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70 4. The magneto-ionic medium around 3C 449 12. Assuming these variations of density and field strength with radius, a structure-function analysis can be used to estimate the outer scaleΛ max of the magnetic-field fluctuations. I find excellent agreement forΛ max ≈ 65 kpc ( f min = 0.0053 arcsec −1 ). 4.7.2 Comparison with other sources These results are qualitatively similar to those of Laing et al. (2008) on 3C 31. The maximum RM fluctuation amplitudes are similar in the two sources, as are their environments. For sphericallysymmetric gas density models, the central magnetic fields are almost the same: B 0 ≈ 2.8µG for 3C 31 and 3.5µG for 3C 449. Both results are consistent with the idea that the RM fluctuation amplitude in galaxy groups and clusters scales roughly linearly with density, ranging from a few rad m −2 in the much sparsest environments (e.g. NGC 315; Laing et al. 2006a), through intermediate values≈30 – 100 rad m −2 in rich groups such as 3C 31 and 3C 449 to∼ 10 4 rad m −2 in the centers of clusters with cool cores. The RM distribution of 3C 31 is asymmetrical, the northern (approaching) side of the source showing a much lower fluctuation amplitude, consistent with the inclination of≈ 50 ◦ estimated by Laing & Bridle (2002a). Detailed modeling of the RM profile led Laing et al. (2008) to suggest that there is a cavity in the X-ray gas, but this would have to be significantly larger than the observed extent of the radio lobes and is, as yet, undetected in X-ray observations. A broken power-law scaling of magnetic field with density, similar to that found for 3C 449 in the present work, would also improve the fit to theσ RM profile for 3C 31; alternatively, the effects of cavities around the inner lobes and spurs of 3C 449 might be significant. Deeper X-ray observations of both sources are needed to resolve this issue. In neither case is the magnetic field dynamically important: for 3C 449 the ratio of the thermal and magnetic-field pressures is≈30 at the nucleus and≈400 at the core radius of the group gas, r c = 19 kpc. The magnetic field is therefore not dynamically important, as in 3C 31. The magnetic-field power spectrum in both sources can be fit by a broken power-law form. The low-frequency slopes are 2.1 and 2.3 for 3C 449 and 3C 31 respectively. In both cases, the power spectrum steepens at higher spatial frequencies, but for 3C 31 a Kolmogorov index (11/3) provides a good fit, whereas I find that the depolarization data for 3C 449 require a cut-off below a scale of 0.2 kpc and a high-frequency slope of 3.0. The break scales are≈5 kpc for 3C 31 and≈11 kpc for 3C 449. It is important to note that the simple parametrized form of the power spectrum is not unique, and that a smoothly curved function would fit the data equally well. The gas-density structure on large scales in the 3C 31 group is uncertain, so Laing et al. (2008) could only give a rough lower limit to the outer scale of magnetic-field fluctuations,Λ max > ∼ 70 kpc. For 3C 449, we findΛ max ≈ 65 kpc. The projected distance between 3C 449 and its nearest 70
4.7. Summary and comparison with other sources 71 neighbour is≈33 kpc (Birkinshaw et al. 1981), similar to the scale on which the jets first bend through large angles (Fig. 4.1). As in 3C 31, it is plausible that the outer scale of magnetic-field fluctuations is set by interactions with companion galaxies in the group. 71
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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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Page 37 and 38: Chapter 3 Magnetic fields in the ho
Page 39 and 40: 3.1. Introduction 23 Figure 3.1: Ex
Page 41 and 42: 3.1. Introduction 25 to the relativ
Page 43 and 44: 3.2. Faraday Rotation 27 The RM can
Page 45 and 46: 3.2. Faraday Rotation 29 Figure 3.4
Page 47 and 48: 3.3. Depolarization 31 3.3 Depolari
Page 49 and 50: 3.5. The magnetic field profile 33
Page 51 and 52: 3.6. Tangled magnetic field 35 rad
Page 53 and 54: 3.7. The magnetic field power spect
Page 59 and 60: Chapter 4 Structure of the magneto-
Page 61 and 62: 4.1. The radio source 3C 449: gener
Page 63 and 64: 4.3. The Faraday rotation in 3C 449
Page 65 and 66: 4.3. The Faraday rotation in 3C 449
Page 67 and 68: 4.4. Depolarization 51 Figure 4.4:
Page 69 and 70: 4.4. Depolarization 53 1.25 arcsec
Page 71 and 72: 4.5. Two dimensional analysis 55 sm
Page 73 and 74: 4.5. Two dimensional analysis 57 Fi
Page 75 and 76: 4.6. Three-dimensional analysis 59
Page 83 and 84: 4.7. Summary and comparison with ot
Page 85: 4.7. Summary and comparison with ot
Page 89 and 90: Chapter 5 Ordered magnetic fields a
Page 91 and 92: 5.1. The Sample 75 35 49 00 ROSAT P
Page 93 and 94: 5.1. The Sample 77 5.1.1 0206+35 02
Page 95 and 96: 5.2. Analysis of RM and depolarizat
Page 97 and 98: 5.3. Rotation measure images 81 IMA
Page 99 and 100: 5.3. Rotation measure images 83 cor
Page 101 and 102: 5.4. Depolarization 85 Therefore, a
Page 103 and 104: 5.5. Rotation measure structure fun
Page 105 and 106: 5.6. Rotation-measure bands from co
Page 111 and 112: 5.7. Rotation-measure bands from a
Page 113 and 114: 5.7. Rotation-measure bands from a
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
Page 123 and 124: 5.9. Conclusions and outstanding qu
Page 125 and 126: Chapter 6 Faraday rotation in two e
Page 127 and 128: 6.2. Two-dimensional analysis: rota
Page 135 and 136: 6.3. Two-dimensional analysis: stru
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6.4. Preliminary conclusions 121 Ta
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6.4. Preliminary conclusions 123
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Summary and conclusions The goal of
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6.5. Summary 127 responsible for th
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6.6. General conclusions 129 radio
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6.7. Future prospects 131 and is th
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Appendix 133
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136 Data reduction and imaging of l
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144 BIBLIOGRAPHY Bîrzan, L., Raffe
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146 BIBLIOGRAPHY Ensslin, T.A. & Go
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148 BIBLIOGRAPHY Jeltema, T.E. & Pr
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150 BIBLIOGRAPHY Owen, F.N., 1989,
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152 BIBLIOGRAPHY 152
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