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

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98 CHAPTER 4. PACMAN – A NEW RM MAP MAKING ALGORITHM 6. For the calculation of power spectra it is always preferable to use a window weighting scheme which has to be carefully selected. 7. Finally, under or overestimation of the measurement errors of polarisation angles (which will propagate through all calculations due to error propagation) could influence the final results. A reduced χ 2 ν test was performed in order to test if the errors are over or under estimated. One can conclude that the calculation of RM maps is a very difficult task requiring a critical view to the data and a careful noise analysis. However, Pacman offers a good opportunity to calculate reliable RM maps and to understand the data and its limitations better. Furthermore, improved RM maps and the according error analysis for Hydra North and A2255E were presented in this chapter.
Chapter 5 A Bayesian View on Faraday Rotation Maps – Seeing the Magnetic Power Spectra in Galaxy Clusters In the last chapter, a method was introduced in order to calculate reliable Faraday rotation maps from multi-frequency polarisation data sets suppressing map making artefacts. In order to use the full potential of these high quality RM maps, an accurate power spectrum estimator based on Bayesian maximum likelihood methods is developed and successfully applied in this chapter. This work is submitted as Vogt & Enßlin to Astron. & Astrophys. 5.1 Introduction In Chapter 3, a method in order to determine the magnetic power spectra by Fourier transforming RM maps was proposed. Based on these considerations, this method was applied to observational data and the magnetic power spectrum of three clusters (Abell 400, Abell 2634 and Hydra A) was determined from RM maps of radio sources located in these clusters. Furthermore, field strengths of ∼ 12 µG were determined for the cooling flow cluster Hydra A, 3 µG and 6 µG for the non-cooling flow clusters Abell 2634 and Abell 400, respectively. This analysis revealed spectral slopes of the power spectra with spectral indeces −2.0 . . . −1.6. However, it was realised that using the proposed analysis, it is difficult to reliably determine differential quantities such as spectral indeces due to the complicated shapes of the used emission regions which lead to a redistribution of magnetic power within the spectra. Recently, Murgia et al. (2004) proposed a numerical method in order to determine the magnetic power spectrum in clusters. They infer the magnetic field strength and structure by comparing simulations of RM maps as caused by multi-scale magnetic fields with the observed polarisation properties of extended cluster radio sources such as radio galaxies and haloes. They argue that field strengths derived in the literature using analytical expressions have been overestimated the field strengths by a factor of 99
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Investigations of Faraday Rotation
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”Vom Himmel lächelte der Herr zu
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vi CONTENTS 3.4.2 Real Space Analys
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List of Figures 1.1 nπ-ambiguity .
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x LIST OF FIGURES
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xii ABSTRACT correlation function a
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xiv ABSTRACT
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2 CHAPTER 1. INTRODUCTION in heat c
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28 CHAPTER 1. INTRODUCTION where n
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30 CHAPTER 2. IS THE RM SOURCE-INTR
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