A Bayesian view on Faraday rotation maps - Seeing the magnetic power spectra in galaxy clusters

We present a Bayesian maximum likelihood analysis of Faraday rotation measure (RM) maps of extended radio sources to determine magnetic field power spectra in clusters of galaxies. Using this approach, it is possible to determine the uncertainties in the measurements. We apply this approach to the RM map of Hydra A and derive the power spectrum of the cluster magnetic field. For Hydra A, we measure a spectral index of -5/3 over at least one order of magnitude implying Kolmogorov type turbulence. We find a dominant scale of about 3 kpc on which the magnetic power is concentrated, since the magnetic autocorrelation length is lambda_B = 3 +/- 0.5 kpc. Furthermore, we investigate the influences of the assumption about the sampling volume (described by a window function) on the magnetic power spectrum. The central magnetic field strength was determined to be about 7 +/- 2 muG for the most likely geometries.