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

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ABSTRACT
correlation function and similarly the Fourier power spectrum of an RM map of an
extended background radio source can be used to measure the components of the magnetic
autocorrelation and power spectrum tensor within a foreground Faraday screen.
It is possible to reconstruct the full non-helical part of this tensor in the case of an
isotropic magnetic field distribution statistics. The magnetic field strength, the energy
spectrum and the autocorrelation length λ B can be obtained from this non-helical part
alone. It is demonstrated that λ B can differ substantially from λ RM , which is the
characteristical scale of an RM map. In typical astrophysical situations λ RM > λ B .
Strategies to analyse observational data are discussed, taking into account – with
the help of a window function – the limited extent of the polarised radio source, the
spatial distribution of the electron density and the average magnetic energy density in
the screen, and allowing for noise reducing data weighting. The effects of possible
observational artefacts, and strategies to avoid them are briefly discussed.
This technique of Faraday rotation measure map analysis is applied to three galaxy
clusters, Abell 400, Abell 2634 and Hydra A, in order to estimate cluster magnetic field
strengths, length scales and power spectra under the assumption that typical field values
scale linearly with the electron density. The difficulties involved in the application
of the analysis to observational data are investigated. Magnetic power spectra are derived
for the three clusters and influences on their shapes caused by the observational
nature of the data such as limited source size and resolution are discussed. Various
tests are successfully applied to validate the assumptions of the analysis.
It is shown that magnetic fluctuations are probed on length scales ranging over at
least one order of magnitude. Using this range for the determination of the magnetic
field strengths of the central cluster gas yields 3 µG in Abell 2634, 6 µG in Abell 400
and 12 µG in Hydra A as conservative estimates. The magnetic field autocorrelation
length λ B is determined to be 4.9 kpc for Abell 2634, 3.6 kpc for Abell 400 and
0.9 kpc for Hydra A. For the three clusters studied, it is found that λ RM ≃ 2...4λ B .
Furthermore, in a response analysis it is investigated if it is possible to determine
the spectral slopes of the power spectra. It is found that the integrated numbers can
be reliably determined from this analysis but differential parameters such as spectral
slopes have to be treated differently.
Realising that such a statistical analysis can be corrupted by map making artefacts,
a new method to calculate Faraday rotation measure maps from multi-frequency polarisation
angle data sets is proposed. In order to solve the so called nπ-ambiguity
problem which arises from the observational ambiguity of the polarisation angle determined
only up to additions of ±nπ, where n is an integer, it is suggested to use a
global scheme. Instead of solving the nπ-ambiguity for each data point independently,
the proposed algorithm, which was chosen to be called Pacman (Polarisation Angle
Correcting rotation Measure ANalysis), solves the nπ-ambiguity for a high signal-tonoise
region “democratically” and uses this information to assist the computations in
adjacent low signal-to-noise areas.
The Pacman algorithm is tested on artifically generated RM maps and applied to
two polarisation data sets of extended radio sources located in the Abell 2255 and Hydra
A cluster. The RM maps obtained using Pacman are compared to RM maps obtained
employing already existing methods. The reliability and the robustness of Pacman
is demonstrated. In order to study the influence of map making artefacts, which
are imprinted by wrong solutions to the nπ-ambiguities, and of the error treatment of