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18 2. The X-ray environment of radio galaxies MS0735.6 7421 with two large cavities, each roughly 20 kpc in diameter (McNamara et al. 2005). Other spectacular examples of cavities associated with cluster sources are Hydra A (McNamara et al. 2000), Centaurus A (Fabian et al. 2000) and Cygnus A (Carilli et al. 1994). Cavities are observed also in group environments of FR I sources (e.g. Croston et al. 2008; Giacintucci et al. 2011; Gitti et al. 2010). The cavities observed so far have an average radius of 10 kpc (e.g. Bîrzan et al. 2004), but there are examples with radii up to 100 kpc (Hydra A, Nulsen et al. 2005a). The absence of soft X-ray emission from cavities shows that they cannot contain much thermal plasma, unless it is much hotter than the surroundings (kT ≥ 10 keV). One possibility is that cavities are filled entirely with synchrotron-emitting plasma associated with radio lobes (Nulsen et al. 2002; Bîrzan et al. 2008 and reference therein), but the inference of an apparent pressure deficit in the lobes of FR I radio galaxies (Sec. 1.3.5) suggests that there may also be a significant amount of heated and entrained thermal plasma. The energy required to inflate a cavity E cav adiabatically can be estimated roughly using only X-ray observations. For cavities containing only relativistic mono-atomic gas, E cav = 4PV, where P is the pressure internal to the lobe and V is the volume of gas displaced by the radio lobe. A power-law relation is found between E cav and the radio-source luminosity. However, this relation shows a large scatter (Bîrzan et al. 2004, 2008; Cavagnolo et al. 2010). E cav is a lower limit to the energy supplied by the radio source, some of which may be dissipated (e.g. in shocks) or used to inflate further undetected cavities (e.g. McNamara & Nulsen 2007). E cav estimates based only on enthalpy range from 10 55 up to 10 61 erg s −1 , reaching the highest values in rich clusters. The energy deposition rates are high enough to prevent gas cooling below 2 keV in several systems (e.g. Bîrzan et al. 2008). 2.3.2 Gas compression and heating by radio galaxies If radio lobes are expanding supersonically 3 , at least in the forward direction of the jets, then a bow shock is expected to form ahead of them (Fig. 2.3). The shock velocity is essentially the expansion velocity of the lobe. Shock waves are characterized by a discontinuous and very sharp change in the characteristics of the gas. Density and temperature jumps across the shock surface (Rankine-Hugoniot conditions) can be derived from conservation of mass, momentum and energy across the shock. In a perfect gas and for an adiabatic shock traveling normal to the gas flow the jump conditions for the densityρand temperature T (Landau & Lifshitz 1987) are: ρ 2 ρ 1 = γ+1 γ−1+ 2 M 2 (2.4) 3 with respect to the sound speed of the X-ray emitting diffuse gas. 18
2.3. Radio source – environment interactions 19 Bow Shock Rlobe 1 2 3 4 Rshell Radio Lobe ISM Shell Figure 2.3: Schematic diagram of the regions around a supersonically expanding lobe in the ISM. Region 1 is the radio lobe, region 2 the observed X-ray enhancement region, region 3 is a physically thin layer where the Rankine-Hugoniot shock conditions are met, and region 4 is the ambient ISM. The figure is taken from Kraft et al. (2003). ρ 1 T 2 = 2γM2 −γ+1 (2.5) T 1 γ+1 ρ 2 where the subscripts 1 and 2 stand for the unshocked and shocked gas, andMis the Mach number of the shock wave.M is defined as the ratio between the shock velocity v and the sound speed in the un-shocked gas:M=v/c 1 . In the limit of a very strong shock (M≫1), the two ratios become: ρ 2 = γ+1 ρ 1 γ−1 (2.6) T 2 M 2 = 2γ(γ− 1) T 1 (2γ+ 1) 2. (2.7) These show that for a very supersonic lobe expansion, T can be arbitrarily large, whereas the density jump attains a finite maximum value, which is 4 for a thermal mono-atomic plasma (a reasonable approximation for the hot IGM). The gas compression and heating take place over the mean free path of the gas and hence the shock front is expected to be narrow. The presence of shocks surrounding radio lobes can be confirmed using deep X-ray observations by extracting surface brightness and spectra profiles. These allow the detection of density and temperature jumps, respectively, (Eqs.2.3 and 2.2) and from these the shock Mach numberMcan be estimated. So far the two known cases of strong shocks associated with expanding radio-galaxy lobes are found in the FR I sources Cen A and NGC 3801. In these sources the shocked hot gas is 10 and 4-5 times hotter than the surroundings, corresponding respectively 19
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: 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 83 and 84: 4.7. Summary and comparison with ot
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4.7. Summary and comparison with ot
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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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