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

Free access article

Issue		A&A Volume 434, Number 1, April IV 2005


Page(s)		67 - 76
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:20041839

A&A 434, 67-76 (2005)
DOI: 10.1051/0004-6361:20041839

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

C. Vogt and T. A. Enßlin

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Postfach 1317, 85741 Garching, Germany

(Received 12 August 2004 / Accepted 16 December 2004)

Abstract
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 ~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 ~ $7\pm2\,\mu$ G for the most likely geometries.

Key words: magnetic fields -- radiation mechanism: non-thermal -- galaxies: active -- interplanetary medium -- galaxies: cluster: general -- radio continuum: general

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