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We construct a simple and robust approach for deriving constraints onmagnetic fields in galaxy clusters from rotation measure (RM) maps. Relaxingthe commonly used assumptions of a correlation between the magnetic fieldstrength and the plasma density and of a power-law (in wave number) magneticfield power spectrum, and using an efficient numerical analysis method, we testthe consistency of a wide range of magnetic field models with RM maps of 11extended sources in 5 clusters, for which the data were made available to us.We show that the data reveal no indication for a radial dependence of theaverage magnetic field strength, and in particular no indication for acorrelation between the gas density and the field strength. The RM maps of aconsiderable fraction of the sources either require or are consistent with thepresence of a spatially uniform magnetic field of a relatively small strength,0.02-0.3 muG, which contributes significantly to the RM. The RM maps of all butone source do not require a power-law magnetic field power spectrum, and mostare consistent with a power spectrum dominated by a single wave length. Theuncertainties in the magnetic field strengths (and spatial correlation lengths)derived from RM maps exceed an order of magnitude (and often more). Theseuncertainties imply, in particular, that there is no indication in current RMdata for a systematic difference between the magnetic field strengths inradio-halo clusters and in radio-quiet clusters. With the improvement expectedin the near future of the quality and quantity of RM data, our analysis methodwill enable one to derive more accurate constraints on magnetic fields ingalaxy clusters.

What can we really learn about Magnetic Fields in Galaxy Clusters from Faraday Rotation observations?