Dark Matter Annihilation in the Epoch of Reionisation Sarah Schön Doctor of Philosophy 2017 School of Physics The University of Melbourne Submitted in Total Fulfillment of the Requirements of the Degree of Doctor of Philosophy Abstract Dark matter constitutes about 26% of the Universe’s mass-energy content, compared to the 5% that make up the familiar matter described by the Standard Model of par- ticle physics. Besides the ubiquitous gravitational effects, astrophysical observations have also shown dark matter to be at most weakly interacting with ordinary matter. Furthermore the fundamental particle nature of dark matter remains unclear though a number of potential models have been proposed, many of which arise naturally as part of theoretical frameworks beyond the Standard Model. In addition dark matter plays an instrumental role in the evolution of observable structure and fully situating dark matter within the Standard Models of both particle physics and cosmology remains a critical pursuit of modern physics. Amongst the most promising of dark matter models are those that self-annihilate to Standard Model particles. In astrophysical settings, the presence of annihilating dark matter could be inferred from either the presence of high energy annihilation products or through the modification of standard astrophysical phenomenology, an in particular events such as the Epoch of Reionisation, by the additional heating and ionisation provided by dark matter annihilation. In this thesis, the potential impact of self-annihilating dark matter on early structure is investigated. A vital aspect of this calculation is the detailed treatment of the energy transfer. To this end, a Monte Carlo code was written to track the full evolution of the injected particles and the subsequent secondary particle cascades and record the energy deposited in and around dark matter halos. Since there is considerable uncertainty as to the precise dark matter density distributionofhighredshiftobjects,arangeofprofilesandmass-concentrationrelations are compared. A number of different dark matter particle masses and annihilation models are also considered. Besides the self-heating of the halos, the impact of the escaped particle on circumgalactic medium is investigated as well as how the additional heatingcansuppresstheinfallofgasontothehalo. Lastlythepowerfromthehaloitself iscomparedtothatfromotherssourcessuchasthediffusedarkmatterbackgroundand CGM. Declaration This is to certify that: • This thesis entitled “Dark matter annihilation in the Epoch of Reionisation” com- prises only my original work towards the PhD, except where indicated otherwise. • Due acknowledgement has been made in the text to all other material used. • This thesis is no longer than 105 pages in length, exclusive of tables, figures, bibliographies and appendices. .......................................................... Sarah Schön Acknowledgements My first few months in Melbourne I frequently spent in a delighted panic while coming to terms with the idea that what had been a somewhat inevitable final step in my schooling had acquired a very real deadline. Four of the most illuminating years later, and I would like to thank the people who helped me to not only finish my thesis but convinced me that I could in the first place. Foremost thanks must go to my supervisors Katie Mack and Stuart Wyithe about whomnotenoughgoodthingscanbesaid. Iwillalwaysbegratefultothemforallowing me this opportunity, as well as for their patience, good humour and unfailing generosity when it came to both their time and vast expertise. I would also like to acknowledge all those individuals who not only enriched my understanding of the universe but also the academic world (the latter of which can at times appear far more daunting than the former). Special thanks go to Jonathan McDowell, Carmelo Evoli and Andrea Ferrara for not only their assistance and but also for being wonderful hosts in far off lands and to Tracy Slatyer for amongst other things, the invaluable discussion on the finer points of Inverse Compton scattering. Last but not least, I’m immensely grateful to Elisabetta Barberio for her ongoing support, and to her Masters student Cassandra Avram for the tremendous company along the way. I’ve never been the most sociable person in the world but the astrophysics depart- ment at the University of Melbourne has been one of the most welcoming and positive communities I have ever had the good fortune to be a part of and you are some of the kindest, smartest and supportive people I have ever had the pleasure of knowing. Thanks to my wonderful sisters, Melanie (as well as her boys) for always making me smile and Sophia, my best friend, for her unconditional support. Finally there will never be enough words of thanks for my mother, who is the embodiment of grace and resilience. Contents Chapter 1: Searches for Dark Matter I; A brief introduction informed by astrophysics 1 1.1 A New Kind of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Early Discoveries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The Missing Mass Problem and Galaxy Rotation Curves . . . . . . . . . . 3 1.2.1 Extended Galaxy Rotation Curves . . . . . . . . . . . . . . . . . . . 3 1.3 Brief Foray into Cosmological Matters . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.2 Dark Matter and Structure Formation . . . . . . . . . . . . . . . . . 7 1.4 Epoch of Reionisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.1 21-cm Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 N-Body Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Further Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.6.1 Gravitational Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.6.2 CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6.3 Bullet Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7 Towards the Fundamental Nature of Dark Matter . . . . . . . . . . . . . . 16 1.7.1 MOND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7.2 Baryonic Dark Matter Candidates . . . . . . . . . . . . . . . . . . . 16 Chapter 2: Searches for Dark Matter II: A brief introduction informed by particle physics 19 2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Physics Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Potential Dark Matter Candidates . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.2 Extra-dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.3 Axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.4 Sterile Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Contents v 2.4 Modelling Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.1 Effective Dark Matter Models . . . . . . . . . . . . . . . . . . . . . . 24 2.4.2 Annihilation Cross-Section . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.3 Annihilation Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4.4 PYTHIA Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 Searches for Dark Matter Particles . . . . . . . . . . . . . . . . . . . . . . . 29 2.5.1 Collider Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5.2 Direct Detection Experiments . . . . . . . . . . . . . . . . . . . . . . 31 2.5.3 Indirect Searches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.4 Global Impact Searches. . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6 Outline of the Following Work . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6.1 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Chapter 3: Atomic Physics 37 3.1 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.1 Lyman Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.2 Photo-ionisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.1.3 Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1.4 Pair-Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.5 Photon Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2 Electrons and Positrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Electro-ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.2 Electron-excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.3 Coulomb Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.4 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.5 Inverse-Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.6 Positrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3 Other Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3.2 Protons and Anti-protons . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4 Energy Transfer Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4.1 MEDEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4.2 Halo Energy Transfer Code . . . . . . . . . . . . . . . . . . . . . . . 47 3.4.3 Physics not Covered . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4.4 Code Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Chapter 4: Self-heating Dark Matter Halos 55 4.1 Structure of a Dark Matter Halo. . . . . . . . . . . . . . . . . . . . . . . . . 56 4.1.1 Density Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 vi Contents 4.1.2 Mass-Concentration Relation . . . . . . . . . . . . . . . . . . . . . . 59 4.1.3 Baryonic Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2 Dark Matter Annihilation Power from Halos . . . . . . . . . . . . . . . . . 62 4.2.1 Dark Matter Annihilation Power . . . . . . . . . . . . . . . . . . . . 62 4.3 Binding Energy Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.1 Over the entire Halo . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 Energy Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4.1 Total Energy Lost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.5 Binding Energy Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.5.1 Uncertainty due to f . . . . . . . . . . . . . . . . . . . . . . . . . . 74 abs 4.5.2 Choice of Baryonic Profile . . . . . . . . . . . . . . . . . . . . . . . . 74 4.6 Potential for Modification of Structure Formation . . . . . . . . . . . . . . 76 Chapter 5: Self-heating Dark Matter Halos II A Closer Look 80 5.1 Halo and Dark Matter Models . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.1.1 Dark Matter Candidates . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.1.2 Density Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Energy Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2.1 Role of Inverse Compton Scattering . . . . . . . . . . . . . . . . . . 86 5.3 Code Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.3.1 Heating and Ionisation . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3.2 Comparison with Gravitational Binding Energy . . . . . . . . . . . 101 Chapter 6: Heating of the Circumgalactic Medium 109 6.1 Minimal Baryonic Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.1.1 Baryonic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2 Modified Dark Matter Annihilation Spectrum . . . . . . . . . . . . . . . . . 113 6.2.1 Filtered Annihilation Spectra . . . . . . . . . . . . . . . . . . . . . . 118 6.3 Heating of the Circumgalactic Medium . . . . . . . . . . . . . . . . . . . . . 125 6.3.1 Gas Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.3.2 Energy Transfer Code in the CGM . . . . . . . . . . . . . . . . . . . 125 6.3.3 Code Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.3.4 Heating and Ionisation . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.4 Raising the Jeans Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.4.1 Change in δ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 b 6.4.2 Change in the Minimal Baryonic Mass. . . . . . . . . . . . . . . . . 141 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Contents vii Chapter 7: Halos as non-isolated Objects 144 7.1 Heating from Diffuse Background . . . . . . . . . . . . . . . . . . . . . . . . 146 7.1.1 Photon Bath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 7.1.2 Code Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.1.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.2 Heating from the CGM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 7.2.1 Code Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 7.2.2 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.3 Comparison of Heating Sources of the CGM. . . . . . . . . . . . . . . . . . 154 7.3.1 Diffuse Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7.3.2 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Chapter 8: Concluding Thoughts 161 8.1 Summary of Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.1.1 Self-Heating Dark Matter Halos . . . . . . . . . . . . . . . . . . . . . 161 8.1.2 Energy Transfer Code. . . . . . . . . . . . . . . . . . . . . . . . . . . 163 8.1.3 Self-heating Dark Matter Halos Revisited . . . . . . . . . . . . . . 164 8.1.4 The Impact of Dark Matter Annihilation on the CGM . . . . . . . 165 8.1.5 Comparison of Heating Sources . . . . . . . . . . . . . . . . . . . . . 166 8.2 Future Applications and Final Thoughts . . . . . . . . . . . . . . . . . . . . 166 AppendixA:The lightest neutralino in minimal SUSY 186 A.1 MSSM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 A.1.1 Supersymmetric Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 186 A.1.2 Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 A.1.3 R-Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 A.1.4 The Lightest Neutralino . . . . . . . . . . . . . . . . . . . . . . . . . 188 Appendix B:Derivation of the IC photon spectrum 192 B.1 Derivation in the Relativistic Limit . . . . . . . . . . . . . . . . . . . . . . . 192 B.1.1 Relativistic Kinematics during IC Scattering . . . . . . . . . . . . . 192 B.1.2 IC Spectrum in Relativistic Limit . . . . . . . . . . . . . . . . . . . 193 B.1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 AppendixC:Additional Results and Code Outputs 197 List of Tables 3.1 Fitting parameters for electro - ionisation cross-sections. . . . . . . . . . . 39 3.2 Fitting parameters for electro - ionisation cross-sections. . . . . . . . . . . 43 3.3 Fitting parameters for electro - excitation cross-sections. . . . . . . . . . . 44 4.1 Summary of the different dark matter halo models considered in this chapter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Summary of the different dark matter annihilation models considered in this work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.1 Summary of the different dark matter annihilation models considered in this chapter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Summary of the different dark matter halo models considered in this chapter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.1 Energybreakdownfor130MeVannihilatingviaelectrons/positronsdark matter model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.2 Energy breakdown for 5 GeV annihilating via muons dark matter model 119 6.3 Energy breakdown for 80 GeV annihilating via W boson dark matter model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 A.1 Summary of MSSM fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187