Diffuse Radio Emission from Galaxy Clusters

4.1.1 Results from RM Studies

The presence of magnetic field in clusters is demonstrated by statistical studies. The comparison between the RMs of polarized extragalactic radio sources in the line of sight of galaxy clusters and RM measurements made outside of the projected cluster regions shows excess of the standard deviations of RM values in the cluster areas (cf., Clarke et al. 2001; Böhringer et al. 2016), see Fig. 4. This is consistent with ubiquitous cluster magnetic fields of a few μGauss strength, coherent cells of about 10 kpc, and a magnetic field energy density of a few per mille of the thermal energy density.

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Information about the magnetic field in individual clusters through RM studies has been obtained so far for about 30 objects, including both merging and relaxed clusters. The best studied cluster is Coma, whose magnetic field has been obtained with RM information on 7 radio galaxies in the cluster central region (Bonafede et al. 2010), and 7 additional radio galaxies in the peripheral Coma southwest region, where the NGC 4839 infalling group and the cluster radio shock are located (Bonafede et al. 2013). A single-cell model is not appropriate to describe the observed data, which are generally consistent with a turbulent field following a Kolmogorov power-law spectrum. From energy considerations, i.e., to avoid that the magnetic pressure exceeds the thermal pressure in the outer cluster regions, it is inferred that the magnetic field profile scales with the gas density \(n_{th}\) as \(B \propto n_{th}^{\eta }\). The value of the index \(\eta \) reflects the magnetic field formation and amplification. It is expected that \(\eta =2/3\) in the case of adiabatic compression during a spherical collapse due to gravity. In this case, the field lines are frozen into the plasma and compression of the plasma results in compression of the flux lines (as a consequence of magnetic flux conservation). A value \(\eta =1/2\) is instead expected if the energy in the magnetic field scales as the energy in the thermal plasma. Other values of \(\eta \) may be obtained by specific combinations of compression orientation and magnetic field orientation.

The Coma cluster magnetic field is well represented by a Kolmogorov power spectrum with minimum scale of ∼2 kpc and maximum scale of ∼34 kpc. The central field strength is 4.7 μGauss and the radial slope is \(\propto n_{th}^{0.7}\) (Bonafede et al. 2010), see Fig. 5. The magnetic field of the southwest peripheral region is found to be ∼2 μGauss, i.e., higher than that derived from the extrapolation of the radial profile obtained for the cluster center; a boost of magnetic field of ∼ a factor of 3 is required. The magnetic field amplification does not appear to be limited to the cluster radio shock region, but it must occur throughout the whole southwestern cluster sector, including the NGC 4839 group (Bonafede et al. 2013).

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In the clusters analyzed so far, it is derived that cool core clusters have central magnetic field intensities of the order of a few 10 μGauss, while merging clusters are characterized by intensities of a few μGauss. The fields are turbulent, with spatial scales in the range 5–500 kpc, and coherence lengths of a few 10 kpc. The values of the profile index \(\eta \) are in the range 0.4–1, therefore no firm conclusion can be drawn on the radial trend of the magnetic field. Recently, Govoni et al. (2017) found a correlation between the central electron density and mean central magnetic field strength (\(\eta =0.47\)) using data for 9 clusters. No correlation seems to be present between the mean central magnetic field and the cluster temperature. In conclusion, good information about the central magnetic field intensity in clusters has been obtained, whereas the magnetic field structure (profile, coherence scale, minimum and maximum scales, power spectrum, link to cluster properties) is still poorly known.

4.1.2 Statistical Studies from Fractional Polarization

From the analysis of the fractional polarization of radio sources in a sample of X-ray luminous clusters from the NVSS, a clear trend of the fractional polarization increasing with the distance from the cluster center has been derived (Bonafede et al. 2011). The low fractional polarization in sources closer to the cluster center is interpreted as the result of higher beam depolarization, occurring in the ICM because of fluctuations within the observing beam and higher magnetic field and gas densities in these regions. Results are consistent with fields of a few μGauss, regardless of the presence or not of radio halos. A marginally significant difference between relaxed and merging clusters has been found.

4.1.3 Lower Limits from IC Emission

CR electrons present in the ICM should scatter photons from the CMB, creating a hard power-law of X-ray emission, on top of the thermal Bremsstrahlung from the ICM (Rephaeli 1979; Rephaeli et al. 1994; Sarazin and Kempner 2000). Despite several claims made over the last decades, it seems that there is no conclusive evidence yet for this IC emission from the diffuse CR component of the ICM (e.g., Fusco-Femiano et al. 2000, 2001; Rephaeli and Gruber 2004; Rossetti and Molendi 2004; Fusco-Femiano 2004; Rephaeli et al. 2008; Eckert et al. 2008; Wik et al. 2009, 2014; Ajello et al. 2009; Molendi and Gastaldello 2009; Kawaharada et al. 2010; Wik et al. 2012; Gastaldello et al. 2015). The difficultly associated with the detection of IC emission is related to the requirement of accurately modeling the contributions of the instrumental and astronomical backgrounds.

By deriving upper limits on the IC X-ray emission and combining that with radio flux density measurements of radio halos, lower limits on the global ICM magnetic field strength can be computed. For radio halos, it is generally challenging to obtain stringent lower limits. The reason is that radio halos are typically faint. In addition, the IC emission is co-spatial with the thermal ICM, making it harder to separate the components. Furthermore, bright radio galaxies located in the cluster center can also produce non-thermal X-ray emission. The obtained lower magnetic field strength limits are therefore less constraining than the ones obtained for radio shocks (see Sect. 4.2). The lower limits that have been computed for radio halo hosting clusters range around \(0.1\mbox{--}0.5\) μGauss. For example, for the Coma cluster Rossetti and Molendi (2004) found \(B > 0.2\mbox{--}0.4\) μGauss and Wik et al. (2009) reported \(B > 0.15\) μGauss. For the Bullet cluster a limit of \(B > 0.2\) μGauss was determined (Wik et al. 2014). Magnetic field strength limits for the cluster Abell 2163 are \(B>0.2\) μGauss and \(B>0.1\) μGauss (Sugawara et al. 2009; Ota et al. 2014). A recent overview of constraints on the volume-average magnetic field for radio halo and relic hosting clusters is given by Bartels et al. (2015).

5.1.1 Morphology

Radio halos typically have a smooth and regular morphology with the radio emission approximately following the distribution of the thermal ICM. This is supported by quantitative studies which find a point-to-point correlation between the radio and X-ray brightness distributions (Govoni et al. 2001a; Feretti et al. 2001; Giacintucci et al. 2005; Brown and Rudnick 2011; Rajpurohit et al. 2018)), although there are some exceptions. One example is the Bullet cluster, where no clear correlation is found (Shimwell et al. 2014).

A few radio halos with more irregular shapes have been uncovered (e.g., Giacintucci et al. 2009b; Giovannini et al. 2009, 2011). One striking example is MACS J0717.5+3745, where a significant amount of small scale structure is present within the radio halo (van Weeren et al. 2017a). Although, it is not yet clear whether these structures really belong to the radio halo or if they are projected on top of it. Two other peculiar cases are the “over-luminous” halos in the low luminosity X-ray cluster Abell 1213 (Giacintucci et al. 2009b) and 0217+70 (Brown et al. 2011a). Giovannini et al. (2011) discussed the interesting possibility that over-luminous halos represent a new class. However, better data is required to further investigate this possibility since none of these “peculiar” halos have been studied in great detail, making the classification and interpretation more uncertain. For example, the peculiar “halo” in A523 has also been classified as a possible radio shock by van Weeren et al. (2011b).

5.1.2 Radio Spectra

The spectral properties of radio halos can provide important information about their origin. Therefore, considerable amount of work has gone into measuring the spectral properties of halos.

A complication is that reliable flux density measurements of extended low signal to noise ratio sources are often not trivial to obtain. Reported uncertainties on flux density measurements in the literature often take into account the (1) map noise, assuming the noise is Gaussian distributed and not varying spatially across the radio halo, (2) flux-scale uncertainty, usually somewhere between 2 and 20%, and (3) uncertainty in the subtraction of flux from discrete sources embedded in the diffuse emission. Correctly assessing latter effect can be hard, in particular at low frequencies when extended emission from radio galaxies (i.e., their tails and lobes) becomes more prominent and partly blends with the halo emission. Errors from incomplete uv-coverage and deconvolution are usually not included in the uncertainties. However, in principle they can be determined but this requires some amount of work. The uncertainties related to calibration errors, for example coming from model incompleteness or ionosphere, are often not fully taken into account. Calibration errors affect discrete source subtraction, the map noise distribution, deconvolution, and can lead to flux “absorption”. For the above reasons, the reported uncertainties on radio halo flux-density measurements and spectral index maps in the literature can usually be thought of as lower limits on the true uncertainty.

5.1.3 Integrated Spectra

Most radio halos have integrated spectral indices in the range \(-1.4<\alpha <-1.1\) (e.g., Giovannini et al. 2009).

The spectral information of most radio halos is based on measurements at just two frequencies. Recently, two systematic campaigns have been carried out with the GMRT to follow-up clusters at lower frequencies to obtain spectra (Macario et al. 2013; Venturi et al. 2013). Flux density measurements at more than three frequencies that also cover a large spectral baseline are rare. Therefore, deviations from power-law spectral shapes are difficult to detect. The best example of a radio halo with an observed spectral steepening, displayed in Fig. 7, is the Coma cluster (Thierbach et al. 2003). Importantly, it has also been shown that most of this steepening is not due to the Sunyaev-Zel’dovich effect (SZ) decrement (Brunetti et al. 2013). Other halos with well sampled spectra include the Toothbrush and Bullet cluster which show power-law spectral shapes (Liang et al. 2000; van Weeren et al. 2012b; Shimwell et al. 2014).

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There is some evidence that the integrated spectra of radio halos show a correlation with the global ICM temperature of clusters, where hotter clusters host halos with flatter spectra (Feretti et al. 2004a; Giovannini et al. 2009). However, Kale and Dwarakanath (2010) pointed out that comparing the average values of ICM temperatures and of spectral indices can give inconclusive results.

5.1.4 Resolved Spectra

The first detailed study of the spatial distribution of the radio spectral index across a radio halo was carried out by Giovannini et al. (1993). They found a smooth spectral index distribution for the Coma cluster radio halo, with evidence for radial spectral steepening. For Abell 665 and Abell 2163 hints of radial spectral steepening where also found in undisturbed cluster regions (Feretti et al. 2004b). A caveat of these studies is that they were not done with matched uv-coverage, which could lead to errors in the derived spectral index distributions. Some other studies of radio halo spectral index distributions are Giacintucci et al. (2005), Orrú et al. (2007), Pizzo and de Bruyn (2009), Kale and Dwarakanath (2010), Shimwell et al. (2014), Pearce et al. (2017). Two examples radio halo spectral index maps, for the massive merging clusters Abell 2744 and the Toothbrush, are shown in Fig. 8. It shows that the spectral index is rather uniform across these radio halos.

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A spatial correlation between radio spectral index and ICM temperature (\(T\)) for Abell 2744 was reported by Orrú et al. (2007), with flatter spectral index regions corresponding to higher temperatures. However, using deeper VLA and Chandra data this result was not confirmed (Pearce et al. 2017). Similarly, no clear evidence for such a correlation was founding in Abell 520 (Vacca et al. 2014), the Toothbrush Cluster (van Weeren et al. 2016), the Bullet cluster (Shimwell et al. 2014), and Abell 2256 (Kale and Dwarakanath 2010). The current results therefore indicate there is no strong \(T-\alpha \) correlation present, although more studies are necessary. It has been noted that even in the presence of an underlying \(T-\alpha \) correlation, projection effects might also significantly reduce the detectability (Kale and Dwarakanath 2010).

5.1.5 Ultra-Steep Spectrum Radio Halos

The prime example of a USSRH is found in Abell 521 (Brunetti et al. 2008; Dallacasa et al. 2009), Other clusters with USSRH or candidate USSRH are Abell 697 (Macario et al. 2010, 2013; van Weeren et al. 2011b), Abell 2256 (Brentjens 2008), Abell 2255 (Feretti et al. 1997a; Pizzo and de Bruyn 2009), Abell 1132 (Wilber et al. 2018b), MACS J0416.1–2403 (Pandey-Pommier et al. 2015), MACS J1149.5+2223 (Bonafede et al. 2012), Abell 1300 (Reid et al. 1999; Venturi et al. 2013), and PSZ1 G171.96–40.64 (Giacintucci et al. 2013). It should be noted that a number of these USSRH still need to be confirmed. The reason is that reliable spectral index measurements are difficult to obtain because of differences in uv-coverage, sensitivity, resolution, and absolute flux calibration. This situation will improve with the new and upgraded radio telescopes that have become operational, in particular at low frequencies. One example of a candidate radio halo with an ultra-steep spectrum was Abell 1914 (Bacchi et al. 2003). Recent LOFAR and GMRT observations suggest that the most of the diffuse emission in this cluster does not come from a halo but instead from a radio phoenix (Mandal et al. 2018).

5.1.6 Polarization

Radio halos are found to be generally unpolarized. This likely is caused by the limited angular resolution of current observations, resulting in beam depolarization. This effect is significant when the beam size becomes larger than the angular scale of coherent magnetic field regions. Even at high-angular resolution, magnetic field reversals and resulting Faraday rotation will reduce the amount of observed polarized flux.

For three clusters, Abell 2255, MACS J0717.5+3745, and Abell 523 significant polarization has been reported (Govoni et al. 2005; Bonafede et al. 2009b; Girardi et al. 2016), but it is not yet fully clear whether this emission is truly from the radio halos, or from polarized cluster radio shocks projected on-top or near the radio halo emission (Pizzo et al. 2011; van Weeren et al. 2017a).

Govoni et al. (2013) modeled the radio halo polarization signal at 1.4 GHz and inferred that radio halos should be intrinsically polarized. The fractional polarization at the cluster centers is about 15–35%, varying from cluster to cluster, and increasing with radial distance. However, the polarized signal is generally undetectable if it is observed with the low sensitivity and resolution of current radio interferometers. The Govoni et al. (2013) results are based on MHD simulations by Xu et al. (2011, 2012) which are probably not accurate enough yet to resolve the full dynamo amplification. Whether this will affect the predicted fractional polarization levels is not yet clear, see Donnert et al. (2018). If the polarization properties of radio halos can be obtained from future observations it would provide very valuable information on the ICM magnetic field structure.

5.1.7 Samples and Scaling Relations, Merger Connection

Statistical studies of how the radio halo properties relate to the ICM provide important information on the origin of the non-thermal CR component.

It is well known (e.g., Liang et al. 2000; Enßlin and Röttgering 2002; Feretti 2003; Yuan et al. 2015) that the radio power (luminosity) of giant halos correlates with the cluster X-ray luminosity (\(L_{\mathrm{{X}}}\)), and thus cluster mass. For observational reasons, the radio power at 1.4 GHz (\(P_{\text{{1.4~GHz}}}\)) is commonly used to study scaling relations. The X-ray luminosity is often reported in the 0.1–2.4 keV ROSAT band. Figure 9 shows a compilation of radio halos and upper limits on a mass-\(P_{\text{{1.4~GHz}}}\) and \(L_{\mathrm{{X}}}\)–\(P _{\text{{1.4~GHz}}}\) diagram. Detailed investigations of the scaling relations between radio power and X-ray luminosity (or mass), based on the turbulent re-acceleration model, were performed by Cassano et al. (2006, 2007, 2008a). These models were also used to predict the resulting statistics for upcoming radio surveys (Cassano et al. 2010a, 2012; Cassano 2010). More recently, the integrated Sunyaev-Zel’dovich Effect signal (i.e., the Compton \(Y_{\mathrm{{SZ}}}\) parameter) has been used as a proxy of cluster mass (Basu 2012; Cassano et al. 2013; Sommer and Basu 2014). The advantage from using this proxy stems from the fact that \(Y_{\mathrm{ {SZ}}}\) should be less affected by the dynamical state of a cluster, providing less scatter compared to \(L_{\mathrm{{X}}}\) (e.g., Motl et al. 2005; Wik et al. 2008).

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Radio halos are rather common in massive clusters. An early study by Giovannini et al. (1999) showed that about 6%–9% of \(L_{\mathrm{ {X}}} < 5\times 10^{44}~\text{erg}\,\text{s}^{-1}\) clusters host halos at the limit of the NVSS survey, while this number increases to 27%–44% above this luminosity. Extensive work, mainly using the GMRT, provided further improvements on the statistics, showing that the occurrence fraction for clusters with \(L_{\mathrm{{X}}} > 5\times 10^{44}~\text{erg}\,\text{s}^{-1}\) is about 30% (Venturi et al. 2007, 2008; Cassano et al. 2013; Kale et al. 2015). For a mass-selected sample (\(M >6\times 10^{14}~\mbox{M}_{\odot }\)), Cuciti et al. (2015) found evidence for a drop in the halo occurrence fraction for lower mass clusters. For clusters with \(M >8\times 10^{14}~\mbox{M}_{\odot }\) this fraction is \(\approx 60\%\mbox{--}80\%\), dropping to \(\approx 20\%\mbox{--}30\%\) below this mass.

An important result from observations is that giant radio halos are predominately found in merger clusters, as indicated by a disturbed ICM and/or other indicators of the cluster’s dynamical state, e.g., the velocity distribution of cluster member galaxies, presence of multiple BCGs, and galaxy distribution. Early work already established evidence that radio halos were related to cluster merger events as determined from X-ray observations (e.g., Feretti et al. 2000; Buote 2001; Schuecker et al. 2001, 2002; Feretti 2002; Giovannini and Feretti 2002; Böringer and Schuecker 2002). This conclusion is also supported by optical studies (Ferrari et al. 2003; Boschin et al. 2004, 2006, 2008, 2009, 2012b,a; Girardi et al. 2006, 2008, 2010, 2011, 2016; Barrena et al. 2007a, 2014; Golovich et al. 2016). A common method is to use the cluster’s X-ray morphology as an indicator of the cluster’s dynamical state, such as the centroid shift, power ratio, and concentration parameter (Buote 2001; Cassano et al. 2010b). Almost all giant (\(\gtrsim 1\) Mpc) radio halos so far have been found in dynamically disturbed clusters. Recent studies also confirm this general picture (Cassano et al. 2013; Kale et al. 2015; Cuciti et al. 2015), but see Sect. 5.2.3 for some exceptions.

Further support for the relation between cluster mergers and the presence of radio halos was presented by Brunetti et al. (2009). They found that there is a radio bi-modality between merging and relaxed clusters. Merging clusters host radio halos, with the radio power increasing with \(L_{\mathrm{X}}\). Relaxed clusters do not show the presence of halos, with upper limits located well below the expected correlation. Similarly, Rossetti et al. (2011), Brown et al. (2011b) find that the occurrence of halos is related to the cluster’s evolutionary stage. Early work by Basu (2012) reported a lack of a radio bimodality in the Y–P plane. However, this was not confirmed by Cassano et al. (2013). On the other hand, X-ray selected cluster samples are biased towards selecting cool core clusters, which generally do not host giant radio halos, and hence the occurrence fraction of radio halos in SZ-selected samples is expected to be higher (Sommer and Basu 2014; Andrade-Santos et al. 2017). Recently, Cuciti et al. (2018) found two radio halos that occupy the region below the mass-\(P_{\text{1.4 GHz}}\) correlation. These two underluminous radio halos do not have steep spectra and could be generated during minor mergers where turbulence has been dissipated in smaller volumes, or be “off-state” radio halos originating from hadronic collisions in the ICM.

Some merging clusters that host cluster double radio shocks (see Sect. 6.1.2), do not show the presence of a radio halo (Bonafede et al. 2017). This absence of a radio halo might be related to early or late phase mergers, and the timescale of halo formation and disappearance. Although, these results are not yet statistically significant given the small sample size.

Cassano et al. (2016) investigated whether giant radio halos can probe the merging rate of galaxy clusters. They suggested that merger events generating radio halos are characterized by larger mass ratios. Another possible explanation is that radio halos may be generated in all mergers but their lifetime is shorter than the timescale of the merger-induced disturbance. The lack of radio halos in some merging clusters can also be caused by the lack of sufficiently deep observations. One prime example is Abell 2146 (Russell et al. 2011) where no diffuse emission was found in GMRT observations. However, recent deep VLA and LOFAR observations revealed the presence of a radio halo in this cluster (Hlavacek-Larrondo et al. 2018; Hoang et al. 2018a).

5.1.8 Origin of Radio Halos

The origin of radio halos have been historically debated between two models: the hadronic and turbulent re-acceleration models. In the hadronic model, radio emitting electrons are produced in the hadronic interaction between CR protons and ICM protons (Dennison 1980; Blasi and Colafrancesco 1999; Dolag and Enßlin 2000; Miniati et al. 2001a; Pfrommer et al. 2008; Keshet and Loeb 2010; Enßlin et al. 2011). In the re-acceleration model, a population of seed electrons (e.g., Pinzke et al. 2017) is re-accelerated during powerful states of ICM turbulence (Brunetti et al. 2001; Petrosian 2001; Donnert et al. 2013; Donnert and Brunetti 2014), as a consequence of a cluster merger event. While indirect arguments against the hadronic model can be drawn from the integrated radio spectral (Brunetti et al. 2008) and spatial characteristics of halos, and from radio-X-ray scaling relations (for a review see Brunetti and Jones 2014), only gamma-ray observations, which will be discussed in more detail below (Sect. 5.1.9), of the Coma cluster directly determined that radio halos cannot be of hadronic origin. The spatial distribution of spectral indices across radio halos, which can go from being very uniform to more patchy, might provide further tests for turbulent re-acceleration model. Furthermore, additional high-frequency (\(\gtrsim 5\) GHz) observations of known radio halos would enable a search for possible spectral cutoffs. Such cutoffs are expected in the framework of the turbulent re-acceleration model, but have so far rarely been observed (see Sects. 5.1.3 and 5.1.5). Such measurements would be quite challenging though, requiring single dish observations to avoid resolving out diffuse emission.

Nowadays, turbulent re-acceleration is thought to be the main mechanism responsible for generating radio halos, even if other mechanisms as magnetic reconnection have been proposed (e.g., Brunetti and Lazarian 2016). However, one of the main open questions for the re-acceleration model is the source of the seed electrons. There are several possibilities, with secondary electrons coming from proton-proton interactions being an obvious candidate (Brunetti and Blasi 2005; Brunetti and Lazarian 2011). The seed electrons could also have been previously accelerated at cluster merger and accretion shocks. A third possibility is that the seed electrons are related to galaxy outflows and AGN activity. The latter, in particular, is becoming more and more evident thanks to the recent low-frequency observation of re-energized tails (de Gasperin et al. 2017a, see Sect. 6.3) and fossil plasma sources (e.g., Shimwell et al. 2016). While it is difficult to determine the possible contribution of these primary sources of seed electrons, gamma-ray observations can be used to study the contribution of secondary electrons. Another important open question in this context is the connection with the generation mechanism for mini-halos that will be discussed in Sect. 5.2.3.

Eckert et al. (2017) used the amplitude of density fluctuations in the ICM as a proxy for the turbulent velocity. Importantly, they inferred that radio halo hosting clusters have one average and a factor of two higher turbulent velocities. However, this indirect method relies on number of assumptions making the result somewhat open to interpretation. Direct measurements of ICM turbulence have so far only been performed for the Perseus cluster with the Hitomi satellite (Hitomi Collaboration et al. 2016, 2018), finding a line-of-sight velocity dispersion of \(164 \pm 10~\text{km}\,\text{s}^{-1}\). Future measurements with XRISM (X-ray Imaging and Spectroscopy Mission) and Athena (Nandra et al. 2013; Barret et al. 2016) of the turbulent motions in halo and non-halo hosting clusters will provide crucial tests for the turbulent re-acceleration model.

5.1.9 Gamma-Ray Upper Limits

Gamma-rays in clusters of galaxies are expected from neutral pion decays coming from proton-proton interactions (for more details see Reimer 2004; Blasi et al. 2007; Pinzke et al. 2011). As mentioned earlier, CR protons can be injected in clusters by structure formation shocks and galaxy outflows, and can accumulate there for cosmological times. The quest for the detection of these gamma-rays have been going on for about two decades now (Reimer et al. 2003; Reimer and Sreekumar 2004; Aharonian et al. 2009; Ackermann et al. 2010, 2014, 2016; Aleksić et al. 2010; Arlen et al. 2012; Huber et al. 2012, 2013; Zandanel and Ando 2014; Prokhorov and Churazov 2014; Griffin et al. 2014; Liang et al. 2016; Branchini et al. 2017). Unfortunately, the detection of diffuse gamma-ray emission connected with the ICM has been so far elusive. There is no conclusive evidence for an observation yet.

Nevertheless, gamma-ray observations have been very important in the last few years for three reasons: to put a direct limit on the CR content in clusters, to test the hadronic nature of radio halos and mini-halos, and to test the contribution of secondary electrons in re-acceleration models. The number of works on this topic are numerous, thanks to the observations of imaging atmospheric Cherenkov telescopes and of gamma-ray satellites, and the most relevant ones have been cited in the previous paragraph.

Of particular importance for this review are the observations of Coma and Perseus clusters (results for the Perseus cluster will be discussed in Sect. 5.2.4), and of larger combined samples of nearby massive and X-ray luminous clusters. The combined likelihood analysis of the Fermi-Large Area Telescope (LAT; Atwood et al. 2009) satellite of 50 HIFLUGCS clusters have been a milestone in constraining the amount of CR protons in merging clusters to be below a few percent (Ackermann et al. 2014). However, the most constraining object is the Coma cluster due to its high mass, closeness and radio-halo brightness. In fact, thanks to the Fermi-LAT observations, we are now able to exclude the hadronic origin of the prototypical radio halo of Coma independently from the exact magnetic field value in the cluster (Brunetti et al. 2012, 2017), a long standing issue in the field (e.g., Jeltema and Profumo 2011). In particular, the CR-to-thermal energy in Coma is limited to be \(\lesssim 10\)%, almost independently (within a factor or two) from the specific model considered, i.e., re-acceleration or hadronic, and from the magnetic field (Brunetti et al. 2017). Additionally, the Fermi-LAT observations of Coma are starting to test re-acceleration models. These first gamma-ray constraints on re-acceleration are obtained under the assumption that only CR protons and their secondaries are present in the ICM (Brunetti et al. 2017). While we obviously know that this is not the case (see the discussion in the previous Sect. 5.1.8), it is possible that CR protons and their secondaries give the dominant seed contribution.

5.1.10 Radio Halo-Shock Edges

In a handful of clusters the radio halo emission seems to be bounded by cluster shock fronts (Markevitch et al. 2005; Brown and Rudnick 2011; Markevitch 2010; Planck Collaboration et al. 2013; Vacca et al. 2014; Shimwell et al. 2014; van Weeren et al. 2016). Two of these examples of “halo-shock edges” are shown in Fig. 10. The nature of these sharp edges is still unclear.

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It is possible that some of the “halo” emission near these shocks comes from CR electrons compressed at the shock. Alternatively, these edges are cluster radio shocks where electrons are (re-) accelerated. When these electrons move further downstream they will be re-accelerated again, but now by turbulence generated by the merger. Then, depending on the observing frequency, magnetic field strength (which sets the cooling time), and timescale for the turbulent cascade and re-acceleration, the radio shock and halo emission might blend forming these apparent halo-shock edges.

On the other hand, so far no polarized emission has been observed at these halo-shock edges (Shimwell et al. 2014) which would indicate compression. Also, no clear strong downstream spectral gradients due to electron energy losses have been found so far (e.g., van Weeren et al. 2016; Rajpurohit et al. 2018; Hoang et al. 2018c). If the synchrotron emission purely comes from a second order Fermi process at these edges, it would imply that there is sufficient post-shock MHD turbulence immediately after the shock (see for example Fujita et al. 2015). However, if this turbulence is generated by the shock passage downstream there might be insufficient time for this turbulence to decay to the smaller scales that are relevant for particle acceleration. To fully understand the nature of halo-shock edges, future high-resolution spectral and polarimetric observations will be crucial.

5.2.1 Statistics

Giacintucci et al. (2014b) found no clear correlation between the mini-halo radio power and cluster mass, unlike giant radio halos. However, Cassano et al. (2008b), Kale et al. (2013), Gitti et al. (2015) did report evidence for a correlation between radio power and X-ray luminosity. The slope of the correlation was found to be similar to that of giant radio halos (Gitti et al. 2015). Larger samples are required to obtain better statistics and confirm the found correlations, or lack thereof.

Giacintucci et al. (2017) determined the occurrence of radio mini halos in a sample of 58 clusters with \(\mbox{M}_{500} > 6 \times 10^{14}~\mbox{M} _{\odot }\). They found that 80% of the cool core clusters hosted mini-halos. Therefore, mini-halos are common phenomenon in such systems. No mini-halos were found in non-cool core systems. In addition, tentative evidence was found for a drop in the occurrence rate for lower cluster masses. Kale et al. (2013) found a mini-halo occurrence rate of about 50% in the Extended GMRT Radio Halo Survey (\(L _{\text{{X, 0.1--2.4 keV}}} > 5 \times 10^{44}~\text{erg}\,\text{s}^{-1}\), \(0.2< z<0.4\)), also indicating mini-halos are rather common.

5.2.2 Origin of Radio Mini-Halos

Similar to giant radio halos, hadronic (e.g., Pfrommer and Enßlin 2004) or turbulent re-acceleration models (Gitti et al. 2002) been invoked to explain the presence of the CR synchrotron emitting electrons. Unlike giant radio halos, where the turbulence is induced by major cluster mergers, mini-halos would trace turbulence in the cluster cores generated by gas sloshing (ZuHone et al. 2013, 2015). The central AGN is a likely candidate for the source of the fossil electrons that are re-accelerated (e.g., Fujita et al. 2007). The confinement of mini-halos by cold fronts (Mazzotta and Giacintucci 2008) support a scenario where turbulence induced by gas sloshing motions re-accelerates particles. Simulations by Fujita and Ohira (2013), ZuHone et al. (2013, 2015) provided further support for this scenario, reproducing some of the observed morphology, where the emission is bounded by cold fronts.

The radio spectral properties of mini-halos provide another discriminator for the origin of the CR electrons. If the electrons are re-accelerated by magnetohydrodynamical turbulence, the integrated spectra of mini-halos should display a spectral break caused by a cutoff in the electron energy distribution. Due to the limited number of spectral studies available, no clear conclusion can be drawn on the general occurrence of spectral breaks in mini-halo spectra.

5.2.3 Unification

Despite of the their differences, it is possible that mini-halos and giant halos in clusters are physically related to each other. For example, cluster merger events could transport CR from cluster cores to larger-scales where they are re-accelerated again (see Brunetti and Jones 2014). This could lead to “intermediate” cases where mini-halos could evolve into giant radio halos and vice-versa. This could either be a transition been turbulent re-acceleration due to core sloshing and merger induced turbulent re-acceleration. Or alternatively, a transition between hadronic mini-halos and merger induced turbulent re-acceleration (Zandanel et al. 2014). Recent observations have provided evidence for such scenarios, finding (mini-)halos with unusual properties.

Bonafede et al. (2014b) discovered a large 1.1 Mpc radio halo in CL1821+643 which contains a strong cool core. If this halo is caused by a merger event, the cluster is in a stage where the merger has not (yet) been able to disrupt the cool core as also noted by Kale and Parekh (2016). For example, because the merger is an off-axis event, or the merger is still in an early stage. CL1821+643 could therefore be a transitional object, where a mini-halo is switching off and a giant radio halo is just being formed. Similarly, Sommer et al. (2017), Savini et al. (2018a) reported the presence of a ∼1 Mpc radio halo in the semi-relaxed cluster Abell 2261,¹³ questioning the assumption that giant radio halos only occur in clusters undergoing major mergers.

Another peculiar case is the sloshing, minor-merger cluster Abell 2142. Early work already hinted at the presence of diffuse emission Harris et al. (1977), Giovannini et al. (1999), Giovannini and Feretti (2000) in this cluster. This was confirmed by Farnsworth et al. (2013) which showed a 2 Mpc radio halo. Venturi et al. (2017) found that the radio halo consists of two components. The inner component has a higher surface brightness, with properties similar to that of a mini-halo. The outer larger component has a steeper spectrum. They proposed that the inner component is powered by central sloshing turbulence. The outer component might probe turbulent re-acceleration induced by a less energetic merger event. Alternatively, the different components are the result from a transition between hadronic and turbulent re-acceleration processes.

The cluster PSZ1 G139.61+24.20 (\(z = 0.267\)) was listed as a candidate mini-halo by Giacintucci et al. (2017). Savini et al. (2018b) presented the discovery of steep-spectrum emission extending beyond the cool core region of the cluster with LOFAR. They argued that the emission outside the core is produced by turbulent re-acceleration from a minor merger event that has not disrupted the cool core. If this scenario is correct, it indicates that both a giant radio halo and mini halo could co-exist. A very similar situation has recently been found in the cluster RX J1720.1+2638. Here, Savini et al. (2018a) discovered extended faint diffuse steep spectrum emission beyond the cold front and mini-halo region (Mazzotta and Giacintucci 2008; Giacintucci et al. 2014a).

5.2.4 Gamma-Ray Upper Limits

The most important gamma-ray limits on mini-halos come from the observations of the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes of Perseus (Aleksić et al. 2010, 2012; Ahnen et al. 2016), and from the combined likelihood analysis of HIFLUGCS clusters with the Fermi-LAT satellite data (Ackermann et al. 2014). As is the case of Coma for merging clusters, Perseus is the most constraining object when it comes to mini-halos because of its high mass, closeness, and mini-halo brightness. Perseus host two gamma-ray bright AGNs—the central radio galaxy NGC 1275 and IC 310—detected both by Fermi (Abdo et al. 2009) and by MAGIC (Aleksić et al. 2012; Ahnen et al. 2016). The poor angular resolution of Fermi at low (<10 GeV) energies makes it difficult to target the possible diffuse gamma-ray emission in Perseus, and makes the MAGIC Perseus observations the most constraining for relaxed cool core clusters hosting mini-halos.

Differently from the case of the Coma radio halo, the gamma-ray upper limits on Perseus do not yet allow to exclude the hadronic origin of its mini-halo. The CR energy density in Perseus is constrained to be below about 1–10% of the thermal energy density, with the exact number depending on the assumptions made regarding the CR-spectral and spatial distribution, e.g., the steeper the spectrum and/or the flatter spatial (radial) distribution, the looser the constraints become. This strong dependence of the constraints on the CR content in clusters on the proton spectral and spatial distributions should be kept in mind when quoting these limits.

Assuming the mini-halo emission is hadronic, the gamma-ray upper limit can be turned in a lower limit on the magnetic field needed to generate the radio emission with secondary electrons. This is similar to what has been done for the Coma radio halo where the magnetic field needed for the hadronic interpretation would be extremely high with an energy density of 1/3 or more of the thermal energy density (Brunetti et al. 2017). In the case of Perseus, current gamma-ray limits imply central magnetic fields above \(\sim 5\) μGauss, still well below the \(\sim 25\) μGauss inferred from Faraday rotation measurements (Taylor et al. 2006).

6.1.1 Morphology and Sizes

Cluster radio shocks typically have elongated shapes, examples are the sources found in the Coma cluster (Giovannini et al. 1991), CIZA J2242.8+5301 (van Weeren et al. 2010), Abell 3667 (Röttgering et al. 1997; Johnston-Hollitt 2003), Abell 115 (Govoni et al. 2001b), and Abell 168 (Dwarakanath et al. 2018). These elongated shapes are expected for sources that trace shock waves in the cluster outskirts and are seen close to edge-on. Examples of radio shocks that are less elongated are found in Abell 2256 (e.g., Clarke and Enßlin 2006) and ZwCl 2341.1+0000 (Bagchi et al. 2002; van Weeren et al. 2009b). Cluster radio shocks have sizes that roughly range between 0.5 to 2 Mpc, see Fig. 15. Most large radio shocks that are found in the cluster outskirts show asymmetric transverse brightness profiles, with a sharp edge on the side away from the cluster center. On the side of the cluster center, the emission fades more gradually, see Fig. 16.

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Deep high-resolution observations of large elongated radio shocks have also revealed a significant amount of filamentary substructures, see Figs. 16 and 17. Large radio shocks that display these filamentary structures are found in Abell 2256, CIZA J2242.8+5301, Toothbrush, MACS J0717.5+3745, Abell 3376, and Abell 3667. The nature of the filamentary structures is not fully understood. One possibility is that they trace changes in the magnetic field. Alternatively, they reflect the complex shape of the shock surfaces. The filamentary morphology of cluster radio shocks seems to be ubiquitous because all radio shocks that have been studied with good signal to noise and at high resolution display them.

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6.1.2 Cluster Double Radio Shocks

A particular interesting class of cluster radio shocks are so-called “double shocks”. Here two large elongated convex radio shocks are found diametrically with respect to the cluster center, see Fig. 14. The radio shocks are oriented perpendicular with the respect to the elongated ICM distribution (and merger axis) of the cluster, see Figs. 18 and 19. Double radio shocks are an important subclass of radio shocks as the cluster merger scenario can be relatively well constrained. In addition, these system seems to be observed close to edge-on. Note that we reserve the classification of a double radio shock for a pair of shock waves that were generated at the same time during core passage. So the presence of two radio shocks in a cluster alone is not a sufficient condition to classify it as a double radio shocks.

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About a dozen well-defined double radio shock systems are known, see Table 1. The first cluster double radio shock was found in Abell 3667 (Röttgering et al. 1997). It was realized by Roettiger et al. (1999), Johnston-Hollitt et al. (1999) that these radio sources could have resulted from particles accelerated at shocks from a binary merger event. The presence of a shock in the ICM at the location of the northwestern radio source in Abell 3667 was confirmed via X-ray observations by Finoguenov et al. (2010). The second double radio shock system was discovered by Bagchi et al. (2006) in Abell 3376. Other well studied cluster double radio shocks are the ones in CIZA J2242.8+5301 (van Weeren et al. 2010), ZwCl 0000.8+5215 (van Weeren et al. 2011c), MACS J1752.0+4440 (van Weeren et al. 2012a; Bonafede et al. 2012), PSZ1 G108.18-11.53 (de Gasperin et al. 2015a), and Abell 1240 (Kempner and Sarazin 2001; Bonafede et al. 2009a).

6.1.3 Radio Spectra

The integrated radio spectra of cluster radio shocks display power-law shapes (but see Sect. 6.1.8), with spectral indices ranging from about −1.0 to −1.5 (e.g., Bonafede et al. 2012; Feretti et al. 2012; de Gasperin et al. 2014). One notable exception of a flatter integrated spectrum, with good data available, is Abell 2256 where the spectral index is about −0.8 (Brentjens 2008; van Weeren et al. 2012c; Trasatti et al. 2015). This flat spectral index is difficult to reconcile with particle acceleration models and electron energy losses, see van Weeren et al. (2012c) for a discussion. Another example appeared to be ZwCl 2341.1+0000 (van Weeren et al. 2009b) but more recent observations indicate that the spectral index is within the normally observed range (Giovannini et al. 2010; Benson et al. 2017).

Cluster radio shocks often show a clear spectral index gradient across their width, see Figs. 20 and 19. The region with the flattest spectral index is located on the side away from the cluster center. Towards the cluster center the spectral index steepens. This steepening is thought to be caused by synchrotron and IC losses in the shock downstream region. The majority of well-studied cluster radio shocks, both single shocks (see Fig. 8) and double shocks, show this behavior.

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6.1.4 Polarization

Cluster radio shocks are amongst the most polarized sources in the extragalactic sky. Very elongated radio shocks usually show the highest polarization fraction, which is expected if they trace edge-on shock waves (Enßlin et al. 1998). For example, CIZA J2242.8+5301 shows polarization fractions of ∼50% or more at GHz frequencies for some parts of the radio shock (van Weeren et al. 2010), see Fig. 20.

For large cluster radio shocks the intrinsic polarization angles, corrected for the effect of Faraday Rotation, are found to be well aligned. The polarization magnetic field vectors are oriented within the plane of the radio shock (e.g., Bonafede et al. 2009a; van Weeren et al. 2010; Bonafede et al. 2012; Pearce et al. 2017, see also Figs. 20 and 21). Only a few Faraday rotation studies have been performed so far of radio shocks. They indicate that for radio shocks projected at large cluster centric radii the Faraday Rotation is mostly caused by the galactic foreground. Faraday Rotation caused by the cluster can be seen for (parts of) radio shocks at smaller cluster centric radii (Bonafede et al. 2009b; Pizzo et al. 2011; van Weeren et al. 2012b; Owen et al. 2014). From the limited studies available, it seems that large cluster radio shocks strongly depolarize at frequencies \(\lesssim 1\) GHz (Brentjens 2008; Pizzo et al. 2011; Ozawa et al. 2015). Therefore, high-frequency observations (above \(\gtrsim 2\) GHz) are best suited to probe the intrinsic polarization properties of radio shocks. For example, the fractional linear polarization in for main ‘Sausage’ and ‘Toothbrush’ radio shocks is on average 40% at 5–10 GHz, reaching 70% in localized areas (Kierdorf et al. 2017; Loi et al. 2017).

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6.1.5 Comparison Between Radio and X-Ray Observations of ICM Shocks

Because of their shapes, locations, and spectral and polarimetric properties, cluster radio shocks are considered to trace particles accelerated at shocks. These shocks can be generated by cluster merger activity or accretion flows from surrounding large-scale structures (e.g., Enßlin et al. 1998). If this assumption is correct, shock waves should coexist at the location of radio shocks. From X-ray observations, the intensity of shock structure can be estimated from the Rankine-Hugoniot jump condition (Landau and Lifshitz 1959). Assuming a ratio of specific heats as \(\gamma =5/3\), we have

$$\begin{aligned} \frac{T_{2}}{T_{1}} =& \frac{5{\mathcal{M}}^{4}+14{\mathcal{M}}^{2}-3}{16 {\mathcal{M}}^{2}} \end{aligned}$$

(12)

$$\begin{aligned} \frac{\rho _{2}}{\rho _{1}} =& C=\frac{4{\mathcal{M}}^{2}}{\mathcal{M} ^{2}+3} , \end{aligned}$$

(13)

where the subscripts 1 and 2 refer to the pre- and post-shock ICM density (\(\rho \)) or temperature (\(T\)), respectively. The ratios of ICM properties as a function of the shock strength (ℳ) are shown in Fig. 22. On the other hand, based on the assumption of simple DSA theory, the Mach number can be also estimated from the radio injection spectral index (\(\alpha _{\mathrm{inj}}\)) via

$$ {\mathcal{M}_{\mathrm{radio}}=\sqrt{ \frac{2\alpha _{\mathrm{inj}}-3}{2 \alpha _{\mathrm{inj}}+1}}} . $$

(14)

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In principle, both X-ray and radio approaches are independent methods to characterize the shock strength, meaning shock strengths inferred from these different wavelength regimes should match each other, if underlaying assumptions are correct. Therefore, the comparison of the shock properties inferred from X-ray and radio data is an important tool to investigate shock related ICM physics. Until recently, observational information of radio shocks at X-ray wavelengths were limited because radio shocks are typically located in the cluster periphery, where the ICM X-ray emission is very faint. This makes it challenging to characterize the X-ray shock properties.

The first detection of a shock wave, co-located with a cluster radio shock (relic), was in the nearby merging cluster Abell 3667 using XMM-Newton observations. Finoguenov et al. (2010) found a sharp X-ray surface brightness discontinuity at the outer edge of the radio shock, and a significant drop in the ICM temperature at the same location. These discontinuities are consistent with a \(\mathcal{M} \sim 2\) shock, see Fig. 23. These results have been confirmed by Akamatsu et al. (2012b), Sarazin et al. (2016).

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At radio wavelength, there are also observational challenges to derive shock properties. One particular difficulty is to measure \(\alpha _{\mathrm{inj}}\). The integrated spectral index of a radio shock reflects a balance between acceleration and energy losses. As a result, the index of the integrated spectrum is 0.5 steeper compared to \(\alpha _{\mathrm{inj}}\). This relation (\(\alpha _{\mathrm{int}}= \alpha _{\mathrm{inj}}+0.5\), Kardashev 1962) is however somewhat simplistic, since the shock properties do evolve over time, see also Sect. 6.2. Alternatively, with spatially resolved spectral index maps one can obtain more reliable measurements of \(\alpha _{\mathrm{inj}}\), avoiding some of the problems with energy losses. Here one needs to measure the spectral index as close as possible to the shock location. However, even in this case some mixing of different electron energy populations will occur, depending on the spatial resolution, shape of the shock surface, and projection effects.

For the northern radio shock in CIZA J2242.8+5301 a number of detailed comparison between the radio and X-ray derived Mach numbers have been performed. van Weeren et al. (2010) reported a radio injection spectral index of \(-0.60\pm 0.05\) resulting in \(\mathcal{M} = 4.6^{+1.3} _{-0.9}\) (68% confidence range). In the X-rays, Akamatsu and Kawahara (2013), Akamatsu et al. (2015) reported a temperature increase across the radio shock with an amplitude of a factor ∼3 resulting giving \(\mathcal{M}=2.7^{+0.7}_{-0.4}\) (including systematics due to the background estimation). This kind of tension, \(\mathcal{M}_{\mathrm{radio}}> \mathcal{M}_{\mathrm{X}}\), has been found for other radio shocks, see Fig. 24. If this discrepancy is indeed real, this may point to problems in the DSA scenario for shocks in clusters. To explain the observational results, several solutions have been proposed.

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For example, it is possible that the X-ray derived Mach numbers are somewhat underestimated due to unfavorable viewing angles and the complexity of the shock surface. In addition, the shock acceleration efficiency is a thought to be a strong function of shock Mach number (Hoeft and Brüggen 2007). Therefore the CR-energy-weighted Mach number is expected to be higher than the kinetic-energy-weighted Mach number (Ha et al. 2018). Thus radio measured Mach numbers will be biased towards parts of the shock with the highest Mach numbers. Difficulties and possible biases with radio based measurements are discussed in Stroe et al. (2014a), van Weeren et al. (2016), Hoang et al. (2017). The re-acceleration of fossil plasma has also been invoked, see Sect. 6.2. Akamatsu et al. (2017) investigated possible systematic errors associated with X-ray observations. We refer the reader to Sect. 4.3. in their paper for more details.

Future X-ray satellites, such as Athena (Nandra et al. 2013), will provide precise measurements of cluster merger shocks. This will shed further light on the apparent discrepancy between the Mach numbers derived from radio and X-ray observations. With the improved collecting area with respect to current satellites, the shock properties in faint cluster outskirt can also be determined.

6.1.6 SZ Observations

The thermal ICM electrons in galaxy clusters interact with CMB photons through inverse Compton scattering, resulting in the so-called SZ effect (Sunyaev and Zeldovich 1970). The SZ effect provides a complementary way of studying the ICM and, because of its redshift-independent nature, is particularly powerful at high-redshift where the X-ray surface brightness suffers from significant cosmological dimming. Low-resolution studies measuring the bulk SZ signal have been very successful at selecting large samples of both relaxed and disturbed clusters up to \(z\sim \)1.5 (e.g., Planck Collaboration et al. 2016; Bleem et al. 2015).

In the last decade, efforts at the very highest radio frequencies (above 90 GHz) have focused on measuring SZ at high spatial resolution with the aim of detecting small scale features in the ICM, such as shocks in merging clusters. Great strides have been made possible by the introduction of high-resolution, large field-of-view instruments such as MUSTANG-2¹⁵ installed on the 100-m Green Bank Telescope (\(9^{\prime \prime }\) resolution at 90 GHz) and NIKA/NIKA2¹⁶ on the 30-m IRAM telescope (reaching \(10^{\prime \prime }\)–\(20^{\prime \prime }\) resolution at 150 and 260 GHz). The power of these instruments has already been demonstrated through high-resolution SZ images showing substructure in merging clusters and in the cores of relaxed clusters (Adam et al. 2017; Romero et al. 2018; Adam et al. 2018). For the nearby Coma cluster the Planck satellite has provided resolved SZ images (Planck Collaboration et al. 2013), including the likely detection of two \(\mathcal{M} \sim 2\) shocks in the cluster periphery.

Following pioneering work detecting a weak shock in MACS0744+3927 (Korngut et al. 2011), more recent observational work with the Atacama Large Millimeter/submillimeter Array (ALMA)¹⁷ has enabled a direct detection and measurement of a cluster merger shock in ‘El Gordo’ (Basu et al. 2016a). These observations demonstrate great potential for future SZ determinations of shock properties (particularly the Mach number), especially at large cluster-centric distances and high-redshift, where X-ray measurements of the ICM properties become challenging.

6.1.7 Gamma-Rays from Cluster Radio Shocks

Apart from (re-)accelerating electrons, shocks should also accelerate protons. For DSA, the number of accelerated protons should be much larger than electrons. Similar to the secondary model for radio halos, these CR protons should collide with the thermal ICM and produce gamma-rays via hadronic interactions.

It has been noted by Vazza and Brüggen (2014), Vazza et al. (2015a, 2016) that the expected gamma-ray emission for DSA shock acceleration at radio shocks is in tension with gamma-ray upper limits for some clusters. This indicates that the relative acceleration efficiency of electrons and protons is at odds with predictions from DSA. Adding the re-acceleration of fossil particles to this prediction does not change this conclusion. One possible explanation for the lack CR protons is that the magnetic field at radio shocks is predominantly perpendicular to the shock normal. Work by Caprioli and Spitkovsky (2014) indicates that the acceleration efficiency of protons is strongly suppressed at such shocks. Simulations by Wittor et al. (2017) indicate this could reduce the tension with the low gamma-ray upper limits.

Recently, claims of gamma-ray emission from the virial shocks around the Coma cluster (Keshet et al. 2017), as well as from a stacking of other clusters (Reiss et al. 2017), have been put forward. We underline, however, that so far these claims have been not been confirmed (Arlen et al. 2012; Zandanel and Ando 2014; Prokhorov 2014; Ackermann et al. 2016).

6.1.8 High-Frequency Studies of Radio Shocks

Owing to their steep spectra, radio shocks have been classically observed at relatively low frequencies (\(<2\) GHz). In this Section we review the current state-of-the-art high-frequency observations of radio shocks, by focusing on observations above 5 GHz. High-frequency observations pose particular challenges: (i) radio shocks have steep-spectra making them very faint at high-frequencies; (ii) radio interferometers typically have small fields of view at high frequency and thus have difficulty in detecting extended diffuse sources. Until 2014, the highest frequency detection of a radio shocks were in the clusters Abell 521 and MACS J0717.5+3745 at 5 GHz (Giacintucci et al. 2008; Bonafede et al. 2009b). The interest in high-frequency observations of cluster radio shocks, and the number of detections, has grown over the past few years. This interest has been motivated by the study of the injected electrons and their aging mechanism (as discussed for example by Kang 2016a; Donnert et al. 2016; Kang and Ryu 2016).

Instruments that helped make progress at high frequencies include interferometers, such as the Arcminute Microkelvin Imager (AMI, 16 GHz), the Combined Array for Research in Millimeter-wave Astronomy (CARMA, 30 GHz) and the VLA (4–10 GHz), and single dish antennas such as Effelsberg (up to 10 GHz) and the Sardinia Radio Telescope (SRT, up to 19 GHz), see Fig. 25.

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At the moment of writing, six clusters benefit from radio shock detections above 5 GHz: the main radio shocks in the ‘Sausage’ and the ‘Toothbrush’ clusters (both up to 30 GHz, Stroe et al. 2014b, 2016; Kierdorf et al. 2017; Loi et al. 2017), Abell 2256 (at 5 GHz, Trasatti et al. 2015), the ‘Bullet’ cluster radio shock (5.5 and 9 GHz, Malu et al. 2016), ZwCl 0008.8+5215 and Abell 1612 (at 5 and 8 GHz, Kierdorf et al. 2017). In combination with low frequency measurements, integrated cluster radio shock spectra spanning over 3 orders of magnitude in frequency have been produced, for example, covering the range from 74/150 MHz to 30 GHz, as is the case for the ‘Sausage’ and the ‘Toothbrush’ radio shocks (van Weeren et al. 2012b; Stroe et al. 2016).

Interferometric observations from 150 MHz to 30 GHz have revealed a possible steepening of the integrated radio shock spectra beyond 2–5 GHz (Stroe et al. 2014b, 2016; Trasatti et al. 2015), which challenges the radio shock formation model involving DSA acceleration at planar shocks. However, studies combining high-frequency single-dish observations with low-frequency interferometric observations (Kierdorf et al. 2017; Loi et al. 2017) do not corroborate this finding (for more details on the caveats of both methods, see below). The mismatch between observations and theory has sparked a discussion as to what is causing the decrement in the flux density of cluster radio shocks at high frequencies (see also Sect. 6.2). One possibility is that the decrement is not intrinsic to the CR electron distribution at the shock, but is caused by the SZ effect. At 10–30 GHz, the SZ effect is expected to result in a decrement in flux density. Even though the radio shocks are typically located \(1\mbox{--}1.5\) Mpc away from the cluster center, authors have argued that the sharp pressure discontinuity from the shock could explain \(\sim 20\mbox{--}50\%\) of the decrement (for more typical examples such as the ‘Sausage’, ‘Toothbrush’, or Coma cluster), even up to 100% at the highest frequencies for extreme cases, such as the ‘El Gordo’ or Abell 2256 clusters (depending on the shock geometry, Erler et al. 2015; Basu et al. 2016b).

Various alternatives to the simple shock acceleration model have also been proposed. By contrast to acceleration at time invariant shocks, which results in power-law integrated spectra, curved spectra could be a natural result of spherically-expanding ICM shocks (Kang 2015b,a). The simple radio shock formation model assumes that the associated shock wave injects thermal electrons. A scenario where the shock predominantly injects non-thermal fossil electrons, pre-accelerated by previous AGN activity, could also reproduce the observed curved radio spectra (Kang and Ryu 2015). The downstream steepening, as well as the steepening of the integrated spectrum, can be recovered if there is non-uniform magnetic field in the downstream area of the shock (Donnert et al. 2016) or if the electrons, after shock acceleration, are further re-accelerated by turbulence (Fujita et al. 2015; Kang 2017). Tailored DSA simulations aimed at reproducing the observed parameters of radio shocks with good spectral coverage are now also becoming available (Kang and Ryu 2015; Kang 2016b; Kang et al. 2017).

6.1.9 Scaling Relations

Similar to radio halos, a correlation is found between cluster X-ray luminosity and radio power of cluster radio shocks (Feretti et al. 2012). This correlation likely reflects an underlying correlation between mass an radio power, with \(P \propto M ^{2.8}\) (de Gasperin et al. 2014). In addition, there is a correlation between the largest linear size (LLS) and distance from the cluster center of the radio shock (van Weeren et al. 2009c; Bonafede et al. 2012; de Gasperin et al. 2014). This is in line with the prediction that in the periphery of clusters the shock surfaces are larger. There is no clear evidence for a correlation between LLS and radio spectral index. Previously, the existence such a correlation has been reported by van Weeren et al. (2009c). However, this LSS-\(\alpha \) correlation was produced by the radio phoenices present in the van Weeren et al. (2009c) sample, because radio phoenices generally have smaller LLS and steeper spectra than radio shocks. Nuza et al. (2012), Araya-Melo et al. (2012), Nuza et al. (2017) investigated whether simulations can reproduce the luminosity function, shapes, and LLS distribution of radio shocks. They found reasonable agreement with the properties of radio shocks detectable in the NVSS survey.

6.3.1 Radio Phoenices and Revived Fossil Plasma

The currently favored scenario is that phoenices trace old radio plasma from past episodes of AGN activity. When a shock compresses this old plasma, the resulting increase in the momentum of the relativistic electrons and the magnetic field strength can produce a source characterized by a steep and curved radio spectrum (Enßlin and Gopal-Krishna 2001). Simulations also predict that these sources should often have complex morphologies (Enßlin and Brüggen 2002). It should be noted that so far direct observational evidence for a connection between shocks waves and phoenices is still missing. Therefore, the formation scenario for these revived fossil plasma sources remains somewhat uncertain.

Compared to cluster radio shocks, revived fossil plasma sources and phoenices are on average found at smaller cluster centric distances (Feretti et al. 2012), have smaller sizes (≲300–400 kpc, see Fig. 15, and have lower radio powers. These revived fossil sources have a range of morphologies, from roundish shapes (e.g., Abell 1664, Giovannini et al. 1999; Govoni et al. 2001b; Kale and Dwarakanath 2012)) to elongated and filamentary (e.g., Abell 13, Abell 85, Abell 2048, Abell 4038, Abell 2443, Abell 1033,¹⁹ Abell 1914, Abell 1931, and the Ophiuchus cluster, Slee et al. 1983, 2001; van Weeren et al. 2011d; de Gasperin et al. 2015b; van Weeren et al. 2009a; Werner et al. 2016; Murgia et al. 2010a; Brüggen et al. 2018; Mandal et al. 2018). The elongated and filamentary morphologies, see Fig. 30, are the most common (e.g., Slee and Roy 1998; Slee et al. 2001). Some of these objects are found in cool core clusters such as Abell 85, Abell 1664, and Abell 4038, unlike cluster radio shocks. This indicates that major merger events are not required for their formation.

Radio phoenices and revived fossil sources have integrated spectra that are typically steeper than −1.5. In many instances the spectra are curved (Cohen and Clarke 2011; Slee et al. 2001; van Weeren et al. 2009c), showing high-frequency spectral steepening, see Fig. 29 for an example. The spectral index distribution across these sources is irregular without clear common trends (van Weeren et al. 2011d; Cohen and Clarke 2011; Kale and Dwarakanath 2012).

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Polarized emission from radio phoenices and revived fossil sources has also been detected. The polarization fractions are generally lower than for cluster radio shocks and show larger variations (e.g., Slee et al. 2001). However, it should be remarked that only a few polarization studies have been performed so far of these sources.

6.3.2 Re-Acceleration and Fossil Plasma

As discussed before, DSA shock models proposed for CRe acceleration have found that the acceleration efficiency is often low when electrons are accelerated directly from the thermal pool. This low efficiency is hard to reconcile with the observed brightness and radio spectrum of some cluster radio shocks which suggest a higher acceleration efficiency (e.g., Kang and Ryu 2011; Vazza and Brüggen 2014). AGN activity continuously supplies fresh CRs in the ICM creating bright radio galaxies. Due to synchrotron losses, these CRs are visible only for few tens of Myr at Gigahertz frequencies. Although direct observations are prohibitive, a certain amount of CRe with \(\gamma \sim 100\) should be present mixed with the ICM Sarazin (1999), Petrosian (2001), Pinzke et al. (2013). Therefore, CR electrons might be re-accelerated from this seed population in the ICM (Enßlin et al. 1998; Markevitch et al. 2005; Kang and Ryu 2011; Kang et al. 2012), mitigating some of the DSA requirements (see also Sect. 6.2). An underlying assumption here is that the jets and lobes of radio galaxies are lepton-dominated (e.g., Vazza et al. 2016). Otherwise many CR protons would be re-accelerated, possibly causing problems with the Fermi gamma-ray upper limits (Sect. 6.1.7).

Instead of fossil (\(\gamma \sim 100\)) CRe, more energetic CRe from the lobes of a currently active radio galaxy could also re-accelerated (Kang and Ryu 2016). A few observational pieces of evidence for this scenario were recently reported. In PLCK G287.0+32.9, two large radio shocks have been discovered (Bagchi et al. 2011; Bonafede et al. 2014a). One of the two radio shocks appears to be connected to the lobes of a radio galaxy. However, no optical counterpart for the radio galaxy could be located and the radio spectral index across the source remains difficult to interpret. In the Bullet cluster (1E 0657–55.8), a 930 kpc long radio shock is located opposite to the bullet direction (Shimwell et al. 2015). In this radio shock, a region of 330 kpc has a much higher surface brightness. This might haven be caused by a pre-existing population of CRe of AGN origin. The best example of CRe of AGN origin re-accelerated by a merger shock comes from Abell 3411-3412 (van Weeren et al. 2017b; Johnston-Hollitt 2017). In this mering system a morphological connection between a radio galaxy and a radio shock is evident. Both polarization and spectral features are in agreement with particle re-acceleration. Furthermore, X-ray data show the presence of a surface brightness discontinuity at the radio shock’s outer edge. However, in the great majority of cases, the presence of a source of CR electrons near the radio shock is missing, leaving unanswered the question: are pre-energized CRe necessary to power all radio shocks? A similar problem is present with radio halos that also require an initial reservoir of mildly energetic CRe to re-energize (Brunetti and Jones 2014).

With the increase in resolution, sensitivity, and sky coverage of low-frequency telescopes more steep spectrum fossil sources are being discovered. This should shed more light on the connection between diffuse cluster radio sources and AGN fossil plasma in the near future. It has already become clear that galaxy cluster host sources with such steep spectra that they are completely missed at GHz frequencies. Several of these examples have now been uncovered with LOFAR, such as in Abell 1033 (see Sect. 6.3.3), Abell 1931, and Abell 2034. Recently, the MWA has also found a significant number of new fossil plasma sources and candidates (Duchesne et al. 2017).

6.3.3 GReET

From observations of extended radio sources in the galaxy cluster Abell 1033 (see Fig. 31; de Gasperin et al. 2017a), the presence of a possible new mechanism to energize old radio plasma was inferred. In this cluster a WAT source fades into a pair of fairly thin filaments within which the emission starts to brighten and the synchrotron spectrum flattens again. This process of re-energization is so gentle that it barely balances the radiative losses of cosmic rays, with a particle acceleration time-scale comparable to the radiative loss time-scale of the electrons emitting at <100 MHz. This source has been labeled “GReET” (gently re-energized tail).

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A proposed physical explanation for the re-energization mechanism is that Rayleigh-Taylor and Kelvin-Helmholtz instabilities in the tails generate turbulent waves that re-accelerate electrons via second order Fermi mechanisms. The challenge is to understand how the re-acceleration rate is maintained quasi-constant in the tail over a long time-scale. A proposed solution is to assume that turbulence is continuously forced in the tail by the interaction between perturbations in the surrounding medium with the tail itself (de Gasperin et al. 2017a). These perturbations are driven in the medium by the cluster dynamics for a time-scale and on spatial-scales that are larger/comparable to that of the GReET.

If this gentle re-energizing process observed in Abell 1033 is common in tails of radio galaxies in galaxy clusters, then electrons released by radio galaxies in the ICM could live as long as seen in the case of Abell 1033 (\(>0.5\) Gyr) and they would be able to accumulate in larger quantities and with higher energies. This could produce a seed population of energetic particles for merger-induced re-acceleration mechanisms, such as turbulence and shocks, that were proposed to explain cluster-scale radio sources. Two other possible GReETs are present in ZwCl 0634.1+4750 (Cuciti et al. 2018) and in Abell 1314 (Wilber et al. 2018a). In both cases a tailed radio galaxy shows an increase in surface brightness along its tail and an unexpected flattening in the spectral index. Because very few examples of GReETs are known, the precise nature of GReETs and their existence as a distinct class of objects remains to be confirmed.

6.3.4 Future Prospects

A vast phenomenology of re-energized plasma of AGN origin has recently been emerging, and it attests to the different mechanisms at play: compression (radio phoenices; Enßlin and Gopal-Krishna 2001), Fermi-I shock re-acceleration (cluster radio shocks; van Weeren et al. 2017b), turbulence ((mini-)halos; ZuHone et al. 2013) or complex plasma interactions (GReETs; de Gasperin et al. 2017a). In most of these cases the re-energization is mild and the radio spectrum is steep, implying that conventional GHz-frequency telescopes overlooked the great majority of these phenomena.

With the current low-frequency telescopes LOFAR, MWA, and the uGMRT, and the future SKA-low, many more revived fossil plasma sources are to be discovered. This should help to better understand the variety of sources present and their spatial distribution in the ICM. Future low-frequency observations should also reveal more connections with cluster radio shocks and possibly with radio halos. These connections can then be studied in more detail. Particularly interesting will be to push these observations towards to lowest frequencies possible (\(\lesssim 10\mbox{--}50\) MHz) as current MWA, LOFAR, and uGMRT observations in the 100–300 MHz range probably only probe the tip of the iceberg.