Master of Science Thesis Thermalisation of inelastic dark matter in the Sun with a light mediator Simon Israelsson Particle and Astroparticle Physics, Department of Physics, School of Engineering Sciences, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden Stockholm, Sweden 2018 Typeset in LATEX Examensarbetesuppsats f¨or avl¨aggande av Masterexamen i Teknisk fysik, med in- riktning mot Teoretisk fysik. Master's thesis for a Master's degree in Engineering Physics in the subject area of Theoretical physics. TRITA-SCI-GRU 2018:308 c Simon Israelsson, August 2018 Printed in Sweden by Universitetsservice US AB Abstract Particle dark matter is a popular solution to the missing mass problem present in the Universe. If dark matter interacts with ordinary matter, even very weakly, it might be the case that it is captured and accumulated in the Sun, where it may then annihilate into particles that we can observe here on Earth. The interaction between dark matter and standard model particles may be mediated by a light dark sector particle. This would introduce an extra recoil energy suppression into the scattering cross section for collision events, which is of the form needed to possibly also alleviate some of the observed small scale structure issues of collisionless cold dark matter. In this work we perform numerical simulations of the capture and subsequent scattering of inelastic dark matter in the Sun, in the presence of a light mediator particle. We find that the presence of the mediator results in a narrower capture region than expected without it and that it mainly affects the scattering rate in the phase space region where the highest scattering rates are found. How- ever, it is not seen to cause any noticeable difference to the radial distribution of dark matter in the Sun. No steady state is reached and the captured dark matter does not reach thermal equilibrium in the Sun. Key words: dark matter, solar capture, inelastic dark matter, light mediator. iii Sammanfattning M¨orka materiapartiklar ¨ar en popul¨ar l¨osning till avsaknaden av materia i uni- versum. Om m¨ork materia interagerar med vanlig materia, ¨aven v¨aldigt svagt, s˚askulle det kunna vara fallet att de f˚angasin och ansamlas i solen d¨ar de se- dan f¨orintas och resulterar i partiklar vi kan observera h¨ar p˚ajorden. Interaktio- nen mellan m¨ork materia och vanlig materia skulle kunna f¨ormedlas av en l¨att kraftb¨arare i den m¨orka sektorn. Detta skulle introducera ett rekylenergi-beroende i spridningstv¨arsnittet f¨or kollisioner av samma form som beh¨ovs f¨or att potentiellt avhj¨alpa ett antal observerade problem som i dagsl¨aget finns f¨or kollisionsl¨os kall m¨ork materia. I detta arbete har vi utf¨ort numeriska simuleringar av inf˚angningen och den efterf¨oljande spridningen av m¨ork materia inuti solen d˚aen l¨att kraftb¨arare ¨ar n¨arvarande. Vi kommer fram till att den l¨atta kraftb¨araren resulterar i ett mindre inf˚angningsomr˚ade ¨an vad man v¨antar sig utan dess existens, samt att den p˚averkar spridningen som mest i omr˚adenav fasrummet d¨ar den totala spridningen ¨ar som st¨orst. D¨aremot s˚averkar den inte leda till n˚agonurskiljbar skillnad f¨or den radi- ella distributionen av m¨ork materia i solen. Inget station¨art beteende n˚asoch den inf˚angadem¨orka materian uppn˚arinte termisk j¨amvikt i solen. Nyckelord: m¨ork materia, solinf˚angning,inelastisk m¨ork materia, l¨att kraftb¨arare. iv Preface Acknowledgements I would like to begin by thanking my supervisor Tommy Ohlsson for enabling me to work on this project, and Mattias Blennow for making me aware that the project was available. I would also like to thank Stefan Clementz for allowing me to pick up where he left off, for allowing me to inherit his simulation code, and for all the help and guidance he has provided throughout the project. Further I would like to thank my other office mates, Marcus and Anton, who together with Stefan provided an amusing working environment filled with interesting discussions. For their insights provided during the regularly held journal clubs and other discussions, I would also like to thank Florian and Sofiane, as well as Sandhya and Sushant. Lastly I would like to thank my family and friends who have supported me throughout the semester and the entirety of my time at KTH. v Contents Abstract . iii Sammanfattning . iv Preface v Acknowledgements . .v Contents vii 1 Introduction 1 1.1 Outline . .2 2 Background 3 2.1 Dark matter . .3 2.2 Observational evidence . .3 2.2.1 Rotation curves . .4 2.2.2 Weak lensing observations . .4 2.2.3 The cosmic microwave background . .5 2.3 Alternatives to dark matter . .6 2.4 Structure issues of dark matter . .6 2.4.1 Missing satellites . .6 2.4.2 Cusp versus core . .7 2.4.3 Too big to fail . .7 3 General theory 9 3.1 Inelastic dark matter . .9 3.2 Kinematics . 10 3.3 Orbital mechanics . 12 3.4 Differential scattering cross section . 15 3.5 Decay of the χ2 state . 18 vii viii Contents 4 Dark matter in the Sun 21 4.1 Solar capture . 22 4.2 Scattering in the Sun . 24 4.3 Dark matter distribution in the Sun . 24 5 Numerical simulations and results 27 5.1 Numerical setup . 27 5.2 Solar capture rate . 30 5.3 Solar scattering rate . 34 5.4 Time evolved distributions . 36 6 Summary and conclusions 45 Bibliography 47 Chapter 1 Introduction The first half of the 20th century resulted in some of the most successful descrip- tions of our universe as of yet in physics. The development of quantum mechanics, and later quantum field theory, provided excellent descriptions of physics on small scales explaining phenomena involving elementary particles, atoms, and molecules. Meanwhile, Einstein's theory of general relativity (GR) allowed for us to make ac- curate predictions concerning gravitational effects. It was through gravitational interactions, albeit still working using Newtonian gravity, that scientists started noticing discrepancies in the behaviour of astronomical objects [1]. The conclusion was reached that additional matter had to be unaccounted for in order to describe the observed phenomena. The nature of this matter, other than the fact that it was not visible, was, and to a large extent still is, unknown. The name dark mat- ter (DM), or \dunkle Materie" in German, was given to this missing matter [2]. Discrepancies between theory and observations were not limited to the astrophysi- cal sector. Within the particle physics community clear signs of physics beyond the standard model (SM) had also appeared. For example neutrinos, extremely light and very weakly interacting particles, are predicted by the SM to be massless [3]. This has since been proven to be incorrect as the phenomenon of neutrino oscilla- tions, which was experimentally verified in the late 90s [4] and later confirmed in the early 21st century [5], requires there to be a mass difference between the three neutrino mass eigenstates [6]. Astrophysics and particle physics now often go hand in hand attempting to resolve both issues in one go. Particle physicists attempt to extend the SM and resolve its issues while also incorporating candidates for DM and the dark sector in general, and the astrophysicists can deduce, as well as measure, astrophysical observables that constrain the particle physics models. Attempts to further probe this new dark sector have yielded no positive results and the nature of DM, beyond its gravitational interactions, is still unknown. Indirect searches for DM aim to explore this new sector by observing particle and radiation by-products due to DM interactions. A target for these types of observations is the Sun. Mas- sive bodies, such as the Sun, that generate significant gravitational potentials may 1 2 Chapter 1. Introduction capture DM particles on the occasion that they lose sufficient energy in a scattering event while passing through the body [7]. A class of DM known as inelastic DM was originally introduced to alleviate tension between the DAMA experiment [8] and the CDMS experiment [9] as they had obtained disagreeing results. Inelastic DM consists of at least two different DM states that are separated by a very small mass difference that may have significant effects on the scattering kinematics of the DM particles [10]. This thesis is concerned with the thermalisation of inelastic DM in the Sun, where the heavier state is unstable and subsequently decays. A light mediator particle is also included to mediate the scattering process between DM and target particles. For the case where both states are stable and the scattering events are point like it has previously been shown [11] that neither a steady state or equilibrium is reached in general. 1.1 Outline This thesis is organized as follows: In chapter 2 we cover some general background material concerning DM. In chapter 3 we review the basics of the DM framework known as inelastic DM and we cover most of the necessary theory for this thesis. Moving on to chapter 4 we concern ourselves with the connection between DM and the Sun. Finally, we present the results of this project in chapter 5 and summarise and conclude the thesis in chapter 6. Chapter 2 Background 2.1 Dark matter Even though the evidence for the existence of DM, covered briefly below, is rather convincing, the true nature of what exactly it is remains unknown. The list of candidates that have been proposed is very long and include, amongst many other, SM neutrinos, particles from supersymmetry, and axions.