
060123 | ILT J115847.46+453050.9 | 0.562 | — | $67.0^{+23.4}_{-20.9}$ | — | —
091130B | ILT J133235.11+340524.3 | 0.282 | — | $26.0^{+3.8}_{-3.5}$ | — | —
110903A | ILT J130815.16+585857.2 | 0.311 | — | $11.4^{+3.1}_{-2.9}$ | — | —
150213B | ILT J165348.36+341126.2 | 0.704 | — | $96.9^{+32.6}_{-29.0}$ | — | —
220412A | ILT J081553.01+302035.9 | 0.402 | — | $43.1^{+12.0}_{-10.8}$ | — | $379.8\pm 44.8$
071020 | ILT J075839.09+325133.9 | 2.146 | $<9.43$ | $1082.7^{+432.2}_{-369.6}$ | $>3999.6$ | —
060206 | ILT J133144.19+350305.6 | 4.050 | — | $6276.5^{+2233.7}_{-1862.7}$ | — | —
140808A | ILT J144453.38+491305.9 | 3.290 | — | $5610.7^{+1323.5}_{-1115.9}$ | — | —
191101A | ILT J164720.21+434437.0 | 0.681 | — | $112.0^{+26.7}_{-23.6}$ | — | $4597.7\pm 560.7$
050509B | ILT J123613.00+285902.9 | 0.225 | $11.08^{+0.03}_{-0.03}$ | $79.9^{+9.5}_{-8.5}$ | $48.7^{+16.3}_{-10.0}$ | —
050509B | ILT J123612.26+285929.2 | 0.225 | — | $143.2^{+14.5}_{-13.0}$ | — | $316.4\pm 40.6$

  * •

${\dagger}$Giarratana et al. (2023) find significantly different flux
densities in FIRST and NVSS. Here, the first value uses the FIRST flux density
and the second uses the NVSS flux density.

The star formation history of a galaxy has a significant effect on the rate of
GRBs that take place within it. In particular, long GRB progenitors are
massive and short-lived stars so the hosts of such GRBs are generally found to
have significantly higher SFRs than the majority of the field galaxy
population. Here, we examine these properties of our putative hosts.

####  4.4.1 Star-forming galaxies

The spectral index of a galaxy can be indicative of whether it is star-forming
and we therefore compare our measured spectral indices to those expected of
star-forming galaxies. The radio SEDs of such objects are typically expected
to be a superposition of two power laws, a thermal and a non-thermal component
(e.g. Duric et al., 1988):

$S_{\rm tot}(\nu)=S_{\rm
th}(\nu_{0})\left(\frac{\nu}{\nu_{0}}\right)^{-0.1}+S_{\rm
nth}(\nu_{0})\left(\frac{\nu}{\nu_{0}}\right)^{\alpha_{\rm nth}}$ (4)

The thermal fraction is estimated to be $f_{\rm th}\sim 10$% (Niklas et al.,
1997; Tabatabaei et al., 2017) and hence our measured $\alpha_{\rm LoTSS}$ and
$\alpha_{\rm wide}$ should be comparable or slightly smaller in absolute terms
than $\alpha_{\rm nth}$ (Tabatabaei et al., 2017).

The radio spectral index of star-forming galaxies is typically thought to be
$\alpha_{\rm nth}\sim-1.0$ for the non-thermal index and $\sim-0.8$ for the
total index (Tabatabaei et al., 2017). However, this simple picture of
superimposed power laws does not appear consistent with observations at lower
frequencies. For instance, the sample of galaxies examined by Klein et al.
(2018) displayed a broken or exponentially declining power law spectrum, with
the break or decline occurring between 1–12 GHz, as $\alpha_{\rm nth}$ varies
with frequency. The resultant power law at lower frequencies is significantly
shallower than at higher frequencies, with a spectral index of $\sim-0.6$.
This behaviour has also been identified in studies that reach even lower to
MHz frequencies (Yun & Carilli, 2002; Calistro Rivera et al., 2017; An et al.,
2021).

From the spectral indices in Table 3, the most likely candidates for star-
forming galaxies are ILT J130402.61+293839.3, ILT J130635.93+415811.3 and ILT
J123612.26+285929.2. From their WISE colours, only ILT J130402.61+293839.3 was
consistent with being star-forming while the other two sources had been
categorised as ULIRG/AGN, although high star formation is still likely to be
present as discussed above. There were two other sources classified as star-
forming by their WISE colours, ILT J081553.01+302035.9 and ILT
J133144.19+350305.6. Unfortunately, these sources’ spectral indices are either
unavailable or poorly constrained due to a low number of data points. It is
therefore difficult to determine if the radio evidence independently points
towards them being star-forming.

####  4.4.2 Star formation rates with LoTSS flux densities

To derive SFRs for our matched sources with redshifts, we returned to
Equations 2 and 3. As noted above, Equation 3 requires the mass of the host to
be known which is only the case for ILT J123613.00+285902.9 (Savaglio et al.,
2009), and an upper limit for ILT J075839.09+325133.9 (Perley et al., 2016).
We were therefore able to derive 12 SFRs using Equation 2 and two using
Equation 3. Where we have both estimates, we find they are generally
comparable. The remaining discrepancies may due to the sensitivity of Equation
3 to the galaxy mass and therefore the accuracy of its measurement.

We found that three of our matched sources (ILT J075839.09+325133.9, ILT
J133144.19+350305.6 and ILT J144453.38+491305.9), in addition to a significant
proportion of the general population, exhibit apparent extreme star formation
rates of several thousand $M_{\odot}$ yr-1 or greater. There are examples of
such high values in previous work, such as the estimate of SFR $>$ 1000
$M_{\odot}$ yr-1 for the high redshift GRB 090404 (Perley et al., 2017). There
is also a possibility of afterglow contamination, as suggested for the case of
GRB 100814A (Stanway et al., 2014), but it is unlikely that these sources are
significantly affected. Such high values could indicate incorrectly assigned
redshifts rather than the hosts, or significant contributions from other
emission sources. Recent work using LoTSS to examine the cosmic star formation
history showed that significant scatter in the relationship between $L_{150}$
and SFR is likely the result of AGN (Cochrane et al., 2023). It is therefore
probable that these apparently extreme SFRs are actually AGN rather than star
formation emission.

To provide a comparison, we also derived SFRs for the CCSNe sample and the
InactiveField sample using Equation 2. To account for nearby resolved CCSNe
host galaxies, we summed the SFRs of all LoTSS counterparts for each
supernova. To compare the GRB hosts to our CCSNe and general sample, we set an
upper limit on the SFR of 200 $M_{\odot}$ yr-1. This limits our sample to the
SFRs most likely to be real for both for the GRB hosts and the comparison
samples. Excluding the possible hosts of the short GRB 050509B, we found that
the long GRB hosts have a mean SFR of $66.8\pm 38.2$ $M_{\odot}$ yr-1, while
the general inactive galaxy population has a mean SFR of $18.2\pm 33.1$
$M_{\odot}$ yr-1. It is clear that our putative long GRB hosts have
significantly greater apparent SFRs than most galaxies in the field, although
AGN contamination could still contribute to apparently enhanced radio flux, a
factor we address in Section 4.5. We note also that the InactiveField’s
inferred SFR distribution is somewhat higher than might be expected for a
general galaxy population, which may be indicative of incorrect crossmatching,
redshift assignments or lingering AGN contamination. The CCSNe hosts have even
lower SFRs than either of the other two samples at $8.5\pm 23.3$ $M_{\odot}$
yr-1, possibly due to their small redshifts, and therefore their low
luminosities and being resolvable into multiple components. This low SFR
behaviour was again common to all types of CCSNe.

The results for the matches to the short GRB 050509B are more surprising,
specifically ILT J123613.00+285902.9. For this source, both our methods
indicate SFRs of tens of $M_{\odot}$ yr-1, much greater than the UV measured
$<0.2$ $M_{\odot}$ yr-1 of Gehrels et al. (2005). While dust obscuration is
likely to cause some discrepancy between measurements in these two regimes, it
is implausible that two orders of magnitude difference is possible. If the
radio is, indeed, dominated by star formation, it is therefore likely that ILT
J123613.00+285902.9 is not the radio counterpart to the optically-assigned
large elliptical galaxy 2MASX J12361286+285858026 despite their spatial
consistency. Alternatively, it is possible that this source is dominated by
AGN emission and we discuss this further below.

####  4.4.3 Star formation rates with flux densities from other radio surveys

For those sources with higher frequency counterparts, we can also use the
prescription of Bell (2003) to derive SFRs, similarly to Michałowski et al.
(2009). Using the luminosity of the source at 1.4 GHz, $L_{1.4}$, in W Hz-1,
the SFR is found to be

$\psi_{\rm B}=\begin{cases}5.52\times 10^{-22}L_{1.4},&L_{1.4}>L_{c}\\\
\frac{5.52\times 10^{-22}}{(0.1+0.9(L_{1.4}/L_{c})^{0.3}}L_{1.4},&L_{1.4}\leq
L_{c}\end{cases}$ (5)

where $L_{c}=6.4\times 10^{21}$ W Hz-1 is some critical 1.4 GHz luminosity.

Four sources have both higher frequency counterparts and associated redshifts
allowing us to evaluate their SFRs with Equation 5. We found that there was
reasonable agreement (a factor of a few) for two of these sources, ILT
J130402.61+293839.3 and ILT J123612.26+285929.2, but there were much more
significant discrepancies for ILT J081553.01+302035.9 (a factor of $\sim 9$)
and ILT J164720.21+434437.0 (a factor of $\sim 40$). We note that the spectrum
of J081553.01+302035.9 is significantly flatter than a typical star-forming
galaxy, but other evidence, such as the WISE colours do point towards this
source as being star-forming. It is therefore unclear why such a large
discrepancy is present. ILT J164720.21+434437.0, on the other hand, is an AGN
candidate and it is likely that the higher frequency flux density and
therefore this SFR measurement is actually dominated by AGN activity rather
than star formation.

###  4.5 AGN contamination

A large proportion of the radio source population is made up of active
galaxies and as such they represent a significant possible contaminant in our
sample of putative hosts. We therefore investigated our sample to determine
whether any sources were likely to actually be AGN and therefore most probably
unrelated to the GRBs.

####  4.5.1 Literature candidates

LoTSS has previously been extensively investigated for AGN and we initially
compared our source list to the AGN catalogues for HETDEX Spring Field of
LoTSS DR1 (Williams et al., 2019; Hardcastle et al., 2019; Mingo et al., 2019)
and LoTSS Deep Fields Data Release 1 (Best et al., 2023). No crossmatches were
identified and we therefore also performed a wider literature search. This
identified ILT J164720.21+434437.0 (Lyke et al., 2020) and ILT
J140245.38+481150.7 (Truebenbach & Darling, 2017), the putative hosts of GRB
191101A and GRB 201229A respectively, as having possible AGN counterparts.
While the separation of GRB 191101A indicates that this is unlikely to be an
accurate match, the crossmatch between GRB 201229A and ILT J140245.38+481150.7
inspires much more confidence. Truebenbach & Darling (2017) suggest that ILT
J140245.38+481150.7 is an AGN due to a combination of radio/IR emission but a
lack of optical detections and find such methods to be consistent with other
AGN selection criteria. However, when we perform similar analysis below, we
find that it differs in its behaviour from the vast majority of AGN while its
WISE colours are consistent with both AGN and ULIRG classifications. If this
were an AGN, the small separation could mean that this is the first long GRB
to be found to be associated with an active galaxy.

####  4.5.2 Radio behaviour

The morphology of a radio source can indicate the presence of an AGN. In
particular, irregular morphologies or the physical size of a source can be the
result of activity. This extends to the LoTSS frequencies, as shown for
Fanaroff-Riley class galaxies in the LoTSS-Deep field (Mingo et al., 2022).
None of our sources have physical extents comparable to Mingo et al.’s sample,
however, and in general our sources’ morphologies are significantly more
regular. There a few exceptions, namely ILT J162131.13+602837.1, ILT
J10543713+690416.8 and ILT J123613.00+285902.9. We have already determined
that ILT J162131.13+602837.1’s morphology is the result of two galaxies being
close enough to be unresolved in LoTSS DR2, however, the other sources are
both plausibly AGN dominated. In particular, the irregular and elongated
morphology of ILT J123613.00+285902.9 is consistent with the presence of a
radio jet. Elliptical galaxies are not uncommon hosts for low power radio
galaxies and it is possible that 2MASX J12361286+285858026 is the host of ILT
J123613.00+285902.9. However, there are other optical sources spatially
consistent with ILT J123613.00+285902.9 as shown by Hjorth et al. (2005a). The
middle panel of their Figure 1 shows the field with 2MASX J12361286+285858026
subtracted out and a new source identified to its North. While Hjorth et al.
do not examine this source in greater detail and it is unclear whether it is
foreground or background, we encourage further investigations to determine
whether it is the true counterpart to ILT J123613.00+285902.9.

The radio spectrum of a galactic source can also be a clue as to its activity.
The canonical radio spectral index for AGN is typically taken to be $\sim-0.7$
(Condon et al., 2002) and the low-frequency samples examined by Calistro
Rivera et al. (2017) and Gürkan et al. (2018) in addition to the AGN sample in
LoTSS DR1 appeared consistent with this value (Figure 3 of Sabater et al.,
2019). However, as the flux density of an AGN at 1.4 GHz decreased, its
spectral index became significantly shallower. Four of our sources with 1.4
GHz detections have indices consistent with the canonical value (ILT
J130402.61+293839.3, ILT J130635.93+415811.3, ILT J081553.01+302035.9 and ILT
J123612.26+285929.2). As previously mentioned, ILT J164720.21+434437.0’s
spectral index is sensitive to the fit and it is plausible that this is also
consistent. The poorly constrained nature of $\alpha_{\rm LoTSS}$ means we
cannot firmly determine whether any of the remaining sources are also
consistent.

However, a great deal of diversity around the canonical spectral index has
been observed across the AGN population. For instance, peaked spectrum (PS)
sources have spectra with distinct peaks and steep drops around them (e.g.
O’Dea et al., 1991; O’Dea & Saikia, 2021), possibly as the result of
synchrotron self-absorption or free-free absorption (Bicknell et al., 1997).
Such sources include GHz peaking sources (GPS) and compact steep spectrum
(CSS) sources which peak at lower frequencies of a few hundred MHz. This means
that in the regime probed by LOFAR and the catalogued data, they can actually
display positive (by our convention) or flat spectral indices (e.g. O’Dea,
1998; Sadler, 2016). The turnover suggested in the SED of ILT
J130635.93+415811.3 could be due to it being such a CSS source. There are
other classes of AGN that could display diverging spectral behaviour, such as
AGN with emission primarily arising from advection dominated accretion flows
(ADAFs, e.g. Narayan & Yi, 1994; Narayan et al., 1998; Mahadevan, 1998).
Finally, low luminosity jets can also result in flat spectra (e.g. Falcke &
Biermann, 1999). We also note that the canonical spectral index for AGN is
very similar to that of starforming galaxies (e.g. Calistro Rivera et al.,
2017), further diluting spectral behaviour as an indicator of AGN behaviour.

It is therefore difficult to determine which sources could be AGN solely from
their spectral indices and the majority of our host candidates display
behaviour which could be consistent with an AGN origin. We therefore return to
the infrared behaviour of the sources in the following section.

####  4.5.3 WISE colours and $q_{\rm IR}$

The WISE colours detailed in Section 4.3 can be an indicator of AGN and seven
of the sources in our sample were found to have colours consistent with AGN
classification. However, only one source (ILT J164720.21+434437.0) is
sufficiently constrained to ensure this classification. We note also that the
$W1-W2$ criterion does not necessarily confirm a lack of AGN behaviour, as
some classes of AGN such as Seyferts may lie below it. There are also
significant evolutionary effects with redshift that can greatly change a
source’s position on this diagram (Assef et al., 2013). It is therefore
possible that sources with redshifts of $z>1$ are misclassified. For our
sample, this includes ILT J075839.09+325133.9, ILT J133144.19+350305.6 and ILT
J144453.38+491305.9. We therefore investigate further criteria to more fully
examine possible AGN contamination.

The ratio of IR to radio emission can also indicate the presence of AGN
behaviour (e.g. Helou et al., 1985; Condon et al., 1991),

$q_{\rm IR}=\log\frac{S_{\rm IR}}{S_{\rm radio}}$ (6)

where $S$ is the flux density in a given filter or at a given frequency. Radio
AGN generally have significantly lower values of $q_{\rm IR}$ than star
forming galaxies which also display an evolution with redshift (e.g. Calistro
Rivera et al., 2017). While typically longer wavelengths and higher
frequencies are employed for $S_{\rm IR}$ and $S_{\rm radio}$ respectively, a
significant AGN correlation could still be expected for the WISE bands and 144
MHz LoTSS frequency we have available. We calculated $q_{\rm IR}$ for each
source for each available WISE band counterpart and show these in Table 5.

Table 5: The log ratio of IR to radio emission, $q_{\rm IR}$, for each WISE band of our putative hosts ordered by GRB class and $P_{\rm chance}$. GRB | LoTSS match | $q_{W1}$ | $q_{W2}$ | $q_{W3}$ | $q_{W4}$
---|---|---|---|---|---
200716C | ILT J130402.61+293839.3 | $-0.19^{+0.03}_{+0.03}$ | $-0.14^{+0.05}_{+0.05}$ | $1.03^{+0.17}_{+0.17}$ | —
201229A | ILT J140245.38+481150.7 | $-0.36^{+0.10}_{+0.09}$ | $-0.04^{+0.13}_{+0.12}$ | — | —
190211A | ILT J130635.93+415811.3 | $-2.29^{+0.04}_{+0.04}$ | $-2.08^{+0.09}_{+0.09}$ | — | —
060123 | ILT J115847.46+453050.9 | $0.23^{+0.17}_{+0.13}$ | $0.24^{+0.21}_{+0.17}$ | $1.93^{+0.23}_{+0.19}$ | —
091130B | ILT J133235.11+340524.3 | $0.38^{+0.06}_{+0.05}$ | $0.51^{+0.06}_{+0.06}$ | $1.89^{+0.10}_{+0.10}$ | $2.88^{+0.19}_{+0.18}$
110903A | ILT J130815.16+585857.2 | $0.46^{+0.13}_{+0.11}$ | $0.58^{+0.15}_{+0.13}$ | $2.15^{+0.18}_{+0.16}$ | —
081025 | ILT J162131.13+602837.1 A | $-1.09^{+0.06}_{+0.06}$ | $-1.21^{+0.18}_{+0.17}$ | — | —
150213B | ILT J165348.36+341126.2 | $-0.06^{+0.17}_{+0.14}$ | $-0.02^{+0.24}_{+0.21}$ | — | —
220412A | ILT J081553.01+302035.9 | $0.37^{+0.12}_{+0.10}$ | $0.43^{+0.15}_{+0.12}$ | — | —
081025 | ILT J162131.13+602837.1 B | $-0.36^{+0.03}_{+0.03}$ | $-0.29^{+0.03}_{+0.03}$ | — | —
071020 | ILT J075839.09+325133.9 | $0.66^{+0.17}_{+0.13}$ | $0.78^{+0.19}_{+0.15}$ | $2.18^{+0.25}_{+0.20}$ | —
110521A | ILT J080031.58+454950.2 | $-0.43^{+0.17}_{+0.14}$ | $-0.18^{+0.21}_{+0.18}$ | — | —
060206 | ILT J133144.19+350305.6 | $0.48^{+0.13}_{+0.11}$ | $0.59^{+0.15}_{+0.12}$ | $1.65^{+0.30}_{+0.28}$ | —
080507 | ILT J153442.14+562609.0 | $0.04^{+0.13}_{+0.11}$ | $0.27^{+0.15}_{+0.12}$ | — | —
140808A | ILT J144453.38+491305.9 | $-0.45^{+0.10}_{+0.10}$ | $-0.03^{+0.12}_{+0.11}$ | — | $2.76^{+0.26}_{+0.25}$
191101A | ILT J164720.21+434437.0 | $0.81^{+0.12}_{+0.11}$ | $1.13^{+0.09}_{+0.08}$ | $2.23^{+0.12}_{+0.11}$ | $3.31^{+0.18}_{+0.17}$
080916B | ILT J105437.13+690416.8 | $0.01^{+0.29}_{+0.18}$ | $0.18^{+0.30}_{+0.19}$ | $1.83^{+0.31}_{+0.20}$ | $3.00^{+0.34}_{+0.23}$
050509B | ILT J123613.00+285902.9 | $0.02^{+0.03}_{+0.03}$ | $0.13^{+0.04}_{+0.04}$ | — | —
050509B | ILT J123612.26+285929.2 | $-1.69^{+0.09}_{+0.09}$ | — | — | —

We also calculated $q_{\rm IR}$ for the ActiveField and InactiveField samples
and compare them to our matched sources in Figure 5 in the red shading and
greyscale contours respectively. For our putative hosts without known
redshifts, we assumed $z=1$. While the peak of the long GRB redshift
distribution is $\sim 2.2$ (Evans et al., 2009), we choose a lower value to
account for the inherent bias in a radio search towards lower redshift
sources. We find that the majority of AGN do exhibit smaller values of $q_{\rm
IR}$ than the field galaxies, although there is significant crossover and the
redshift distribution of the field galaxies is much smaller than that of the
AGN. There is also the possibility of incomplete or inaccurate classifications
in SIMBAD. Nevertheless, it appears that most of our GRB host candidates
exhibit different behaviour to the vast majority of the AGN sample. While this
does not preclude any of them from being AGN, it does imply that they would be
outliers to the main AGN population.

However, there are noticeable outliers to the other GRB hosts in the top two
panels of Figure 5. These are ILT J130635.93+415811.3, ILT J162131.13+602837.1
A and ILT J123612.26+285929.2 associated with GRBs 190211A, 081025 and 050509B
respectively. There is significant evidence that both ILT J130635.93+415811.3
and ILT J123612.26+285929.2 are indeed AGN and their selection was due to the
extreme flux densities induced by their active nature. However, it is more
difficult to confirm if ILT J162131.13+602837.1 A is an AGN due to a lack of
redshift constraint. However, from the measured fluence of GRB 081025, we
expect $z\sim 2.5$ for $E_{\gamma,{\rm iso}}\sim 10^{53}$ erg, typical for a
long GRB, or $z\sim 0.4$ for $E_{\gamma,{\rm iso}}\sim 10^{51}$ erg, if GRB
081025 is an extremely low luminosity GRB. While this lower redshift could
place it towards the higher density AGN parameter space, the more probable
higher redshift is inconsistent with the majority of AGN. We also note it is
less of an outlier to our putative host distribution than the other two
sources.

Figure 5: $q_{\rm IR}$ calculated using each WISE band and the LoTSS 144 MHz
flux densities. The red shaded regions indicate the distribution of, from top
to bottom, 11102, 11003, 8104 and 5356 SIMBAD AGN, the greyscale contours
indicate the distribution of apparently inactive field galaxies and the blue
points indicate our putative GRB hosts. Note the red shading is log scale and
the varying range of each panel’s y axis.

##  5 Final candidate host sample

We now refine the initial list of associations given in Table 1 to define a
final sample of GRBs and their hosts that are most likely accurate
crossmatches.

From our original sample in Table 2, the large angular or physical separations
between 10/19 possible associations (GRB 190211A/ILT J130635.93+415811.3, GRB
081025/ILT J162131.13+602837.1 B, GRB 071020/ILT J075839.09+325133.9, GRB
110521A/ILT J080031.58+454950.2, GRB 060206/ILT J133144.19+350305.6, GRB
140808A/ILT J144453.38+491305.9, GRB 191101A/ILT J164720.21+434437.0, GRB
080916B/ILT J105437.13+690416.8 and GRB 050509B/ILT J123612.26+285929.2) casts
doubts on these being accurate counterparts. Two of these GRBs also have
crossmatches at lower separations (GRB 081025/ILT J162131.13+602837.1 A and
GRB 050509B/ILT J123613.00+285902.9) which are more likely to be the true
counterpart.

In addition, a significant number of sources are likely to be AGN and
therefore most likely unrelated to the GRBs. While we cannot necessarily
ensure any of our crossmatches aren’t subject to AGN contamination, 7/19
candidates (GRB 190211A/ILT J130635.93+415811.3, GRB 110521A/ILT
J080031.58+454950.2, GRB 080507/ILT J153442.14+562609.0, GRB 140808A/ILT
J144453.38+491305.9, GRB 191101A/ILT J164720.21+434437.0, GRB 050509B/ILT
J123613.00+285902.9 and GRB 050509B/ILT J123612.26+285929.2) are most probably
AGN related.

Eliminating these sources therefore leaves a final sample of eight matches,
all for long GRBs, given in Table 6. We note that these criteria also
eliminate the sources with extreme SFRs $\gtrsim 200$ $M_{\odot}$ yr-1
implying that these were likely due to inaccurate crossmatching and therefore
redshift assignments or that their radio flux is actually AGN dominated.

Table 6: Our final sample of GRB and host crossmatch candidates ordered by $P_{\rm chance}$. *s indicate sources where the WISE colours and therefore classifications are not fully constrained. GRB | LoTSS match | Redshift | Implied WISE class | $\psi_{\rm G}$ | $\psi_{\rm B}$
---|---|---|---|---|---
|  |  |  | ($M_{\odot}$ yr-1) | ($M_{\odot}$ yr-1)
200716C | ILT J130402.61+293839.3 | 0.341 | Starforming | $111.1^{+11.9}_{-10.7}$ |  $167\pm 21.2$ / $338.3\pm 84.6$
201229A | ILT J140245.38+481150.7 | — | ULIRG/AGN* | — | —
060123 | ILT J115847.46+453050.9 | 0.442 | ULIRG | $39.0^{+13.3}_{-12.0}$ | —
091130B | ILT J133235.11+340524.3 | 0.282 | ULIRG* | $26.0^{+3.8}_{-3.5}$ | —
110903A | ILT J130815.16+585857.2 | 0.311 | ULIRG | $11.4^{+3.1}_{-2.9}$ | —
081025 | ILT J162131.13+602837.1 A | — | ULIRG* | — | —
150213B | ILT J165348.36+341126.2 | 0.704 | ULIRG* | $96.9^{+32.6}_{-29.0}$ | —
220412A | ILT J081553.01+302035.9 | 0.402 | Starforming* | $43.1^{+12.0}_{-10.8}$ | $379.8\pm 44.8$

The redshift distribution of this sample is low compared to the majority of
the long GRB population. This is bias is consistent with that expected from
selection effects, as discussed in Section 3.1. In terms of offsets, the
angular offsets for the majority of this sample are less than 10", the only
exception being between GRB 081025 and ILT J162131.13+602837.1 A at $\sim
16$". These lead to normalised offsets of $\leq 6.6$, consistent with the
findings of Blanchard et al. (2016), while the mean physical offset is
$31.3\pm 15$ kpc. This is larger than would typically expected for a long GRB
host correlation, however, we note there are significant errors on the
individual physical separations.

Similarly to the full sample of our cross-matched sources, this final sample
is dominated by ULIRGs. Two sources have radio spectral indices and IR colours
consistent with star-forming galaxies, although we note that our sources’
spectral indices are generally poorly constrained. We find a mean SFR of
$59.2\pm 36.1$ $M_{\odot}$ yr-1, significantly greater than that exhibited by
the general population population of field galaxies and the CCSNe host sample.

##  6 Conclusions

We have presented the results of a search for GRB host galaxies using the
recent LoTSS DR2 catalogues. Using the density of sources in LoTSS DR2 to
evaluate $P_{\rm chance}$, we identified 18 sources matched to 17 GRBs. This
process indicated crossmatches at relatively large angular and normalised
separations. This was likely to be partly an effect of the differences between
optical and radio galaxy morphology but also implied some inaccurate
crossmatches. We further evaluated the properties of the sources using both
LoTSS data and that available in other catalogues.

We found that a majority of our sources are consistent with ULIRG
classifications, while a small minority are more likely to be AGN and
unrelated to the matched GRBs. Our comparison CCSN host sample was also
dominated by ULIRGs. We evaluated the star formation of our long GRB host
sample, finding that they exhibited SFRs significantly higher (mean $66.8\pm
38.2$ $M_{\odot}$ yr-1) than that of both field galaxies (mean $18.2\pm 33.1$
$M_{\odot}$ yr-1) and the CCSN host sample (mean $8.5\pm 23.3$ $M_{\odot}$
yr-1).

Based on both the results of our crossmatching process and the properties of
the sources themselves, we have identified a final sample of eight
crossmatches that are likely to be accurate host galaxy-GRB pairings. This
sample consists entirely of long GRBs and is again dominated by ULIRGs
exhibiting enhanced star formation (mean $59.2\pm 36.1$ $M_{\odot}$ yr-1).

Future observations by LOFAR will expand this sample over the coming years
while also reaching to even lower frequencies with the low-band antennas. This
will enable a more complete picture of GRB hosts in this regime to be
developed and determine how their properties influence and drive the formation
of GRB progenitors.

## Acknowledgements

We thank Emily Eyles-Ferris, Klaas Wiersema and Beatriz Mingo for invaluable
discussion and insight.

We also thank the anonymous referee for their useful comments and
improvements.

RAJEF acknowledges funding from the UK Space Agency and the European Union’s
Horizon 2020 Programme under the AHEAD2020 project (grant agreement number
871158). RLCS acknowledges STFC support.

This work made use of data supplied by the UK Swift Science Data Centre at the
University of Leicester; the VizieR catalogue access tool, CDS, Strasbourg,
France (DOI : 10.26093/cds/vizier); the Wide-field Infrared Survey Explorer,
which is a joint project of the University of California, Los Angeles, and the
Jet Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration.

Analysis of GRB 050509B is based in part on observations collected at the
European Southern Observatory, Paranal, Chile (ESO program 075.D-0261, PI J.
Hjorth).

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.

This research made use of the Dutch national e-infrastructure with support of
the SURF Cooperative (e-infra 180169) and the LOFAR e-infra group. The Jülich
LOFAR Long Term Archive and the German LOFAR network are both coordinated and
operated by the Jülich Supercomputing Centre (JSC), and computing resources on
the supercomputer JUWELS at JSC were provided by the Gauss Centre for
Supercomputing e.V. (grant CHTB00) through the John von Neumann Institute for
Computing (NIC).

This research made use of the University of Hertfordshire high-performance
computing facility and the LOFAR-UK computing facility located at the
University of Hertfordshire and supported by STFC [ST/P000096/1], and of the
Italian LOFAR IT computing infrastructure supported and operated by INAF, and
by the Physics Department of Turin university (under an agreement with
Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing
Centre, Italy.

## Data Availability

LOFAR LoTSS data are available at https://lofar-surveys.org/. Swift-XRT data
are available at https://www.swift.ac.uk. ESO VLT data are available at
https://archive.eso.org/. The WISE, NVSS, WENSS, FIRST, VLASS and other
catalogued data used in this work are available via the VizieR library at
https://vizier.cds.unistra.fr, DOI : 10.26093/cds/vizier.

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##  Appendix A Source images

Figure 6: The LoTSS image mosaics for the matches to our GRB sample. All
images show the full LoTSS band centred at 144 MHz and are ordered by GRB
class and $P_{\rm chance}$. The Swift-XRT error region for each GRB is
indicated with the blue circle, LoTSS matches are indicated with red $+$s and
the AllWISE counterpart location to the LoTSS sources are indicated with
purple $\times$s. Note the varying angular and flux density scales for each
image. The LoTSS crossmatch is given in the title of each panel. For GRB
050509B, each crossmatch is labelled and for GRB 081025, each component of ILT
J162131.13+602837.1 is labelled.

Figure 7: continued

Figure 8: continued Figure 9: The VLT image of the region around GRB 050509B
and its matched LoTSS sources (Hjorth et al., 2005b, a; Gehrels et al., 2005).
The Swift-XRT error region is indicated with the blue circle, the LoTSS
matches are indicated with the red $+$s and the orange contours indicate
0.001, 0.002, 0.003 and 0.004 mJy/beam in the LoTSS mosaic. ILT
J123613.00+285902.9 is clearly coincident with the large elliptical galaxy
assumed to be GRB 050509B’s host. Figure 10: The LoTSS image mosaic around GRB
051022. The mosaic is the full LoTSS band centred at 144 MHz. The Swift-XRT
error region is indicated with the blue circle, the LoTSS match is indicated
with the red $+$ and the AllWISE counterpart location is indicated with the
purple $\times$.

##  Appendix B Spectral energy distributions

Figure 11: The SEDs of our matched sources over 128 MHz to 3 GHz ordered by
GRB class and $P_{\rm chance}$. Power laws fitted with only the LoTSS in-band
flux densities are shown in black and those fitted with additional data from
other catalogues are shown in blue.

Figure 12: continued