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

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vi CONTENTS 3.4.2 Real Space Analysis . . . . . . . . . . . . . . . . . . . . . . 56 3.4.3 Fourier Space Analysis . . . . . . . . . . . . . . . . . . . . . 58 3.4.4 Test the model and assess the influence of the window function 60 3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 Pacman – A new RM Map Making Algorithm 71 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 The new Pacman algorithm . . . . . . . . . . . . . . . . . . . . . . . 73 4.2.1 The Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.2.2 The Basic Algorithm . . . . . . . . . . . . . . . . . . . . . . 74 4.2.3 Improving Quality . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.4 Restricting Gradients . . . . . . . . . . . . . . . . . . . . . . 78 4.2.5 Topological Defects . . . . . . . . . . . . . . . . . . . . . . 78 4.2.6 Spurious Points . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.7 Multi-Frequency Fits . . . . . . . . . . . . . . . . . . . . . . 79 4.2.8 Additional Information . . . . . . . . . . . . . . . . . . . . . 80 4.3 Testing the Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 Statistical Characterisation of Improved RM Maps . . . . . . . . . . 81 4.4.1 Gradient Vector Product Statistic . . . . . . . . . . . . . . . 81 4.4.2 Error Under or Over Estimation . . . . . . . . . . . . . . . . 82 4.4.3 Magnetic Power Spectra . . . . . . . . . . . . . . . . . . . . 83 4.5 Application to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.5.1 Abell 2255E . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.5.2 Hydra North . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.5.3 The Quest for Hydra South . . . . . . . . . . . . . . . . . . . 94 4.6 Lessons & Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 97 5 A Bayesian View on Faraday Rotation Maps 99 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Maximum Likelihood Analysis . . . . . . . . . . . . . . . . . . . . . 100 5.2.1 The Covariance Matrix C RM . . . . . . . . . . . . . . . . . . 100 5.2.2 Evaluation of the Likelihood Function . . . . . . . . . . . . . 103 5.2.3 Binning and Rebinning . . . . . . . . . . . . . . . . . . . . . 103 5.2.4 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3 Testing the Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4 Application to Hydra A . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.4.1 The Data ∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.4.2 The Window Function . . . . . . . . . . . . . . . . . . . . . 109 5.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Conclusions 117 Bibliography 119 Acknowledgements 125
List of Tables 2.1 A and V statistics of various data sets . . . . . . . . . . . . . . . . . 38 3.1 Results for the correlation analysis . . . . . . . . . . . . . . . . . . . 66 vii
Page 1 and 2: Investigations of Faraday Rotation
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Page 8 and 9: List of Figures 1.1 nπ-ambiguity .
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42 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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