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Constraining the Particle Nature of Dark Matter: Model-Independent Tests from the Intersection of Theory and Observation

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Constraining the Particle Nature of Dark Matter: Model-Independent Tests from the Intersection of Theory and Observation CONSTRAINING THE PARTICLE NATURE OF DARK MATTER: MODEL-INDEPENDENT TESTS FROM THE INTERSECTION OF THEORY AND OBSERVATION DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Gregory Daniel Mack, B.A., M.S. * * * * * The Ohio State University 2008 Dissertation Committee: Approved by Prof. John F. Beacom, Adviser Prof. James Beatty Adviser Prof. Eric Braaten Graduate Program in Prof. Terrence Walker Physics ABSTRACT Dark matter is one of the greatest mysteries of modern astrophysics. It comprises about 83% of the matter density in the Universe and approximately 22% of the total energy density, yet its identity and particle properties are unknown. Gravitational interactions reveal its presence, but it does not readily interact with light or nor- mal matter. The purpose of this dissertation is to provide insight into the particle properties of this exotic type of matter in a model-independent fashion. Dark mat- ter is expected to be its own antiparticle, but the strength of its self-annihilation is not known. It is often assumed to be consistent with that which gives the correct abundance if dark matter were produced as a thermal relic in the early Universe, but that has not been proven. Constraints on the dark matter self-annihilation cross section are found over a wide range of masses, both for the separate cases of monoen- ergetic neutrino and monoenergetic photon production, and the corresponding limits on the total self-annihilation cross section. This is done by comparing the theoretical flux from a region of annihilating dark matter to observational data of that region. While larger than the thermal relic value, the resulting upper bounds are surpris- ingly stringent and among the first model-independent limits of their kind. A specific application of residual dark matter annihilations during the time of Big Bang Nu- cleosynthesis is analyzed, adding a lower limit to the value of the annihilation cross section for a certain mass range to couple with the calculated upper bounds mentioned ii above. The interaction strength of dark matter with normal matter is constrained by the case of dark matter capture in Earth and the resulting heat flow from an- nihilation in the core. When compared to observation, the analysis rules out many possible interaction strengths between dark matter and normal matter, showing that the interaction, as measured by the interaction cross section, must be truly weak for the usually considered mass range. These model-independent investigations help to shrink the range of possible dark matter property values in a generic fashion, aiding in better understanding and more focused analyses. iii To my parents, family, and friends, who have always shown their support. To those who find the analytic in the artistic, and the aesthetic in the logic. iv ACKNOWLEDGMENTS I would like to first and foremost acknowledge my adviser, Dr. John Beacom, for mentoring me these last several years. I have learned a great deal from John about astrophysics, particle physics, doing research, writing papers, giving talks, the politics of science, ice-cycling in Wisconsin, and even how to grow an impressive goatee. I would also like to thank the other members of my committee, Drs. Terry Walker, Jim Beatty, and Eric Braaten, for seeing me through this process, and especially Terry for encouraging me in joining the Astrophysics group in my initial graduate school stages (and therefore having me interact with such hooligans as Andrew, Savvas, and Louie). I also need to thank my undergraduate professors at Ohio Wesleyan University, Barbara Andereck, Brad Trees, and Bob Harmon, without whom I would not have made it to graduate school. I am also grateful for my collaborators, Gianfranco Bertone, Nicole Bell, Hasan Yuksel,¨ Thomas Jacques, and Gary Steigman, who along with John were essential for my research and publications. Along those lines, I acknowledge Eric Braaten, Stuart Raby, Stefano Profumo, Frederick Kuehn, Matt Kistler, Louie Strigari, Jordi Miralda- Escud´e, Jerry Newsom, Wendy Panero, Ralph von Frese, Laura Baudis, Andy Gould, Shin'ichiro Ando, Shantanu Desai, Michael Kachelriess, Manoj Kaplinghat, Eiichiro Komatsu, Robert Scherrer, Shmuel Nussinov, and Casey Watson for discussions and advice in completing the publications. v On a more personal note, I would like to thank my parents, Gene and Carlotta, and the rest of my family, especially Ed and Amanda, for always giving me support. I have to thank my good friends, too, for putting up with me and my irrationalities during this process: Chad Johns, Sara Florkey, Jenn Schmelzer, and Beth Cademar- tori for infinitely many, many, many things including for tolerating me the past ten years; Dave Boley for studying at many different coffee shops with me, sometimes cooking for me, showing me how to cook, scrabble, and the gracious use of his park- ing pass; Marian Homan for innumerable wake-up calls; my \twin sister" Sarah Hixon for having me as a part of Hixon Dance, performing in her works, and sharing ranting sessions; Maggie Page and Noelle Chun, with whom it is always great to dance on- stage; and Ric Rader, Deb Friedes, Andy Vogel, Brian Hauser, and Christina Xydias, for the \Wednesday night grad student gatherings". I also like to think that I greatly supported the local business scene in Columbus, Ohio, by frequenting (rather often) the coffee shops Caff´e Apropos and Cup O Joe (the Short North location, but much more often in German Village). Countless cups of coffee contributed to the writing of this dissertation. vi VITA 5 June 1980 . Born { Cleveland, OH May 2002 . .B. A. in Physics and Astronomy, Ohio Wesleyan University, Delaware, OH September 2002 { August 2005 . Fowler Fellowship, The Ohio State Uni- versity, Department of Physics, Colum- bus, OH August 2005 . .M.S. in Physics, The Ohio State Uni- versity, Columbus, OH September 2005 { June 2008 . Graduate Research Associate, The Ohio State University, Department of Physics, Columbus, OH vii PUBLICATIONS \Towards Closing the Window on Strongly Interacting Dark Matter: Far- Reaching Constraints from Earth's Heat Flow," G. D. Mack, J. F. Beacom and G. Bertone, Phys. Rev. D 76, 043523 (2007) [arXiv:0705.4298 [astro-ph]]. \General Upper Bound on the Dark Matter Total Annihilation Cross Sec- tion," J. F. Beacom, N. F. Bell and G. D. Mack, Phys. Rev. Lett. 99, 231301 (2007) [arXiv:astro-ph/0608090]. \Conservative Constraints on Dark Matter Annihilation into Gamma Rays," G. D. Mack, T. D. Jacques, J. F. Beacom, N. F. Bell and H. Yuksel, (2008) arXiv:0803.0157 [astro-ph]. FIELDS OF STUDY Major Field: Physics viii TABLE OF CONTENTS Page Abstract . ii Dedication . iv Acknowledgments . v Vita . vii List of Tables . xii List of Figures . xiii Chapters: 1. An Introduction to Dark Matter . 1 1.1 A General Introduction . 1 1.2 A Historical Perspective . 4 2. How Much Dark Matter is There? . 16 2.1 Necessary Cosmological Formalism . 16 2.2 Measuring an Imprint of the Early Universe: the Cosmic Microwave Background . 22 2.3 The Universe is \Darker" Than Originally Thought: a Case for Λ . 29 2.4 Correlating Cosmological Measurements . 30 3. Dark Matter: Where, What, How? . 34 3.1 Where is the Dark Matter? . 34 3.2 What Could Dark Matter Be? . 40 ix 3.2.1 Supersymmetry . 41 3.2.2 Universal Extra Dimensions . 43 3.2.3 Other Viable Candidates . 44 3.3 How Can We Find Dark Matter? . 45 3.3.1 Direct Detection: The Slightest Touch . 46 3.3.2 Indirect Detection: Measuring Dark Matter's Disappearance 50 3.3.3 Unitarity: An Existing Annihilation Constraint . 52 4. Towards Closing the Window on Strongly Interacting Dark Matter: Far-Reaching Constraints from Earth's Heat Flow . 57 4.1 Introduction . 58 4.2 Review of Prior Constraints . 64 4.2.1 Indirect Astrophysical Constraints . 64 4.2.2 Direct Detection Constraints . 66 4.3 Earth's Heat Flow . 67 4.4 Dark Matter Capture Rate of Earth . 69 4.4.1 Maximum Capture Rate . 70 4.4.2 Dark Matter Scattering on Nuclei . 73 4.4.3 Dark Matter Capture Efficiency . 75 4.5 Dark Matter Annihilation and Heating Rates in Earth . 81 4.5.1 Maximal Annihilation and Heating Rates . 81 4.5.2 Equilibrium Requirements . 83 4.5.3 Annihilation and Heating Efficiencies . 86 4.6 Discussion and Conclusions . 88 4.6.1 Principal Results . 88 4.6.2 Comparison to Other Planets . 89 4.6.3 Future Directions . 90 5. Upper Bound on the Dark Matter Total Annihilation Cross Section . 92 5.1 Introduction . 92 5.2 Probing Dark Matter Disappearance . 96 5.3 Revealing Neutrino Appearance . 97 5.4 Cosmic Diffuse Neutrinos: Signal . 98 5.5 Cosmic Diffuse Neutrinos: Backgrounds . 102 5.6 Conclusions . 104 6. Conservative Constraints on Dark Matter Annihilation into Gamma Rays 107 6.1 Introduction . 108 6.2 Cross Section Constraints . 110 x 6.3 Calculation of Dark Matter Signals . 112 6.3.1 Dark Matter Halos . 112 6.3.2 Milky Way and Andromeda Signals . 115 6.3.3 Cosmic Diffuse Signal . 116 6.4 Specific Observations and Derived Annihilation Constraints . 117 6.4.1 COMPTEL and EGRET . 120 6.4.2 H.E.S.S. 121 6.4.3 INTEGRAL . 122 6.4.4 Andromeda Halo Results . 123 6.4.5 Cosmic Diffuse Results . 124 6.5 Discussion and Conclusions . 125 6.5.1 Limits on the Cross Section to Gamma Rays . 125 6.5.2 Limits on the Total Cross Section . 128 6.5.3 Conclusions and Prospects . 131 7. The Effects of Residual Dark Matter Annihilations on Big Bang Nucle- osynthesis . 133 7.1 Annihilations in the Early Universe .
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