Phenomenology and Astrophysics of Gravitationally-Bound Condensates of Axion-Like Particles

Phenomenology and Astrophysics of Gravitationally-Bound Condensates of Axion-Like Particles Joshua Armstrong Eby B.S. Physics, Indiana University South Bend (2011) A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics of the College of Arts and Sciences Committee Chair: L.C.R. Wijewardhana, Ph.D Date: 4/24/2017 ii iii Abstract Light, spin-0 particles are ubiquitous in theories of physics beyond the Standard Model, and many of these make good candidates for the identity of dark matter. One very well-motivated candidate of this type is the axion. Due to their small mass and adherence to Bose statistics, axions can coalesce into heavy, gravitationally-bound condensates known as boson stars, also known as axion stars (in particular). In this work, we outline our recent progress in attempts to determine the properties of axion stars. We begin with a brief overview of the Standard Model, axions, and bosonic condensates in general. Then, in the context of axion stars, we will present our recent work, which includes: numerical estimates of the macroscopic properties (mass, radius, and particle number) of gravitationally stable axion stars; a cal- culation of their decay lifetime through number-changing interactions; an analysis of the gravitational collapse process for very heavy states; and an investigation of the implications of axion stars as dark matter. The basic conclusions of our work are that weakly-bound axion stars are only stable up to some calculable maximum mass, whereas states with larger masses collapse to a small radius, but do not form black holes. During collapse, a rapidly increasing binding energy implies a fast rate of decay to relativistic particles, giving rise to a Bosenova. Axion stars that are otherwise stable could be caused to collapse ei- ther by accretion of free particles to masses above the maximum, or through astrophysical collisions; in the latter case, we estimate the rate of collisions and the parameter space relevant to induced collapse. iv v Acknowledgements I would first like to thank my advisor, L.C.R. Wijewardhana, who as a mentor and role-model, pushed me to be successful; I could not have asked for a more supportive, encouraging, or dedicated advisor. I would also like to thank Peter Suranyi, from whom I have learned a great deal and without whom this work would not have been possible. I also thank my family, for providing encouragement throughout this process; where friendship is fragile, family is robust, and I thank them for their unwavering support. In my development as a physicist, I am indebted to Philip Argyres, Paddy Fox, Roni Harnik, Frank Pinski, and Jure Zupan, who provided important guidance, as well as many opportunities that would not have existed otherwise. In my development as a person, I sincerely thank Stephanie Burkus, Carrie Doyle, Matteo Lotito, Brian Maddock, Patrick Malsom, Jonathan Thompson, Douglas Tuckler, Kelsey Turner, and Sarah Unser, who were by my side as I traversed the best and worst of graduate school. This road would have been much more difficult without them. I further thank Kay Kinoshita, Chris Kouvaris, Madelyn Leembruggen, Joseph Leeney, Michael Ma, Niklas Gronlund Nielsen, and Cenalo Vaz, who made crucial contributions to this work as well. Finally, I would like to thank Jerry Hinnefeld, Ilan Levine, Monika Lynker, and Rolf Schimmrigk, for guidance in my very early years of studying science, and for nurturing the potential they saw in me. To the latter, I have not forgotten that I owe a paper on the topic of General Relativity. Though it is now more than six years late, I hope this will suffice. vi vii Preface This dissertation describes my research related to axions and axion stars as a com- ponent of dark matter. Chapter1 gives a basic introduction to the Standard Model of particle physics and the LCDM model of cosmology, and briefly outlines the relevant successes and failures of both. Axions are introduced in Chapter2, which is followed by a historical and pedagogical introduction to boson stars in Chapter3. We turn then to the particular case of axion stars. The macroscopic properties, including mass and radius, of weakly-bound axion stars are calculated in Chapter4. In Chapter5, we take into account axion self-interactions which lead to number-changing transitions in an axion star, leading to a nontrivial lifetime for axion stars to decay to relativistic free particles. The collapse of gravitationally unstable states is detailed in Chapter 6, and in Chapter7, the question is considered whether collapse can be triggered by astrophysical collisions. Concluding remarks are found in Chapter8. In what follows, we will use Greek characters (a, b, g, etc.) to denote Lorentz indices, early-alphabet Latin characters (a, b, c, etc.) for gauge indices, and later-alphabet Latin characters (i, j, k, etc.) for other indices. We employ the Einstein summation convention, and use natural units, whereh ¯ = c = 1. viii Contents List of Figures xiii List of Tables xvii List of Abbreviations xix 1. Introduction3 1.1. The Standard Model of Particle Physics...................3 1.2. The LCDM Model of Cosmology.......................6 1.3. Summary.....................................9 2. Axions in the Early Universe 11 2.1. The Strong CP Problem............................. 11 2.2. Axion Mass and Self-Interactions....................... 14 2.3. Axions as Dark Matter............................. 16 2.3.1. The Primordial Axion Density.................... 16 2.3.2. Constraints on Cosmic Axions.................... 20 2.4. Other Types of Axions............................. 22 2.5. Summary..................................... 23 3. Methods in Investigations of Boson Stars 25 3.1. Bose Statistics and Field Theory........................ 25 3.2. Historical Overview.............................. 29 3.3. Boson Stars as Classical Fields......................... 30 3.4. Semiclassical Boson Stars............................ 33 3.5. Nonrelativistic Limit for Boson Stars..................... 34 3.5.1. Thomas-Fermi Approximation.................... 36 3.5.2. Numerical Methods.......................... 37 3.5.3. Variational Method........................... 41 3.6. Summary..................................... 44 4. Axion Stars in the Infrared Limit 47 4.1. Ruffini-Bonazzola Method for Axion Stars.................. 47 ix x Contents 4.2. Double Expansion of Equations of Motion.................. 49 4.3. Numerical Methods and Physical Quantities................ 52 4.4. Results...................................... 56 4.5. The Chiral Potential............................... 60 4.6. Summary..................................... 60 5. The Lifetime of Axion Stars 63 5.1. Symmetries and Conservation Laws..................... 63 5.2. Decay Rates................................... 66 5.2.1. Spherical Waves (Alternative Derivation).............. 71 5.3. Constraints.................................... 73 5.4. Summary..................................... 77 6. Collapse of Axion Stars 79 6.1. Setup....................................... 79 6.2. Spectrum of Axion Star States......................... 83 6.3. Collapse Process................................. 90 6.4. Emission of Relativistic Axions........................ 92 6.5. The Chiral Potential............................... 94 6.6. Summary..................................... 97 7. Collisions of Dark Matter Axion Stars 99 7.1. Axion Stars as Dark Matter.......................... 99 7.2. General Framework............................... 101 7.3. Collisions Between Pairs of Axion Stars................... 105 7.3.1. Collision Rate.............................. 105 7.3.2. Induced Collapse............................ 107 7.4. Collisions Between Axion Stars and Ordinary Stars............ 111 7.4.1. Collision Rate.............................. 111 7.4.2. Induced Collapse............................ 113 7.5. Collisions Between Axion Stars and Neutron Stars............. 118 7.5.1. Collision Rate.............................. 118 7.6. Summary..................................... 120 8. Conclusions 123 A. Expectation Values of the Axion Potential 127 A.1. N-particle Potential............................... 127 A.2. Number-Changing Operators......................... 128 B. Binding Energy Corrections to the Axion Star Mass 131 Contents xi C. Computation of the Integral I3 135 D. Boundedness of the Instanton Potential 137 Bibliography 143 xii List of Figures 1.1. The particle content of the Standard Model of particle physics. For each particle, both their spin class (spin = 0, 1/2, or 1) and mass [13] are included. Lepton and gauge boson mass uncertainties are at the < 10−4 level and are omitted...............................4 3.1. An illustration of the balance of forces for boson stars with repulsive (left) and attractive (right) self-interactions. The gravitational force is always attractive, represented by inward-pointing arrows, and the quantum kinetic pressure is always repulsive, represented by outward-pointing arrows....................................... 28 3.2. The mass-radius relation for a boson star with attractive interactions. The three circles correspond to the density profiles in Figure 3.3. The dimen- sionless variables in the plot are defined in terms of the dimensionful q m M m R ˜ = j j ˜ = 99 ones as M a˜ 2 and R99 p . Figure reproduced from [120]. 39 MP ja˜j 3.3. Three examples of density profiles in the case

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