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

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70 CHAPTER 3. MEASURING MAGNETIC FIELD POWER SPECTRA
Chapter 4 Pacman - A new RM Map Making Algorithm The statistical analysis of RM measurements in terms of correlation functions and equivalently power spectra requires that the RM’s are unambiguously determined as discussed in the last chapter. Thus, any ambiguous RM can lead to misinterpretation of the data investigated. This ambiguity results from the observational fact that the polarisation angles are only determined up to additions of ±nπ. In this chapter, a new map making algorithm - called Pacman - is described. Instead of solving the nπ-ambiguity for each data point independently, the proposed algorithm solves the nπ-ambiguity for a high signal-to-noise region and uses this information to assist computations in adjacent low signal-to-noise areas. This work is submitted to Mon. Not. Roy. Astron. Soc. as two papers (Dolag et al. 2004; Vogt et al. 2004). My part in this work was the contribution to the development of the algorithm, the data handling, the statistical characterisation and tests of the various RM maps and describing the algorithm in the two scienfic publications. Pacman was implemented by Klaus Dolag. 4.1 Introduction For the calculation of rotation measures (RM) and intrinsic polarisation angles (ϕ 0 ) using the relationship ϕ = RM λ 2 + ϕ 0 (see Eq. (1.42)), a least squares fit is normally applied to the polarisation angle data. Since the measured polarisation angle ϕ is constrained only to values between 0 and π leaving the freedom of additions of ± nπ, where n is an integer, the determination of RM and ϕ 0 is ambiguous, causing the so called nπ-ambiguity. Therefore, a least squares fit has to be applied to all possible nπcombinations of the polarisation angle data at each data point of the polarised radio source while searching for the nπ-combination for which χ 2 is minimal. In principle, χ 2 can be decreased to infinitely small numbers by increasing RM substantially. Vallée & Kronberg (1975) and Haves (1975) suggested to avoid this problem by introducing an artificial upper limit for |RM| ≤ RM max . Since this is a biased approach, Ruzmaikin & Sokoloff (1979) proposed to assume that no nπambiguity exists between the measurements of two closely spaced wavelengths taken from a whole wavelength data set. The standard error of the polarisation measurements 71
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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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10 CHAPTER 1. INTRODUCTION fluctuat
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12 CHAPTER 1. INTRODUCTION where a
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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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