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

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96 CHAPTER 4. PACMAN – A NEW RM MAP MAKING ALGORITHM 1e+10 ε B (k) [G 2 cm] 1e+09 south - pacman - simple south - pacman - thresh south - sdtfit - simple south - sdtfit - thresh north - pacman - thresh 1e+08 0.1 1 10 100 k [kpc -1 ] Figure 4.11: Various power spectra for the RM maps of the south lobe of the Hydra source are compared with the power spectrum of the north lobe calculated from the Pacman RM map (k min = 5, σk max = 35 ◦ ) employing a threshold weighting with σ0 RM = 50 rad m −2 represented as filled circles. Concentrating on the comparison of the simple window weighted power spectra of the south lobe in Fig. 4.11 (the solid line is from Pacman RM map and the dashed line is from standard fit RM map) to the one of the north lobe, one finds that the power spectrum calculated from the Pacman RM map is closer to the one from the north lobe than the power spectrum derived from the standard fit RM map. This indicates that the Pacman RM map might be the right solution to the RM determination problem for this part of the source. However, this difference vanishes if a different window weighting scheme is applied to the calculation of the power spectrum. This can be seen by comparing the threshold window weighted power spectra (dotted line for the power spectra of the Pacman RM map and dashed dotted line for the power spectra from the standard fit RM map) in Fig. 4.11. Since the choice of the window weighting scheme seems to have also an influence on the result the situation is still inconclusive. An indication for the right solution of the nπ-ambiguity problem may be found in the application of the gradient vector product statistic Ṽ to the Pacman maps and the standard fit maps of the south lobe (as shown in Fig. 4.3). The calculations yield a ratio Ṽ stdfit /Ṽpacman = 12. This is a difference of one order of magnitude and represents a substantial decrease in correlated noise in the Pacman maps. The calculation of the normalised quantity yields V stdfit = −0.69 for the standard fit maps and V pacman = −0.47 for the Pacman maps. This result strongly indicates that the Pacman map should be the preferred one.
4.6. LESSONS & CONCLUSIONS 97 The final answer to the question about the right solution of the RM distribution problem for the south lobe of Hydra A has to be postponed until observations of even higher sensitivity, higher spatial resolutions and preferably also at different frequencies are available. 4.6 Lessons & Conclusions A new algorithm for the calculation of Faraday rotation maps from multi-frequency polarisation data sets was presented. Unlike other methods, this algorithm uses global information and connects information about individual neighbouring pixels with one another. It assumes that if regions exhibit small polarisation angle gradients between neighbouring pixels in all observed frequencies simultaneously, then these pixels can be considered as connected, and information about one pixel can be used for neighbouring ones, and especially, the solution to the nπ-ambiguity should be the same. It is stressed here, that this is a very weak assumption, and – like all other criteria used within the Pacman algorithm – only depends on the polarisation data at hand and the signal-to-noise ratio of the observations. The Pacman algorithm is especially useful for the calculation of RM and ϕ 0 maps of extended radio sources and its robustness was demonstrated. Global algorithms as implemented in Pacman are preferable for the calculation of RM maps and needed if reliable RM values are desired from low signal-to-noise regions of the source. The Pacman algorithm reduces nπ-artefacts in noisy regions and makes the unambiguous determination of RM and ϕ 0 in these regions possible. Pacman allows to use all available information obtained by the observation. Any statistical analysis of the RM maps will profit from these improvements. In the course of this work, the following lessons were learned: 1. It is important to use all available information obtained by the observation. It seems especially desirable to have a good frequency coverage. The result is a smoother, less noisy map. 2. For the individual least-squares fits of the RM, it is advisable to use an error weighting scheme in order to reduce the noise. 3. Global algorithms are preferable, if reliable RM values are needed from low signal-to-noise regions at the edge of the source. 4. Sometimes it is necessary to test many values of the parameters RM max , σ max k and σ ∆ max, which govern the Pacman algorithm, in order to investigate the influence on the resulting RM maps. 5. One has to keep in mind that whichever RM map seems to be most believable, it might still contain artefacts. One should do a careful analysis by looking on individual RM pixel fits but one also should consider the global RM distribution. The gradient vector product statistic Ṽ was presented as a useful tool to estimate the level of reduction of cross-correlated noise in the calculated RM and ϕ 0 maps.
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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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22 CHAPTER 1. INTRODUCTION standard
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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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42 CHAPTER 3. MEASURING MAGNETIC FI
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44 CHAPTER 3. MEASURING MAGNETIC FI
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