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Significant progress has been made recently in our knowledge on the non-thermal component of galaxy clusters. A number of open questions arise in assessing the current theoretical and observational status.

First of all, we need to test the current theories on the origin of the large-scale non-thermal component in clusters (magnetic field and cosmic rays). If at present primary models seem to be the favourite acceleration mechanisms for intracluster electrons, secondary models cannot be ruled out. Among other things, it will be necessary to establish: How common is the non-thermal component in clusters? Is it really hosted only in merging systems (as present observational results suggest) or do all clusters have a radio halo/relic? If this latter hypothesis is correct, how should we modify the radio power versus X-ray luminosity correlation (Sect. 2.1)? If shocks and turbulence related to cluster mergers are instead the mechanisms responsible for electron re-acceleration, why have extended radio sources not been detected in all merging clusters? Is this related to other physical effects (i.e. the merging event alone is not enough to produce intracluster cosmic rays), as the correlation between radio power and cluster mass seems to indicate, or it is due to a lack of sensitivity of the current instruments (i.e. all merging clusters host radio halos and relics, but a large fraction of these sources lies below the sensitivity limit of present telescopes)?

Among the previous questions, the most difficult to answer at present are those that involve the study of low-luminous X-ray clusters, for which the limits of current radio observations are particularly severe. By extrapolating to low radio and X-ray luminosity the Pnu - LX relation (Sect. 2.1), Feretti & Giovannini (2007) have estimated that, if present, halos with typical sizes of 1 Mpc in intermediate/low-luminous X-ray clusters (LX[0.1 - 2.4 keV] ltapprox 5 × 1044 h70-2 erg s-1) 6 would actually have a radio surface brightness lower than the current limits obtained in the literature and in the NVSS. At higher X-ray luminosities, more constraints on radio halo statistics have recently been obtained by Venturi et al. (2007) and Brunetti et al. (2007). They carried out GMRT 7 observations at 610 MHz of 34 luminous (LX[0.1 - 2.4 keV] gtapprox 5 × 1044 h70-2 erg s-1) clusters with 0.2 ltapprox z ltapprox 0.4. The bulk of the galaxy clusters in their sample does not show any diffuse central radio emission, with radio luminosity upper limits that are well below the Pnu - LX relation derived from the previously known radio halos. The net bimodality of the cluster distribution in the Pnu - LX plane support primary models against secondary models. Actually, the former predict a relatively fast (approx 108 yrs) transition of clusters from a radio quiet state to the observed Pnu - LX correlation, where they remain for ltapprox 1 Gyr. A significantly wider scatter around the Pnu - LX correlation is instead expected in the frame of secondary models, that could be reconciled with observations only assuming the existence of strong dissipation of magnetic fields in clusters (see Brunetti et al. 2007 and references therein).

On smaller scales, a larger sample of radio mini-halos is required to test the current theories on the origin of radio emission in this class of sources (Gitti et al. 2002, Pfrommer & Enßlin 2004). Recent results suggest that cooling flows and mergers could act simultaneously, when they co-exist, in providing energy to the relic population of relativistic electrons injected into the ICM by AGNs, thus powering mini-halo radio emission (Gitti et al. 2007a).

As discussed in Sect. 4, radio observations of galaxy clusters offer a unique tool to estimate strength and structure of large-scale magnetic fields, allowing to test the different scenarios of their origin. Several observational results show that magnetic fields of the order of ~ µG are common in clusters. Through combined numerical and observational analyses, Murgia et al. (2004) and Govoni et al. (2006) have shown that detailed morphology and polarisation information of radio halos may provide important constraints on the strength and structure of intracluster magnetic fields. However, discrepant results have been obtained up to now (Sect. 4.4) and more detailed information on magnetic fields is still needed.

A better knowledge of the physics of the non-thermal component in galaxy clusters will have important cosmological implications. If it will be confirmed that the presence of giant halos and relics is related to cluster mergers, the statistical properties of these radio sources will allow us to test the current cluster formation scenario, giving important hints on large-scale structure formation and, thus, cosmological parameters (e.g. Evrard & Gioia 2002).

Additionally, we will be able to estimate how the gravitational energy released during cluster mergers is redistributed between the thermal ICM and the relativistic plasma (e.g. Sarazin 2005). The effects of magnetic fields on the thermodynamical evolution of large-scale structures will be evaluated, as well as the contribution of the non-thermal pressure to the estimate of mass and temperature in galaxy clusters (e.g. Dolag & Schindler 2000, Dolag et al. 2001a, Colafrancesco et al. 2004). Cluster scaling laws, such as mass vs. temperature, are actually key ingredients to derive cosmological constraints from galaxy clusters (e.g. Ettori et al. 2004, Arnaud et al. 2005).

Finally, a better knowledge of extended radio sources in clusters is indeed essential for complementary cosmological studies, e.g. the epoch of re-ionisation (EoR). It has been proven that radio halos and relics are the strongest extra-galactic foreground sources to be removed in order to probe the EoR through the study of the redshifted 21 cm emission from neutral hydrogen (e.g. Di Matteo et al. 2004). Better models for the diffuse radio emission have to be inserted into numerical simulations of the EoR 21 cm emission, in order to understand how to remove efficiently the contamination due to radio halos and relics.

An increase in the number of known radio halos/relics, as well as higher resolution and sensitivity observations, are essential to answer the main open questions, summarised at the beginning of this section, about the nature of diffuse radio emission in clusters. As shown in Fig. 7, halos and relics are difficult to detect in the GHz range due to their steep spectra. Several observations performed with the currently available low-frequency instruments (e.g. GMRT: Venturi et al. 2007; VLA: Kassim et al. 2001, Orrù et al. 2007) confirm the interest in studying this class of radio sources at high wavelengths. A short term perspective in the study of radio halos and relics is thus to fully exploit those instruments that are already available for observations in the MHz range of the electromagnetic spectrum with good enough sensitivity (approximately from some tens of µJy/beam to some mJy/beam) and angular resolution (roughly some tens of arcsec). However, in order to make a proper comparison between observational results and current theoretical models about the origin of radio halos and relics, we need multi-frequency observations of statistical samples of diffuse radio sources. Current telescopes require too long exposure-time per cluster (gtapprox 1-2 hours) to reach the sensitivity limits necessary for detecting radio halos/relics, making statistical analyses of diffuse radio emission in clusters extremely time-demanding.

Figure 7

Figure 7. Spectrum of the diffuse radio source in A 1914 (from Bacchi et al. 2003). Superimposed the frequency range covered by LWA (10 MHz - 88 MHz, in blue), LOFAR (Low Band: 30 MHz - 80 MHz, High Band: 110 MHz - 240 MHz, in red) and SKA (100 MHz - 25 GHz, in green). The low-frequency domain covered by the next generation radio-telescopes is optimal for the detection of high spectral index radio sources, such as radio halos, mini-halos and relics.

The low-frequency range covered by a new generation of radio telescopes (Long Wavelength Array - LWA; Low Frequency Array - LOFAR; Square Kilometre Array - SKA), together with their gain in sensitivity and resolution, will increase dramatically the statistics on the number of known radio halos and relics. Not only these instruments will cover the optimal frequency range for halo/relic detection (see Fig. 7), but also their gain in sensitivity and resolution will be of the order of 10 to 1000 (see Table 2 of Brüggen et al. 2005), allowing observations of statistical samples of diffuse and extended radio sources. A LOFAR survey at 120 MHz, covering half the sky to a 5 sigma flux limit of 0.1 mJy (1 hour integration time per pointing), could detect ~ 1000 halos/relics, of which 25% at redshift larger than z ~ 0.3 (Röttgering 2003). Feretti et al. (2004b) have estimated that, with 1 hour integration time at 1.4 GHz, 50% of the SKA collecting area will allow us to detect halos and relics of total flux down to 1 mJy at any redshift, and down to 0.1 mJy at high redshift. Based on our current knowledge, more than three (fifteen) hundred diffuse cluster radio sources are expected at 1.5 GHz on the full sky at the 1 mJy (0.1 mJy) flux limit (Enßlin & Röttgering 2002).

With statistical samples of halos and relics over a wide redshift range, we will be able to a) test the correlation between the non-thermal component and the physical properties of clusters (dynamical state, mass, X-ray luminosity and temperature...), b) analyse the redshift evolution of halos and relics, with the advantages for cosmological studies stressed above, and c) fill the gap in our knowledge of the last phases of radio galaxy evolution in clusters (see Sect. 2.3). Particularly interesting will be the study of possible presence of non-thermal radio emission at z ~ 1, i.e. the epoch of formation of the massive galaxy clusters observed in the local Universe.

The excellent sensitivity, high angular resolution and large number of spectral channels of the next generation instruments, together with new techniques of RM synthesis (Brentjens & de Bruyn 2005), will allow polarisation mapping and RM studies of radio emission in clusters, significantly improving our estimates of large-scale magnetic fields.

Future radio observations of galaxy clusters, combined with the new generation instruments at other wavelengths 8 (e.g. sub-mm: ALMA; X-ray: XEUS, Simbol-X; gamma-rays: GLAST, H.E.S.S., MAGIC 9; ...), will allow us to open a new window in cosmological studies.

The authors thank ISSI (Bern) for support of the team "Non-virialized X-ray components in clusters of galaxies". CF and FG warmly thank Luigina Feretti and Matteo Murgia for many useful discussions on the subject of this paper. CF and SS acknowledge financial support by the Austrian Science Foundation (FWF) through grants P18523-N16 and P19300-N16, by the Tiroler Wissenschaftsfonds and through the UniInfrastrukturprogramm 2005/06 by the BMWF. FG acknowledges financial support through Grant ASI-INAF I/088/06/0 - High Energy Astrophysics.

6 Converted from the bolometric X-ray luminosity limit in Feretti & Giovannini (2007) to the 0.1 - 2.4 keV band luminosity using Table 5 of Böhringer et al. (2004) and assuming typical ICM temperature values (TX ~ 5 - 10 keV). Back.

7 The Giant Metrewave Radio Telescope (GMRT) is operated by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research (NCRA-TIFR). Back.

8 See also Paerels et al. (2008) - Chapter 19, this volume. Back.

9 A new generation of ground based imaging Cherenkov telescopes will be available soon. The measurements above 10 TeV are crucial to distinguish between the Compton scattering and hadronic origins of gamma-ray emission from clusters of galaxies. Back.

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