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34 3. Intergalactic magnetic fields and magnetic energy. Dolag et al. (2001, 2006) foundη≈1 from the correlation between the observed rms RM and X-ray surface brightness in galaxy groups and clusters and showed that this is consistent with the results of MHD simulations. 3.6 Tangled magnetic field Most of the published RM images of radio galaxies located in different environments show random structures with patches of different size, ranging from a few kpc up to tens of kpc (Fig. 3.5). From these RM distributions it is clear that the magnetic fields are not regularly ordered on cluster (Mpc) scales, but highly turbulent. It is indeed likely that anisotropies in the magnetic field would reflect themselves in the RM images, since the projection connecting field and RM conserves anisotropy. Faraday rotation by tangled intergalactic magnetic fields was considered in several early theoretical papers (e.g. Lawler & Dennison 1982; Tribble 1991; Felten 1996). The simplest RM modeling invokes a Faraday screen in which the magnetic field fluctuates on a single scaleΛ c . The screen can be thought as made of cells of constant size and magnetic field strength, but random magnetic field direction. The RM from such a screen will be produced by a random walk along the line-of-sight. Because of the large number of cells, the RM distribution is expected to be described by a Gaussian function with zero mean and dispersionσ RM given by: ∫ σ 2 RM =〈RM2 〉=812 2 Λ c (n e B z ) 2 dz. (3.8) Considering a thermal density distribution which follows aβ-profile (Eq. 2.3), and an isotropic field (so that B= √ 3B z ), Eq. 3.8 can be integrated analytically and gives (Felten 1996) σ RM (r ⊥ )= KBn 0rc 1/2 Λ 1/2 √ c (1+ r ⊥ Γ(3β−0.5)Γ(3β) (3.9) rc ) (6β−1)/4 whereΛ c is the cell size, r ⊥ is the projected distance of from the cluster center,Γis the Gamma function, and K is a factor which depends on the location of the radio source along the line-of-sight (e.g. Carilli & Taylor 2002). The central field strength can be estimated by using Eq. 3.9:σ RM (r ⊥ ) can be measured from spatially resolved RM images and at a first level of approximationΛ c can be assumed to be equal to the coherence length, deduced by-eye, of the RM map. It must however borne in mind that the magnetic fields in this model are not divergence-free (Enßlin & Vogt 2003). This method has been applied to both statistical samples (Clarke 2004) and to single objects, e.g. Hydra A (Taylor & Perley 1993) 1993), A 119 (Feretti et al. 1999b), 3C 295 (Allen et al. 2001), A 514 (Govoni et al. 2001a), 3C 129 Taylor2001, A 400 and A 2634 (Eilek & Owen 2002). The magnetic field strengths deduced from these analyses are in the range 4-20µG, assumingΛ c 34
3.6. Tangled magnetic field 35 rad m −2 RAD/M/M rad m −2 -150 -100 -50 0 -100 -50 0 50 100 -15 36 00 100 kpc -15 38 00 -15 40 00 (a) (b) (c) Figure 3.5: RM images of radio galaxies with tails: PKS 2149-158 and PKS 2149-158b (a), 3C 31 (b), and 3C 75 (c). Figures respectively taken from: Guidetti et al. (2008), Laing et al. (2008), Eilek & Owen (2002). of about 10 kpc, with the highest values found for radio galaxies in cooling-core clusters. None of these magnetic fields are thought to be dynamically important, since they provide negligible pressure compared with that of the thermal component. Although RM images in general are not expected to show perfectly Gaussian distributions because of the partial sampling of large spatial scales, the Gaussian function is found to be a good representation for many RM distributions, supporting the scenario of a tangled and isotropic magnetic field component along the line-of-sight. However, in contrast with this scenario the majority of the RM distributions show non-zero means〈RM〉 if averaged over areas of size comparable with that of the radio source, even after removing the Galactic contribution. These 〈RM〉’s are thought to be due to large-scale magnetic field structure, whose fluctuations occur on scales larger than those producing the RM dispersion. Therefore, the magnetic field cannot be tangled only on a single scale, but it must have fluctuations over a wide range of spatial scales: small-scale components are necessary to produce the smallest structures observed in the RM images (Fig. 3.5) and structures on larger scales are needed to account for the non-zero RM mean. For this reason, the investigation of the magnetic field power spectrum has been object of many recent papers. Several studies (Enßlin & Vogt 2003; Enßlin & Vogt 2005; Murgia et al. 2004; Govoni et al. 2006; Guidetti et al. 2008; Laing et al. 2008; Kuchar & Enßlin 2009) have shown that detailed RM images of radio galaxies can be used to infer not only the strength of the cluster magnetic field, but also its power spectrum. All of these studies agree that random RM structures can be accurately reproduced if the magnetic field is isotropic and randomly variable with fluctuations on a wide range of spatial scales. 35
Page 1: Alma Mater Studiorum Università de
Page 5: To Hypatia from Alexandria in Egypt
Page 9 and 10: Contents Abstract i 1 Physics of ra
Page 11 and 12: 4.6.3 The outer scale of the magnet
Page 13 and 14: Abstract The existence of diffuse m
Page 15 and 16: 2. Two-dimensional Monte Carlo simu
Page 17 and 18: Chapter 1 Physics of radio galaxies
Page 19 and 20: 1.2. Non-thermal emission mechanism
Page 21 and 22: 1.2. Non-thermal emission mechanism
Page 23 and 24: 1.3. Radio galaxies 7 FR II sources
Page 25 and 26: 1.3. Radio galaxies 9 (a) (b) Figur
Page 27 and 28: 1.3. Radio galaxies 11 pressure, th
Page 29 and 30: Chapter 2 The X-ray environment of
Page 31 and 32: 2.2. The thermal component 15 Figur
Page 33 and 34: 2.3. Radio source - environment int
Page 35 and 36: 2.3. Radio source - environment int
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: 3.5. The magnetic field profile 33
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 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
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5.5. Rotation measure structure fun
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5.6. Rotation-measure bands from co
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5.7. Rotation-measure bands from a
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5.7. Rotation-measure bands from a
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5.8. Discussion 99 5.8 Discussion 5
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5.8. Discussion 101 line−of−sig
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5.8. Discussion 103 flat slopes. I
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5.9. Conclusions and outstanding qu
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5.9. Conclusions and outstanding qu
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Chapter 6 Faraday rotation in two e
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6.2. Two-dimensional analysis: rota
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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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