Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf

More documents

Recommendations

Info

56 4. The magneto-ionic medium around 3C 449 the structure function, including convolution (Laing et al. 2008), and therefore to avoid numerical integration. The fits were quite good, but systematically gave slightly too much power on small spatial scales and over-predicted the depolarization. I therefore fit a cut-off power law (CPL) power spectrum of the form Ĉ( f ⊥ ) = 0 f ⊥ < f min = C 0 f −q ⊥ f ⊥ ≤ f max = 0 f ⊥ > f max . (4.3) Initially, I consider values of f min sufficiently small that their effects on the structure functions over the observed range of separations are negligible. The free parameters of the fit in this case are the slope, q, the cut-off spatial frequency f max and the normalization of the power spectrum, C 0 . In Table 4.2, I give the best-fitting parameters for CPL fits to all of the individual regions. The fitted model structure functions are plotted in Fig. 4.7(a)–(f), together with error bars derived from multiple realizations of the power spectrum as in Laing et al. (2008). In order to constrain RM structure on spatial scales below the beam-width, I estimated the depolarization expected from the best power spectrum for each of the regions with 1.25-arcsec RM images, following the approach of Laing et al. (2008). To do this, multiple realizations of RM images have been made on an 8192 2 grid with fine spatial sampling. I then derived the Q and U images at our observing frequencies, convolved to the appropriate resolution and compared the predicted and observed mean degrees of polarization. These values are given in Table 4.4. The uncertainties in the expected< k > in Table 4.4 represent statistical errors determined from multiple realizations of RM images with the same set of power spectrum parameters. The predicted and observed values are in excellent agreement. A constant value of f max = 1.67 arcsec −1 predicts very similar values, also listed in Table 4.4. I have not compared the depolarization data at 5.5-arcsec resolution in the spurs because of limited coverage of large spatial scales in the I images (Sec. 4.2), which is likely to introduce systematic errors at 4.6 and 5.0 GHz. I performed a joint fit of the CPL power spectra, minimizing theχ 2 summed over all six subregions, giving equal weight to each and allowing the normalizations to vary independently. In this case the free parameters of the fit are the six normalizations (one for each sub-region), the slope, and the maximum spatial frequency. The joint best-fitting single power-law power spectrum has q=2.68. A single power law slope does not give a good fit to all of the regions simultaneously, however. It is clear from Fig. 4.7 and Table 4.2 that there is a flattening in the slope of the observed structure 56
4.5. Two dimensional analysis 57 Figure 4.7: (a)-(f): Plots of the RM structure functions for the sub-regions showed in Fig.4.2. The horizontal bars represent the bin widths and the crosses the centroids for data included in the bins. The red lines are the predictions for the CPL power spectra described in the text, including the effects of the convolving beam. The vertical error bars are the rms variations for the structure functions derived using a CPL power spectrum with the quoted value of q on the observed grid of points for each sub-region. (g)-(l): as (a)-(f), but using a BPL power spectra with fixed slopes and break frequency, but variable normalization. functions on the largest scales (which are sampled primarily by the spurs). In order to fit all of the data accurately with a single functional form for the power spectrum, I adopt a broken power law form (BPL) for the RM power spectrum: Ĉ( f ⊥ ) = 0 f ⊥ < f min = D 0 f (q l−q h ) b f −q l ⊥ = D 0 f −q h ⊥ f b ≥ f ⊥ f max ≥ f ⊥ > f b = 0 f ⊥ > f max . (4.4) I performed a BPL joint fit in the same way as for the CPL power spectra. In this case 57
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 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: 4.5. Two dimensional analysis 55 sm
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
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
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
6.3. Two-dimensional analysis: stru
Page 137 and 138:
6.4. Preliminary conclusions 121 Ta
Page 139 and 140:
6.4. Preliminary conclusions 123
Page 141 and 142:
Summary and conclusions The goal of
Page 143 and 144:
6.5. Summary 127 responsible for th
Page 145 and 146:
6.6. General conclusions 129 radio
Page 147 and 148:
6.7. Future prospects 131 and is th
Page 149:
Appendix 133
Page 152 and 153:
136 Data reduction and imaging of l
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
144 BIBLIOGRAPHY Bîrzan, L., Raffe
Page 162 and 163:
146 BIBLIOGRAPHY Ensslin, T.A. & Go
Page 164 and 165:
148 BIBLIOGRAPHY Jeltema, T.E. & Pr
Page 166 and 167:
150 BIBLIOGRAPHY Owen, F.N., 1989,
Page 168 and 169:
152 BIBLIOGRAPHY 152
show all

Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf

Create successful ePaper yourself

Delete template?

Save as template?