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Thesis Is Submited in Partial Fulfilment of the Requirements for the Award of the Degree of Doctor of Philosophy of the University of Portsmouth

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Thesis Is Submited in Partial Fulfilment of the Requirements for the Award of the Degree of Doctor of Philosophy of the University of Portsmouth Techniques for Cosmological Analysis of Next Generation Low to Mid-Frequency Radio Data Michael Tarr Department of Technology THE THESIS IS SUBMITED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY OF THE UNIVERSITY OF PORTSMOUTH May 2018 Declaration Whilst registered as a candidate for the above degree, I have not been registered for any other research award. The results and conclusions embodied in this thesis are the work of the named candidate and have not been submitted for any other academic award. This dissertation contains 51,523 words not including appendices, bibliography, footnotes, tables and equations, and has 68 figures. Michael Tarr May 2018 Acknowledgements First, I would like to give my most sincere thanks to David. It goes without saying that I can not imagine having completed this work without you. Your enthusiasm and belief in me has been a constant source of motivation from day one to the eleventh hour. You are an inspiration and model of a perfect superior. I cannot overstate how much I appchiate your effort, and I am eternally grateful. My love and thanks also to my parents, who have provided nothing but loving support, despite all my whims and phases. I can only hope it was all worth it to find something I have finally stuck with. Thanks should also go to Xan and Matthew, for taking precious time away from their own research to indulge my pet machine learning project. I owe you both and hope to always be friends. Rebecca1, save the final thanks for you. Your support and patience has been wonderful, I will never forget it. I promise to save you from the washing, and make up for all the lost holiday! All my love, “Always”. 1Hello to Jason Isaacs. Dissemination Publications Tarr, M. and Bacon, D. “Measuring gravitational weak lensing from radio visibilities” (in prep). Tarr, M., Sabater, J. et al., “Spectra of faint radio sources in the ELAIS-N1 field” (in prep). Smith, D. J. B. et al., including Tarr, M. “The WEAVE-LOFAR Survey, SF2A-2016: Proc. of FSAA, arXiv:1611.02706 [astro-ph.CO]. Recent Presentations Nov. 2016, Science for the SKA Generation: “Radio Weak Lensing: Potential for the SKA” Jun 2016, UCL seminar: “Radio Weak Lensing: Exploring methods for shear estima- tion” Apr. 2016, SKA – Delivering the Science: “Techniques and tools for weak lensing with the SKA” Mar. 2016, WEAVE-LOFAR team meeting: “LOFAR-BOSS ELIAS-N1: SDSS-III obser- vations of radio galaxies” Sept. 2015, ICG-KASI meeting, Portsmouth: “Radio Weak Lensing: and direct shear mapping using F.I.L.M” Jul. 2015, National Astronomy Meeting, Llandudno: “Fourier Inspection of Lensing Modes (F.I.L.M): A new weak lensing estimator for next generation of radio telescopes” Abstract For centuries, astronomical instrumentation has continued to develop and improve. This has led to the incredible precision seen in recent observations, with ever greater accuracy to come. From their measurements, cosmologists have produced a complex model of the Universe. This indicates that most of the energy in the Universe is in some “dark” form that does not interact directly with the electromagnetic spectrum. One of the greatest challenges of modern cosmology is the understanding of these dark components. In particular weak gravita- tional lensing has emerged as powerful tool for probing these parts of the cosmological model. An area of observation which has undergone an accelerated improvement in recent years, is radio astronomy. The radio regime therefore, is an exciting source of new discoveries and further cosmological constraints. Several studies have shown that the lensing signal can be detected at radio wavelengths2, while others have demonstrated the significant impact of combining the results from next-generation radio and optical telescopes3. In order to fully realise the potential of lensing and other measurements for cosmology, a comprehensive understanding of the radio galaxy population is also required. In this thesis, I consider the future of radio observations for precision cosmology and the required developments in analysis techniques. I aim to contribute to this progress by focusing specifically on: (i) Providing novel estimators for radio weak lensing measurements and (ii) Studying the redshifts and statistics of galaxy populations in the radio, using op- tical spectroscopy. Both of these areas will soon be the subject of large next-generation observations, in the form of the Square Kilometre Array (SKA4) continuum surveys; and a joint experiment between a next-generation spectroscopy facility (WEAVE5) for the William Herschel Telescope (WHT6) and the LOw Frequency ARray (LOFAR7). 2Chang et al.(2004); Patel et al.(2010) 3Bonaldi et al.(2016); Camera et al.(2017); Harrison et al.(2016) 4https://skatelescope.org/ 5http://www.ing.iac.es/weave/about.html 6http://www.ing.iac.es/Astronomy/telescopes/wht/ 7http://www.lofar.org/ Table of contents List of figures xv List of tables xxi 1 Cosmology1 1.1 Basis of Theoretical Cosmology . .2 1.1.1 General Relativity . .2 1.1.2 Friedmann–Lemaître–Robertson–Walker Cosmology . .3 1.2 Observational Cosmology . .5 1.2.1 Hubble’s Law . .5 1.2.2 Cosmic Distance-Ladder Methods . .7 1.2.3 Distances in cosmology . .9 1.2.4 Observational Parameters . 11 1.3 The LCDM Universe . 13 1.3.1 Energy components . 13 1.3.2 Dark Energy Effect without a Cosmological Constant . 18 1.4 Probes of Cosmology . 19 1.4.1 Cosmic microwave radiation . 19 1.4.2 Baryon Acoustic Oscillations (BAO) . 22 1.4.3 Type 1a Supernovae . 23 1.4.4 Time delay strong lensing (TDSL) . 24 1.4.5 Weak Lensing . 26 1.4.6 Gravitational waves . 26 1.5 Overview of this Thesis . 27 1.5.1 Current constrains on LCDM parameters. 30 2 Radio Astronomy 31 2.1 Introduction . 31 xii Table of contents 2.2 Single aperture telescopes . 32 2.3 Interferometry . 34 2.3.1 Spacial coherence of a radiation field . 34 2.3.2 The (u,v,w) coordinate system . 37 2.3.3 Fourier inversions of spatial coherence . 38 2.3.4 Two element interferometer . 40 2.3.5 Interferometry at other wavelengths . 42 2.4 Aperture synthesis . 43 2.4.1 Sampling . 44 2.4.2 Producing an image . 45 2.5 Radio galaxies . 48 2.5.1 Synchrotron radiation . 49 2.5.2 Free-free emission . 51 2.5.3 Radio galaxy populations . 51 3 Spectra of Faint Radio Sources 55 3.1 Radio Observations . 56 3.1.1 The ELAIS-N1 Field . 56 3.1.2 LOFAR . 59 3.1.3 VLA . 61 3.1.4 GMRT . 62 3.2 Optical and spectroscopic observations . 63 3.2.1 SDSS and BOSS . 63 3.2.2 SDSS DR9 matching and target selection . 64 3.2.3 BOSS Observations . 70 3.2.4 Data reduction . 70 3.3 Catalogue . 70 3.4 Redshift efficiency . 72 3.5 Spectra re-analysis . 77 3.5.1 Comparison of visual analysis vs the BOSS pipeline . 79 3.5.2 Redshift error for ZWARNING=0 . 81 3.5.3 Redshift error for ZWARNING=4 . 85 3.5.4 Classification error . 87 3.6 Population . 89 3.7 Conclusions . 91 Table of contents xiii 4 Gravitational Lensing 93 4.1 The Path of Light and Refraction . 94 4.1.1 Geometric Time Delay . 96 4.1.2 Relationship to General Relativity . 98 4.2 The Effects of Lensing . 99 4.2.1 Bend Angle . 99 4.2.2 The Jacobian of Lensing . 100 4.2.3 Inferring lens or source information . 100 4.3 Weak Lensing . 101 4.3.1 Measuring ellipticity . 102 4.3.2 Estimating shear . 103 4.4 Cosmic shear and mass maps . 104 4.5 Shear Correlation Functions . 105 4.6 Optical Observation Challenges . 106 4.6.1 Recent results from optical weak lensing . 109 4.7 Radio Weak Lensing . 111 4.7.1 Advantages of weak lensing at radio wavelengths . 111 4.7.2 Challenges of radio weak lensing . 114 4.7.3 Previous Radio Weak Lensing Approaches and Results . 114 4.7.4 SKA Weak Lensing Cosmology . 116 5 Radio Weak Lensing 119 5.1 My approach: Direct estimation of shear . 120 5.1.1 Analytical model of a radio observation . 120 5.1.2 Constructing the Estimators . 129 5.1.3 Pixel reconstruction mode . 133 5.2 Simulations . 134 5.2.1 True Sky Model . 135 5.2.2 Lensing signal . 136 5.2.3 Simulated observation . 137 5.3 Results . 142 5.3.1 Fourier Estimation (FE) mode . 142 5.3.2 Pixel Reconstruction (PR) mode . 148 5.3.3 Future considerations . 151 5.4 Conclusions . 153 5.4.1 Summary table of results . 155 xiv Table of contents 6 Further Analysis Techniques and Conclusions 157 6.1 Further Work . 158 6.1.1 Imaging of Wide Field LOFAR Data . 158 6.1.2 Ellipticity Measurements in the Boötes Field . 163 6.1.3 Radio-Optical Cross matching using Machine Learning . 170 6.2 Summary and conclusions . 172 References 177 Appendix A Form UPR16 201 Appendix B Ethical Review 203 Appendix C Catalogue sample 207 Appendix D Taylor Expansion of Lensing model 213 D.1 First order terms . 213 D.2 Second Order Terms . 214 List of figures 1.1 Original Hubble diagram (1929) . .6 1.2 The Bullet Cluster (2006) . ..
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