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

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114 CHAPTER 5. A BAYESIAN VIEW ON FARADAY ROTATION MAPS 1e-11 θ = 45 ο θ = 30 ο k -2/3 ε B (k)*k [erg cm -3 ] 1e-12 1e-13 1e-14 0.1 1 10 100 k [kpc -1 ] Figure 5.7: Power Spectra for two different inclination angles θ = 30 ◦ and θ = 45 ◦ and an α B = 0.5 are shown. For comparison a Kolmogorov like power spectrum is plotted as straight dashed line. One can clearly see that the calculated power spectra follow such a power spectrum over at least one order of magnitude. Note that the error bars are larger than in Fig. 5.5 because smaller bin size were used. 5e+59 4.5e+59 4e+59 E B [erg] 3.5e+59 3e+59 2.5e+59 2e+59 0 0.2 0.4 0.6 0.8 1 1.2 α B Figure 5.8: The integrated magnetic field energy E B within the cluster core radius r c2 for the various scaling parameters α B also used in Fig. 5.6 and the corresponding central magnetic field strengths B 0 as determined by the maximum likelihood estimator.
5.6. CONCLUSIONS 115 5.6 Conclusions A maximum likelihood estimator was presented for the determination of cluster magnetic field power spectra from RM maps of extended polarised radio sources. The covariance matrix for RM was introduced under the assumption of statistically homogeneously distributed magnetic fields throughout the Faraday screen. The approach was successfully tested on simulated RM maps with known power spectra. This approach was applied to the RM map of the north lobe of Hydra A. Different power spectra were calculated for various window functions being especially influenced by the scaling parameter between electron density profile and global magnetic field distribution and the inclination angle of the emission region. The scaling parameter α B was determined to be most likely in the range of 0.1 . . . 0.8. It was realised that there is a systematic uncertainty in the values calculated due to the uncertainty in the window parameters itself. Taking this into account, a central magnetic field strength in the Hydra A cluster of B = (7 ± 2) µG was deduced and for the magnetic field correlation length was determined to be λ B = (3.0 ± 0.5) kpc. If the geometry uncertainties could be removed the remaining statistical errors are an order of one magnitude smaller. The difference of these values from the ones found in an earlier analysis of the same dataset of Hydra A which yielded B = 12µG and λ B = 1 kpc (Chapter 3) is a result of the improved RM map using the Pacman algorithm (Chapter 4) and a better knowledge of the magnetic cluster profile, i.e. here α B ≈ 0.5 (instead of α B = 1.0 in Chapter 3). The cluster magnetic field power spectrum of Hydra A follows a Kolmogorov like power spectrum over at least one order of magnitude. However, the analysis reveals that there is a dominant scale ∼ 3 kpc on which the magnetic power is concentrated.
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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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4 CHAPTER 1. INTRODUCTION Maxwell
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