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

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Contents Abstract xi 1 Introduction 1 1.1 Magnetised Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Observing Astrophysical Magnetic Fields . . . . . . . . . . . . . . . 5 1.2.1 The Zeeman Effect . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Polarisation of Optical Starlight . . . . . . . . . . . . . . . . 6 1.2.3 Synchrotron Emission . . . . . . . . . . . . . . . . . . . . . 7 1.2.4 Faraday Rotation . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 The state of the Art - Cluster Magnetic Fields . . . . . . . . . . . . . 16 1.3.1 Radio Haloes and Relics . . . . . . . . . . . . . . . . . . . . 16 1.3.2 Rotation Measures . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Some Statistical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.1 Least-Squares & Error Weighting . . . . . . . . . . . . . . . 21 1.4.2 Autocorrelation and Power Spectra . . . . . . . . . . . . . . 23 1.4.3 Bayesian Statistics . . . . . . . . . . . . . . . . . . . . . . . 25 1.4.4 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . 28 2 Is the RM Source-Intrinsic or not? 29 2.1 A Long Lasting Debate . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 The Argument Reconsidered . . . . . . . . . . . . . . . . . . . . . . 31 2.3 Statistics Comes to Aid . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 Avoidable and Unavoidable Correlated Noise . . . . . . . . . . . . . 36 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3 Measuring Magnetic Field Power Spectra 41 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 The Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3 The Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3.1 Real Space Formulation . . . . . . . . . . . . . . . . . . . . 45 3.3.2 Fourier Space Formulation . . . . . . . . . . . . . . . . . . . 48 3.3.3 Testing the Model & Influences of Observational Artefacts . . 51 3.3.4 Assessing the Influence of the Window Function . . . . . . . 53 3.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4.1 3C75, 3C465 & Hydra A - the Data . . . . . . . . . . . . . . 55 v
Page 1 and 2: Investigations of Faraday Rotation
Page 3: ”Vom Himmel lächelte der Herr zu
Page 7 and 8: List of Tables 2.1 A and V statisti
Page 9 and 10: LIST OF FIGURES ix 5.7 Two power sp
Page 11 and 12: Abstract In this work, statistical
Page 13 and 14: the data, magnetic field power spec
Page 15 and 16: Chapter 1 Introduction Magnetic fie
Page 17 and 18: 1.1. MAGNETISED PLASMA 3 thermodyna
Page 19 and 20: 1.2. OBSERVING ASTROPHYSICAL MAGNET
Page 31 and 32: 1.3. THE STATE OF THE ART - CLUSTER
Page 33 and 34: 1.3. THE STATE OF THE ART - CLUSTER
Page 35 and 36: 1.4. SOME STATISTICAL TOOLS 21 part
Page 37 and 38: 1.4. SOME STATISTICAL TOOLS 23 and
Page 39 and 40: 1.4. SOME STATISTICAL TOOLS 25 wher
Page 41 and 42: 1.4. SOME STATISTICAL TOOLS 27 If t
Page 43 and 44: Chapter 2 Is the Faraday Rotation S
Page 45 and 46: 2.2. THE ARGUMENT RECONSIDERED 31 2
Page 47 and 48: 2.3. STATISTICS COMES TO AID 33 ind
Page 49 and 50: 2.3. STATISTICS COMES TO AID 35 No.
Page 51 and 52: 2.5. RESULTS 37 noise in RM and ϕ
Page 53 and 54: 2.6. CONCLUSIONS 39 Independent evi
Page 55 and 56:
Chapter 3 Measuring the Cluster Mag
Page 57 and 58:
3.2. THE PHILOSOPHY 43 easier acces
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3.3. THE METHOD 45 In many cases, t
Page 61 and 62:
3.3. THE METHOD 47 (e.g. Subramania
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3.3. THE METHOD 49 space counterpar
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3.3. THE METHOD 51 3.3.3 Testing th
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3.3. THE METHOD 53 function is chan
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3.4. APPLICATION 55 could have any
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3.4. APPLICATION 57 10000 A2634 A40
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3.4. APPLICATION 59 1e+10 Abell 263
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3.4. APPLICATION 61 10 1 χ 2 (r) 0
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3.4. APPLICATION 63 w exp p (k)/[G2
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3.5. RESULTS 65 1e+57 1e+56 w(k) [G
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3.6. CONCLUSIONS 67 there is a rand
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3.6. CONCLUSIONS 69 Fourier space.
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Chapter 4 Pacman - A new RM Map Mak
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4.2. THE NEW PACMAN ALGORITHM 73 th
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4.2. THE NEW PACMAN ALGORITHM 75 ϕ
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4.2. THE NEW PACMAN ALGORITHM 77 an
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4.2. THE NEW PACMAN ALGORITHM 79 an
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4.4. STATISTICAL CHARACTERISATION O
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4.5. APPLICATION TO DATA 83 4.4.3 M
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4.5. APPLICATION TO DATA 85 A2255E
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4.5. APPLICATION TO DATA 87 ter σk
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4.5. APPLICATION TO DATA 89 separat
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4.5. APPLICATION TO DATA 91 1e+10 1
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4.5. APPLICATION TO DATA 93 0 5 10
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4.5. APPLICATION TO DATA 95 Figure
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4.6. LESSONS & CONCLUSIONS 97 The f
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Chapter 5 A Bayesian View on Farada
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5.2. MAXIMUM LIKELIHOOD ANALYSIS 10
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Page 119 and 120:
Page 121 and 122:
5.3. TESTING THE ALGORITHM 107 wher
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5.4. APPLICATION TO HYDRA A 109 DEC
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5.5. RESULTS AND DISCUSSION 111 pre
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5.5. RESULTS AND DISCUSSION 113 410
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5.6. CONCLUSIONS 115 5.6 Conclusion
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Conclusions This work was aimed to
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Bibliography Allen, S. W., Taylor,
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BIBLIOGRAPHY 121 Feretti, L., Dalla
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BIBLIOGRAPHY 123 Pacholczyk, A. G.
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Acknowledgements Most of all, I am
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CURRICULUM VITAE Birth: Nationality
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