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32 3. Intergalactic magnetic fields resolution, is expected from beam depolarization (Eq. 3.5). The external depolarization is correlated with the amount of the RM gradient, while that occurring internally is expected to be correlated with the geometry of the source and the RM values, in the sense that regions of small RM correspond to low depolarization. Finally, bandwidth depolarization occurs when a significant rotation of the polarization angle of the radiation is produced across the finite bandwidth of the receiving system. The rotation of the polarization angle across the observing band is: ∆Ψ=−2RMλ 2∆ν ν (3.6) where∆ν is the bandwidth and ν is the central frequency. This will reduce the observed polarization level by a quantity sin(∆Ψ)/∆Ψ below that for monochromatic radiation. None of the observations used in this work are affected by significant bandwidth depolarization. 3.4 RM analysis Observations of Faraday rotation variations across extended radio galaxies, once corrected for the contribution from our Galaxy (Sec 3.2.3), allow us to derive information about the integral of the density-weighted line-of-sight field component. The hot (T≃10 7 − 10 8 K) plasma emits in the X-ray energy band via thermal bremsstrahlung (Sec. 2.2.1). When high quality X-ray data for a radio-source environment are available, it is possible to infer the gas density distribution and therefore to separate it from that of the magnetic field (Eq. 3.2), subject to some assumptions about the relation of field strength and density. Consequently, uncertainties on these field estimates come from the assumed magnetic field topology and gas density profile. Faraday rotation measure analysis has a number of advantages over other methods for estimating the magnetic field. RM studies can be carried out across radio galaxies hosted in less dense environments, allowing the study of magnetic fields in systems too sparse for radio halos to be detected. Moreover, the analysis of diffuse radio emission requires low-resolution and low-frequency observations, making it difficult to derive detailed information on the structure of the intergalactic magnetic field. These limitations do not affect RM maps, which can be produced even at sub-arcsec angular resolution at high frequencies (≥5 GHz) as long as the radio galaxies are bright enough in polarized intensity. A detailed study of intergalactic magnetic fields through the analysis of diffuse radio sources is also limited by the fact that these are affected by strong internal depolarization, intrinsically related to the nature of the diffuse synchrotron emission itself. In contrast, so far there is little evidence for internal depolarization in radio galaxies. 32
3.5. The magnetic field profile 33 Faraday rotation studies also provide information about the direction of the magnetic field, being the positive (negative) when the magnetic field direction points towards (away from) the observer. One potential problem is that there could be numerous field reversals along the line of sight, which would be averaged out. The minimum field strength can be derived by assuming a constant magnetic field along the line-of-sight. Such estimates generally give fields of about 1µG. Finally, through an extrapolation of Eq. 3.1 to zero wavelength, RM studies allow us to determine the intrinsic distribution of the projected magnetic field of radio galaxies, and its relation to the environment. 3.5 The magnetic field profile In order to estimate the magnetic field strength, the equipartition and IC analyses assume a constant magnetic field through the whole halo or relic volume. This assumption is an oversimplified picture as is clear from a simple energy-balance argument: if the field was uniform on Mpc scales, the magnetic pressure would exceed the thermal pressure in the outskirts of the clusters. Jaffe (1980) first suggested that the magnetic field distribution in a cluster might be similar to those of the thermal gas density and the volume density of massive galaxies and therefore would decline with the cluster radius. Observations, analytical models and MHD simulations of galaxy clusters all suggest that the magnetic field intensity should scale with the thermal gas density (e.g. Brunetti et al. 2001; Dolag 2006; Dolag, Bykov & Diaferio 2008; Guidetti et al. 2008). Govoni et al. (2001a) found a two-point spatial correlation between the X-ray and radio halo surface brightness in the galaxy clusters of their sample suggesting that the thermal and non-thermal components might have similar radial scalings. Another indication of a radial decrease of the magnetic field strength comes from the radial steepening observed in a few radio halos (Coma, A665, A2163, Giovannini et al. 1993; Feretti et al. 2004a) which are expected in the modeling of radio halos formation including such a radial decrease. Multiple works based on RM simulations (e.g. Murgia et al. 2004; Govoni et al. 2006; Guidetti et al. 2008; Laing et al. 2008; Kuchar & Enßlin 2009; Bonafede et al. 2010) have considered a radial field-strength variation of the form: 〈B 2 (r)〉 1/2 = B 0 [ ne (r) n 0 ] η (3.7) Here, B 0 is the rms magnetic field strength at the group/cluster centre and n e (r) is the thermal electron gas density. The results from the simulations are in favour ofηin the range 0.5-1. This functional form is consistent with other observations, analytical models and numerical simulations. In particular,η=2/3 corresponds to flux-freezing andη=1/2 to equipartition between thermal 33
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: 3.3. Depolarization 31 3.3 Depolari
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 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
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5.6. Rotation-measure bands from co
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Page 109 and 110:
Page 111 and 112:
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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Page 131 and 132:
Page 133 and 134:
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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