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Conversion of Cold Dark Matter Axions to Photons in Astrophysical Magnetic Fields

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Conversion of Cold Dark Matter Axions to Photons in Astrophysical Magnetic Fields CONVERSION OF COLD DARK MATTER AXIONS TO PHOTONS IN ASTROPHYSICAL MAGNETIC FIELDS A thesis submitted to the University of Manchester for the degree of Master of Science in the Faculty of Engineering and Physical Sciences April 2019 By Sankarshana Srinivasan School of Physics and Astronomy Contents Abstract8 Declaration9 Copyright 10 Acknowledgements 12 1 Introduction 14 1.1 History................................. 15 1.2 The Current Picture of Cosmology................. 18 1.2.1 Evolution of the Universe.................. 18 1.3 Problems with ΛCDM........................ 25 1.3.1 Horizon and Flatness Problems - Inflation......... 25 1.4 Evidence for Dark Matter...................... 30 1.4.1 Galactic Rotation Curves.................. 30 1.4.2 Galaxy Clusters........................ 32 1.4.3 Cosmological Evidence.................... 34 1.5 Dark Matter Candidates....................... 37 1.5.1 Weakly Interacting Massive Particles (WIMPS)...... 37 2 1.5.2 Primordial Black Holes and Massive Astrophysical Com- pact Halo Objects (MACHOs)................ 38 1.5.3 Axions............................. 40 2 Axion Models and Constraints 43 2.1 What are axions?........................... 44 2.2 Properties and models of axions................... 46 2.3 Experimental Constraints...................... 49 2.3.1 Axion Helioscopes....................... 49 2.3.2 Haloscope Experiments.................... 52 2.3.3 Laboratory based experiments................ 57 2.3.4 Critical Analysis....................... 61 2.4 Theoretical Constraints........................ 63 2.4.1 Astrophysical constraints................... 63 2.4.2 Constraints from Cosmology................. 66 2.5 Discussion............................... 72 2.5.1 This Project.......................... 73 3 Decay in Cosmological Sources 76 3.1 Introduction.............................. 77 3.2 Evaluation of Flux and Intensity................... 78 3.2.1 Physical Observables and Quantities............ 78 3.2.2 Intensity and Flux...................... 81 3.3 Astrophysical Magnetic Fields.................... 87 3.4 Detectability.............................. 89 3.4.1 Galactic Centre........................ 91 3.4.2 Virialised Objects....................... 93 3.5 Discussion............................... 100 3 4 The Axion-Photon Decay in Neutron Stars 107 4.1 Introduction.............................. 108 4.2 Modification of Maxwell's Equations................ 109 4.3 Goldreich-Julian Calculation..................... 111 4.4 General Formalism.......................... 117 4.5 Critical Analysis of Literature.................... 121 4.5.1 Raffelt and Stodolsky..................... 121 4.5.2 Hook et al........................... 125 4.5.3 The Landau-Zener Solution................. 130 4.6 Discussion............................... 137 5 Conclusions 143 Bibliography 149 4 List of Tables 2.1 Critical comparison of axion experiments.............. 62 3.1 Table of distances, velocity widths and masses of local dwarf galaxies 96 3.2 Table of distances, velocity widths and masses of clusters of galaxies.101 3.3 Table of integration times from beam mass estimation....... 105 5 List of Figures 1.1 The scale factor as a function of time................ 20 1.2 The energy budget of the Universe................. 23 1.3 History of the Universe (WMAP).................. 29 1.4 The rotation curve of the Andromeda (M31) Galaxy........ 31 1.5 The Bullet Cluster.......................... 34 1.6 The temperature angular power spectrum from Planck...... 36 1.7 Constraints on the WIMP parameter space by PandaX-II.... 38 1.8 Limits on primordial black holes................... 40 2.1 Axion parameter space........................ 45 2.2 Axion-Photon decay mechanisms.................. 48 2.3 The CAST helioscope at CERN................... 51 2.4 CAST exclusion plot......................... 52 2.5 The ADMX experiment....................... 53 2.6 ADMX limit on CDM axions.................... 54 2.7 The CROWS Experiment...................... 57 2.8 Representation of photon regeneration experiments........ 59 2.9 Limits on axion parameter space by photon regeneration experi- ments.................................. 60 2.10 Axion cooling constraints....................... 66 6 2.11 Axion couplings to gluons and pions................. 70 2.12 Summary of axion constraints.................... 73 3.1 Magnetic field power spectrum of the Coma cluster........ 88 3.2 Radio signal detection schematic................... 90 3.3 Detection regimes for virialised objects............... 94 3.4 Integration time trends for resolved and unresolved detections.. 103 3.5 1-σ sensitivities from Virgo observations.............. 106 4.1 Probability of axion-photon conversion............... 130 4.2 1 − σ sensitivities from neutron star observations......... 140 7 Abstract The cold dark matter (CDM) problem is one of the important unsolved problems in cosmology today. The axion is one of the well motivated CDM candidates whose weak spontaneous decay to photons is enhanced in the presence of magnetic fields. This thesis examines the prospects of detecting the axion-photon decay in astrophysical magnetic fields using radio telescopes, with special reference to cosmological objects and neutron stars. Cosmological objects are found to be ill- suited to the detection of the enhanced decay because of the large scale structure of magnetic fields in such objects. However, nearby massive galaxy clusters might offer a chance of detection of the spontaneous decay, although this requires a clear understanding of the density profile of such clusters. Neutron stars and their magnetospheres are home to a resonance effect that could be one of the best chances of detection in future searches. We develop a general formalism that allows us to determine the different assumptions that lead to different results in the literature. We also examine the detectability of the flux from this resonant decay and find that radio telescopes are sensitive enough to probe the regions of CDM axion parameter space hitherto unexplored. 8 Declaration No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institution of learning. 9 Copyright i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the Intellectual Property) and any reproductions of copy- right works in the thesis, for example graphs and tables (Reproductions), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property 10 and/or Reproductions described in it may take place is available in the University IP Policy (see http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual- property.pdf), in any relevant Thesis restriction declarations deposited in the Uni- versity Library, The University Librarys regulations (see http://www.manchester.ac.uk/library/ aboutus/regulations) and in The University's policy on presentation of The- ses. 11 Acknowledgements I would like to thank my supervisor Professor Richard Battye for the support and knowledge he has provided me over the course of my MSc. I would also like to thank Dr Francesco Pace for his invaluable help, patience, guidance and support. Special thanks to Susmita Sett, Dirk Scholte, Anthony Gilfelon, David Whitworth, Tracy Garratt, Suheil Harjani and Thomas Peasley for their help and encouragement. Finally, I thank my parents for their constant support and faith. 12 Chapter 1 Introduction to Cosmology and Dark Matter 14 1.1. HISTORY 15 1.1 History Cosmology, the study of the origin, evolution and fate of the universe can be traced back to ancient times. The word cosmology comes from the Greek words Kosmos, which means \world" and -logia which means \study of". The first cos- mological theories can be traced back to Mesopotamia and India. Mesopotamian cosmology describes a flat circular Earth surrounded by a cosmic ocean. The Rigveda has some verses which detail a qualitative cosmological theory that de- scribes a cyclic universe expanding from a point called the \bindu" and collapsing back to it. In the West, the earliest cosmological theories were geocentric theories proposed by Greek philosophers such as Ptolemy and Aristotle. They observed the sun rising in the East and setting in the West, as well as observed the move- ment of constellations in the night sky through the year. Thus, this system, dubbed the \Ptolemaic System" was the generally accepted one as it fit
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