Magnetic power spectra from Faraday rotation maps - REALMAF and its use
  on Hydra A
  We develop a novel maximum-a-posteriori method to measure magnetic power
spectra from Faraday rotation data and implement it in the REALMAF code. A
sophisticated model for the magnetic autocorrelation in real space permits us
to alleviate previously required simplifying assumptions in the processing. We
also introduce a way to treat the divergence relation of the magnetic field
with a multiplicative factor in Fourier space, with which we can model the
magnetic autocorrelation as a spherically symmetric function. Applied to the
dataset of Hydra A north, we find a power law power spectrum on spatial scales
between 0.3 kpc and 8 kpc, with no visible turnover at large scales within this
range and a spectral index consistent with a Kolmogorov-like power law regime.
The magnetic field strength profile seems to follow the electron density
profile with an index alpha=1. A variation of alpha from 0.5 to 1.5 would lead
to a spectral index between 1.55 and 2.05. The extrapolated magnetic field
strength in the cluster centre highly depends on the assumed projection angle
of the jet. For an angle of 45 degree we derive extrapolated 36 muG in the
centre and directly probed 16 muG at 50 kpc radius.
