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122 6. Faraday rotation in two extreme environments The results of this analysis can be summarized as follows: • The polarization position angles accurately follow theλ 2 relation. Together with the observed low depolarization, this confirms yet again that the Faraday rotation is primarily in front of the radio emission. The residual depolarization is consistent with unresolved RM fluctuations. • The amplitude of the RM fluctuations in 0755+37 is smaller than for FR I sources embedded in groups of galaxies (Chapter 5) and comparable to that in NGC 315, which is also in a very sparse environment (Laing et al. 2006a). This reinforces the hypothesis the most of the Faraday rotating material is due to the hot atmosphere of the associated galaxy. • In M 87 the amplitude of the RM fluctuations is typical of that found in other cool-core clusters such as Cygnus A and Hydra A (e.g. Carilli & Taylor 2002; Laing et al. 2008). • The profiles ofσ RM (which are not shown) and〈k〉 for both sources have higher average values for the receding lobes. Thus both resolved and sub-beam fluctuations of RM are higher on the receding side (the Laing-Garrington effect; Laing 1988; Garrington et al. 1988). • Both approaching jets show low and uniform rotation measures. In M 87, the associated depolarization is also anomalously low. • There is other evidence for anisotropic RM fluctuations in 0755+37: the leading edge of the W lobe shows arc-like RM structures with sign reversals. These are reminiscent of the RM bands discussed in Chapter 5. The RM structures of both 0755+37 and M 87 appear reasonably isotropic elsewhere. • Except in the restricted areas showing obvious anisotropic structure, it is reasonable to treat the RM as a Gaussian, random, isotropic variable and to estimate its power spectrum. The power spectra are well described by power laws with slopes ranging from 2.2 to 2.5 in 0755+37 and slightly steeper (≈3.0) in M 87. These are comparable with the slopes deduced for 3C 449, 3C 31 (Laing et al. 2008) and the regions not dominated by RM bands in 0206+35, 3C 270 and 3C 353 (Chapter 5). They are all significantly flatter than the value of 11/3 expected for Kolmogorov turbulence. • These power spectra are consistent with the observed depolarization for minimum field scales of 0.1 kpc in 0755+37 and 0.06-0.25 kpc in M 87. The nearby location and high surface brightness of M 87 have allowed an accurate determination of its RM power spectrum on scales smaller than those accessible for other objects. 122
6.4. Preliminary conclusions 123 • The derived magnetic-field auto-correlation lengths λ B are 0.1-1.4 kpc in 0755+37 (depending on the sub-region), and 0.2 kpc in M 87. • The central magnetic field strength required to match the RM fluctuations, deduced from the single-scale approximation including cavities and assuming these values ofλ B as scalelengths, is≈1.0µG in 0755+37 and≈35µG in M 87. This confirms the trend for stronger fields to be seen in richer environments (Carilli & Taylor 2002), although subject to confirmation by three-dimensional modelling. Significant imprecision is certainly introduced by the assumption of constant integration path required to interpret the RM structure functions over limited sub-regions. This can be corrected in future three-dimensional simulations, but better constraints on the source geometries and the distributions of hot gas will be required. This will be particularly challenging for M 87, where the hot-gas structure is extremely complicated (Forman et al. 2007). 123
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Alma Mater Studiorum Università de
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To Hypatia from Alexandria in Egypt
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Contents Abstract i 1 Physics of ra
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4.6.3 The outer scale of the magnet
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Abstract The existence of diffuse m
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2. Two-dimensional Monte Carlo simu
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Chapter 1 Physics of radio galaxies
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1.2. Non-thermal emission mechanism
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1.2. Non-thermal emission mechanism
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1.3. Radio galaxies 7 FR II sources
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1.3. Radio galaxies 9 (a) (b) Figur
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1.3. Radio galaxies 11 pressure, th
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Chapter 2 The X-ray environment of
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2.2. The thermal component 15 Figur
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2.3. Radio source - environment int
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2.3. Radio source - environment int
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Chapter 3 Magnetic fields in the ho
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3.1. Introduction 23 Figure 3.1: Ex
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3.1. Introduction 25 to the relativ
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3.2. Faraday Rotation 27 The RM can
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3.2. Faraday Rotation 29 Figure 3.4
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3.3. Depolarization 31 3.3 Depolari
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3.5. The magnetic field profile 33
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3.6. Tangled magnetic field 35 rad
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3.7. The magnetic field power spect
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Chapter 4 Structure of the magneto-
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4.1. The radio source 3C 449: gener
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4.3. The Faraday rotation in 3C 449
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4.3. The Faraday rotation in 3C 449
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4.4. Depolarization 51 Figure 4.4:
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4.4. Depolarization 53 1.25 arcsec
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4.5. Two dimensional analysis 55 sm
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4.5. Two dimensional analysis 57 Fi
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4.6. Three-dimensional analysis 59
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4.7. Summary and comparison with ot
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4.7. Summary and comparison with ot
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Page 97 and 98: 5.3. Rotation measure images 81 IMA
Page 99 and 100: 5.3. Rotation measure images 83 cor
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Page 115 and 116: 5.8. Discussion 99 5.8 Discussion 5
Page 117 and 118: 5.8. Discussion 101 line−of−sig
Page 119 and 120: 5.8. Discussion 103 flat slopes. I
Page 121 and 122: 5.9. Conclusions and outstanding qu
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Page 127 and 128: 6.2. Two-dimensional analysis: rota
Page 135 and 136: 6.3. Two-dimensional analysis: stru
Page 137: 6.4. Preliminary conclusions 121 Ta
Page 141 and 142: Summary and conclusions The goal of
Page 143 and 144: 6.5. Summary 127 responsible for th
Page 145 and 146: 6.6. General conclusions 129 radio
Page 147 and 148: 6.7. Future prospects 131 and is th
Page 149: Appendix 133
Page 152 and 153: 136 Data reduction and imaging of l
Page 160 and 161: 144 BIBLIOGRAPHY Bîrzan, L., Raffe
Page 162 and 163: 146 BIBLIOGRAPHY Ensslin, T.A. & Go
Page 164 and 165: 148 BIBLIOGRAPHY Jeltema, T.E. & Pr
Page 166 and 167: 150 BIBLIOGRAPHY Owen, F.N., 1989,
Page 168 and 169: 152 BIBLIOGRAPHY 152
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