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Measurements of synchrotron radio emission at several frequencies usually provide the first evidence for the presence of a significant population of relativistic electrons and magnetic fields. This has been the prime evidence for IC fields and electrons. In addition, Faraday Rotation (FR) of the plane of polarisation of radiation from cluster and background radio galaxies has provided mostly statistical evidence for IC magnetic fields. Main results from these very different sets of observations are briefly reviewed in the next two subsections.

2.1. Extended IC Emission

In clusters the task of actually determining that the observed emission is from extended IC regions is quite challenging, since high resolution observations of the various discrete radio sources (that are mostly in the member galaxies) are required, in addition to the (lower resolution) observations of the extended low brightness emission. The truly extended emission is mapped upon subtraction of the respective contributions of these sources to the spectral flux. Observations of extended radio emission had begun some 50 years ago with measurements of Coma C in the central region of the Coma cluster by Seeger et al. (1957), followed by various other measurements at frequencies in the range 0.01-4.85 GHz, including the first detailed study at 408 MHz and 1407 MHz by Willson (1970).

Appreciable effort has been devoted to measure extended emission regions in clusters, which has resulted in the mapping of centrally located (`halo') and other (`relic') regions in about 50 clusters. Some 32 of these were found in a VLA survey (Giovannini et al. 1999, Giovannini & Feretti 2000) of 205 nearby clusters in the ACO catalogue, only about a dozen of these were previously known to have regions of extended radio emission. Primary interest (certainly to us here) is in the former sources, which constitute a truly cluster phenomenon. A central extended radio region (which is somewhat inappropriately referred to as `halo') typically has a size of ~ 1-2 Mpc, and a luminosity in the range 1040 - 1042 erg s-1 (for H0 = 70 km s-1 Mpc-1) over the frequency band ~ 0.04-5 GHz. With radio indices usually in the range ~ 1-2, the emission is appreciably steeper than that of (most) radio galaxies.

The clusters in which radio halos and relics have already been found include evolving systems with a substantial degree of subclustering, as well as well-relaxed clusters that seem to have attained hydrostatic equilibrium. Halo morphologies are also quite varied, from roughly circular (projected) configuration to highly irregular shape, as can be seen in the contour maps produced by Giovannini et al. (1999), Giovannini & Feretti (2000), Giovannini et al. (2006). The spatial variety is reflected also in the wide distribution of values of the spectral index across the halo; e.g. see the maps in Giovannini et al. (1999).

Obviously, the magnetic field strength and relativistic electron density cannot both be determined from radio measurements alone, unless it is assumed that they are related so both can be determined from a single observable. It is commonly assumed that the total energy density of particles (mostly, protons and electrons) is equal to that in the magnetic field. The validity of this equipartition assumption is not obvious, especially in clusters where the particles and fields may have different origins and evolutionary histories. Moreover, the complex nature of the radio emission, and the expected significant variation of the magnetic field strength and relativistic electron density across a halo, imply that only rough estimates of these quantities can be obtained from measurements of the (spectral) flux integrated over the halo. When available, values of the halo mean equipartition field, Beq, are also listed in Table 1; generally, these substantially uncertain values are at the few µG level.

2.2. Faraday Rotation

IC magnetic fields can also be estimated by measuring the statistical depolarisation and Faraday Rotation of the plane of polarisation of radiation from background radio sources seen through clusters (e.g. Kim et al. 1991), and also from radio sources in the cluster. FR measurements sample the line of sight component of the randomly oriented (and spatially dependent) IC fields, weighted by the gas density, yielding a mean weighted value which we denote by Bfr. This quantity was estimated by analysing the rotation measure (RM) distribution of individual radio sources in several clusters, including Cygnus A (Dreher et al. 1987), Hydra A (Taylor & Perley 1993, Vogt & Enßlin 2003), A 119 (Feretti et al. 1999, Dolag et al. 2001), A 400, and A 2634 (2003 Vogt & Enßlin). Analyses of FR measurements typically yield values of Bfr that are in the range of 1-10 µG.

Most FR studies are statistical, based on measurements of radio sources that are inside or behind clusters. An example is the work of Clarke et al. (2001), who determined the distribution of RM values with cluster-centric distance for 27 radio sources within or in the background (15 and 12, respectively) of 16 nearby clusters. Analysis of this distribution (including comparison with results for a control sample of radio sources seen outside the central regions of the clusters in the sample) yielded a mean field value of ~ 5-10 (ell / 10 kpc)-1/2 µG, where ell is a characteristic field spatial coherence (reversal) scale. In further work the sample of radio sources was significantly expanded (to about 70; Clarke 2004). In comparing different measures of the mean strength of IC fields it should be remembered that the selective sampling of locally enhanced fields in high gas density regions in cluster cores broadens the RM distribution, resulting in overestimation of the field mean strength.

Deduced values of Bfr yield substantially uncertain estimates of the mean field across a halo. The major inherent uncertainties stem from the need to separate the several contributions to the total RM (including that which is intrinsic to the radio source), the unknown tangled morphology of IC fields and their spatial variation across the cluster, as well as uncertainty in modelling the gas density profile. A discussion of these uncertainties, many aspects of which have already been assessed in some detail (e.g., Goldshmidt & Rephaeli 1993, Newman et al. 2002, Rudnick & Blundell 2003, Enßlin et al. 2003, Murgia et al. 2004), is out of the scope of our review.

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