# MOSS I: Double radio relics in the Saraswati supercluster

V. Parekh1,2, R. Kincaid1, K. Thorat3, B. Hugo1,2, S. Sankhyayan4,5, R. Kale4,
N. Oozeer6,2, O. Smirnov1,2, I. Heywood7,1,2, S. Makhathini8, K. van der
Heyden9
1Department of Physics and Electronics, Rhodes University, PO Box 94,
Makhanda, 6140, South Africa
2South African Radio Astronomy Observatory, 2 Fir Street, Black River Park,
Observatory, Cape Town, 7925, South Africa
3University of Pretoria, Lynnwood Rd, Hatfield, Pretoria, 0002, South Africa
4National Centre for Radio Astrophysics, Savitribai Phule Pune University
Campus, Ganeshkhind, Pune, Maharashtra 411007, India
5Tartu Observatory, University of Tartu, Observatooriumi 1, 61602 Tõravere,
Estonia
6African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg 7945,
South Africa
7Department of Physics, University of Oxford, Oxford OX1 2JD, UK
8School of Physics, University of the Witwatersrand, 1 Jan Smuts Avenue,
Johannesburg, 2000, Republic of South Africa
9Department of Astronomy, R W James Building, University of Cape Town,
Rondebosch, Cape Town, 7700, Republic of South Africa
E-mail<EMAIL_ADDRESS>
(Accepted 2021 October 14. Received 2021 October 13; in original form 2021
August 19)

###### Abstract

Superclusters are the largest objects in the Universe, and they provide a
unique opportunity to study how galaxy clusters are born at the junction of
the cosmic web as well as the distribution of magnetic fields and relativistic
particles beyond cluster volume. The field of radio astronomy is going through
an exciting and important era of the Square Kilometer Array (SKA). We now have
the most sensitive functional radio telescopes, such as the MeerKAT, which
offers high angular resolution and sensitivity towards diffuse and faint radio
sources. To study the radio environments around supercluster, we observed the
(core part of) Saraswati supercluster with the MeerKAT. From our MeerKAT
Observation of the Saraswati Supercluster (MOSS) project, the initial results
of the pilot observations of two massive galaxy clusters, A2631 and
ZwCl2341.1+0000, which are located around the dense central part of the
Saraswati supercluster, were discussed. In this paper, we describe the
observations and data analysis details, including direction-dependent
calibration. In particular, we focus on the ZwCl2341.1+0000 galaxy cluster,
which hosts double radio relics and puzzling diffuse radio source in the
filamentary network. We have imaged these double radio relics in our high
resolution and sensitive L-band MeerKAT observation and a puzzling radio
source, located between relics, in the low-resolution image. We also derived
the spectra of double radio relics using MeerKAT and archival GMRT
observations. A following papers will focus on the formation of radio relics
and halo, as well as radio galaxy properties in a supercluster core
environment.

###### keywords:

Radio galaxies; clusters of galaxies; intra-cluster medium

††pubyear: 2021††pagerange: MOSS I: Double radio relics in the Saraswati
supercluster–LABEL:lastpage

##  1 Introduction

Both high sensitivity observations and simulations show that the matter
content in the Universe is not randomly distributed but resides in a complex
structure called the ‘cosmic web’ (Jasche et al., 2015; Vazza et al., 2015,
2014; Lemson & Virgo Consortium, 2006; Springel et al., 2005; Bond et al.,
1996). Billions of stars, quasars, galaxies, and intergalactic gas make up the
pattern of thin walls or filaments inside the Large-Scale Structure (LSS).
These filaments are on the scales of a few tens to hundreds of Mpc and are
surrounded by large voids. Furthermore, dense and massive galaxy clusters are
born at the intersection of filaments. Hence, it is essential to study galaxy
clusters in the ‘cosmic web’ environment to understand how the Universe
evolved and how matter flows within filaments and interacts with galaxy
clusters.

To date, mapping of the ‘cosmic web’ was generally done using optical redshift
surveys; finding densities in galaxy distributions was the only available tool
to trace large scale filaments (Tempel et al., 2014). Thankfully, technical
enhancements in the observations of superclusters at other wavelengths such as
radio band, have enhanced our knowledge of the cosmic web, its origin,
evolution, physical condition, and properties (Vacca et al., 2018; Venturi et
al., 2017; Araya-Melo et al., 2012). Further, there are many other critical
questions that depend on the future high quality and sensitive multiwavelength
observations to directly measure baryon density and its distribution in the
cosmic web, as well as the total energy budget to drive the material inside
filaments, magnetic field strength and overall growth of the structure.

In the last two decades, galaxy clusters have been extensively studied in the
radio bands. Low-frequency radio observations (at 1 GHz and below) have
revealed the existence of Mpc size diffuse radio sources associated with the
cluster formation process (Feretti et al., 2012, and references therein).
These extended diffuse radio sources further split into two classes – radio
halos and relics (van Weeren et al., 2019, and references therein). These two
classes of sources are similar in their radio properties, aside from their
positions and morphologies. Giant radio halos are spherical and can generally
be found at the cluster centre or core, while radio relics are elongated in
one direction and located at the cluster peripheries. Formation mechanisms of
these radio sources are an open debate; however, observations hint that these
radio sources are generated due to the turbulence (radio halos) and shock
structures (radio relics) activated by the cluster merging process. Recently,
low-frequency observations have also revealed another class of diffuse radio
source, know as ‘radio-ridge’ found between two galaxy clusters in low dense
regions (Govoni et al., 2019; Botteon et al., 2019). The formation mechanism
of this new class of radio source is not yet fully understood (Brunetti &
Vazza, 2020).

In the present era, with the ability to conduct high sensitivity and angular
resolution radio observations with next-generation telescopes, such as the
MeerKAT (Camilo et al., 2018; Jonas, 2009), Australian Square Kilometer Array
Pathfinder (ASKAP; McConnell et al. (2016)), and LOw Frequency ARray (LOFAR;
van Haarlem et al. (2013)), the time has arrived to utilise these telescopes
to observe superclusters and filaments in order to detect shocks, particle
acceleration and magnetic fields beyond cluster volume (Brunetti & Vazza,
2020; Govoni et al., 2019; Botteon et al., 2019). We have observed the
Saraswati supercluster (Bagchi et al., 2017) with the MeerKAT telescope to
study the supercluster environment in radio frequency regime, characterise
cluster merger shock and/or accretion shock related to relics, and mapping of
diffuse radio sources with high dynamic range imaging.

With the advancement in radio interferometric observations, there is an
increase in demand to produce the most sensitive radio maps with the highest
dynamic range (Smirnov, 2011b). In order to do so, one has to deal with many
observational and data calibration errors, which place constraints on
achieving such sensitivity. These errors include antenna pointing inaccuracy,
time and frequency-dependent primary beam variation across fields, stability
of the ionosphere over which observation is conducted, unknown radio frequency
interference (RFI) sources, thermal noise and gain variation of receivers, to
name a few. These time and frequency varying errors can also be related to one
or more source-specific directions, known as direction-dependent errors.
Sometimes strong point sources in the primary beam can limit the sensitivity
required for observations. This problem is more severe when studying diffuse
radio sources in the vicinity of a strong radio source(s) which hampered the
observation by generating artefacts. Primary calibration processes (even self-
calibration) are not adequate enough to fully characterise the properties of
these strong radio sources, hence these poorly deconvolved sources challenge
us in the imaging of faint and diffuse radio sources. One common solution to
this issue is known as “source peeling” (Noordam, 2004). The general principle
here is to obtain source-specific calibration solutions towards the strong
source (which we need to be peeled) location or, in other words, apply
direction-dependent calibration towards the particular source direction and
solve the complex gain of that source and then subtracted it from the
visibility. A number of software packages implement variations on this
approach (e.g. Kenyon et al., 2018; Rioja et al., 2018; van Weeren et al.,
2016; Intema, 2014; Noordam & Smirnov, 2010; McMullin et al., 2007), with the
aim of producing the best scientific images.

###  1.1 Saraswati supercluster

The Saraswati supercluster was recently discovered in the famous Stripe 82
region (Hodge et al., 2011) of the Sloan Digital Sky Survey (SDSS; York et al.
2000), at redshift $z$ $\sim$ 0.3 (Bagchi et al., 2017). The total mass and
size of this supercluster are $\sim$ 2 $\times$ 1016 $M_{\odot}$ and $\sim$
200 Mpc, respectively, making it one of the largest observed structures in the
Universe. This massive supercluster hosts 43 galaxy clusters at a mean
redshift of $z$ $\sim$ 0.28 and has an average density contrast of
$\delta=1.62$. Furthermore, it is surrounded by a complex network of galaxy
filaments and large voids. There are a total of 24 voids of the size $\sim$
40-170 Mpc identified in the vicinity of the supercluster. The clean
spectroscopic redshifts are derived from the LEGACY (Abazajian et al., 2009),
BOSS (Dawson et al., 2013) and
SOUTHERN111https://www.sdss.org/dr12/algorithms/legacy_special_target/#southern
(LBS) programs of the SDSS-III DR12 database (Alam et al., 2015). A total of
3016 galaxies have been found within and around the Saraswati supercluster
region (Bagchi et al., 2017).

The Saraswati supercluster’s dense central (gravitationally bound) region
extends to a radius of 20 Mpc and encompasses a mass of at least 4 $\times$
1015 $M_{\odot}$ (20% of total supercluster mass) comprised of five massive
galaxy clusters, including Abell 2631. These five massive clusters form the
dense, bound core of the Saraswati supercluster. Abell 2631 is the most
massive cluster located in the core of the Saraswati supercluster, and it is
also extremely rich (richness class 3) and hot ($\sim$ 9.60 keV, Cavagnolo et
al. 2009). The complex merging galaxy cluster ZwCl 2341.1+0000, which is
situated at $\sim$ 45 Mpc from the core, is the second massive cluster and is
located in the trail of galaxies which makes up a southern filamentary network
that is connected to the main central region. In the NRAO VLA Sky Survey
(NVSS) data (Condon et al., 1998), it was found that ZwCl 2341.1+0000 hosts
double giant diffuse radio relics connected by faint ‘radio-bridge’. The
overall structure is indicative of the infall and merger dynamics of several
galaxy groups/clusters during the initial phase of the cluster formation
process (Bagchi et al., 2002). Later on, in the Giant Meterwave Radio
Telescope (GMRT) low-frequency observation of ZwCl 2341.1+000, double radio
relics were detected, but there was no radio bridge or halo found between
double relics (van Weeren et al. 2009, hereafter V09). However, there was
marginalised faint radio emission detected between these two relics, along the
filament network, in the Very Large Array (VLA) L-band observation (Giovannini
et al. 2010, hereafter G10). However, due to lack of sensitivity in the VLA
data, the nature of this faint emission could not be determined and could thus
not be studied further. The estimated virial radii of both clusters are $\sim$
1.93 Mpc and $\sim$ 1.62 Mpc, respectively, corresponding to the angular sizes
of 8′ and 6.5′.

In this paper, we present our MeerKAT and GMRT (archival data) analysis
results of the MOSS. Firstly, we focus on the direction-dependent calibration
technique for MeerKAT data for improving our images. We also show the point
source subtraction method used to analyse diffuse radio sources. Both these
techniques make use of new in-house software.

As this section has provided a clear introduction to the research, the rest of
the paper will be structured as follows: §2 gives details of the radio
observation of the Saraswati supercluster; §3 describes the radio data
reduction procedures; §4 presents our results; §5 gives the discussion and
conclusion. In this paper, we have assumed $H_{0}$ = 70 km s-1 Mpc-1,
$\Omega_{\mathrm{M}}$ = 0.3 and $\Omega_{\Lambda}$ = 0.7. At redshift $z$ of
0.27, 1′′ = 4.14 kpc, and luminosity distance $D_{\mathrm{L}}$ = 1376 Mpc.

##  2 Radio observations

###  2.1 MeerKAT L-band observation

MeerKAT is the precursor of the Square Kilometer Array (SKA) located in the
Karoo desert of South Africa (Camilo et al., 2018; Jonas, 2009). We observed
the central part of the Saraswati supercluster with the MeerKAT, which
includes two pointings centred on each of the A2631 and ZwCl2341.1+0000 galaxy
clusters. The separation between the two pointing is 1.5∘. MeerKAT
observational details are provided in Table 1.

Table 1: MeerKAT observations of the Saraswati supercluster. | Observation date: | 2019-06-15
---|---|---
| Observation time: | 00:41:27.8
| Number of pointings: | 2
| Phase centre of A2631 | 23h37m40.6s
|  | +0d16m36.0s
| Phase centre of ZwCl2341.1+0000 | 23h43m39.7s
|  | +0d19m51.0s
| Number of antennas: | 60
| Total observation time: | 14hrs
| Central frequency: | 1283 MHz
| Total bandwidth: | 900 MHz
| Channel width: | 208 kHz
| Total number of channels: | 4016
| Dump time: | 8s
| Cross products: | XX,XY,YX,YY
| Bandpass and flux calibrator: | J1939–6342
| Gain calibrator: | J2357–1125

###  2.2 GMRT 325 MHz observation

ZwCl 2341.1+0000 was observed with the legacy GMRT on 24 June 2011 and 20 July
2011 at 325 MHz. To the best of our knowledge, this archival data set was not
published before. The pointing of antennas were chosen at RA:
23h43m45.012482s, DEC: +00d18m00.08115s. The total observation time was 22
hours. This observation was performed using 256 channels, 30 MHz bandwidth and
four cross products. To fix the absolute amplitude scale and bandpass
calibration, 3C286 and 3C48 calibrators were observed, along with the
J2340+135 (RA: 23h40m33.232373s; DEC: +13d33m00.98106s) phase calibrator.

##  3 Data analysis

We reduced both the MeerKAT and GMRT data sets using the Containerized
Automated Radio Astronomy Calibration
(CARACal111https://caracal.readthedocs.io/en/latest/) pipeline (Józsa et al.,
2020). The use of this pipeline is also mentioned in our previous work Parekh
et al. (2020). Briefly, the CARACal pipeline is written using the
Stimela222https://github.com/ratt-ru/Stimela pipelining framework, which is
python-based and uses containers (Docker and Singularity) specially developed
for independent radio interferometry scripting, which allows users to use
general radio astronomy software. This permits the combination of the
appropriate radio astronomy software packages into a single pipeline. CARACal
is an open-source and flexible pipeline that comes with pre-defined input
settings for the reduction of data from MeerKAT and other telescopes like GMRT
and JVLA in a variety of configuration files, which can be modified by the
user as per their individual needs. We also made use of the Stimela package to
carry out tasks such as excising discrete radio point sources (from uv domain)
blended with extended emission and direction-dependent calibration. More
details of both these methods are given in §3.5 and §3.6.

###  3.1 MeerKAT data analysis

We used standard bandpass and gain calibration tasks of Common Astronomy
Software Application (CASA) for cross-calibration inside the CARACal pipeline,
with several rounds of automatic RFI flagging (before and after calibration).
We then used the AOFlagger (Offringa et al., 2012) software with a custom
strategy optimised for MeerKAT data to remove the RFI. We also applied the
mask of known RFI-affected channels to the data. In order to fix the absolute
scale of the flux calibrator, we used the local sky model of the calibrator
derived using the Reynolds scale (Reynolds, 1994). The absolute flux density
of the primary or flux calibrator J1939–6342 is $\sim$ 14.90 Jy at the rest
frequency of 1.4 GHz. After bootstrapping the flux density scale from the flux
calibrator, the flux density of the secondary calibrator J2357–1125 is 2.07
$\pm$ 0.01 at 1.28 GHz (at 1.4 GHz, its value is $\sim$ 1.8 Jy and after
scaling to 1.28 GHz with a spectral index value of -0.7, its expected value is
$\sim$ 1.9 Jy). Once the data were calibrated, we then split the two target
sources from the multi-source measurement set. To reduce the data size and
imaging time, we averaged every five channels in the target data. We then
imaged ZwCl 2341.1+0000 and A2631 fields separately in the self-calibration
rounds. In the pipeline, for direction-independent imaging and self-
calibration tasks, we used the WSClean (Offringa et al., 2014) and CubiCal
(Kenyon et al., 2018) software. We performed three phase-only self-calibration
rounds to improve the antenna-based phase solutions. In the deconvolution
procedure, we employed wide-band and multiscale cleaning options to better
image the diffuse emission. We performed joint deconvolution on five sub-bands
and generated a multi-frequency synthesis (MFS) cube (the bandwidth of each
sub-band image is 170 MHz and has 164 channels). In joint deconvolution, we
used the 2nd order polynomial (nterms = 2) in the spectral fitting. We made
images with different Briggs robust weighting values to generate high- and
low-resolution images. Further, we used these self-calibrated visibilities of
ZwCl 2341.1+0000 and A2631 fields for direction-dependent calibration.

###  3.2 GMRT data analysis

For the 325 MHz GMRT archival data reduction, we also used the CARACal
pipeline. We used the default settings to perform the initial flux and gain
calibrations. For RFI removal, we used the tfcrop and rflag options of CASA,
accessible inside the pipeline. For the flux calibrator, we used the Perley-
Butler 2010 (hereafter PB10) scale. This gave the flux density of the flux
calibrator 3C286 to be $\sim$ 24.83 Jy. The phase calibrator for this
observation was 2340+135 (RA:23h40m33.22s, Dec:+13d33m00.92s). Similar to the
MeerKAT data, we performed the joint deconvolution on five sub-bands (each
sub-band of 6 MHz bandwidth with 51 channels) with multiscale cleaning and
generated an MFS image using the 2nd order polynomial fitting. We performed
three rounds of phase and two rounds of amplitude and phase self-calibration.
The goal of the present data analysis is to test the CARACal pipeline for the
GMRT antennas and tune the pipeline for uGMRT wide-band data analysis for
future use.

###  3.3 MeerKAT and GMRT flux calibration accuracy

In order to obtain the calibration accuracy, we compared the flux densities of
unresolved and discrete point radio sources between MeerKAT and NVSS
observations of the ZwCl2341.1+0000 and A2631 fields. In both images, we
manually selected isolated bright point sources (of flux density $>$ 1 mJy) to
avoid any source blending or overlapping. We made a list of these point
sources and used the CASA’s imfit task to fit the Gaussian and measure the
flux densities from both MeerKAT and NVSS images. In this analysis, we used
the MeerKAT primary beam (Asad et al., 2021) corrected images. We scaled the
1283 MHz MeerKAT flux density values to 1400 MHz with a spectral index value
of -0.7. We have shown our flux densities comparison result in Figure 1. We
found that the overall (mean) flux density accuracy between MeerKAT and NVSS
is $\sim$ 10% and median flux density accuracy $\sim$ 8%.. For GMRT
observations, this error is also estimated to be 10% (Chandra et al., 2004).

Figure 1: Total flux density comparison between MeerKAT and NVSS for
ZwCl2341.1+0000 and A2631 fields. The solid black line shows the best-fit
relationship between two observations and dashed red line shows the one-to-one
relationship. Each side histogram shows the flux density distribution for
MeerKAT and NVSS, with the blue line indicating the median value.

###  3.4 Flux density error estimation and calibration scales

In the procedure of uncertainty estimation on the total flux densities, two
main factors should be evaluated. The first factor is the data calibration
accuracy. From our estimation (§3.3), this calibration error was measured to
be $\sim$ 10$\%$. The second factor is the noise present in the data. For
extended radio sources, this error is characterised by the rms in the image
multiplied with the square root of the ratio of the solid angle (of the
extended source) to that of the synthesised beam, which is the number of beams
across the extended source. In addition to this, we also included uncertainty
due to point source subtraction from uv data (van Weeren et al., 2019). These
three uncertainties factors are unrelated; therefore they are added in
quadrature to estimate the absolute error on the flux densities of the
extended sources, as shown below:

$\Delta{S}=[(\sigma_{\mathrm{amp}}S)^{2}+(\sigma_{\mathrm{rms}}\sqrt{n_{\mathrm{beams,ext}}})^{2})+\sigma_{sub}^{2}]^{1/2},$
(1)

where $S$ is the flux density, $\sigma_{\mathrm{amp}}$ is the flux calibration
uncertainty (10%), $\sigma_{\mathrm{rms}}$ is the image rms noise, and
$n_{\mathrm{beams,ext}}$ is the number of beams in the full extent of the
extended source, $\sigma_{sub}^{2}$ =
$\sum_{i}(\sigma_{\mathrm{rms}}\sqrt{n_{\mathrm{beams,pt}}})^{2}$, where
$n_{\mathrm{beams,pt}}$ is the number of beams in the subtracted point
sources.

The GMRT (325 MHz) and MeerKAT flux densities are on the PB10 and Reynolds
(1994) scales, respectively. The agreement between these two scales is within
2% (private communication with MeerKAT commissioning team). For spectral index
measurements (§6), we took measured flux densities at 241 and 610 MHz from the
V09. The authors used the Baars et al. (1977) standard; hence we scaled the
325 MHz flux densities by the ratio between the Baars et al. (1977) to PB10
standards.

###  3.5 Direction-dependent calibration

Radio interferometric wide-band and wide-field of view observations are often
dynamic range limited. A number of instrumental and observational errors
affect the quality of such radio observations. These errors typically manifest
themselves as artefacts associated with bright and strong sources in the
observed field, particularly off-axis sources. These artefacts can extend
throughout the map (being, in a sense, modulated by the extensive sidelobes of
the radio interferometer point spread function (PSF)) and therefore hamper the
detection of faint and diffuse emission and imaging of extended radio
source(s) elsewhere in the map (including at the centre). There are several
techniques available to minimise this problem by employing some form of
direction-dependent calibration (e.g. Williams et al., 2019; Kazemi et al.,
2011; Smirnov, 2011a; Intema et al., 2009). One of the first such methods
proposed was “source peeling” which deals with strong sources by solving for
the gain towards them one by one, followed by the source subtraction from the
visibility (uv) data. A generalization of this is the “differential gains”
technique (Smirnov, 2011a, b), which can be seen as a form of simultaneous
peeling, calibrating and correcting towards multiple bright sources
simultaneously. In this work, we employed the CubiCal software (Kenyon et al.,
2018) in conjunction with the DDFacet imaging software (Tasse et al., 2018) to
peel bright and strong sources. CubiCal solves the following Radio
Interferometer Measurement Equation (RIME)

$D_{p,q}=G_{p}(\sum_{i=1}^{n}dE^{(i)}_{p}P^{(i)}_{p}S_{p,q}^{(i)}P_{q}^{{}^{(i)}H}dE_{q}^{{}^{(i)}H}+S_{p,q}^{\mathrm{(di)}})G_{q}^{H}$
(2)

where $G$ terms are the direction-independent errors affecting the entire
field of view. In our case, we constrain these to phase-only solutions (the
equivalent of traditional phase selfcal). The $dE$ terms represent direction-
dependent effects associated with $i=1...n$ bright sources. These use full
complex 2x2 Jones matrix solutions (Smirnov & Tasse, 2015). The $P$ terms
implemented antenna-specific primary beam models (time and frequency varying).
The $S^{(i)}$ terms denote _intrinsic_ (and direction-dependent) sky models
for the individual sources being peeled, while $S^{\mathrm{(di)}}$ represents
the “direction-independent” model for the rest of the emission in the field,
derived from clean model components.

The sky model is generated using the DDFacet imaging software, and source-
specific models (direction-dependent) are predicted using on-the-fly targeted
faceting from subsets of the sky model. CubiCal can solve for both of these
($G$ and $dE$) errors simultaneously, while taking into account most of the
sky flux. This limits the flux suppression of underlying radio sources
(compact and extended sources).

Firstly, self-calibrated visibilities (i.e. with a $G$ solution only) are used
to generate an initial sky model with DDFacet. We then designate regions
(using the SAOImage ds9 viewer) corresponding to the individual bright sources
that require peeling. CubiCal then uses these regions to split the sky model
predict into $S^{(i)}$ and $S^{\mathrm{(di)}}$ components, and performs
simultaneous $G$ and $dE$ solutions as per the RIME above. The bright sources
(using their best-fitting $dE$ solutions) are subtracted from the
visibilities, the residuals are corrected for $G$, and then re-imaged again
using DDFacet. This procedure results in images with the bright sources (and
associated artefacts) mostly removed, with improved image quality.

###  3.6 Point source subtraction

In radio interferometry observations generally, unresolved and discrete point
sources are blended with extended diffuse radio emission. Sometimes, the
brightness of diffuse emission is obscured due to the presence of very bright
point sources, and hence it is not easy to image the extended sources. In
order to estimate the flux densities of extended sources, we need to subtract
these point sources blended with the diffuse emission. Removing point sources
is also an important task for generating a high-resolution spectral index map.
There are various techniques available for excising point sources. A standard
method is to use the box cleaning option in various clean algorithms. These
boxes can be used for (affecting) strong point sources while cleaning and
generating the model, which will later be subtracted from calibrated data. The
other widely used method is to image the data with uniform weighting (and
exclude the inner interferometry baselines that correspond to the angular size
of the extended source that needs to be image) to generate the high-resolution
map. This high-resolution data should contain only point sources and resolve
out any extended emission. This will create models (of only point sources)
which can then be subtracted from the calibrated data before re-imaging the
residual visibility at lower resolution. Both methods, however, depend on the
different angular scales of the underlying radio sources and are performed
iteratively. They are, therefore, time-consuming when the data volume is
large. Hence, it is necessary to develop a method that can subtract the point
sources efficiently in a standard imaging procedure without more iterations.
To do this, we used the Crystalball
software333https://github.com/paoloserra/crystalball which can be employed in
a Stimela script (or pipeline) to perform the point source subtraction. In
this procedure, a user has to first make a region file that lists the
coordinates of point sources which they want to remove. This region file can
be manually generated via the SAOImage ds9 viewer. The user then runs WSClean
with the -save-source-list option (in the final self-calibration imaging).
This will generate a clean components
file444https://sourceforge.net/p/wsclean/wiki/ComponentList/. Crystalball
takes these two files, point source regions and clean component list, and
generates another column in a given Measurement Set. This can be subtracted
from the visibility and the residuals re-imaged. In our case, we made a source
list from a high-resolution map of the ZwCl2341.1+0000 (uniform weighting and
excluding inner MeerKAT baselines of 1 km resulting in 5′′ beam size). In this
high-resolution map, there are 1800 point sources that have been detected in
the PyBDSF (Mohan & Rafferty, 2015) generated catalogue. We selected only
compact sources i) detected in the high-resolution image (uniform weighting),
ii) blended in double radio relics and nearby strong sources (Figure A.1) and
iii) situated in between relics region. This technique of point source
subtraction from visibilities is very efficient in the removal of many point
sources simultaneously. The advantage of this method is that the Crystalball
software does a direct Fourier transform (DFT) on the clean component list
generated by the WSClean. This is more accurate than using model images
because it can predict a smooth spectral polynomial at native channel
resolution. The other advantage of this method is that all the required
software are part of the Stimela container; hence one can implement all
mentioned tasks in a pipeline.

##  4 Results

We have shown our MeerKAT results from Figure 2 to Figure 4 as well as from
Figure A.1 to Figure A.6. In this section, our main focus is to study the
diffuse and extended radio sources after direction-dependent calibration.
There are double radio relics that have already been discovered in the ZwCl
2341.1+0000 (Bagchi et al., 2002). We show the MeerKAT and GMRT direction-
independent images of double radio relics in Figure 2. To compare and match
the resolutions, we tapered the MeerKAT image (robust = 0) with 10′′ to match
the beam size of the GMRT image. As previously shown in the GMRT and VLA
observations (G10,V09), there are two double radio relics; one in the north-
west and another in the south-east directions clearly visible in the MeerKAT
L-band and 325 MHz GMRT data. Similar to the previous observations, these two
relics are situated perpendicular to the merger axis (north-south).
Furthermore, they are located outside the hot and dense X-ray intra-cluster
medium (ICM) region at the periphery of the merger. Both relics have a regular
symmetric structure, slightly deviating from the usual elongated arc-like
structure attributed to relics. We also noticed that the southern relic is
larger (496 $\times$ 1241 kpc2) in size and more elongated compared to the
northern relic (270 $\times$ 426 kpc2). The size of the southern relic is
similar to the 610 MHz observation as measured by V09, but the linear size of
the northern relic in the MeerKAT observation is larger than the 610 MHz
measurements.

In the MeerKAT data, there is a strong and unresolved point source
(RA:23:43:16.569, Dec:+0:26:20.392) located at a distance of $\sim$ 7′ ($\sim$
1.7 Mpc) from the north relic (NR), $\sim$ 15′ ($\sim$ 3.7 Mpc) from the south
relic (SR) and $\sim$ 9′ from the phase-centre (pointing centre) of the ZwCl
2341.1+0000 field, marked in the green box region in Figure 3 (left). The
total flux density of this radio source is $\sim$ 87 mJy, and it causes
artefacts and hence poor image quality around the central part of the cluster
where two relics are situated. In Figure 3 (left) shows the CARACal image
(final self-calibrated) generated with WSClean. As seen in this Figure,
clearly the artefacts are affecting both north and south radio relics. Then in
addition to this strong source, we also chose four different strong point
sources or directions to apply the direction-dependent calibration. We used
DDFacet to generate the facet based initial sky model required to calibrate
the data in different directions. Figure 3 (middle) shows the DDFacet
generated image which is still uncalibrated for distinct directions. Finally,
Figure 3 (right) shows the direction-dependent calibrated image. We have seen
clear improvement around the relic region before and after the direction-
dependent calibration. We found a 25$\%$ rms noise decrease in the region
between two relics after the direction-dependent calibration. All these maps
are made at robust = 0 value. This results in a FWHM of 8′′ $\times$ 6′′.
Figure A.2 shows the full field of the ZwCl 2341.1+0000 before (left image)
and after (right image) the direction-dependent calibration. In Figure A.4, we
have shown four different point sources towards calibration applied and peeled
the sources in order to improve the image quality. Similar to this, we also
applied direction-dependent calibration to the A2631 field and results are
shown in Figure A.5 and Figure A.6. In both of these fields, for every peeled
source, we estimated local rms, minimum clean component value and sum of the
total negative components around 8′ region. We have given these values in
Table A.1.

In the ZwCl2341.1+0000 radio map, we noticed discrete and blended point
sources as shown in Figure A.1. Some of them are also reported in V09 which we
labelled in Figure A.1(left). Figure A.1(right) shows the image of only
discrete point sources, generated using the Crystalball (as mentioned in
§3.6). We subtracted these point sources from the MeerKAT (direction-dependent
calibrated) and GMRT visibilities using our point source subtraction
technique. We listed the properties of subtracted point sources in Table A.2.
We have shown results in Figure 4(a) and (b) for MeerKAT and GMRT,
respectively. We calculated flux densities of both radio relics and reported
these values in Table 2. We also compared flux densities of compact radio
sources before and after direction-dependent calibration and showed the result
in Figure A.7. We found an agreement within 2$\%$; if we include only bright
point sources (of $>$ 1 mJy), then the agreement is within 0.5%.

In our forthcoming papers, we will give (1) a detailed analysis of these
relics and the MeerKAT sub-band spectral index map (Kincaid et al. in prep.)
and (2) radio source identifications and catalogue, spectral indices, and
overall radio galaxy populations and their properties (for clusters - ZwCl
2341.1+0000 and A2631) in the core region of the Saraswati Supercluster
(Parekh et al. in prep.)

((a))

((b))

Figure 2: (a) ZwCl 2341+0000 Chandra smoothed X-ray color image. The green
contours show the MeerKAT observation. (b) GMRT 325 MHz radio contours on
MeerKAT radio color image. In both images, the contour levels are
[1,2,4,8,16,32,64,128] $\times$ 3$\sigma$. Negative contours are shown by the
magenta color. For the MeerKAT radio image, the beam size is 12′′ $\times$
10′′ and 1$\sigma$ = 20 $\mu$Jy beam-1. In the GMRT radio image, the beam size
is 11′′ $\times$ 7′′ and 1$\sigma$ = 30 $\mu$Jy beam-1. Figure 3: Results of
direction-dependant calibration. The left image (only shown central part of
ZwCl 2341.1+0000) is the self-calibrated direction-independent image generated
from the CARACal. The middle image is the self-calibrated image generated
using the DDFacet. The right image is the direction-dependent image (after
calibrating towards five directions using the CubiCal). In the left image, we
marked the bright and strong radio source in the green box, which affects the
region of relics. All images have the same resolution of 8′′ $\times$ 6′′ and
colour scale. We calculated the local rms, minimum pixel and sum of total
negative component values inside the 8′ box size around the marked strong
source before and after direction-dependent calibration. These values are
listed in Table A.1.

((a))

((b))

Figure 4: Discrete point sources around radio relics have been subtracted for (a) MeerKAT (direction-dependent image) and (b) GMRT (direction-independent image). For the MeerKAT radio image, the beam size is 8′′ $\times$ 6′′ and in the GMRT radio image, the beam size is 11′′ $\times$ 7′′. Table 2: Flux density measurements of diffuse radio sources. Frequency (MHz) | 343 | 1283
---|---|---
Synthesized beam (′′ $\times$ ′′,∘) | 11 $\times$ 8, 79 | 8 $\times$ 6, -3
rms ($\mu$Jy beam-1) | 30 | 14
North relic (mJy) | 18.0 $\pm$ 1.85 | 5.0 $\pm$ 0.51
South relic (mJy) | 64.0 $\pm$ 6.41 | 17.0 $\pm$ 1.72
Synthesized beam (′′ $\times$ ′′,∘) |  | 50 $\times$ 50, 0
rms ($\mu$Jy beam-1) |  | 77
Halo (mJy) | - | 3.3 $\pm$ 0.50

##  5 Is there diffuse halo present in ZwCl2341.1+0000?

In the high-resolution (robust = 0) MeerKAT observation of ZwCl2341.1+0000, we
could not detect any large radio emission between two radio relics. We applied
uv-tapering to the MeerKAT data to match the resolution with the NVSS where
Bagchi et al. (2002) have been known to show the possibility of an extended
radio bridge between relics. We generated images with different tapering using
the direction-dependent calibrated- and point source subtracted data. At 50′′
resolution, as shown in Figure 5, we detected a radio source between double
radio relics. This suggests that the specific radio emission is resolved out
in the high-resolution images. Based on its position, it could be a candidate
radio halo, however, the nature of this radio source is not clear. The radio
emission visible in the MeerKAT data is irregular and complex. This radio
emission is patchy and faint (surface brightness of $\sim$ 0.13 mJy beam-1)
and extended around the central region of ZwCl2341.1+0000, connected with both
radio relics. The detection level of this diffuse emission is only 2$\sigma$
in the present data. The rms of the image is 77 $\mu$Jy beam-1 which is a
factor of two better than previous detections in the VLA (L-band,
D-configuration) as reported in G10, and five times better than the NVSS.
Their beam sizes, however, were $\sim$ 80′′ and 45′′, respectively. We have
not detected a halo emission in the 80′′ beam size of the MeerKAT data (of
which rms $\sim$ 0.2 mJy beam-1). We found the size of the possible candidate
halo (at 2$\sigma$ level) is $\sim$ 221′′ $\times$ 286′′ (914 $\times$ 1183
kpc2) which is comparable to typical radio halo sizes. The flux density within
2$\sigma$ level is reported in Table 2. It is difficult to study its
morphology and other radio properties in the current data. More data is needed
to confirm this detection.

Figure 5: MeerKAT image of ZwCl 2341.1+0000 with 50′′ beam size and rms
sensitivity $1\sigma=77\mu$Jy beam-1 (after direction-dependent calibration).
The Contour levels are $[1,3,5,7,9,11]\times 2\sigma$. The first contour is
drawn at 2$\sigma$.

##  6 Spectral index plot of relics and P1.4 GHz values

We have shown a spectral index plot of both radio relics in Figure 6. We
derived the spectra between 241 to 1283 MHz. We took 241 and 610 MHz
measurements from V09 and 323 and 1283 MHz from this work. For the SR, we
combined flux densities of regions RS-1, RS-2, and RS-3 as labelled by V09. We
matched the different calibration scales (§3.4) in order to estimate flux
densities. The minimum separation between antenna pairs of MeerKAT is 29 m,
hence MeerKAT is insensitive to image a structure larger than $\sim$ 27′ at
1283 MHz. Similarly, GMRT is sensitive only up to $\sim$ 32′and 17′ at 325 and
610 MHz bands, respectively. This should be considered while comparing flux
densities of extended sources using different arrays. In our case, the sizes
of both relics are less than these largest detectable structures of different
data sets. We found a straight power-law fit for the SR of spectral index
value $\alpha_{\mathrm{south}}$ = -1.01 $\pm$ 0.08. For the NR, we found a
break at 610 MHz, and the single power-law model (red solid line in Figure 6,
of $\alpha$ = -0.98 $\pm$ 0.10) does not fit the data. We found a flat
spectrum between 241 to 610 MHz, which became steep thereafter. We measured
two slopes, $\alpha_{\mathrm{1,north}}$ = -0.51 $\pm$ 0.10 and
$\alpha_{\mathrm{2,north}}$ = -1.38. The value of $\alpha_{\mathrm{1,north}}$
is similar to the value given by V09 ($\alpha_{\mathrm{north}}$ = -0.49 $\pm$
0.18).

For double radio relics and the candidate halo, we estimated its K-corrected
(rest-frame) radio power ($P_{1.4\mathrm{GHz}}$) using the following:

$P_{1.4\mathrm{GHz}}=\frac{4\pi D_{\mathrm{L}}^{2}S_{v}}{(1+z)^{1+\alpha}},$
(3)

where $D_{\mathrm{L}}$ is the source luminosity distance at $z$ = 0.27, and
$S_{v}$ is the source flux density. For the north radio relic, $\alpha$ $\sim$
-1.3 (between 610 and 1283 MHz) gives radio power at 1.4 GHz to be
$P_{1.4\mathrm{GHz}}$ = (1.08 $\pm$ 0.11) $\times$ 1024 W Hz-1. For the south
radio relic, $\alpha$ $\sim$ -1.0 gives radio power to be
$P_{1.4\mathrm{GHz}}$ = (3.53 $\pm$ 0.35) $\times$ 1024 W Hz-1. For radio
halo, $P_{1.4\mathrm{GHz}}$ = (7.17 $\pm$ 1.08) $\times$ 1023 W Hz-1. We used
$\alpha$ = -1.3 to scale the halo flux density to 1.4 GHz.

Figure 6: 1D spectral index plot for north relic (NR) and south relic (SR).
The red solid line shows the best-fit line between 241 and 1283 MHz for the
NR.

##  7 Discussion and conclusion

Using the MeerKAT telescope, we observed the centrally surrounded two massive
galaxy clusters, A2631 and ZwCl 2341.1+0000, of the Saraswati supercluster. In
this work, we aimed to test the direction-dependent calibrations on wide-field
of view and broadband MeerKAT data and show the improvement in diffuse radio
source imaging. Furthermore, we also studied particular of the ZwCl2341.1+0000
merging galaxy cluster. The cluster is elongated and displays the disturbances
in X-ray emission. For more details about the dynamics and merging geometry of
the cluster, we refer to Ogrean et al. (2014). Previously, in low frequency
and high-resolution GMRT data, two radio relics have been detected (V09). NVSS
and low-resolution VLA data also suggested the presence of relics and extended
diffuse radio source in the cosmic web environments in overlap with a chain of
galaxies.

###  7.1 Direction-dependent effects

The peeling techniques we have employed to improve the image qualities of our
MeerKAT data are discussed in §3.5. In our direction-dependent analysis, we
found that within 35′ from the phase centre, strong, poorly deconvolved
sources can be peeled quite well, with considerable attenuation of the
associated artefacts.

Figure A.4 shows the peeled sources, ordered in increasing distance from
centre. Our first peeled source (shown in Figure 3) is 8′ off-axis, and was
dramatically improved by the direction-dependent calibration. The other four
sources (Figure A.4(a), (b), (c) and (d)) are at distances of 12′, 26′, 31′
and 38′, respectively. As one can see, sources within $<$ 35′ can be improved.
For the other field of A2631, the three selected strong sources (Figure
A.6(a), (b) and (c)) are at distances of 23′, 30′ and 51′, respectively, from
the phase-centre. As one can see, the level of artefacts around the first two
sources are improved after the direction-dependent calibrations, whilst
residual artefacts are still visible (albeit at a low level) for the third
source. As a quantitative measure, we calculate the local rms, minimum pixel
and sum of total negative pixel values in an $8^{\prime}\times 8^{\prime}$ box
centred on each peeled source (Table A.1). The rationale for looking at
negative pixels is that imaging artefacts due to calibration errors manifest
themselves in a positive-negative pattern (fundamentally, because PSF
sidelobes are positive-negative), while physical emission is all positive. The
distribution of the negative pixels is therefore indicative of the artefact
level. As we can see in Table A.1 (sources are given in order of increasing
distance from centre), there are clear decrements in the (absolute) sum of
negative values after direction-dependent calibration. Local rms is also
improved after the direction-dependent calibration, and (absolute) minimum
pixel values are also reduced after the direction-dependent calibration,
although this does not seem to be a significant indicator.

The success of the peeling process will also depend on source location in the
given image as well as source structure. Since MeerKAT provides wide-bandwidth
observations, it is important to account for the variation of the primary beam
across the broad frequency range. The size of the primary beam and its half-
power points vary radially with the frequencies within the MeerKAT band.
Furthermore, if antenna beam patterns are not modelled well across the wide
bandwidth, then accuracy in the estimate of the flux densities of off-axis
sources (away from the phase-centre) decrease (Iheanetu et al., 2019). Hence,
the calibration process computes incorrect gains for these sources. This makes
it difficult to improve residual artefacts around strong sources situated at
the edges of image. With the advancement in MeerKAT future beam modeling, we
can hope to further alleviate the artefacts associated with such edge sources.

###  7.2 Diffuse radio sources in ZwCl2341.1+0000

The candidate radio halo (or bridge) in ZwCl2341.1+0000 was first detected in
the NVSS survey which provides a beam size of $\sim$ 45′′ and was not detected
in high-resolution GMRT observation, even at low frequencies. In low-
resolution VLA L-band observation of ZwCl2341.1+0000 (G10), it was not
possible to separate three diffuse components of the north and south radio
relics and candidate radio halo lying between them. Our MeerKAT L-band
observation provides the highest resolution and sensitivity compared to the
previous 1.4 GHz observations. We could not detect the candidate radio halo in
a high-resolution (8′′ $\times$ 6′′) MeerKAT image. However, we do see a
tentative detection of it at a 2 sigma significance level after tapering the
MeerKAT image to a 50′′ beam size. The candidate halo emission is resolved out
in high-resolution data and could be detected with compact array
configurations only where extended radio emissions have higher surface
brightness. The radio halo emission in the MeerKAT observation is very
irregular and patchy. The rms statistics and detection level are better in the
direction-dependent tapered image than the direction-independent image. The
tapering of the uv data increases the rms noise; hence we could not taper to
larger beam sizes to improve the surface brightness of the halo emission.
Based on the cluster X-ray mass and halo size scaling relationship (Cassano et
al., 2013; Cassano et al., 2007), the expected linear size of the halo is
$\sim$ 756 kpc, however, the largest linear size of the halo that we could
measure was $\sim$ 1183 kpc. This is comparable to the size estimated by G10.
The flux density measurement of the halo in MeerKAT observation is $\sim$ 3
times lower than that reported by G10. This could be due to the difference in
beam sizes and array configurations of MeerKAT and VLA. The expected power of
the radio halo based on the scaling relation (Cassano et al., 2013) is $\sim$
8.5 $\times$ 1023 W Hz-1, which is close to our measurement (7.17 $\pm$ 1.08)
$\times$ 1023 W Hz-1, in MeerKAT data. It has been shown that the radio power
of giant radio halos is correlated with the X-ray masses of their host
clusters (Yuan et al., 2015; Liang et al., 2000). Based on this, the radio
power of the candidate halo of ZwCl 2341.1+0000 is consistent with the
$P_{1.4GHz}$ vs Mass relation of giant halo clusters. However, the nature of
this candidate radio halo emission is still unclear and it could also be
related to the cosmic web network of the Saraswati supercluster. Its formation
mechanism could also be related to the LSS formation instead of cluster
merger. More data is required to characterise the properties of this puzzling
candidate radio halo.

G10 have reported the total flux density of all three components as $\sim$
28.5 mJy. In our observation, we found total flux densities of the double
radio relics and halo are = 25.3 $\pm$ 1.86 mJy, which is comparable. G10
measured the total linear size of all three diffuse components as $\sim$ 2.2
Mpc, while we estimated the total linear size as $\sim$ 2.4 Mpc. We also
noticed that the NR (in MeerKAT observation) has a larger linear size than
compared to the 610 MHz data (V09), but we also note that these observations
have different sensitivities and background rms values. This could suggest
that our sensitive MeerKAT observations have detected more diffuse emissions
in the northern radio relic (towards the north direction) than previous
observations. Based on radio relics cluster $P_{1.4GHz}$ vs Mass relationship
(Kale et al., 2017), the radio power of both NR and SR are consistent with
this relation. Furthermore, G10 reported the spectral index value between 610
and 1400 MHz for north and south relics as $\sim$ -1.2. We fitted a straight
line with spectral index, $\alpha_{1283\mathrm{}}^{610\mathrm{}}$ $\sim$ -1.2
for the SR, which is comparable with G10. The spectral index value for SR,
$\alpha_{1283\mathrm{}}^{241\mathrm{}}$ = -1.01 $\pm$ 0.08. Based on radio
relic spectral indices compilation (Wittor et al., 2021), we found an average
spectral index value of known radio relics is $\sim$ -1.2. The spectral index
value of the SR is comparable to this average value. The NR is faint compared
to the SR, and its spectrum appears complex (Figure 6). There is a spectral
break at 610 MHz with a steeper spectrum
($\alpha_{1400\mathrm{}}^{610\mathrm{}}$ $\sim$ -1.38) towards the high
frequency and a flattening towards lower frequencies
($\alpha_{610\mathrm{}}^{241\mathrm{}}$ = -0.51 $\pm$ 0.10). This spectral
break, if confirmed with further sensitive low frequency data, then is very
unusual and inconsistent with the diffusive shock acceleration (DSA) mechanism
(Drury, 1983), which advocates the single power-law distributions for relic
spectra. In the last decade, several radio relics have been observed over $>$
1 GHz frequency bands (Trasatti et al., 2015; Stroe et al., 2014; Owen et al.,
2014; Stroe et al., 2013). It was found that the A2256 also shows uncommon
spectral break at $>$ 1.4 GHz (Trasatti et al., 2015). This indicates the
halting of injection of electrons in the relic system, which eventually leads
to cutoff at high frequencies of the integrated spectrum. The alternative
explanation could be for this spectral break is clusters merging process is
happening recently (young merger) where relics have just formed, and the
electrons have not yet had time to lose their energy to steepen the spectrum.
We will study this spectral break in more detail in our forthcoming paper
(Kincaid et al. in prep.). We emphasize that all different instruments
(MeerKAT, VLA and GMRT) have different uv coverage, antenna configurations,
observation conditions and sensitivities; hence our spectral indices
comparisons with other observations are affected by these constraints.

In this work, we have shown the direction-dependent calibration technique for
galaxy cluster fields. It both improves the image quality and allow us to
estimate the flux densities of diffuse radio sources after eliminating
artefacts caused by strong sources. This method is important in the wide-
bandwidth and wide-field of view observations of superclusters or galaxy
clusters in order to detect faint and diffuse radio emissions in the presence
of strong radio source(s). This technique can be implemented in a pipeline and
can be applied to other data. In our next paper, we will study the merger
shock properties in the supercluster environment and broadband spectral index
studies of diffuse radio sources.

Acknowledgements. The financial assistance of the South African Radio
Astronomy Observatory (SARAO) towards this research is hereby acknowledged.
The MeerKAT telescope is operated by the South African Radio Astronomy
Observatory, which is a facility of the National Research Foundation, an
agency of the Department of Science and Innovation. This work is based upon
research supported by the South African Research Chairs Initiative of the
Department of Science and Technology and National Research Foundation. V.
Parekh acknowledge Hiroki Akamatsu, Bill Cotton and Annalisa Bonafede for
fruitful discussion. (Part of) the data published here have been reduced using
the CARACal pipeline, partially supported by ERC Starting grant number 679629
“FORNAX”, MAECI Grant Number ZA18GR02, DST-NRF Grant Number 113121 as part of
the ISARP Joint Research Scheme, and BMBF project 05A17PC2 for MeerKAT.
Information about CARACal can be obtained online under the URL:
https://caracal.readthedocs.io. RK acknowledges the support of the Department
of Atomic Energy, Government of India under project no. 12-R&D-TFR-5.02-0700.
SS acknowledges the support of the European Regional Development Fund and the
Mobilitas Pluss postdoctoral research grant MOBJD660.
Data Availability. The data underlying this article are subject to an embargo.
Once the embargo expires the data will be available
[https://archive.sarao.ac.za/; https://www.sarao.ac.za/wp-
content/uploads/2019/12/MeerKAT-Telescope-and-Data-Access-Guidelines.pdf].

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##  Appendix A Appendix

Figure A.1: (left) MeerKAT direction-dependent calibration image of
ZwCl2341.1+0000 (robust = 0). We marked sources with alphabets as labelled by
V09. The beam size is 8′′ $\times$ 6′′, pa = -3∘ and (global) rms is 14
$\mu$Jy beam-1. (right) Same as the left image, but only showing the compact
point sources (generated with the Crystalball) which were subtracted from the
visibility. We marked each source from A1 to A28. Figure A.2: Full MeerKAT
image (1∘ field of view) of ZwCl2341.1+0000. Left image is direction-
independent and right image is direction-dependent image. In both images, the
beam size is the same as Figure A.1. The rms in the left image is 20 $\mu$Jy
beam-1 and right image is 14 $\mu$Jy beam-1.

((a))

((b))

((c))

((a)) Figure A.4: ZwCl 2331.1+0000: cutouts of four point sources towards
direction-dependent calibration applied and peeled from the visibility.
Sources are arranged from their distance from the phase-centre. We marked
every source in box. Left cutout (from Figure A.2(a)) is direction-independent
and right cutout (from Figure A.2(b)) is after direction-dependent
calibration. In each cutout, we calculated the local rms, minimum pixel and
sum of total negative component values inside the 8′ box size around the
marked sources. These values are listed in Table A.1. Figure A.5: Full MeerKAT
image (1∘ field of view) of A2631. Left image is direction-independent and
right image is direction-dependent image. In both images, beam size is the
same as Figure A.1. The rms in the left image is 32 $\mu$Jy beam-1 and right
image is 13 $\mu$Jy beam-1.

((a))

((b))

((c))

Figure A.6: A2631: cutouts of three point sources towards direction-dependent calibration applied and peeled from the visibility. Sources are arranged from their distance from phase-centre. We marked every source by box. Left cutout (from Figure A.5(a)) is direction-independent and right cutout (from Figure A.5(b)) is after direction-dependent calibration. In each cutout, we calculated the local rms, minimum pixel and sum of the total negative component values inside the 8′ box size around the marked sources. These values are listed in Table A.1. Figure A.7: Flux densities comparison of discrete point sources before and after direction-dependent calibration for both A2631 and ZwCl 2341.1+0000. Table A.1: Local rms, minimum of pixel and sum of total negative component values calculated around peeled sources for two sets of cutouts of direction-independent (DI) and direction-dependent (DD). Clusters | RMS ($\mu$Jy beam-1) | Min. of pixel (mJy beam-1) | Sum of negative (Jy beam-1)
---|---|---|---
| DI | DD | DI | DD | DI | DD
ZwCl2341.1+0000 | 37 | 16 | -1.26 | -0.091 | -1.17 | -0.63
| 23 | 17 | -0.40 | -0.20 | -0.77 | -0.64
| 37 | 18 | -1.11 | -1.57 | -0.98 | -0.72
| 38 | 24 | -1.33 | -0.61 | -0.99 | -0.65
| 201 | 30 | -8.23 | -60.0 | -4.13 | -2.53
A2631 | 113 | 41 | -2.21 | -1.84 | -2.22 | -1.14
| 147 | 29 | -3.75 | -1.56 | -2.65 | -0.93
| 183 | 21 | -4.02 | -0.28 | -3.29 | -0.68
Table A.2: List of point sources subtracted from the ZwCl 2341.1+0000 data. Point source | RA | Declination | Flux density | Flux density error | Peak flux | Peak flux error
---|---|---|---|---|---|---
| H :M :S | D :M :S | mJy | mJy | mJy beam-1 | mJy beam-1
A1 | 23:43:39.4 | +0:18:45.0 | 15.59 | 1.36 | 4.65 | 0.32
A2 | 23:43:40.8 | +0:20:30.0 | 0.89 | 0.01 | 0.82 | 0.01
A3 | 23:43:40.3 | +0:20:54.0 | 3.67 | 0.14 | 2.31 | 0.06
A4 | 23:43:39.7 | +0:17:55.5 | 0.41 | 0.01 | 0.36 | 0.00
A5 | 23:43:37.5 | +0:17:28.5 | 0.30 | 0.00 | 0.31 | 0.00
A6 | 23:43:47.3 | +0:16:55.5 | 0.41 | 0.01 | 0.39 | 0.01
A7 | 23:43:46.0 | +0:15:34.5 | 1.29 | 0.02 | 1.16 | 0.01
A8 | 23:43:50.1 | +0:22:40.5 | 7.20 | 0.07 | 6.92 | 0.04
A9 | 23:43:58.6 | +0:14:59.9 | 1.03 | 0.01 | 0.99 | 0.01
A10 | 23:43:56.0 | +0:18:31.4 | 0.24 | 0.01 | 0.23 | 0.01
A11 | 23:43:34.7 | +0:20:37.5 | 0.64 | 0.01 | 0.57 | 0.01
A12 | 23:43:41.4 | +0:18:27.0 | 0.17 | 0.03 | 0.14 | 0.01
A13 | 23:43:43.9 | +0:20:39.0 | 0.40 | 0.01 | 0.31 | 0.01
A14 | 23:43:23.8 | +0:16:11.9 | 0.70 | 0.01 | 0.67 | 0.01
A15 | 23:43:48.5 | +0:15:09.0 | 0.93 | 0.06 | 0.66 | 0.03
A16 | 23:43:49.8 | +0:15:07.5 | 0.76 | 0.05 | 0.39 | 0.02
A17 | 23:43:48.8 | +0:15:31.5 | 0.96 | 0.02 | 0.50 | 0.01
A18 | 23:43:45.9 | +0:16:09.0 | 2.91 | 0.19 | 0.98 | 0.05
A19 | 23:43:34.5 | +0:15:31.5 | 0.20 | 0.01 | 0.17 | 0.00
A20 | 23:43:34.5 | +0:17:00.0 | 0.23 | 0.03 | 0.18 | 0.01
A21 | 23:43:25.0 | +0:16:53.9 | 0.27 | 0.01 | 0.27 | 0.01
A22 | 23:43:42.2 | +0:15:42.0 | 0.19 | 0.01 | 0.16 | 0.00
A23 | 23:43:36.3 | +0:20:51.0 | 0.40 | 0.01 | 0.26 | 0.00
A24 | 23:43:33.9 | +0:20:00.0 | 0.30 | 0.01 | 0.22 | 0.00
A25 | 23:43:32.9 | +0:14:28.5 | 0.26 | 0.00 | 0.23 | 0.00
A26 | 23:43:37.3 | +0:20:38.5 | 0.17 | 0.01 | 0.14 | 0.00
A27 | 23:43:37.0 | +0:21:41.4 | 0.28 | 0.00 | 0.28 | 0.00
A28 | 23:43:48.0 | +0:14:00.8 | 0.44 | 0.00 | 0.32 | 0.00