| Abstract
| - Aims. The goal of this work is to constrain the strength and structure of the magnetic field associated with the environment of the radio source 3C 449 by using observations of Faraday rotation, which we model with a structure function technique, and by comparison with numerical simulations. We assume that the magnetic field is a Gaussian isotropic random variable and that it is embedded in the hot intra-group plasma surrounding the radio source. Methods. For this purpose, we present detailed rotation measure images for the polarized radio source 3C 449, previously observed with the Very Large Array at seven frequencies between 1.365 and 8.385 GHz. All of the observations are consistent with pure foreground Faraday rotation. We quantify the statistics of the magnetic-field fluctuations by deriving rotation measure structure functions, which we fit using models derived from theoretical power spectra. We quantify the errors due to sampling by making multiple two-dimensional realizations of the best-fitting power spectrum. We also use depolarization measurements to estimate the minimum scale of the field variations. We then develop three-dimensional models with a gas density distribution derived from X-ray observations and a random magnetic field with this power spectrum. By comparing our simulations with the observed Faraday rotation images, we can determine the strength of the magnetic field and its dependence on density, as well as the outer scale of the magnetic turbulence. Results. The rotation measure and depolarization data are consistent with a broken power-law magnetic-field power spectrum, with a break at about 11 kpc and slopes of 2.98 and 2.07 at smaller and larger scales respectively. The maximum and minimum scales of the fluctuations are ≈65 and ≈0.2 kpc, respectively. The average magnetic field strength at the cluster centre is 3.5 ± 1.2 μG, decreasing linearly with the gas density within ≈16 kpc of the nucleus. At larger distances, the dependence of field on density appears to flatten, but this may be an effect of errors in the density model. The magnetic field is not energetically important.
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