Investigations of Faraday Rotation Maps of Extended Radio Sources ...

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38 CHAPTER 2. IS THE RM SOURCE-INTRINSIC OR NOT? source FWHM beam A V A + V PKS 1246-410 4” 0.07 − 0.17 − 0.10 Cygnus A 2” 0.07 − 0.07 0.00 Hydra A 1” 0.05 − 0.03 0.02 3C465 9.5” 0.13 0.03 0.16 ϕ east 0 -RM west − 0.02 − 0.02 − 0.21 ϕ west 0 -RM east 0.10 − 0.30 − 0.20 independent 0.06 0.05 0.11 co-aligned 0.89 − 0.03 0.86 Table 2.1: The values for the statistics A and V obtained for various data sets. In the upper part of the table the resulting values for the statistics of the observational data are presented. For this data the FWHM is given to which the maps were smoothed. In the middle part, the values obtained for the exchanged subregions of PKS 1246-410 are given which can serve as an estimate of the statistical uncertainty. For comparison the lower part summarises the values obtained for a realisation of independent and co-aligned RM and ϕ 0 maps. Applying the statistics to the data at hand (see the end of Sect. 2.3) yields for PKS1246-410 A = 0.07, V = −0.17, A + V = −0.10 (after smoothing to a 4 ′′ FWHM beam), for Cygnus A A = 0.07, V = −0.07, A + V = 0.00 (FWHM = 2 ′′ ), for Hydra A A = 0.05, V = −0.03, A + V = 0.02 (FWHM = 1 ′′ ), and for 3C465 A = 0.13, V = 0.03, A + V = 0.16 (FWHM = 9.5 ′′ ). Only 3C465 shows a marginal signature of source intrinsic co-alignment. However, its map size in terms of resolution elements is significantly smaller than e.g. the maps of Hydra A and Cygnus A, therefore a larger statistical variance of the alignment measurement is plausible. In contrast to the observed maps, the synthetic maps are free of correlated noise. This is clearly revealed by the statistics, which give for the independent pair of maps A = 0.06, V = 0.05, A + V = 0.11, and for the co-aligned pair of maps A = 0.89, V = −0.03, A + V = 0.86. This illustrates the ability of the statistics introduced to discriminate between spurious and astrophysical signals. In order to have an estimate of the statistical uncertainties, the approach was also applied to the swapped RM map of PKS 1246-410. This yields for the ϕ east 0 -RM west comparison A = −0.02, V = −0.19, A + V = −0.21, and for the ϕ west 0 -RM east comparison A = 0.10, V = −0.30, A + V = −0.20. This indicates that the statistical error is of the order δA ∼ 0.1 and δV ∼ 0.2 for this dataset, taking into account that the swapped maps have less corresponding pixel pairs compared to the original pair of maps. Note that an inspection by eye reveals several sharp steps in the original RM map of PKS 1246-410, which are on length-scales below the beam size and therefore very likely map making artefacts (see Sect. 2.4). Thus, it is uncertain if this dataset has sufficiently high signal-to-noise to make it suitable for a ϕ 0 -RM alignment analysis. In summary it can be concluded that no evidence for a significant large-scale coalignment of ϕ 0 and RM maps of polarised radio sources in galaxy clusters was found.
2.6. CONCLUSIONS 39 Independent evidence for the validity of the assumption of an external Faraday screen can be found in the detection of the Laing-Garrington effect which was already mentioned in Sect. 1.3.2. It manifests itself by an asymmetric Faraday depolarisation of double radio lobes located within galaxy clusters (Garrington et al. 1988; Laing 1988). This asymmetry is caused by different path lengths for radio emission through the Faraday active medium between source and observer as suggested by Garrington & Conway (1991). However, this effect could also be explained by an asymmetric mixing layer being thin close to the head side of a FR II while getting thicker on the back-flow side of it. However, this explanation fails to give a convincing explanation for the large RM and depolarisation asymmetry observed for the FR I source Hydra A (Taylor & Perley 1993). Further independent evidence for cluster wide magnetic fields is provided by the recent statistical RM investigation of point sources performed by Clarke et al. (2001) mentioned in Sect. 1.3.2. As described, it revealed larger RM values for sources observed through the intra-cluster gas in comparison to a control sample of sources where no intra-cluster gas was located between source and observer. This suggests that the enhancement of the RM towards the cluster centre results most probably from the magnetised cluster gas. 2.6 Conclusions It was investigated if there is evidence for co-aligned structures in RM and ϕ 0 maps of extended radio sources in galaxy clusters as claimed by Rudnick & Blundell (2003) in order to argue for source-local RM generating magnetic fields. First, it was demonstrated that the experiment performed by Rudnick & Blundell was poorly designed for testing the correlation between ϕ 0 and RM in PKS 1246- 410. The lack of phase coherence in their simulated data resulted in less clustering in the simulated ϕ 0 -RM scatter plots compared to the observational scatter plots. Using independent, patchy distributions of ϕ 0 and RM it was shown that the correlations due to the mutual overlap of the RM and ϕ 0 patches produce horizontal and vertical chains of clusters as seen in the PKS 1246-410 data, whereas co-aligned ϕ 0 and RM patches produce diagonal stripes. The observed clustering therefore favours independent ϕ 0 and RM maps as expected from foreground intra-cluster magnetic fields. Second, a novel gradient alignment statistic A was introduced. This statistic reveals ϕ 0 and RM correlations regardless of whether they are source intrinsic or due to artefacts in the observation or the RM map making process. Applying this statistic to a number of radio galaxies (PKS 1246-410, Cygnus A, Hydra A, and 3C465) does not reveal any significant large-scale co-alignment of ϕ 0 and RM maps. Significant smallscale co-alignment is found in all observed map pairs, but they can be fully identified with map making artefacts by another new suitable statistical test, the gradient vector product statistic V . Thus, two new tools were introduced in order to analyse data of Faraday rotation studies of extended radio sources. They are powerful in revealing and discriminating observational or map making artefacts (by V ), and source-intrinsic ϕ 0 -RM correlations (by A + V ), both are indicators of potential problems for RM based intra-cluster magnetic field estimates. Future, sensitive searches for potential, weak source-intrinsic ϕ 0 -RM correlations
Page 1 and 2: Investigations of Faraday Rotation
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88 CHAPTER 4. PACMAN - A NEW RM MAP
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118 CONCLUSIONS tually statisticall
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120 BIBLIOGRAPHY Conway, R. G. & St
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122 BIBLIOGRAPHY Ikebe, Y., Makishi
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124 BIBLIOGRAPHY Simard-Normandin,
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126 ACKNOWLEDGEMENTS in his long em
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Publications Journals 1. A Bayesian
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