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11institutetext: INAF - Istituto di Radioastronomia, via P. Gobetti 101,
40129, Bologna, Italy
11email<EMAIL_ADDRESS>22institutetext: Hamburger Sternwarte,
Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
33institutetext: Leiden Observatory, Leiden University, PO Box 9513, 2300 RA
Leiden, The Netherlands 44institutetext: Dipartimento di Fisica e Astronomia,
Università di Bologna, Via P. Gobetti 93/2, 40129 Bologna, Italy
55institutetext: ASTRON, the Netherlands Institute for Radio Astronomy, Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands 66institutetext:
Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA 77institutetext: Department of Physics, Astronomy and Mathematics,
University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK
88institutetext: GEPI & ORN, Observatoire de Paris, Université PSL, CNRS, 5
Place Jules Janssen, 92190 Meudon, France 99institutetext: Department of
Physics & Electronics, Rhodes University, PO Box 94, Grahamstown, 6140, South
Africa

# Ultra-low frequency LOFAR spectral indices of cluster radio halos

T. Pasini Ultra-low frequency LOFAR spectral indices of cluster radio
halosUltra-low frequency LOFAR spectral indices of cluster radio halosUltra-
low frequency LOFAR spectral indices of cluster radio halosUltra-low frequency
LOFAR spectral indices of cluster radio halos F. De Gasperin Ultra-low
frequency LOFAR spectral indices of cluster radio halosUltra-low frequency
LOFAR spectral indices of cluster radio halos M. Brüggen Ultra-low frequency
LOFAR spectral indices of cluster radio halosUltra-low frequency LOFAR
spectral indices of cluster radio halos R. Cassano Ultra-low frequency LOFAR
spectral indices of cluster radio halosUltra-low frequency LOFAR spectral
indices of cluster radio halos A. Botteon Ultra-low frequency LOFAR spectral
indices of cluster radio halosUltra-low frequency LOFAR spectral indices of
cluster radio halos G. Brunetti Ultra-low frequency LOFAR spectral indices of
cluster radio halosUltra-low frequency LOFAR spectral indices of cluster radio
halos H. W. Edler Ultra-low frequency LOFAR spectral indices of cluster radio
halosUltra-low frequency LOFAR spectral indices of cluster radio halos R. J.
van Weeren Ultra-low frequency LOFAR spectral indices of cluster radio
halosUltra-low frequency LOFAR spectral indices of cluster radio halos V.
Cuciti Ultra-low frequency LOFAR spectral indices of cluster radio halosUltra-
low frequency LOFAR spectral indices of cluster radio halosUltra-low frequency
LOFAR spectral indices of cluster radio halosUltra-low frequency LOFAR
spectral indices of cluster radio halosUltra-low frequency LOFAR spectral
indices of cluster radio halosUltra-low frequency LOFAR spectral indices of
cluster radio halos T. Shimwell Ultra-low frequency LOFAR spectral indices of
cluster radio halosUltra-low frequency LOFAR spectral indices of cluster radio
halosUltra-low frequency LOFAR spectral indices of cluster radio halosUltra-
low frequency LOFAR spectral indices of cluster radio halos G. Di Gennaro
Ultra-low frequency LOFAR spectral indices of cluster radio halosUltra-low
frequency LOFAR spectral indices of cluster radio halos M. Gaspari Ultra-low
frequency LOFAR spectral indices of cluster radio halosUltra-low frequency
LOFAR spectral indices of cluster radio halos M. Hardcastle Ultra-low
frequency LOFAR spectral indices of cluster radio halosUltra-low frequency
LOFAR spectral indices of cluster radio halos H. J. A. Rottgering Ultra-low
frequency LOFAR spectral indices of cluster radio halosUltra-low frequency
LOFAR spectral indices of cluster radio halos C. Tasse Ultra-low frequency
LOFAR spectral indices of cluster radio halosUltra-low frequency LOFAR
spectral indices of cluster radio halosUltra-low frequency LOFAR spectral
indices of cluster radio halosUltra-low frequency LOFAR spectral indices of
cluster radio halos

###### Abstract

Context. A fraction of galaxy clusters harbor diffuse radio sources known as
radio halos. The currently adopted scenario for their formation is based on
second-order Fermi re-acceleration of seed electrons that is driven by merger-
driven turbulence in the intra-cluster medium. This mechanism is expected to
be inefficient, which implies that a significant fraction of halos should have
very steep energy spectra ($\alpha<-1.5$).

Aims. We start investigating the potential and current limitations of the
combination of the two surveys conducted by LOFAR, LoTSS (144 MHz), and LoLSS
(54 MHz), to probe the origin of radio halos.

Methods. We follow up the 20 radio halos detected in the DR1 of LoTSS, which
covers the HETDEX field, with the LoLSS survey, and we study their spectral
properties between 54 and 144 MHz.

Results. After the removal of compact sources, 9 halos were excluded due to
unreliable halo flux density measurements at 54 MHz. Our main finding is that
7 out of 11 ($\sim$64%) exhibit an ultra-steep spectrum ($\alpha<-1.5$), which
is a key prediction of turbulent re-acceleration models. We also note a
tentative trend for more massive systems to host flatter halos, although the
currently poor statistics does not allow for a deeper analysis.

Conclusions. Our sample suffers from low angular resolution at 54 MHz, which
limits the accuracy of the compact-sources subtraction. Nevertheless, this
study is the first step towards providing compelling evidence for the
existence of a large fraction of radio halos with very steep spectrum, which
is a fundamental prediction of turbulent re-acceleration models. In this
regard, the forthcoming second data release of LoLSS, along with the
integration of LOFAR international stations and the instrumental upgrade to
LOFAR2.0, will improve both the statistics and the low-frequency angular
resolution, allowing to conclusively determine the origin of radio halos in
galaxy clusters.

###### Key Words.:

LOFAR – radio halos – LoLSS – galaxy clusters

##  1 Introduction

Radio halos are diffuse sources observed in the central regions of disturbed
galaxy clusters (Willson 1970; van Weeren et al. 2019). They trace synchrotron
emission by relativistic Cosmic-Ray (CR) electrons in the presence of magnetic
fields in the Intra-Cluster Medium (ICM, Brüggen et al. 2012; Brunetti & Jones
2014), the hot ($\sim 10^{7}-10^{8}$ K) plasma which permeates galaxy
clusters. The synchrotron spectrum of radio halos can be described to a first
approximation by a power-law $S_{\nu}\propto\nu^{\alpha}$, with $S_{\nu}$ the
flux density at a frequency $\nu$, and $\alpha$ the spectral index. Given
their (usually) $\sim$Mpc size, the electrons producing the radio emission
need to be re-energised or injected in-situ since they cannot fill the
emitting volume within their synchrotron cooling time (Jaffe 1977). Their
origin has been attributed to either re-acceleration by merger-driven subsonic
turbulence (turbulent models, Brunetti et al. 2001; Petrosian 2001; Cassano &
Brunetti 2005; Brunetti & Lazarian 2007; Beresnyak et al. 2013; Donnert &
Brunetti 2014; Miniati 2015) or injection of secondary electrons in-situ by
proton-proton collisions (hadronic models, Dolag & Enßlin 2000; Pfrommer et
al. 2008; Enßlin & Pfrommer 2011). The observed correlation between radio
halos and the cluster dynamical status, with halos being usually associated
with more dynamically-disturbed systems, rather than with more relaxed
clusters (Buote 2001; Cassano et al. 2010b; Cuciti et al. 2021; Cassano et al.
2023), together with gamma-ray constraints (Brunetti et al. 2017; Adam et al.
2021) and arguments based on the CR protons (CRp) energy budget in the case of
steep-spectrum radio halos (Brunetti et al. 2008; Brunetti & Jones 2014; Bruno
et al. 2021), support the turbulent re-acceleration scenario. Therefore purely
hadronic models are currently disfavoured, but they might still play a role
(Brunetti & Lazarian 2011; Pinzke et al. 2017; Adam et al. 2021; Nishiwaki et
al. 2021).

Turbulent re-acceleration models assume that mergers between galaxy clusters
can generate turbulence in the ICM, which amplifies seed magnetic fields
(Dolag et al. 2005) and re-accelerates relativistic particles via second-order
Fermi mechanisms (Brunetti et al. 2001; Cassano & Brunetti 2005; Brunetti &
Lazarian 2007; Pinzke et al. 2017; Nishiwaki et al. 2021). However, due to the
low efficiency of this mechanism (see e.g. Brunetti & Lazarian 2011), these
models predict the existence of a large population of radio halos with very
steep spectra (Cassano et al. 2006; Brunetti et al. 2008). Specifically, due
to synchrotron and Inverse Compton (IC) losses, the maximum energy of
electrons that are re-accelerated by second-order mechanisms in the ICM is
generally estimated to be in the range 1-10 GeV, implying a maximum
synchrotron frequency ($\nu_{\rm b}$, break frequency) in the radio band and a
gradual steepening of the synchrotron spectrum above this frequency (Cassano
et al. 2010a), which is proportional to the ICM acceleration efficiency $\chi$
(Cassano et al. 2006):

$\centering\nu_{b}\propto\dfrac{B\chi^{2}}{(B^{2}+B^{2}_{\rm CMB})^{2}}\
,\@add@centering$ (1)

where $B$ represents the cluster magnetic field, while $B_{\rm
CMB}=3.2(1+z)^{2}\,\mathrm{\mu{G}}$ is the equivalent magnetic field strength
of the Cosmic Microwave Background (CMB) at redshift z. In this scenario, the
acceleration efficiency depends on the specific acceleration mechanism and
turbulent properties of the ICM. It is generally expected to increase with
cluster mass, as the turbulent energy budget and turbulent energy flux in more
massive clusters are larger (e.g., $\chi\propto M^{4/3}$, with $M$ mass of the
main cluster undergoing the merger111This comes from the proportionality
between break frequency and mass, see e.g. Cassano & Brunetti (2005)., see
also Eq. 3 of Cassano et al. 2010a). This leads to the prediction of turbulent
models that less energetic merger events, i.e. minor mergers or mergers in
less massive systems, generate radio halos with steeper spectra (Cassano et
al. 2006; Brunetti & Lazarian 2007; Brunetti et al. 2008). Since the vast
majority of mergers in the universe involve low-mass systems, these models
predict the existence of a vast population of radio halos with very steep
spectra (Cassano et al. 2010a). These radio halos, referred to as ultra-steep
spectrum radio halos (USSRH), are predicted to have synchrotron spectral
indices $\alpha<-1.5$. This is steeper than the typical
$\alpha\sim-1.2$—$-1.3$ found in radio halos observed in high-frequency radio
surveys (e.g. Giovannini et al. 1999), that are usually associated with more
massive clusters.

Thus, observations of USSRH constitute a unique tool to constrain the origin
of radio halos. In recent years, a growing number of USSRH have been found
through single-target studies of galaxy clusters (e.g. Brunetti et al. 2008;
Bonafede et al. 2012; Wilber et al. 2018; Di Gennaro et al. 2021; Bruno et al.
2021; Edler et al. 2022). The existence of these systems has also been used to
further challenge an hadronic origin of giant radio halos (Brunetti et al.
2008; Bruno et al. 2021). However, it is still unclear whether they are hints
of the emergence of a large population or if they constitute peculiar cases.

In this letter, we explore the potential of the two radio surveys that are
being carried out by the LOw Frequency ARray (LOFAR, van Haarlem et al. 2013)
for the study of the spectral properties of radio halos in galaxy clusters. We
will present the results based on the currently available data, demonstrating
their potential impact but also their present weaknesses. Our results will
also be put into context with state-of-the-art theoretical models for the
origin of radio halos, with the caveat that the present data do not allow to
derive any final conclusions on their nature. Throughout this work, we adopt a
$\Lambda$CDM cosmology with H${}_{0}=70$ km s-1 Mpc-1, $\Omega_{\Lambda}=0.7$
and $\Omega_{\text{M}}=1-\Omega_{\Lambda}=0.3$.

##  2 Sample and spectral index measurement

Cluster name | S${}_{1r_{\mathrm{e}}}^{54\rm MHz}$ | S${}_{3\sigma}^{54\rm MHz}$ | S${}_{1r_{\mathrm{e}}}^{144\rm MHz}$ | S${}_{3\sigma}^{144\rm MHz}$ | $\alpha_{1r_{\mathrm{e}}}$ | $\alpha_{3\sigma}$ | Image
---|---|---|---|---|---|---|---
| [mJy] | [mJy] | [mJy] | [mJy] |  |  |
PSZ2G086.93+53.18 | 6 $\pm$ 3 | 25 $\pm$ 7 | 0.7 $\pm$ 0.2 | 3.1 $\pm$ 0.5 | -2.20$\pm$ 0.61 | -2.15 $\pm$ 0.32 | T90 (=150 kpc)
PSZ2G096.83+52.49 | 122 $\pm$ 21 | 288 $\pm$ 43 | 20.8 $\pm$ 2.2 | 43.8 $\pm$ 4.5 | -1.80 $\pm$ 0.30 | -1.92 $\pm$ 0.17 | T100 kpc
PSZ2G099.86+58.45 | 34 $\pm$ 5 | 22 $\pm$ 4 | 6.5 $\pm$ 0.8 | 4.3 $\pm$ 0.6 | -1.67 $\pm$ 0.26 | -1.66 $\pm$ 0.27 | T50 kpc
PSZ2G107.10+65.32N | 205 $\pm$ 14 | 1084 $\pm$ 69 | 65.5 $\pm$ 6.6 | 314.8 $\pm$ 31.5 | -1.16 $\pm$ 0.24 | -1.26 $\pm$ 0.04 | T100 kpc
PSZ2G107.10+65.32S | 78 $\pm$ 15 | 248 $\pm$ 33 | 24.8 $\pm$ 2.9 | 83.7 $\pm$ 8.9 | -1.17 $\pm$ 0.46 | -1.11 $\pm$ 0.26 | T50 kpc
PSZ2G111.75+70.37 | 37 $\pm$ 7 | 205 $\pm$ 26 | 5.1 $\pm$ 0.6 | 27 $\pm$ 3.0 | -2.02 $\pm$ 0.27 | -2.07 $\pm$ 0.14 | T100 kpc
PSZ2G114.31+64.89 | 149 $\pm$ 12 | 324 $\pm$ 23 | 23.9 $\pm$ 2.4 | 43.2 $\pm$ 4.4 | -1.87 $\pm$ 0.16 | -2.05 $\pm$ 0.05 | T50 kpc
PSZ2G133.60+69.04 | 318 $\pm$ 33 | 590 $\pm$ 54 | 62.7 $\pm$ 6.3 | 115.8 $\pm$ 12.1 | -1.66 $\pm$ 0.20 | -1.66 $\pm$ 0.11 | T50 kpc
PSZ2G135.17+65.43 | 36 $\pm$ 8 | 50 $\pm$ 10 | 10.7 $\pm$ 1.2 | 16.6 $\pm$ 1.8 | -1.24 $\pm$ 0.47 | -1.12 $\pm$ 0.39 | T50 kpc
PSZ2G139.18+56.37 | 303 $\pm$ 20 | 1249 $\pm$ 82 | 96.5 $\pm$ 9.7 | 292.3 $\pm$ 29.3 | -1.17 $\pm$ 0.24 | -1.48 $\pm$ 0.04 | T50 kpc
PSZ2G143.26+65.24 | 33 $\pm$ 6 | 115 $\pm$ 14 | 7.3 $\pm$ 1.0 | 28.3 $\pm$ 3.0 | -1.54 $\pm$ 0.35 | -1.43 $\pm$ 0.19 | T100 kpc
Table 1: The table lists, from first to last column: cluster name, 54 MHz halo
flux density estimated within 1 $e-$folding radius and within 3$\sigma$ 144
MHz contours, 144 MHz halo flux density estimated within 1 $e$-folding radius
and within 3$\sigma$ 144 MHz contours, spectral index estimated within 1
$e$-folding radius and within 3$\sigma$ 144 MHz contours, source-subtracted
image used for flux density measurement (T50 kpc = taper 50 kpc, T100 kpc =
taper 100 kpc, T90 = taper 90′′).

We use the Data Release 1 (DR1) of the LOFAR LBA Sky Survey (LoLSS, de
Gasperin et al. 2021; de Gasperin et al. 2023), performed at a central
frequency of 54 MHz, together with the DR2 of the LOFAR Two-Metre Sky Survey
(LoTSS, Shimwell et al. 2017, 2019, 2022) at 144 MHz. We examine emission from
galaxy clusters in the HETDEX Spring field222RA: 11h to 16h and Dec:
45$\degree$ to 62$\degree$, Hill et al. (2008), which has been mapped by both
surveys for a total area of $650\,\rm{deg}^{2}$. Our aim is to measure the
spectral index of radio halos in an as-large-as-possible sample of systems,
estimate the fraction of USSRH, and thus constrain theoretical models. We
start from the all-sky Planck Sunyaev-Zeldovich 2 (PSZ2) catalog of galaxy
clusters (Planck Collaboration 2016), which provides SZ masses, and match them
to LoLSS DR1. If a system is covered by at least one pointing and the primary
beam response at its position is above 30%, 144 MHz LoTSS observations are
also retrieved and the cluster is included in our initial sample. This sample
contains 49 PSZ2 galaxy clusters with observations at both 54 and 144 MHz. For
33 of these systems, we also retrieved archival X-ray observations with either
Chandra or XMM-Newton (Botteon et al. 2022; Zhang et al. 2023). The
calibration strategy for LOFAR data is described in Appendix A, while a
discussion of possible selection effects and biases is reported in Appendix D.
After calibration, for all galaxy clusters in our sample we produced 54 and
144 MHz images at multiple angular resolutions. To avoid spurious emission
from Active Galactic Nuclei (AGN), we subtracted compact sources from the uv-
data by removing all sources in the field of the target with a Largest Linear
Size (LLS) smaller than 250 kpc at each cluster redshift. Additional detail
can be found in A.

We then carefully inspected the 54 MHz images of our initial sample, and
compared them with the 144 MHz LoTSS catalogs of radio halos by Botteon et al.
(2022) and van Weeren et al. (2021), where a first classification of diffuse
emission had already been performed. Among the 49 clusters of our sample, in
these studies 19 were reported to host either a confirmed or a
candidate333i.e. radio emission detected but no X-ray observation available,
as defined in Botteon et al. (2022). radio halo, with one system
(PSZ2G107.10+65.32, i.e. A1758) previously known to host two (Botteon et al.
2018). At 54 MHz, we were able to confirm the presence of diffuse emission
even at low frequency in all these 19 clusters (20 halos in total). X-ray
observations were eventually exploited to confirm the detection, when
available. We note that we do not detect diffuse emission at 54 MHz in
clusters for which no radio halos had previously been found at 144 MHz.

Since our aim is to include only radio halos whose classification and spectral
index can be accurately determined, we decided to exclude a number of systems
whose diffuse emission was too complicated to disentangle from spurious
sources. This is mostly due to complex compact-source subtraction, uncertain
classification at 54 MHz, and contamination by AGN emission. Furthermore, most
of these systems did not have a conclusive classification at 144 MHz in van
Weeren et al. (2021) and Botteon et al. (2022), and were labeled as candidate
halos444Although this was purely based on the lack of X-ray observations able
to confirm their nature.. The masses of the excluded systems cover the entire
mass range of our initial sample. Additionally, our selection criteria are
independent of cluster mass and are solely dictated by instrumental
limitations. In addition, we also applied a cut in redshift at $z<$ 0.7. This
is motivated by the fact that, at higher redshift, a $\sim$250 kpc diffuse
source (which is the threshold of our compact-source subtraction) would be
smaller than $\sim$30′′, which is roughly 1/3 of the lowest image beam used to
detect our radio halos. Therefore, at this redshift it would not be possible
to distinguish diffuse emission from spurious sources (e.g. remnant AGN
plasma, leftovers of source subtraction etc.). Because of this threshold, one
system (PSZ2G084.10+58.72, $z=0.731$) was excluded from the final sample. In
Table 2 (see Appendix B) we provide a complete list of all the initial 19
systems hosting diffuse emission, specifying whether they are included or
excluded in the final sample and, in the latter case, we shortly explain the
main reason. These limitations, that significantly affect our analysis, have a
much higher impact in LoLSS compared to LoTSS, where the higher resolution
allow for a more accurate subtraction of spurious emission.

After this cut, the final sample includes 10 galaxy clusters with halos,
including A1758 which hosts two, for a total of 11 radio halos. The complete
list can be found in Table 1. We have then measured the flux density of our
radio halos at 54 and 144 MHz, and calculated their integrated spectral index.
The measurement is done from circular regions centered on the peak of the halo
as detected at 144 MHz in Botteon et al. (2022), and with a radius
corresponding to one e-folding radius ($r_{\mathrm{e}}$) as estimated at 144
MHz. We also tested the accuracy of this method by performing an additional
flux density estimate at both frequency within 3$\sigma$ contours derived at
144 MHz. A thorough and detailed discussion of all these measurements, of
their motivations and impact on our results can be found in Appendix C. The
k-corrected flux densities of our halos derived within $r_{\mathrm{e}}$ and
within 3$\sigma$ contours and the resulting spectral indices555see Appendix C
for more details are listed in Table 1.

##  3 Results and discussion

Figure 1: The spectral index distribution of our sample of 11 radio halos,
estimated within a region centered on the halo and with radius 1
$r_{\mathrm{e}}$.

In Fig. 1 we show the spectral index distribution for our sample. Out of 11
halos, seven ($\sim$64%) exhibit $\alpha<-1.5$. Therefore, with the currently
available data and techniques, a large fraction of the low-frequency ($<150$
MHz) radio halo population seems to show an ultra-steep spectrum, in line with
predictions from e.g. Cassano et al. (2010a), who argued that more than half
of radio halos that would have been observed with LOFAR would have a ultra-
steep spectral index. This key prediction is tied to the fact that the spectra
of radio halos are expected to become statistically steeper in radio halos
generated in less massive systems (Cassano et al. 2006; Cuciti et al. 2021).
Sunyaev-Zeldovich (SZ) mass estimates are available for our entire sample: the
vast majority of these systems ($>80$%) has $M<7\times 10^{14}M_{\odot}$,
suggesting that a large fraction should host steep spectrum halos, which is
consistent with our findings. While previous single-target studies (see Sec.
1) had already found a number of halos with steep spectra, this is the first
time that this can be confirmed through a larger (albeit still small), self-
consistent sample. Our result hints at the fact that previous $\sim$GHz
surveys might have only scratched the surface of the halo population, since
they were able to detect only halos with flat-enough spectra
($\alpha\sim-1.2$) to shine even at relatively high frequency. However,
considering these findings, the vast majority of the halo population could
instead exhibit ultra-steep spectra, which leads to very strong constrains on
their origin. As thoroughly discussed in Brunetti et al. (2008), hadronic
models struggle to explain the formation of such sources, since this would
imply a steep spectral energy distribution for protons and, as a consequence,
a domination of non-thermal protons in clusters. On the other hand, the
existence of USSRH is naturally predicted from turbulent models, as already
discussed in Sec. 1. This being said, it is important to note the limitations
and potential sources of errors of our method.

First of all, the starting sample of 20 radio halos has been significantly
reduced to a point where the statistics, despite still being relevant, are too
poor to derive any kind of conclusive result. With currently available data
there is no way to improve it, apart from including systems that we previously
excluded because of uncertain spectral index measurement, which would in any
case introduce different kinds of uncertainties in our results. In the very
next future LoLSS DR2 will, however, allow to increase the number of radio
halos: Botteon et al. (2022) finds a total of 80 galaxy clusters hosting radio
halos in the DR2 of LoTSS. It is likely that, when combining it with LoLSS, we
will still be forced to exclude a number of systems because of the same issues
that impacted this work (low resolution, poor complex source subtraction
etc.). If we assume to lose a similar fraction (around 50%) of clusters, 40
radio halos will still constitute a significantly large sample, and the
results will be considerably more robust. Finally, high-resolution
observations that will be performed thanks to LOFAR International Stations
(IS) and LOFAR2.0 in the next years will result in a much more accurate
compact-sources subtraction.

Finally, it is worth noting that a potential tendency is detected for less
massive systems in our sample to host halos with steeper spectrum, while
massive clusters seem to exhibit flatter halos. While this is a crucial
prediction of turbulent models, the statistics is too low to allow for any
kind of deeper analysis. Thus, we reserve this discussion to a future work,
where we will exploit the full DR2 of LoLSS to significantly increase the
sample of halos. This is essential since, if confirmed, this would be a robust
proof that radio halos with very steep spectrum are common in radio surveys at
low frequencies. The results would clearly support the currently prevalent
theoretical picture, which assumes that relativistic electrons in the ICM
originate from re-acceleration mechanisms activated by cluster merger-driven
turbulence, rather than from hadronic processes. Finally, it would
conclusively indicate that a fraction of the kinetic energy associated with
the motions of the matter on large scales is channelled into electromagnetic
fluctuations in the plasma and on non-thermal components.

##  4 Conclusions

In this paper, we have combined data from currently available observations of
the two LOFAR surveys, LoTSS and LoLSS, to derive integrated spectral indices
for a sample of radio halos. We have discussed our results, including the
potential sources of errors and limitations, and their impact on formation
models of halos. Our results can be summarised as follows:

  * •

We have followed-up with LoLSS a sample of 20 radio halos that were first
observed with LoTSS. All these sources are also detected at 54 MHz. After
compact-sources subtraction, we excluded 9 halos because of leftover
AGN/compact emission resulting from the relatively low resolution of LoLSS,
which does not always allow for accurate subtraction of spurious sources.

  * •

We have measured the halo spectral index between 54 and 144 MHz for all the
remaining 11 radio halos. We find that seven of them ($\sim$64%) have an
ultra-steep spectrum ($\alpha<-1.5$). This is in line with theoretical
expectations from turbulent re-acceleration models, which predict an high
fraction of ultra-steep spectrum halos at low frequency.

  * •

We find a tentative trend for more massive clusters to host flatter radio
halos; however, given the currently poor statistics, we remind this discussion
to a future work which will exploit a much larger sample.

  * •

We have discussed the limitations of our study. The current status of LoLSS
and its relatively low resolution result in low statistics, which cannot
conclusively determine the origin of radio halos. LoLSS DR2 will allow to
significantly increase the sample, as LoTSS DR2 recently detected $\sim$80
radio halos. Combined with the increased resolution which will be provided by
LOFAR international stations, it will finally elucidate the role of turbulent
re-acceleration for the origin of radio halos in galaxy clusters.

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##  Appendix A Data calibration

###  A.1 LBA observations and calibration procedure

The observations of our clusters were taken as part of the LoLSS survey. LoLSS
is performed by observing different pointings so that the Northern Sky at DEC
$>$24° is covered with a sensitivity which is close to uniform (see de
Gasperin et al. 2021 and de Gasperin et al. 2023 for more detail). Each
pointing is independently calibrated using the automated Pipeline for LOFAR
LBA (PiLL666Publicly available at https://github.com/revoltek/LiLF). Since all
the details are thoroughly discussed in de Gasperin et al. (2021) and de
Gasperin et al. (2023), here we only summarise the main steps. Phase and
bandpass solutions are derived through the Default Pre-Processing Pipeline
(DP3, van Diepen et al. 2018) from calibrators that are simultaneously
observed with the targets (making use of the multi-beam capability of LOFAR),
and transferred to the target field. Faraday rotation, second-order beam
errors and direction-averaged ionospheric delays are then corrected through
direction-independent calibration. To correct for direction-dependent errors,
all sources are subtracted from the visibilities, and then only the brightest
source is re-added (DD calibrator). Calibration solutions are derived from
this source through self-calibration in DP3, then subtracting again the DD
calibrator more accurately. This process is performed on every sufficiently
bright source in the field of view (FoV). The FoV is then divided into facets
depending on the positions of all DD sources, calibrating each facets using
the solutions of the corresponding DD source. This latter process is performed
through DDFacet (Tasse et al. 2021).

###  A.2 Extraction and imaging

Each cluster of our sample is covered by one or more survey pointings, which
have been calibrated following the standard procedure described above.
However, survey images are often affected by issues such as calibration
artefacts, smearing (i.e. elongation or blurring of sources) and reduction in
dynamic range. These effects occur as a result of beam errors and ionospheric
disturbances, that can be relevant especially in the case of wide-field
images. In order to improve the image fidelity and dynamic range, we post-
process LoLSS data by exploiting a strategy that has been already applied
successfully to both 144 MHz observations (van Weeren et al. 2021; Botteon et
al. 2022) and 54 MHz observations (e.g., Edler et al. 2022; Cuciti et al.
2022; Pasini et al. 2022). The corresponding workflow is summarised in van
Weeren et al. (2021) for 144 MHz data, while we already described our 54 MHz
implementation in detail in Pasini et al. (2022). We summarise here the main
steps, with the algorithm that has been suitably improved to deal with all
current and future LoLSS observations. In each pointing with beam sensitivity
at the target position above 30$\%$, a region is chosen around the target
source. The choice is based on the flux density within this region, which
typically has an extent of $15^{\prime}-20^{\prime}$. All sources outside this
extraction region are subtracted, shifting the phase centre to the centre of
the region and averaging all data in time and frequency. Pointings with higher
beam sensitivity contribute more to the final, combined dataset. Self-
calibration is then performed through WSClean (Offringa et al. 2014) and DP3.
The accuracy of the flux density scale was compared to LoLSS to check for
correctness. The extraction pipeline is included in the LiLF
package777https://github.com/revoltek/LiLF/tree/master/pipelines.

For each target we have produced images at nominal and high resolution,
setting Briggs 0 and Briggs -0.6, respectively. We also produced a number of
images at low resolution. This was done by setting Briggs -0.3, but tapering
visibilities at 30′′, 90′′ and to an angular scale corresponding to 50 and 100
kpc at the cluster redshift. In addition, to better highlight the diffuse
emission we also subtracted compact sources using the following procedure.
First, we produced an high-resolution image by setting Briggs -1 and by
cutting visibilities below a certain threshold, so that everything with a
largest linear size (LLS) below 250 kpc gets removed. The angular size of the
threshold depends therefore on the cluster redshift. We also tested different
values, including 350 and 400 kpc, since extended AGN emission (e.g. remnant
plasma from past AGN outbursts) likely constitutes the dominant contaminating
factor, especially at 54 MHz, when studying diffuse emission. We found that
250 kpc works best for our purposes, since it removes the vast majority of AGN
emission and leaves diffuse emission intact. The clean components of this
high-resolution image, that constitute our model, are then subtracted from the
overall visibilities, leaving only the diffuse emission. For these source-
subtracted datasets, we separately produced multiple low-resolution images
applying the same tapering discussed above. The typical rms noise is
$\sim$1.5, $\sim$2.5 and $\sim$4 mJy beam-1 for nominal resolution, 30′′\- and
90′′-tapered images, respectively, while tapering visibilities at 50 and 100
kpc usually leads to 1.5 and 1.7 mJy beam-1. Images of the whole sample at
both 54 and 144 MHz can be found in Appendix E.

###  A.3 HBA observations

To estimate the synchrotron spectral index, we exploited the 144 MHz LoTSS
observations of our clusters discussed in van Weeren et al. (2021). In
particular, we use the same data that was previously extracted and calibrated
in Botteon et al. (2022)888https://lofar-surveys.org/planck_dr2.html. All
targets have undergone a similar procedure to what was described above for 54
MHz, including a consistent compact source-subtraction. We refer the reader to
van Weeren et al. (2021) and Botteon et al. (2022) for further details.

###  A.4 X-ray observations

Since radio halos are known to be spatially and physically correlated (Cassano
et al. 2010b) with thermal emission from the Intra-Cluster Medium (ICM), we
have used the same X-ray observations exploited in Botteon et al. (2022) and
Zhang et al. (2023) to check the presence of halos at 54 MHz. These are
typically archival Chandra or XMM-Newton observations, that were processed
with CIAO 4.11 using CalDB v4.8.2 and SAS v16.1.0 following the standard data
reduction procedure for the two instruments. We refer to van Weeren et al.
(2021) for further detail about calibration, and to Botteon et al. (2022) for
the combination with 144 MHz observations.

##  Appendix B Initial sample

Table 2 provides a complete table of the initial sample of PSZ galaxy clusters
analysed in this work.

PSZ2 Name | Abell Name | $z$ | Mass | Included | Reason for exclusion
---|---|---|---|---|---
|  |  | [1014 M⊙] |  |
PSZ2G080.16+57.65 | A2018 | 0.0878 | 2.51 $\pm$ 0.21 | No | Halo emission mixed with old plasma
PSZ2G080.70+48.31 | A2136 | 0.235 | 3.20 $\pm$ 0.41 | No | Small-scale emission (mini-halo?)
PSZ2G081.02+50.57 | / | 0.501 | 4.69 $\pm$ 0.54 | No | Complex source subtraction
PSZ2G084.10+58.72 | / | 0.731 | 5.40 $\pm$ 0.62 | No | High redshift
PSZ2G086.93+53.18 | / | 0.6752 | 5.45 $\pm$ 0.51 | Yes | /
PSZ2G096.83+52.49 | A1995 | 0.318 | 4.92 $\pm$ 0.37 | Yes | /
PSZ2G099.86+58.45 | / | 0.616 | 6.85 $\pm$ 0.49 | Yes | /
PSZ2G106.61+66.71 | / | 0.3314 | 4.67 $\pm$ 0.56 | No | Complex source subtraction
PSZ2G107.10+65.32N | A1758N | 0.2799 | 8.00 $\pm$ 0.50 | Yes | /
PSZ2G107.10+65.32S | A1758S | 0.2799 | 5.10 $\pm$ 0.40 | Yes | /
PSZ2G111.75+70.37 | A1697 | 0.183 | 4.34 $\pm$ 0.33 | Yes | /
PSZ2G112.48+56.99 | A1767 | 0.070 | 2.99 $\pm$ 0.15 | No | Complex source subtraction
PSZ2G114.31+64.89 | A1703 | 0.2836 | 6.76 $\pm$ 0.37 | Yes | /
PSZ2G118.34+68.79 | / | 0.2549 | 3.77 $\pm$ 0.49 | No | Complex source subtraction
PSZ2G133.60+69.04 | A1550 | 0.254 | 5.88 $\pm$ 0.40 | Yes | /
PSZ2G135.17+65.43 | / | 0.5436 | 6.01 $\pm$ 0.60 | Yes | /
PSZ2G139.18+56.37 | A1351 | 0.322 | 6.87 $\pm$ 0.38 | Yes | /
PSZ2G143.26+65.24 | A1430 | 0.3634 | 7.65 $\pm$ 0.43 | Yes | /
PSZ2G150.56+58.32 | / | 0.466 | 7.55 $\pm$ 0.51 | No | Complex source subtraction
PSZ2G156.26+59.64 | / | 0.6175 | 6.77 $\pm$ 0.60 | No | Complex source subtraction
Table 2: The table lists our initial sample of PSZ2 galaxy clusters hosting
either confirmed or candidate radio halos, following the classification of
(Botteon et al. 2022), together with their Abell name, redshift and mass. The
last two columns report whether the cluster was included in the final sample
and, if not, the main reason for the exclusion.

##  Appendix C Flux density and spectral index measurement

In order to calculate the spectral indices of these 11 halos, we measured
their flux density at 54 and 144 MHz. This was done for each system at the
highest resolution at which the combination of image quality, source
subtraction and halo visibility was best. To measure the halo flux density,
recent studies (e.g., Osinga et al. 2021; Botteon et al. 2022; Bruno et al.
2023) have exploited the Halo-FDCA algorithm (Boxelaar et al. 2021), which
fits the surface brightness radial profile of radio halos with an exponential
function. However, the low S/N ratio of most radio halos at 54 MHz does not
allow a reliable fit with this procedure. Furthermore, the algorithm is
currently not able to simultaneously fit the surface brightness at the two
frequencies (see Botteon et al. 2022 for a discussion of the algorithm
limitations). The latter restriction impacts our analysis since performing
independent fits at the two frequencies would likely lead us to sample
(slightly) different areas of diffuse emission, which would translate into an
erroneous spectral index value.

Hence, the calculation of the halo flux density at each frequency is done from
circular regions centered on the peak of the halo as detected at 144 MHz in
Botteon et al. (2022)999Spurious sources which are not part of the halo
emission (e.g. leftovers of the source subtraction, old and diffuse AGN
plasma) were excluded from the flux density calculation when clearly
distinguishable., with a radius corresponding to one e-folding radius
($r_{\mathrm{e}}$) as estimated at 144 MHz. This is motivated by the fact that
$r_{\mathrm{e}}$, which describes the size of the radio halo through an
exponential profile $I(r)\propto e^{-r/r_{\mathrm{e}}}$, is defined as the
radius at which the halo surface brightness goes down by a factor 1/e (and
thus is roughly 1/3 of the emission peak). Therefore, it yields a constant
fraction $S_{r_{\mathrm{e}}}$ $\sim$ 30% of the total flux density (e.g.,
Bruno et al. 2023; Cassano et al. 2023). Typically, 3$r_{\mathrm{e}}$ is used
as a reference, which recovers $\sim$80% of the total flux density. However,
we decided to use 1$r_{\mathrm{e}}$ in order to exclude as much as possible
any kind of contamination by spurious sources. In some of our systems, using
3$r_{\mathrm{e}}$ would have implied to make a wide use of masks, which we
tried to avoid in order to provide a consistent, easily-reproducible
measurement. Even though we might miss halo flux in the outskirts, it should
still provide accurate estimates of the integrated spectral index. Currently,
there are only a few known cases of radio halos showing gradients in the
synchrotron spectrum steepness moving from the halo centre towards the
periphery. It is worth noting that one of these is the halo hosted in Coma,
which is the closest known to-date (Brunetti et al. 2001; Bonafede et al.
2022). Nevertheless, we expect the integrated spectral index to be barely
affected by any gradient, as it is weighted by the flux density.

Uncertainties on the flux density, $S$, are then derived using:

$\sigma_{S}^{2}=N_{\rm{beams}}\sigma_{\rm{rms}}^{2}+\sigma_{\rm{sub}}^{2}+\left(f\times
S\right)^{2}\mbox{ ,}$ (2)

where $f=0.1$ for 144 MHz data and $f=0.06$ for 54 MHz data is the absolute
flux-scale uncertainty (Shimwell et al. 2019, 2022; de Gasperin et al. 2023),
$N_{\rm{beams}}$ the number of beams covering the halo (within 1
$r_{\mathrm{e}}$), $\sigma_{\rm{rms}}$ the image noise, and
$\sigma_{\rm{sub}}$ the uncertainty due to compact source subtraction. The
latter is given by:

$\sigma_{\rm{sub}}^{2}=\sum_{i}N_{\rm{beams,i}}\sigma_{\rm{rms}}^{2}\mbox{ ,}$
(3)

where the sum is taken over all the $i$ sources that were subtracted within
the region in which the flux density is estimated.

Residual images were carefully inspected to check for the presence of non-
deconvolved emission, which could lead to overestimating the flux density. For
all our systems, the flux density within the same region (i.e. a circle with
radius = 1$r_{\mathrm{e}}$) as measured from residual images was found to be
consistent with 0, as expected.

In addition, as an independent check, we have also calculated the spectral
index by measuring the flux density of each halo at the two frequencies within
the 3$\sigma$ contours derived at 144 MHz. With this method we might
mistakenly include spurious emission that was not completely subtracted by our
procedure, but for the majority of the sample we should still be able to get a
good spectral index estimate. With this alternative measurement, our aim is to
confirm that using 1$r_{\mathrm{e}}$ did not yield any bias due, for example,
to the relatively small dimensions of the region. Finally, we checked the
literature for the few systems for which a spectral index (within the same or
a different frequency interval) had already been measured Botteon et al.
(2020); Di Gennaro et al. (2021); Hoeft et al. (2021); Pasini et al. (2022).
We find consistent values for the spectral index with all three methods, the
only exception being PSZ2G099.86+58.45. In this system, ref. Di Gennaro et al.
(2021) reports an overall integrated spectral index of
$\alpha_{144}^{650}=1.00\pm 0.13$ (measured on the whole halo extent). With
our data, we find instead $\alpha=-1.67\pm 0.26$ between 54 and 144 MHz
(within 1$r_{\mathrm{e}}$). The discrepancy is most likely due to the
combination of relatively high redshift (z =0.616), complex morphology of the
source and large number of radio AGN located within the halo (see also Fig.
A.4 of ref. Di Gennaro et al. (2021)), which all make the subtraction of
compact sources significantly harder, especially at 54 MHz where the S/N is
lower and the image beam larger. It is also worth noting that ref. Di Gennaro
et al. (2021) reports regions with a significantly steeper spectral index
($\alpha\sim-1.6$) in the central part of the halo. Albeit deeper observations
would be beneficial to shed more light on this issue, we choose to still
include the system in our sample, in order not to introduce a selection
effect.

Finally, the spectral index and associated error were estimated by using:

$\alpha_{\nu 1}^{\nu 2}=\dfrac{\ln S_{1}-\ln
S_{2}}{\ln\nu_{2}-\ln\nu_{1}}\pm\dfrac{1}{\ln\nu_{2}-\ln\nu_{1}}\sqrt{\bigg{(}\frac{\sigma_{1}}{S_{1}}\bigg{)}^{2}+\bigg{(}\frac{\sigma_{2}}{S_{2}}\bigg{)}^{2}},$
(4)

where $S_{1}$ and $S_{2}$ are the flux densities at frequencies $\nu_{1}$ and
$\nu_{2}$, respectively, while $\sigma$ is the corresponding error.

##  Appendix D Selection bias

Figure 2: Radio power at 54 MHz of radio halos vs. redshift (red circles). The
purple curve represents the 50% PSZ2 completeness line converted to 54 MHz
radio power following the power-mass correlation of (Cassano et al. 2023) and
assuming $\alpha=-1.5$. The blue curve is the minimum luminosity detectable at
54 MHz by LOFAR following Eq. 2 of (Cassano et al. 2023), estimated assuming
$r_{\mathrm{e}}=$ 150 kpc and a resolution of 100 kpc. The red, green and
yellow curves report instead the minimum luminosity detectable at 144 MHz by
LOFAR under the same assumptions, converted to 54 MHz assuming
$\alpha=-2,-1.5$ and $-1$, respectively.

In this section, we discuss about the possibility that the detection of a
significant population of USSRH in Fig. 1 might be driven by selection effects
that originate from the different sensitivity of LoTSS and LoLSS at their
respective frequency. First of all, a straightforward calculation (see also de
Gasperin et al. 2023) shows that, if we take into account the reported
sensitivity of the two surveys ($\sim$0.1 and $\sim$1 mJy beam-1 at 144 and 54
MHz, respectively), and we rescale them to the same beam, the spectral index
between them is $\sim$-0.5. This means that sources that are on the edge of
LoTSS sensitivity might be not detected in LoLSS if their spectrum is flatter
than this value, since their emission at 54 MHz would fall below its
sensitivity limit. On the other hand, we should detect all sources with a
spectrum steeper than -0.5, including all radio halos.

We have also compared the radio power of our halos as a function of the
redshift with the sensitivity curves of LoTSS and LoLSS. First we have used
Eq. 2 from (Cassano et al. 2023) to derive the minimum luminosity detectable
at 54 MHz by LoLSS by assuming $r_{\mathrm{e}}$ = 150 kpc101010rescaled to
angular size at a given redshift, and correspondent to $\theta_{e(z)}$ in Eq.
2. at a resolution of 100 kpc (converted in arcsec at the cluster redshift),
which is the typical resolution of the images that we have used to detect
radio halos. We have assumed a conservative rms noise of 3 mJy/beam, which is
the highest noise we find among the images of our halos at that resolution. We
have done the same for LoTSS, converting the 144 MHz luminosity to 54 MHz by
assuming different spectral indices: -1, -1.5 and -2. Finally, we have sampled
the PSZ2 selection effect, similarly to what was done in (Cassano et al.
2023). We estimated the 150 MHz radio power corresponding to the 50% PSZ2
completeness curve ($M$, $z$) in Fig. 1 of (Cassano et al. 2023), using the
radio power-cluster mass correlation found for LoTSS-DR2 radio halos (see Eq.
1 of (Cassano et al. 2023)). We then converted the 150 MHz radio power to 54
MHz by assuming a spectral index $\alpha=-1.5$. The result is shown in Fig. 2.

The plot clearly shows that, within the redshift range of our clusters (0.18
$<z<$ 0.7), the detection of radio halos is not dominated by the sensitivity
of either LoTSS or LoLSS, as the vast majority of our systems lie above or is
consistent with their minimum luminosity curves. This is also supported by the
fact that all our radio halos detected in LoTSS are also observed in LoLSS. In
fact, the distribution of our clusters in the radio power-redshift plane of
Fig. 2 is determined by the PSZ2 completeness curve, which dominates over the
sensitivity of the two surveys. There is one system (PSZ2G086.93+53.18) which
lies well below the sensitivity curves. However, the corresponding images are
characterized by a lower rms noise than the the sensitivity curve ($\sim$3
mJy/beam), and it is the only halo that we detected by tapering visibilities
to 90′′. We can thus conclude that our results are not substantially driven by
selection effects that could prevent the detection of radio halos with
different spectral properties, such as the LOFAR sensitivity at the two
frequencies.

##  Appendix E Images

In this section we show high- and source-subtracted low-resolution images at
54 and 144 MHz of our sample of radio halos. For each target, the low-
resolution images are at the resolution from which the halo flux density was
estimated. Images of the whole initial sample of clusters, as well as X-ray
maps, can be found at https://lofar-surveys.org/planck_dr2.html.

‘

Figure 3: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G086.93+53.18. Low-
resolution images were produced by tapering visibilities at 90′′. Their rms
noise is $\sim$5 and $\sim$1 mJy beam-1 at 54 and 144 MHz, respectively. The
yellow circle denotes 1 $r_{\mathrm{e}}$.

Figure 4: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G096.83+52.49. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 100 kpc at the cluster redshift. Their rms noise is $\sim$4
and $\sim$0.15 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 5: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G099.86+58.45. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 50 kpc at the cluster redshift. Their rms noise is $\sim$1.7
and $\sim$0.1 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 6: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G107.10+65.32. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 100 kpc at the cluster redshift. Their rms noise is $\sim$2.5
and $\sim$0.18 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circles
denote 1 $r_{\mathrm{e}}$ for both the N and the S halos.

Figure 7: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G111.75+70.37. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 100 kpc at the cluster redshift. Their rms noise is $\sim$4.4
and $\sim$0.22 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 8: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G114.31+64.89. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 50 kpc at the cluster redshift. Their rms noise is $\sim$2.4
and $\sim$0.1 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 9: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G133.60+69.04. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 50 kpc at the cluster redshift. Their rms noise is $\sim$1.5
and $\sim$0.12 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 10: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G135.17+65.43. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 50 kpc at the cluster redshift. Their rms noise is $\sim$1.5
and $\sim$0.11 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 11: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G139.18+56.37. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 50 kpc at the cluster redshift. Their rms noise is $\sim$2.3
and $\sim$0.09 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.

Figure 12: From left to right: 54 MHz briggs, 144 MHz briggs, 54 MHz low-
resolution and 144 MHz low-resolution images of PSZ2G143.26+65.24. Low-
resolution images were produced by tapering visibilities at an angular scale
corresponding to 100 kpc at the cluster redshift. Their rms noise is $\sim$1.8
and $\sim$0.17 mJy beam-1 at 54 and 144 MHz, respectively. The yellow circle
denotes 1 $r_{\mathrm{e}}$.