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

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List of Figures 1.1 nπ-ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 RM distribution of Hydra A . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Radio map of the Coma cluster . . . . . . . . . . . . . . . . . . . . . 17 1.4 RM cluster point source sample . . . . . . . . . . . . . . . . . . . . 20 2.1 RM distribution of PKS 1246-410 . . . . . . . . . . . . . . . . . . . 30 2.2 RM - ϕ 0 scatter plots . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.1 RM autocorrelation function of A400, A2634 and Hydra A . . . . . . 57 3.2 Magnetic autocorrelation function w(r) in real space . . . . . . . . . . 58 3.3 Magnetic energy spectrum for A2634, A400 and Hydra A . . . . . . . 59 3.4 Dependence of the magnetic field strength on the integration interval . 60 3.5 Testing the window function by calculating χ 2 (x ⊥ ) . . . . . . . . . . 61 3.6 Fourier transformed RM map of A400 and Hydra A . . . . . . . . . 62 3.7 Response function for A2634 . . . . . . . . . . . . . . . . . . . . . . 63 3.8 Expected and measured magnetic field in comparison . . . . . . . . . 64 3.9 Determination of the spectral indeces . . . . . . . . . . . . . . . . . . 65 4.1 Flow chart of the algorithm Pacman . . . . . . . . . . . . . . . . . . 75 4.2 Testing the Pacman algorithm . . . . . . . . . . . . . . . . . . . . . 81 4.3 Comparision between Pacman and standard fit RM aps . . . . . . . . 85 4.4 A pixel-by-pixel comparison between Pacman and standard fit RM Map 86 4.5 Various Power Spectra for the Cluster Source A2255E . . . . . . . . 87 4.6 A pixel-by-pixel comparison between Pacman and standard fit RM Map for Hydra A North . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.7 Various power spectra for Hydra North . . . . . . . . . . . . . . . . . 91 4.8 Various power spectra for Hydra North using different thresholds . . . 92 4.9 A reduced χ 2 νij and Ṽ map of Hydra North . . . . . . . . . . . . . . 93 4.10 Individual RM fits across an RM jump . . . . . . . . . . . . . . . . 95 4.11 Various power spectra for Hydra South . . . . . . . . . . . . . . . . . 96 5.1 Generated RM maps with known power spectrum . . . . . . . . . . . 106 5.2 Calculated power spectra for the test case . . . . . . . . . . . . . . . 107 5.3 RM maps of Hydra North . . . . . . . . . . . . . . . . . . . . . . . 109 5.4 Window function in comparison to the RM dispersion . . . . . . . . 110 5.5 Various power spectra for different scaling exponents α B . . . . . . . 112 5.6 The log-likelihood for various scaling parameters α B . . . . . . . . . 113 viii
LIST OF FIGURES ix 5.7 Two power spectra for different inclination angles θ . . . . . . . . . . 114 5.8 The integrated magnetic field energy E B for various scaling parameters α B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Page 1 and 2: Investigations of Faraday Rotation
Page 3: ”Vom Himmel lächelte der Herr zu
Page 6 and 7: vi CONTENTS 3.4.2 Real Space Analys
Page 10 and 11: x LIST OF FIGURES
Page 12 and 13: xii ABSTRACT correlation function a
Page 14 and 15: xiv ABSTRACT
Page 16 and 17: 2 CHAPTER 1. INTRODUCTION in heat c
Page 18 and 19: 4 CHAPTER 1. INTRODUCTION Maxwell
Page 20 and 21: 6 CHAPTER 1. INTRODUCTION broadenin
Page 22 and 23: 8 CHAPTER 1. INTRODUCTION This sync
Page 24 and 25: 10 CHAPTER 1. INTRODUCTION fluctuat
Page 26 and 27: 12 CHAPTER 1. INTRODUCTION where a
Page 28 and 29: 14 CHAPTER 1. INTRODUCTION where L
Page 30 and 31: 16 CHAPTER 1. INTRODUCTION 1.3 The
Page 32 and 33: 18 CHAPTER 1. INTRODUCTION In gener
Page 34 and 35: 20 CHAPTER 1. INTRODUCTION Figure 1
Page 36 and 37: 22 CHAPTER 1. INTRODUCTION standard
Page 38 and 39: 24 CHAPTER 1. INTRODUCTION Consider
Page 40 and 41: 26 CHAPTER 1. INTRODUCTION • Prob
Page 42 and 43: 28 CHAPTER 1. INTRODUCTION where n
Page 44 and 45: 30 CHAPTER 2. IS THE RM SOURCE-INTR
Page 56 and 57: 42 CHAPTER 3. MEASURING MAGNETIC FI
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44 CHAPTER 3. MEASURING MAGNETIC FI
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72 CHAPTER 4. PACMAN - A NEW RM MAP
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100 CHAPTER 5. A BAYESIAN VIEW ON F
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118 CONCLUSIONS tually statisticall
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120 BIBLIOGRAPHY Conway, R. G. & St
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122 BIBLIOGRAPHY Ikebe, Y., Makishi
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124 BIBLIOGRAPHY Simard-Normandin,
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126 ACKNOWLEDGEMENTS in his long em
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Publications Journals 1. A Bayesian
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