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,
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. 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. 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 make
three-dimensional models with a gas density distribution derived from X-ray
observations and a random magnetic field with this power spectrum. Under these
assumptions we find that both 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 around 65
and 0.2 kpc, respectively. The average magnetic field strength at the cluster
centre is 3.5 +/-1.2 micro-G, decreasing linearly with the gas density within
about 16 kpc of the nucleus.Comment: 19 pages; 14 figures; accepted for publication on A&A. For a high
quality version use ftp://ftp.eso.org/pub/general/guidetti
