11institutetext: Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112,
21029 Hamburg, Germany
11email<EMAIL_ADDRESS>22institutetext: INAF - Istituto di
Radioastronomia, via P. Gobetti 101, 40129, Bologna, Italy 33institutetext:
Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, The
Netherlands 44institutetext: Dipartimento di Fisica e Astronomia, Università
di Bologna, via Gobetti 93/2, 40129 Bologna, Italy 55institutetext: Thüringer
Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany 66institutetext:
INAF - IASF Milano, via A. Corti 12, I-20133 Milano, Italy 77institutetext:
INAF - Osservatorio di Astrofisica e Scienza dello Spazio, via P. Gobetti
93/3, I-40129 Bologna, Italy 88institutetext: Department of Astrophysical
Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544-1001, USA
99institutetext: CSIRO Space & Astronomy, PO Box 1130, Bentley, WA 6102,
Australia

# Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550

T. Pasini Particle re-acceleration and diffuse radio sources in the galaxy
cluster Abell 1550Particle re-acceleration and diffuse radio sources in the
galaxy cluster Abell 1550 H. W. Edler Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550Particle re-acceleration and
diffuse radio sources in the galaxy cluster Abell 1550 M. Brüggen Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell
1550Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550 F. de Gasperin Particle re-acceleration and diffuse radio sources
in the galaxy cluster Abell 1550Particle re-acceleration and diffuse radio
sources in the galaxy cluster Abell 1550Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550Particle re-acceleration and
diffuse radio sources in the galaxy cluster Abell 1550 A. Botteon Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell
1550Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550 K. Rajpurohit Particle re-acceleration and diffuse radio sources in
the galaxy cluster Abell 1550Particle re-acceleration and diffuse radio
sources in the galaxy cluster Abell 1550Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550Particle re-acceleration and
diffuse radio sources in the galaxy cluster Abell 1550Particle re-acceleration
and diffuse radio sources in the galaxy cluster Abell 1550Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell 1550 R. J.
van Weeren Particle re-acceleration and diffuse radio sources in the galaxy
cluster Abell 1550Particle re-acceleration and diffuse radio sources in the
galaxy cluster Abell 1550 F. Gastaldello Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550Particle re-acceleration and
diffuse radio sources in the galaxy cluster Abell 1550 M. Gaspari Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell
1550Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550Particle re-acceleration and diffuse radio sources in the galaxy
cluster Abell 1550Particle re-acceleration and diffuse radio sources in the
galaxy cluster Abell 1550 G. Brunetti Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550Particle re-acceleration and
diffuse radio sources in the galaxy cluster Abell 1550 V. Cuciti Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell
1550Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550 C. Nanci Particle re-acceleration and diffuse radio sources in the
galaxy cluster Abell 1550Particle re-acceleration and diffuse radio sources in
the galaxy cluster Abell 1550Particle re-acceleration and diffuse radio
sources in the galaxy cluster Abell 1550Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550 G. di Gennaro Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell
1550Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550 M. Rossetti Particle re-acceleration and diffuse radio sources in
the galaxy cluster Abell 1550Particle re-acceleration and diffuse radio
sources in the galaxy cluster Abell 1550 D. Dallacasa Particle re-acceleration
and diffuse radio sources in the galaxy cluster Abell 1550Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell 1550 D. N.
Hoang Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550Particle re-acceleration and diffuse radio sources in the galaxy
cluster Abell 1550 C. J. Riseley Particle re-acceleration and diffuse radio
sources in the galaxy cluster Abell 1550Particle re-acceleration and diffuse
radio sources in the galaxy cluster Abell 1550Particle re-acceleration and
diffuse radio sources in the galaxy cluster Abell 1550Particle re-acceleration
and diffuse radio sources in the galaxy cluster Abell 1550Particle re-
acceleration and diffuse radio sources in the galaxy cluster Abell
1550Particle re-acceleration and diffuse radio sources in the galaxy cluster
Abell 1550

###### Abstract

Context. Radio observations of galaxy clusters reveal a plethora of diffuse,
steep-spectrum sources related to the re-acceleration of cosmic-ray electrons,
such as halos, relics and phoenices. In this context, the LOFAR LBA Sky Survey
provides the most sensitive images of the sky at 54 MHz to date, allowing to
investigate re-acceleration processes in a poorly-explored frequency regime.

Aims. We study diffuse radio emission in the galaxy cluster Abell 1550, with
the aim of constraining particle re-acceleration in the intra-cluster medium.

Methods. We exploit observations at four different radio frequencies: 54, 144,
400 and 1400 MHz. To complement our analysis, we make use of archival Chandra
X-ray data.

Results. At all frequencies we detect an ultra-steep spectrum radio halo
($S_{\nu}\propto\nu^{-1.6}$) with an extent of $\sim$ 1.2 Mpc at 54 MHz. Its
morphology follows the distribution of the thermal intra-cluster medium
inferred from the Chandra observation. West of the centrally located head-tail
radio galaxy, we detect a radio relic with a projected extent of $\sim$ 500
kpc. From the relic, a $\sim$600 kpc long bridge departs and connect it with
the halo. Between the relic and the radio galaxy, we observe what is most
likely a radio phoenix, given its curved spectrum. The phoenix is connected to
the tail of the radio galaxy through two arms, which show a nearly constant
spectral index for $\sim$ 300 kpc.

Conclusions. The halo could be produced by turbulence induced by a major
merger, with the merger axis lying in the NE-SW direction. This is supported
by the position of the relic, whose origin could be attributed to a shock
propagating along the merger axis. It is possible that the same shock has also
produced the phoenix through adiabatic compression, while we propose that the
bridge could be generated by electrons which were pre-accelerated by the
shock, and then re-accelerated by turbulence. Finally, we detect hints of
gentle re-energisation in the two arms which depart from the tail of the radio
galaxy.

##  1 Introduction

Radio observations reveal the presence of diffuse synchrotron emission in
galaxy clusters which is not directly associated with galaxies. This kind of
emission is thought to be produced by the (re-)acceleration of cosmic-ray (CR)
electrons due to shocks and turbulence in the Intra-Cluster Medium (ICM)
(Brüggen et al. 2012; Brunetti & Jones 2014). The synchrotron spectra of these
electrons typically show a power-law distribution,
$S(\nu)\propto\nu^{\alpha}$, with $S(\nu)$ being the flux density at frequency
$\nu$, and $\alpha$ being the spectral index.

Giant radio halos (RH) are Mpc-scale sources centered in the central regions
of merging clusters (Cassano et al. 2010). They usually exhibit spherically
symmetric morphology, even though filamentary structures are sometimes
detected (van Weeren et al. 2017; Botteon et al. 2020b). The radio emission is
spatially correlated to the distribution of the ICM revealed by X-ray
observations (Govoni et al. 2001; Giacintucci et al. 2005; Rajpurohit et al.
2018), suggesting a link between thermal and non-thermal plasma. The
integrated spectral index of RHs typically ranges between
$-1.1\leq\alpha\leq-1.4$ (Giovannini et al. 2009; Feretti et al. 2012).
Nevertheless, an increasing number of RHs with ultra-steep spectra (USSRH)
were discovered, with indices in the range $-1.5\leq\alpha\leq-2$ (e.g.
Brunetti et al. 2008; Macario et al. 2010; Dallacasa et al. 2009; Bonafede et
al. 2012; Wilber et al. 2018; Bruno et al. 2021; Duchesne et al. 2022). The
luminosity of RHs correlates with the host cluster’s X-ray luminosity, making
their detection easier in high-mass objects (e.g., Cassano et al. 2013; Cuciti
et al. 2015). Radio halos are mainly observed in merging clusters (Cassano et
al. 2013; Cuciti et al. 2015) and their origin is traced back to mechanisms
driven by large-scale turbulence (e.g., Brunetti et al. 2009; Cassano et al.
2010; Eckert et al. 2017). Cuciti et al. (2021) found that, in their sample of
75 galaxy clusters, 90% of halos are hosted in disturbed objects, while only
10% are in relaxed systems.

Cluster radio relics are usually found in the outskirts of merging galaxy
clusters. They exhibit elongated morphologies and high degrees of polarisation
above 1 GHz (up to 70%, Ensslin et al. 1998; Bonafede et al. 2014; Loi et al.
2019; de Gasperin et al. 2022). The resolved spectral index in radio relics
shows a gradient: it steepens towards the cluster centre and flattens towards
the outskirts. Their size can reach up to $\sim$2 Mpc, and high-resolution
observations have revealed filamentary structures within relics themselves (Di
Gennaro et al. 2018; Rajpurohit et al. 2020; de Gasperin et al. 2022;
Rajpurohit et al. 2022a, b). The Largest Linear Sizes (LLS) and radio powers
of relics are correlated, as well as the integrated spectral index and the
radio power (van Weeren et al. 2009; Bonafede et al. 2012; de Gasperin et al.
2014). Relics trace ICM shock waves with relatively low (M$<$3) Mach numbers
(Finoguenov et al. 2010; Akamatsu et al. 2013; Shimwell et al. 2015; Botteon
et al. 2016). The acceleration of electrons is believed to proceed via
diffusive shock acceleration (DSA) in the ICM (Ensslin et al. 1998; Roettiger
et al. 1999), in which particles scatter back and forth across the shock front
gaining energy at every crossing. Nevertheless, this mechanism has been shown
to be rather inefficient in accelerating electrons from the thermal pool
(Vazza & Brüggen 2014; Vazza et al. 2016; Botteon et al. 2020a; Brüggen &
Vazza 2020; see Brunetti & Jones 2014 for a review). Recently, it has been
suggested that seed electrons could originate from the tails and lobes (driven
by AGN outflows) of cluster radio galaxies (Bonafede et al. 2014; van Weeren
et al. 2017; Stuardi et al. 2019), which alleviates the requirements of high
acceleration efficiencies at cluster shocks (e.g., Markevitch et al. 2005;
Kang et al. 2012; Botteon et al. 2016; Eckert et al. 2016; Kang et al. 2017).
In some cases, double relics have been detected on opposite sides of the
cluster center (e.g. Rottgering et al. 1997; van Weeren et al. 2010, 2012;
Bonafede et al. 2012; de Gasperin et al. 2015). In these clusters it is
possible to constrain the merger history, providing important information
about the formation processes of relics.

Relativistic electrons with higher energies lose energy faster via synchrotron
and Inverse Compton (IC) radiation. Therefore, the emission at high
frequencies fades first. An old population of relativistic electrons,
sometimes referred to as fossil plasma, can in some cases be ”revived”, e.g.
by adiabatic compression (Enßlin & Gopal-Krishna 2001), leading to radio
phoenices. These sources are characterized by steep and curved spectra
($\alpha<$ -1.5, van Weeren et al. 2009; Clarke et al. 2013; de Gasperin et
al. 2015; Mandal et al. 2019). They can exhibit different morphologies, even
though in most cases they look elongated and filamentary (e.g. Slee et al.
2001). Compared to relics, phoenices are found at smaller distances from the
cluster centre (Feretti et al. 2012) and they are smaller ($<$500 kpc). They
can also be found in relaxed objects (e.g. van Weeren et al. 2011), suggesting
that major mergers are not strictly necessary for their formation. An
alternative mechanism to re-accelerate old plasma was recently proposed by de
Gasperin et al. (2017). This was based on radio observations of Abell 1033
(A1033), in which long tails of radio bright plasma, generated by a radio
galaxy moving within the cluster environment, are seen to brighten, in
coincidence with a spectral index flattening. A possible explanation is that
instabilities, generated by the interaction of the magnetically confined
plasma in the tails and the turbulence in the surrounding medium, can lead to
turbulent waves. These, in turn, are able to accelerate seed electrons through
second-order Fermi mechanisms. This source was labeled Gently Re-Energised
Tail (GReET) since the re-acceleration mechanism is barely efficient enough to
balance the radiative losses of the electrons. Low-frequency observations of
galaxy clusters are detecting an increasing number of tailed radio galaxies
undergoing similar re-acceleration processes (e.g., Cuciti et al. 2018; Wilber
et al. 2018; Botteon et al. 2021; Ignesti 2022; Brienza et al. 2022; Pandge et
al. 2022).

The contribution of the LOw-Frequency ARray (LOFAR, van Haarlem et al. 2013)
is essential to achieve a better understanding of re-acceleration processes
because of its unprecedented combination of sensitivity at low frequencies and
resolution. Two surveys are currently being carried out with LOFAR. The LOFAR
Two-Metre Sky Survey (LoTSS, Shimwell et al. 2017, $<rms>\sim 100\mu$Jy
beam-1) will observe the Northern Sky at a nominal frequency of 144 MHz (High
Band Antennas, HBA) with a resolution of $\sim$6″. This survey is currently
undergoing the second Data Release (DR2, Shimwell et al. 2022), covering
$\sim$6000 deg2, while DR1 covered the HETDEX spring field111RA: 11h to 16h
and Dec: 45$\degree$ to 62$\degree$ (Hill et al. 2008). (Shimwell et al.
2019). Similarly to LoTSS, the Lofar LBA Sky Survey (LoLSS, de Gasperin et al.
2021) will observe the Northern Sky at a nominal frequency of 54 MHz (Low Band
Antennas, LBA) with a resolution of $\sim$15″, with the first Data Release
covering HETDEX (de Gasperin et al. 2021). The data reduction and calibration
of HETDEX is now completed. The analysis of all known galaxy clusters in this
field at 54 MHz, similarly to what was done at 144 MHz by van Weeren et al.
2021 (hereafter VW21), will be carried out in a forthcoming publication
(Pasini et al. in prep.).

In this paper, we present LOFAR, Upgraded Giant Metrewave Radio Telescope
(uGMRT) and Very Large Array (VLA) observations of one of the most interesting
HETDEX clusters, Abell 1550 (alternatively PSZ2G133.60+69.04, hereafter
A1550). This is a dynamically disturbed cluster located at $z\sim 0.254$, with
$M_{500}$222Mass within R500, defined as the radius at which the medium
density is 500 times the critical density of the Universe. $\sim 5.88\times
10^{14}M_{\odot}$ (Planck Collaboration et al. 2016). According to Wen & Han
(2013), the cluster hosts about a hundred confirmed member galaxies within
$R_{200}\sim 2$ Mpc. Extended emission was already claimed by Govoni et al.
(2012) through 1.4 GHz Very Large Array (VLA) data in D and C configuration.
LOFAR observations at 144 MHz confirm the presence of diffuse emission (VW21,
Botteon et al. 2022), albeit on a greater scale of 1.8 Mpc. The difference in
size is due to the high sensitivity and low frequency coverage of LOFAR. A
Chandra 7 ks archival observation is also available, while the ROSAT All-Sky
Survey (RASS) measures an X-ray luminosity of $L_{X}\sim 3.5\times 10^{44}$
erg s-1 in the 0.1-2.4 keV band (Böhringer et al. 2000). In Sec. 2 we discuss
the data reduction and calibration, while in Sec. 3 we present our results
which are then discussed in Sec. 4. Finally, in Sec. 5 we summarise our main
conclusions. We assume a standard $\Lambda$CDM cosmology with H${}_{0}=70$ km
s-1 Mpc-1, $\Omega_{\Lambda}=0.7$ and
$\Omega_{\text{M}}=1-\Omega_{\Lambda}=0.3$, and errors are at 68$\%$
confidence level (1$\sigma$).

##  2 Data analysis

Figure 1: A1550 seen in 144 MHz emission (red) as detected by LOFAR overlaid
on the PanSTARSS optical (RGB filters) image. The radio image has a resolution
of 13″$\times$8″, and the beam is shown on the bottom right. The most
prominent structures that are discussed in the text are labeled. Compact
sources are subtracted to enhance diffuse emission as described in Sec. 2.1.
The yellow cross marks the cluster X-ray centre, defined as the peak of the
emission and estimated from the Chandra image presented in Sec. 2.5.

###  2.1 LBA observations

The galaxy cluster A1550 was observed by LOFAR in the 42 – 66 MHz band as part
of the HETDEX field, which is the first region of the sky targeted by LoLSS
(de Gasperin et al. 2021). The cluster is covered by four different pointings
(see Table 1 for details), for a total of 27 hours after data reduction and
calibration.

Data were calibrated using the automated Pipeline for LOFAR LBA
(PiLL333Publicly available at https: //github.com/revoltek/LiLF). The pipeline
was independently run for each of the pointings and it is described in detail
in de Gasperin et al. (2021). Here, we summarise the main steps. First, phase
and bandpass solutions of the calibrator are determined and transferred to the
target field. Then, direction-independent calibration of the target field is
performed to correct for the direction-averaged ionospheric delays, Faraday
rotation and second-order beam errors. At this step, wide-field images are
produced and direction-dependent (DD) errors, mainly due to ionospheric
inhomogeneities, still affect the data. To correct these errors, we adopt the
following strategy for direction-dependent calibration: we subtract all
sources from the visibilities using the model obtained during direction-
independent calibration. Then, we re-add the brightest source to the data and
derive calibration solutions for the direction corresponding to this source
using self-calibration. Using these solutions and the improved source model,
we subtract the source again, this time more accurately. This cycle is
repeated for all sufficiently bright sources (DD sources) in the field of view
(FoV). We then divide the FoV into facets whose position and shape depend on
the position of DD sources. Each facet is calibrated for DD effects during
imaging using the correction of the respective calibrator. This is done using
DDFacet (Tasse et al. 2018), and produces a DD-calibrated wide-field image. To
further improve image quality, we repeat the steps of the direction-dependent
calibration, starting from the DD-calibrated image.

It is still possible to optimize the calibration for a specific target of
interest (not included among DD sources), as in our case for A1550. Here, we
adapted the extraction process described in VW21 to LBA data. The procedure
has already been tested in Biava et al. (2021). During DD calibration, it is
assumed that DD effects are uniform across the facet. By selecting a smaller
region (typically 15′ – 20′) around the target, it is possible to relax this
assumption and improve calibration (see also VW21 for more details). The
extraction region should contain enough flux density to allow a good
calibration of the target.

The procedure consists of the following steps: first, we subtract all sources
outside the extraction region. We then shift the phase centre of the
observation to the centre of the region, and we average the data in frequency
and time. We apply a correction to account for the LOFAR primary beam response
at the new phase centre through IDG (Image-Domain Gridder, van der Tol et al.
2018). Pointings for which the beam response drops below 30% are excluded,
while all the others are combined and weighted so that pointings with higher
beam sensitivity contribute more to the extracted dataset. Then we perform
self-calibration cycles as in VW21 to further reduce the noise and improve the
quality of the images. Final imaging is carried out using WSClean (Offringa et
al. 2014) applying suitable weighting and tapering of the visibilities in
order to obtain images at different resolutions. Also we use multi-scale
deconvolution (Offringa 2016), and we assume that flux errors are $\sim$10%,
as for LoLSS (de Gasperin et al. 2021).

In some cases we needed to highlight the emission from diffuse sources. When
specified, we subtracted compact sources as follows: first, we produced a
high-resolution image by applying Briggs -0.6 and cutting visibilities below
100$\lambda$, which correspond to angular scales above 35′. We chose the
resolution such that only compact sources with a Largest Linear Size (LLS)
below a given threshold are imaged. Through the predict option of WSClean, the
clean components of the previous image are stored as model. Finally, we
subtract this model out of the uv-data. This leaves us with only the
visibilities of the diffuse emission.

Observation | Central frequency | RA | DEC | Total exposure | Target distance | Antenna configuration
---|---|---|---|---|---|---
|  |  [hh:mm:ss] |  [deg:mm:ss] |  | [deg] |
P183+47 | 54 MHz | 12:13:09.65 | +47:15:17.30 | 6hr | 2.75 | LOFAR LBA_OUTER
P186+50 | 54 MHz | 12:27:40.70 | +49.46.59.83 | 7hr | 2.09 | LOFAR LBA_OUTER
P187+47 | 54 MHz | 12:28:25.34 | +47.16.29.19 | 7hr | 0.45 | LOFAR LBA_OUTER
P190+47 | 54 MHz | 12:43:41.37 | +47.17.41.33 | 7hr | 2.48 | LOFAR LBA_OUTER
P23Hetdex | 144 MHz | 12:21:08.60 | +47:29:24.00 | 8hr | 1.30 | LOFAR HBA_DUAL_INNER
P26Hetdex | 144 MHz | 12:29:37.60 | +49:44:24.00 | 8hr | 2.13 | LOFAR HBA_DUAL_INNER
P27Hetdex | 144 MHz | 12:38:06.70 | +47:29:24.00 | 8hr | 1.55 | LOFAR HBA_DUAL_INNER
12435 | 400 MHz | 12:28:54.00 | +47:36:44.00 | 3hr | 0.03 | uGMRT BAND 3
18A-172∗ | 1.4 GHz | 12:29:12.7 | +47:42:25.38 | 1hr | 0.09 | JVLA C array
18A-172∗ | 1.4 GHz | 12:29:12.7 | +47:42:25.38 | 1hr | 0.09 | JVLA D array
Table 1: The table shows the details of the LBA, HBA, uGMRT and JVLA
observations used for the analysis of A1550. From left to right:
pointing/observation name, nominal frequency of the observation, coordinates
of the phase centre, distance of A1550 from the phase centre and configuration
of the antennae of the related observation. ∗: Project name. Figure 2: First
to last row: 54, 144, 400 MHz and 1.4 GHz, low- (left column) and high-
resolution (right column) images of A1550, produced by tapering visibilities
at 30″and applying Briggs -0.6, respectively. The yellow circle denotes
$R_{500}=1173$ kpc (Botteon et al. 2022). Row A, left panel: 54 MHz low-
resolution image. The beam is 38″$\times$25″, with rms noise $\sigma\sim$1.6
mJy beam-1. Contours are at [-3, 3, 6, 12, 24] $\times\sigma$. Row A, right
panel: 54 MHz high-resolution image. The beam is 18″$\times$11″, with rms
noise $\sigma\sim$1.5 mJy beam-1. Row B, left panel: 144 MHz low-resolution
image. The beam is 35″$\times$32″, with rms noise $\sigma\sim$0.14 mJy beam-1.
Row B, right panel: 144 MHz high-resolution image. The beam is 8″$\times$4″,
with rms noise $\sigma\sim$69$\ \mu$Jy beam-1. Row C, left panel: 400 MHz low-
resolution image. The beam is 38″$\times$26″, with rms noise $\sigma\sim$0.28
mJy beam-1. Row C, right panel: 400 MHz high-resolution image. The beam is
6″$\times$3″, with rms noise $\sigma\sim 60\ \mu$Jy beam-1. Row D, left panel:
1.4 GHz low-resolution image. The beam is 32″$\times$32″, with rms noise
$\sigma\sim 26\ \mu$Jy beam-1. Row D, right panel: 1.4 GHz high-resolution
image. The beam is 13″$\times$12″, with rms noise $\sigma\sim 18\ \mu$Jy
beam-1.

###  2.2 HBA observations

A1550 was observed by LOFAR in the frequency range 120-166 MHz as part of the
second Data Release (DR2) of LoTSS (Shimwell et al. 2022). The cluster is
covered by three pointings (see Table 1 for details), for a total of $\sim$24
hours. The data were processed with a set of fully automated pipelines
developed by the LOFAR Surveys Key Science Project team: prefactor (van Weeren
et al. 2016; Williams et al. 2016; de Gasperin et al. 2019) and ddf-pipeline
(Tasse et al. 2021). These pipelines are able to correct for both direction-
independent and direction-dependent effects. The pipelines also include
flagging of the radio frequency interference (RFI). Then the uv-data is
averaged in time and frequency, and complex gains, clock offsets and phase
delays are obtained and applied to each station. The calibration of direction-
dependent effects (DDE) is then performed using the same facet method
discussed for LBA.

In this work, we exploit the same datasets which were recently presented in
Botteon et al. (2022). New images were produced through WSClean with different
sets of parameters, depending on our purposes, applying multiple weighting
schemes and visibility tapering. The flux density scale was aligned with the
LoTSS-DR2 data release (Botteon et al. 2022), where the flux calibration
uncertainty is estimated to be $\sim$10% (Hardcastle et al. 2021). Where
explicited, compact-source subtraction was performed exploiting the same
method described in Sec. 2.1.

###  2.3 GMRT observation

A1550 was observed by uGMRT on September 17th, 2020, for a total integration
time of 3 hours (ObsID = 12435, PI V. Cuciti). Observations were carried out
in band 3 (330-500 MHz), with nominal frequency 400 MHz. 3C286 was used as
absolute flux density calibrators. Data reduction and calibration were carried
out using the Source Peeling and Atmospheric Modeling (SPAM) pipeline (Intema
et al. 2009, 2017), which corrects for ionospheric effects and removes
direction-dependent gain errors. Direction-dependent gains were derived
through bright sources in the field of view. Finally, data were corrected for
the system temperature variations between calibrators and target. Imaging is
carried out through WSClean applying different weightings and visibility
tapering. The flux uncertainty is assumed to be 6% (Chandra et al. 2004). When
specified, we applied the same compact-source subtraction procedure described
in Sec. 2.1.

###  2.4 JVLA observations

We obtained JVLA observations of A1550 in the 1-2 GHz JVLA L-band, in C and D
antenna configuration (Project ID = 18A-172, PI R. J. van Weeren). The former
was performed on January 19, 2019 for a total of 1 hour, pointed at
RA=12h29m12.75s DEC=47$\degree$42′25.4″, while the latter is a 1 hour
observation performed on 20 September, 2018 and pointed at the same
coordinates. Data reduction was carried out with the National Radio Astronomy
Observatory (NRAO) Common Astronomy Software Applications package (CASA,
version 6.1.2.7), exploiting 3C286 as primary calibrator for both
observations, while J1219+4829 was used as phase calibrator. First, RFI and
bad visibilities for calibrators and target were flagged. Amplitude and phase
solutions were derived from the calibrators, and applied to the target. For
the purpose of self-calibration, phase-solutions are then calculated from the
model of the target, produced by a first, shallow imaging, and computed on a
given timescale for which the phase is assumed to be constant. After applying
these solutions, the cycle is repeated in order to increase the Signal-to-
Noise (S/N) ratio and improve the quality of the image, decreasing the
interval at each cycle. After this step, datasets were accurately combined to
achieve longer integration time and increase the sampling of the uv-plane.
Final imaging is carried out with WSClean, and the flux uncertainty is assumed
to be 5%. When specified, we applied the same compact-source subtraction
procedure described in Sec. 2.1. Finally, for polarisation calibration, the
leakage response was determined using the unpolarised calibrator 3C147. The
absolute position angle (the R-L phase difference) was corrected using the
polarised calibrator 3C286. The polarisation intensity ($P$) and polarisation
angle $(\Psi$) maps were derived from Stokes Q and U maps:

$\centering\begin{split}P=\sqrt{Q^{2}+U{{}^{2}}},\\\
\Psi=\frac{1}{{2}}\tan^{-1}{\frac{U}{Q}}\end{split}\@add@centering$ (1)

Finally, the fractional polarisation map was obtained as:

$\centering p=\frac{P}{I},\@add@centering$ (2)

where $I$ and $P$ are the total intensity and polarization intensity,
respectively, of the source.

###  2.5 Chandra observation

The Chandra data of A1550 (obsID 11766) were taken with the Advanced CCD
Imaging Spectrometer (ACIS) in S configuration, operating in VFAINT mode, with
a short exposure time of $\sim$7 ks. The ACIS-S configuration consists of an
array of 6 chips. We use the ACIS-S3 chip, where the aimpoint of the telescope
lies. Unfortunately, the cluster emission covers a projected region larger
than the CCD area (8.3${}^{\prime}\times 8.3^{\prime}$). For this reason, part
of the cluster emission is out of the FoV and cannot be studied. The maximal
area that can be reached lies within a radius of 4 arcmin from the cluster
centre, which corresponds to $\sim$0.8R500.

The data were reprocessed with CIAO 4.11444https://cxc.harvard.edu/ciao/ using
CALDB 4.8.4.1. The Chandra_repro script was executed to perform the standard
calibration process. Background flares were removed and the Blanksky template
files, filtered and normalized to the count rate of the source in the hard
X-ray band (9-12 keV), were exploited to model the background contribution to
the emission. Finally, point sources were identified and removed using the
CIAO task WAVDETECT with a default significance threshold of 10-6. The final
exposure time is 6948 s. Exposure-corrected images were produced in the 0.5-7
keV band.

##  3 Results

###  3.1 HBA and LBA comparison

In Fig. 1 we show the radio emission as detected at 144 MHz by HBA, overlaid
on the Panoramic Survey Telescope and Rapid Response System (PanSTARRS,
Chambers et al. 2016) image of A1550. Projected at the cluster centre, an
head-tail (HT) radio galaxy (labelled as AGN+tail in the figure) dominates the
emission. The galaxy is embedded within the giant radio halo originally
detected by Govoni et al. (2012). In the South-West, a roundish patch of
emission (A) is observed, without a clear optical counterpart. North-West of
source A, we clearly detect a source which resembles a radio relic, as already
hinted at in VW21 and Botteon et al. (2022). From this image, it is not clear
whether the putative relic and source A are part of the same structure. From
here, two filaments extend to the East and West directions. The eastern
filament (bridge) looks connected to the halo, as already found at 144 MHz by
VW21 from low-resolution images. The western filament, labeled B, has no clear
counterpart as well, even though its morphology suggests that it could be a
radio galaxy, possibly unrelated to the diffuse emission. An elliptical
depletion of radio emission is observed between the bridge, the head-tail and
source A. Finally, in the North-East region of the cluster, we observe an arc-
shaped extension of emission. As already discussed in VW21, it lies in front
(at least in projection) of a group of galaxies with the same redshift of
A1550. Low-resolution images at 144 MHz showed that it is likely connected to
the halo (VW21 and Botteon et al. 2022). We will return on this throughout
this paper.

Figure 3: Top left: 54 MHz source-subtracted image of A1550 obtained applying
Briggs -0.3 and tapering the visibilities to 30″. The beam, shown on the
bottom left, is 46″$\times$36″, with rms noise $\sigma\sim$ 1.9 mJy beam-1.
Contours are at -3, 3, 6, 12, 24 $\times\sigma$. Top right: 144 MHz source-
subtracted image of A1550 obtained applying Briggs -0.3 and tapering the
visibilities to 30″. The beam is 36″$\times$35″, with rms noise $\sigma\sim$
0.14 mJy beam-1. Contours are the same as above. Bottom left: 400 MHz source-
subtracted image of A1550 obtained applying Briggs -0.3 and tapering the
visibilities to to 30″. The beam is 36″$\times$26″, with rms noise
$\sigma\sim$ 0.23 mJy beam-1. Bottom right: 1.4 GHz source-subtracted image of
A1550 obtained applying Briggs -0.3 and tapering the visibilities to to 30″.
The beam is 32″$\times$32″, with rms noise $\sigma\sim$ 23 $\mu$Jy beam-1.

With the purpose of unveiling the nature and morphology of each of these
structures, we produced images at different frequencies and resolution. In the
left panels of the first two rows in Fig. 2, we show the cluster as detected
at 54 MHz and 144 MHz by tapering visibilities at 30″. The head-tail dominates
the radio emission, with integrated flux density inside 3$\sigma$
contours555If not specified otherwise, all flux densities are calculated
within 3$\sigma$ contours. of $S_{144\rm{MHz}}=264\pm 26$ mJy and
$S_{54\rm{MHz}}=707\pm 71$ mJy, respectively. The putative relic and halo are
clearly visible at both frequencies, and the morphology and orientation of the
NE extension suggest that it is connected to the halo. The bridge connecting
the candidate relic to the halo, while resolved in HBA, is hardly
distinguishable in the LBA image due to lower resolution.

In order to resolve all the detected structures, we produced high-resolution
images by setting Briggs -0.6 and excluding baselines shorter than
100$\lambda$. The halo almost disappears at both frequencies (see right panels
of Fig. 2), while we are still able to see the candidate relic and source A.
At 144 MHz, the emission that connects source A to the AGN/halo is split into
two arms, which will be better defined and analysed in Sec. 4.3. The lack of
optical counterparts, together with the shape and orientation of the head-tail
radio galaxy and relic, might suggest that source A could be constituted by
re-accelerated electrons (see Sec. 4.3).

We then subtracted compact sources as described in Sec. 2.1 on the HBA and LBA
observations and tapered visibilities at 30″, with the purpose of imaging more
accurately the diffuse emission. The resulting images are shown in Fig. 3.
Without the AGN, it is much easier to assess the different structures observed
in A1550, and we can therefore estimate their physical properties, such as
flux density and extent, more accurately.

To estimate the flux density of the halo, we used the Halo Flux Density
CAlculator (Halo-FDCA, Boxelaar et al. 2021) on the subtracted maps. This code
fits the surface brightness of radio halos to 2D exponential models using
Bayesian inference, and calculates the flux density analytically. The plots of
the halo models and masks used for the fit are shown in Appendix A. After
accounting for the contribution of the radio galaxy tail and masking both
source A and NE extension, we measure a flux density for the halo of
$S_{144\rm{MHz}}=108\pm 11$ mJy, which is in agreement with what we measure
from 2$\sigma$ contours, and a maximum extent of $\sim$1 Mpc. The fit also
provides an estimate of the e-folding radius of $r_{e}=183\pm 4$ kpc. We note
that VW21 reported a flux density of $S_{144\rm{MHz}}=129\pm 26$ mJy, while
Botteon et al. (2022) provides an estimate of $S_{144\rm{MHz}}=145\pm 18$ mJy.
The difference with the previous results is likely related to the fact that
although VW21 and Botteon et al. (2022) also used FDCA, they performed the fit
with an elliptical model, while we used a circle model. In Botteon et al.
(2022), this resulted in radii of $377\pm 5$ and $201\pm 4$ kpc, for the major
and minor axes respectively. Given the wealth of radio data studied in this
work, the circle model appears to better suit the morphology of the halo
emission. From the LBA image, we find $S_{54\rm{MHz}}=498\pm 57$ mJy and
projected LLS$\sim$1.2 Mpc. This implies a relatively steep spectral index of
$\alpha_{54\rm MHz}^{144\rm MHz}=-1.6\pm 0.2$. The e-folding radius is
estimated to be $r_{e}=177\pm 6$ kpc, consistent within errors with HBA.

The putative relic shows $S_{144\rm{MHz}}=94\pm 9$ mJy, with a projected
length of $\sim$500 kpc. With LBA, we measure $S_{54\rm{MHz}}=265\pm 26$ mJy.
This implies $\alpha_{54\rm MHz}^{144\rm MHz}=-1.1\pm 0.2$, which is typical
of relics (VW21). Finally, for source A we find $S_{144\rm{MHz}}=27\pm 3$ mJy
and $S_{54\rm{MHz}}=165\pm 17$ mJy, resulting in a steep spectrum with
$\alpha_{54\rm MHz}^{144\rm MHz}=-1.9\pm 0.2$. A more detailed investigation
of spectral indices in this cluster is presented in Sec. 3.4. In Table 2, we
summarise the flux densities at different frequencies of the halo, candidate
relic and source A. Their spectra are plotted in Fig. 4.

Source | S54MHz | S144MHz | S400MHz | S1.4GHz | $\alpha_{54\rm MHz}^{144\rm MHz}$ | $\alpha_{144\rm MHz}^{400\rm MHz}$ | $\alpha_{400\rm MHz}^{1.4\rm GHz}$
---|---|---|---|---|---|---|---
| [mJy] | [mJy] | [mJy] | [mJy] |  |  |
Halo | 498 $\pm 57$ | 108 $\pm$ 11 | 25 $\pm$ 3 | 2.6 $\pm$ 0.2 |  $-$1.6 $\pm$ 0.2 |  $-$1.4 $\pm$ 0.1 |  $-$1.8$\pm$ 0.1
Relic | 265 $\pm$ 26 | 94 $\pm$ 9 | 25 $\pm$ 2 | 5.2 $\pm$ 0.3 |  $-$1.1 $\pm$ 0.2 |  $-$1.3 $\pm$ 0.2 |  $-$1.2 $\pm$ 0.2
Source A | 165 $\pm$ 17 | 27 $\pm$ 3 | 3.1 $\pm$ 0.2 | $<0.13^{*}$ |  $-$1.9 $\pm$ 0.2 |  $-$2.1 $\pm$ 0.1 | /
Table 2: Flux densities and integrated spectral indices of halo, relic and
source A at different radio frequencies.∗: 3$\sigma$ upper limit, with
$\sigma$ being the rms noise of the 1.4 GHz image. Figure 4: Flux density as a
function of frequency for the halo, the relic and source A at the four
frequencies covered in our analysis. Colored areas denote flux density errors.
Note that the flux density at 1.4 GHz for source A is a 3$\sigma$ upper limit,
with $\sigma$ being the rms noise of the 1.4 GHz image.

###  3.2 The cluster at 400 MHz

In the third row of Fig. 2 we show the 400 MHz low- and high-resolution images
of A1550. The head-tail radio galaxy dominates the emission. To the West of
the head-tail, the putative relic is clearly visible, with a flux density
$S_{\rm 400MHz}=25\pm 2$ mJy. Hence, its integrated spectral index between 144
and 400 MHz is $\alpha_{144\rm MHz}^{400\rm MHz}=-1.3\pm 0.2$, consistent with
what estimated at LOFAR frequencies. At 400 MHz we do not see the bridge,
suggesting that it has a steep spectrum. Furthermore, it is not trivial to
understand whether the emission between the head-tail and the candidate relic
belongs to source A or comes from these two sources. Instead, around the radio
galaxy we clearly observe the radio halo.

As before, we then subtracted compact sources and tapered visibilities to a
resolution of 30″, with the result shown in the bottom-left panel of Fig. 3.
We observe what is probably a hint of emission of source A, even though it is
detected barely at 3$\sigma$ significance. At this frequency, we measure a
maximal extent of the halo of $\sim$950 kpc and a flux density (with Halo-
FDCA) of $S_{\rm 400MHz}=25\pm 3$ mJy. This translates into a spectral index
between 144 MHz and 400 MHz of $\alpha_{144\rm MHz}^{400\rm MHz}=-1.4\pm 0.2$,
consistent within errors with the one estimated between 54 and 144 MHz. The
e-folding radius is $r_{e}=171\pm 10$ kpc, which is comparable to those
estimated at lower frequencies.

Finally, the flux density of source A at this frequency is $S_{\rm
400MHz}=3.1\pm 0.2$ mJy. The integrated spectral index between 144 and 400 MHz
is as steep as $\alpha_{144\rm MHz}^{400\rm MHz}=-2.1\pm 0.2$. We therefore
observe a steepening at higher frequencies, hinting that the spectrum of
source A might be significantly curved.

###  3.3 The cluster at 1.4 GHz

Figure 5: Top Left: Spectral index map between 54 MHz and 144 MHz, generated
by combining total intensity maps produced with matching uv-cut
80$\lambda$-14k$\lambda$. Contours are at 3$\sigma$ from the LBA map. The beam
is 25″$\times$13″. Top Middle: Spectral index map between 144 MHz and 400 MHz,
generated by combining total intensity maps produced with matching uv-cut
80$\lambda$-14k$\lambda$. The beam is 20″$\times$17″. Top Right: Spectral
index map between 400 MHz and 1.4 GHz, generated by combining total intensity
maps produced with matching uv-cut 140$\lambda$-14k$\lambda$. The beam is
38″$\times$32″. Bottom Left: Spectral index error map between 54 MHz and 144
GHz. Bottom Middle: Spectral index error map between 144 MHz and 300 MHz.
Bottom Right: Spectral index error map between 400 MHz and 1.4 GHz.

In the bottom panels of Fig. 2 we show A1550 at 1.4 GHz as observed by JVLA,
at low and high resolution. At this frequency the halo appears less extended,
as expected, but still clearly visible. We also detect the candidate relic,
while we observe no emission from source A and the bridge which are detected
with LOFAR. North-East to the halo, there is a hint of what probably is the
high-frequency counterpart of the extension. As above, we performed the
subtraction of compact sources, with the caveat that JVLA array D provides, by
definition, low-resolution, making the subtraction trickier. The result is
shown in the bottom right panel of Fig. 3.

The total extent of the halo is $\sim$900 kpc. Similarly to what observed at
144 MHz, the inconsistency with the previous measurement ($\sim$1.4 Mpc) by
Govoni et al. (2012), performed exploiting older VLA datasets, might be due to
the exclusion of the NE extension (allowed by the higher resolution), other
than to a better uv-coverage of the most recent observations. We estimate a
total flux density for the halo (with Halo-FDCA666Note that, due to a less
trivial source subtraction for JVLA, we had to use a larger number of masks
for the flux density estimate. See also Appendix.) of $S_{\rm 1.4GHz}=2.6\pm
0.2$ mJy, implying $\alpha_{\rm 400MHz}^{\rm 1.4GHz}=-1.8\pm 0.1$, consistent
within errors with the spectral index determined at LOFAR frequencies. Govoni
et al. (2012) provided an estimate of $\sim 7.7$ mJy at the same frequency.
However, their calculation included, both, the NE extension and source A. Even
after source subtraction we do not detect the latter, confirming that it might
have a steep spectrum. The e-folding radius is $r_{e}=174\pm 18$ kpc,
consistent with the value at lower frequencies within errors. For the
candidate relic, we measure $S_{\rm 1.4GHz}=5.2\pm 0.3$ mJy, leading to
$\alpha_{\rm 144MHz}^{\rm 1.4GHz}=-1.2\pm 0.2$.

###  3.4 Spectral analysis

To investigate the nature of the diffuse emission, we have produced spectral
index maps making use the frequency coverage available for A1550. First, HBA,
LBA and uGMRT maps were produced by applying the same visibility cut of 80
$\lambda$-14 k$\lambda$ and Briggs -0.3, in order to compensate for the
different uv-coverage of the instruments and match spatial scales. To avoid
possible artefacts produced by the source subtraction, this procedure was
applied to the non-subtracted data. The spectral index map was generated by
estimating $\alpha$ and $\Delta\alpha$ in each pixel as:

$\alpha_{\nu 1}^{\nu 2}=\dfrac{\ln S_{1}-\ln
S_{2}}{\ln\nu_{2}-\ln\nu_{1}}\pm\dfrac{1}{\ln\nu_{2}-\ln\nu_{1}}\sqrt{\bigg{(}\frac{\sigma_{1}}{S_{1}}\bigg{)}^{2}+\bigg{(}\frac{\sigma_{2}}{S_{2}}\bigg{)}^{2}},$
(3)

where $S_{1}$ and $S_{2}$ are the flux densities at frequencies $\nu_{1}$ and
$\nu_{2}$, respectively, while $\sigma$ is the corresponding error. Similarly,
spectral index maps between 1.4 GHz (VLA) and 400 MHz were produced by
applying a baseline cut at 140$\lambda$-14k$\lambda$ and Briggs -0.3.
Visibilities were tapered at 30″ to highlight the diffuse emission.

The spectral index map between 54 and 144 MHz is shown in the top-left panel
of Fig. 5. The spectral index looks flatter (-1$<\alpha<$-0.5) in the position
of the AGN and of the point source South to A, as expected from compact
objects where self-absorption is relevant. A similar behaviour is observed in
the patch labeled B, West to the candidate relic, with the spectrum being
flatter ($\alpha\sim$ -0.4) in the centre and becoming steeper ($\alpha\sim$
-0.8) moving to the periphery. This suggests that source B is likely a double-
lobed radio galaxy, even though we cannot find any obvious optical
counterpart. The region of the halo East to the head-tail shows a steep index
ranging between -1.2 and -2.2, which becomes even steeper at the periphery
and, more interestingly, West to the tail of the AGN, where source A is
located. In this region we observe a mean index of $\alpha\simeq-1.7$, but it
reaches $\alpha\simeq-2.3$ around A. The bridge East to the candidate relic
also shows a similar spectrum. At the position of the relic, we observe a
spectral index which steepens from $\alpha\simeq-0.5$ to $\alpha\simeq-1.8$ in
the westernmost region, even though the relatively low resolution makes it
hard to observe the typical gradients observed in relics. Finally, the NE
extension shows $\alpha\simeq-1.8$ in the direction of the cluster centre,
while moving to the outskirts we observe a steepening to $\alpha\simeq-2.2$.

In the top-middle panel of Fig. 5 we show the spectral index map between 144
and 400 MHz. We placed upper and lower limits on the spectral index where the
emission was not detected at the higher or lower frequency, respectively. This
might be due to the different frequency range of the instruments, and to the
spectral curvature of the sources. We observe a number of lower limits around
the main emission, which are likely uGMRT calibration artifacts which could
not be improved. The region of the halo looks consistent with what observed
between 54 and 144 MHz, with $\alpha$ ranging between -1.2 and -1.9. Due to
the lower resolution set to detect the halo, it is hard to assess the spectral
index gradient in the relic. However, we observe a steep ($\alpha<-2$)
spectrum for source A, for which we are only able to place upper limits
because of the low emission detected by uGMRT. This indicates a relatively
high curvature at high frequencies, suggesting a cutoff in the electron energy
spectrum.

Finally, in the top-right panel of Fig. 5 we show the spectral index map
between 400 MHz and 1.4 GHz. Upper limits are placed where no emission is
observed with VLA. Due to the lower resolution, it is hard to resolve all the
structures which are observed by LOFAR (especially HBA) and uGMRT. The
spectral index across the halo is consistent with what we found at lower
frequencies, and steepens towards the candidate relic and source A, which is
not detected at 1.4 GHz. Hints of upper limits $\alpha<-2$ can be observed
around the position of source A, even though they are not as clear as in the
LOFAR-uGMRT map. In the putative relic we seemingly observe a flattening of
the spectrum moving towards the cluster outskirts, even though the low
resolution makes this result uncertain.

###  3.5 Diffuse radio emission and thermal plasma

The short exposure time of the Chandra observation does not allow us to
perform a thorough analysis of the ICM in A1550. Still, we can study the
morphology of the X-ray emission and compare it to the structures observed in
the radio band.

Figure 6: Chandra exposure-corrected, background-subtracted 0.5-7 keV image of
A1550, smoothed to a resolution of 30 kpc at the cluster redshift. LOFAR LBA
contours are overlaid in white. The image is cut at the edge of the CCD FoV.

In Fig. 6 we show the Chandra image of A1550 in the 0.5-7 keV band, where the
emission of the ICM is best visible. The morphology of the ICM looks roughly
elliptical (ellipticity777Estimated as the ratio between the minor and major
axes. = $\epsilon\sim 0.75$) from the current X-ray image. The morphological
parameters presented in Table A.2 of Botteon et al. 2022, such as
concentration ($c=(8.67\pm 0.89)\times 10^{-2}$) and centroid shift
($w=(3.80\pm 0.35)\times 10^{-2}$), confirm that the cluster is disturbed,
accordingly to the thresholds defined in Cassano et al. (2010). This is
consistent with the presence of radio diffuse emission. The X-ray peak is
found at $\sim$150 kpc ($\sim$38″) from the AGN, and the morphology of the
emission seems to roughly correlate with that of the radio halo. The archival
observation does not show hints of either X-ray cavities or cold fronts, apart
from a $\sim 50$ kpc depression between the AGN and its tail. However, due to
the significant smoothing that was applied, it is currently hard to confirm
whether this structure is real, or just an artefact. This putative detection
needs to be supported by a surface brightness analysis to quantify the
possible depression, which is not feasible with the current Chandra
observation. We do not detect X-ray emission in the region of the candidate
relic and source A, even though the small area of the CCD does not allow us to
cover the whole extent of the radio structure. A faint, arc-shaped patch of
X-ray plasma stretches in the NE direction. Interestingly, the NE radio
extension seems to follow the same morphology, and may be confined by the
X-ray emission. This suggests that it could be part of the radio halo, as also
supported by our HBA and LBA observations which clearly show that the
extension is not detached from the halo emission. Nevertheless, this could
also be due to projection effects. The correlation between the X-ray and radio
surface brightness can be of help here to investigate which structures are
part of the halo, and which constitute a separate kind of diffuse emission
(Bruno et al. 2021; Rajpurohit et al. 2021; Duchesne et al. 2021). To this end
we performed a point-to-point (ptp) analysis, in which the surface brightness
at the two bands was sampled through a grid. One of the first applications of
this analysis in galaxy clusters can be found in Govoni et al. (2001), and a
dedicated algorithm was recently published by Ignesti (2022). First, we drew
three grids: one on the halo, one on the NE extension and one on the bridge
and source A (see Fig. 7). The size of the squares was chosen to be 1.5 times
the radio beam. This is large enough to allow for relatively small error bars,
especially for the X-ray image where the exposure time is short, but small
enough to provide enough statistics. Nevertheless, the available X-ray
observation prevents us from using smaller areas, which would increase our
statistics.

Figure 7: Left: Grids used to sample the halo (black), the NE extension (red)
and the bridge+source A region (orange). The dimension of the squares is 1.5
times the radio beam, with the beam being 22″$\times$19″. Right: Point-to-
point correlation between radio (144 MHz) and X-ray surface brightness. Black
data represents the halo, red represents the NE extension, while orange refers
to the South-West region including the bridge and source A.

The surface brightness was then extracted from each square through the
procedure extensively described in Ignesti (2022). The analysis was carried
out on the HBA image, since the structures are better resolved, on the
emission above 3$\sigma$. The result is shown for all three grids in Fig. 7. A
sub-linear correlation is found for the halo, with slope $k=0.37\pm 0.11$. The
Pearson and Spearman coefficients are 0.53 and 0.56, respectively, suggesting
that a correlation may exist, albeit weak. Given that such link is always
observed in radio halos (see references above), it is likely that the short
exposure time of the X-ray image, which led to the fit having low statistics,
could be the reason for the relatively low coefficients. Furthermore, the
slope is flatter than the values usually found in halos, which range between
$\sim$0.5 and $\sim$0.7 (e.g., Rajpurohit et al. 2021). Similar sub-linear
slopes were also found in the Bullet cluster (Shimwell et al. 2014) and in
A520 (Hoang et al. 2019), and were interpreted as the halo being in a
different evolutionary state with respect to typical halos. Longer X-ray
observations in the future may provide smaller error bars and a larger number
of bins, leading to a more reliable fit. On the other hand, we see no clear
correlation for NE extension and for the SW region. The Pearson and Spearman
coefficients are 0.18 and 0.13 for the NE extension, and -0.3 and -0.4 for the
bridge and source A. The distribution of their X-ray and radio surface
brightness values across the plot looks random, suggesting that they might not
be part of the halo, but may constitute another kind of diffuse emission. This
is relevant especially for the NE extension, given that both LBA and HBA
detected patches of emission connecting it to the halo.

Finally, it would be interesting to perform the same kind of analysis at all
four different frequencies, to assess if and how the slope eventually changes.
However, as discussed above, the short X-ray exposure would significantly
affect the results. Possibly, an accurate comparison of the X-ray and radio
morphology in A1550 will be performed in the next future thanks to deeper
observations.

##  4 Discussion

There are a number of interesting sources in A1550. As often observed in
disturbed galaxy clusters, the optical BCG which hosts the head-tail radio
galaxy is found relatively far from the X-ray peak ($\sim$ 150 kpc),
suggesting that the hot gas is disturbed. This is also supported by the lack
of a central peak in the ICM, as well as from morphological parameters
estimated in Botteon et al. (2022) and already discussed above. The radio
diffuse emission spans a length of $\sim$2 Mpc, suggesting that a major merger
might have occurred. Optical images are sometimes useful to assess the merger
dynamics, but in the case of A1550 we do not see obvious hints from SDSS and
PanSTARSS observations, since we do not detect any evidence for a companion
cluster. As also briefly discussed in VW21, SDSS detects a subgroup of $\sim$
20 galaxies North of the extension, which shows the same redshift of A1550.
However, it lies far ($\sim$1 Mpc) from the cluster centre and from the
diffuse emission. Therefore, given also its relatively small extent, it is
unlikely to be the cause of the extended emission detected in A1550. The
orientation of the candidate radio relic might suggest that the merger axis
lies in the NE-SW direction. This is also supported by the X-ray surface
brightness distribution that is elongated in the same direction. Nevertheless,
it is possible that diffuse emission is elongated along the line of sight, and
that we are therefore underestimating its size. A method to infer the
orientation of a cluster through observations of relics was recently suggested
in Wittor et al. (2021). It exploits the ratio of the total projected X-ray
luminosity of the cluster to the projected X-ray luminosity emitted within the
candidate relic region. If the ratio approaches $\sim 1$, it is likely that we
are observing the cluster merger face-on. On the other hand, lower ratios
indicate that the cluster is elongated in the plane of the sky. Unfortunately,
the Chandra observation does not fully cover the relic, preventing us from
performing this test.

###  4.1 The ultra-steep radio halo and the NE extension

Regardless of the cluster orientation, the spectral index observed for the
halo at all available frequencies suggests that it is a USSRH. Despite the
number of detected USSRH is still low, radio halos with steep indices are
being discovered more and more frequently in the last years thanks to the
improved observational capabilities of low-frequency instruments such as GMRT,
MWA (Murchison Widefield Array) and LOFAR (Shimwell et al. 2016; Wilber et al.
2018; Bruno et al. 2021; Di Gennaro et al. 2021; Duchesne et al. 2022). An in-
depth analysis of all radio halos hosted in Planck clusters and observed in
LoTSS, including A1550, has recently been presented in Botteon et al. (2022).
USSRH are a prediction of turbulent re-acceleration models (Cassano et al.
2006; Brunetti et al. 2008), in which particles are re-accelerated by
turbulence (Brunetti et al. 2001; Petrosian 2001; Brunetti & Lazarian 2011;
Brunetti et al. 2017). On the other hand, the detection of such steep indices
is not expected from hadronic (or secondary) models, in which the emission of
halos comes from the production of secondary electrons from hadronic
collisions between thermal and CR protons (Blasi & Colafrancesco 1999; Dolag &
Enßlin 2000; Pfrommer et al. 2008). Given that the integrated spectral index
observed for the USSRH with LOFAR is $\alpha_{54\rm MHz}^{144\rm
MHz}\sim-1.6$, we expect an index for the spectral energy
distribution888Defined as $N(E)\propto E^{-\delta}$, with $E$ being the
energy. $\delta=2\alpha-1=-4.2$. If there is no break in the spectrum, the
energy budget for these particles would be untenable (Brunetti et al. 2008).
Therefore, a break at low energies ($\sim$ GeV) should exist, suggesting a
possible interplay between radiative losses and turbulent re-acceleration
during the lifetime of emitting electrons (Brunetti & Jones 2014). Moreover,
re-acceleration models predict that a large fraction of halos associated with
clusters of masses between 4-7 $\times 10^{14}$ M⊙ should exhibit steep
spectra (Cassano et al. 2010, 2012; Brunetti & Jones 2014; Cuciti et al.
2021). The mass of A1550 of $\sim 6\times 10^{14}$ M⊙ estimated from Planck
Collaboration et al. (2016) falls in this range.999Since the correlation
between the halo luminosity and the cluster mass has recently been studied for
the whole LOFAR Planck-DR2 sample in Botteon et al. (2022), including A1550,
we will not report it again in this work.

Assuming a NE-SW merger axis, the morphology and orientation of the NE
extension suggest that this might also be a candidate relic. It is symmetric
to the SW candidate relic with respect to the X-ray peak, and both relics lie
along the merger axis. It is possible that the extension was generated by the
re-acceleration of electrons caused by the counter-shock of the front that
produced the SW relic. However, the X-ray observation is too shallow and the
Chandra FoV too limited to detect any shock, in both directions. Furthermore,
the spectral index distribution looks rather uniform across the source, albeit
it steepens in the Easternmost part. In fact, the same spectral index
distribution seems more consistent with the halo, and even slightly steeper in
some regions. Low-resolution images at both LOFAR frequencies (see e.g. Fig.
3) show a patch of emission connecting the extension to the halo. The Chandra
observation also detects X-ray plasma in the same region which seems to
confine the radio emission. This supports the idea that the extension is part
of the central radio halo. If this were true, one would expect the point-to-
point analysis for the halo and the extension to have a similar brightness
distribution. This is apparently not the case (see Fig. 7 and Sec. 3.5), even
though the X-ray exposure time is too short to allow for good statistics. As
for the bridge, deeper X-ray observations could shed light on the nature of
the detected NE emission. Similar structures have also been detected in other
radio halos (Markevitch 2010; Bonafede et al. 2022; Hoang et al. 2019), and
are presumably due to advection of plasma by motions and shocks. In this case,
the compression of magnetic fields in such structure and the abrupt drop of
the brightness upstream of the edge may also affect the ptp correlation, which
could explain why we do not see the same trend observed for the halo.

###  4.2 The relic and the bridge

Figure 8: Left: High-resolution spectral index map of the candidate relic
between 54 and 144 MHz. The beam (15″$\times$10″) is shown on the bottom-left
as a white circle. Only pixels with flux density above 4$\sigma$ are shown.
Middle: Polarisation degree map for the relic in A1550. Right: Polarised
intensity map of A1550. Magnetic field vectors are overlaid in green, while
3$\sigma$ total power contours of the relic are shown in white. The vectors
are corrected for Faraday rotation effect.

The source that we have classified as a relic shows an elongated shape and
lies at $\sim$1 Mpc from the X-ray primary peak. However, due to the
relatively low resolution of the LOFAR spectral index map (left panel of Fig.
5) it is hard to assess whether there is a real spectral index gradient
towards the cluster center. We have produced a high-resolution
(15″$\times$10″) spectral index map between 54 and 144 MHz (shown in Fig. 8)
since these frequencies provide the best combination of resolution,
sensitivity and uv-coverage.

In the easternmost part, close to the bridge, the spectral index is as steep
as $\alpha\sim-2$. Then, moving towards the outskirts, we observe a flattening
from $\sim-1.5$ to $\sim-0.75$, reaching a lower limit of $\sim-0.2$ at the
edge. The flatter spectrum is aligned with the presumed orientation of the
merger, suggesting that the shock front has first accelerated electrons closer
to the cluster centre, and is now travelling in the NE-SW direction.
Unfortunately, we cannot independently confirm the presence of a shock at this
location via X-ray observations.

We have produced polarisation maps for the candidate relic, as described in
Sec. 2.4. As shown in Fig. 8 middle panel, a large portion of the relic shows
a degree of polarisation which varies from $\sim 10\%$ to $\sim 25\%$.
Interestingly, the highest polarisation is found in the South-Eastern region,
close to the bridge and source A. The magnetic field vectors are aligned with
the source orientation (see right panel of Fig. 8). The combination of
elongated shape, spectral index gradient, location and degree of polarisation
confirm the classification as a relic.

As already discussed in Sec. 3, we measure a total extent of $\sim$500 kpc at
LOFAR frequencies and $\sim$460 kpc at 1.4 GHz. It is well-known that the
radio power of relics correlates with the relic LLS (Bonafede et al. 2012), as
well as with the host cluster mass (de Gasperin et al. 2014). To investigate
whether the dynamic environment of A1550 has affected such relations, we can
compare the radio power, LLS and cluster mass with systems studied in Bonafede
et al. (2012), for the radio power-LLS correlation, and de Gasperin et al.
(2014) for the radio power-cluster mass correlation. We find that the
properties of the relic in A1550 are consistent with both relations.

We see that the relic is connected to the halo via a bridge. Similar cases of
connected diffuse emission were also detected in Markevitch et al. (2005),
Markevitch (2010), in the Toothbrush cluster (van Weeren et al. 2012;
Rajpurohit et al. 2018; de Gasperin et al. 2020), in A3667 (Carretti et al.
2013; de Gasperin et al. 2022) and others (e.g., Bonafede et al. 2018). In
most of these clusters the halo is directly connected to the relic, at least
seen in projection. One of the most spectacular examples of bridges is found
in the Coma cluster where turbulence is believed to produce the radio emission
in the bridge (Bonafede et al. 2021). In A1550 the nature of sources is
different from Coma, since the bridge is apparently not related to the radio
galaxy. If the merger proceeded along the NE-SW axis, as suggested by the
(projected) orientation of the relic and by the morphology of the X-ray
emission, then the bridge could consist of electrons that were pre-accelerated
by the shock (e.g., Fujita et al. 2016), and then re-accelerated by the
substantial merger-driven turbulence (e.g., Gaspari et al. 2014). However, the
source of seed electrons is unclear. Furthermore, an elliptical region void of
radio emission, labelled as ’depletion’ in Fig. 1 and with a major axis of
$\sim$ 400 kpc, is observed North of the radio galaxy. It is confined by the
halo in the East and the relic and the phoenix in the West. It is possible
that this region is related to a low-density region in the ICM since a
spherical depression is also observed in the Chandra image (see Fig. 6). It is
currently not clear if and how this depletion can be physically connected to
the bridge.

###  4.3 Source A and gentle re-acceleration

Figure 9: Left: Regions from which the spectral index between 54 and 144 MHz
was extracted, overlaid on the high-resolution HBA map. Each region is as
large as the smallest common circular beam (9.7″$\times$ 9.7″). The AGN, the
tip of the AGN tail and source A are labeled. Right: Results of the fit of the
spectral index. Top panel: flux density at 54 (blue) and 144 (orange) MHz for
each region, starting from the AGN position. Bottom panel: spectral index,
fitted with a JP aging model. The curve becomes dashed from the point where
the model was extrapolated, indicated by the grey vertical line.

In the HBA high-resolution map (see Fig. 2) we observe two faint
arms101010Also visible in Fig. 9. that depart from the bright tail of the
central AGN, connecting the centre of the diffuse emission to source A, and
that might be related to previous outbursts of the AGN. Although the tail of
the radio galaxy looks well-confined, the high-resolution image seems to
suggest that the electrons which constitute the arms are originally injected
from the head-tail. Corresponding to source A, the surface brightness
increases again, producing a roundish structure with no visible counterparts
in optical (SDSS) catalogs and spectral index $\alpha_{54\rm MHz}^{144\rm
MHz}=-1.9\pm 0.2$. When moving to 400 MHz, from the spectral index map in the
middle panel of Fig. 5 we find an upper limit for the index of $\alpha_{144\rm
MHz}^{400\rm MHz}\leq-2$. This hints at a curved spectrum, as also shown in
Fig. 4111111The flux density for source A at 1.4 GHz is an upper limit.. The
increase in terms of surface brightness compared to the region closer to the
AGN, combined with the spectrum break-off, suggests that source A could be AGN
plasma (e.g. phoenix) which was revived through re-acceleration. To trace the
behaviour of the electron energy spectrum from the tail to source A, we have
sampled the spectral index in regions as large as the smallest common beam
(9.7″$\times$ 9.7″) from high-resolution HBA, LBA and uGMRT images, which
allow us to resolve both the arms and source A, and to get a reasonable
statistics. This is done with the assumption that the arms are related to the
head-tail radio galaxy, even though it is possible that they might just
constitute some form of bridge/filaments, as observed East of the relic. We
fit the distribution by applying a non-linear least squares regression, with a
Jaffe-Perola (JP) electron aging model (Jaffe & Perola 1973), which is assumed
to be the same (i.e. same break frequency at same distance) at all
frequencies. According to that model, the ageing only depends on the magnetic
field and the projected velocity of the radio galaxy through the ICM. We have
assumed a minimum energy magnetic field of $B_{\rm
min}=\frac{3.25}{\sqrt{3}}\times 10^{-10}(1+z)^{2}$ T = 2.95 $\mu$G, similar
to Edler et al. (subm.). We fit the model directly to the spectral index, with
the only free parameter being the radio galaxy velocity, to remove any
dependence on the normalisation (see Edler et al. subm.). The sampling regions
were drawn from the high-resolution HBA image, and are shown in Fig. 9
together with the results of this analysis.

The spectral index between 54 and 144 MHz from the AGN to the tip of the tail,
at a distance of $\sim$350 kpc, is in the range $-0.58<\alpha_{54\rm
MHz}^{144\rm MHz}<-1.41$. From the AGN position to the tip, the index keeps
getting steeper as we are moving further from where electrons are injected.
From the tip to source A, the distribution reaches a plateau around
$\alpha_{54\rm MHz}^{144\rm MHz}\sim-1.9$, and then finally flattens at
$\alpha_{54\rm MHz}^{144\rm MHz}\sim-1.7$ in the region of source A. The fit
with a JP aging model is accurate ($\chi^{2}/DoF\sim 0.8$) along the tail.
However, when we move towards the arms and source A, it seems that the
spectral index remains fairly uniform and does not follow a pure aging model.
This hints at some kind of re-acceleration process which re-energized the
electrons in the region of source A. An alternative explanation is that the
flatter regions are produced by an increase in the magnetic field strength.
Nevertheless, this would require a precise fine-tuning of the magnetic field,
making this solution less likely.

A possibility is that old radio plasma from past AGN outbursts was compressed
by the same shock that produced the relic. The shock passing through fossil
plasma could have produced the steep, curved spectrum (see Enßlin & Gopal-
Krishna 2001 and Sec. 1 for more references). The curvature observed at 400
MHz for source A from Fig. 5 and the (likely) location of the shock front
support this hypothesis. The small size ($\sim$130 kpc radius) of this source
is also consistent with expectations from revived plasma (VW21), as well as
the apparently irregular distribution of the spectral index observed around
source A (Kale & Dwarakanath 2012).

Finally, the plateau shown by the spectral index distribution in the region of
the two arms might point to some kind of gentle re-acceleration, which is
barely able to compensate the radiative losses of the electrons. A similar
case has been studied in de Gasperin et al. (2017) in the galaxy cluster
A1033, where the spectral index distribution across a long ($\sim$500 kpc)
radio galaxy tail remains level with increasing distance from the injection
point (i.e. the AGN). The re-acceleration that we see in A1550 might be
similar, even though the plateau in A1033 is reached at much steeper spectral
indices ($\alpha\sim-4$), at least between 144 and 323 MHz. In A1033,
compression by shocks is unlikely to explain the plateau as this would require
precise geometrical tuning: the tail is so long that it would be hard for a
shock to re-accelerate all electrons at once. Furthermore, simulations have
shown that even mild (Mach number $\mathcal{M}<2$) shocks are able to disrupt
radio galaxy tails (e.g. O’Neill et al. 2019; Nolting et al. 2019). In A1550
the two arms are shorter than the tail in A1033, but it remains unlikely for a
shock to compress and re-accelerate all particles at the same time across 300
kpc in order to produce a uniform spectral index (Fig. 9). Therefore, it is
possible that the same gentle re-energisation which was invoked for A1033 can
explain the two arms of A1550.

##  5 Conclusions

We have studied a plethora of diffuse emission sources in the galaxy cluster
A1550 through multi-frequency radio observations, ranging from 54 MHz to 1.4
GHz. Our results can be summarised as follows:

  * •

We observe an ultra-steep spectrum radio halo with a mean spectral index
$\alpha\sim-1.6$, and an extent of $\sim$ 1.2 Mpc at 54 MHz. The halo
encompasses the head-tail radio galaxy at the centre of the cluster, and
extends towards the East. The detection of a USSRH favours primary models for
the origin of the relativistic electrons.

  * •

We found a relic West of the head-tail radio galaxy, with a projected extent
of $\sim$ 500 kpc. From the relic, a bridge departs towards East and connects
it to the halo, similarly to other clusters (see Sec. 4 for further details).
The X-ray emission morphology and the orientation of the diffuse emission, and
especially of the relic, point to a merger which occurred in the NE-SW
direction. Then, the bridge could consist of electrons that were pre-
accelerated by shocks, and then re-accelerated by the turbulence which also
produced the halo.

  * •

East of the halo, we detect an extension at low-frequencies that appears to
depart from the halo. Even though its shape and orientation resembles a relic,
the spectral index distribution indicates that it is an extension of the halo,
as also suggested by the physical connection observed between the two. The
point-to-point analysis performed on radio and (short exposure) X-ray images
does not provide conclusive results.

  * •

Between the radio galaxy and the relic, we observe a roundish source that we
classify as a radio phoenix. This is supported by the steep and curved
spectrum, which shows $\alpha\sim-1.9$ at LOFAR wavelengths, but steepens at
values $\alpha<-2.1$ moving to higher frequencies. These electrons may have
been re-accelerated through adiabatic compression by the same shock that has
produced the relic.

  * •

Two arms connect the tail of the radio galaxy to the phoenix. Our analysis
shows that the spectral index in the arms does not steepen with increasing
distance from the electron injection point. Instead, it reaches a plateau
around $\alpha\sim-2$, which is maintained for more than 300 kpc. This is
similar to the mild/gentle re-acceleration observed in GReET sources. It is
also possible that the same shock which produced the relic and the phoenix was
able to re-accelerate electrons along the arms, leading to the observed
plateau in the spectral index distribution. However, it remains difficult for
a shock that travels in the direction along the arms,to re-accelerate all
electrons across 300 kpc at once.

Determining the origin of the different sources in the cluster A1550 remains
complex. Deeper X-ray observations are needed to identify shocks in the ICM in
order to determine the orientation of the merger and study the turbulence that
produced the USSRH. A1550 is among the first of the LoLSS-HETDEX clusters
which we have studied in detail at very low frequencies. In the future, it
will be possible to perform a similar analysis on a much larger sample of
objects. The synergy with other radio telescopes, such as GMRT and VLA, and
complementary X-ray data will be key to shed more light on re-acceleration
processes in galaxy clusters.

## Acknowledgements

TP is supported by the DLR Verbundforschung under grant number 50OR1906. MB
acknowledges support from the Deutsche Forschungsgemeinschaft under Germany’s
Excellence Strategy - EXC 2121 ”Quantum Universe” - 390833306. AB acknowledges
support from the VIDI research programme with project number 639.042.729,
which is financed by the Netherlands Organisation for Scientific Research
(NWO). RJvW acknowledges support from the ERC Starting Grant ClusterWeb
804208. FG, GB and MR acknowledge support from INAF main- stream project
‘Galaxy Clusters Science with LOFAR’ 1.05.01.86.05. MG acknowledges partial
support by NASA Chandra GO9-20114X and HST GO-15890.020/023-A, and the
BlackHoleWeather program. GDG acknowledges support from the Alexander von
Humboldt Foundation. DNH and CJR acknowledges support from the ERC through the
grant ERC-Stg DRANOEL n. 714245. LOFAR (van Haarlem et al. 2013) 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 are collectively
operated by the ILT foundation under a joint scientific policy. The ILT
resources have benefitted 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; 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, and of the
LOFAR-IT computing infrastructure supported and operated by INAF, and by the
Physics Dept. of Turin University (under the agreement with Consorzio
Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing Centre,
Italy. 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].

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##  Appendix A Results of the Halo-FDCA pipeline

In Fig. 10 we show the output of the Halo-FDCA pipeline for the estimate of
the halo flux density at the different frequencies. We fit a circle model and
masked all the emission which we do not classify as being part of the halo. We
applied the same masks at all frequencies except for 1.4 GHz, where we had to
add more due to a trickier source subtraction (see Sec. 3).

Figure 10: From top to bottom, from left to right: 54, 144, 400 and 1400 MHz
modelling of the radio halo, halo centre as detected from a circle model, and
residual images with masks applied to exclude sources from the flux density
calculation.