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100 5. Ordered magnetic fields around radio galaxies Cygnus A Cygnus A is a source in which we might expect to observed RM bands, by analogy with the sources discussed in the present work: it has wide and round lobes and Chandra X-ray data have shown the presence of shock-heated gas and cavities (Wilson, Smith & Young 2006). RM bands, roughly perpendicular to the source axis, are indeed seen in both lobes (Dreher et al. 1987; Carilli & Taylor 2002), but interpretation is complicated by the larger random RM fluctuations and the strong depolarization in the eastern lobe. A semi-circular RM feature around one of the hot-spots in the western lobe has been attributed to compression by the bow-shock (Carilli, Perley & Dreher 1988). Hydra A Carilli & Taylor (2002) have claimed evidence for RM bands in the northern lobe of Hydra A. The Chandra image (McNamara et al. 2000) shows a clear cavity with sharp edges coincident with the radio lobes and an absence of shock-heated gas, just as in the sources analysed in this work. Despite the classification as a tailed source, it may well be that there is significant compression of the IGM. Note, however, that the RM image is not well sampled close to the nucleus. 3C 465 The RM image of the tailed source 3C 465 published by Eilek & Owen (2002) shows some evidence for bands, but the colour scale was deliberately chosen to highlight the difference between positive and negative values, thus making it difficult to see the large gradients in RM expected at band edges. The original RM image (Eilek, private communication) suggests that the band in the western tail of 3C 465 is similar to those I have identified. It is plausible that magnetic-field draping happens in wide-angle tail sources like 3C 465 as a result of bulk motion of the IGM within the cluster potential well, as required to bend the tails. It will be interesting to search for RM bands in other sources of this type and to find out whether there is any relation between the iso-RM contours and the flow direction of the IGM. 5.8.3 Foreground isotropic field fluctuations The coexistence in the RM images of the sources here analysed of anisotropic patterns with areas of isotropic fluctuations suggests that the Faraday-rotating medium has at least two components: one local to the source, where its motion significantly affects the surrounding medium, draping the field, and the other from material on group or cluster scales which has not felt the effects 100
5.8. Discussion 101 line−of−sight > > Figure 5.14: Geometry of a twodimensional toroidal magnetic field as described in Section 5.7.3, seen in the plane normal to its axis. The cross represents the radio core position. of the source. This raises the possibility that turbulence in the foreground Faraday rotating medium might “wash out” RM bands, thereby making them impossible to detect. The isotropic RM fluctuations observed across the sources are all described by quite flat power spectra with low amplitude (Table 5.5). The random small-scale structure of the field along the line-of-sight essentially averages out, and there is very little power on scales comparable with the bands. If, on the other hand, the isotropic field had a steeper power spectrum with significant power on scales similar to the bands, then its contribution might become dominant. I first produced synthetic RM images for 0206+35 including a random component derived from the best-fitting power spectrum (Table 5.5) in order to check that the bands remained visible. I assumed a minimum scale of 2 kpc from the depolarization analysis for 0206+35 (Sec. 5.4), and a maximum scale ofΛ max = 40 kpc, consistent with the continuing rise of the RM structure function at the largest sampled separations, which requiresΛ max > ∼ 30 arcsec (≃20 kpc). The final synthetic RM is given by: ∫ RM syn = RM drap + RM icm = n ′ e B′ z dz+ ∫ n e B z dz (5.6) where RM drap and RM icm are the RM due to the draped and isotropic fields, respectively. The terms n ′ e and B ′ z are respectively the density and field component along the line-of-sight in the draped region. The integration limits of the term RM drap were defined by the surface of the lobe and the draped region, while that of the term RM icm starts at the surface of the draped region and extends to 3 times the core radius of the X-ray gas (Table 5.2). For the electron gas density n e outside the draped region I assumed the beta-model profile of 0206+35 (Table 5.2) and for the field strength a radial variation of the form (Laing et al. 2008, and references therein) 〈B 2 (r)〉 1/2 = B 0 [ ne (r) n 0 ] η (5.7) where B 0 is the rms magnetic field strength at the group centre. I took a draped magnetic field strength of 1.8µG, in order to match the amplitudes for the RM bands in both lobes of 0206+35, 101
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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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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 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
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Page 115: 5.8. Discussion 99 5.8 Discussion 5
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
Page 137 and 138: 6.4. Preliminary conclusions 121 Ta
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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
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150 BIBLIOGRAPHY Owen, F.N., 1989,
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152 BIBLIOGRAPHY 152
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