Investigations of Faraday Rotation Maps of Extended Radio Sources ...

3.6. CONCLUSIONS 67
there is a random magnetic field component of about 30 µG with a correlation length
of 4 kpc. The deviation by a factor of 3 of the field strength from the value revealed by
the presented analysis might be explained by the usage of an improved electron density
profile for the analysis which also takes the cooling flow into account. The value for
the central magnetic field strength B 0 might also be lower due to the conservative
approach of restricting the k-space integration range. Another explanation for the
difference could be sought in the exclusion of the south lobe from the calculation
above. Including the south lobe in the analysis leads to higher central field strengths
but given the influence of the very complicated window function in the case of the
south lobe, it is not clear to what extent the real power spectrum is resembled.
The estimation of the dynamical importance of the magnetic fields derived for the
cluster gas can be done by comparing the thermal pressure (p th = 2n e (0)kT core ) with
the magnetic pressure (p B = B0 2/(8π)). One can calculate p B/p th which yields 0.08
for the case of Abell 2634 (assuming a T core = 1.2 keV (Schindler & Prieto 1997)),
p B /p th = 0.19 for Abell 400 (T core = 1.5 keV (Eilek & Owen 2002)) and p B /p th
= 0.01 for Hydra A (T core = 2.7 keV (David et al. 2001)). It is astonishing that the
value of p B /p th is smaller for Hydra A, which is a cooling flow cluster, than for the
non-cooling flow cluster Abell 400 and Abell 2634. The values of p B /p th = 0.1...0.2
for the latter two clusters give an indication that for those clusters the magnetic field is
of some weak dynamical importance for the cluster gas.
3.6 Conclusions
A new analysis of Faraday rotation maps was developed in order to estimate magnetic
field strength and autocorrelation length and to determine the magnetic power
spectra of the magnetised intra-cluster gas. This analysis relies on the assumption that
the magnetic fields are statistically isotropically distributed throughout the Faraday
screen. A window function was introduced through which any virtually statistically
homogeneous magnetic field can be thought to be observed. This window function
describes the geometry of the source and the global properties of the intra-cluster gas
such as the electron density, known from X-ray measurements, and the global average
magnetic field distribution, which is assumed to scale with the electron density. Furthermore,
two possible approaches in real and Fourier space were developed and tests
were outlined for the evaluation of any influence especially arising from the observational
nature of the data such as limited source size, resolution and pixel noise on the
results obtained. However, the analysis allows to measure average magnetic energies
but it is not sensitive to the particular realisation of the magnetic field structure.
This approach was applied to observational data and reliable results were derived
not only for magnetic field strengths and autocorrelation lengths but also strength and
quality of any results obtained by applying this new analysis to any observational data
was assessed. In order to understand the possible impacts on the results, the Faraday
rotation maps of three extragalactic extended radio sources were reanalysed, i.e. 3C75
in the cluster Abell 400, 3C465 in Abell 2634, which were kindly provided by Frazer
Owen and Jean Eilek, and Hydra A in Abell 780, which was kindly provided by Greg
Taylor. The analysis was performed in real and Fourier space for these three Faraday
rotation maps. While discussing the difficulties involved in the application to the data,