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

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86 CHAPTER 4. PACMAN – A NEW RM MAP MAKING ALGORITHM cussion and description of the application of the method to data, see Chapter 3. In the calculation, it was assumed that the source plane is parallel to the observer plane. Please note, that the application of an RM data filter in order to remove bad data or data which might suffer from a wrong solution to the nπ-ambiguity as described in Chapter 3 is not necessary here and not desirable. This is on the one hand due to the use of an error weighting scheme in the window function to suppress bad data and on the other hand due to the wish to study the influence of noise and map making artefacts on the power spectra. Figure 4.4: A pixel-by-pixel scatter plot of RM stdfit values obtained using the standard fit on the y-axis versus the RM Pacman values calculated from the polarisation data of A2255E by employing the new algorithm Pacman. Black points represent results from an error weighted standard least-squares fit and red points from a non-error weighted standard fit. The points for RM stdfit values of around ± 1000 rad m −2 are artefacts of a wrong solution of the nπ-ambiguity. The RM area used for the calculation of any power spectrum is the RM area which would be covered by the Pacman algorithm while using the same set of parame-
4.5. APPLICATION TO DATA 87 ter σk max , RM max . This ensures that pixels on the border or noisy regions of the image not associated with the source – as seen in the standard fit RM map of A2255E in the upper left panel of Fig. 4.3 – are not considered for the analysis. (The same philosophy also applies for the discussion of the Hydra data in Sect. 4.5.2 and Sect. 4.5.3). 1e+11 1e+10 1e+09 ε B (k) [G 2 cm] 1e+08 1e+07 1e+06 100000 stdfit: (σ = 20 degree) stdfit: err weight (σ= 10 degree) pac: err weight (σ= 20 degree) pac: err and window weight (σ= 20 degree) 10000 0.01 0.1 1 10 k [kpc -1 ] Figure 4.5: Various power spectra for the cluster Abell 2255 determined from different RM map making scenarios are shown. The solid line represents a power spectrum calculated from a standard fit RM map with σk max = 20 ◦ where no error weighting was applied. The dashed power spectrum was obtained from a standard fit RM map with σk max = 10 ◦ where error weighting was applied to the standard fit. The dasheddotted power spectrum was determined from a Pacman RM map with σk max = 20 ◦ and error weighting was applied to the RM fits. The dotted line represents a power spectrum calculated from a Pacman RM map as above, but additionally a simple window weighting was applied for the determination of the power spectra. For comparison, the power spectra of pure white noise is plotted as a straight dashed line. The power spectra calculated for various map making scenarios are shown in Fig. 4.5. The solid and dashed lines represent power spectra calculated from standard fit RM maps. The solid line was calculated from an RM map which was obtained by using σk max = 20 ◦ where no error weighting was applied to the standard fit. The possible window weighting as introduced in Sect. 4.4.3 was also not applied. This scenario is therefore considered as a worst case. The dashed line was calculated from an RM map employing an error weighted standard fit while only allowing errors in the polarisation angle of σk max = 10 ◦ . Again no window weighting was applied. From the comparison of these two power spectra alone, one can see that the large k-scales – and thus, small real space scales – are sensitive to pixel-noise. Therefore, the applica-
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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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6 CHAPTER 1. INTRODUCTION broadenin
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8 CHAPTER 1. INTRODUCTION This sync
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10 CHAPTER 1. INTRODUCTION fluctuat
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12 CHAPTER 1. INTRODUCTION where a
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14 CHAPTER 1. INTRODUCTION where L
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16 CHAPTER 1. INTRODUCTION 1.3 The
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18 CHAPTER 1. INTRODUCTION In gener
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20 CHAPTER 1. INTRODUCTION Figure 1
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22 CHAPTER 1. INTRODUCTION standard
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24 CHAPTER 1. INTRODUCTION Consider
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26 CHAPTER 1. INTRODUCTION • Prob
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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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Page 50 and 51: 36 CHAPTER 2. IS THE RM SOURCE-INTR
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Page 86 and 87: 72 CHAPTER 4. PACMAN - A NEW RM MAP
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Page 132 and 133: 118 CONCLUSIONS tually statisticall
Page 134 and 135: 120 BIBLIOGRAPHY Conway, R. G. & St
Page 136 and 137: 122 BIBLIOGRAPHY Ikebe, Y., Makishi
Page 138 and 139: 124 BIBLIOGRAPHY Simard-Normandin,
Page 140 and 141: 126 ACKNOWLEDGEMENTS in his long em
Page 142: Publications Journals 1. A Bayesian
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