LOFAR observations of galaxy clusters in HETDEX

The LoTSS processing pipeline (DDF-PIPELINE) delivers images of the full field of view (FoV) of the Dutch LOFAR HBA stations (Tasse, 2014a, b; Shimwell et al., 2019). These images have a resolution of 6″and an r.m.s. noise level of the order of 100 $\mu$Jy beam^-1. This is achieved by correcting for the direction dependent effects (DDE) in the LOFAR data (due to the ionosphere and imperfect station beam models). For LoTSS, DDE corrections are applied towards 45 directions (facets). The DDF-PIPELINE is optimized to create images of LOFAR’s full FoV and carry out survey science. The latest version 2 of the DDF-PIPELINE, which we employ in this work, is described in Tasse et al. (2020). Version 2 of the pipeline is a major improvement compared to version 1 which was used for public Data Release 1. The images from DR1 are generally not suitable to study extended low-surface brightness cluster sources (see Section 3.7 in Shimwell et al., 2019).

The individual images produced by the DDF-PIPELINE ¹¹1https://github.com/mhardcastle/ddf-pipeline are very large, $20,000\times 20,000$ pixels with a pixel size of 1.5″. This makes re-imaging with different settings, e.g., uv-ranges, weighting schemes, and deconvolution algorithms, expensive. The tessellation of the sky into 45 calibration facets is done in a fully automated way. The DDE calibration takes all sources in a facet into account, assuming there are no DDE inside a facet. This means that for certain specific targets of interest the facet layout is not optimal. Experience with various faceting schemes has shown that it is often possible to further improve the quality of the DDE calibration for a specific target (sometimes at the expense of other sources).

To allow flexible re-imaging and optimize calibration towards targets of interest, we extended the DDF-PIPELINE with an optional step. In this step all sources are subtracted, apart from those in a specific user defined region, from the visibility data and after applying their DDE calibration solutions. The model visibility prediction is done with the DDFacet imager (Tasse et al., 2018). An important requirement for extraction is that region of interest needs to be quite small, roughly similar to the size of the original facet, but ideally smaller. This is directly related to the fact that we want to improve the DDE calibration, which was limited by the original facet size and the “incorrect” assumption that the DDE correction is constant across that entire facet. This requirement competes with another requirement that there is sufficient flux density available for calibration. A smaller extraction region will have less flux density available for the calibration.

The next step in the “extraction” process for a target of interest is to self-calibrate the data. The starting point of this step are one or more phase shifted and averaged datasets for the target of interest, each one corresponding to a different observation with a potentially different pointing center. The direction independent (DI) full Jones calibrations are carried over from the DDF-pipeline. We do not carry over the DDE solutions to avoid the issue with the “negative haloes” described in Tasse et al. (2020).

The self-calibration steps consist of three rounds of ‘tecandphase’ calibration with DPPP (van Diepen & Dijkema, 2018). This is followed by several rounds of diagonal (i.e., XX and YY) gain calibration using a longer solution interval. The shorter timescale ‘tecandphase’ solutions are pre-applied when solving for the diagonal gains. This scheme somewhat mimics the facet-calibration scheme (van Weeren et al., 2016b) and the DDF-pipeline which also pre-applies fast phase/TEC solutions before solving for slow gain solutions. The diagonal gain solutions are filtered for outliers with LoSoTo (de Gasperin et al., 2019). The solution intervals are automatically determined based on the amount of apparent compact source flux in the extracted region. Solutions intervals for the ‘tecandphase’ calibration are between 16 s and 48 s. Solution intervals for the diagonal gains are between 16 min and 48 min. All solution intervals are set per observation since the apparent flux in the target of interest region can differ. Solution intervals along the frequency axis for the diagonal gains are between 2 MHz and 6 MHz. For HBA data, a minimum of 0.3 Jy compact (apparent) source flux is needed for the self-calibration steps to converge well. If needed, all solution intervals can be manually controlled by the user. An overview of the parameters used is given in Table 1.

The imaging is done with WSClean (Offringa et al., 2014) with wideband joint deconvolution mode (‘channelsout’ 6 default), optionally with multi-scale clean (Offringa & Smirnov, 2017). The DDFacet imager (Tasse et al., 2018) can also be used instead of WSClean. As default Briggs weighting $-0.5$ is used. The imaging includes automatic clean masking from the DDF-pipeline, with a default $5\sigma$ threshold. Baseline based averaging is also employed when imaging for performance. An inner uv-cut of $80\lambda$ is used in the imaging. For the calibration, a default inner uv-cut of $350\lambda$ (corresponding to 0.65°) is employed. This value is a compromise between the number of baselines in the calibration and the increased difficulty of modelling very extended structures.

In Figure 1 we show an example of the self-calibration process. The top panel shows the first image before any self-calibration. Note that here two different observations (L254483 and L719874), with different pointing centers, are jointly imaged and deconvolved. The only calibration that is applied here is the DI calibration from the DDF-pipeline. In the middle panel we show the result after three rounds of ‘tecandphase’ self-calibration. The radial patterns, caused by the ionosphere disappear after this calibration. In the bottom panel we show the results after additional diagonal gain calibration. The diagonal gain calibration corrects for the imperfect knowledge of the station beam response or other slowly varying gain errors.

In Figure 2 we display two comparisons between the default LoTSS mosaics and newly extracted and re-calibrated targets (in this case the clusters Abell 1430 and 1294). As can be seen, the calibration for the targets of interest has improved. The improvement is the result of shrinking the size of the calibration region so that a nearby bright compact source is better calibrated. The extraction and self-calibration scheme has already been successfully applied in various recent works (e.g., Botteon et al., 2020c, b; Mandal et al., 2020; Hardcastle et al., 2019; Cassano et al., 2019; Gu et al., 2019).

The flux density measurements for all sources, except radio halos, were done manually by placing a polygon around the sources and integrating the flux density. The uncertainty on the flux density is given by

where $f=0.2$ is the absolute flux-scale uncertainty (Shimwell et al., 2019), $N_{\rm{beams}}$ the number of beams covering the source, $\sigma_{\rm{rms}}$ the map noise, and $\sigma_{\rm{sub}}$ the uncertainty due to compact source subtraction. The first two terms of Eq. 1 represent the statistical uncertainty on the flux density measurement. The uncertainty on the compact source subtraction is given by

where the sum is taken over all $i$ sources that were subtracted in the polygon.

The radio halo integrated flux densities were determined by fitting exponential profiles (Murgia et al., 2009) to the radio images of the form

where $r_{e}$ is a characteristic $e$-folding radius and $I_{0}$ the central surface brightness. We used the image where compact sources were subtracted. Also, all images were smoothed to a beam size corresponding to a physical scale of 50 kpc at the cluster’s redshift. For the fitting we used Halo-FDCA⁴⁴4https://github.com/JortBox/Halo-FDCA described in Boxelaar et al. (2020). Extended sources, such as large tailed radio galaxies, were masked during the fitting (in case they were not fully subtracted). The flux density was integrated to a radius of $3r_{e}$, as proposed by Murgia et al. (2009). Integrating up to a radius of $3r_{e}$ results in 80% of the flux density when compared to using an infinite radius. This also avoids to some extent the uncertainties related to the extrapolation of the profile to large radii where the radio surface brightness is below the detection limit. The fitting uses a Markov Chain Monte–Carlo method to determine the radio halo parameters and associated uncertainties. For some clusters, when specifically mentioned in Section 4, we fitted an elliptical exponential model (see Boxelaar et al., 2020). In these cases, a major and minor characteristic $e$-folding radius and position angle are determined. This is done for radio halos that clearly display an elongated, rather than circular, shape. In this work we did not use the skewed (asymmetric) models that are available in Halo-FDCA. A full exploration of radio halo fitting models and methods is beyond the scope of this work.

For the total uncertainty on the radio halo integrated flux density we add the uncertainty from the MCMC (statistical errors) and flux calibration uncertainty in quadrature.

We searched the Chandra and XMM-Newton archives for the available X-ray observations of the clusters in the sample. When available, data were retrieved and processed with CIAO 4.11 using CalDB v4.8.2 and SAS v16.1.0 following standard data reduction recipes. We used the time periods of the observations cleaned by anomalously high background to produce cluster exposure-corrected images in the $0.5-2.0$ keV band. These images are used in the paper to investigate the connection between the thermal and non-thermal components in the ICM.

Abell 2018 is relatively nearby cluster located at $z=0.0878$. The Pan-STARRS gri image reveals a number of central galaxies, without a clear dominant BCG. The cluster has a low PSZ2 mass of $M_{500}=2.51^{+0.20}_{-0.21}\times 10^{14}$ M_⊙. The high-resolution radio image, see Figure 5, shows a complex central region with several AGN being present as well as more extended emission. A low-surface brightness arc-like structure is found about 1.3 Mpc to the east of the optical center of the cluster. This source has an LLS of about 1.1 Mpc. In a low-resolution image (made with a 90″ taper), additional faint diffuse emission spanning the central region of the cluster is found. This emission extends all the way to the arc-like structure to the east. This emission has a size of approximately 1.0 Mpc by 1.8 Mpc. The XMM image reveals an EW merging cluster with the main component located at the optical center of the cluster. We classify the arc-like structure to the east as a giant radio relic and the large-scale centrally placed emission as a candidate radio halo. The nature of the central brighter diffuse emission near the AGN remains unclear. It could be related to the radio halo or be revived fossil plasma from the AGNs. For the candidate radio halo we determine an integrated flux density of $S_{144}=92\pm 32$ mJy, where we masked the central brighter diffuse emission around the AGN and the extension towards the radio relic in the fitting. We note that this cluster falls above the correlation between cluster mass and radio power (see Section 5.3). Deeper observations are required to shed more light on this point and on the origin of the extension from the central emission towards the relic.

The XMM-Newton image of this distant ($z=0.73$) cluster shows a disturbed system with a 1 Mpc bar-like structure north of the cluster center, see Figure 6. A hint of centrally located diffuse emission is seen in our image with compact sources subtracted. This emission extends on scales of about 0.5 Mpc. We therefore classify this as a candidate radio halo with $S_{144}=4.2\pm 1.2$ mJy. Di Gennaro et al. (2020) also reported a hint of diffuse emission in this cluster.

Our low-resolution LOFAR image reveals diffuse emission with a largest extent of about 0.6 Mpc in this $z=0.6752$ cluster, see Figure 7. This emission is centrally located and we therefore classify it as a radio halo with a flux density of $12.2\pm 3.6$ mJy. This is consistent within the uncertainties with the value reported by Di Gennaro et al. (2020) who presented the discovery of a radio halo in this cluster. Yuan & Han (2020) classify the cluster as a disturbed system based on Chandra observations.

The XMM-Newton image reveals a disturbed cluster, with the ICM being elongated in the NE-SW direction, see Figure 8. In the LOFAR image we detect two arc-like radio sources to the north (A) and SE (B) of the cluster center. At the redshift of the cluster ($z=0.0701$), these sources have an LLS of 230 and 170 kpc, respectively. Sources A and B are located at projected distances to cluster center of 350 and 150 kpc, respectively. Despite these relatively small distances, we consider these sources to be peripheral given the ICM distribution. A much fainter elongated source (C) is visible NW of source A. No optical counterparts are detected for these sources. A compact double lobed radio galaxy is located just west of source A. Given the peripheral location of source A with respect to the ICM distribution and elongated ICM shape, we classify A as a radio relic. The location of B is somewhat peculiar with respect to the overall ICM elongation. Given that source B is also affected by calibration artefacts from a nearby bright source, we classify source B as a candidate radio relic. If the classification of source B is confirmed this cluster hosts a double radio relic. The (candidate) relics in Abell 1904 are relatively small compared to other well-studied relics, although we note that, for example, the western relic in ZwCl 0008.8+5215 also has a small LLS of 290 kpc (Di Gennaro et al., 2019).

PSZ2 G095.22+67.41 is a relatively nearby cluster located at $z=0.0625$. The XMM-Newton image reveals that the ICM peak coincides with the location of the BCG, see Figure 9. A faint X-ray extension is visible to the east. This suggests that the cluster is not fully relaxed and is undergoing a merger event in the EW direction.

No central diffuse radio emission is found in our LOFAR image. However, we detect a NS elongated source about 0.8 Mpc to the east of the cluster center. The source has an LLS of about 0.4 Mpc and is located south of a brighter radio galaxy. We classify the source as a relic tracing a shock that could have originated from the EW merger event. This is consistent with the NS extent, highly elongated shape, and peripheral location of the radio source. An alternative explanation is that this source traces (old) AGN plasma from a bright elliptical galaxy (MCG+08-25-051, $z=0.0623$) that is located near this source. A faint ($\sim 0.5$ mJy) compact radio counterpart is detected in our LOFAR image for MCG+08-25-051. However, there is no evidence of jets or lobes originating from this source which then suggests that the emission resulted from a previous episode of AGN activity.

PSZ2 G099.86+58.45 is a massive cluster (M${}_{500}=6.85^{+0.48}_{-0.49}\times 10^{14}$ M_⊙) with a global temperature of 8.9${}^{+2.8}_{-1.1}$ keV (Sereno et al., 2018). The cluster is known to be undergoing a merger event. The discovery of a 1 Mpc radio halo in this distant ($z=0.616$) cluster, see Figure 10, was reported by Cassano et al. (2019) based on LOFAR data. From an elliptical fit we determine $S_{144}=14.7\pm 3.2$ mJy. This number somewhat lower than the $25.3\pm 5.7$ reported by Cassano et al. (2019). This difference is caused by a small extension of the radio halo around compact source B (discussed by Cassano et al. (2019)). If this region is included, the measurements are consistent with each other given the uncertainties.

The LOFAR image displays two bright, partly blended tailed radio galaxies in the western part of the cluster, see Figure 11. The Chandra X-ray image shows a cluster without a strongly peaked core. In addition, the cluster is elongated in the direction of the two tailed radio galaxies. In the center of the cluster we detect diffuse radio emission with an LLS of about 0.5 Mpc. Within this diffuse emission we find two compact AGN associated with the cluster, including the BCG. We consider a mini-halo origin unlikely given the lack of centrally peaked X-ray emission. The western part of the central diffuse emission has a rather high surface brightness, suggesting a link with a cluster AGN. On the other hand, some of the emission (in particular the eastern part) has a smooth morphology somewhat similar to a radio halo. For the above reasons we list the source as candidate radio halo.

Abell 1758 is composed of two main clusters, Abell 1758N and Abell 1758S, see Figure 12. These two clusters appear to be in a pre-merger phase (Rizza et al., 1998; David & Kempner, 2004). The individual clusters themselves are disturbed and already undergoing their own merger events. The presence of a radio halo in A1758N was first reported by Kempner & Sarazin (2001) and further studied by Giovannini et al. (2009) and Venturi et al. (2013).

Botteon et al. (2018) studied this cluster with LOFAR HBA observations, a subset of the data used here. They measured a size of about 2 Mpc for the A1758N radio halo and discovered a 1.6 Mpc radio halo and a $\sim 0.5$ Mpc relic (labelled R) in A1758S. In addition, a hint of faint emission was detected between A1758N and A1758S. This “radio bridge” was subsequently confirmed by Botteon et al. (2020c). Two bright patches, labelled S1 and S2, were found in A1758N. They are not directly associated with an optical counterpart and possibly trace compressed AGN fossil plasma.

For the radio halo in A1758N we find a flux of $123\pm 25$ mJy based on the elliptical model fit. This value is lower than the $307\pm 63$ mJy measured earlier by Botteon et al. (2020c). The reason for this difference is that we excluded the region around sources A and B (see Botteon et al., 2018) and S1 and S2. This particular case highlights the difficulties in classifying and separating the emission from different components with uncertain identifications. For the southern radio halo we determine $S_{144}=63\pm 14$ mJy from the elliptical model, consistent with the value reported by Botteon et al. (2018). For a more comprehensive description of the LOFAR findings we refer the reader to Botteon et al. (2018, 2020c).

The XMM-Newton X-ray image shows an elongated cluster without a central concentration. The LOFAR images reveal two prominent radio sources in this cluster, see Figure 13. One is located near the southwestern BCG of the cluster. The second source is more extended and located at the NE periphery of the cluster. This emission is also discussed by Paul et al. (2020) based on LoTSS DR1 images (Shimwell et al., 2019). The source consists of a NW-SE elongated structure with an LLS of about 700 kpc, as well as emission trailing SW towards a second BCG. Compact radio emission from this BCG is detected, but no obvious morphological connection with the extended source is visible. The extended source somewhat resembles the Toothbrush relic (van Weeren et al., 2012). We note that the extended radio source partly overlaps with the nearby irregular dwarf galaxy UGC 8308 (DDO 167; e.g., Tikhonov & Karachentsev, 1998). However, we consider an association of the radio source with the cluster more likely. We therefore classify the source as a radio relic. This classification is also consistent with the elongation of the ICM, suggesting a NE-SW merger event. In the low resolution radio images extended emission is visible in the region between the NE and the SW BCG. This emission is classified as a radio halo since it follows the X-ray emission from the ICM. The flux density of the halo is $27.7\pm 6.3$ mJy. We note that this emission is also discussed by Paul et al. (2020) (“trailing relic emission”) and it is concluded that this emission has an ultra-steep spectrum. We note however that the flux density estimate provided by Paul et al. (2020) is incorrect as the emission is not fully deconvolved in the LoTSS DR1 images and thus measurements directly from those images are complicated. This leads to a large overestimation of the flux density as is discussed by Shimwell et al. (2019). This problem is addressed to some extent in the upcoming DR2.

The massive cluster Abell 1703 has been extensively studied at optical wavelengths due to its gravitational lensing properties. It is generally classified as a relaxed cluster (e.g., Umetsu et al., 2011; Richard et al., 2009). The Chandra image shows an overall regular appearance with the cluster being somewhat elongated in the NNW-SSE direction, see Figure 14. Andrade-Santos et al. (2017) determined the concentration parameters, cuspiness, and central density of the cluster using Chandra X-ray data. These properties, however, point to a non-cool core classification. Furthermore, a recent dynamical analysis from Boschin et al. (2020) indicates that this is a merging cluster consisting of two or three subclumps.

The LOFAR image reveals the presence of central diffuse emission, filling the region around between tailed radio source A and a complex compact region of emission which we labelled B. Source B is likely related to AGN activity. A faint tailed source, labelled C, is located in the SE part of the cluster. The total extent of the diffuse emission is difficult to determine because of A and B. Given the central location and extent of at least 0.5 Mpc, we classify the diffuse emission as a radio halo with a integrated flux density of $91.7\pm 18.6$ mJy based on an elliptical model fit.

The presence of diffuse emission in this cluster was first reported by Venturi et al. (2008) and subsequently studied in more detail by Venturi et al. (2011); Macario et al. (2013); Venturi et al. (2013). LOFAR observations show complex diffuse extended emission extending over a region of more than 1 Mpc, see Figure 15. The Chandra X-ray image displays a disturbed ICM indicating that the cluster is undergoing a merger event. The LOFAR results have been presented in Clarke et al. (2019). Some of the structures in the cluster are related to distorted and tailed radio galaxies. A few regions of the diffuse emission show a steep spectral index of $\alpha\sim-2$. These regions could trace AGN fossil plasma that has been re-accelerated (or revived) by shocks and turbulence related to the ongoing merger event. A candidate radio halo is located near the peak of the X-ray emission, labelled (CH). The complexity of the various radio structures in the vicinity prevent us from measuring its properties.

Several radio galaxies and diffuse emission are detected in this cluster, see Figure 16. An optical image shows two BCGs that are located along a SE-NW axis. The cluster hosts a tailed radio galaxy, labeled A. To the east, a bright patch of emission (B) is found just above the SE BCG. Additional fainter emission is located around B. Given the high surface brightness of B and several nearby radio AGN, B is likely AGN plasma, possibly revived by the passage of a shock.

We also find low-level diffuse emission extending on scales of about 0.4 Mpc in the central regions of the cluster, labelled H. However, it is hard to determine its full spatial extent as it partly blends with other extended radio sources in this region. Since the diffuse emission approximately follows the overall galaxy distribution and has a low surface brightness we classify it as a candidate radio halo. Fitting a circular model we estimate $S_{144}=28\pm 13$ mJy, where we masked the region near B and west of A.

The existence of diffuse emission in Abell 1550 ($z=0.2540$) cluster was first reported by Govoni et al. (2012). Extended radio emission is clearly detected in this cluster by LOFAR. It extends over a significantly larger region than found by Govoni et al., corresponding to an LLS of 1.8 Mpc. This is explained by the shallower depth of the VLA image used Govoni et al. and/or a steep radio spectrum.

The Chandra image shows a roughly roundish ICM distribution. Additional faint X-ray emission is observed NE of the main structure. The main part of the diffuse radio emission, labeled H, traces the X-ray emission from the ICM. We therefore classify it as a giant radio halo with a size of about 0.9 Mpc. Based on the elliptical model fit, we obtain a radio halo integrated flux density of $129\pm 26$ mJy. The radio images also show a bright tailed radio galaxy (A) and several structures in the western part of the cluster (D, E, C) that do not have clear optical counterparts. A diffuse patch of emission, labeled B, is placed near a group of galaxies located at the same redshift as the main cluster. A lower resolution radio image shows that B is connected to the main radio halo. Source B seems to be associated with the NE X-ray extension. Sources E, D, and C look to be relics, possibly related to revived AGN fossil plasma. We note that both D and C are connected to the emission from the main radio halo. Based on the extension of the ICM and placement of the diffuse radio sources, the cluster seems to have undergone a merger event in the NE-SW direction. The location of B in the NE, and C-D-E in the SW could indicate that these structures are related to mergers shocks. If this interpretation is correct the cluster hosts a double radio relic. The combination of a double radio relic and a radio is relatively rare (Bonafede et al., 2017).

The LOFAR image uncovers a large number of radio galaxies in this $z=0.5436$ cluster which are labeled A to F, see Figure 18. One of these, source E, has a physical extent of about 1 Mpc and we classify it as a giant double-double. Sources A to D display head-tail morphologies. Source G is a peripheral source with an extent of about 400 kpc. We do not identify an optical counterpart for this source and tentatively classify it as a relic or an AGN fossil plasma source. The Chandra image of PSZ2 G135.17+65.43 indicates a non-relaxed cluster without a clear central peak. We also detect central diffuse emission in this cluster with a total extent of about 500 kpc, labeled H. Due to the presence of the tailed radio galaxies A and B, the full extent of H is hard to determine but the emission approximately follows the thermal ICM. Given its central location and extent, we classify H as a candidate radio halo with a flux density of $S_{144}=29.0\pm 6.6$ mJy based on the circular model fit.

The LOFAR images reveal the presence of diffuse emission in this cluster which is located at $z=0.3634$, see Figure 19. The LOFAR observations are discussed in more detail in Hoeft et al. (2020), so we only give a brief overview of the main findings. The diffuse emission extends over a region of about 5′ by 2.5′, with the emission being elongated in the EW direction. The angular extent corresponds to physical size of 1.5 Mpc by 0.8 Mpc. Our LOFAR image also reveals two tailed radio galaxies, labelled A and B (Figure 19). An optical image displays two subclusters. The western subcluster corresponds to the main structure seen in the Chandra X-ray image, while the eastern cluster is much fainter in the Chandra image. The radio emission spans the full region between the main western and the smaller eastern subcluster. Given the clear correspondence between the radio and X-ray emission of the western subcluster and the large extent of the diffuse emission, we classify the western part of the diffuse radio emission as a giant radio halo. We measure $S_{144}=29.8\pm 6.6$ mJy for the radio halo from our fitting. We note that this value might be affected by the diffuse emission around the eastern subcluster since it partly overlaps with the radio halo from the western subcluster. The nature of the diffuse emission around the eastern subcluster is not fully clear but it could be a radio bridge (for a discussion on this see Hoeft et al., 2020). The disturbed character of the cluster, both in optical and X-ray images, indicates that the cluster is undergoing a merger event, consistent with the presence of the giant radio halo. A possible source of seed electrons for the radio halo could be the tail of source A, since it blends into the halo emission.

An XMM-Newton image shows a cluster that is elongated in the EW direction, see Figure 20. The galaxy distribution shows a similar elongation and extending all the way to a tailed radio galaxy A. Our LOFAR image reveals faint diffuse emission, with an LSS of about 0.4 Mpc, located at the western part of the cluster. This emission is very faint and close to the detection limit of our observations. A candidate tailed radio galaxy (B) is located just east of the diffuse radio source. The diffuse emission is difficult to classify with the current data in hand. A possibility is that it is related to revived or re-accelerated fossil plasma from source B. On the other hand, it could also be a radio halo, somewhat similar to the “off-axis” radio halo found in Abell 1132 (Wilber et al., 2018). The integrated flux density of the diffuse source is $S_{144}=6.7\pm 1.7$ mJy, based on the circular model fit.

MACS J1115.2+5320 is a massive merging cluster located at $z=0.466$. A Chandra X-ray image reveals an ongoing merger event along a NW-SE axis, see Figure 21. Mann & Ebeling (2012) classified this system as a possible head-on binary cluster merger. The global temperature of the cluster was measured to be $8.6\pm 1.1$ keV by Morandi et al. (2015).

The LOFAR image shows a long 770 kpc tailed radio galaxy (A), with the tail pointing NW. Two additional tailed radio galaxies (B, C) have their tails pointing to the SE. Source D is located just SE of the head-tail source A and has a rather complex morphology in our high-resolution image. Near source D, a possible merger induced cold front is visible in the Chandra image. Low surface brightness radio emission is detected in the region north of source A. This emission extends over 1 Mpc and given its size we classify it as a giant radio halo. Fitting an elliptical model, we determine $S_{144}=71.2\pm 14.5$ mJy for the radio halo.

A bright compact radio source is detected in this $z=0.6175$ cluster which seems to be associated with a BCG, see Figure 22. In our low-resolution images, with compact sources removed, faint diffuse emission is detected in the region above the compact radio source. Only a hint of this emission is detected in our high-resolution image. This diffuse emission has a total extent of about 0.5 Mpc. Given its approximate central location, with respect to the cluster member galaxies as judged from the Pan-STARRS images, and large physical size, we classify this source as a candidate radio halo. For the source we determine a flux density of $7.9\pm 3.7$ mJy.

Peripheral diffuse radio emission in this cluster was first reported by Rudnick & Lemmerman (2009) and subsequently studied by van Weeren et al. (2011). Chandra and Suzaku observations were presented by Itahana et al. (2017) showing the cluster is undergoing a merger event. The peripheral radio source is classified as a relic.

The main LOFAR pointing on this source (P164+55) had to be discarded as it was affected by bad ionospheric conditions. Hence the noise levels in our images are higher than for other clusters. Despite the higher noise, the relic is clearly detected in our LOFAR images (Figure 23) and the source has a similar appearance as in the WSRT observations presented in van Weeren et al. (2011). In the LOFAR image, the relic has an LLS of about 0.75 Mpc. A hint of an extension is visible from the northern tip of the relic (near a compact source) towards the west and north. Combining the LOFAR flux density measurement with the one obtained from the WSRT, we obtain $\alpha=-1.17\pm 0.11$, which is typical for radio relics.

A Chandra X-ray image displays a cluster that is elongated in the NS direction (Figure 24). Diffuse radio emission, also elongated in the NS direction, is detected in this cluster with an LLS of 0.7 Mpc. This radio emission does not peak at the cluster center but south of it. However, some faint diffuse emission is also visible north of the cluster center. We list this source as a candidate radio halo, originating from a possible NS merger event. Additional extended radio emission, with a mostly EW elongation is found in the southern periphery of the cluster, its origin is not fully clear but it might be related to AGN activity as a connection to a cluster member galaxy is suggested. The cluster also hosts a prominent head-tail radio source in the north, with the tail extending south. along the direction of the proposed merger axis. By fitting the elliptical model we determine $S_{144}=15.7\pm 6.8$ mJy for the candidate radio halo.

This nearby low-mass cluster hosts a bright 800 kpc long tailed radio galaxy associated with the galaxy IC 711. The main tails shows a range of complicated linear features, see Figure 25. LOFAR observations of this source are described Wilber et al. (2019). GMRT observations have been presented by Srivastava & Singal (2016); Sebastian et al. (2017). Another smaller bright tailed radio galaxy is associated with IC 708. In addition, a filamentary source is detected near the cluster center. This is a candidate radio phoenix related to the central BCG IC 712. Our new LOFAR images of Abell 1314 reveal some additional details not visible in the previous LOFAR images presented in Wilber et al. (2019) due to the improved calibration. One of these is a thin elongated structure that connects IC 708 to IC 711. Its origin is unclear. In addition, our images show more clearly the filamentary nature of the phoenix source, with an LLS of 0.44 Mpc.

The LOFAR observations for NSC J143825+463744, a nearby $z=0.03586$ system, are affected by bad ionospheric conditions. Despite of the poor image quality, central extended emission is detected with a size of about$\sim 0.4$ Mpc, see Figure 26. NSC J143825+463744 was classified as a galaxy group (MLCG 1495) by Gal et al. (2003). It is composed of two dominant galaxies NGC 5722 and NGC 5717. No X-ray emission is detected from this system by ROSAT, confirming it has a low mass. Given the lack of an ICM detection by ROSAT, low mass of the system, and poor calibration, we list it as unclassified.

Note that a small EW extended source, right of the image center, is associated with NGC 5714. NGC 5714 is foreground galaxy and unrelated to MLCG 1495.

WHL J122418.6+490549 hosts a bright elongated radio source with an LLS of 370 kpc (Figure 27). This radio emission could have originated from the BCG (LEDA 2333420), which is located at the southeastern tip of the elongated source. The cluster is barely detected in a Chandra observation, indicating a low-mass system. The source seems somewhat similar to the revived remnant radio lobe found in low-mass cluster Abell 1931 (Brüggen et al., 2018).

Faint patchy extended emission is detected in our low resolution images of this cluster, see Figure 28. This emission extends over a region of 1.2 Mpc. Given that the emission is approximately centered on the galaxy distribution we classify it as a candidate radio halo.

Patchy diffuse radio emission with an extent of about 0.5 Mpc is detected west of the BCG (Figure 29). Given its approximate central location we classify it as a candidate radio halo.

Extended radio emission is detected in this cluster south of the BCG, see Figure 30. This emission seems to be the extension of a tailed radio galaxy. Additional extended ($\sim 300$ kpc) emission surrounds the BCG. This candidate radio (mini-)halo will need to be confirmed with deeper observations.

In WHL J125836.8+440111 we find extended radio emission with an LLS of 800 kpc, see Figure 31. The northern part of the emission seems to originate from two radio galaxies. However, the emission extends further south, all the way to a distorted double lobed source. Given the large area that is covered by the extended emission we classify part of this emission as a radio halo.

Our LOFAR observations emphasize the challenge of classifying diffuse cluster radio sources in sensitive low-frequency images. In particular, the distinction between diffuse sources and (old) AGN radio plasma is not always clear. The reason for this is that old AGN plasma also has a steep radio spectrum so this plasma brightens significantly in low frequency images. For example, this manifests itself by the longer tails of tailed radio galaxies. Several of the clusters in our sample show extended AGN emission with an LLS of more than 0.5 Mpc (e.g., PSZ2 G114.99+70.36, PSZ2 G135.17+65.43, Abell 1314, and GMBCG J211.77332+55.09968, see Appendix A.10). AGN with an LLS of a few hundred kpc are even more common. When the emission from tailed and distorted AGN starts to overlap with relics and halos the classification of diffuse emission becomes more difficult.

A second reason for that classification is challenging is related to the origin of the diffuse radio emission itself. Particle re-acceleration models require a source of (mildly) relativistic electrons. The LOFAR images reveal that AGNs provide a rich source of fossil electrons and therefore the observational distinction between plasma directly accelerated by the AGN or in-situ re-accelerated in the ICM becomes more difficult. Spectral measurements and a comparison with the thermal ICM properties will therefore be important to correctly classify the extended radio emission.

Based on the number of detected radio halos and relics in the HETDEX area, we can make a prediction for the number of radio halos and relics that will be detected in the completed LoTSS survey. We assume here that the LoTSS survey will have uniform sensitivity over the entire northern sky. We ignore any complications due to differences in the mass and redshift distributions between the PSZ2 clusters in the HETDEX DR1 area in the completed LoTSS survey. The uncertainties are computed based on Poisson statistics.

We first focus on the radio halos in the Planck PSZ2 clusters. We detect a total of 8 radio halos and 8 candidate halos in this sample of 26 clusters (where we count PSZ2 G107.10+65.32, consisting of Abell 1758N and Abell 1758S, only once). The number of PSZ2 clusters without any diffuse emission is 7. We should note that for three of these clusters the noise levels were higher because of bad ionospheric conditions. Four PSZ2 clusters host radio relics. The fraction of confirmed radio halos in PSZ2 clusters is $31\pm 11\%$. Considering that there are 595 PSZ2 clusters above a declination of 0 degrees with confirmed redshifts, we estimate that there will be $183\pm 65$ radio halos detected in the LoTSS survey in PSZ2 clusters. Also including candidate radio halos, the detection fraction is $62\pm 15\%$. The number of PSZ2 halos in the LoTSS survey then becomes $366\pm 92$. The fraction of clusters with some form of diffuse emission is $73\pm 17\%$. This suggests that $435\pm 99$ PSZ2 clusters with diffuse emission will be detected in LoTSS.

We detect one radio halo in the non-PSZ2 clusters and four candidate radio halos. Considering these numbers, and that the region we surveyed covers 424 deg², we expect to find at least $10^{2}$ radio halos in non-PSZ2 clusters in the full LoTSS. Here we assumed that about half of the candidate radio halos are real. The total number of radio halos (PSZ2 plus non-PSZ2) that will be found in the full LoTSS survey will thus be around 400–500, again assuming that half of the candidates are real.

The number of radio halos that our extrapolation predicts for the LoTSS survey agrees with that predicted from re-acceleration models (Cassano et al., 2010a, 2012). These models predict that a significant fraction of halos have steep spectra, especially in clusters with smaller masses and higher redshift, and that the occurrence of halos in clusters declines with cluster mass. The large statistics that is expected from LoTSS will allow to test the dependence of the occurrence of radio halos with cluster mass and redshift.

Interestingly, we did not detect clear examples of radio mini-halos. Radio mini-halos are more difficult to classify due to their smaller sizes and the sample studied here is not known to host any strong cool-core clusters. Therefore, the lack of radio mini-halos might be (partly) related to the properties of our sample. However, there is no consensus that SZ-selected samples are biased against cool-core clusters Eckert et al. (2011); Rossetti et al. (2017); Andrade-Santos et al. (2017). The lack of mini-halos in our sample could also be a reflection of the properties of mini-halos at low frequencies. Several low-frequency studies have found the presence of diffuse emission at larger radii, beyond the extent of the mini-halos measured at GHz frequencies. Thus, low-frequency studies would be less likely to report mini-halos if size is used as a criterion. Whether this extended emission beyond the “classical” mini-halo extent can be considered as a part of the mini-halo, or is an unrelated component more similar to that of a giant radio halo, is unclear (Bonafede et al., 2014b; Brunetti & Jones, 2014; Kale & Parekh, 2016; Venturi et al., 2017; Savini et al., 2018, 2019; Kale et al., 2019).

A further complication for the detection is mini-halos is the presence of a radio bright BCG. The calibration needs to achieve a dynamic range sufficient for a detection. This can be a challenge at low frequencies, see for example Figure 35.

The fraction of radio relic hosting clusters in PSZ2 is $15\pm 8\%$. We thus expect $92\pm 46$ clusters hosting radio relics in LoTSS. One radio relic is detected in a non-PSZ2 cluster. The expected number of radio relics in the LoTSS survey falls about an order of magnitude below the prediction of Nuza et al. (2012). Predictions are not available yet for more recent models (e.g., Nuza et al., 2017; Brüggen & Vazza, 2020).

It is well established that the radio power of giant halos scales with the X-ray luminosity of clusters (e.g., Liang et al., 2000; Cassano et al., 2006, 2013; Kale et al., 2015). A similar scaling exists for the integrated Compton Y parameter which traces the ICM integrated pressure along the line of sight (Basu, 2012; Cassano et al., 2013). Both the X-ray and SZ measurements are proxies of clusters mass. Therefore the suggestion is that the observed correlations originate from an underlying relation between cluster mass and radio power. The explanation for this relation is that a fraction of the gravitational energy released during a merger event, which scales with cluster host mass, is channeled into the re-acceleration of cosmic rays via turbulence (e.g., Cassano & Brunetti, 2005; Cassano et al., 2004).

Traditionally, the radio power is computed at a rest-frame frequency of 1.4 GHz ($P_{\rm{1.4\leavevmode\nobreak\ GHz}}$) and all correlation studies so far have used this quantity. With the new LOFAR radio halo detections it becomes feasible to study this relation at a rest-frame frequency of 150 MHz, with $P_{\rm{150\leavevmode\nobreak\ MHz}}$ given by

with $D_{L}$ the luminosity distance of the cluster. Because our integrated flux density measurements are obtained at 144 MHz, $P_{\rm{150\leavevmode\nobreak\ MHz}}$ is only marginally affected by the adopted (unknown) radio spectral index.

In this work, we determine the M₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ scaling relation for radio halos using clusters from the PSZ2 catalog which provides an SZ-based mass estimate. SZ-based mass selected samples should be less affected by the cluster’s dynamical state compared to X-ray selected sample which are biased towards relaxed cool-core clusters (e.g., Eckert et al., 2011; Rossetti et al., 2017; Andrade-Santos et al., 2017). We complement our new LOFAR measurements with halo detections in the 120–180 MHz range from the literature when reliable measurements are available, see Table 4. These literature values come mostly from previous LOFAR and GMRT studies. A few of them are taken from Murchison Widefield Array (MWA) studies. We do not include all MWA detections, only those with high-quality measurements, as indicated from good spectral fits with low ($<2$) reduced $\chi^{2}$ values (George et al., 2017), and from halos not significantly affected by the uncertainties from compact source subtraction.

Following Cassano et al. (2013) we use the following relation

between radio power and cluster mass. The best fitting parameters are found using the BCES orthogonal regression algorithm (Akritas & Bershady, 1996; Nemmen et al., 2012). Past work has adopted by default BCES bisector fits (which give consistently flatter slopes), although, as is mentioned by Hogg et al. (2010), bisector fits are not recommended. For comparison with previous work we also report the results from the BCES bisector and $Y|X$ (with $X$ the independent variable) fits. Our sample approximately covers the mass range $3-10\times 10^{14}$ M_⊙. The results are shown in Figure 32 (left panel) and Table 5. As is the case for $P_{\rm{1.4\leavevmode\nobreak\ GHz}}$, there is also a clear correlation between between M₅₀₀ and $P_{\rm{150\leavevmode\nobreak\ MHz}}$ and we find a slope of $B=6.13\pm 1.11$ (BCES orthogonal). With the candidate halos included, we find somewhat flatter slopes (see Table 5), but the differences are not significant considering the uncertainties.

We determine the Y₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ radio halo scaling relation using the PSZ2 Compton Y parameter. For that we convert the Y${}_{5R_{500}}$ values from Planck Collaboration et al. (2016) to Y₅₀₀ using Y₅₀₀ = 0.56 Y${}_{5R_{500}}$ (Arnaud et al., 2010). We also convert the units from arcmin² to Mpc² to facilitate the comparison with Cassano et al. (2013). We apply the same fitting methods as for the M₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ correlation, using a relation of the form

The results are plotted in Figure 32 (right panel) and are reported in Table 5. The slope of the best fit BCES orthogonal relation is $B=3.32\pm 0.65$. The slopes are slightly flatter when including the candidate radio halos, but the differences are not significant considering the uncertainties (see Table 5).

The slopes of the 150 MHz scaling relations we find are steeper than the ones obtained at 1.4 GHz by Cassano et al. (2013). For Y₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ they reported $B=2.28\pm 0.35$ from at 1.4 GHz, compared to $B=3.32\pm 0.65$ in this work. For M₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ they reported a slope of $B=4.51\pm 0.78$, compared to our value of $B=6.13\pm 1.11$ in this work. However, considering the uncertainties, the slopes at 150 MHz are still consistent with the ones reported at 1.4 GHz.

Statistical models employing turbulent re-acceleration (Cassano et al., 2013) predict $P_{\rm{1.4\,GHz}}\propto M_{500}^{4}$, or steeper depending on the ICM magnetic field strength with respect to the equivalent magnetic strength of the cosmic microwave background. It should be noted that these models make a number of simplifying assumptions. The most important simplification is that there is no spatial dependence of the magnetic field and acceleration efficiency, see for example Cassano et al. (2010a) about these “homogeneous models”. Cassano (2010) predicts that the slope of the $L_{X}$–$P_{\rm{1.4\leavevmode\nobreak\ GHz}}$ scaling relation should steepen by about $0.4$ due to the ultra-steep spectrum halos visible at low frequencies associated with intermediate mass galaxy clusters. Using the fact that $L_{\rm{X}}\propto M_{500}^{2}$, we thus expect a steepening of about 0.8 for the M₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ scaling relation. In addition, the scatter around the scaling relations should increase. Interestingly, the slopes we find at 150 MHz are indeed steeper than at 1.4 GHz, in line with this prediction. That said, the uncertainties one the determined slopes are still too large for any firm claim. For this reason, extending the sample size and mass range will be crucially important to confirm this result.

One of the limitations of our presented analysis is that due to the small sample size we did not apply any cut in mass or redshift. For a more detailed comparison with the Cassano et al. (2013), a similar redshift and mass cut should be applied. We also note that our sample contains three clusters (Abell 1413, PSZ1 G139.61+24.20 and RX J1720.1+2638) with diffuse sources that were previously classified as mini-halos. Since the diffuse emission in these clusters turns to be more extended⁵⁵5This also includes Abell 1413 based on new LoTSS data at low frequencies than the typical scale of mini-halos, we have included them in our sample. Further investigations are also required of how the low-frequency scaling relations and occurrence rates depend on the cluster dynamical state. Another limitation of our derived scaling relations is the inclusion of literature values that were obtained in a variety of ways, adopting different methods to measure the integrated flux density. That said, the literature values do not seem to be strongly biased either high or low when compared to the measurements obtained in this work for clusters with similar masses, and hence this should not have a large effect on the derived slopes. This limitation will be removed in future work when larger LOFAR samples will become available.

A comparison between the 150 MHz and 1.4 GHz relations allows use to investigate the average spectral index of radio halos in this frequency range. We find that when using $\alpha=-1.2$ a good match is obtained between the two M₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ scaling relations. For Y₅₀₀–$P_{\rm{150\leavevmode\nobreak\ MHz}}$ a slightly flatter spectral index seems to be preferred (the blue line in Figure 32 (right panel) is located mostly above our best fit). Giovannini et al. (2009) obtained a medium spectral index of $-1.3$ for radio halos between 325 MHz and 1.4 GHz, in reasonable agreement our results. However, for a better assessment of the radio halo spectral indices, detailed cluster-to-cluster comparisons are required. In particular, the used scaling relation from Cassano et al. (2013) did not include USSRHs. This could have a direct effect on the derived spectral indices when comparing to a low-frequency sample which potentially contains a significant number of USSRH.