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62 4. The magneto-ionic medium around 3C 449 0.5< ∼ η< ∼ 1 in other sources (Dolag 2006; Guidetti et al. 2008; Laing et al. 2008). The most likely explanation for the low value ofηinferred from the low-resolution image is that the electron density distribution is not well represented by aβ-model (which describes a spherical and smooth distribution) at large radii. In support of this idea, Fig. 4.1 shows that the morphology of the X-ray emission is not spherical at large radii, but quite irregular. Croston et al. (2003, 2008) pointed out that the quality of the fit of a singleβ-model to the X-ray surface brightness profile was poor in the outer regions, suggesting small-scale deviations in the gas distribution. The singleβ-model gave a better fit to the inner region of the X-ray surface brightness profile, where the polarized emission of 3C 449 can be observed at 1.25-arcsec resolution. The aim is to fit theσ RM profiles at both resolutions with the same distribution of n e (r)〈B(r) 2 〉 1/2 . In the rest of this subsection I assume that the density profile n e (r) is still represented by the singleβ-model, even though I have argued that it might not be appropriate in the outer regions of the hot gas distribution. Although the resulting estimates of field strength at large radii may be unreliable, the fit is still necessary for the calculation of the outer scale described in Sec. 4.6.3, which depends only on the combined spatial variation of density and field strength. The best-fitting model at 1.25-arcsec resolution, which is characterized by a more physically reliableη, gives a very bad fit to the low resolution profile at almost all distances from the core (Fig. 4.9a). Conversely, the model determined at 5.5-arcsec resolution gives a very poor fit to the sharp peak inσ RM observed within 20 kpc of the nucleus at 1.25-arcsec resolution, where the radio and X-ray data give the strongest constraints (Fig. 4.9b). I also verified that no single intermediate value ofηgives an adequate fit to theσ RM profiles at all distances from the nucleus. A better description of the observedσ RM profile is provided by the empirical function 〈B 2 (r)〉 1/2 = B 0 [ ne (r) n 0 ] ηint r≤r m = B 0 [ ne (r) n 0 ] ηout r>r m , (4.6) whereη int ,η out are the inner and outer scaling index of the magnetic field and r m is the break radius. I fixedη int =1.0 andη out =0.0, consistent with the initial results, in order to reproduce both the inner sharp peak and the outer flat decline of theσ RM observed at the two resolutions, keeping r m as a free parameter. I made three sets of three-dimensional simulations for values of the outer scaleΛ max = 205, 65 and 20 kpc. Anticipating the result of Sec. 4.6.3, I plotted the results only for Λ max = 65 kpc, but the derivedσ RM profiles are in any case almost independent of the value of the outer scale in this range. The new simulations were made only at a resolution of 5.5 arcsec, since 62
4.6. Three-dimensional analysis 63 (a) (b) Figure 4.8: (a) and (b): Distributions of the best-fitting values of B 0 andηfrom 35 sets of simulations, each covering ranges of 0.5 – 10µG in B 0 and 0 – 2 inη, at 5.5 and 1.25 arcsec respectively. The sizes of the circles are proportional toχ 2 for the fit and the blue crosses represent the means of the distributions weighted by 1/χ 2 . The plot shows the expected degeneracy between B 0 andη. (a) (b) Figure 4.9: (a): Observed and synthetic radial profiles for rms Faradayσ RM at 5.5 arcsec as functions of the projected distance from the radio source center. The outer scale isΛ max =205 kpc. The black points represent the data with vertical bars corresponding to the rms error of the RM fit. The magenta crosses represent the mean values from 35 simulated profiles and the vertical bars are the rms scatter in these profiles due to sampling. (b) as (a), but at 1.25 arcsec. the larger field of view at this resolution is essential to define the change in slope of the profile. In order to determine the best-fitting break radius, r m in Eq. 4.6, I produced 35 sets of synthetic RM images for a grid of values of B 0 and r m for each outer scale, noting the pair of values which gave the minimum unweightedχ 2 for theσ RM profile for each set of simulations. These values are plotted in Fig. 4.10, which shows that there is a degeneracy between the break radius r m and B 0 . As with the similar degeneracy between B 0 andηnoted earlier, there is a clear minimum in χ 2 , and I therefore adopted the mean values of B 0 and r m weighted by 1/χ 2 as the best estimates of the magnetic-field parameters. 63
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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
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 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 77: 4.6. Three-dimensional analysis 61
Page 81 and 82: 4.6. Three-dimensional analysis 65
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
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
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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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