▪ Abstract Magnetic fields in the intercluster medium have been measured using a variety of techniques, including studies of synchrotron relic and halo radio sources within clusters, studies of inverse Compton X-ray emission from clusters, surveys of Faraday rotation measures of polarized radio sources both within and behind clusters, and studies of cluster cold fronts in X-ray images. These measurements imply that most cluster atmospheres are substantially magnetized, with typical field strengths of order 1 μGauss with high areal filling factors out to Mpc radii. There is likely to be considerable variation in field strengths and topologies both within and between clusters, especially when comparing dynamically relaxed clusters to those that have recently undergone a merger. In some locations, such as the cores of cooling flow clusters, the magnetic fields reach levels of 10–40 μG and may be dynamically important. In all clusters the magnetic fields have a significant effect on energy transport in the intracluster medium. We also review current theories on the origin of cluster magnetic fields.

Aims. The aim of the present work is to constrain the Coma cluster magnetic field strength, its radial profile and power spectrum by comparing Faraday rotation measure (RM) images with numerical simulations of the magnetic field.Methods. We have analyzed polarization data for seven radio sources in the Coma cluster field observed with the Very Large Array at 3.6, 6 and 20 cm, and derived Faraday rotation measures with kiloparsec scale resolution. Random three dimensional magnetic field models have been simulated for various values of the central intensity B 0 and radial power-law slope η, where η indicates how the field scales with respect to the gas density profile.Results. We derive the central magnetic field strength, and radial profile values that best reproduce the RM observations. We find that the magnetic field power spectrum is well represented by a Kolmogorov power spectrum with minimum scale ~2 kpc and maximum scale ~34 kpc. The central magnetic field strength and radial slope are constrained to be in the range (B 0 = 3.9 μG; η = 0.4) and (B 0 = 5.4 μG; η = 0.7) within 1σ. The best agreement between observations and simulations is achieved for B 0 = 4.7 μG; η = 0.5. Values of B 0 > 7 μG and <3 μG as well as η < 0.2 and η > 1.0 are incompatible with RM data at 99% confidence level.

We present a numerical approach to investigate the relationship between magnetic fields and Faraday rotation effects in clusters of galaxies. We can infer the structure and strength of intra-cluster magnetic fields by comparing our simulations with the observed polarization properties of extended cluster radio sources such as radio galaxies and halos. We find the observations require a magnetic field which fluctuates over a wide range of spatial scales (at least one order of magnitude). If several polarized radio sources are located at different projected positions in a galaxy cluster, as is the case for A119, detailed Faraday rotation images allow us to constrain both the magnetic field strength and the slope of the power spectrum. Our results show that the standard analytic expressions applied in the literature overestimate the cluster magnetic field strengths by a factor of ~2. We investigate the possible effects of our models on beam depolarization of radio sources whose radiation traverses the magnetized intracluster medium. Finally, we point out that radio halos may provide important information about the spatial power spectrum of the magnetic field fluctuations on large scales. In particular, different values of the index of the power spectrum produce very different total intensity and polarization brightness distributions.