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Seeing the First Light a Study of the Dark and Dim Ages

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Seeing the First Light a Study of the Dark and Dim Ages Seeing the First Light A Study of the Dark and Dim Ages Emma Olivia Chapman Submitted for the degree of Doctor of Philosophy Department of Physics and Astronomy University College London November 2013 I, Emma Chapman, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 1 Abstract The Epoch of Reionization (EoR) represents a major phase shift in the history of our Universe. After a long, dark, period of expansion and cooling, the first ionizing sources began to ionize the surrounding hydrogen atoms. These bubbles of ionized hydrogen grew and overlapped until eventually the Universe was mostly ionized. Though there are some constraints on the duration and end of reionization from CMB experiments such as WMAP, the EoR remains a largely mysterious and unconstrained era. The hyperfine transition of the hydrogen atom produces a photon of wavelength 21-cm. This 21-cm radiation can be measured by current generation radio telescopes such as the Low Frequency Array (LOFAR) to provide statistical information, and future radio telescopes such as the Square Kilometre Array (SKA) to produce tomographic maps. A statistical detection of the EoR is a key priority of the LOFAR-EoR project but is not a straight-forward task due to the considerable contribution of 21-cm radiation from non-EoR sources. Galactic synchrotron, Galactic free-free emission and extragalactic foregrounds dominate the cosmological EoR signal by up to 3 magnitudes and require accurate and precise cleaning in order to make trustworthy constraints on the EoR. In this thesis I introduce two statistical methods for EoR foreground removal: one based on statistical independence and one based on sparsity. Both have had success in CMB foreground removal and I show that they also produce impressive EoR power spectrum reconstructions. I also consider the effect of the movement of the EoR hydrogen atoms on the observations made by a telescope such as LOFAR. The peculiar velocity of a hydrogen atom upon emission of a 21-cm photon has a marked effect on the 21-cm intensity and the frequency at which we observe the photon. This observed `redshift-space' is noticeably different from the `real- space' simulations output by many EoR simulation codes. In this thesis I take the semi-analytic reionization code simfast21 and adapt it to output a multi-frequency observation in redshift space, a `light cone', fully incorporating the peculiar velocities of the atoms. These light cones are essential for accurate comparison with forthcoming observations and I detail the numerous theoretical steps taken to create this code. I show that the result of including these peculiar velocities is non-negligible and in fact very large on small scales. I then go on to tackle the idea that foreground avoidance is a viable alternative to foreground subtraction. Recent publications suggest that there is an area of k-space where the EoR signal is the dominant contribution when compared to the foregrounds - the `EoR window'. This would suggest that statistical analysis could be carried out within that region only, relieving the need for foreground subtraction methods. Unlike the other publications on this topic, I consider a physically-motivated foreground model and show that the supposed EoR window is completely compromised as a result of the varying spectral index in the Galactic synchrotron model. I conclude that, though the EoR window is a useful tool for estimating where statistics will be most accurate, foreground removal is still essential to recover the EoR signal. Finally, I apply my foreground subtraction methods to the first LOFAR-EoR data. Though not quite `science ready', the 54 hours of data provide an exciting glimpse of how the foreground subtraction techniques introduced in this thesis work on real data. I find that GMCA not only removes the foregrounds impressively well for such raw data but actually acts as a powerful tool for the identification of systematics within the data. I identify these systematics and in several cases attempt modification and optimisations of the code in order to mitigate them. I find the results extremely promising and discuss how GMCA can be further optimised for future data and act as a feedback step for the calibration method. Acknowledgements To those I have worked with: I have never met a more friendly group to work with than the LOFAR-EoR team and I am so pleased to have been a part of it. A special thanks to Ger, Saleem, Vibor, Panos and Geraint who answered countless ignorant questions and were so welcoming right from day one. Mario - Thank you for letting me butcher your code and especially for ganging up on Fil with me. Jean-Luc and J´erome- GMCA is awesome, thank you for letting me use it and for explaining every part of it repeatedly to me! To my supervisor: Fil, what can I say? It has been a rollercoaster! You are without a doubt one of the most difficult and frustrating and inspiring people I have encountered. You have put me through the wringer both intellectually and emotionally and I wouldn't take a second of it back. You have led me faultlessly through my PhD - being exceptionally accommodating towards my idiosyncrasies and providing me with a confidence in myself and what I do that I never knew I had. You've made me laugh and you've made me cry, you've sent me to sandy beaches and to A&E but at the end of it all I have been left not only with a PhD but with a good friend. Thank you. To my husband: Steve. I have written this paragraph dozens of times because I just can't find the words! I don't have enough space to write about the countless times you did more than your share at home or made me cups of tea to fuel my writing. I said `just half an hour more' way too many times and I thank you for never making me feel bad about it. Your unfaltering calm attitude made me think about the world in a different way from the moment I met you and helped me enjoy my work so much more once you taught me to relax! You are my best friend and the best father Lyra could wish for - I love you. To my family: Mum and Dad - When I was considering my career options at school, not once did it occur to me that there were limits on what I could aim for and this is thanks to you. You gave me the most loving and wonderful childhood possible and you continue to be the most fantastic support now I have a family of my own. Mum, those early worksheets you created gave me a love of maths which finally led me to physics but your unconditional support for anything I put my mind to gave me the confidence to get there. Dad - growing up you seemed to know everything in the world. It was wanting to be like you that caused me to enjoy studying so much and your praise when I got my SATS, GCSEs and beyond meant more than the actual grade. I love you both so much. To my oldest and best friends. Christine: You have been unconditionally there for me for as long as I can remember. You have never asked for anything and never complained when I wanted to play sylvanian families for the umpteenth time, moaned incessantly about boys or gave you a hug with my baby instead of a birthday present. Thank you, you are a constant and wonderful presence in my life and you never fail to cheer me up. Rachael: We've been through pretty much everything you can go through together and I wouldn't have got through a hell of a lot of it without you. Your limitless passion and fearlessness inspired me to get over my own fears and attack anything that scares me with a roar. You are the most awesome person I know and who the term `kick-ass' surely was invented for. To my little girl: Lyra, you will be too young to read this for quite some time but know that your giggles and smiles picked me up every time I thought I couldn't code another line. I hope that you find something in life which makes you as excited as cosmology makes me - if you do, grab it and don't let go! 4 To Steve ... ... who lights up my Universe 5 Contents 1 Introduction 16 1.1 Timeline of the Universe . 17 1.2 Epoch of Reionization . 24 1.2.1 Reionization Models . 25 1.2.2 Observational Constraints . 30 1.2.3 The 21-cm Cosmological Signal . 38 1.2.4 Spin Temperature . 39 1.2.5 The 21-cm Observable . 42 1.2.6 21-cm Measurements . 43 1.3 Radio Instrumentation . 47 1.3.1 LOFAR and LOFAR-EoR Instrumentation . 49 1.3.2 Other Interferometers . 53 1.4 LOFAR-EoR Foregrounds . 54 1.4.1 Galactic Synchrotron Radiation . 55 1.4.2 Galactic Free-Free Emission . 57 1.4.3 Galactic Dust Emission . 58 1.4.4 Galactic Radio Recombination Lines . 58 1.4.5 Extragalactic Foregrounds . 59 1.5 Foreground Removal Methods . 61 1.5.1 Bright Source Removal . 62 1.5.2 Spectral Fitting . 63 1.5.3 Residual Error Subtraction . 66 1.6 Thesis Outline . 66 2 FastICA 68 2.1 The fastica method . 69 2.1.1 fastica in CMB Data Analysis .
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