## Main

We used the LOw Frequency ARray (LOFAR5) to search for signatures of non-thermal radiation in the outer regions of galaxy clusters. We examined the radio emission at 144 MHz from 310 massive clusters from the Planck Sunyaev–Zel’dovich catalogue6 in the LOFAR Two Meter Sky Survey (LoTSS7,8). After a careful removal of contaminating emission from other astronomical sources (Methods) we found that in four cases the radio halo emission is embedded in a much larger emission that extends over 2–3 Mpc and fills the volume of the cluster, at least up to R500 (Fig. 1), that is the radius within which the mean mass over-density of the cluster is 500 times the cosmic critical density at the cluster redshift (z). The mass enclosed in a sphere with radius R500 is M500. These clusters are ZwCl 0634.1+4750 (z = 0.17, M500 = 6.65 × 1014M), Abell 665 (z = 0.18, M500 = 8.86 × 1014M), Abell 697 (z = 0.28, M500 = 10.99 × 1014M) and Abell 2218 (z = 0.17, M500 = 5.58 × 1014M). All these clusters are dynamically disturbed9 and were known to host radio halos10,11,12, yet the larger-scale emission discovered with LOFAR, that we call the ‘megahalo’, enables us to probe the magnetized plasma in a volume that is almost 30 times larger than the volume occupied by the radio halos.

The radial surface brightness profile of ZwCl 0634.1+4750 (Fig. 2) clearly demonstrates the difference to the radio halo emission. The profiles of the other three clusters are shown in Extended Data Fig. 3. All the profiles show two components: a bright region dominated by the radio halo, the brightness of which decreases relatively fast with cluster-centric distance and an extended, low-surface-brightness component. The region of the profile dominated by the radio halo can be fitted with an exponential function as commonly found for these type of sources13. The emission beyond the radio halo shows a shallower profile implying that at 600–800 kpc from the centre a transition occurs. The surface brightness of the large-scale emission is a factor of at least 10 lower than the surface brightness of the radio halo with an average emissivity of approximatly  20  to 25 times lower than the emissivity of radio halos (Methods). The low surface brightness, combined with its large size, is the reason why this emission has eluded all previous searches but could be detected by LOFAR.

For two clusters, ZwCl 0634.1+4750 and Abell 665, we present deep observations at even lower frequencies (53 MHz and 44 MHz, respectively) for which low-energy relativistic electrons shine brightly. In the observation of ZwCl 0634.1+4750 only the brightest part of the large-scale emission beyond the radio halo is detected, whereas in Abell 665 almost all of it is visible (Extended Data Fig. 1). The combination of the low (144 MHz) and ultra-low (around 50 MHz) frequency observations enables us to constrain the energetics of the particles responsible for the synchrotron emission via the radio spectral index α (defined as S(ν) να, with S being the flux density and ν the frequency). We obtained α = −1.62 ± 0.22 and α = −1.64 ± 0.13 for ZwCl 0634.1+4750 and Abell 665, respectively. Although the uncertianties on the spectral index measurements are relatively large, in both cases we found evidence that the spectrum is steeper than the spectrum of the central radio halos, which is α = −1.25 ± 0.15 for ZwCl 0634.1+4750 and α = −1.39 ± 0.12 for Abell 665. This adds to the evidence that the megahalos are a phenomenon distinct from radio halos.

Our results confirm that magnetic fields and relativistic electrons fill a much larger volume than previously observed, therefore requiring ubiquitous mechanisms for the energization of particles on large scales. The existence of megahalos demonstrates that beyond the edge of radio halos mechanisms operate that maintain a sea of relativistic electrons at energies high enough to emit at frequencies of approximately 100 MHz.

The surface brightness of this feature stays fairly constant over more than 500 kpc, whereas the underlying intracluster medium (ICM) density decreases by a factor of around 5 (ref. 14). This can be used to infer the relative contribution to the cluster energy content from thermal and non-thermal components, which has implications, for example, on the Sunyaev–Zel’dovich effect in cosmology15. If the magnetic field scales with the ICM density as found in ref. 16 (B2nICM, where nICM is the density of the ICM), the ratio between the energy density of non-thermal electrons and the thermal gas energy must increase going towards the outer regions of the cluster. For example, for the cluster Abell 2218, whose ICM density profile has been studied in ref. 17, we found that a constant energy density of relativistic electrons with radius can reproduce the observed surface brightness profile. In this case, the ratio between the energy density of non-thermal electrons and the thermal gas energy must increase by a factor of around 3 going from approximately 0.5 × R500 to approximately R500. Alternatively, the magnetic field strength must approximately be increased by a factor of $$\sqrt{3}$$ over those distances to produce the same radio emission. Reproducing the observed trend of cosmic rays and magnetic fields in such peripheral regions of galaxy clusters, where a mixture of accretion modalities and (re)acceleration mechanisms is present, represents an important challenge for future theoretical models of galaxy clusters.

The steep spectrum that we observe in ZwCl 0634.1+4750 and Abell 665 indicates that turbulence might be responsible for maintaining the relativistic electrons inside a volume of the order of 10 Mpc3 (refs. 18,19,20) and that we may be probing a turbulent component different from that powering radio halos. Numerical simulations seem to support this scenario and show that, in addition to the central merger-driven turbulence responsible for radio halos, there is a broader turbulent component, probably related to the accretion of matter onto the cluster, that can accelerate particles21,22,23 (Methods). The observed characteristics of megahalos suggest a change either in the macrophysical or in the microphysical properties of the plasma when moving from the radio halo to the outer region. In the former case, the properties of turbulence may change going towards the periphery, as suggested by simulations. In the latter case, microphysical properties such as the acceleration efficiency, the mean free path or transport properties, all of which are related, may change in the outer regions.

Although the mechanisms responsible for the formation of the large-scale emission are still unknown, it is reasonable to assume that the mass of clusters plays an important role in determining the energy budget available for particle acceleration, similar to what happens for radio halos. In fact, more powerful radio halos are hosted in more massive clusters24. To understand why we have detected this emission only and exactly in these four clusters, in Fig. 3 we show the mass–redshift distribution of the clusters inspected for this work. The three solid lines show the expected mass–redshift relation taking into account the cosmological surface brightness dimming (SB  (1+z)−4) and assuming a power-law dependence of the large-scale emission surface brightness with the mass of the clusters (SB Mβ, where we assumed three possibilities for β). As the large-scale emission in ZwCl 0634.1+4750 is detected at  around 3σ, we impose the condition that the lines go through that point in the diagram to set the normalization. This means that with current LOFAR observations we expect to be able to detect at more than 3σ the large-scale emission that embeds radio halos in clusters that lie above (that is, higher mass) and to the left (that is, lower z) of the assumed dependencies. Interestingly, all the sources that we detected lie in this region. The other clusters with similar masses and redshift either have low-quality data (because of observations being taken during disturbed ionospheric conditions that distort the radio signal at low frequencies) or they are in particularly complex fields for which an accurate subtraction of contaminating sources is not reliable25,26. The fact that the clusters where we discovered the new large-scale emission lie close or above our estimated detection limit in mass–redshift space suggests that we may be seeing just the tip of the iceberg of a phenomenon common to a large number of clusters that can come to light in deeper low-frequency radio observations.

In this Article, we have highlighted the differences between the diffuse emission in the central and outer regions of galaxy clusters. The results of this work may shed light on recent findings for a few clusters where it has been shown that radio halos become larger at lower frequencies, reaching largest linear sizes of the order of 2 Mpc (refs. 26,27,28). Interestingly, all these clusters are massive and would lie on the top left region of the diagram in Fig. 3, supporting the idea of a new, emerging population of sources. Finally, evidence for a two-component nature of diffuse sources has been claimed in a few non-merging clusters29,30,31. However, they do not probe regions of galaxy clusters different from those of radio halos.

Currently, we can only observe megahalos in clusters that meet a certain combination of mass and redshift. However, our study suggests that deeper observations, such as those that will be made with the upgraded LOFAR 2.0 and Square Kilometre Array32, will unveil many more clusters showing diffuse emission on such large scales (Fig. 3), thus opening the possibility for systematic exploration of the peripheral regions of galaxy clusters. Whether megahalos constitute a new class of sources sitting below or embedding radio halos remains to be seen following deeper searches for this emission on larger samples. Whatever the case, the brightness and spectral index profiles suggest that a new type of phenomenology is at play when going to larger distances from the cluster centre.

These results show that relativistic electrons and magnetic fields fill larges swathes of the cosmos. It helps us to understand how energy is dissipated during the formation of large-scale structures as well as how particles are accelerated in low-density plasmas.

## Methods

### Observations and data reduction

The properties of the final images presented in this paper are listed in Extended Data Table 1, together with the source subtraction performed (see below) and the number of the figure in which they are presented.

### LOFAR high-band antenna data reduction

The LOFAR 144 MHz data presented in this paper are part of the LoTSS7,8,33, which is an on-going 120−168 MHz survey of the entire northern hemisphere performed with the LOFAR high-band antennas (HBA). Data have been processed with the Surveys Key Science Project reduction pipeline v.2.2 (refs. 7,34), which includes corrections for both direction-independent and direction-dependent effects (prefactor35,36,37, killMS38,39 and DDFacet40). We subtract all the sources outside a region of around 0.5 deg2 containing the galaxy clusters from the uv-data by using the model produced by the pipeline. We then phase shift the dataset to the centre of the extracted region, we correct for the LOFAR station beam in that direction and we perform additional loops of phase and amplitude calibrations on the target field to improve the quality of the final image. This extraction procedure is presented in ref. 41 and is routinely used in LOFAR 144 MHz observations. The data reduction of the clusters of the Planck sample is discussed in detail in ref. 42. Here we performed a more accurate procedure for the source subtraction aimed at removing the contribution of the extended radio galaxies embedded in the diffuse emission. The final images are produced with the multifrequency deconvolution scheme in WSClean43,44. Different resolutions are obtained using different weighting schemes. We did not attempt an in-band spectral analysis because of the narrow frequency range of LoTTS, combined with the uncertainties in the flux density scale and the high r.m.s. noise of the in-band images, which especially affects the resolved low signal-to-noise sources, such as megahalos8.

### LOFAR low-band antenna data reduction

ZwCl 0634.1+4750 and Abell 665 have been observed with the LOFAR low-band antennas (LBA) for 8 hours in the frequency range of 30–77 MHz and 30–60 MHz, respectively. We used the LBA_OUTER antenna configuration, for which only the outermost antennas are selected, because this simplifies the calibration by reducing the primary beam size and the electromagnetic crosstalk between the dipoles. Observations were performed in multibeam mode, with one beam continuously pointing at the calibrator and one beam continuously pointing at the target.

The data reduction of the calibrator follows the procedure described in ref. 37 and it is used to isolate direction-independent systematic effects such as the bandpass, the stations’ clocks drifts and the polarization misalignment caused by time delays between the X and Y polarization signals. The solutions are then applied to the target field along with the primary beam correction in the direction of the target.

The self-calibration steps of the target field are described in ref. 45. The self-calibration starts with a model obtained from the combination of existing surveys at higher frequencies: TGSS46, NVSS47, WENSS48 and VLSS49. We estimate the spectral indices of the sources present in these surveys and we extrapolate their flux densities to LBA frequencies. Then, we estimate direction-independent (field-averaged) differential total electron content solutions by calibrating against the predicted model. Next we solve and correct for the average differential Faraday rotation and second-order beam effects. Sources outside the main lobe of the primary beam are imaged and subtracted from the uv-data before proceeding with a second self-calibration cycle. The main errors that still affect the data at this point are the direction-dependent errors caused by the ionosphere. The procedure to correct for direction-dependent errors is discussed in refs. 45,50. As a first step, sources in the direction-independent calibrated image are grouped by proximity and the brightest groups are identified to be used as calibrators in the direction-dependent calibration. All the sources in the field are subtracted using the direction-independent model image. We then iterate on the calibrators, starting with the brightest one. The calibrator’s visibilities are added back to the data and the dataset is phase-shifted in the calibrator direction. We run several rounds of self-calibration and the improved model of the calibrator is re-subtracted to produce a cleaner empty dataset, before repeating the procedure for the next brightest calibrator.

After the wide-field direction-dependent calibration, further improvement of the image quality can be achieved by extraction and self-calibration of a small region around the target of interest. We follow the idea presented in ref. 41 and use an LBA-specific implementation of the extraction strategy. We use the final model and the solutions of the direction-dependent calibration to accurately subtract all sources in the field except for those in a circular region around the targets. The radii of these regions are $$2{3}^{{\prime} }$$ and $$1{4}^{{\prime} }$$ for ZwCl 0634.1+4750 and Abell 665, respectively, and they are chosen to include sufficient compact source flux densities to obtain robust calibration solutions. Then the data is phased-shifted to the centre of this region and further averaged in time and frequency. After correcting for the primary beam in this direction, we perform several rounds of self-calibration on the target, starting from the model obtained using the solutions of the closest direction-dependent calibrator. The images at high and low resolution are shown in Extended Data Fig. 1.

### High-resolution 144 MHz images of the clusters and source subtraction procedure

Following the approach described in ref. 9,13, we derived the azimuthally averaged surface brightness radial profile of the radio emission of the four clusters (Extended Data Fig. 3). We used low-resolution (60) images after subtracting only the sources visible in the high-resolution image to have a good compromise between sensitivity to the extended emission and resolution to characterize the profile, and to possibly distinguish between the radio halo and the more extended emission. We note that the whole extension of the diffuse emission is best detected in the 2′ resolution images (Fig. 1) that we used to measure the size of the sources. If the image contains some residuals from bright diffuse sources, we masked them and we excluded the masked pixels when calculating the surface brightness. This is the case in Abell 665, for which we masked the residuals of a diffuse patch of emission that does not appear to be associated with the megahalo. In Abell 697 we also masked the residuals of a bright compact source in the north and a radio galaxy in the south (these sources are visible in Extended Data Fig. 2). For Abell 665 we considered only the southern part of the cluster because the northern part has been crossed by a shock front51, which may have altered the properties of the diffuse emission. We averaged the radio brightness in concentric annuli, centred on the peak of the radio halo and chose the width of the annuli to be half of the full-width half-maximum of the beam of the image. We considered only annuli with an average surface brightness profile higher than three times the uncertainty associated with the annuli surface brightness. In the images we show the detection limits for each annulus calculated as $${\rm{r.m.s.}}\times \sqrt{{N}_{{\rm{beam}}}}$$, where Nbeam is the number of beams in the annulus.

All the profiles show a discontinuity. The central annuli before the discontinuity follow an exponential profile, similar to other classical radio halos9,13. This first component can be fitted with an exponential law in the form:

$$I(r)={I}_{0}{e}^{-\frac{r}{{r}_{e}}},$$
(1)

where I0 is the central surface brightness and re is the e-folding radius, that is the radius at which the surface brightness is I0/e.

To perform the fit, we first generated a model using equation (1) with the same size and pixel size of the radio image and we convolved it with a Gaussian with a full-width half-maximum equal to the beam of the image. Then, we azimuthally averaged the exponential model with the same set of annuli used for the radio halo. The resulting surface brightness profile is the fit that takes into account the resolution of the image and the uncertainties associated with the sampling of the radial profile.

The discontinuity in surface brightness is less pronounced in Abell 665 than in the other three cases. However, there is a second component that is not consistent with the radio halo profile. In addition, the large-scale diffuse emission in Abell 665 shows clear differences with the central radio halo also in terms of spectrum and emissivity (see below). Hence, we consider it a megahalo.

In two cases, ZwCl 0634.1+4750 and A697, the diffuse emission beyond the classical radio halos is not symmetric with respect to the centre of the radio halo. Therefore, we performed the fit also in the semi-annuli on the left-hand side of the red line shown in Extended Data Fig. 3. The discontinuity is also present in this case.

### Spectral index analysis

We measured the spectral index of the radio halo in ZwCl 0634.1+4750 in the central region shown in Extended Data Fig. 1a. We obtained a flux density of 39.6 ± 4.0 mJy at 144 MHz and 138.3 ± 15.9 mJy at 53 MHz, corresponding to α = −1.25 ± 0.15. The uncertainties on the integrated flux densities in this section take into account the systematic error given by the uncertainty on the flux scale and the statistical error associated with the r.m.s. noise of the image in the integration area. The emission beyond the radio halo in ZwCl 0634.1+4750 is marginally detected by the LBA. Therefore, we focused on the region shown in Extended Data Fig. 1a to estimate the integrated spectral index of this new emission. In this region we measured 35.8 ± 7.5 mJy at 53 MHz and 6.8 ± 0.6 mJy at 144 MHz, which gives a spectral index α = −1.62 ± 0.25. The average surface brightness of the megahalo at 144 MHz, extrapolated at 53 MHz with this spectral index, would be below two times the r.m.s. noise of the lowest resolution LBA image. This explains why we do not detect the whole megahalo emission in the LBA.

We used the HBA and LBA images at 37 resolution to produce the spectral index map of Abell 665 (Extended Data Fig. 4). In these images, the sources visible in the high-resolution image have been subtracted. We produced a pixel-by-pixel spectral index map using all pixels that had a surface brightness above 2σ in both images. We then carried out the linear regression using a bootstrap Monte-Carlo method obtaining 1,000 estimations of the spectral index values per pixel. The reported spectral index is the mean of the distribution of the estimations and the uncertainty is its standard deviation.

The spectral index of the diffuse emission in Abell 665 ranges from around −0.5 to −2. In particular, we note that the spectrum of the northern part is relatively flat. However, a combination of shock and turbulent acceleration could produce a flatter and less uniform spectrum than expected from turbulence alone51. Hence, we focused on the southern part of the cluster, marked by the regions in Extended Data Fig. 1 to derive the integrated spectral index. The choice of the regions is based on the surface brightness radial profile (Extended Data Fig. 3c,d). In particular, the limit between the regions where we measure the flux densities corresponds to the annulus in which the surface brightness profile flattens with respect to the classical radio halo exponential function. In these regions we measured a flux density for the radio halo of 120.3 ± 12.1 mJy at 144 MHz and 614.6 ± 62.9 mJy at 44 MHz, corresponding to α = −1.39 ± 0.12. In the region beyond the radio halo, we measured 58.2 ± 6.1 mJy at 144 MHz and 398. ± 45.8 mJy at 44 MHz, obtaining a spectral index α = −1.64 ± 0.13.

### Emissivity

We calculated the volume-averaged emissivity at frequency ν in radio halos and megahalos by assuming that their radio power, Pν, comes from a sphere of radius R:

$${J}_{\nu }=\frac{{P}_{\nu }}{\frac{4}{3}{\rm{\pi }}{R}^{3}}$$
(2)

We estimated the source radii via $$\sqrt{{R}_{\min }\times {R}_{\max }}$$ (ref. 52), where $${R}_{\min }$$ and $${R}_{\max }$$ are the minimum and maximum radii of the 3σ contours, respectively, in Fig. 1 (we used the 30 resolution images for radio halos and the 2′ resolution images for megahalos). We subtracted the extended radio galaxies in the fields to the best of our abilities given current techniques. However, we are aware that the central regions of the 2′ resolution images shown in Fig. 1 may be affected by residuals from the subtracted radio halos. It seems reasonable to assume that the megahalo also permeates the region of the classical radio halos. Hence, to estimate the flux density of the new type of emission, we measured the mean surface brightness in a region that excludes the central halos and then multiplied it by the total area within the 3σ contours. A direct measurement of the flux density inside the area delimited by the 3σ contours would give marginal differences of the order of 5−15%. To compare these emissivities with the typical emissivity of radio halos24, we estimated the flux density at 1.4 GHz, by assuming a conservative spectral index of −1.3, for both radio halos and megahalos. If the spectral index of the detected emission is steeper, the emissivity at 1.4 GHz would be even lower. The emissivities of radio halos and megahalos for each cluster are listed in Extended Data Table 2, together with the size and the spectral index (when available) of the sources. The uncertainties include the systematic errors given by the uncertainty on the flux scale, the statistical error associated with the r.m.s. noise of the image in the integration area and the subtraction error related to the uncertainty on the subtracted flux. For the latter we used the approach described in ref. 42. We do not take into account the uncertainty in the estimated size of the diffuse emission. The emissivity of megahalos is a factor of  around 20−25 lower than the emissivity of the radio halos in the same clusters. For comparison, the typical emissivity of classical radio halos at 1.4 GHz ranges between 5 × 10−43 and 4 × 10−42 erg s−1 cm−3 Hz−1 in clusters with similar masses24.

### Simulations of turbulence in galaxy clusters

High-resolution hydrodynamic, cosmological simulations of the ICM can shed some light on megahalos. We analysed a set of 20 (M500 ≥3 × 1014M at z = 0.0) galaxy clusters22 and used small-scale filtering to calculate the turbulent kinetic energy flux, $${F}_{{\rm{turb}}}=\rho \,{\sigma }_{v}^{3}/L$$, within simulated cells (each cell having a 323 kpc3 volume), where ρ is the local gas density and σv is the dispersion of the velocity field measured within the scale length L (ref. 53). Then we measured the average distribution of Fturb in relaxed and disturbed clusters, and in the inner as well as outer regions, where megahalos are observed (approximately 0.4 × R500 < r ≤ R500).

Extended Data Fig. 5 shows that the turbulent kinetic energy flux, Fturb, in the central regions of postmerger clusters is elevated by a factor of around 10 compared with relaxed clusters. This is consistent with the idea that radio halos are produced by the dissipation of turbulence following a merger18,19,54,55,56. However, in the outer regions Fturb is notably similar in relaxed and disturbed clusters. This shows the presence of a baseline level of turbulence that is induced by the continuous accretion of matter in cluster outskirts. Hence, this level of turbulence is likely to be common to all clusters. In this picture, megahalos may also be generated by Fermi II re-acceleration in more relaxed clusters without central radio halos. Future deeper observations, such as those that will be made with LOFAR 2.0, will enable us to test this scenario.