Abell 746: A Highly Disturbed Cluster Undergoing Multiple Mergers

We present deep XMM-Newton, Karl G. Jansky Very Large Array, and upgraded Giant Metrewave Radio Telescope observations of Abell 746, a cluster that hosts a plethora of diffuse emission sources that provide evidence for the acceleration of relativistic particles. Our new XMM-Newton images reveal a complex morphology of the thermal gas with several substructures. We observe an asymmetric temperature distribution across the cluster: the southern regions exhibit higher temperatures, reaching ∼9 keV, while the northern regions have lower temperatures (≤4 keV), likely due to a complex merger. We find evidence of three surface brightness edges and one candidate edge, of which three are merger-driven shock fronts. Combining our new data with published LOw-Frequency ARray observations has unveiled the nature of diffuse sources in this system. The bright NW relic shows thin filaments and a high degree of polarization with aligned magnetic field vectors. We detect a density jump, aligned with the fainter relic to the north. To the south, we detect high-temperature regions, consistent with the shock-heated regions and a density jump coincident with the northern tip of the southern radio structure. Its integrated spectrum shows a high-frequency steepening. Lastly, we find that the cluster hosts large-scale radio halo emission. A comparison of the thermal and nonthermal emission reveals an anticorrelation between the bright radio and X-ray features at the center. Our findings suggest that Abell 746 is a complex system that involves multiple mergers.


INTRODUCTION
In the standard hierarchical structure formation scenario, galaxy clusters are expected to form via a sequence of mergers with subclusters.In this process, the plasma contained within the subclusters collides, form-Corresponding author: Kamlesh Laxmi Rajpurohit kamlesh.rajpurohit@cfa.harvard.edu* Clay Fellow ing shocks and cold fronts.X-ray observations have revealed the evidence of these distinct X-ray surface brightness and temperature discontinuities (Markevitch & Vikhlinin 1997;Markevitch et al. 2005;Markevitch & Vikhlinin 2001;Botteon et al. 2016;George et al. 2017;van Weeren et al. 2016;Di Gennaro et al. 2019).Merger shock fronts travel supersonically and are characterized by a temperature jump (also pressure) with higher temperatures downstream.Cold fronts are observed in both relaxed and merging clusters, characterized by a sudden drop in gas density while the gas temperature rises abruptly, maintaining pressure balance across the front (Markevitch & Vikhlinin 2001;Breuer et al. 2020).
Mergers between galaxy clusters can also be detected in the radio band through synchrotron emission originating from steep spectrum1 (α ≤ −1) diffuse sources that are directly associated with the intracluster medium (ICM).Recent rapid improvements in radio telescope sensitivity and resolution are revealing unprecedented structures, previously undetected, and complexity in the ICM (e.g., Bonafede et al. 2021;Brienza et al. 2021;Botteon et al. 2022a;Knowles et al. 2022;Rajpurohit et al. 2022a;Rudnick et al. 2022;Ramatsoku et al. 2020;de Gasperin et al. 2022).Classically these structures include 1) radio relics, which are produced by mergerinduced shock waves, 2) radio halos, produced by turbulence, and 3) radio emission from aged cosmic-ray electrons (CRe) which can be re-energized by several processes, likely related to the dynamics of the ICM (for theoretical and observational reviews, see Brunetti & Jones 2014;van Weeren et al. 2019).
Radio relics are elongated radio sources, typically found in the outskirts of merging galaxy clusters, and they often show irregular surface brightness and filamentary morphology (Owen et al. 2014;van Weeren et al. 2017a;Rajpurohit et al. 2018;Di Gennaro et al. 2018;Rajpurohit et al. 2022a;de Gasperin et al. 2022).One notable characteristic of relics is strong polarization at GHz frequencies and magnetic field vectors along the merger axis of the relic (e.g., Bonafede et al. 2012;van Weeren et al. 2010;Kierdorf et al. 2017;Stuardi et al. 2019;Rajpurohit et al. 2020a;Loi et al. 2021;Rajpurohit et al. 2022b).Relics are believed to be produced by the Diffusive Shock Acceleration (DSA) mechanism (Blandford & Eichler 1987;Drury 1983;Dolag & Enßlin 2000;Hoeft & Brüggen 2007).However, this model suffers from the efficiency problem, that is, the energy dissipated by merger shocks is not enough to reproduce the luminosity of the relics via DSA if particles are accelerated directly from the thermal pool (van Weeren et al. 2016;Botteon et al. 2020).
As a remedy, shock re-acceleration or multiple-shock scenarios have been proposed (Kang & Ryu 2016;Kang 2016Kang , 2021;;Inchingolo et al. 2021).In the first scenario, a shock front re-accelerates electrons via DSA from an existing population of relativistic electrons (Markevitch et al. 2005;Kang & Ryu 2016).There are a few examples that appear to show a connection between relics and lobes/tails of active galactic nuclei (AGN), as a possible source of fossil electrons (e.g., Bonafede et al. 2014;van Weeren et al. 2017b;Stuardi et al. 2019;Shimwell et al. 2015;HyeongHan et al. 2020).In the second scenario, the relics are generated by multiple shocks induced in the turbulent ICM.Both shock reacceleration and multiple-shock scenarios could alleviate the efficiency problem (e.g.Pinzke et al. 2013;Kang 2021;Inchingolo et al. 2021).
Unlike relics, radio halos are centrally located and extend throughout the cluster's volume.They are found in merging clusters and often show a correlation with the X-ray emission, suggesting a strong link between thermal and nonthermal plasma components (e.g., Govoni et al. 2001;van Weeren et al. 2016;de Gasperin et al. 2020;Bonafede et al. 2022;Botteon et al. 2020;Rajpurohit et al. 2021aRajpurohit et al. ,b, 2023)).The turbulent re-acceleration models provide the most promising explanation for their origin, where cosmic-ray electrons (CRe) become radioemitting after undergoing re-acceleration through turbulence injected into the ICM during cluster mergers (Brunetti et al. 2001;Fujita et al. 2003;Cassano & Brunetti 2005;Brunetti & Lazarian 2011;Miniati 2015;Pinzke et al. 2017).
In this paper, we present the results of the combined XMM-Newton and radio analysis of the galaxy cluster Abell 746.The new radio observations were performed with the upgraded Giant Metrewave Radio Telescope (uGMRT) at Band4 (550-750 MHz) and the Karl G. Jansky Very Large Array (VLA) at L-band (1-2 GHz).We also used published LOw-Frequency ARray (LO-FAR;van Haarlem et al. 2013) High Band Antenna (HBA) observations (Botteon et al. 2022a).
The layout of this paper is as follows.In Section 2, we present an overview of the observations and the reduction of data.The new X-ray and radio images are presented in Section 3. The results obtained are described in Sections 3 to 6, followed by a summary in Section 7. Throughout this paper, we adopt a flat ΛCDM cosmology with H 0 = 69.6 km s −1 Mpc −1 , Ω m = 0.286, and Ω Λ = 0.714 (Wright 2006).At the cluster's redshift, 1 ′′ corresponds to a physical scale of 3.73 kpc.

XMM-Newton
Abell 746 was recently observed four times (ObsIDs: 0902630101, 0902630201, 0902630301, 0902630601) by XMM-Newton (PI: C. Jones) with a total exposure time of ∼ 184 ks.Given that the last pointing is significantly shorter (i.e., ∼10 ks) than each of the other three pointings (i.e., >55 ks), we did not include it in the current analysis.
Observation data files were processed with the XMM-Newton Science Analysis System (SAS) v20.0.0.We generated calibrated event files from raw data by running the tasks emchain and epchain.Then we excluded all events with PATTERN>12 for MOS data and with PATTERN>4 for pn data, and we followed the standard procedures for bright pixel and hot column removal (by applying the expression FLAG==0) and pn out-of-time correction.The data were cleaned for periods of high background induced by solar flares using the XMM-ESAS tools mos-filter and pn-filter.The total exposure times after cleaning are 156.8ks for MOS1, 158.1 ks for MOS2, and 104.2 ks for pn.Additionally, we also excluded from the analysis all the CCDs in the socalled 'anomalous state' (see Kuntz & Snowden 2008 for more details).Point sources, identified by running the task edetect-chain, were excluded from the analysis.All the background event files were cleaned by applying the same PATTERN selection, flare rejection criteria, and point-source removal as used for the observation events.
All X-ray images presented in this work were obtained in the 0.7-2 keV band with a binning of 40 physical pixels (corresponding to 2 arcsec) and by refilling the pointsource regions using the CIAO task dmfilth.The surface brightness profiles discussed in Section 4.3 are extracted from a point source subtracted X-ray image with no refilling of point sources.

VLA
We observed the cluster with the VLA in the L-band (1-2 GHz) in 2022 and 2023 in C and B configurations (PI: C. Jones), respectively.For observational details, see Table 1.All four polarization products (RR, RL, LR, and LL) were recorded.In the L-band, for both C and B configurations, 3C147 was included as the primary calibrator, observed for 5-10 minutes at the start of each observing run.The radio source J0834+5534 was included as a phase calibrator and 3C286 was a polarization calibrator.
The data were calibrated and imaged with the Common Astronomy Software Applications (CASA; McMullin et al. 2007;CASA Team et al. 2022) package.Data obtained from C and B configurations were calibrated separately, but in the same manner.The data reduction steps consisted of Hanning smoothing followed by RFI inspection.The bad data were flagged using tfcrop mode from the flagdata task.For target scans, we performed additional flagging using AOFlagger (Offringa et al. 2010).After this, we determined and applied elevation-dependent gain tables and antenna offset positions.We corrected the bandpass using 3C 147.This prevents the flagging of good data due to the bandpass roll-off at the edges of the spectral windows.
We used the L-band 3C147 and 3C286 models provided by the CASA software package and set the flux density scale according to Perley & Butler (2013).An initial phase calibration was performed using both calibrators over a few channels per spectral window.The antenna delays and bandpass response were determined using 3C147, followed by the gain calibration.
For polarization, the leakage response was determined using the unpolarized calibrator 3C147.Finally, the absolute position angle in the sky (the R-L phase difference) was corrected using the polarized calibrator 3C286.All calibration solutions were applied to the tar- get field.The resulting calibrated data were averaged by a factor of 4 in frequency per spectral window to perform rotation measure synthesis (RM-synthesis).
After initial calibration and flagging, several rounds of self-calibration were performed further to refine the calibration for each individual data set.Imaging were done employing the W-projection algorithm in CASA (Cornwell et al. 2008).Clean masks were used for each imaging step.These masks were made using the PyBDSF source detection package (Mohan & Rafferty 2015).The spectral index and curvature were taken into account during deconvolution using nterms = 3 (Rau & Cornwell 2011).
After self-calibration, the C and B configurations data were combined.Final imaging of the combined data sets was done in WSClean (Offringa et al. 2014), using Briggs weighting and employing the wideband and multiscale algorithms.The images were corrected for the primary beam attenuation in CASA.

uGMRT
The cluster was observed with the upgraded GMRT in Band 4 (project code: 40 025, PI: A. Botteon) using the GMRT Wideband Backend (GWB) covering a frequency range of 550-750 MHz.The observations were carried out on May 6, 2021.In Table 1, we summarize the observations.Sources 3C48 and 3C147 were included as flux and phase calibrators.
The wideband GMRT data were processed using the Source Peeling and Atmospheric Modeling (SPAM; In-tema et al. 2009) pipeline2 .For details about the main data reduction steps, we refer to Rajpurohit et al. (2021b).In summary, the data were first split into six sub-bands.The flux densities of the primary calibrators were set according to Scaife & Heald (2012).Following flux density scale calibration, the data were averaged, flagged, and corrected for bandpass.We started selfcalibration with a global sky model obtained with the GMRT narrow-band data.To produce deep full continuum images, the calibrated sub-bands were combined.The final deconvolution was performed in WSClean using multiscale and Briggs weighting.

LOFAR
Abell 746 was observed with LOFAR HBA as part of the LOFAR Two-metre Sky Survey (LoTSS; Shimwell et al. 2017Shimwell et al. , 2019Shimwell et al. , 2022)).The observations were conducted in HBA dual inner mode.To summarize, data reduction and calibration were performed with the LoTSS DR2 pipeline (Tasse et al. 2021) followed by a final "extraction+self-calibration" scheme (van Weeren et al. 2021).Since Abell 746 is a PSZ2 cluster in the LO-FAR DR2 data release (Botteon et al. 2022a), we used the same calibrated data.For a detailed description of the observation and data reduction, we refer to Botteon et al. (2022a).Table 2, IM1.
The overall flux scale for all observations (LOFAR, uGMRT, and VLA) was verified by comparing the spectra of compact sources within the field of view between 144 MHz and 2 GHz.The uncertainty in the flux density measurements was estimated as where f is the absolute flux density calibration uncertainty, S is the flux density, σ rms is the RMS noise, and N beams is the number of beams.We assumed absolute flux density uncertainties of 10% for LOFAR HBA data (Shimwell et al. 2022), 5% for uGMRT Band 4, and 2.5% for the VLA data (Perley & Butler 2013).
The flux density values and the overall extent of the radio emission are extracted/measured, unless specified otherwise, in regions where the emission is ≥ 3σ.All output images are in the J2000 coordinate system and are corrected for primary beam attenuation.

X-ray Emission
In Figure 2, we present the combined, backgroundsubtracted, exposure-corrected, Gaussian-smoothed (6 ′′ ) 0.7−2.0keV XMM-Newton surface brightness map.All compact sources are subtracted except for a bright source, shown with cross marks.The disrupted X-ray morphology in the center, featuring several substructures, is clearly visible.The X-ray emission from the cluster is asymmetrical, with a roughly triangular morphology, see Figure 2. The central bright region of the cluster appears elongated along the southeast to northwest direction.The cluster does not exhibit a single surface brightness concentration instead, it reveals multiple distinct concentrations.Similar to the distribution observed in other complex clusters such as MACS J0416.1-2403(Ogrean et al. 2015) and MACS J0717.5+3745 (van Weeren et al. 2017b), it shows distinct features in the inner region.Moreover, the cluster X-ray center cannot be identified by its mor-phology.The brightest part of the ICM consists of a "Vshaped" structure which suggests some ongoing dynamical process in this cluster.A similar type of structure is seen in the multi-merger cluster MACS J0717.5+3745(van Weeren et al. 2017b).
The X-ray emission to the southwest shows a clear "concave-bay" morphology which extends from southwest to southeast, see Figure 2.This structure is apparently similar to the one reported in Abell 2256, known as 'shoulder' cold front (Sun et al. 2002;Breuer et al. 2020;Ge et al. 2020).To the southeast, there is a surface brightness decrement, followed by a curved X-ray substructure, labeled as the arc.Table 3. Properties of the diffuse radio sources in the cluster Abell 746.
Notes.Flux densities were extracted from images created with robust = −0.5 and a uv -cut of 0.1kλ.The image properties are given in Table 2, IM4, IM8, and IM14.The regions where the flux densities were extracted are indicated in the Figure 7. Absolute flux density scale uncertainties are assumed to be 10% for LOFAR, 5% for the uGMRT Band4, and 2.5% for the VLA L-band data.† The LLS measured at 144 MHz; ⋆ The integrated spectral index obtained by fitting a single power-law fit.

Radio emission
In Figure 3, we show the high (left panel) and lowresolution (right panel) radio images of the cluster using VLA, uGMRT, and LOFAR observations.The high radio surface brightness of the northwest relic allowed its detection at all observed frequencies in the highresolution images, while other features are not prominently visible due to their lower surface brightness.The northwest relic has the largest linear size (LLS) of 1.1 Mpc, 1.4 Mpc, and 1.8 Mpc at 1.5 GHz, 650 MHz, and 144 MHz, respectively.The NW relic's southwest tip displays diffuse emission that extends progressively towards lower frequencies, see Figure 3 right panel.Additionally, the northwest relic appears wider as the frequency decreases, measuring 260 kpc at 1.5 GHz and 600 kpc at 144 MHz.This behavior is a characteristic feature of relics and is attributed to the cooling of electrons in the downstream region of the shock front (e.g., Markevitch et al. 2005;van Weeren et al. 2016;Rajpurohit et al. 2020b).
In the high-resolution images, the NW relic shows two distinct, bright parallel filaments, which appear broken or fragmented, similar to the Sausage relic (Di Gennaro et al. 2018) and the double threads in the Toothbrush relic (Rajpurohit et al. 2018(Rajpurohit et al. , 2020b)).Highresolution observations often reveal filamentary features in radio relics.These filaments could be tracing the complex shock morphology, the underlying magnetic field or MHD turbulence (Domínguez-Fernández et al. 2019;Wittor et al. 2021Wittor et al. , 2023)).Alternatively, they can be related to AGN bubbles buoyantly transported outside and -at some point-crossed and compressed/stretched by a shock.At the southwest edge of the relic, there exists a compact source; however, its morphology does not suggest any connection to the NW relic.
The low-resolution images have a common resolution of 20 ′′ (in Figure 3 right).R2 is only detected at 144 MHz, and R1 is detected at all the observed frequencies.Morphologically, R1 and R2 appear disconnected, suggesting that they are very likely two separate structures.
R3 is situated symmetrically to the northwest relic, suggesting the possibility of it being a double relic system.The LLS of R3 at 144 MHz is 950 kpc.We determined the size from a high-resolution LOFAR map to prevent potential contamination from the low surface brightness halo emission.In Figure 4 left panel, we present the Subaru/Hyper-Suprime Cam (HyeongHan et al. 2023) zoom-in view of R3 with 144 MHz radio contours overlaid.There are 10 bright spots within R3 (shown with circles).The absence of optical counter-parts, associated with bright spots within R3, is indicated by the dashed cyan circles.The compact nature of the southwest tip of R3 suggests that it might be the core of a tailed-angle galaxy.However, we did not find any optical counterpart.Additionally, the morphology of the radio emission does not resemble that of a tailed radio galaxy.Since an elliptical galaxy in the cluster should be easily detectable at that core, this rules out that R3 is a tailed galaxy.
At 1.5 GHz, 650 MHz and 144 MHz frequencies, there is evidence of diffuse low surface brightness emission that appears to extend in the north-to-south direction, see Figure 3 right panel for labeling.It has an LLS of 1 Mpc at 1.5 GHz and 1.7 Mpc at 650 MHz.We emphasize that above 650 MHz, R3 is apparently separated from the low surface brightness emission.At 144 MHz, this emission is further extended filling the central region, and is apparently connected to R3.Based on its location, combined with its low surface brightness, we suggest that it is likely a radio halo.The spectral analysis in Section 4.5 rules out the possibility of the halo being the tail of R3.Since the halo emission is visible in high-resolution images, this allows us to decide the rough boundary of the halo and R3 (dashed line in Figure 3 right-bottom).In our high-frequency images, we also detected at least 40 discrete sources within the central region of the cluster.

X-ray: general properties
Due to the highly disturbed X-ray morphology of the cluster, the assumptions of equilibrium and spherical symmetry are not valid.As a result, obtaining the cluster's mass using the X-ray properties is not straightforward.Hence, we estimated the mass from the average cluster temperature using the relations from Lovisari et al. (2020).Our estimated cluster mass M = 3.0±0.1×10 14M ⊙ was derived considering the temperature within R 500 .The estimated mass differs moderately from the mass obtained by SZ measurements which is M 500 = 5.34 +0.39  −0.40 × 10 14 M ⊙ (Planck Collaboration et al.

2016).
The centroid shift (w) and concentration parameter (c) are among the most robust morphological parameters used to characterize the dynamical state of galaxy clusters (e.g., Lovisari et al. 2017).The centroid shift measures the standard deviation of the projected separation between the X-ray peak and the centroid of the X-ray emission within different apertures.Low (high) w values point to a relaxed (disturbed) system.The concentration parameter measures the ratio between the X-ray surface brightness within two different aper- tures.A higher concentration parameter implies a more centrally concentrated X-ray emission, while a lower value indicates a more extended distribution.The w(< R 500 ) = 0.078 and c=SB(<0.1R500 )/SB(< R 500 )=0.074measured for the cluster place the cluster in the bottom right quadrant of the c − w diagram (Cassano et al. 2010), a region known to be mainly associated with clusters hosting radio halos.

Gaussian gradient magnitude filter and unsharp mask images
Gaussian Gradient Magnitude (GGM) filtering images and unsharp masking serve as powerful tools for identifying regions with surface brightness edges, displaying pronounced and abrupt changes in brightness, or detecting substructures (Sanders et al. 2016;Walker et al. 2016).Applying the GGM filter to the 0.7 − 2.0 keV band XMM-Newton image of Abell 746 reveals the pres- ence of notable surface brightness features in the eastern, western, and central regions, as shown in Figure 5.The most prominent structures are characterized by triangular and bay-shaped edges, for labeling see Figure 5.The bay structure extends approximately 500 kpc in length.However, the presence of a bright X-ray point source prevents us from determining whether it forms a continuous edge or not.
To the southeast of the cluster is a triangle-shaped edge (SB1), clearly seen in the original X-ray image.It is approximately 700 kpc large in size.The north side of the cluster shows inner edges, see Figure 5.At the north and northwest, where the data quality is poorer, are long linear edges, labeled outer edges.The northern edge is coincident with the edge of R1.To the southwest of the bay structure, there seems to be a blob-like feature.
The unsharp-masked image of the cluster generated by subtracting images convolved with σ 1 = 2 ′′ and σ 2 = 12 ′′ Gaussian is shown with overlaid LOFAR 144 MHz contours in Figure 6.The image highlights the presence of the same four distinct features, which were already evident in the GGM-filtered images.The northeast tip of R3 seems to be confined within the positions of the two inner edges.There is an apparent anti-correlation between the bright radio and the X-ray features.

Surface brightness profiles
The examination of the GGM-filtered and unsharp mask images already provides initial evidence of potential discontinuities in Abell 746.To confirm the presence of surface brightness discontinuities, we analyze the surface brightness profiles in sectors around the features seen in GGM-filtered and unsharp mask images and at the location of R1, R2, and R3.The XMM-Newton point-source masked (without dmfilth) exposure corrected image was used to extract surface brightness profiles.We used Pyproffit (Eckert et al. 2020) to extract and fit the surface brightness profiles.Following the work of Markevitch & Vikhlinin (2007), the surface brightness profiles were fitted using broken power-law density models across the edges.The model assumes that the X-ray emissivity is proportional to the density squared and can be used to describe a density jump linked to a shock or cold where α 1 and α 2 define the slopes of the power-laws and the subscripts 1 and 2 denote the upstream and downstream regions, respectively.The electron density jump is characterized by the parameter C = n 2 /n 1 .The n 0 is a normalization factor, r denotes the radius from the center of the sector, and r i is the position of the jump.
In the case of a shock, n 2 /n 1 is related to the Mach number (M) and can be determined by using the Rankine-Hugoniot jump condition where γ is the adiabatic index of the gas and is assumed to be 5/3 (i.e., a monoatomic gas).Using the canonical shock jump conditions for temperature, the nature of surface brightness discontinuities and M can be obtained through the following relation where T 1 and T 2 represent the upstream and downstream temperatures, respectively.In cases where the ratio T 1 /T 2 > 1, this indicates the presence of a shock front.Conversely, when T 1 /T 2 < 1, it implies the occurrence of a cold front.As shown in Figure 8, XMM-Newton surface brightness profiles reveal the presence of four edges.Blue and red lines are best fitting broken power-law and single power law models, respectively.Residuals on the bottom are from broken power law fits.The sectors where the profiles were fitted and the positions of the relative edges are in Figure 7 right panel.
model reveals the presence of a density jump at four edges, see Table 4.For SB1, we find that C = 1.27 ± 0.12 and a temperature jump from T 1 = 3.18 +0.45  −0.35 to T 2 = 3.78 +0.41 −0.37 .This suggests the presence of a shock front.For SB2 and SB4, we measure C = 1.48 ± 0.28 and C = 1.6 ± 0.6, respectively.The low counts do not allow us to derive the pre and post temperatures at SB4.However, the density jump is detected at the northern edge of R1 suggesting a shock with M S = 2.4 ± 0.8.
For the southwest edge (SB3), we find that the surface brightness jump is not that significant, see Table ??.Moreover, the GGM-filtered and unsharp mask images show other arc-like features, as shown in Figures 5 and  6, labeled inner and outer edges, however, we do not find a discontinuity in the SB profile fitting.

ICM temperature distribution
Abell 746 is a very disturbed cluster, therefore a standard radial profile analysis would only provide a partial view of the temperature distribution.We there-  fore investigated its 2-dimensional spectroscopic properties.To this end, we subdivided the R 500 volume into small regions from which spectra were extracted.The regions were obtained using the Weighted Voronoi Tessellation (WVT) binning algorithm by Diehl & Statler (2006), which is a generalization of the Cappellari & Copin (2003) Voronoi binning algorithm, by requiring a signal-to-noise S/N ∼ 30, which allowed us to estimate the temperature with a statistical uncertainty of 10-20% (see Lovisari & Reiprich 2019, for more details).
The resulting temperature map, with overlaid X-ray and radio contours, along with the corresponding uncertainties, is shown in Figure 9.The disturbed morphology of the cluster is highlighted by the temperature variation, in particular in the core region (within 2-3 ′ ).Despite the 'global' temperature of the cluster being 4 keV, it is not isothermal at this temperature.We find that the cluster shows an asymmetric temperature distribution; the southern part of the cluster appears to have higher temperatures than the northern region (≤ 4 keV).The temperature at the northern tip of R3 is the highest, reaching 9 keV.A possible explanation for this could be a shock front, which leads to the heating of the ICM.The presence of a 0.9 Mpc elongated diffuse source (i.e., R3) further supports this hypothesis.
The V-shaped region has a temperature of kT ∼ 5 keV which is hotter than its immediate surroundings.To the west of the V-shaped region, the temperature decreases kT ∼ 3.5 keV.There is tentative evidence suggesting that a large region, located southeast of the SB1 edge, exhibits lower temperatures, see Figure 9 left panel.The same trends are observed for SB3.

Integrated radio spectra
We combined our new uGMRT and VLA observations with published LOFAR HBA data (Botteon et al. 2022b) to investigate the spectral characteristics of the diffuse radio sources in the field.We created images with a common inner uv-cut of 100λ chosen as the minimum well-sampled baseline in the uGMRT Band4 data.This ensures we recover the flux density on the same spatial scales at all observed frequencies.It is a known fact that different resolution and imaging weighting schemes bias the flux density measurements (e.g., Stroe et al. 2016;Rajpurohit et al. 2018).Therefore, we imaged each data set at a common resolution and with robust = −0.5.
In Figure 10 left, we show the integrated spectra of NW, R1, R3, and the halo.The regions used for flux density extraction are shown in the right panel.The overall spectrum of the NW relic and R1 can be described by a simple power law within the frequency range of 144 MHz to 1.5 GHz.In the stationary shock approximation (i.e., the cooling time of electrons is considerably shorter than the timescale on which the shock strength or geometry changes), the integrated spectrum, α int , is steeper than the injection spectrum α inj , Moreover, the integrated index is related to the Mach number of the shock as (Blandford & Eichler 1987): Simulations have consistently shown that the slope of the radio spectrum exhibits non-linear features for nonplanar shocks, such as spherically expanding shocks (e.g., Kang & Ryu 2016).This is because these shocks are expanding into a medium with decreasing density and temperature.In multifrequency radio observations, the majority of relics exhibit a power law behavior across a wide frequency range and adhere to the stationary shock condition (Rajpurohit et al. 2020b,a;Loi et al. 2021;Rajpurohit et al. 2021c).The integrated spectral index of the NW relic is −1.26 ± 0.04 and for R2 −1.35 ± 0.07.Like other well-known relics, sources NW and R1 in Abell 746 follow the stationary state shock condition.Using Equation 5, we obtained a Mach number of M N W = 2.9 +0.3 −0.1 and M R1 = 2.6 ± 0.2.Our XMM-Newton data indicates the presence of a discontinuity that aligns with R1.The X-ray Mach number obtained from the density jump is M R1,X−ray = 2.4 ± 0.8, which agrees within uncertainties with the radio determined Mach number.
To extract the flux density of R3, we subtracted the contribution from compact sources marked in Figure 10  right panel.Additionally, we subtracted the flux density of three compact regions within R3 (marked with cyan circles in Figure 4) that do not show any optical counterparts.The integrated spectrum of R3 exhibits a high-frequency steepening, rather than a power law.Its low-frequency spectral index is −1.6 ± 0.1, while the high-frequency one is −2.5 ± 0.2.It is possible that R3 is observed in projection with the halo emission, resulting in its contribution to the total flux density of R3, particularly at 144 MHz.To minimize the contamination from the halo, we measured the flux density of R3 using a 7 ′′ resolution image.This higher resolution allows us to minimize flux contamination from the halo to the greatest extent possible.However, the resulting spectrum of R3 is inconsistent with a single power-law.
To measure the flux density of the halo accurately, it is necessary to subtract the flux density contribution of the point sources embedded within it.Due to the low flux density of the halo in Abell 746 and the presence of a large number of point sources, modeling and subtracting their contributions from the data is challenging.Furthermore, at 144 MHz, the majority of unrelated sources within the halo are not distinguishable from the surrounding diffuse emission.Therefore, we used high-frequency images to mark their locations and subsequently manually measured and subtracted their flux density from the halo emission.The resulting values are reported in Table 3.
The halo's overall spectrum can be characterized by a single power law between 144 MHz and 1.5 GHz, with a slope of −1.48 ± 0.10.The spectral index of the halo is relatively flat compared to R3, supporting the claim that the radio emission in this region is not associated with R3.
Using optical, radio, and X-ray observations, Hyeong-Han et al. ( 2023) proposed a possible merging scenario that involves two successive mergers with three subclusters, which can explain the presence of three relics.According to their scenario, a near head-on collision along the east-west direction between two subclusters results in the formation of relics R1 and R3.Subsequently, a third subcluster moves from south to north, influencing the trajectories of the first two subclusters and leading to the formation of the NW relic.
Using the flux densities measured at 1.5 GHz and 144 MHz, we estimate the total radio power of the halo.The total rest-frame radio powers of the halo are P 1.4 GHz ∼ 2 × 10 23 W Hz −1 and P 150 MHz ∼ 5 × 10 24 W Hz −1 .The radio power of halos (at 1.4 GHz and 150 MHz) exhibits a well-defined correlation with the mass and X-ray luminosity of the host cluster (Cassano et al. 2013;van Weeren et al. 2021;Duchesne et al. 2021;Cuciti et al. 2021).The halo in Abell 746 fits well in the radio power versus mass relation at 1.4 GHz and 150 MHz.

Spectral index maps
Spectral index studies of radio relics provide important information on their formation and connection to cluster merger processes.Merger-shock models pre-dict an increasing spectral gradient in the post-shock areas of relics, as seen, for example, in the Sausage and Toothbrush relics (van Weeren et al. 2010;Stroe et al. 2013;Hoang et al. 2017;Di Gennaro et al. 2018;van Weeren et al. 2011avan Weeren et al. , 2016;;Rajpurohit et al. 2018Rajpurohit et al. , 2021c)).We created high and medium-resolution spectral index maps.For spectral index maps, we only considered a common region where pixels with flux density are above 3σ rms in both maps.
Figure 11 displays the high-resolution spectral index map of the NW relic and the cluster created between 144 MHz and 650 MHz, where the resolution is 7 ′′ (left) and 20 ′′ (right).In the high-resolution spectral index map, specific features show noteworthy characteristics within the NW relic.The northern filament edge displays a relatively flat spectral index (−0.80 to −0.95), while downstream (i.e., toward the cluster center), the spectrum steepens (−1.8).At the southern filament, however, the spectral index once again becomes flatter, followed by a subsequent steepening.A similar type of trend is seen across the "double strands" in the Toothbrush relic which may hint at a new injection (Rajpurohit et al. 2018(Rajpurohit et al. , 2020b)).At the eastern tip of the relic, the spectral index is as steep as −1.8.The low-resolution spectral index map of displays a clear spectral index gradient toward the cluster center, as expected due to electron aging, consistent with observations of other relics.We emphasize that the low surface brightness regions of the NW relic are recovered in the low-resolution images, therefore the 20 ′′ resolution spectral index map shows a clear spectral index gradient.
As shown in Figure 11 right panel, R1 exhibits a hint of a spectral index gradient towards the cluster center.The spectral index behavior at R3 is inconsistent with that of a tailed galaxy, where there is typically a spectral steepening in the tail as a function of distance from the AGN due to the aging of CRe.At the southwestern part of R3, there is tentative evidence of a spectral index gradient toward the cluster center.However, the relatively low flux density of R3 at 650 MHz hinders its clear appearance in the spectral index map.

Radio power vs LLS
Radio relic powers (at 1.4 GHz and 150 MHz) correlate with LLS, consistent with larger shock surfaces at cluster peripheries (van Weeren et al. 2009;Bonafede et al. 2012;de Gasperin et al. 2014;Jones et al. 2023).The integrated spectral indices of the NW relic and R1 are −1.26 ± 0.04 and −1.36 ± 0.07.This results in the monochromatic radio powers of 3.9 × 10 24 and 1.6 × 10 23 , respectively at 1.4 GHz.The radio powers at 150 MHz are P 150 MHz,NW = 7.7 × 10 25 and P 150 MHz,R1 = 3.8 × 10 24 .The NW relic and R1 fall within the known relic relation between the radio power of a relic and LLS.
The integrated spectral index of R3 between 144 MHz and 1.5 GHz is curved.By adopting the low frequency spectral index of −1.6, the estimated radio power of the source at 150 MHz and 1.5 GHz is 1 × 10 25 and 1 × 10 23 , respectively.However, this is potentially an underestimate because we exclude the flux density from three compact bright regions (lacking optical counterparts) that are embedded within R3.It fits well with the known correlation between the radio power of a relic and LLS.

L-BAND POLARIZATION
van Weeren et al. (2011a) reported that the NW relic in Abell 746 is polarized at 1.4 GHz and shows aligned magnetic field vectors along its major axis.We present a Faraday Rotation Measure (RM) analysis covering the frequency range of 1-2 GHz.
We create VLA L-band Stokes IQU cubes at 20 ′′ resolution.The same images are used to perform RMsynthesis.These images were obtained employing ro-bust=0.5weighting and a uv taper of 15 ′′ .As the output images have slightly different resolutions, all images were smoothed to a common resolution, namely 20 ′′ resolution.All maps were corrected for the primary beam attenuation.Images with low sensitivity or significant artifact contamination were excluded from the analysis.The polarization fraction (f), linear polarized intensity (p), and polarization angle (χ)can be determined from the I, Q, and U images via The resulting polarization intensity map of the NW relic is shown in Figure 12.At 1-2 GHz, the relic is polarized over its entire length.The morphology of the polarized emission is similar to the total power emission, in particular, we can see two filaments clearly.No significant polarization is detected for R1 and R3.
Figure 13 left panel shows that the polarization fraction across the NW relic varies between 1 and 65%, where it can be measured.The northern filament edge exhibits the highest degree of polarization; this is the region where we anticipate that acceleration is happening.Subsequently, a decrease in the fractional polarization is observed as we move away from this region.At the southern filament, again, the fractional polarization increases.The fractional polarization in the eastern part of the relic is lower compared to the western part.Specifically, at the eastern tip of the relic, the fractional polarization is below 15%.There is a hint that the degree of polarization decreases in the downstream regions.This is consistent with what has been observed in other relics, for example, the Sausage, Abell 2744 and MACS J0717.5+3745relics (Di Gennaro et al. 2021;Rajpurohit et al. 2021bRajpurohit et al. , 2022b)).According to simulations, the presence of shock and downstream turbulence is likely to produce the observed trends in polarization (Dominguez-Fernandez et al. 2020;Domínguez-Fernández et al. 2021).As previously reported by van Weeren et al. (2011a), the magnetic field vectors exhibit a remarkable alignment with the major axis of the relic emission.
RM-synthesis (Brentjens & de Bruyn 2005) was performed on Stokes IQU cubes with 51 spectral channels using "pyrmsynth".The RM cube synthesizes a range of RM from −300 rad m −2 to 300 rad m −2 with a bin size of 5 rad m −2 .In Figure 13 (right panel), we show the Faraday map of the NW relic where the RM values vary between −30 to +30 rad m −2 .The RM across the entire relic shows a well-defined single peak.Additionally, there are some observable small-scale fluctuations in the RM.The mean RM across the NW relic is −10 rad m −2 .At the position of Abell 746, the average Galactic RM contribution is −20 rad m −2 .Therefore, the detected RMs seem to be consistent with the average Galactic foreground.

Magnetic field estimates of the NW relic
The magnetic field at the NW relic can also be estimated, at least to a zeroth order level, assuming equipartition between the energy densities of cosmic rays in the plasma, and the magnetic energy ϵ CR = ϵ B (e.g.Brunetti et al. 1997;Beck & Krause 2005), which also gives a value close to the minimum of the combined energy densities, ϵ B + ϵ CR .In radio relics it is realistic to assume that the spectrum of cosmic ray electrons in the downstream results from the combination of injection, transport and energy losses.Following the formalism in Locatelli et al. (2020), the equipartition estimate of the magnetic field can in this case be obtained by assuming that the magnetic field has the same energy density of the cosmic rays downstream: where k is the ratio of energies budget between cosmic ray protons and electrons, ρ and v are the gas density and shock velocity computed upstream ( u ) and downstream ( d ) of the shock front.Based on the total radio spectrum of the relic, we use a shock Mach number M = 2.6 to estimate ρ and v at both sides of the shock discontinuity, assuming Rankine-Hugoniot jump conditions.At NW, T d ∼ 5.57 keV, which implies T u = 1.89 keV, and an upstream sound speed of c s = 709 km/s, and hence a shock speed v s = M c s = 1845 km/s = v u .The downstream gas velocity is thus ).If we assume somewhat canonical (albeit far from being certain) values of ξ e = 10 −4 for the electron injection efficiency at this Mach number, we get B equip ≈ 0.9µG for k = 100, B equip ≈ 0.2µG for k = 10 and B equip ≈ 0.1µG for k = 1.Manifestly, the various uncertainties on the amount of electrons and protons present in the relic region make this estimate uncertain, and with the additional uncertainties on the estimate of the shock Mach number, a more accurate estimate will be difficult to obtain.Under a few simplifying assumptions, the magnetic field strength can also be estimated using the observed Faraday dispersion (σ ϕ , Sokoloff et al. (1998); Kierdorf et al. (2017): where ⟨n e ⟩ is the average thermal electron density of the ionized gas in cm −3 , B turb is the magnetic field strength in µG.L and t are the path length through the thermal gas and turbulence scale, respectively, in pc and f the volume filling factor of the Faraday-rotating plasma.
For the NW relic, the average σ ϕ = 10 rad m −2 .We assume that the thermal density along the line of sight is 10 −4 cm −3 , L ∼ 1 Mpc, t = 50 kpc and f = 0.5 Murgia et al. (2004); Kierdorf et al. (2017).By inserting all values in Equation 8, we obtained B = 0.7µG.This is consistent with the estimates from the equipartition using k = 100.
6. ORIGIN OF NW, R1, R2, AND R3 Based on the morphology of the diffuse source NW, its location, high degree of polarization, power-law spectrum, and the presence of spectral index gradient in the downstream regions, we classify it as a radio relic.R1 morphology is arc-shaped and it is more extended toward low frequencies.Given its peripheral location, spectral properties, the radio power vs. LLS relation, and the presence of a density jump, we conclude that this source is also a radio relic.
R3 is located symmetrical to the NW relic, suggesting that it could be a double radio relic system.The location of R3, its megaparsec size, the radio power vs. LLS relation, and the detected surface brightness jump across the sector SB3 suggest that it could be a relic.However, its integrated spectral index is inconsistent with this since in the case of the shock acceleration a power-law spectrum is expected while the R3 spectrum exhibits a high frequency steepening.Low-frequency observations (LOFAR 50 MHz and uGMRT band3) might allow an accurate measurement of the spectral index distribution.If R3 shows a radial spectral index steepening that would favor shock re-acceleration and the complex spectrum can be explained that the low-frequency spectrum marks the original slope of the fossil seeds electrons and the high frequency would represent the power-law of DSA (re-acceleration).The nature of R2 is not clear since it is only detected at 150 MHz.

SUMMARY AND CONCLUSIONS
In this work, we presented deep XMM-Newton (∼150 ks), uGMRT Band4 (550-750 MHz) and VLA Lband (1-2 GHz) observations of the complex galaxy cluster Abell 746.The main aims of our analysis were to identify signs of merger activity in the ICM and to detect and characterize diffuse radio sources.Below is a summary of our main results: 1.The XMM-Newton images reveal a complex ICM distribution in Abell 746, which includes a Vshaped feature, an elongated central region, and concave bay and arc-like features.We find evidence of asymmetric temperatures across the cluster ranging from (≤ 4 keV) in the north and ∼ 9 keV in the south.
2. We detected three surface brightness edges and one candidate edge.Three of these are mergerdriven shock fronts located in the southeast, southwest, and north of the cluster.
3. Abell 746 possibly hosts double radio relics, in addition to two fainter relics to the east (R1 and R2) and a radio halo with low surface brightness.
4. The main northwest relic shows filamentary morphology.We measure a power law spectrum, a clear spectral index gradient, and a high degree of polarization, as expected for acceleration from an outward traveling shock, with radiative losses in the region downstream regions.The relic shows a single RM component with a mean RM (−10 rad m −2 ) very close to the Galactic foreground, indicating very little Faraday-rotating intervening material along the line of sight.
5. The integrated spectral index of the fainter northern relic R1 is α 1.5 GHz 144 MHz = −1.36 ± 0.07, implying a shock of Mach number M = 2.4±0.2.This is consistent with X-ray obtained shock Mach number of M = 2.6 ± 0.8.6. R3 shows a high-frequency steepening in the overall spectrum.The ICM temperature across a part of R3 is high, consistent with shock heating.We find evidence of a density jump in this region.
7. Abell 746 is host to a 1.7 Mpc large radio halo with low surface brightness.The integrated spectrum of the halo follows a power law and has a slope of α 1.5 GHz 144 MHz = −1.48± 0.10.The radio power of the halo at 1.4 GHz and 144 MHz is consistent with the P − M 500 and P − L X relations of known radio halos.Unlike other known halos, we do not find a morphological connection between the radio halo emission and the thermal X-ray emission.
While progress has been made in understanding particle acceleration and the origin of non-thermal emission in galaxy clusters through both radio and X-ray observations, questions remain.Multiwavelength observations combined with simulations will shed light on the underlying particle acceleration mechanisms and the complex interplay between thermal and nonthermal plasma.In particular, sensitive low frequencies radio observations, such as those that can be obtained with the LOFAR Low Band Antennas (LBA) will be ideal to probe the existence and spatial distribution of older electron populations.Finally, Chandra high resolution observations may allow to characterize the localized regions and investigate the connection between the radio features and the detected discontinuities.

Figure 1 .
Figure 1.X-ray and radio overlay of Abell 746.The intensity in blue shows the XMM-Newton emission in the 0.7-2.0keV band.The intensity in red shows the radio emission observed with LOFAR at a central frequency of 144 MHz.The presence of four relics (R1, R2, R3, and NW relic) and the halo suggests a complex caused by multiple mergers.R2 and the halo are not clearly visible at this resolution, though, due to their low surface brightness, they were thus recovered better in the low-resolution images; see Figure 3 right panels.The LOFAR image properties are given in Table 2, IM1.

Figure 2 .
Figure 2. XMM-Newton surface brightness map.The 0.7−2.0keV band image was exposure-corrected and smoothed with a Gaussian kernel of 6 ′′ FWHM.All point sources are removed, with the exception of the one indicated by a cross mark.The image reveals multiple substructures, indicating the highly disturbed state of the cluster.

Figure 3 .
Figure 3. High (left) and low (right) resolution VLA L-band (top), uGMRT Band4 (middle), and LOFAR HBA (bottom) images of Abell 746 in square root scale.All low-resolution images are created at a common 20 ′′ resolution.The radio surface brightness unit is mJy beam −1 .The beam size is indicated in the bottom left corner of each image.The images reveal a low surface halo emission and highlight the morphology of the diffuse emission sources as a function of observing frequency.The dashed line shows the separation between R3 and the halo.The image properties are given in Table 2; IM1, IM5, IM9, IM3, IM7, and IM11.

Figure 4 .
Figure 4. Left: Subaru/Hyper-Suprime Cam zoom-in view of R3 (HyeongHan et al. 2023) overlaid with LOFAR 144 MHz 7 ′′ resolution radio contours.For image properties, see Table 2, IM2.The magenta circles mark the point sources embedded within R3 which have optical counterparts (with available redshift), while the cyan dashed circles represent compact regions without optical counterparts.The newly detected shock front position is indicated by the yellow dashed lines.Right: XMM-Newton image overlaid with 144 MHz LOFAR contours.The radio contours are from the 20 ′′ resolution image (point source subtracted) and drawn at [1, 2, 4, 8...] × 3.0σrms where rms = 130 µJy beam −1 .

Figure 5 .Figure 6 .
Figure 5. GGM filtered XMM-Newton images with σ = 2 (left), and σ = 12 (right) pixels.The images reveal the presence of surface brightness edges in the eastern, western, and central regions of the cluster.

Figure 7 .
Figure 7. XMM-Newton image overlaid with four regions of interest are defined and their surface brightness profiles are shown in Figure 8.The dashed lines mark the X-ray edges with density jumps.

Figure 8 .
Figure8.Surface brightness profiles for all four edges (SB1, SB2, SB3 and SB4).Black data points are from XMM-Newton.Blue and red lines are best fitting broken power-law and single power law models, respectively.Residuals on the bottom are from broken power law fits.The sectors where the profiles were fitted and the positions of the relative edges are in Figure7right panel.

Figure 9 .
Figure 9. Left: Projected temperature map and the relative uncertainties (right), overlaid with the 144 MHz LOFAR contours (in green).The X-ray contours are displayed in The image shows that the temperature distribution is asymmetric across Abell 746: the northern part of the cluster has lower temperatures than the southern part.Right: corresponding temperature uncertainty map.

Figure 10 .
Figure10.Left: Integrated radio spectra of NW, R1, R3, and the halo measured between 144 MHz and 1.5 GHz.Dashed lines show the fitted power law and the dotted dash a curved spectrum.The spectra for NW, R1, and the halo are well described by a single power-law.The spectrum of R3 shows a high-frequency steepening and cannot be explained by a single power law.Right: LOFAR 20 ′′ resolution image depicting the regions where the integrated flux densities were measured.Flux density contributions from compact sources (shown with red circles) within NW, R1, and R4 were manually subtracted from their total flux densities.

Figure 12 .
Figure 12.Vector map of the NW relic (at 15 ′′ resolution) showing the orientation of the magnetic field vectors overlaid on the linear polarized intensity image.The vectors are corrected for the Faraday rotation due to the Galactic foreground.The Stokes I contours are from the GMRT 15 ′′ uv-tapered image and are plotted at levels of [1, 2, 4, 8, . ..] × 4.0σrms where rms = 12µ Jybeam −1 .

Figure 13 .
Figure 13.Left: The fractional polarization map of the NW relic, obtained at a resolution of 20 ′′ , reveals a high degree of polarization, reaching up to 65%.The degree of polarization decreases in the downstream regions of the relic.Right: Rotation Measure map of the NW relic measured over 1.0-2.0GHz using RM-synthesis technique.The RM varies across the relic with coherence lengths of 70-100 kpc.

Table 2 .
Image properties

Table 4 .
Surface Brightness Profile