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Cosmic Ray Propagation Through Turbulent Magnetic Fields

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Cosmic Ray Propagation Through Turbulent Magnetic Fields Cosmic Ray Propagation Through Turbulent Magnetic Fields Ehza Switalska Submitted in fuffilment of the requirements for the degree of Master of Scíence School of Chemistry and Physics (Faculty of Sciences) The University of Adelaide September 2006 I)ecleration I certify that this thesis does not incorporate, without acknowledgement, any material previously submitted for any degree, or diploma in any university and that to the best of my knowledge and beliet it does not contain any material previously published, or written by another person, except where due reference is made in the text. I give consent to this copy of my thesis, when deposited in the University Library, being made available for loan and photocopylng. Eliza Switalska 07110106 Acknowledgements I would like to thank my supervisor Prof. Roger Clay for his guidance and never ending patience and support. Special thanks to Melanie Johnston-Hollitt for her advice and use of astronomical data. Many, many thanks to Mariusz and to my family and friends (especially Juliet) for their continuous support and encouregement. J CONTENTS Abstract 8 Preface 9 CHAPTER 1 Cosmic Rays t2 1.1 Introduction 12 1.2 Overview of Cosmic Rays 13 1.2.1 Cosmic Ray Arrival Directions t6 r.2.2 GZK Cut-off t6 1.2.3 High-Energy Cosmic Ray Propagation t7 1.2.4 Cosmic Ray Acceleration t9 CHAPTER 2 Magnetic Fields 2t 2.1 The Galactic and Extragalactic Magnetic Fields 2t 2.2 The origin of the Galactic Magnetic Field 2t 2.3 Methods in Determining Magnetic Field Strengths 23 2.3.1 The Zeeman Effect 23 2.3.2 Optical Dust Absorption and Polarization of Sub-mm and mm Emission 24 2.3.3 Synchrotron Radiation 25 2.3.4 Radio Faraday Rotation 28 2.3.5 Factors in the I)etermination of the Rotation Measure of Galaxies 32 2.3.6 Faraday Depolarization 34 2.3.7 Energy Equipartition between Magnetic Fields and Cosmic Rays 35 2.5 Magnetic Field Turbulence 36 2.5.1 Kolmogorov Scale Turbulence 37 2.6 Magnetic Fields in Galaxy Clusters 39 2.6.1 The Local Group of Galaxies 4l 2.6.2 The Virgo Cluster and Nearby Superclusters 43 2.6.3 Radio and X-Ray Methods for Probing Cluster Magnetic Fields 46 CHAPTER 3 RADIO ASTRONOMY 49 3.1 Introduction 49 3.2 Observational Techniques and Instruments Used 49 4 3.2.1 The Very large Array (VLA) 51 3.2.2 The Australia Telescope Compact Array 53 3.3 Radio Synthesis Imaging 54 CHAPTER 4 Estimation of the Scale of the Turbulent Magnetic Field in Galaxy Clusters 55 4.1 Introduction 55 4.2 Galaxy Clusters and the 43667 Cluster 56 4.2.1 Radio Interferometer - Amplitude vs Baseline Length 57 4.2.2 Amplitude vs Baseline ptot of 43667 58 4.3 Procedure 60 4.3.1 Modified A3ó67 Ptot 60 4.3.2 Analysis of the Modified Spectrum 6l 4.3.3 Results 6r CHAPTER 5 Modelling of Cosmic Ray Propagation in a Magnetic Field 64 5.1 Previous Studies in Propagation Simulations 64 5.2 Generation of Random Magnetic Fields 66 5.3 Simulation of a Turbulent Magnetic Field 68 CHAPTER 6 Processes Involved in Generating Simulated Turbulent Magnetic Fields and a Study of the Effects of Field Scale Variations 70 6.1 Introduction 70 6.2 Random Magnetic Field Component 7l 6.3 Results of Scale Length Variation 7l 6.3.1 Properties of the Magnetic Field Model 72 6.4 Effects of Clumpiness on the Magnetic Field 83 6.4.1 Small-Scale Clumpiness Results 83 6.4.2 Large-Scale Clumpiness Results 86 6.4.3 Conclusion 88 CHAPTER 7 Cosmic Ray Propagation Through Turbulent Magnetic Fields 90 7.1 Computer Simulation of Propagation 90 5 7.2 Procedure 90 7.3 Results 92 7.3.1 Results for Propagation through Large Scale Turbulence 92 7.3.2 Results for Propagation through Small Scale Turbulence 93 7.3.3 Comments on the Results 94 CHAPTER 8 Conclusion 96 References 99 Bibliography 101 APPENDIX A r02 Diffusion 102 APPENDIX B 105 Programs 105 6 List of Figures and Tables Page Figure 1(a) Cosmic ray spectrum A 14 Figure 1(b) Cosmic ray spectrum B 15 Figure 2(a) Faraday rotation diagram Figure 2(b) Plot of integratedpolanzation and position angle JJ Figure 2(c) Rotation measure sky map 34 Figure 2(d) Illustration showing the Universe within 500,000 l.y. 42 Figure 2(e) Illustration showing the Universe within 5 million l.y. 43 Figure 2(f) Illustration showing the Universe within 100 million 1.y. 44 Figure 2(g) Illustration showing the Universe within I billion l.y 45 Figure 3(a) Aerial view of the VLA 52 Figure 3(b) The Australia Telescope Compact Array (ATCA) 53 Figure 4(a) Amplitude vs baseline plot (43667) 59 Figure a@) Modified amplitude vs baseline plot (A3667) 60 Figure 4(c) Plots representing the logarithms of amplitude vs spacing 62 Figure 6(a)-(c) B* distribution vs spacing plot for various turbulence sclae 74-76 Figure 6(d)-(h) Histogram plots for the various iteration values 79-8r Figure 6(i)-(l) Original and clumpy field histograms in small scales 84-85 Figure 6(m)-(o) Plots for clumpy field histograms in large scales 87-88 Figure 7(a) Plot of the cosmic ray energy vs the number of cycles in large scales 93 Table 6(a) Integrated field variations through the various iterations 77 Table 6(b) The mean and standard deviation values obtained for iterations 82 Table 7(a) Results for Large Scale Turbulence 92 Table 7(b) Results for Small Scale Turbulence 94 7 Abstract This study begins with an overview of cosmic ray literature in relation to the origin and propagation of high-energy particles in extragalactic space. It follows with a review of recent methods used in the observation and measurement of extragalactic magnetic fields and describe the radio astronomy techniques used. The later chapters describe computer simulations, which were used for producing turbulent magnetic field models and then follow on to show how these can be used to estimate the probable turbulent scales of such fields. These models are then applied to data from an actual galaxy cluster, where the turbulence spectrum of the Abell galaxy cluster (using data from a recent observational study of A3667) is estimated. The final part of this thesis is concerned with the study of cosmic ray propagation within such turbulent magnetic fields. This is achieved by altering the turbulent scale-lengths and observing the behaviour of cosmic rays within, both large ans small-scale magnetic fields, thereby giving an indication as to the actual paths they may follow in space and consequently providing some clues as to their origins. 8 Preface Cosmic rays are high energy charged particles which propagate from their sources to us through the turbulent magnetic fields which permeate the Universe. Over the years, as far back as the 1930s, models have been proposed for cosmic ray propagation in both the galactic and extragalactic environments. The one underlying requirement in all these models is the understanding of the strength and structure of the galactic and extragalactic magnetic fields. This is because cosmic rays are highly energetic charged particles and their propagation is therefore affected while travelling within these fields. Honda (1987) has described a method for simulating a turbulent magnetic field such that it contains a Kolmogorov spectrum of scales. The effect and extent of these interactions is examined in this study of propagation in such fields. Cosmic rays, being highly energetic charged particles, can be greatly affected by cosmic magnetic fields. Therefore a greater understanding of the properties of such fields is currently needed to provide a more accurate glimpse into the propagation of cosmic rays. There are many ongoing studies concerned with the estimation and measurement of extragalactic magnetic fields, but many still disagree and thus make it more difficult to interpret cosmic ray propagation correctly. The magnetic fields themselves are turbulent with irregularities of various scales. This turbulence is of major concern in this particular study. Propagation simulations, which follow high energy particles through the various turbulence scales, will provide a better understanding of the affects these irregularities may have on the paths of the cosmic rays and are therefore discussed and analyzed in this work. Sophisticated propagation studies date back to the late 50s and 60s, and two of the major studies, which were conducted during these years are relevant here. These two particular studies looked at propagation in two extremes. The first, carried out by Gleeson and Axford (1967), studied the propagation of cosmic rays with a gyroradius which was large compared to the scale of the irregularities. This study involved the "scattering centers" approach. The other study was conducted by Jokipii and Parker (1969), and considered propagation where the gyroradius was small compared to the magnetic irregularity scales. Some years later, Honda (1987), extended propagation studies to the case where the gyroradius and the scale of the irregularity of the magnetic field were comparable. In this more complicated case, a numerical approach had to be adopted instead of the previous analytical ones applied in the earlier studies. Therefore, as in this later study, a numerical 9 computer simulation was used to generate an irregular magnetic field model, before following particle propagation through the treld. For any of these approaches to provide useable results, as much information as possible is needed on the real astrophysical magnetic fields. There are many methods which can be used to obtain this information, the main one being Faraday rotation measures (RMs).
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