# Magnetoresistance hysteresis in the superconduting state of Kagome CsV3Sb5

Tian Le1,2, Corresponding author<EMAIL_ADDRESS>Jinjin Liu3,4
Zhiwei Wang3,4,5 and Xiao Lin1,2,
1Institute of Natural Sciences, Westlake Institute for Advanced Study,
Hangzhou 310024, P. R. China
2Key Laboratory for Quantum Materials of Zhejiang Province, Department of
Physics,
School of Science and Research Center for Industries of the Future,
Westlake University, Hangzhou 310030, P. R. China
3Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum
Architecture and Measurement (MOE),
School of Physics, Beijing Institute of Technology, Beijing 100081, China
4Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems,
Beijing Institute of Technology, Beijing 100081, China
5Material Science Center, Yangtze Delta Region Academy of Beijing
Institute of Technology, Jiaxing 314011, China Corresponding author.
<EMAIL_ADDRESS>
###### Abstract

The hysteresis of magnetoresistance observed in superconductors is of great
interest due to its potential connection with unconventional
superconductivity. In this study, we perform electrical transport measurements
on Kagome superconductor CsV3Sb5 nanoflakes and uncover unusual hysteretic
behaviour of magnetoresistance in the superconducting state. This hysteresis
can be induced by applying either a large DC or AC current at temperatures
($T$) well below the superconducting transition temperature ($T_{\rm c}$). As
$T$ approaches $T_{\rm c}$, similar weak hysteresis is also detected by
applying a small current. Various scenarios are discussed, with particular
focus on the effects of vortex pinning and the presence of time-reversal-
symmtery-breaking superconducting domains. Our findings support the latter,
hinting at chiral superconductivity in Kagome superconductors.

Keywords: hysteresis, magnetoresistance, Kagome superconductor, Chiral
superconductor

PACS: 74.78.-w;74.25.F-;85.25.-j;74.25.-q;

##  1 Introduction

Hysteresis is a phenomenon whereby the response of a system to an external
disturbance, such as magnetic field ($H$), electric field, temperature ($T$)
or mechanical stress, depends on the history of applied perturbation.
Understanding of hysteresis is beneficial for designing materials of improved
quality and predicting novel properties [1, 2, 3, 4, 5, 6]. In
superconductors, the presence of hysteretic magnetoresistance has attracted
considerable attention, because of its relation to several intriguing
dynamics, including magnetic vortices, ferromagnetism, chiral superconducting
domains and spin-triplet paring symmetry [7, 8, 9, 10, 11, 12, 13, 14, 15,
16]. Relevant investigation will provide valuable insights for the development
of novel superconducting materials and various quantum technologies, ranging
from energy transmission to quantum computation.

As a member of Kagome superconductors, CsV3Sb5 (CVS) has garnered significant
interest due to its unique electronic properties and diverse quantum orders of
matter [17, 18]. In addition to the fully gapped superconductivity [19, 20,
21, 22], a pair density wave was detected by scanning tunneling microscopy,
showing remarkable resemblance to that in cuprates [23]. Moreover, multicharge
flux quantization was observed in mesoscopic CVS ring devices, suggesting the
possibility of higher charge superconductivity [24]. Numerous theoretical
studies have predicted chiral superconductivity in CVS, given the Kagome
lattice formed by vanadium atoms and breaking of time-reversal symmetry (TRS)
in the normal state [25, 26, 27, 28, 29, 30, 31, 32]. Recently, a technique
combining the zero-field superconducting diode effect and interference
patterns was employed to demonstrate the presence of TRS-breaking
superconducting order with dynamic domains in CVS [33].

In this study, we performed electrical transport measurements on CVS
nanoflakes under various DC bias current ($I_{\mathrm{DC}}$), AC excitation
current ($I_{\mathrm{AC}}$) and $T$. In the superconducting state, an
intriguing hysteresis of magnetoresistance within a field range of $\pm$ 20 mT
was observed when sweeping the field in opposite directions. In this context,
the potential roles of vortex pinning effects and chiral superconducting
domains were discussed in elucidating the origin of the observed phenomena.

##  2 Experimental methods

Single crystals of CsV3Sb5 were grown through flux methods by using Cs (purity
99.8%) bulk, V (purity 99.999%) pieces and Sb (purity 99.9999%) shot as the
precursors and Cs0.4Sb0.6 as the flux agent. The starting elements were placed
in an alumina crucible and sealed in a quartz ampoule in an argon-filled glove
box. The ampoule was then gradually heated up to 1000 ℃ in 200 h and held at
that temperature for 24 h in an oven. It was subsequently cooled down to 200 ℃
at a rate of 3.5 ℃/h. The resulting product was immersed in deionized water to
remove the flux. Finally, shiny CsV3Sb5 crystals with hexagonal shape were
obtained. CsV3Sb5 nanoflakes were mechanically exfoliated from the bulk
crystals with a thickness exceeding 40 nm, using Nitto blue tape and
transferred onto silicon substrates capped with 300 nm SiO2. The contacts were
deposited with Ti (5 nm)/Au (80 nm) via electron beam evaporation. In order to
improve the quality of the contacts, the flakes were cleaned by Ar plasma
prior to deposition.

The transport measurements were performed in Quantum Design physical property
measurement system (PPMS). The resistance ($R$) and differential resistance
(d$V$/d$I$) for three devices (D1-D3) were measured by a standard four-
terminal method. d$V$/d$I$ in the positive ($I_{\textrm{+}}$) and negative
($I_{\textrm{-}}$) bias current regimes was collected by sweeping
($I_{\mathrm{DC}}$) from 0 to $I_{\textrm{max+}}$ and $I_{\textrm{max-}}$,
respectively. $I_{\mathrm{DC}}$ was supplied by a current source meter
(Keithley 2450). A lock-in amplifier (Stanford Research, SR830) combined with
a 100 k$\Omega$ buffer resistor was used to offer small $I_{\mathrm{AC}}$
($11~{}\mathrm{Hz}-173$ Hz, $1~{}\mu\mathrm{A}-50~{}\mu$A) to detect the
differential resistance (d$V$/d$I$ = $V_{\textrm{AC}}$/$I_{\textrm{AC}}$).

##  3 Results and discussion

Fig. 1. (a) Temperature dependent resistance for D1 from 300 K to 1.8 K. The
lower inset is the enlarged curve around $T_{\mathrm{c}}$. The upper inset
shows the optical image of D1 with a scalar bar of 4 $\mu$m. (b) Magnetic
field dependent resistance for D1 at 1.8 K. The red and blue curves represent
the field swept from 0 to 2 T and 2 to 0 T, respectively. (c) The differential
resistance as a function of current bias at 1.8 K for D1. The red(blue) curve
represents the current swept from 0 $\mu$A to positive (negative) bias. The
dashed lines mark the bias current at 100 $\mu$A, 200 $\mu$A, 300 $\mu$A and
400 $\mu$A, respectively. (d) Field dependent differential resistance at four
bias current marked in (c). All curves are swept with a field cycling
beginning at negative field. The blue dashed lines denote the onset of
hysteresis. The red dashed lines denote the coercive field. The field sweep
rate is 0.3 mT/s.

Figure. 1(a) illustrates $R$ versus $T$ for D1 in a full temperature range,
which indicates high sample quality with a residual-resistance-ratio (RRR) of
60. The transitions of charge density wave (CDW) and superconductivity occur
at $T_{\rm CDW}$ = 82 K and $T_{\rm c}$ = 4.3 K, respectively. Fig. 1(b) shows
the magnetoresistance measured at $T=1.8$ K and $I_{\rm AC}$ = 3 $\mu$A by
sweeping $H$ in a large field range, i.e. from 0 T to 2 T (red) and back from
2 T to 0 T (blue) respectively. It clear that two curves collapse without
detectable hysteresis. As $H$ increases, the fast enhancement of finite
resistance could be attributed to vortex depinning effect. The absence of
hysteresis observed in Fig. 1(b) suggests that this pinning effect is not
prominent [34, 7, 8, 9, 10].

In Fig. 1(c), we present d$V$/d$I$ as a function of $I_{\rm DC}$ at 1.8 K,
where the superconducting state sustains up to 420 $\mu$A. The discrepancy
between positive ($I_{\rm+}$) and negative ($I_{\rm-}$) sweeping curves arises
from the superconducting diode effect, as reported in our previous work[33].
The presence of multiple transition peaks implies signatures of
superconducting domains, likely chiral domains [33]. Figure 1(d) present
d$V$/d$I$ versus $H$ for $I_{\mathrm{DC}}=100-400~{}\mu$A, corresponding to
the vertical lines in Fig. 1(c). At $I_{\rm DC}=200-400~{}\mu$A, these curves
exhibit a notably bow-tie-shaped hysteresis loop within the superconducting
state. This resembles the behavior in ferromagnetic superconductors [11, 12],
where the positions of dips (peaks) in the d$V$/d$I$ curves define the
coercive field $H_{\mathrm{co}}$. The hysteresis merges at slightly higher
field ($\pm 20$ mT), corresponding to the full polarization of domains,
denoted as $H_{\rm hys}$. However, it is well-established that there is no
ferromagnetism in CVS [17, 18]. On the other hand, in the superconducting
mixed state, vortex depinning occurs once its Lorentz force exceeds the
pinning force caused by defects, with the former proportional to the product
of the external field and current density ($J$) [35]. Therefore, the higher
the current, the lower the depinning field. This is in stark contrast with the
observation in Fig. 1(d), wherein even as $I_{\mathrm{DC}}$ increases, both
$H_{\mathrm{co}}$ and $H_{\rm hys}$ remain roughly unchanged.

In a chiral superconductor, it is energetically favorable to form domain
structures between degenerate superconducting phases of opposite chiralities.
Similar to ferromagnetic domains, these superconducting domains are pinned by
disorder or defects. The field strength, exceeding the pinning force, can
switch the chirality of domains, resulting in hysteresis during field cycling
[36]. This field is independent of the applied current, consistent with the
observation in Fig. 1(d). At $I_{\rm DC}$ = 100 $\mu$A, the hysteresis is
negligible since the resistance is zero within $\pm H_{\rm hys}$. Subsequent
data will extend the discussion in the frame of chiral domains.

Fig. 2. (a) Field dependent resistance for D1 at various $T$ around
$T_{\mathrm{c}}$. The field sweep rate is 0.3 mT/s. (b) Field dependent
resistance for D1 at $T=1.8$ K, $I_{\rm DC}=300~{}\mu$A and $I_{\rm
AC}=3~{}\mu$A with the field sweep rates of 0.05 mT/s, 0.1 mT/s and 0.3 mT/s,
respectively.

In Fig. 2(a), we examine the field-dependent resistance at $I_{\mathrm{DC}}=0$
for device D1 by varying $T$. At low $T$, the resistance is nearly zero,
displaying no detectable hysteresis when the field cycles between $\pm$50 mT.
As $T$ approaches $T_{\mathrm{c}}$ and above, $R$ becomes finite and an
observable bow-tie-shaped hysteresis loop emerges, similar to that in Fig.
1(d). However, the width of the hysteresis, for instance indicated by
$2H_{\mathrm{co}}$ $\sim$ 1.4 mT, becomes much smaller than the value of
$\sim$ 3.2 mT in Fig. 1(d). This weaker hysteresis can be ascribed to the
reduction of the domain pinning force due to strengthened thermal fluctuation
as $T$ rises, which aligns with the chiral superconducting domain scenario. At
even higher $T$ (in the normal state), this hysteresis disappears implying
that it is inherent to the superconducting state. It is worth noting that
vortices have been depinned at $T>T_{\rm c}$, making them irrelevant here.

Fig. 3. (a) Field dependent resistance for D2 at various AC excitation $I_{\rm
AC}$. The inset shows an optical image of D2 with a scalar bar of 2 $\mu$m.(b)
Field dependent resistance for D3 with different field sweep ranges at $I_{\rm
AC}$ = 50 $\mu$A and $I_{\rm DC}$ = 0 $\mu$A. The numbers (1-5) represent the
sweep protocols in sequence. The red dashed lines denote the coercive field.
The inset is an optical image of D3 with the scalar bar of 6 $\mu$m.

We note that artificial hysteresis may occur such that the field sweep rate
exceeds the data collection rate of the computer in the measurements of
$R$-$H$ curves. To check this, we measured $\textrm{d}V/\textrm{d}I$ versus
$H$ for D1 by varying the field sweep rates from 0.05 mT/s to 0.3 mT/s, as
shown in Fig. 2(b). All curves exhibit hysteresis and collapse with each
other. It seems insensitive to the sweep rate, ruling out this possibility.
Moreover, hysteresis can also be induced by heating effects from the field
sweep around 0 mT. In this case, the characteristics of hysteresis would
depend on the heating power related to the sweep rate. This is clearly not the
case here. Therefore, the hysteresis observed in our devices is unlikely to be
artificial.

Similar hysteresis can be reproduced in other CVS devices. In Fig. 3(a), we
inspect the $R$-$H$ curves with different $I_{\mathrm{AC}}$ at 1.8 K and
$I_{\rm DC}=0~{}\mu$A for D2. As $I_{\rm AC}$ increases, the depinning and
subsequent motion of vortices generate finite resistance in a magnetic field.
At $I_{\rm AC}$ = 20 $\mu$A, the resistance remains small with marginal
hysteresis. As $I_{\rm AC}$ increases from 30 to 50 $\mu$A, the hysteresis of
magnetoresistance becomes increasingly remarkable, which resembles the data
collected by varying $I_{\mathrm{DC}}$ or $T$ in Fig. 1 and 2.

In the following, let’s delve into the switching characteristics of hysteresis
by varying the maximum sweeping field ($H_{\mathrm{max}}$). The measurements
were performed on D3 with $I_{\rm DC}=0~{}\mu$A and $I_{\rm AC}=50~{}\mu$A at
$T=1.8$ K. During the measurements, we initially ramped $H$ from 0 to a
positive field $H_{\mathrm{max}}^{\mathrm{+}}$, then returned to
$H_{\mathrm{max}}^{\mathrm{-}}$ and finally back to
$H_{\mathrm{max}}^{\mathrm{+}}$ again. As seen in Fig. 3(b), the hysteresis in
the $R$-$H$ curve is indetectable at $\left|{H_{\rm max}}\right|$ = 1 mT. As
$\left|{H_{\rm max}}\right|$ increases to 2 mT, a discernible hysteresis
emerges. Further increasing $\left|{H_{\rm max}}\right|$ results in a
pronounced hysteresis, as observed for $\left|{H_{\rm max}}\right|=3$ and $5$
mT. This hysteresis showcases a retarded manner, i.e. the $R$-$H$ curves
shifts to negative (positive) as the field sweep from the
$H_{\mathrm{max}}^{\mathrm{+}}$ ($H_{\mathrm{max}}^{\mathrm{-}}$). This
phenomenon is a typical feature of domain switching with $H_{\mathrm{co}}$
marked by the vertical dashed lines in Fig. 3(b). At $H_{\mathrm{max}}\approx
H_{\mathrm{co}}$, the chirality of domains is minimally switched during the
field cycling, resulting in the absence of hysteresis. As $H_{\mathrm{max}}$
rises, an increasing number of domains are switched in both sweeping protocols
towards $H_{\mathrm{max}}^{\mathrm{\pm}}$ and leads to a more conspicuous bow-
tie-shaped hysteresis, as seen in the curves for $\left|{H_{\rm
max}}\right|=5$ mT.

Note that in several candidates of chiral superconductors, such as Sr2RuO4
[15] and Bi/Ni bilayer [14], an ”advanced” form of hysteresis has been
observed in the transport properties (e.g. superconducting critical current)
of their Josephson junction or SQUID devices. This feature is thought to arise
from the response of chiral domains to the interaction between the Meissner
screening supercurrent and the change in the applied field. This phenomenon
requires the system to be in the Meissner state [36, 14]. In contrast, in our
case, detecting the hysteresis is challenging in a Meissner state, since it
will be hidden by zero resistance. A large DC or AC current is required to
stimulate the vortex motion and generate finite resistance in the mixed state.

The aforementioned hysteresis in CVS is properly interpreted by the model
involving the pinning of TRS-breaking domains in the superconducting state.
This aligns with recent literature demonstrating a TRS-breaking order
parameter with dynamic superconducting domains in CVS [33]. Previous
theoretical studies have also proposed a chiral superconducting phase based on
the Kagome lattice of CVS [37, 38, 39]. Therefore, the observed hysteretic
magnetoresistance may serve as an indirect evidence for the possible existence
of chiral superconductivity.

##  4 Conclusion

In summary, we observe a retarded hysteresis of magnetoresistance in the
superconducting mixed state of CVS. Before reaching a final conclusion, let’s
extend the discussion of the possible explanation involving strong vortex
pinning effect. First of all, strong pinning generally exists in inhomogeneous
superconductors and may lead to an “advanced” feature of hysteresis in the
mixed state, as accounted for by a two-level critical-state model [34, 7, 8,
9, 10]. This differs from our observation. And the absence of hysteresis shown
in Fig. 1(b) also suggests weak vortex pinning strength in our single
crystalline devices. Second, in our case, the hysteresis occurs in a finite
resistance regime where vortices are already depinned by large DC or AC
current. Therefore, the dynamics of chiral superconducting domains in CVS
provides a more plausible explanation. Our research lays the foundation for
investigating chiral superconductivity using current-tuning transport
measurements.

## Acknowledgment

This research is supported by the China Postdoctoral Science Foundation (Grant
No. 2022M722845 and No. 2023T160586). X.L. acknowledges support by the
Zhejiang Provincial Natural Science Foundation of China for Distinguished
Young Scholars under Grant No. LR23A040001 and the Research Center for
Industries of the Future (RCIF) at Westlake University under Award No.
WU2023C009. Z.W. is supported by the National Key R$\&$D Program of China
(Grants Nos. 2020YFA0308800 and 2022YFA1403400) and the Beijing Natural
Science Foundation (Grants No. Z210006).The authors thank the support provided
by Dr. Chao Zhang from Instrumentation and Service Center for Physical
Sciences at Westlake University.

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# The MeerKAT Galaxy Clusters Legacy Survey: star formation in massive
clusters at $0.15<z<0.35$

K. C. Kesebonye1,2 , M. Hilton1,2,3, K. Knowles1,4,5, W. D. Cotton5,6, T. E.
Clarke7, S. I. Loubser8, K. Moodley1,2, S. P. Sikhosana1,2
1Astrophysics Research Centre, University of KwaZulu-Natal, Durban 4041, South
Africa
2School of Mathematics, Statistics, and Computer Science, University of
KwaZulu-Natal, Westville 3696, South Africa
3Wits Centre for Astrophysics, School of Physics, University of the
Witwatersrand, Private Bag 3, 2050, Johannesburg, South Africa
4Centre for Radio Astronomy Techniques and Technologies, Department of Physics
and Electronics, Rhodes University, P.O. Box 94, Makhanda 6140, South Africa
5South African Radio Astronomy Observatory, 2 Fir Street, Observatory 7925,
South Africa
6National Radio Astronomy Observatory, Charlottesville, VA 22903, USA
7Naval Research Laboratory, Washington, DC 20375, USA
8Centre for Space Research, North-West University, Potchefstroom, 2520, South
Africa Contact e-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We investigate dust-unbiased star formation rates (SFR) as a function of the
environment in 20 massive clusters ($M_{200}>4\times 10^{14}\,{\rm
M}_{\odot}$) between $0.15<z<0.35$ using radio luminosities ($L_{\rm 1.4GHz}$)
from the recently released MeerKAT Galaxy Cluster Legacy Survey catalogue. We
use optical data from the Dark Energy Camera Legacy Survey to estimate
photo-$z$s and assign cluster membership. We observe a steady decline in the
fraction ($f_{\rm SF}$) of star-forming galaxies from $2R_{200}$ to the
cluster centres in our full cluster sample, but notice a significant
difference in $f_{\rm SF}$ gradients between clusters hosting large-scale
extended radio emission in the form of haloes and relics (associated with
ongoing merger activity) and non-radio-halo/relic hosting clusters. For star-
forming galaxies within $R_{200}$, the $f_{\rm SF}$ in clusters hosting radio
haloes and relics ($0.148\pm 0.016$) is $\approx 23\%$ higher than in non-
radio-halo/relic hosting clusters ($0.120\pm 0.011$). We observe a $3\sigma$
difference between the total SFR normalised by cluster mass for non-radio-
halo/relic hosting clusters ($21.5\pm 1.9$ M⊙yr-1/$10^{14}$M⊙) and for
clusters with radio haloes and relics ($26.1\pm 1.4$ M⊙yr-1/$10^{14}$M⊙).
There is a $\approx 4\times$ decline in the mass normalised total SFR of
clusters for galaxies with SFR above the luminous infrared galaxies (LIRGs)
SFR limit at our redshift slice, corresponding to 2 Gyr in look-back time.
This is consistent with the rapid decline in SF activity with decreasing
redshift amongst cluster LIRGs seen by previous studies using infrared-derived
SFR.

###### keywords:

galaxies: clusters: general – galaxies: star formation – galaxies: evolution

††pubyear: 2022††pagerange: The MeerKAT Galaxy Clusters Legacy Survey: star
formation in massive clusters at $0.15<z<0.35$–A

##  1 Introduction

Probing star formation (SF) activity of galaxies in different cosmic
environments paves an important path to understanding the dynamics behind
galaxy evolution. Various studies have shown that SF decreases steadily with
redshift from $z\approx 2.5$ (e.g., Lilly et al., 1996; Karim et al., 2011;
Sobral et al., 2014) and this has been shown to be the case in all
environments (Koyama et al., 2013). Results from Peng et al. (2010) show that
the suppression of SF activity in galaxies can be imposed by the galaxy
environment (cluster/density-dependent) and can also be a result of internal
processes (galaxy stellar mass-dependent), with both suppression effects
acting on the galaxies independently. Some studies argue that the environment-
induced suppression is secondary to the internal/stellar mass-induced
suppression (e.g., Hahn et al., 2015). Darvish et al. (2016) suggests that the
environmental suppression is only relevant at $z\leq 1$ whereas the stellar
mass suppression dominates at $z\geq 1$.

The internal or galaxy stellar mass regulation of SF results in a strong
linear correlation between star formation rates (SFR) and stellar mass within
galaxies called the star formation main sequence (MS, see Brinchmann et al.,
2004; Elbaz et al., 2011; Speagle et al., 2014; Schreiber et al., 2015;
Katsianis et al., 2016). The MS has been shown to be visible out to $z\approx
6$ (Speagle et al., 2014) with an intrinsic scatter of $\approx 0.2-0.3$ dex
that is constant throughout cosmic time.

In the local Universe, SF activity in galaxies has been shown to be strongly
dependent on the galaxy environment through comparative studies of galaxies in
high-density (groups/clusters) environments and galaxies in the field (e.g.,
Balogh et al., 1998; Lewis et al., 2002; Haines et al., 2015). These studies
conclude that the fraction of star-forming galaxies in cluster environments is
lower compared to low-density/field environments. Galaxy clusters are
populated by two broad classes of galaxies: red-and-dead elliptical galaxies
with little to no SF activity, mostly residing in cluster cores, and blue
spiral galaxies with ongoing SF activity, mostly found in the cluster
outskirts (e.g., Baldry et al., 2004; Taylor et al., 2015; Haines et al.,
2017). This leads to the relation between the fraction of star-forming
galaxies and the clustercentric radius noted by various studies (e.g., Lewis
et al., 2002; Gómez et al., 2003; Haines et al., 2015). A number of physical
processes have been proposed and observed to occur within clusters leading to
the suppression of SF activity among cluster galaxies. Some of these processes
may be driven by galaxy to galaxy interaction (harassment or tidal
interactions, Farouki & Shapiro, 1981; Moore et al., 1996). In other cases,
the galaxies may be sensitive to the large-scale cluster environment (ram
pressure stripping, Gunn & Gott, 1972) or be quenched by "burning up" as they
enter the cluster environment (Larson et al., 1980; Balogh et al., 2000).

Several cluster studies have observed a rapid decline in SF activity with
redshift when examining the total SFR per unit cluster mass
($\Sigma(\text{SFR})/M$). These studies found $\Sigma(\text{SFR})/M$ to be
redshift dependent with a relation of
$\Sigma(\text{SFR})/M\propto(1+z)^{\alpha}$, with $\alpha\simeq 5-7$ for
clusters out to redshifts $z\approx 1.6$ (see, e.g., Kodama et al., 2004; Bai
et al., 2009; Popesso et al., 2012; Webb et al., 2013; Alberts et al., 2014).
The $\Sigma(\text{SFR})/M$ is derived from the sum of SFR for individual
galaxies identified as cluster members normalised by the cluster mass. This
quantity allows for comparison of SF activity between clusters of different
masses.

SFR for normal galaxies (galaxies that do not host an active galactic nucleus)
can be estimated from various tracers at different wavelengths across the
spectrum (see, e.g., reviews by Kennicutt, 1998; Kennicutt & Evans, 2012;
Madau & Dickinson, 2014). Rest-frame ultraviolet (UV) emission directly traces
newly formed stars but suffers a great deal of attenuation from dust, thus
requiring corrections for reliable star formation estimates (Bell, 2003). When
the UV emission from the newly formed stars interacts with the dust, it heats
the dust which then re-emits at infrared wavelengths, paving a way to trace
SFR via obscured UV light (Kennicutt, 1998). Emission line tracers (H$\alpha$,
[Oii], Ly$\alpha$), observed at optical/near-infrared wavelengths are also
used for SFR measurements. Just like UV emission, emission line tracers face
the challenge of dust attenuation and thus require corrections to get reliable
SFR estimates. Another way of tracing SFR is through the radio continuum
emission from star-forming galaxies. Radio emission is made up of thermal
free-free (bremsstrahlung) radiation and non-thermal synchrotron radiation.
The thermal free-free emission is a direct tracer of SFR due to ionized
hydrogen from massive stars in young stellar populations. At frequencies $\leq
5$ GHz, thermal free-free radiation contributes weakly to the radio continuum
flux and non-thermal radiation accounts for $90\%$ of the signal (Condon,
1992). Due to the tight correlation between radio emission and far-infrared
(FIR) emission at 1.4 GHz (e.g., Helou et al., 1985; Condon et al., 1991; Yun
et al., 2001), the radio continuum emission has a standard model for SFR
estimation at this frequency. Being free from dust interactions, radio
emission emerges as an advantageous tracer for estimating SFR in normal
galaxies compared to other SFR tracers (see Kennicutt & Evans (2012) for a
comprehensive review).

Several studies have investigated the environmental effects on the population
and SFR of galaxies residing in high-density environments like galaxy groups
and clusters. Recently, efforts have been made toward understanding the
influence of cluster morphology on the overall SF activity of galaxies in
clusters by comparing dynamically relaxed clusters to clusters hosting giant
radio haloes and relics (regarded as evidence of past or ongoing merger
activity). Merger/unrelaxed clusters have been observed to have enhanced SF
activity at low redshifts in individual cluster studies (e.g., Owen et al.,
2005; Ma et al., 2010; Ebeling & Kalita, 2019) as well as in statistical
studies of multiple clusters (e.g., Cohen et al., 2014; Cohen et al., 2015;
Stroe et al., 2017; Yoon & Im, 2020; Stroe & Sobral, 2021). Radio haloes are
large-scale extended radio emission spanning over 500 kpc in linear size. The
origin of radio haloes has been strongly linked with the reacceleration of
relativistic particles by cluster mergers (e.g., Brunetti et al., 2009;
Cassano et al., 2013; Lindner et al., 2014; Kale et al., 2015). Radio relics
are extended synchrotron radio emission residing in the periphery of galaxy
clusters. They are elongated Mpc-scale sources linked with shock fronts
induced in the intra-cluster medium (ICM) during cluster mergers (e.g., Ogrean
et al., 2013; van Weeren et al., 2016, 2019).

Various processes have been suggested to occur from cluster mergers that lead
to the enhanced SF activity that is observed in merger clusters. Bekki et al.
(2010) used numerical simulations to show that compressed cold gas from the
rising external pressure of ICM during mergers could explain the SF activity
enhancement in merger clusters. Stroe et al. (2017) suggests that the observed
enhanced SF activity in merger clusters may be caused by shock waves in the
ICM resulting from merging clusters or galaxy groups as well as the accretion
of filaments.

In this paper, we present a statistical study of SF activity in multiple
clusters using radio observations from the MeerKAT Galaxy Cluster Legacy
Survey (MGCLS DR1; Knowles et al., 2022). MGCLS is a project of $L$-band
observations (900-1670 MHz) by the MeerKAT telescope (Jonas & MeerKAT Team,
2016) of 115 galaxy clusters between $-80\deg$ and $15\deg$ declination. Our
MGCLS radio data is crossmatched with DECaLS photometry to obtain a
homogeneous set of radio-optical data with photo-$z$s. With the MeerKAT field
of view of $2\,$deg2, we were able to probe to twice the $R_{200}$ of our
clusters in our analysis. Extended radio emission is detected in 15 out of 20
clusters in our sample, 5 of which are new detections, and marked as
candidates for radio haloes, relics and a mini-halo depending on their
morphology (see Knowles et al., 2022). Fourteen clusters in our sample host
extended emission in the form of either a radio-halo, a relic or a phoenix (a
subclass of a relic, van Weeren et al., 2019). With this article, we aim to
investigate SF activity in cluster environments and its relationship with the
dynamical state of the cluster. We compare our results to previous studies of
multiple clusters carried out using FIR as a tracer for SFR.

The structure of this paper is as follows. In Section 2 we describe the radio
data, photometric data, cluster masses as well as the AGN identification and
membership selection process. In Section 3 we discuss our SFR estimates,
fraction of star-forming galaxies, SFR and cluster mass relation as well as
the mass normalised total SFR relation with redshift. We discuss our results
in Section 4. We end the paper by summarising our conclusions and laying out
some future work in Section 5.

We assume a cosmology with $H_{0}$ = 70 km s-1 Mpc-1, $\Omega_{\rm m,0}=0.3$
and $\Omega_{\rm\Lambda,0}=0.7$. $M_{200}$ denotes the mass enclosed within a
sphere of radius $R_{200}$ in which the mean enclosed overdensity is equal to
200 times the critical density of the Universe at the cluster redshift. The
Chabrier (2003) initial mass function (IMF) is used for SFR calculations.

##  2 Data

###  2.1 Cluster sample

The selection of the 20 clusters from the parent MGCLS sample was guided by
the availability of cluster photometric data in the Dark Energy Camera Legacy
Survey (DECaLS DR8; Dey et al., 2019) as well as the availability of cluster
masses ($M_{200}$) from the Atacama Cosmology Telescope (ACT DR5; Hilton et
al., 2021). The ACT DR5 catalogue has a homogeneous selection of clusters with
consistently derived mass estimates which consists of 4195 optically confirmed
Sunyaev-Zel’dovich (SZ) galaxy clusters with redshift measurements. The ACT
DR5 catalogue provides a set of mass estimates that have been re-scaled
according to a richness-based weak-lensing mass calibration through a
technique described in Hilton et al. (2018). The DECaLS photometric data is
complete for WISE (3.4 µm) W1 band apparent magnitude (mag) $m_{3.4}\leq
19.7$. This corresponds to an absolute mag limit $M_{3.4}=-20.8$, K-corrected
to our sample median redshift ($z=0.25$). We are sensitive down to a limit of
$\approx M\begin{subarray}{c}*\\\ 3.4\end{subarray}$+1.5, using $m^{*}$ (18.2)
of the IR-selected cluster sample luminosity function best-fit from the
Spitzer Infrared Array Camera (IRAC) $3.6\,\micron{}$-band (Mancone et al.,
2010). $M^{*}$ is scaled down by 0.08 mag to correct for the colour difference
between W1 (3.4 µm) and Spitzer IRAC channel one (3.6 µm). The IR luminosity
function is a good tracer of the stellar mass function since the 3.6 µm
photometry probes the peak of the stellar light.

The MGCLS catalogue is made up of a heterogeneous sample of 115 clusters with
no general selection criteria guided by cluster mass or redshift. MGCLS
comprises two subsamples grouped as “radio-selected” and “X-ray-selected” with
each subsample contributing 41 and 74 clusters respectively. The MGCLS radio-
selected subsample was picked to be biased towards high-mass clusters with
extended radio emission. The X-ray-selected subsample was guided by the Meta-
Catalogue of X-ray-detected Clusters (MCXC; Piffaretti et al., 2011), which is
a heterogeneous compilation of X-ray-selected clusters with no direct prior
biases towards or against clusters with extended radio emission.

Of the total 115 MGCLS clusters, 66 had optical counterparts with complete
coverage in DECaLS and 38 of the 66 clusters have cluster masses from the ACT
catalogue. The MGCLS field data is classified by image data quality ranging
from 0 to 3. The data quality from 0 to 1 is classified as good to moderate
dynamic range whereas 2 to 3 is classified as poor dynamic range with ripples
and source artefacts on the data. For this study, we only work with fields
that are flagged 0 and 1 to ensure that our data has the least amount of
contamination.

Figure 1 shows the mass distribution of our final cluster sample with
redshifts for 20 clusters which have reliable photo-$z$s estimates and ACT SZ-
derived cluster masses, all falling in the redshift range $0.15<z<0.35$. The
cluster sample selection was limited to clusters with $z>0.15$ due to the
large scatter observed in photo-$z$s estimates at $z<0.15$, making them
unreliable (see Figure 2). The cluster sample properties are listed in Table
1. Our final sample has 10 clusters from the radio-selected subsample, 9 of
which are hosts of extended emission in the form of a radio halo and/or relic
and 1 cluster with no extended emission. The other 10 clusters in our final
sample are from the X-ray-selected subsample with 5 hosting extended emission
in the form of a radio halo and/or relic, 1 hosting extended emission in the
form of a mini-halo and 4 with no extended emission.

Fourteen clusters in our sample host large-scale extended emission (haloes and
relics) linked to on-going merger activity. The presence of large-scale
extended emission has been linked to the dynamical state of mergers or
unrelaxed clusters by (e.g., Cassano et al., 2010, from their study of haloes
using radio data and X-ray observations). The 6 clusters with no large-scale
extended emission are assumed to be relatively dynamically relaxed or
undergoing minor mergers and likely to be less disturbed in contrast to the 14
clusters hosting haloes and relics. We conducted a visual inspection on the
dynamical state of 4 of the 6 non-halo/relic-hosting clusters in our sample
using archival X-ray imaging from Chandra and XMM Newton surveys. The X-ray
images indicate that the clusters are likely to be dynamically relaxed.
Lovisari et al. (2017) classified the dynamical state of some of the clusters
that overlap with our sample as either ‘disturbed’, ‘relaxed’, or ‘mixed’,
using criteria based on seven parameters. Clusters J0449.9-4440 and
J0525.8-4715 are classified as relaxed systems while J0510.2-4519 (hosting a
mini-halo) is noted as a mixed system by the Lovisari et al. (2017)
classification criteria. They point out that the mixed systems classification
may be subjective and that a cluster falling under this category depends on
the parameters chosen to optimise completeness and purity. Given the high
masses of clusters in our sample, the clusters without large-scale extended
emission are likely relaxed systems or have only minor mergers and can be
considered to be less disturbed environments for star-forming galaxies.

Figure 1: The mass ($M_{200}$) and redshift distribution of the cluster sample used in this work. We use a subset of the SZ-selected ACT DR5 sample (Hilton et al., 2021) to ensure a homogeneous set of cluster mass estimates. The black markers show clusters with merger-linked extended radio emission and the orange markers show relaxed clusters with no extended emission and non-merger-linked extended emission. Each symbol represents the type of extended radio emission a cluster hosts. (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
---|---|---|---|---|---|---|---|---|---
Cluster | RA | DEC | z | RMS | $M_{200}$ | $R_{200}$ | $f_{\textbf{SF}}$ | $\Sigma{\textbf{SFR}}$ | State
|  |  |  | ($\mu$J b-1) | (1014 M⊙) | (Mpc) |  | M⊙yr-1 |
Abell 209 | 22.970833 | -13.609444 | 0.206 | 3.6 | $11.1\begin{subarray}{c}+2.7\\\ -2.3\end{subarray}$ | 2.0 | $0.242$ | $380.54\pm 42.87$ | halo
Abell 2744 | 3.578333 | -30.383333 | 0.307 | 2.9 | $19.2\begin{subarray}{c}+4.2\\\ -3.7\end{subarray}$ | 2.3 | $0.113$ | $366.31\pm 68.29$ | halo, relic
Abell 2813 | 10.851667 | -20.621389 | 0.292 | 3.4 | $15.0\begin{subarray}{c}+3.3\\\ -2.9\end{subarray}$ | 2.1 | $0.084$ | $272.05\pm 50.64$ | halo‡
Abell 2895 | 19.546250 | -26.973056 | 0.228 | 3.0 | $11.0\begin{subarray}{c}+2.6\\\ -2.2\end{subarray}$ | 2.0 | $0.241$ | $302.31\pm 32.77$ | phoenix‡
Abell 521 | 73.537917 | -10.238611 | 0.248 | 3.4 | $9.6\begin{subarray}{c}+2.3\\\ -2.0\end{subarray}$ | 1.9 | $0.132$ | $309.21\pm 45.54$ | halo, relic
Abell S1063 | 342.181250 | -44.528889 | 0.348 | 2.6 | $28.1\begin{subarray}{c}+6.1\\\ -5.4\end{subarray}$ | 2.6 | $0.194$ | $682.19\pm 109.97$ | halo
Abell S295 | 41.399167 | -53.038056 | 0.300 | 2.3 | $15.6\begin{subarray}{c}+3.4\\\ -3.0\end{subarray}$ | 2.2 | $0.149$ | $458.36\pm 65.78$ | halo
J0051.1-4833 | 12.796667 | -48.559722 | 0.187 | 2.6 | $4.9\begin{subarray}{c}+1.3\\\ -1.1\end{subarray}$ | 1.5 | $0.133$ | $106.24\pm 6.36$ | relaxed
J0217.2-5244 | 34.302500 | -52.746944 | 0.343 | 2.8 | $4.9\begin{subarray}{c}+1.2\\\ -1.1\end{subarray}$ | 1.4 | $0.146$ | $245.21\pm 47.80$ | relic‡
J0225.9-4154 | 36.477500 | -41.909722 | 0.220 | 2.7 | $4.8\begin{subarray}{c}+1.2\\\ -1.0\end{subarray}$ | 1.5 | $0.139$ | $103.29\pm 15.59$ | halo
J0232.2-4420 | 38.070000 | -44.347500 | 0.284 | 2.6 | $18.1\begin{subarray}{c}+4.0\\\ -3.5\end{subarray}$ | 2.3 | $0.229$ | $452.7\pm 57.25$ | halo
J0336.3-4037 | 54.077917 | -40.622222 | 0.172 | 3.5 | $10.9\begin{subarray}{c}+2.7\\\ -2.3\end{subarray}$ | 2.0 | $0.12$ | $161.97\pm 12.07$ | relaxed
J0449.9-4440 | 72.480000 | -44.678056 | 0.150 | 2.6 | $6.1\begin{subarray}{c}+1.7\\\ -1.4\end{subarray}$ | 1.7 | $0.074$ | $89.59\pm 3.58$ | relaxed
J0510.2-4519 | 77.557500 | -45.321111 | 0.200 | 3.0 | $8.1\begin{subarray}{c}+2.0\\\ -1.7\end{subarray}$ | 1.8 | $0.123$ | $172.26\pm 10.28$ | relaxed, mini-halo‡
J0516.6-5430 | 79.158333 | -54.514167 | 0.295 | 3.1 | $9.0\begin{subarray}{c}+2.0\\\ -1.8\end{subarray}$ | 1.8 | $0.108$ | $241.93\pm 36.16$ | halo,relic
J0525.8-4715 | 81.465000 | -47.250556 | 0.191 | 3.0 | $9.9\begin{subarray}{c}+2.4\\\ -2.1\end{subarray}$ | 1.9 | $0.173$ | $242.16\pm 30.04$ | relaxed
J2023.4-5535 | 305.850000 | -55.591700 | 0.232 | 2.7 | $13.9\begin{subarray}{c}+3.2\\\ -2.8\end{subarray}$ | 2.1 | $0.201$ | $360.01\pm 42.34$ | halo, relic
MACS J0257.6-2209 | 44.422083 | -22.153889 | 0.322 | 3.2 | $11.8\begin{subarray}{c}+2.6\\\ -2.3\end{subarray}$ | 2.0 | $0.114$ | $310.40\pm 49.84$ | relic‡
RXC J0528.9-3927 | 82.234583 | -39.462778 | 0.284 | 2.6 | $13.1\begin{subarray}{c}+2.9\\\ -2.6\end{subarray}$ | 2.1 | $0.193$ | $311.16\pm 46.45$ | halo
RXC J0543.4-4430 | 85.851667 | -44.505278 | 0.164 | 3.6 | $4.2\begin{subarray}{c}+1.3\\\ -1.1\end{subarray}$ | 1.5 | $0.151$ | $135.02\pm 12.59$ | relaxed
Table 1: The cluster sample. Columns: (1) Name of the cluster; (2,3) MeerKAT
pointing coordinates: J2000 Right Ascension and Declination in degrees; (4)
Cluster redshift; (5) MeerKAT image sigma-clipped standard deviation in micro-
Jy per beam; (6) Cluster mass in $10^{14}$M⊙; (7) virial radius $R_{200}$ in
Mpc; (8) The fraction of all star-forming galaxies within $R_{200}$ (see
Section 3.1); (9) Total SFR for galaxies within $R_{200}$ (see Section 3.2.1);
(10) The dynamical state of a cluster. The clusters with newly detected
extended radio emission in the MGCLS are marked as candidates based on their
morphology are indicated by ‡.

###  2.2 MeerKAT data

The MGCLS DR1 (Knowles et al., 2022) is a publicly released catalogue of 115
galaxy clusters observed by the MeerKAT telescope in the $L$-band throughout
900 – 1670 MHz. Each cluster is observed at full polarization for $\approx$ 6
– 10 hours. The MGCLS DR1 offers raw MeerKAT continuum visibilities, basic
image cubes at $\approx 8^{\prime\prime}$ resolution as well as enhanced
spectral and polarization image cubes at $\approx$ $8^{\prime\prime}$ and
$15^{\prime\prime}$ resolutions. MGCLS image products are sensitive within a
range of $\approx$ 3 $\mu$Jy beam-1 for an $8^{\prime\prime}$ beam to
$\approx$ 10 $\mu$Jy beam-1 for a $15^{\prime\prime}$ beam. The basic cubes
span a $2\,$deg2 field of view (FoV). The enhanced data products are primary
beam corrected within a $1.2\,$deg2 FoV. The survey gives good detections up
to $\approx$ $10^{\prime}$ and has a wide bandwidth that enables spectral and
Faraday rotation mapping.

The Python Blob Detection and Source Finder (PyBDSF; Mohan & Rafferty, 2015)
software was used to create catalogues for all 115 clusters from the 1.28 GHz
images at a threshold of $5\sigma$ source detection (see Knowles et al., 2022,
for more details on source detection). The complete MGCLS DR1 catalogue has a
combined total of $\approx 626000$ compact sources from all 115 cluster data
sets.

###  2.3 DECaLS data

The DECaLS data comes from images captured by the Dark Energy Camera (DECam
$\approx 3.2\,$deg2 FoV; Flaugher et al., 2015) located at the 4-m Blanco
telescope at the Cerro Tololo Inter-American Observatory. DECam is a highly
sensitive camera optimised for a wide-field survey across a broad wavelength
range ($\approx 400-1000$ nm). DECaLS is part of the three surveys that
integrate to make the DESI Legacy Survey, alongside the Beijing-Arizona Sky
Survey (BASS; Zou et al., 2017) and the Mayall z-band Legacy Survey (MzLS;
Silva et al., 2016). DECaLS provides optical $grz$ photometry combined with
3.4, 4.6 µm photometry from the Wide-field Infrared Survey Explorer mission
(WISE; Wright et al., 2010). The DECaLS $grz$ photometry data has 5$\sigma$
depth levels of $g=24.0$, $r=23.4$ and $z=22.5$ in AB magnitudes.

###  2.4 Photometric redshifts

We use the zCluster111https://github.com/ACTCollaboration/zCluster package
(see, Hilton et al., 2021; Pillay et al., 2021) to estimate the maximum
likelihood galaxy photo-$z$s and their probability distribution, using a
template-fitting method. We use a combination of the Coleman et al. (1980)
templates and a subset of the spectral templates used in the COSMOS survey
(Ilbert et al., 2009; Salvato et al., 2011), representing a range of normal
galaxies and AGNs. We test the accuracy of the photo-$z$s using 219,380
galaxies within the DECaLS footprint that have spec-$z$s in SDSS DR16 (Ahumada
et al., 2020). We also use this sample to calibrate zero-point offsets to the
DECaLS photometry to minimise the bias of the photometric redshift (photo-$z$)
residuals ($\Delta z=z_{\rm s}-z_{\rm p}$, where $z_{\rm s}$ is the
spectroscopic redshift (spec-$z$), and $z_{\rm p}$ is the photo-$z$). After
this procedure, we find mean $\Delta z/(1+z_{\rm s})=0.008$, and scatter
$\sigma_{\rm bw}=0.03$, as estimated using the biweight scale (e.g., Beers et
al., 1990). We find that 93% of the galaxies have $\Delta z/(1+z_{\rm
s})<0.09$, i.e., 7% of the photo-$z$s are expected to be “catastrophic
outliers”. Figure 2 shows a comparison of the photometric and spec-$z$s for
this test sample.

###  2.5 Cluster membership selection

Figure 2: Comparison of photo-$z$s estimated using zCluster on DECaLS
photometry with spec-$z$s from SDSS (219,380 galaxies, $0.1<z<1$). The
photo-$z$s are evaluated on a grid with step size $\Delta z=0.01$, hence the
linear order of data points along the vertical axis. The orange line shows the
median redshift residual in bins of width $\Delta z_{\rm s}=0.2$. It becomes
slightly biased at higher redshift, but this is well above our cluster sample
redshift range as indicated by the vertical dashed lines. The photo-$z$s do
not perform well at $z_{\rm s}<0.15$ due to the lack of $u$-band mags in
DECaLS.

The most unequivocal way to select cluster members is by use of reliable
spec-$z$s. However, extensive spec-$z$ catalogues covering our cluster sample
are not available. For this study, we rely solely on photo-$z$s to achieve a
homogeneous dataset. In Section 2.4, we discuss the process for deducing the
photo-$z$ using zCluster and their accuracy.

Instead of relying only on a single best-fitting photometric redshift estimate
for each galaxy without considering its uncertainty, our membership process
uses the full redshift probability distribution $P(z)$ provided by zCluster.
We follow a method developed by Pelló et al. (2009) to identify cluster
members. This method builds on a technique by Brunner & Lubin (2000), which
calculates the probability ($P_{\rm member}$) of being a member galaxy at a
redshift range centred at the cluster redshift ($z_{\text{cl}}$), with a width
($\delta z$) that depends on the accuracy of the photo-$z$s (see Section 2.4),

$P_{\rm member}=\int_{z_{\text{cl}}-\delta z}^{{z_{\text{cl}}+\delta
z}}P(z)\,dz\,.$ (1)

For our case, $\delta z=n\sigma_{\rm bw}(1+z_{\rm cl})$. This approach works
well for this study as we mainly focus on the integrated properties of the
cluster galaxy population (i.e., total cluster SFR or fraction of star-forming
galaxies), rather than the properties of individual galaxies. We use the three
clusters in our sample with available extensive spec-$z$s (A209, A2744,
AS1063) in the literature to calibrate cluster membership selection for the
rest of the sample. We classify galaxies with spec-$z$s as members that
satisfy the condition $|z_{\rm cl}-z_{\rm spec}|<3\sigma_{\rm cl}(1+z_{\rm
cl})$, where $\sigma_{\rm cl}$ is the cluster velocity dispersion. The Abell
209 spec-$z$s were obtained from the Cluster Lensing And Supernova survey with
Hubble (CLASH-VLT; Annunziatella et al., 2016) and the Arizona Cluster
Redshift Survey (ACReS; described in Haines et al., 2015). The spec-$z$s for
Abell 2744 are from the Multi Unit Spectroscopic Explorer (MUSE; Mahler et
al., 2018) and Anglo-Australian Telescope (AAT; Owers et al., 2011)
catalogues. The Abell S1063 spec-$z$s were obtained from the CLASH-VLT
catalogue (Mercurio et al., 2021).

From the stacked catalogue of all the three clusters with spec-$z$s, we get
$\sigma_{\rm bw}=0.08$ from the redshift residuals, $\Delta z/(1+z_{\rm s})$.
The spectroscopic completeness level $C=82\%$ and the field contamination
$F=17\%$ using $n=2$ and $P_{\rm member}\geq 0.5$. The $n$ and $P_{\rm
member}$ values were chosen to maximise $C$ and minimise $F$ while selecting
galaxies that are likely to be members using redshift probability distribution
functions. The spectroscopic completeness level describes the number of
confirmed spec-$z$ members correctly identified as members by the photo-$z$s
selection criteria. The field contamination shows the percentage level of
spec-$z$s that are non-members/field galaxies but selected by the photo-$z$s
membership criteria.

The $\sigma_{\rm bw}$ from the stacked catalogue is higher than the one
estimated with the SDSS spec-$z$s mentioned in section 2.4. We adopt the
larger value as a more conservative estimate of the cluster member photometric
redshift accuracy. Table 2 shows the $C$ and $F$ percentage levels reached for
each cluster. We use the same selection parameters to identify members using
only photo-$z$s for all our 20 clusters, assuming a $C>80\%$ and $F<20\%$ for
our full sample. We further attempt to mitigate the field contamination in two
ways: (1) we check the effect of using a higher $P_{\rm member}$ on our
results, and (2) we use $P_{\rm member}$ as a weight for each galaxy when
investigating integrated cluster properties. We find that increasing the
$P_{\rm member}$ threshold has minimal effect on our overall conclusions while
reducing the completeness level in the spectroscopic sample and with little
change in the field contamination level.

We obtain a total of 14,419 galaxies out to 2$R_{200}$ for the W1 complete
DECaLS membership sample for the 20 clusters. This gave us a sample of 3054
cluster member galaxies observed by MeerKAT. The MeerKAT-detected member
galaxies sample is complete above a $5\sigma$ detection limit of SFR = 1.9
M${}_{\odot}\,$yr-1 in our most distant cluster ($z=0.35$).

Figure 3: Thumbnail images of galaxies within $R_{\rm 200}$ classified as radio-loud AGN. Each thumbnail has the galaxy identified as radio-loud centred on the image, the coordinates of the galaxy at the top of the image and the MeerKAT source ID at the bottom. (1) | (2) | (3) | (4) | (5) | (6)
---|---|---|---|---|---
Cluster | $z_{\rm cl}$ | No. of spec-$z$s | $\sigma_{\rm bw}$ |  $C$ (%) |  $F$ (%)
Abell 209 | 0.206 | 2377 (753) | 0.10 | 81 | 15
Abell 2744 | 0.307 | 971 (463) | 0.06 | 81 | 13
Abell S1063 | 0.348 | 1626 (751) | 0.08 | 84 | 25
Table 2: Quantities derived from the three clusters in our sample with
spec-$z$s: (1) Cluster name; (2) Cluster redshift; (3) the total number of
matched spectroscopic galaxies within $R_{200}$. The number of spec-$z$
galaxies within $|z_{\rm cl}-z_{\rm spec}|<3\sigma_{\rm cl}(1+z_{\rm cl})$ is
shown in brackets; (4) the scatter in the redshift residual derived from the
biweight estimator; (5) spec-$z$s completeness level; (6) fraction of spec-$z$
field galaxies.

###  2.6 AGN identification

Galaxies hosting active galactic nuclei (AGN) pose a significant challenge
when using radio observations to estimate SFR in galaxies. Previous studies
(e.g., Sadler et al., 2002; Condon et al., 2002; Mauch & Sadler, 2007) have
shown that radio-AGN may contribute up to $50\%$ of the radio luminosities in
the local Universe at luminosities just below $L_{\rm 1.4GHz}\approx 10^{23}$
W Hz-1, and that at luminosities over $10^{23}$ W Hz-1 AGN dominate the
population over star-forming galaxies. It is therefore essential for us to
remove AGN-hosting galaxies from our dataset to achieve an unbiased star-
forming sample. To identify X-ray AGN, we cross-matched our member galaxies
sample with the Chandra serendipitous source catalogue (CSC 2.0; Evans et al.,
2019) and the fourth XMM-Newton serendipitous source catalogue (4XMM-DR11;
Webb et al., 2020). X-ray sources above the rest-frame (2-10 keV) X-ray
luminosity, $L_{\text{X}}>10^{42}$ erg s-1 are expected to be AGN, whereas
those below this limit are expected to be powered by star formation. We used
the cross-matching radius of $4^{\prime\prime}$ for both X-ray catalogues,
yielding 65 and 54 sources respectively. There are four clusters in our sample
with no coverage or matches within the X-ray catalogues. Of the 119 galaxies
with X-ray cross-matches, we remove 94 galaxies that are above the X-ray AGN
luminosity cut.

To determine additional AGN, we adopt the ‘R90’ WISE IR-selection criteria by
Assef et al. (2018) (see also Stern et al., 2012; Assef et al., 2013) for AGN
classification. This uses only the WISE W1 and W2 bands to identify AGN based
on their W1-W2 colour, compared to a threshold that depends on the W2 band mag
(see equation 4 of Assef et al., 2018, which identifies AGNs with 90%
reliability). With this AGN separation method, we removed 28 sources
classified as AGN-hosting galaxies from our sample.

Figure 4: Left panel: The fraction of star-forming galaxies, $f_{\rm SF}$ as a
function of projected radial distance, in units of $R_{200}$ from the cluster
centre. We only plot MGCLS cluster members with SFR greater than the $5\sigma$
detection limit of SFR = 2 M${}_{\odot}\text{yr}^{-1}$ for comparison with IR-
derived results from Haines et al. (2015) using Spitzer/MIPS 24 $\mu$m fluxes
down to the same SFR limit. The red squares indicate $f_{\rm SF}$ values for
MeerKAT-detected cluster members in 20 clusters at $0.15<z<0.35$ and their
1$\sigma$ uncertainties. The black triangles show the $f_{\rm SF}$ values by
Haines et al. (2015) in 30 clusters at $0.15<z<0.30$ with binomial statistics
derived uncertainties. Middle panel: The comparison of $f_{\rm SF}$ trends
between clusters hosting radio haloes/relics (blue star markers) and relaxed
clusters (green circles). Right panel: The $f_{\rm SF}$ trends of clusters
split by median cluster mass ($1.09\times 10^{15}\,M_{\odot}$) and by cluster
dynamical state.

Finally, to reduce contamination from radio-loud AGN, we apply a radio
luminosity cut on our sample for galaxies with $L_{\rm 1.4GHz}>10^{23}$ W Hz-1
(Condon et al., 2002). This cut removes 80 galaxies, some of which may be
star-forming, but a relatively small number (<3$\%$) of the total sample. Only
30 galaxies with the luminosity above the radio-loud AGN cut are within our
total sample $R_{200}$. Figure 3 shows Legacy Surveys DR9 images of the 30
radio-loud galaxies within $R_{200}$ of our cluster sample to visually confirm
AGN status. Most of the galaxies show evidence of early-type morphology and
are likely to be AGN hosts and not star-forming. A handful of galaxies show
disky morphology with observed dust lines visible across their images. We
observe three galaxies within the radio-loud sample with ambiguous morphology.
These are; MKTCS J024536.66-525542.0 and MKTCS J224833.25-443538.0, which
shows the structure that is consistent with quasar morphology and the MKTCS
J051033.09-451647.8, which appears to be two galaxies colliding with two
noticeable bulges and disturbed spiral arms. It is also worth noting that low
luminosity radio-loud AGN may be left out by the radio luminosity cut and we
assume that their number does not significantly affect our results.

After removing 203 galaxies identified as AGN hosts, we obtain a total sample
of 2851 MeerKAT-detected galaxies out to 2$R_{200}$, which we assume to be
powered by star formation in the sections that follow. After removing 436
X-ray and WISE AGN from the photometric DECaLS selected members sample, we
obtain 13,983 galaxies.

##  3 Star formation rates

We used the Bell (2003) calibration of the radio–FIR correlation (see also
Karim et al., 2011) to convert radio luminosities to SFR scaled down by 1.74
from the Salpeter IMF to the Chabrier IMF:

${\rm SFR}~{}(\rm M_{\odot}\,{\rm y}r^{-1})=\begin{cases}3.18\times
10^{-22}L,&L>L_{\rm c}\\\ \dfrac{3.18\times 10^{-22}L}{0.1+0.9(L/L_{\rm
c})^{0.3}},&L\leq L_{\rm c}\par\end{cases}$ (2)

where $L=L_{\rm 1.4GHz}$ is the radio luminosity in W Hz-1 derived from the
MGCLS 1.28 GHz total flux density, using a power-law scaling and assuming a
non-thermal spectral index of -0.8 (Condon, 1992). $L_{\rm c}=6.4\times
10^{21}W\,$Hz-1is taken to be the typical radio luminosity of an $L_{*}$-like
galaxy. Bell (2003) argues that galaxies with low luminosities could have
their non-thermal emission significantly suppressed and therefore need to be
separated from the population with higher luminosities.

###  3.1 Star formation activity as a function of clustercentric distance

Previous studies have shown that SF activity is suppressed with decreasing
distance from the cluster centre (Balogh et al., 1998; Lewis et al., 2002;
Haines et al., 2015). We study the population distribution of our radio-
derived SFR for the 20 clusters with respect to their clustercentric radius in
units of $R_{200}$. We define the fraction of star-forming galaxies as $f_{\rm
SF}=N_{\rm SF}/N_{\rm tot}$, where $N_{\rm SF}$ is the number of galaxies
classified as star-forming cluster members and $N_{\rm tot}$ is the total
number of cluster members. The left panel of Figure 4 shows the $f_{\rm SF}$
for MeerKAT-detected sources in radial bins compared with $f_{\rm SF}$ results
from Haines et al. (2015), obtained from infrared-derived SFR using
Spitzer/MIPS 24$\mu$m observations for 30 clusters at $0.15<z<0.30$ and a
$5\sigma$ detection limit of $2\,\text{M}_{\odot}\text{yr}^{-1}$. The Haines
et al. (2015) study calculates SFR using the Kroupa (2002) IMF, which yields
results that are nearly identical to the Chabrier (2003) IMF. The fraction of
star-forming galaxies from radio observations is generally higher than the
$f_{\rm SF}$ of Haines et al. (2015) with the data points having differences
ranging between 1-3$\sigma$. The observed higher $f_{\rm SF}$ in our sample
could be a result of a bias towards merger-linked clusters. The Haines et al.
(2015) cluster sample is comprised of uniformly selected clusters with no
significant bias towards either merger or relaxed clusters. They notice that
even at large radii, 2$R_{200}$, the $f_{\rm SF}$ of clusters ($\approx 0.23$)
remained well below that of field galaxies ($f_{\rm SF}=0.33\pm 0.01$). They
conclude that this is not due to cluster galaxies having higher stellar masses
than field galaxies, as it is known for $f_{\rm SF}$ to decrease with
increasing stellar mass (e.g., Haines et al., 2007). They suggest that $f_{\rm
SF}$ being low out to large clustercentric radii may be due to the star-
forming galaxies being pre-processed in lower-density environments such as
galaxy groups before they enter cluster environments.

The central panel of Figure 4 shows the $f_{\rm SF}$ of the MeerKAT cluster
sample split by whether they have radio haloes/relics. Our sample has 14
clusters with extended emission in the form of radio haloes and relics (found
in merger clusters) and their $f_{\rm SF}$ trend is shown in blue stars. The
$f_{\rm SF}$ trend for the 6 relaxed clusters without radio haloes/relics is
shown in green circles. The relaxed clusters have a shallower decline from
$1.9R_{200}$ to the centre in contrast to the steeper decline noticed in the
merging clusters. Recent studies (Cohen et al., 2014; Cohen et al., 2015; Yoon
& Im, 2020) estimate that the fraction of star-forming galaxies is $20-30\%$
higher in merger clusters than in relaxed clusters. The median $f_{\rm SF}$
for clusters with merger activity ($0.148\pm 0.016$) in our sample is $\approx
23\%$ higher than the relaxed clusters ($0.120\pm 0.011$) for all star-forming
galaxies within $R_{\rm 200}$. The difference rises to $\approx 34\%$ for all
star-forming galaxies within 2$R_{200}$ between merger clusters ($0.225\pm
0.019$) and relaxed clusters ($0.168\pm 0.012$). The $1\sigma$ errorbars are
calculated using bootstrap resampling of the SF galaxies in the clusters.

Figure 5: Total SFR in MGCLS clusters plotted against their cluster masses.
Clusters with extended radio emission linked to merger activity are plotted in
black markers (Clusters hosting only haloes are plotted in dots, those hosting
haloes and relics are in upward-facing triangles and the ones with only relics
and a phoenix are in diamonds and squares respectively). Relaxed clusters are
plotted in orange markers (relaxed clusters with no diffuse emission are shown
in star markers and the mini-halo is indicated by a downward-facing triangle).
The error bars indicate $1\sigma$ uncertainties. The median values for relaxed
and merger clusters are shown by the X-shaped markers with bootstrapped
resampled errorbars. The blue line shows the least-squares line of best fit
derived from the full cluster sample between the mass limits
$4.19<M_{200}(10^{14}M_{\odot})<28.13$ Figure 6: The Evolution of
$\Sigma(\text{SFR})/M_{200}$ \- redshift relation among cluster LIRGs. The
blue diamonds indicate the total SFR normalised by the cluster mass for all
the cluster LIRGs within $R_{200}$ for each MGCLS cluster as a function of
redshift. The purple triangles indicate the averaged values for the MGCLS
clusters in four redshift bins in steps of 0.5. There are 4 clusters at
$0.15<z<0.20$, 6 clusters at $0.20<z<0.25$, 4 clusters at $0.25<z<0.30$ and 5
clusters at $0.30<z<0.35$. We use bootstrap resampling in the
$\Sigma(\text{SFR})/M_{200}$ scatter of clusters in each bin to estimate
$1\sigma$ uncertainties. The Ha13 clusters are indicated by black rings and
their redshift binned average values are shown in green squares. Ha13 also
included the analysis of local clusters at $0.02<z<0.05$ shown by the green
triangle. The black and magenta squares are from the Po12 clusters and groups
respectively which are made up of composite systems from GOODS, COSMOS and
individual systems. The black star indicates the merging Bullet cluster also
from Po12. The black curve shows the best fit $\Sigma(\text{SFR})/M_{200}$
relation for the Po12 cluster sample excluding the Bullet cluster and the
magenta curve shows the relation for the group/poor clusters sample. The Po12
clusters and groups best-fit lines were deduced from their study of clusters
and groups at $0.1<z<1.6$. For our study, we plot the Po12 best-fit lines at
the part that highlights our redshift slice.

To investigate if our results could have a hidden dependence on cluster mass
since all relaxed clusters in our sample have masses below the median mass, we
divided our sample into two mass bins split by median mass ($1.09\times
10^{15}\,M_{\odot}$). The right panel of Figure 4 shows the $f_{\rm SF}$
trends for 10 clusters below the median mass split by their dynamical state,
with 5 relaxed clusters (green circles) and 5 clusters with radio
haloes/relics (brown diamonds). The remaining 10 clusters above the median
mass host radio haloes/relics are shown in blue stars. The $f_{\rm SF}$ trend
of merger-linked clusters below the median mass shows more SF activity than
seen in the trend of the relaxed clusters in the same mass bin, roughly
consistent with the $f_{\rm SF}$ trend of merger-linked clusters in the higher
mass bin. This enhanced SF activity in merger-linked clusters below median
mass is also evident in Figure 5 which is discussed in the following section.

We notice similar $f_{\rm SF}$ trends within $1\sigma$ between clusters that
host only haloes and the clusters that host only relics and those with both
relics and haloes in our sample.

###  3.2 SFR – $M_{200}$ relations

####  3.2.1 Total star formation rates versus cluster mass

To investigate how our cluster sample SFR relates with cluster mass, we summed
the SFR for member galaxies within $R_{200}$ and plotted them against cluster
masses as shown in Figure 5. The clusters that have been identified to have
merger-related extended radio emission are plotted in black markers and
relaxed clusters are plotted in orange markers. Figure 5 shows that the total
SFR correlates not only with cluster mass but is also dependent upon the
dynamical state of the cluster. This result is consistent with recent claims
that mergers enhance SF activity in clusters at low redshifts (e.g., Cassano
et al., 2013; Cohen et al., 2014; Stroe & Sobral, 2021). We observe a marginal
difference (within $3\sigma$) between median values for mass normalised total
SFR in relaxed clusters ($21.5\pm 1.9$ M⊙yr-1/$10^{14}$M⊙) and clusters with
merger activity ($26.1\pm 1.6$ M⊙yr-1/$10^{14}$M⊙). The errors on the median
values were estimated from bootstrap resampling.

####  3.2.2 Star formation activity per unit cluster mass

A number of recent studies have examined the evolution of SF activity with
redshift in clusters by using the total SFR per cluster mass for clusters
hosting luminous infrared galaxies (LIRGs) (e.g., Popesso et al., 2012; Haines
et al., 2013; Webb et al., 2013). This is done by summing the SFR of
individual galaxies that are confirmed to be members within $R_{200}$ for each
cluster and normalising it by $M_{200}$, $\Sigma(\text{SFR})/M_{200}$. This
approach enables the comparison of SF activity for clusters with different
masses. Although methods employed by the various studies to define cluster
properties differ from one another, including this one, they all consistently
come to the conclusion of a rapid decline in SF activity within clusters with
decreasing redshift.

To understand the evolution of SF activity within our sample, we follow the
analysis of Popesso et al. (2012), hereafter Po12, which studies the
$\Sigma(\text{SFR})/M_{200}$ – redshift relation for LIRGs in rich/massive
clusters and groups/poor clusters at $0.1<z<1.6$ using infrared luminosities
from Herschel/PACS 100$\mu$m and 160$\mu$m. Following Po12, we summed up the
SFR of all the MeerKAT galaxies with SFR values above the LIRG luminosity
limit corresponding to $L_{\rm 1.4GHz}\approx 3.14\times 10^{22}\,W$ Hz-1 or
10 M⊙yr-1 in SFR for each of the 20 clusters in our sample. All clusters in
our sample contain at least one LIRG within $R_{200}$. Figure 6 shows a plot
of $\Sigma(\text{SFR})/M_{200}$ – redshift relation for our sample including
results from Po12 scaled down by 1.74 from the Salpeter IMF to Chabrier IMF.
Figure 6 includes results from Haines et al. (2013), hereafter Ha13, which
also followed the Po12 study of LIRGs at $0.15<z<0.3$ using infrared
luminosities from Spitzer/MIPS 24$\mu$m. It is worth noting that there are
differences in cluster mass estimation methods between our study and both the
Po12 and the Ha13 studies. The Po12 study uses dynamical mass estimates
derived from optical spectroscopy and the Ha13 study relies on X-ray-derived
masses. This means that for clusters that are common among the studies, the
total SFR within $R_{\rm 200}$ would be estimated out to different radii, due
to differences in the mass measurements between the studies. None of the
clusters in our sample overlap with the Po12 cluster sample and only one
cluster from our sample (Abell 209) appears in the Ha13 study. The
$\Sigma(\text{SFR})/M_{200}$ value for Abell 209 from Ha13 is $\approx 7.1$
M⊙yr-1/$10^{14}$M⊙. This is within $1.5\sigma$ of our estimated value for the
same cluster, ($10.99\pm 2.69$) M⊙yr-1/$10^{14}$M⊙.

We estimate the overall evolutionary trend by dividing our cluster sample into
four redshift bins as indicated by the purple triangles in Figure 6. We
observe a $\approx 4\times$ decline in the level of SF activity per cluster
mass in MeerKAT clusters in contrast to the $\approx 5\times$ decline seen by
Ha13 in green squares over the $0.15<z<0.3$ redshift slice. Just as observed
in Ha13, we also see a decline in the number of cluster LIRGs with redshift
bins, reducing from 87 LIRGs in 5 cluster systems at $0.3<z<0.35$ to 10 LIRGs
in 5 systems at $0.15<z<0.20$.

Figure 6 includes the $\Sigma$(SFR)/$M_{\rm 200}$ of the Bullet cluster from
Po12 (indicated by the black star), which is known to have an ongoing violent
merger. The Bullet cluster has a higher $\Sigma$(SFR)/$M_{\rm 200}$,
consistent within errorbars with the clusters in our sample, most of which
host extended radio emission linked to merger activity. Even with noted
differences in our study and those from other authors, the evolutionary trend
for MGCLS clusters also indicate that there is a rapid decline in star
formation activity among cluster galaxies at lower redshifts, roughly
consistent with observations made by Po12 and Ha13.

##  4 Discussion

In the previous section, we studied the effect of cluster dynamical state on
the SF activity of galaxies in relaxed clusters and clusters with merger-
linked extended emission. Our results infer that clusters with merger-linked
extended emission have enhanced SF activity compared to relaxed clusters. We
estimate a $23\%$ higher SF activity in clusters with radio haloes and/or
relics within $R_{\rm 200}$ and $34\%$ out to 2$R_{\rm 200}$. We note that our
dynamical state subsamples are unevenly distributed across the full sample
redshift range as shown in Figure 1. The relaxed clusters fall within the
lower redshift bin while unrelaxed/merger clusters are all above $z=0.2$. The
$f_{\rm SF}$ in clusters has been shown to increase with redshift, forming a
relation known as the Butcher & Oemler (1978, hereafter BO) effect. The BO
effect is the increase in the fraction of blue galaxies in clusters with
redshift. Since our study uses $f_{\rm SF}$ to compare SF activity between
subsamples, we expect some fraction of the differences in the overall cluster
$f_{\rm SF}$ to be due to the BO effect. However, as suggested by this
investigation as well as previous studies that have investigated SF activity
in clusters, the dynamical state of a cluster plays an influential role in its
SF activity. Observing a homogeneous sample (not subject to MGCLS
heterogeneous nature) will allow us to confirm this result and rule out
whether or not the BO effect affected our results and by how much.

Figure 7: The fraction of star-forming galaxies including trends for clusters
split by their MGCLS subsamples. The $f_{\rm SF}$ trend for clusters from the
radio-selected subsample is plotted in orange dots and the trend for clusters
from the X-ray-selected subsample is plotted in cyan dots.

Figure 8: $\Sigma{\rm SFR}$ – $M_{200}$ relation for clusters from the MGCLS
radio-selected (left) and the X-ray-selected (right) subsamples. The open
symbol shows the $\Sigma{\rm SFR}$ – $M_{200}$ for cluster J0225.9-4154
(J0225) at the Planck SZ mass estimate from the Planck Sunyaev-Zeldovich
sources catalogue (PSZ2, Planck Collaboration et al., 2016). The dashed blue
line shows the difference between the $\Sigma{\rm SFR}$ – $M_{200}$ from the
ACT mass estimate and the PSZ2 mass estimate.

Results from our study are consistent with observations made by previous
studies that looked at the effect of cluster dynamical state on SF activity.
Cohen et al. (2014) studied 107 clusters at $0.04<z<0.1$ using the Sloan
Digital Sky Survey (SDSS) and uses substructure within clusters to identify
clusters with multiple substructure components (mergers) from single component
clusters (relaxed). They found merger clusters to have $\approx 30\%$ more SF
activity than relaxed clusters. Yoon & Im (2020) estimates up to $\approx
24\%$ more SF activity within $R_{\rm 200}$ in multiple component clusters
compared to single component clusters from their study of 105 clusters at
$0.015<z<0.060$ using SDSS. The enhanced SF activity in merger clusters has
also been observed by Stroe & Sobral (2021) from their study of H$\alpha$
emitters in 14 clusters at $0.15<z<0.31$.

In contrast to the results of these low-redshift studies, Mansheim et al.
(2017) observed that SF activity may be suppressed in merger clusters from the
study of an individual cluster system at high redshift ($z\approx 1.105$).
More recently, Maier et al. (2022) observed higher SF activity in clusters
with an actively star-forming BCG (indicative of a relaxed cool-core cluster)
than in clusters with passive BCGs (indicative of a non-relaxed cool-core
cluster) using a study of 18 clusters at $0.15<z<0.26$ from the Local Cluster
Substructure Survey (LoCuSS). The Chung et al. (2010) study of the merging
Bullet cluster argues that, depending on the cluster, mergers may not be the
driver for the enhanced SF activity but could be a result of the infalling
galaxy population. Wittman (2019) suggests that claims made by various studies
that cluster mergers suppress, enhance or have no effect on SF activity may
not be conflicting but can be explained by how much time has passed since the
pericenter passage (the age of the merger), the relative velocity at the first
pericenter, and the viewing angle.

We observe a linear correlation between $\Sigma{\rm SFR}$ and cluster mass
($M_{200}$), consistent with results from previous studies (e.g., Goto, 2004;
Popesso et al., 2006). This correlation has been described as a richness
effect, $\Sigma{\rm SFR}\propto{N_{\rm gal}}$, where $N_{\rm gal}$ is the
number of galaxies in a cluster. The number of galaxies in a cluster scales
with cluster mass in that the higher the mass, the higher the number of star-
forming galaxies. Figure 5 shows the linear correlation of $\Sigma{\rm SFR}$
and $M_{200}$. We also observe the contribution of cluster dynamical state to
the $\Sigma{\rm SFR}$, something that was not considered by previous studies.
The contribution of cluster dynamical state is particularly evident along
clusters with mass estimates within $1\sigma$ of each other but with different
relaxation states. This difference is noticeable in clusters within the mass
range $0.8-1.2\times 10^{15}\,M_{\odot}$. There are 8 clusters that fall
within this range and we observe that the median $\Sigma{\rm SFR}$ for relaxed
clusters ($172.3\pm 12.1$ M⊙yr-1) is $\approx 0.5\times$ lower than the one
for clusters with radio haloes and/or relics ($309.2\pm 42.9$ M⊙yr-1).

As described in Section 2.1, the MGCLS catalogue is made up of a combination
of two subsamples. One from the radio-selected subsample (biased towards
extended emission) and the other from the X-ray-selected subsample with no
prior biases towards or against clusters with extended emission but selected
with no redshift or X-ray luminosity criteria followed. Our cluster sample is
biased towards clusters with extended radio emission, albeit equally split
between clusters from each MGCLS subsample. To check our results, we look at
clusters from the X-ray-selected subsample by splitting clusters in our sample
by their MGCLS subsamples and re-plotting Figures 4 and 5.

Figure 7 shows the $f_{\rm SF}$ profiles of our clusters broken down by their
subsample. The radio-selected subsample comprises 9 merger-linked extended
emission clusters and one relaxed cluster in the redshift range $0.15<z<0.35$.
The X-ray-selected clusters subsample is evenly distributed between 5 merger-
linked extended emission clusters and 5 relaxed clusters also in the redshift
range of $0.15<z<0.35$. The radio-selected subsample has an $f_{\rm SF}$ of
$0.253\pm 0.019$ within 2$R_{\rm 200}$ while the X-ray-selected subsample is
$0.241\pm 0.012$ out to the same radius. The $1\sigma$ errorbars are
calculated using bootstrap resampling of the SF galaxies in the clusters. The
radio-selected $f_{\rm SF}$ trend is slightly higher than that of the X-ray-
selected sample and the $f_{\rm SF}$ values lie within $1-1.5\sigma$ between
the subsamples. The observed higher $f_{\rm SF}$ trend of the radio-selected
subsample is likely due to the selection bias towards clusters with haloes
and/or relics, and therefore to massive mergers.

Figure 8 shows the plot of $\Sigma{\rm SFR}$ versus $M_{200}$ for clusters in
our sample separated into each respective subsample. The left panel shows the
plot of the clusters from the radio-selected subsample and the right panel
shows the plot of the clusters from the X-ray-selected subsample. Although
clusters from the X-ray-selected sample is limited in quantity, a correlation
between $\Sigma{\rm SFR}$ and $M_{200}$ is observed in the right panel of
Figure 8. Results from the X-ray-selected clusters are consistent with merger
clusters having higher SF activity than relaxed clusters. Due to the
limitation of a small cluster sample, future observations of a larger sample
will be required to confirm these results.

We observe one halo-hosting cluster, J0225.9-4154 (J0225 hereafter), that has
a $\Sigma{\rm SFR}$ profile of relaxed clusters at its mass on the X-ray
subsample. Dynamical state studies of J0225 reveal that it is an interesting
binary cluster system of two merging clusters (A3017 and A3016) connected by
an X-ray filament (see Foëx et al., 2017; Parekh et al., 2017; Chon et al.,
2019, for detailed reviews of the on-going merger). Dynamical studies show
that J0225 is a face-on merger at its early stage with multiple substructures
within its virial radius. The dynamical mass estimate ($M_{200}$) for J0225
according to Foëx et al. (2017) is $18.6\begin{subarray}{c}+2.6\\\
-2.0\end{subarray}\times 10^{14}\,M_{\odot}$ but after accounting for the
substructure in the line of sight they obtain an estimate of
$8.4\begin{subarray}{c}+1.3\\\ -1.5\end{subarray}\times 10^{14}\,M_{\odot}$.
Their estimate is in good agreement with the mass estimate from the Planck
Sunyaev-Zeldovich sources catalogue (PSZ2, Planck Collaboration et al., 2016)
re-scaled to $M_{200}$, $8.9\pm 0.4\times 10^{14}\,M_{\odot}$. The Foëx et al.
(2017) and the PSZ2 mass estimate for J0225 are approximately double the ACT
mass estimate ($4.8\begin{subarray}{c}+1.2\\\ -1.0\end{subarray}\times
10^{14}\,M_{\odot}$) but fall within $3\sigma$ of each other. The right panel
of Figure 8 includes the data point for $\Sigma{\rm SFR}$ at the PSZ2 mass
estimate for J0225 and shows the difference in $\Sigma{\rm SFR}$ between the
two mass estimates of the cluster. The $\Sigma{\rm SFR}$ from the PSZ2 mass
estimate is higher by a factor of 1.6 and has $R_{200}$ at 1.9 Mpc,
$1.3\times$ higher than $R_{200}$ from the ACT mass estimate. The
extraordinary nature of J0225 raises the need for a multi-wavelength analysis
to get a clear picture of its properties.

##  5 Conclusions

We have studied SF activity in cluster environments at low redshifts
($0.15<z<0.35$) using dust-unbiased radio continuum data from the MGCLS. This
provides the first-look at SFR in clusters using radio data from the MeerKAT
telescope. The investigation of SF activity in and around clusters is crucial
in understanding how galaxies evolve with time in high-density environments
and how the dynamical state of a cluster affects SF activity in galaxies.
Below is the summary of our main results:

  1. 1.

We measure a $f_{\rm SF}$ population trend out to a similar limit at
$2R_{200}$ with the Haines et al. (2015) study, noting a 1-3$\sigma$
difference between the radio SFR and IR SFR data points which is likely due to
the MGCLS selection bias towards merger-linked clusters. Both the radio-
derived and IR-derived $f_{\rm SF}$ are lower than the Haines et al. (2015)
field galaxies $f_{\rm SF}$ even at 2$R_{200}$. This is consistent with the
suggestion that in-falling galaxies may be pre-processed in their prior
environments such as galaxy groups, before they enter cluster environments,
which could explain the lower $f_{\rm SF}$ even at radii over $2R_{200}$.

  2. 2.

There is a difference in SF activity between clusters that host extended radio
emission (relics and haloes) linked to cluster mergers and clusters that are
non-halo/relic hosting, likely to be dynamically relaxed or only minor
mergers. We see the differences in the $f_{\rm SF}$ as well as the $\Sigma{\rm
SFR}$ between merger clusters and relaxed clusters. Merger clusters have a
higher fraction of star-forming galaxies and consequently a higher $\Sigma{\rm
SFR}$ compared to relaxed clusters.

  3. 3.

We find a rapid decline in the SF evolutionary trend among radio-selected
galaxies with SFR corresponding to those of cluster LIRGs in our sample. We
observe a $\approx 4\times$ decline in $\Sigma{\rm SFR}/M_{200}$ from redshift
of 0.35 till 0.15, corresponding to 2 Gyr in lookback time. This observation
is roughly consistent with IR-derived SFR studies by Popesso et al. (2012) and
Haines et al. (2013).

One limitation of this work is that the underlying sample (MGCLS) is
heterogeneous and made up of two subsamples, with one biased towards clusters
with extended emission and the other probing X-ray clusters with no selection
criteria followed. A follow-up study will be conducted in the future using a
catalogue of unbiased cluster samples selected only by mass from the MeerKAT
Exploration of Relics, Giant Halos, and Extragalactic Radio Sources (MERGHERS
program, see Knowles et al., 2021).

## Acknowledgements

We are grateful to the referee (Christopher P. Haines) for their invaluable
comments and suggestions that improved the clarity of the paper. The authors
would like to thank Lawrence Rudnick and Bruce Partridge for useful
discussions that helped to improve the quality of this work. The MeerKAT
telescope is operated by the South African Radio Astronomy Observatory, is a
facility of the National Research Foundation, an agency of the Department of
Science and Innovation. The authors acknowledge the contribution of those who
designed and built the MeerKAT instrument. The National Radio Astronomy
Observatory is a facility of the (US) National Science Foundation, operated
under a cooperative agreement by Associated Universities, Inc.

KK acknowledges funding support from the South African Radio Astronomy
Observatory (SARAO) through the HCD scholarship. Computations were done on the
hippo cluster at the University of KwaZulu Natal.

## Data Availability

The MeerKAT 1.28 GHz radio continuum data is accessed from the MeerKAT Galaxy
Clusters Legacy Surveys (MGCLS222https://archive-
gw-1.kat.ac.za/public/repository/10.48479/data_releases/The_MeerKAT_Galaxy_Cluster_Legacy_Survey_DR1/index.html)
data archive. The data generated in this study will be shared on reasonable
request to the corresponding author and will be made public through the MGCLS
data archive in the future.

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##  Appendix A Legacy Surveys images

Here we present Legacy Surveys DR9 images for our cluster sample and the
identified radio-loud galaxies within $R_{\rm 200}$. See discussion in Section
2.

Figure 9 shows the Legacy Surveys DR9 images of our cluster sample with the
identified MeerKAT-detected cluster members.

Figure 9: Legacy Surveys DR9 images of the 20 clusters with radio detected
galaxies highlighted in small green and red circles representing star-forming
galaxies and radio-loud AGN respectively. The large yellow circles show the
$R_{200}$ of the cluster.