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4 1. Physics of radio galaxies intrinsic degree of polarization has the value (Longair 1994): P Int = δ+1 δ+ 7 , (1.5) 3 and the electric vector is perpendicular to the projection of the magnetic field onto the plane of the sky. For typical values of the index of the energy spectrumδ = 2.5, the intrinsic polarization degree in an uniform field is expected to be≈70%, which represents the maximum allowed value. they exceed 0.3-0.4. Degrees of polarization≥ 0.1 are often observed at 1.4 GHz; less commonly A reduction of the expected degree of polarization might stem from an intrinsically complex magnetic field structure within the source and/or depolarization effects, as discussed in Secs. 3.2.1 and 3.3. If the magnetic field can be expressed as the superposition of two components, one uniform B u , the other isotropic and random B r , the observed degree of polarization is approximately given by (Burn 1966): B 2 u P Obs = P Int B 2 u+B 2 . (1.6) r which gives the ratio of the energy in the uniform field over the energy in the total field, and is an indicator of the field uniformity and structure. However, random magnetic fields are likely to be anisotropic, in which case Eq. 1.6 does not hold. A mathematically convenient way to describe the linear polarization state is given by the Stokes parameters I, Q and U (Stokes, 1852). The polarized intensity and the polarization angle of linearly polarized radiation can be described by: P λ = (Q 2 λ + U2 λ )1/2 (1.7) and Ψ λ = 1 2 arctan ( Uλ Q λ ) , (1.8) Images of polarized intensity P, degree of polarization P/I and position angleΨ(and in turn magnetic field) can be derived across radio galaxies from the I, Q, and U images through radio observations in full polarization mode. Once corrected for the Faraday rotation (Sec. 3.2) the projected magnetic field in the plane of the sky appears to be tangential to the edges of the lobes in both low- and high-power radio sources. The field orientation in the jets differs between the two classes. Low-power jets usually show magnetic field parallel to the jet axis close to the core with a transition to perpendicular field as the jet expands. In contrast, in powerful sources the magnetic field is usually parallel to the jet axis for the whole length of the jets. 4
1.2. Non-thermal emission mechanisms of active galaxies 5 Therefore, the measurement of synchrotron emission from radio galaxies provides information about the index of the energy distribution of particles and the strength of magnetic fields inside the source, while the degree of polarization is an important indicator of the field uniformity and structure. The high degrees of linear polarization observed from radio-galaxy jets and lobes make them ideal probes of the foreground magnetised medium (Sec. 3.2). 1.2.3 Inverse Compton emission Relativistic electrons in a radiation field can scatter low-energy photons to high energy through the inverse-Compton (IC) effect. The reason for the adjective “inverse” is that the electrons lose energy rather than the photons as in the usual Compton scattering. IC scattering increases the frequency of the scattered photonsν ph by a factor 4 3 γ2 , whereγis the Lorentz factor of the relativistic electrons (e.g. Rybicki & Lightman 1986). The low-energy scattered photons are often dominated by the ubiquitous 3K cosmic microwave background (CMB). In the presence of relativistic particles withγ∼10 3−4 , CMB photons are scattered from the original frequency around 10 11 Hz to about 10 17−18 Hz, corresponding to the X-ray andγ-ray domains (0.8- 20 keV). Since the power radiated via the IC process by an electron has the same functional dependence on the electron energy as in Eq. 1.1, if the synchrotron and IC emission originate from the same relativistic electron population their fluxes are related. For the electron energy distribution of Eq. 1.3, the two spectra share the same spectral indexα. The spectral index relates to the photon index of the IC emission asΓ X =α+1. Given that the synchrotron emissivity is proportional to the magnetic energy density U B , while the IC emissivity is proportional to the energy density in the photon field U ph , it follows that: S syn S IC ∝ U B U ph , (1.9) where S syn and S IC are the synchrotron and IC fluxes, respectively. From the ratio between the IC and synchrotron fluxes, in principle one can derive an estimate of the total magnetic field, averaged over the emitting volume. In terms of observational parameters this is: B[µG] 1+α S syn (ν r )[Jy] = h(α) S IC(E1 −E 2 )[ergs −1 cm −2 ] (1+z)3+α (0.0545ν r [MHz]) α × (1.10) × (E 2 [keV] 1−α − E 1 [keV] 1−α , where S syn(νr ) is the synchrotron flux at the radio frequencyν r and the flux S IC(E1 −E 2 ) is integrated over the energy interval E 1 − E 2 . 5
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: 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 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
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4.5. Two dimensional analysis 55 sm
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4.5. Two dimensional analysis 57 Fi
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4.6. Three-dimensional analysis 59
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4.7. Summary and comparison with ot
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Chapter 5 Ordered magnetic fields a
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5.1. The Sample 75 35 49 00 ROSAT P
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5.1. The Sample 77 5.1.1 0206+35 02
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5.2. Analysis of RM and depolarizat
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5.3. Rotation measure images 81 IMA
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5.3. Rotation measure images 83 cor
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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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