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 \sim 3 kpc on which the magnetic power is concentrated , since the magnetic autocorrelation length is \lambda _ { B } = 3 \pm 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 \sim 7 \pm 2 \mu G for the most likely geometries .