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Application of Novel Analysis Techniques to Cosmic Microwave Application of novel analysis techniques to Cosmic Microwave Background astronomy Aled Wynne Jones Mullard Radio Astronomy Observatory and King’s College, Cambridge. A dissertation submitted for the degree of Doctor of Philosophy in the University of Cambridge. arXiv:astro-ph/9903173v1 11 Mar 1999 i Preface This dissertation is the result of work undertaken at the Mullard Radio Astronomy Observatory, Cambridge between October 1994 and September 1997. The work described here is my own, unless specifically stated otherwise. To the best of my knowledge it has not, nor has any similar dissertation, been submitted for a degree, diploma or other qualification at this, or any other university. This dissertation does not exceed 60 000 words in length. Aled Wynne Jones To Isabel and Ffion ii I am not sure how the universe was formed. But it knew how to do it, and that is the important thing. Anon. (child) It is enough just to hold a stone in your hand. The universe would have been equally incomprehensible if it had only consisted of that one stone the size of an orange. The question would be just as impenetrable: where did this stone come from? Jostein Gaarder (in ‘Sophie’s World’) Acknowledgements Firstly I would like to thank the two people who have introduced me to the immense field of microwave background anisotropies, Anthony Lasenby and Stephen Hancock. Without them I would not have begun to uncover the beauty at the beginning of time. I would also like to thank Joss Bland-Hawthorn whose supervision and enthusiasm during my time in Australia has made me more inquisitive in my field. The many collaborations involved in this project have introduced me to many people without whom this thesis would not have been written; Graca Rocha and Mike Hobson at MRAO, Carlos Gutierrez, Bob Watson, Roger Hoyland and Rafael Rebolo at Tenerife, and Giovanna Giardino, Rod Davies and Simon Melhuish at Jodrell Bank. iii I want to say a special thank you to the two women in my life that have kept me going for the last few years. Thanks to Ffion, my sister, whose insanity has kept me sane and thanks to Isabel whose support and encouragement I could not have done without and whose love has made it all worth while. Martina Wiedner, Marcel Clemens and Dave St. Jacques deserve a special men- tion for making my time in the department a little more bearable. Anna Moore for putting up with me for three months in Australia. Cynthia Robinson, Martin Gunthorpe, Nicholas Harrison, Liam Cox and Dafydd Owen for putting up with me for the first years of my research. I could not finish thanking people without mentioning Pam Hicks and David Titterington (special thanks for all the colour overhead transparencies) who have kept the department running smoothly. I am also very grateful to PPARC for awarding me a research studentship. May they know better next time. Yn olaf diolch yn fawr i fy rhieni sydd wedi rhoi i fyny efo fi am yr ugain mlynedd diwethaf. iv Contents 1 Introduction 1 1.0.1 Outline of thesis content . 2 2 The Universe and its evolution 5 2.1 Symmetrybreakingandinflation . 5 2.2 Darkmatter................................ 8 2.3 Comingofage............................... 9 2.3.1 Thedipole............................. 10 2.3.2 Sachs-Wolfeeffect......................... 10 2.3.3 Dopplerpeaks........................... 11 2.3.4 Defectanisotropies ........................ 11 2.3.5 Silk damping and free streaming . 12 2.3.6 Reionisation . 12 2.3.7 Thepowerspectrum ....................... 13 2.4 Themiddleages.............................. 14 2.4.1 Sunyaev–Zel’dovich effect . 14 2.4.2 Extra–galacticsources . 15 2.4.3 Galacticforegrounds . 17 2.5 Growingold................................ 24 3 Microwave Background experiments 25 3.1 Atmosphericeffect ............................ 26 3.2 GeneralObservations. .. .. .. 27 3.2.1 Skydecomposition ........................ 27 3.2.2 Theeffectofabeam ....................... 27 3.2.3 Sample and cosmic variance . 28 3.2.4 The likelihood function . 28 3.3 JodrellInterferometry . 29 3.4 TheTenerifeexperiments. 31 3.5 TheCOBEsatellite............................ 32 3.6 ThePlanckSurveyorsatellite . 33 3.7 TheMAPsatellite ............................ 34 v vi CONTENTS 4 The data 37 4.1 JodrellInterferometry . 37 4.1.1 Pre–processing .......................... 37 4.1.2 Calibration . 38 4.1.3 Dataprocessing.......................... 39 4.2 TheTenerifescans ............................ 41 4.2.1 Pre–processing .......................... 41 4.2.2 Stackingthedata......................... 42 4.2.3 Calibration . 42 4.2.4 Errorbarenhancement. 43 4.2.5 8.3◦ FWHMexperiment ..................... 43 4.2.6 5◦ experiments .......................... 46 5 Producing sky maps 55 5.1 CLEAN .................................. 56 5.2 Singular Value Decomposition . 56 5.3 Bayes’theorem .............................. 57 5.3.1 Pos/negreconstruction . 58 5.4 MEMinrealspace ............................ 59 5.4.1 Long period baseline drifts. 59 5.4.2 Thebeam ............................. 60 5.4.3 ImplementationofMEM . 61 5.4.4 ErrorsontheMEMreconstruction . 64 5.4.5 Choosing α andm ........................ 65 5.4.6 Galactic extraction . 66 5.5 MEMinFourierspace .......................... 67 5.5.1 Implementation of MEM in Fourier space . 68 5.5.2 Updatingthemodel ....................... 68 5.5.3 Bayesian α calculation ...................... 69 5.5.4 Errorsonthereconstruction . 70 5.6 TheWienerfilter ............................. 71 5.6.1 ErrorsontheWienerreconstruction . 73 5.6.2 ImprovementstoWiener . 73 6 Testing the algorithms 75 6.1 CLEANvs.MEM............................. 75 6.2 ThePlanckSurveyorsimulations . 77 6.2.1 The simulations . 77 6.2.2 Singular Value Decomposition results . 79 6.2.3 MEMandWienerreconstructions . 82 6.2.4 SZreconstruction ......................... 88 6.2.5 Powerspectrumreconstruction . 89 6.3 TheMAPsimulations .......................... 90 6.3.1 MEMandWienerresults. 92 6.4 MEMandWiener:theconclusions . 92 CONTENTS vii 6.5 Tenerifesimulations............................ 95 6.6 Discussion................................. 97 7 The sky maps 99 7.1 TheJodrellBank5GHzinterferometer . 99 7.1.1 Wide–spacingdata ........................ 99 7.1.2 Narrow–spacingdata . .103 7.1.3 Joint analysis . 104 7.2 TheTenerifeexperiments. .108 7.2.1 Reconstructing the sky at 10.4 GHz with 8◦ FWHM. .108 7.2.2 Non-cosmological foreground contributions . 110 7.2.3 The Dec 35◦ 10and15GHzTenerifedata. 111 7.2.4 The full 5◦ FWHMdataset ...................112 8 Analysing the sky maps 117 8.1 Thepowerspectrum ...........................117 8.2 GenusandTopology ...........................118 8.2.1 WhatisGenus?..........................118 8.2.2 Simulations . 123 8.2.3 TheTenerifedata.. .. .. .125 8.2.4 Extending genus: the Minkowski functionals . 128 8.3 Correlationfunctions . .129 8.3.1 Two point correlation function . 129 8.3.2 Three point correlation function . 130 8.3.3 Four point correlation function . 131 9 Conclusions 135 9.1 Discussion.................................135 9.2 ThefutureofCMBexperiments . .137 References 139 viii CONTENTS Chapter 1 Introduction The Big Bang is the name given to the theory that describes how the Universe came into existence about 15 billion years ago at infinite density and temperature and then expanded to its present form. The very early Universe was opaque due to the constant interchange of energy between matter and radiation. About 300,000 years after the Big Bang, the Universe cooled to a temperature of 3000◦C because of ∼ its expansion. At this stage the matter does not have sufficient energy to remain ionised. The electrons combine with the protons to form atoms and the cross section for Compton scattering with photons is dramatically reduced. The radiation from this point in time has been travelling towards us for 15 billion years and has now cooled to a blackbody temperature of 2.7 degrees Kelvin. At this temperature the Planck spectrum has its peak at microwave frequencies ( 1 1000 GHz) and its study forms a branch of astronomy called Cosmic Microwave∼ Backgr− ound astronomy (hereafter CMB astronomy). In 1965 Arno Penzias and Robert Wilson (Penzias & Wilson 1965) were the first to detect this radiation. It is seen from all directions in the sky and is very uniform. This uniformity creates a problem. If the universe is so smooth then how did anything form? There must be some bumps in the early universe that could grow to create the structures we see today. In 1992 the NASA Cosmic Microwave Background Explorer (COBE) satellite was the first experiment to detect the bumps. These initial measurements were in the form of a statistical detection and no physical features could be identified. Today, experiments all around the world are finding these bumps that eventually grew into galaxies and clusters of galaxies. The required sensitivities called for new techniques in astronomy. The main principle behind all of these experiments is that, instead of measuring the actual brightness, they measure the difference in brightness between different regions of the sky. The experiments at Tenerife produced the first detection of the real, individual CMB fluctuations. There are many different theories of how the universe began its life and how it evolved into the structures seen today. Each of these theories make slightly different predictions of how the universe looked at the very early stages which up until now have been impossible to prove or disprove. Knowing the structure of the CMB, within a few years it should be possible for astronomers to tell us
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