Axel Widmark There is evidence that dark matter constitutes a majority of the Universe's matter content. Yet, we are ignorant about its nature. Dark Matter in the Solar System, Understanding dark matter requires new physics, possibly in the form of a new species of fundamental particles. So far, the evidence Galaxy, and Beyond supporting the existence of dark matter is purely gravitational, ranging from mass measurements on galactic scales, to cosmological probes Dark Matter in Solar System,the Galaxy, and Beyond such as the cosmic microwave background radiation. For many Axel Widmark proposed models of particle dark matter, the strongest constraints to its properties do not come from particle collider or direct detection experiments on Earth, but from the vast laboratory of space. This thesis focuses on such extra-terrestrial probes, and discusses three different indirect signatures of dark matter. They span a great range of spatial scales — from stellar interactions relevant to our own solar system, to the mass distribution of the Milky Way, and even cosmological signals from the dawn of the first stars. Through the macroscopic phenomenology of dark matter, the microscopic particle nature of dark matter can be constrained. Doing so is a window into new physics and a deeper understanding of the Universe we live in.

ISBN 978-91-7911-120-5

Department of Physics

Doctoral Thesis in Theoretical Physics at Stockholm University, Sweden 2020

Dark Matter in the Solar System, Galaxy, and Beyond Axel Widmark Academic dissertation for the Degree of Doctor of Philosophy in Theoretical Physics at Stockholm University to be publicly defended on Monday 25 May 2020 at 14.15 in sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21.

Abstract There is evidence that dark matter constitutes a majority of the Universe's matter content. Yet, we are ignorant about its nature. Understanding dark matter requires new physics, possibly in the form of a new species of fundamental particles. So far, the evidence supporting the existence of dark matter is purely gravitational, ranging from mass measurements on galactic scales, to cosmological probes such as the cosmic microwave background radiation. For many proposed models of particle dark matter, the strongest constraints to its properties do not come from particle collider or direct detection experiments on Earth, but from the vast laboratory of space. This thesis focuses on such extra-terrestrial probes, and discusses three different indirect signatures of dark matter. (1) A first part of this thesis is about the process of dark matter capture by the Sun, whereby dark matter annihilating in the Sun's core could give rise to an observable flux of high-energy neutrinos. In this work, I was the first to thoroughly test the common assumption that captured dark matter particles thermalise to the Sun's core temperature in negligible time. I found that the thermalisation process is short with respect to current age of the Sun, for most cases of interest. (2) A second part concerns a radio signal associated with the epoch when the first stars were born. A measurement of this signal indicated an unexpectedly low hydrogen gas temperature, which was speculated to be explained by cooling via dark matter interactions. In my work, I proposed an alternative and qualitatively different cooling mechanism via spin- dependent dark matter interactions. While bounds coming from stellar cooling excluded significant cooling for the simple model I considered, perhaps the same cooling mechanism is allowed in an alternative dark matter model. (3) Thirdly, a significant part of this thesis is about the mass distribution of the Galactic disk, which can be measured by analysing the dynamics of stars under the assumption of equilibrium. Although most of the matter in the Galactic disk is made up of stars and hydrogen gas, exact measurements can still constrain the amount of dark matter. Potentially, dark matter could form a dark disk that is co-planar with the stellar disk, arising either from the Galactic accretion of in-falling satellites or by a strongly self-interacting dark matter subcomponent. Together with my collaborators, I made significant progress in terms of the statistical modelling of stellar dynamics. I measured the matter density of the solar neighbourhood using Galactic disk stars and data from the Gaia mission. I found a surplus matter density close to the Galactic mid-plane, with respect to the observed baryonic and extrapolated dark matter halo densities. This result could be due to a dark disk structure, a misunderstood density of baryons, or due to systematics related to the data or equilibrium assumption. I also developed an alternative method for weighing the Galactic disk using stellar streams. This method does not rely on the same equilibrium assumption for stars in the Galactic disk, and will be used to provide a complementary mass measurement in future work. The different indirect probes of dark matter discussed in this thesis span a great range of spatial scales − from stellar interactions relevant to our own solar system, to the matter distribution of the Milky Way, and even cosmological signals from the dawn of the first stars. Through the macroscopic phenomenology of dark matter, the microscopic particle nature of dark matter can be constrained. Doing so is a window into new physics and a deeper understanding of the Universe we live in.

Keywords: dark matter: phenomenology, dark matter: indirect detection, dark matter: particle nature, Galactic dynamics, Galactic composition.

Stockholm 2020 http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-180534

ISBN 978-91-7911-120-5 ISBN 978-91-7911-121-2

Department of Physics

Stockholm University, 106 91 Stockholm

DARK MATTER IN THE SOLAR SYSTEM, GALAXY, AND BEYOND

Axel Widmark

Dark Matter in the Solar System, Galaxy, and Beyond

Axel Widmark ©Axel Widmark, Stockholm University 2020

ISBN print 978-91-7911-120-5 ISBN PDF 978-91-7911-121-2

Cover image: Stars in a jar, oil on canvas, Axel Widmark

Printed in Sweden by Universitetsservice US-AB, Stockholm 2020 This thesis is dedicated to my parents.

Abstract

There is evidence that dark matter constitutes a majority of the Universe’s matter content. Yet, we are ignorant about its nature. Understanding dark matter requires new physics, possibly in the form of a new species of fundamental particles. So far, the evidence supporting the existence of dark matter is purely gravitational, ranging from mass measurements on galactic scales, to cosmological probes such as the cosmic microwave background radiation. For many proposed models of particle dark matter, the strongest constraints to its properties do not come from particle collider or direct detection experiments on Earth, but from the vast laboratory of space. This thesis focuses on such extra-terrestrial probes, and discusses three di↵erent indirect signatures of dark matter. (1) A first part of this thesis is about the process of dark matter capture by the Sun, whereby dark matter annihilating in the Sun’s core could give rise to an observable flux of high-energy neutrinos. In this work, I was the first to thoroughly test the common assumption that captured dark matter particles thermalise to the Sun’s core temperature in negligible time. I found that the thermalisation process is short with respect to current age of the Sun, for most cases of interest. (2) A second part concerns a radio signal associated with the epoch when the first stars were born. A measurement of this signal indicated an unexpectedly low hydrogen gas temperature, which was speculated to be explained by cooling via dark matter interactions. In my work, I proposed an alternative and qualitatively di↵erent cooling mechanism via spin-dependent dark matter interactions. While bounds coming from stellar cooling excluded significant cooling for the simple model I considered, perhaps the same cooling mechanism is allowed in an alternative dark matter model. (3) Thirdly, a significant part of this thesis is about the mass distribution of the Galactic disk, which can be measured by analysing the dynamics of stars under the assumption of equilibrium. Although most of the matter in the Galactic disk is made up of stars and hydrogen gas, exact measurements can still constrain the amount of dark matter. Potentially, dark matter could form a dark disk that is co-planar with the stellar disk, arising either from the Galactic accretion of in-falling satellites or by a strongly self-interacting dark matter subcomponent. Together with my collaborators, I made significant progress in terms of the statistical modelling of stellar dynamics. I measured the matter density of the solar neighbourhood using Galactic disk stars and data from the Gaia mission. I found a surplus matter density close to the Galactic mid-plane, with respect to the observed baryonic and extrapolated dark matter halo densities. This result could be due to a dark disk structure, a misunderstood density of baryons, or due to systematics related to the data or equilibrium assumption. I also developed an alternative method for weighing the Galactic disk using

iii iv Abstract stellar streams. This method does not rely on the same equilibrium assumption for stars in the Galactic disk, and will be used to provide a complementary mass measurement in future work. The di↵erent indirect probes of dark matter discussed in this thesis span a great range of spatial scales – from stellar interactions relevant to our own solar system, to the mass distribution of the Milky Way, and even cosmological signals from the dawn of the first stars. Through the macroscopic phenomenology of dark matter, the microscopic particle nature of dark matter can be constrained. Doing so is a window into new physics and a deeper understanding of the Universe we live in. Svensk sammanfattning

Det finns bevis f¨oratt m¨ork materia utg¨oren majoritet av universums massa. Trots det ¨arvi ovetande om dess natur. Att f¨orst˚am¨ork materia kr¨aver ny fysik, m¨ojligtvis i form av en ny fundamentalpartikel. Hittills ¨arbevisen f¨orm¨ork materia enbart rent gravitationella, fr˚anv¨agningar av galaxer till m¨atningar p˚akosmologisk skala s˚asom den kosmiska bakgrundsstr˚alningen. F¨orm˚anga hypotetiserade partikelmodeller s˚akommer de starkaste gr¨anserna f¨orden m¨orka materiens egenskaper inte fr˚andirektdetektions- eller partikelkollisionsexperiment p˚ajorden, men ist¨allet fr˚anett betydligt st¨orre laboratorium – rymden. Den h¨aravhandlingen handlar om s˚adana utomjordiska m¨atningar, i synnerhet tre olika s¨att att indirekt observera den m¨orka materians e↵ekter. (1) En f¨orsta del av den h¨aravhandlingen handlar om solens inf˚angning av m¨ork materia, i vilken m¨ork materia skulle kunna annihilera i solens k¨arna och ge upphov till ett m¨atbart fl¨ode av h¨ogenergetiska neutriner. I det h¨ararbetet var jag den f¨orsta som noggrant testade det vanliga antagandet att termaliseringstiden f¨orinf˚angade m¨ork materia-partiklar ¨ar f¨orsumbar. Jag fann att termaliseringstiden ¨arkort j¨amf¨ort med solens ˚alder, f¨orde flesta fall av intresse. (2) En andra del handlar om en radiosignal f¨orknippad med epoken d˚ade f¨orsta stj¨arnorna bildades. En m¨atning av denna signal indikerade en mycket l˚agv¨atgastemperatur, vilket har f¨oreslagits bero p˚aspinn-oberoende interaktioner med m¨ork materia. I mitt arbete f¨oreslog jag en alternativ och kvalitativt annorlunda kylningsmekanism, via spinn-beroende interaktioner med m¨ork materia. Den enkla partikelmodell jag unders¨okte visade sig vara utesluten av gr¨anser som kommer fr˚anstj¨arnors nedkylning. Kanske kan en alternativ partikelmodell undvika dessa gr¨anser och ˚astakomma kylning enligt en liknande mekanism. (3) En tredje och stor del av den h¨aravhandlingen handlar om dynamiska v¨agningar av v˚aregen galax och dess skiva. Dess vikt kan m¨atas genom att analysera stj¨arnors position och hastighet, under antagande om ekvilibrium. St¨orre delen av massan i galaxskivan best˚arav stj¨arnor och v¨atgas, men trots det kan en exakt m¨atning begr¨ansa den totala m¨angden m¨ork materia. Potentiellt kan m¨ork materia bilda en m¨ork skiva, parallell med den stell¨ara skivan, antingen genom att ackumulera massa fr˚aninfallande galaxsatelliter eller genom en sj¨alvinteragerande subdominant m¨ork materia-komponent. Tillsammans med mina medarbetare s˚ahar jag gjort stora framsteg i fr˚agaom den statistiska modelleringen av stj¨arnpopulationers dynamik. Jag har uppm¨att den totala materiedensiteten i solens n¨aromr˚ade med hj¨alp av stj¨arnor i galaxskivan och data fr˚an Gaia-teleskopet. Mina resultat indikerar ett ¨overskott av massa i skivplanet, i f¨orh˚allande till summan av den observerade m¨angden baryonsk materia och den m¨orka materie-halons densitet. Detta resultat kan bero av en m¨ork skiva, en missf¨orst˚add m¨angd baryonsk materia, systematiska fel i datan eller

v vi Svensk sammanfattning ett felaktigt antagande om ekvilibrium. Jag har ocks˚autvecklat en alternativ metod f¨or att v¨agagalaxskivan med hj¨alp av stell¨ara str¨ommar. Denna metod beror inte av samma ekvilibriumantagande och utg¨ord¨arf¨orett komplement till v¨agningar som grundar sig i analys av stj¨arnor i galaxskivan. Denna avhandling behandlar olika indirekta metoder f¨oratt begr¨ansa den m¨orka mate- riens egenskaper. De sp¨anner ¨over ett brett register av rumsliga avst˚and – fr˚anv˚art eget solsystems storlek, till Vintergatans massf¨ordelning och signaler p˚akosmologisk skala. Genom dess makroskopiska fenomenologi kan den m¨orka materiens mikroskopiska partikelegenskaper begr¨ansas. Detta ¨arett s¨att att n¨arma sig ny fysik och n˚aen djupare f¨orst˚aelse f¨ordet universum vi lever i. Contents

Abstract iii

Svensk sammanfattning v

Preface xvii

I COMPREHENSIVE SUMMARY 1

1 Introduction 5 1.1 Evidence for dark matter 5 1.2 Dark matter candidates 10 1.3 Dark matter detection 11

2 Dark matter particle phenomenology 15 2.1 Dark matter capture by the Sun 15 2.1.1 E↵ectivefieldtheory...... 16 2.1.2 WIMP capture and annihilation ...... 18 2.1.3 Thermalisation ...... 20 2.1.4 Conclusion ...... 21 2.2 Spin-dependent dark matter and 21 cm cosmology 23 2.2.1 Reionisation and 21 cm cosmology ...... 23 2.2.2 The EDGES measurement ...... 25 2.2.3 Spin-dependent dark matter ...... 26 2.2.4 Bounds and exclusion limits ...... 28 2.2.5 Conclusion ...... 30

3 Dynamical mass measurements of the Galactic disk 31 3.1 Gaia 31 3.2 Dynamical mass measurements 33 3.2.1 Jeansmodelling...... 34 3.2.2 Distribution function modelling ...... 35 3.3 Weighing the Milky Way disk 36 3.3.1 Weighing the disk with TGAS ...... 39 3.3.2 Weighing the disk with Gaia DR2 ...... 41 3.3.3 Weighing the disk with streams ...... 47

vii viii Contents

3.4 Outlook 50

4 Conclusion 51

Bibliography 53

II INCLUDED PAPERS 65

1 Paper I 67

2 Paper II 87

3 Paper III 107

4 Paper IV 125

5 Paper V 151 List of Figures

1.1 Rotational velocity as a function of distance from the galactic centre, for spiral galaxy NGC6503. The dots represent the measured data, while the lines are contributions from gas, stellar disk, and halo dark matter. The figure is taken from Begeman et al. [12]. 7

1.2 The Bullet Cluster, in optical (yellow) and X-ray light (pink), and mass distri- bution inferred from weak lensing (blue). Image Credit: X-ray: NASA/CXC/ M.Markevitch et al. Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al. Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al. 8

1.3 Temperature fluctuations of the CMB, as measured by the Planck satellite, seen in a Mollweide projection of the sky. Orange (blue) regions correspond to high (low) temperatures. Image credit: ESA and the Planck Collaboration [16]. 9

1.4 Power spectrum of the CMB, as measured by the Planck satellite. Image credit: ESA and the Planck Collaboration [16]. 9

1.5 Feynman diagram illustrating three di↵erent strategies for detecting particle dark matter. In this diagram, an interaction (represented by the question mark) takes place between dark matter () and the Standard Model (f and f¯). Reading the diagram with time moving from left to right corresponds to indirect detection, whereby dark matter annihilates to observable Standard Model particles. Time moving in the vertical direction corresponds to direct detection and a dark matter scattering event. Time moving from right to left corresponds to producing dark matter in a collider experiment. 12

2.1 Thermalisation time medians for operators ˆ , with isoscalar (upper panel) Oi and isovector (lower panel) couplings. The coupling strength is normalized to a capture rate such that the equilibration time (t (C C ) 1/2) is equal eq. ' c a to the current age of the Sun. Using this capture rate and the current age of the solar system, significant annihilation has come into e↵ect. This is Figure 4 in Paper I. 22

2.2 CMB temperature (T), kinetic hydrogen gas temperature (TK ), and spin

temperature (Ts), as a function of redshift (z). Because the redshift decreases with time, time goes from right to left in this figure. This is figure 1 in Paper II. 25

ix x List of Figures

2.3 Form factor F (v, E ) for excitation and deexcitation as a function of colli- ± ? sional velocity. The dark fermion mass is set to m =1MeV in this figure. The constant form factor of elastic collision is also shown. This is figure 2 in Paper II. 27

2.4 CMB temperature (T), kinetic hydrogen gas temperature (TK ), and spin

temperature (Ts), as a function of redshift, where the spin temperature is a↵ected by dark matter interactions. The spin temperature is plotted for three di↵erent cases of heating of the dark fermion gas. The dark fermion is assumed to constitute 10 % of the total dark matter abundance and the

masses are m = 10 MeV and mV =1eV. The dark sector coupling constants of the three cases are independently normalised, such that all give rise to

Ts = 3 K at z = 17. This is figure 4 in Paper II. 29

3.1 Parallax of a star. In the special case that the angles ✓ and ✓0 are equal, they

also correspond to the parallax angle (✓ = ✓0 = $). The relative scales of this figure are not representative for actual stars. 32

3.2 Baryonic densities in the solar neighbourhood, as a function of height with respect to the Galactic plane (Z). The coloured regions correspond to the 1- bands for the sum total, the stars and dwarfs, and three di↵erent gas components. This is figure 3 from Paper III. 38

3.3 Completeness as a function of angular position on the sky, in a Mollweide projection. The horizontal and vertical axes correspond to Galactic longitude and latitude (increasing to the left and upwards), where the centre point is (l, b) = (0, 0). The completeness is modelled as the ratio of stars included in TGAS versus Tycho-2, where the latter is assumed to be perfectly complete. Masked regions of the sky are white. This is figure 2 in Paper III. 40

3.4 The lower panel shows the joint posterior probability density for the total

dynamical matter density in the plane (⇢0) and the density’s second order curvature with respect to height above the plane (k), for samples S1–S4 (in order green, blue, red, black). The region enclosed by the solid (dashed) line contains 68 % (90 %) of the total posterior density. The upper panel shows a

histogram over ⇢0 only. This is figure 5 in Paper III. 42

3.5 Inferred total matter density (⇢) as a function of height with respect to the Galactic plane (Z), in terms of a summary statistic over all eight samples. The three coloured bands correspond to three di↵erent ways of handling the velocity information. The grey band is the expected baryonic distribution, corresponding to the black band in Figure 3.2. This is figure 4 in Paper IV. 45 List of Figures xi

3.6 Data and model fit of a mock data stellar stream. The observables are parallax ($), Galactic longitude and latitude (l and b), proper motion in the

longitudinal and latitudinal directions (µl and µb), and radial velocity (vRV ). The dots correspond to the observed values of the respective observables (including observational errors), while the solid line is the inferred orbit of the stream, using the median values for all model parameters of the inferred

posterior density. The radial velocity (vRV ) is plotted only for the subset of stars for which it is available (60 out of 300). This is figure 4 from Paper V. 49

List of Tables

2.1 Leading order interaction operators of non-relativistic e↵ective field theory. 17

2.2 WIMP response functions, where j is the WIMP’s spin. 18

3.1 Stellar samples of Paper III. The columns are: sample name, the interval of observed absolute magnitude in the Tycho-2 V-band, the number of stars, the interval of observed parallax, the distance range corresponding to this parallax interval. 39 3.2 Stellar samples of Paper IV. The columns are: sample name, range of observed absolute magnitude in the Gaia G-band, number of stars in the sample, the percentage of stars with available radial velocity measurements, and the percentage of stars with radial velocity uncertainties smaller than 3 km/s. 43

xiii

List of accompanying papers

The following papers are included in this thesis, and are referred to by the Roman numbers assigned below.

I A. Widmark, “Thermalization time scales for WIMP capture by the Sun in e↵ective theories”, JCAP 1705, (2017), no. 05 046. DOI: 10.1088/1475-7516/2017/05/046 [arXiv:1703.06878 [hep-ph]]

II A. Widmark, “21 cm cosmology and spin temperature reduction via spin-dependent dark matter interactions”, JCAP 1906, (2019), no. 06 014. DOI: 10.1088/1475- 7516/2019/06/014 [arXiv:1902.09552 [astro-ph.CO]]

III A. Widmark, G. Monari, “The dynamical matter density in the solar neighbourhood in- ferred from Gaia DR1”, MNRAS 482, (2019) 1, 262-277. DOI: 10.1093/mnras/sty2400 [arXiv:1711.07504 [astro-ph.GA]]

IV A. Widmark, “Measuring the local matter density using Gaia DR2”, A&A 623, (2019), no. A30. DOI: 10.1051/0004-6361/201834718 [arXiv:1811.07911 [astro-ph.GA]]

V A. Widmark, K. Malhan, P.F. de Salas, S. Sivertsson, “Measuring the matter density of the Galactic disk using stellar streams”, submitted to MNRAS, (2020) [arXiv:2003.04318 [astro-ph.GA]]

The following papers are not included in the thesis.

A R. Catena, A. Widmark, “WIMP capture by the Sun in the e↵ective theory of dark matter self-interactions”, JCAP 1612, (2016), no. 12 016. DOI: 10.1088/1475- 7516/2016/12/016 [arXiv:1609.04825 [astro-ph.CO]]

B A. Widmark, B. Leistedt, D. W. Hogg, “Inferring binary and trinary stellar populations in photometric and astrometric surveys”, ApJ 857, (2018), no. 02. DOI: 10.3847/1538- 4357/aab7ee [arXiv:1801.08547 [astro-ph.SR]]

C A. Widmark, D. J. Mortlock, H. V. Peiris, “A Bayesian model for inferring properties of the local white dwarf population in astrometric and photometric surveys”, MNRAS 485, (2019) 1, 179-188. DOI: 10.1093/mnras/stz367 [arXiv:1808.00474 [astro-ph.SR]]

xv xvi List of accompanying papers

Reprints were made with permission from the publishers. Credit for Paper I and Paper II: c IOP Publishing Ltd and Sissa Medialab. Reproduced with permission. All rights reserved. Preface

Contributions to the papers

Paper I. I wrote this single-author paper as a follow-up on my Master’s Thesis, which was also on the subject of dark matter capture by the Sun. I received advice during regular meeting with Joakim Edsj¨oand Sofia Sivertsson.

Paper II. For this single-author paper, I had help from many people both in and outside the Oskar Klein Centre. Garrelt Mellema and Joakim Edsj¨owere especially helpful.

Paper III. The idea for this project came from Douglas Spolyar (my original supervisor, on sick leave). Giacomo Monari introduced me to the project idea and general method- ology. With his advice, I constructed a statistical model, carried out all numerical computations and produced the results. Writing the paper was a joint e↵ort.

Paper IV. I wrote this single-author paper as a follow-up on Paper III. Hiranya Peiris and Daniel Mortlock advised me on how to interpret and present my results.

Paper V. I had the original idea for this paper, constructed the statistical model, carried out all numerical computations and produced the results. My co-authors advised me throughout the development of this project. Writing the paper was a joint e↵ort.

Material from the Licentiate thesis

Some material of this Doctoral thesis are taken from my Licentiate thesis, which was written in May 2018. Specifically, this includes most of Chapter 1, most of Section 2.1, and some parts of Section 3.3.1 of this thesis.

Acknowledgements

First of all, I want to thank Douglas Spolyar for o↵ering me a doctoral position at Stockholm University and the Oskar Klein Centre. I had looked forward greatly to working under his supervision, but sadly he went on sick leave two months before my starting date. I am sure that working with him would have been a joyous and productive experience. Secondly, I

xvii xviii Preface

want to extend a heartfelt thanks to Joakim Edsj¨o,who has been my assistant supervisor throughout my doctoral studies. He has been a great mentor and support, not least in practical matters. Without his help, I doubt this thesis would have been written at all. Thirdly, I want to thank Jens Jasche, who has stepped in as my main supervisor towards the end of my doctoral studies. At a time I needed it, he reminded me how fun and rewarding research can be. I want to thank both Joakim and Jens for encouraging me to continue with research in the academic world. The Oskar Klein Centre has been a wonderful and inspiring research environment. The scientific expertise is broad, with many opportunities for interdisciplinary collaboration. I want to give a great thanks to all my fellow PhD students in the CoPS group for their friendship and interesting discussions about science and not science, and to the more senior members for fostering such an energetic and open atmosphere. Great thanks to my co-authors – Riccardo Catena, Giacomo Monari, Boris Leistedt, David W. Hogg, Daniel J. Mortlock, Hiranya V. Peiris, Khyati Malhan, Pablo F. de Salas, Sofia Sivertsson – as well as everyone else at the Oskar Klein Centre who have contributed to my education and body of work. Thanks to Hiranya V. Peiris for providing me with computational resources and for helping me set up collaborations with external institutions. Thanks to David W. Hogg for hosting me during a visit at the Flatiron Institute in New York. Thanks to Boris Leistedt for hosting me at University College London. Thanks to Annika Peter and John Beacom for hosting me at the Ohio State University. I am also grateful for the essential support and advice in matters not directly related to research questions – special thanks to Edward M¨ortsell, Jan Conrad, and J´onGudmundsson. Thanks to Jens Jasche, Tim Linden, Chad Finley and Francesco Torsello for their contributions to the writing of this thesis. Finally, I want to thank my family and friends, especially my parents, to whom this thesis is dedicated.

Axel Widmark Stockholm, April 2020 Part I

COMPREHENSIVE SUMMARY

1

What science cannot discover, mankind cannot know.

Bertrand Russell

Abandon knowledge and your worries are over.

Tao Te Ching, Lao Tzu

Chapter 1

Introduction

In the current cosmological paradigm, only a fraction of the total energy content of the Universe is constituted by ordinary matter. Most of the mass in the Universe, roughly five times more than the mass of ordinary matter, is of unknown nature and has only been seen through its gravitational e↵ects. Due to its elusive properties, it is known by the name of dark matter. Not only is the lion’s share of the Universe’s mass invisible to us – a dark energy of space itself, only observed through the accelerating expansion of the Universe, constitutes an even larger amount of energy. The abundances of dark matter and dark energy are well constrained in mainstream cosmological theory, to about 26 % and 69 % of the Universe’s total energy, leaving 5 % of ordinary matter [1]. The nature of dark matter and dark energy are the great mysteries of modern cosmology and astrophysics. This thesis focuses on the former. The scientific articles of this thesis, found in Part II, cover various aspects of dark matter. Paper I is about dark matter capture by the Sun, a hypothesised process that could potentially be detected in the near future. Paper II is about the possibility that a specific type of dark matter interactions could cause an observable signal in the hydrogen gas before the era of reionisation. Paper III, Paper IV and Paper V are about inferring the matter density of the Galactic disk, which informs us of the local distribution of dark matter. Before going into the details of these two articles, in Chapters 2 and 3, I present a general overview of dark matter. I discuss the evidence supporting the existence of dark matter in Section 1.1, a selection of viable candidate particles in Section 1.2, and possible methods of detection in Section 1.3. More extensive information on dark matter can be found in reviews by Bergstr¨om[2] and by Bertone et al. [3].

1.1 Evidence for dark matter

In 1687, Isaac Newton published the treatise PhilosophiæNaturalis Principia Mathematica, containing the Newtonian laws of motion and theory of gravity. With this, he provided the tools to detect unseen or invisible objects through their gravitational influence on other bodies. An astonishing application is from 1846, when the French and English astronomers Urbain Le Verrier and John Couch Adams proposed the existence of an unseen planet, in

5 6 1. Introduction order to explain the anomalous orbit of Uranus. Indeed, their German colleague John Galle could identify the planet of Neptune the very night after receiving a letter with instructions of where to look. A side-note is that Urbain Le Verrier also observed an anomaly in Mercury’s orbit and erroneously proposed the existence of another unseen planet – this anomaly would eventually be explained with Einstein’s general theory of relativity. In the early 20th century, many astronomers speculated about and attempted to measure the amount of “dark matter” in our own Galaxy, as well as other galaxies and galaxy clusters [4]. At the time, the term “dark matter” (“mati`ere obscure” in French, “dunkle Materie” in German) did not have the modern connotations of an unknown and new type of matter, but referred to any non-luminous astronomical objects, such as cold stars, asteroids, or clouds of gas. Lord Kelvin, Jules Henri Poincar´e, Ernst Opik,¨ Jacobus Kapteyn, Jan Oort, James Jeans, and Bertil Lindblad performed early dynamical mass measurements of the solar neighbourhood and were able to place rough upper limits to the local amount of non-luminous matter. In 1930, the Swedish professor Knut Lundmark measured the rotational velocities of five galaxies, and found that the mass that was necessary to keep the galaxies stable were many times larger than that of the visible matter [5]. The inferred mass-to-light ratio of the five galaxies varied from 6 to 100 times the measured mass-to-light ratio of the solar neighbourhood. Unfortunately, Lundmark’s results are largely forgotten. Often cited as the first indication of dark matter is studies of the Coma galaxy cluster in 1933 by the Swiss astronomer Fritz Zwicky. Using the virial theorem, which relates the radius and velocity dispersion of a gravitationally bound cluster of objects to the total mass of the cluster, he found a mass-to-light ratio that was very high, about 100 times that of the solar neighbourhood [6]. An interesting detail is that Zwicky relied on the Hubble constant in order to obtain the distance to the Coma cluster. At the time, the Hubble constant was over-estimated by almost an order of magnitude, which also inflated the estimated mass-to-light ratio by the same factor [3]. However, a large amount of non-luminous matter remains even after this correction. In the 1970’s, Vera Rubin made more detailed measurements of rotational velocities in spiral galaxies, and how the rotational velocity varies as a function of galactocentric radius [7]. Accounting only for the amount of visible baryonic matter, the rotational velocity of the disk in a spiral galaxy should decrease with distance from the galactic centre. Rubin measured something else, namely that the rotational velocity approaches an approximately constant value with increasing distance from the galactic centre, indicating large amount of non-luminous matter in the galaxies’ outer regions. This is illustrated in Figure 1.1. This striking observation was also confirmed and extended by other astronomers [8, 9, 10, 11]. The modern understanding is that the stellar disk of a spiral galaxy lies embedded in a larger, spherically distributed halo of dark matter. Dynamical measurements such as these are still one of the most intuitive and compelling pieces of evidence for non-collisional dark matter. In the same vein, dynamical mass measurements of spheroidal dwarf galaxies or spiral galaxies using satellite probes such as globular cluster can trace the gravitational potential and mass distribution. Today we have 1.1. Evidence for dark matter 7

Figure 1.1: Rotational velocity as a function of distance from the galactic centre, for spiral galaxy NGC6503. The dots represent the measured data, while the lines are contributions from gas, stellar disk, and halo dark matter. The figure is taken from Begeman et al. [12]. strong evidence that most of the matter in the Universe is dark, not only in the sense that it is non-luminous, but also that it is non-baryonic. We still know of dark matter only due to its gravitational e↵ects. Even so, there is evidence for dark matter in a vast range of distance scales, ranging from the sub-galactic to the cosmological scale. Another way to measure the mass of a galaxy or galaxy cluster is by gravitational lensing. Light is bent when traversing a strong gravitational field, as described by Einstein’s theory of general relativity. If two galaxies are in the same line-of-sight, the foreground galaxy will bend the light coming from the background galaxy, acting like a lens. Knowing the distance to the two objects, the strength of that lens can be related to the mass of the foreground galaxy. It is also possible to measure the mass of a galaxy cluster by studying the X-ray emissions from its intergalactic gas. In the deep gravitational well of a galaxy cluster, intergalactic gas is aggregated to form a superheated plasma which emits X-rays. The temperature of this gas is related to the total kinetic energy gained when falling into the cluster’s gravitational well, which becomes a probe for the cluster’s mass. A striking piece of evidence for non-collisional particle dark matter is the Bullet Cluster [13] and other similar systems. The Bullet Cluster, visible in Figure 1.2, consists of two separate galaxy clusters that have collided and passed through each other. While the luminous galaxies have continued on their trajectories unimpeded, the intergalactic gas has been slowed down and heated up, emitting an observed flux of X-rays. The mass distribution of the system is traced by weak gravitational lensing, where a di↵use matter distribution is seen as enveloping the luminous galaxies. This is strong evidence for non-collisional dark matter, as the di↵use matter distribution has collided and passes through without 8 1. Introduction

Figure 1.2: The Bullet Cluster, in optical (yellow) and X-ray light (pink), and mass distribu- tion inferred from weak lensing (blue). Image Credit: X-ray: NASA/CXC/M.Markevitch et al. Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al. Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.

interacting. At the cosmological scale, the cosmic microwave background radiation (CMB) is a hugely informative probe of the Universe’s composition. The CMB is a remnant from when the Universe was 380,000 years old, when the free protons and electrons of the primordial plasma bound to form neutrally charged atoms. With this phase-transition, the Universe became transparent, leaving the CMB as its last scattering surface. The CMB is very close to a perfect black body spectrum, with a present day temperature of 2.726 K. It has small deviations from a perfect black body, in the form of temperature anisotropies of 5 order 10 K. These temperature fluctuations, visible in Figure 1.3, have been measured by surveys like the Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and the Planck Satellite. These anisotropies are well described by a power spectrum of spherical harmonics, which is shown in Figure 1.4. The shape of the power spectrum is a product of primordial density fluctuations and the medium through which those fluctuations have propagated. A review on the subject of CMB cosmology can be found in for example a review by Samtleben et al. [14] or Weinberg’s Cosmology textbook [15]. The mainstream cosmological theory is called Lambda Cold Dark Matter cosmology (⇤CDM), where Lambda signifies dark energy. It is a model with six free parameters, one of 1.1. Evidence for dark matter 9

Figure 1.3: Temperature fluctuations of the CMB, as measured by the Planck satellite, seen in a Mollweide projection of the sky. Orange (blue) regions correspond to high (low) temperatures. Image credit: ESA and the Planck Collaboration [16].

Figure 1.4: Power spectrum of the CMB, as measured by the Planck satellite. Image credit: ESA and the Planck Collaboration [16]. 10 1. Introduction which is the abundance of dark matter. ⇤CDM is hugely successful in describing the CMB and its anisotropies, the abundance of light elements (hydrogen, helium, and lithium), and the accelerating expansion of the Universe. The CMB bears a clear signature of a dominant dark matter component, about 85 % of all matter, that interacts very weakly or not at all with baryonic matter. Furthermore, the large-scale structure formation of the Universe, whereby matter col- lapses to form galaxies and galaxy clusters, is driven by dark matter. Without the gravi- tational collapse of cold dark matter, small density perturbations of the baryonic matter would be washed out by radiation, delaying galaxy formation. Detailed large-scale struc- ture formation simulations, such as the Millennium Simulation [17], are consistent with observations, further supporting the ⇤CDM model and the dark matter paradigm.

1.2 Dark matter candidates

As of yet, all the particles that we know to exist are described by the Standard Model [18]. The Standard Model is a hugely successful theory, although it has some shortcomings: it describes three of the known forces of nature, but not gravity; neutrinos are massless in the Standard Model, which is inconsistent with observed neutrino oscillations; it su↵ers from some theoretical problems of naturalness or fine-tuning, where free parameters of the model have very small values (there is in principle no hinderance to very small values, but a fine-tuned value is unlikely and could be explained in a larger theoretical framework). Another reason to consider beyond Standard Model physics is that no known particle fits the criteria for dark matter. Given the observational evidence discussed in Section 1.1, particle dark matter must be: weakly interacting and invisible; • stable enough not to decay over the current age of the Universe; • cold, meaning that its kinetic energy must be small compared to its rest mass, in order • to explain the CMB and large-scale structure formation. Any electrically charged particle is excluded; the lifetime of the neutron is too short; the neutrino, produced by freeze-out1 in the early Universe, is too hot. In short, if dark matter is a particle, it is of a hitherto unknown nature. The dark matter particle candidate that is most relevant for this thesis, namely the one studied in Paper I, is the Weakly Interacting Massive Particle (WIMP). A WIMP is somewhat of an umbrella term, referring to a particle that interacts with Standard Model particles via the weak nuclear force (or perhaps a fifth force of similar properties), typically thermally produced by freeze-out in the early Universe and with a mass of around 100 GeV [19]. Such a particle is theoretically motivated by the supersymmetric extension (SUSY) to the Standard Model, which is proposed as a solution to the so-called hierarchy problem.

1The term freeze-out refers to a process of producing a relic particle density. Consider a particle that is in equilibrium at early times, when the Universe is hot and dense. As the Universe expands and cools, the particle falls out of equilibrium, meaning that its interaction rate becomes small with respect to the Hubble rate (the speed of the Universe’s expansion). Because production and annihilation of the particle stops, the Universe is left with a thermal relic of that particle, whose abundance is set by its equilibrium number density at the time of freeze-out. 1.3. Dark matter detection 11

This problem concerns the fine-tuning of the Higgs particle’s mass (mh = 125 GeV), which is the only dimensionful parameter of the Standard Model. The Standard Model is widely believed to be a low-energy e↵ective theory, and there is a priori nothing that decouples the Higgs mass from the energy scale of the theory’s ultra-violet completion (which could be the scale of quantum gravity, 1018 GeV). This is where the problem lies, because why ⇠ should the Higgs mass be so small, when in principle it should be comparable to an energy regime that is many orders of magnitude larger? SUSY provides a decoupling from this energy scale by introducing additional particles, shielding the Higgs mass from one-particle loop corrections and renormalisation [20, 21]. In SUSY’s extended set of particles, there are neutral and stable super-partners to, for example, the B, W3, and Higgs boson that could constitute potential WIMP dark matter. What makes many types of WIMPs especially interesting is that they are not only cold, massive and weakly interacting, but they also quite naturally give rise to the observed dark matter relic abundance, simply from assuming electroweak scale masses and interaction strengths [22]. This coincidence is oftentimes referred to as the “WIMP miracle”. Another well studied dark matter particle candidate is the axion. It was introduced in order to solve another fine-tuning problem of the Standard Model, known as the CP-problem of quantum chromodynamics. Quantum chromodynamics seems to obey CP-symmetry, but is lacking a clear motivation as to why it should, something that the existence of the axion would explain. It turns out that it is also a viable dark matter candidate. The axion is a boson and would be very light, of meV mass or lighter. Other possible dark matter candidates are heavier sterile neutrinos that do not interact via weak-force but through neutrino oscillations. An exotic alternative is Kaluza-Klein particles, which arise in models with additional spatial dimensions, introduced by Kaluza in 1921 when he unified electromagnetism and gravity in a theory of five dimensions. There are yet plenty of other proposed candidates: the very heavy Wimpzilla, mirror particles, very light fuzzy dark matter, primordial black holes (which do not necessarily require the existence of beyond Standard Model particles), etc.

1.3 Dark matter detection

There is a large global e↵ort to detect particle dark matter non-gravitationally. Particle dark matter is searched for in collider experiments, and indirect and direct detection experiments. These three strategies are illustrated in the diagram of Figure 1.5. They correspond to three di↵erent types of interactions and set complementary limits to dark matter particle models. Some models will have a strong signature with regards to only one of the three strategies, depending on for example the dark matter mass and annihilation mechanism. Particle dark matter can be produced in a particle collider, given that the mass of the dark matter particle is within reach of the collider’s energy. Dark matter is searched for in terms of missing energy and momentum, a sign that something very weakly interacting has been produced and escaped undetected. Collider production is especially relevant for various SUSY dark matter scenarios, which are searched for in the Large Hadron Collider 12 1. Introduction

Figure 1.5: Feynman diagram illustrating three di↵erent strategies for detecting particle dark matter. In this diagram, an interaction (represented by the question mark) takes place between dark matter () and the Standard Model (f and f¯). Reading the diagram with time moving from left to right corresponds to indirect detection, whereby dark matter annihilates to observable Standard Model particles. Time moving in the vertical direction corresponds to direct detection and a dark matter scattering event. Time moving from right to left corresponds to producing dark matter in a collider experiment. 1.3. Dark matter detection 13 at CERN. The Large Hadron Collider has for example been able to exclude the minimal Kaluza-Klein particle dark matter models [23]. For more information on dark matter in collider experiments, see reviews by Bertone et al. [24], Goodman et al. [25], and Klasen et al. [26]. In direct detection, a dark matter particle can scatter against the detector material and deposit energy that can be measured. In noble-gas detectors, a dark matter particle would cause excitation or ionisation in the detector medium. Currently, the most sensitive noble-gas experiment is XENON1T [27], using liquid xenon, which is sensitive to WIMP-like particles in the approximate range of 10 GeV to 10 TeV. The slightly lower mass range of a few GeV is probed by, for example, the cryogenic experiments Super-CDMS [28], using germanium semiconductors, and CRESST-II [29], using scintillating CaWO4 crystals. Axion dark matter is searched for with so-called cavity haloscopes, where a strong magnetic field can convert axions into photons [30, 31]. Direct detection experiments have for example excluded the sneutrino (Standard Model neutrino super-partner) as the dominant WIMP dark matter particle [32, 33, 34]. For more information on direct detection, see a review by Undagoitia [35]. Finally, there are also methods of indirect detection, whereby dark matter particle decay or annihilation could be inferred from the detection of Standard Model particles. For example, high energy photons coming from dark matter annihilation could make a convincing signal, as energy and directional origin can be well resolved. Such signals are searched for with gamma ray detectors such as the Fermi Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope [36], or by Cherenkov telescopes such as the High Energy Stereoscopic System (HESS) in Namibia [37], or the High-Altitude Water Cherenkov Observatory (HAWC) in Mexico [38]. Interestingly, an excess of di↵use gamma-rays has been observed from the centre of the Milky Way, peaked around a photon energy of a few GeV [39, 40, 41], consistent with WIMP annihilation. However, it is yet unclear whether or not this excess is explained by some other astrophysical source such as unresolved millisecond pulsars [42, 43]. Other products of dark matter annihilation could be cosmic-rays, meaning high energy particles such as protons, electrons, or neutrinos. A detection of anti-matter cosmic-rays, for example positrons, would be especially telling, because the background of anti-matter particles from other sources is very low. Two detectors that measure charged cosmic-ray particles are PAMELA [44], mounted on a Russian satellite, and the Alpha Magnetic Spectrometer [45], installed on the International Space Station. Most neutrino detectors are so-called Cherenkov light detectors, which detect electrons and mainly muons that have been produced by neutrino interactions. The largest such detector is the IceCube neutrino observatory [46]. A signal of dark matter annihilation or decay could come from the galactic core, dwarf galaxies, or even a di↵use background. The signal source relevant for Paper I is the Sun itself, where WIMPs could amass and annihilate to produce a detectable neutrino signal. This is discussed in more detail in Section 2.1.

Chapter 2

Dark matter particle phenomenology

This chapter is based on two separate articles on the topic of particle dark matter phe- nomenology – or more specifically, potential indirect non-gravitational signals of dark matter. Paper I and Section 2.1 is about dark matter capture by the Sun in a rather standard Weakly Interacting Dark Matter (WIMP) scenario, which could give rise to an observable neutrino signal coming from WIMP annihilation in the Sun’s core. Paper II and Section 2.2 concerns a more exotic dark sector that could a↵ect the spin states of hydrogen in the era of the first stars.

2.1 Dark matter capture by the Sun

In this section, I discuss the process of dark matter capture by the Sun and present my own research results on the subject, as is published in Paper I. Assuming that WIMPs are the dominant dark matter constituent, such particles will interact with massive bodies like stars or planets via the weak nuclear force. A star that is travelling through the Milky Way and its dark matter halo will have a flux of WIMPs constantly passing through its interior. Due to the WIMPs’ weak interactions (meaning rare, in this context), only a small fraction of these WIMPs will collide with atomic nuclei within this body. In some of these collisions, the WIMP will lose enough kinetic energy to become gravitationally bound, after which it is only a matter of time before the same WIMP collides again. With enough collisions, the WIMP will dissipate its kinetic energy and settle to thermal equilibrium in the host’s core. In the context of our own Sun, it could be possible to detect such a process. WIMPs that are captured by the Sun would thermalise to the Sun’s core temperature. As the population of WIMPs is built up in the core, the high concentration could cause WIMP pair annihilation into Standard Model particles. While most of these particles would be undetectable, neutrinos produced in this process could escape the Sun. They would be distinguishable from the neutrinos of the Sun’s fusion process due to the di↵erent energy scale – solar fusion neutrinos have energies of MeV scale, while WIMP annihilation would be GeV scale. Detecting a flux of high energy neutrinos from the Sun would be a smoking

15 16 2. Dark matter particle phenomenology gun of indirect dark matter detection. So far, no such signal has been seen, although it is continually searched for. The lack of a signal places limits on dark matter properties [47]. The WIMP-nucleus interactions are modelled in a framework of non-relativistic e↵ective field theory, which is described in Section 2.1.1. The capture and annihilation rates are discussed in Section 2.1.2. The thermalisation process and results of Paper I are presented in Section 2.1.3, followed by a conclusion in Section 2.1.4.

2.1.1 E↵ective field theory

The WIMP collisions with atomic nuclei are modelled in a framework of non-relativistic e↵ective field theory of WIMP-nucleon interactions, as developed by Fitzpatrick et al. [48, 49]. An e↵ective theory is an approximate description of a full theory, often in a limit of low energy. In this specific case, the full theory would describe relativistic WIMP interactions with nucleons (protons or neutrons), mediated through a heavy particle. The escape velocity of the Sun’s core is 1380 km/s, so the WIMP-nucleus collisions relevant in this scenario are far from relativistic. Hence, we can consider a non-relativistic e↵ective theory of WIMP-nucleon interactions, where the heavy mediator field has been integrated out. Even though the full theory is not known, the e↵ective field theory approach can be used as long as the symmetries of the low energy regime are respected. While a relativistic theory obeys the symmetries of Lorentz invariance, in the non-relativistic case the quantum operators must obey the symmetries of Galilean invariance. The possible quantum operators of such a theory must be built from a combination of these Hermitian operators:

N , iˆq , ˆv ?, Sˆ, SˆN , (2.1) where is the identity, ˆq is the transferred momentum of the collision, v v + q/(2µ) N ? ⌘ is called the tranverse velocity (where v is the relative velocity of the two particles before collision), and Sˆ and SˆN are the WIMP and nucleon spins. The e↵ective field theory used in this work assumes that the underlying mediator particle is heavy (with respect to other energies of the interaction) and has spin equal to or lower than 1. The possible leading order operators that can be obtained given these restrictions are listed in Table 2.1. They amount to a total of 15 operators, although operator ˆ = ˆv ? ˆv ? O2 · is excluded because it cannot be obtained as a non-relativistic limit from leading order operators in a relativistic field theory. Because there are two types of nucleons for the WIMP to interact with, the degrees of freedom for this e↵ective field theory amounts to 2 14 = 28. The interactions are ⇥ parameterized in terms of isospin: in the isoscalar case, a WIMP scatters o↵protons and neutrons in the same way; in the isovector case, they scatter o↵protons and neutrons with opposite signs (giving rise to destructive interference in a He4 nucleus, for example). Let ⌧ be the index signifying isospin (0 for isoscalar and 1 for isovector), k be the index over possible operators, and i be an index over the A nucleons in a given nucleus, then the WIMP-nucleus Hamiltonian density is 2.1. Dark matter capture by the Sun 17

ˆq ˆ1 = N ˆ9 = iSˆ SˆN O O · ⇥ mN ˆq ˆq ˆ3 = iSˆN ˆv ? ˆ10 = iSˆN ⇣ ⌘ O · mN ⇥ O · mN ˆq ˆ4 = Sˆ Sˆ⇣N ⌘ ˆ11 = iSˆ O · O · mN ˆq ˆ5 = iSˆ ˆv ? ˆ12 = Sˆ SˆN ˆv ? O · mN ⇥ O · ⇥ ˆq ˆq ˆq ˆ6 = Sˆ ⇣ SˆN ⌘ ˆ13 = i Sˆ⇣ ˆv ? SˆN⌘ O · mN · mN O · · mN ˆq ˆ7 = S⇣ˆN ˆv ? ⌘⇣ ⌘ ˆ14 = i ⇣Sˆ ⌘⇣SˆN ˆv ?⌘ O · O · mN · ˆq ˆq ˆ8 = Sˆ ˆv ? ˆ15 = ⇣ Sˆ ⌘⇣ SˆN ⌘ˆv ? O · O · mN ⇥ · mN ⇣ ⌘h⇣ ⌘ i Table 2.1: Leading order interaction operators of non-relativistic e↵ective field theory.

A 15 ˆ(r)= c⌧ ˆ(i)(r)t⌧ . (2.2) H kOk (i) ⌧=0,1 Xi=1 X Xk=1 ⌧ The quantity t(i) is a matrix that projects a nucleon state onto a isospin or isoscalar state. ⌧ The coecients ck are the 28 coupling constants. They have dimension of inverse mass squared. The interaction rate for WIMP-nuclei collisions is expressed in terms of a di↵erential cross section, that depend on the amplitudes of the transferred momentum (q) and the collisional velocity (w), according to

d 1 2m q2 T 2 2 T ⌧⌧0 2 ⌧⌧0 2 (w , q )= 2 RM vT? , 2 WM (q ) dER 2JT +1 w ( mN ⌧ ⌧ 0 ✓ ◆ X2 X 2 ⌧⌧ 2 q ⌧⌧ 2 ⌧⌧ 2 q ⌧⌧ 2 + R 0 v? , W 0 (q )+R 0 v? , W 0 (q ) ⌃00 T m2 ⌃00 ⌃0 T m2 ⌃0 ✓ N ◆ ✓ N ◆ 2 2 2 q ⌧⌧ 2 q ⌧⌧ 2 ⌧⌧ 2 q ⌧⌧ 2 + R 0 v? , W 0 (q )+R 0 v? , W 0 (q ) m2 00 T m2 00 00M T m2 00M N " ✓ N ◆ ✓ N ◆ q2 q2 ⌧⌧0 2 ⌧⌧0 2 ⌧⌧0 2 ⌧⌧0 2 + R˜ vT? , 2 W˜ (q )+R vT? , 2 W (q ) 0 m 0 m ✓ N ◆ ✓ N ◆ 2 ⌧⌧ 2 q ⌧⌧ 2 + R 0 v? , W 0 (q ) , (2.3) ⌃0 T m2 ⌃0 ✓ N ◆ #) where ER is the recoil energy in the target rest frame, JT is the spin of the target nucleus, 2 mT and mN are the masses of the target nucleus and an individual nucleon, vT? is the squared transverse velocity with respect to the nuclei as a whole, R⌧⌧0 are the WIMP response functions (listed in Table 2.2), and W ⌧⌧0 are the nuclear response functions (unique for each nucleus). More details can be found in Refs. [48, 49, 50]. 18 2. Dark matter particle phenomenology

2 2 ⌧⌧0 ⌧ ⌧ 0 j(j+1) q 2 ⌧ ⌧ 0 2 ⌧ ⌧ 0 q ⌧ ⌧ 0 RM = c1c1 + 3 2 vT? c5c5 + vT? c8c8 + 2 c11c11 mN mN 2 ⇣ 2 2 ⌘ ⌧⌧0 q ⌧ ⌧ 0 j(j+1) ⌧ q ⌧ ⌧ 0 q ⌧ 0 R = 4m2 c3c3 + 12 c12 m2 c15 c12 m2 c15 00 N N N ⇣ 2 ⌘⇣ ⌘ ⌧⌧0 ⌧ ⌧ 0 j(j+1) ⌧ q ⌧ ⌧ 0 R M = c3c1 + 3 c12 m2 c15 c11 00 N ⇣ 2 ⌘ ⌧⌧0 j(j+1) ⌧ ⌧ 0 q ⌧ ⌧ 0 R˜ = 12 c12c12 + 2 c13c13 0 mN 2 ⇣ ⌘ 2 ⌧⌧0 q ⌧ ⌧ 0 j(j+1) ⌧ ⌧ 0 q ⌧ ⌧ 0 ⌧ ⌧ 0 R⌃ = 2 c10c10 + 12 c4c4 + 2 (c4c6 + c6c4 )+ 00 4mN mN 4 2 q ⌧ ⌧ 0 2 ⌧ ⌧h0 q 2 ⌧ ⌧ 0 + 4 c6c6 + vT? c12c12 + 2 vT? c14c14 mN mN 2 i 2 ⌧⌧0 1 q 2 ⌧ ⌧ 0 2 ⌧ ⌧ 0 j(j+1) ⌧ ⌧ 0 q ⌧ ⌧ 0 R⌃ = 8 2 vT? c3c3 + vT? c7c7 + 12 c4c4 + 2 c9c9 + 0 mN mN v 2 2 2 2 ⇣T? ⌧ q ⌧ ⌧ 0 ⌘ q ⌧ 0 hq 2 ⌧ ⌧ 0 + 2 c12 m2 c15 c12 m2 c15 + 2m2 vT? c14c14 N N N ⇣ 2 ⌘⇣ ⌘i ⌧⌧0 j(j+1) q ⌧ ⌧ 0 ⌧ ⌧ 0 R = 3 2 c5c5 + c8c8 mN j (j +1) ⇣ ⌘ R⌧⌧0 = c⌧ c⌧ 0 c⌧ c⌧ 0 ⌃0 3 5 4 8 9 ⇣ ⌘

Table 2.2: WIMP response functions, where j is the WIMP’s spin.

2.1.2 WIMP capture and annihilation

The process of capture and annihilation of WIMPs in the Sun is described by the following di↵erential equation, dN = C C N 2, (2.4) dt c a

where N is the number of captured WIMPs, Cc is the capture rate by solar nuclei, and Ca is the annihilation rate. The annihilation factor has an N 2 dependence, as WIMPs annihilate in pairs. The di↵erential equation has the solution

C N = c tanh C C t , (2.5) C c a r a ⇣p ⌘ where t = 0 is the time of the Sun’s formation (at which the amount of captured WIMPs was N = 0). In these equations, it is assumed that we can neglect the process of evaporation (whereby captured WIMPs are up-scattered to above solar escape velocity, relevant only for very light WIMPs [51, 52], m . 3 GeV), and also the time it takes for captured WIMPs to thermalise. Whether or not the thermalisation time can be neglected is discussed in Section 2.1.3. In order to calculate the capture rate of WIMPs, we need to model the velocity distri- bution of WIMPs in the solar rest frame, the probability of scatter with di↵erent atomic nuclei, and the kinematics of such a collision. Given these pieces, the capture rate can be calculated as an integral over the flux of WIMPs passing through the Sun, the density of di↵erent nuclear species in the Sun, times the probability of a scattering event that results in a WIMP velocity lower than the escape velocity. This is described below. 2.1. Dark matter capture by the Sun 19

First, I make the following definitions. The quantity u always refers to the speed of a WIMP that is unperturbed by the Sun’s gravitational field. When including the Sun’s gravitational e↵ects, the speed is written

w = u2 + v(r)2, (2.6) p where v(r) is the escape velocity at radius r with respect to the Sun’s centre. As is commonly assumed, I take the WIMP velocity distribution to be a thermal Maxwell- Boltzmann distribution of 3D velocity dispersion v¯ = 270 km/s. The velocity distribution in the solar rest frame is found by boosting the velocity distribution by the Sun’s speed through the galaxy, taken to be v = 220 km/s. This gives a velocity distribution of WIMPs in the solar rest frame, unperturbed by the Sun’s gravitational field,

4 2 x2 ⌘2 sinh 2x⌘ f(u)du = n x e e dx, (2.7) p⇡ 2x⌘ where n is the number density of WIMPs at the Sun’s position, given by the dark matter mass density of 0.4 GeV/cm3; x is proportional to the WIMP speed u according to x2 = 3(u/v¯)2/2; and ⌘ is proportional to the Sun’s velocity v according to ⌘2 = 3(v /v¯)2/2. In order to calculate the total capture rate, let us first consider the capture rate by a thin shell of matter sitting in the gravitational potential of the Sun [53]. Assuming homogeneity for the dark matter halo at distances far enough not to be perturbed by the Sun’s gravitational field, the rate of WIMPs passing the Sun with speed u and angular momentum per unit mass J is f(u) 2⇡JdJ du. (2.8) u Consider a spherical shell of thickness dr and radius r, where the escape velocity is v(r). To reach this shell, the angular momentum per unit mass must fulfil that J

1/2 J 2 2 1 dr, (2.9) rw  ⇣ ⌘ where the factor 2 comes from the WIMP going both in and out, and the factor in brackets comes from the inclination angle of the WIMP’s orbit. The total capture rate of WIMPs with speed u for this thin shell is thus

J=rw 2 1/2 f(u) ⌦r(w) J 2 f(u) 2⇡JdJ du 2 1 dr =4⇡r drw⌦r(w) du, (2.10) J=0 u w rw u Z  ⇣ ⌘ where ⌦r(w) is the probability per unit time for the WIMP to scatter to a velocity lower than escape velocity. It is implicit that the WIMP speed at the point of scatter (w)is dependent on the WIMP speed una↵ected by gravity (u) and the local escape velocity (v), according to Equation (2.6). 20 2. Dark matter particle phenomenology

The total capture rate of the Sun becomes

r=R u= f(u) C = 4⇡r2 1 w⌦ (w) du dr. (2.11) c r u Zr=0 Zu=0

This expression looks quite compact, but a lot of information is hidden in the factor ⌦r(w). It is a sum over the relevant nuclear species, with their respective probabilities and kinematics of scatter. It can be written

2 EkµT /µ µT +,T dT ⌦r = nT w✓ 2 dEr (w, Er), (2.12) 2 u 2 2 dE µ+,T 2 ! Eku /w r XT w Z where the index T denotes the relevant target nuclear species, µ m /m is the ratio T ⌘ T between the target nucleus mass and the WIMP mass, µ (µ + 1)/2, E is the kinetic +,T ⌘ T k energy of the WIMP, Er is the recoil energy of the collision (more specifically, the energy transferred to the nucleus in the nucleus rest frame), and dT /dEr is the di↵erential cross section. The ✓ function is the Heaviside step function, to ensure that capture is kinematically possible. The lower limit of the integral corresponds to the case where the velocity of the WIMP after collision is equal to the local escape velocity.

In the expression above, the di↵erential cross section dT /dEr depends on the target nucleus, WIMP mass, and the governing interaction operator. This is modelled in a framework of e↵ective field theory, described in Section 2.1.1. When a sucient concentration of WIMPs has been amassed inside the Sun, WIMPs will start annihilating into Standard Model particles. The rate of annihilation is equal to

4⇡ v 1 C = h A i ✏2(r)r2dr, (2.13) a N 2 Z0 which is in integral over radius with respect to the Sun’s centre, where ✏ is the number density of captured WIMPs, and v =2 10 26 cm3/s is the thermally averaged annihilation h A i ⇥ cross section [54]. It is commonly assumed that WIMPs thermalise to a density profile given by the Sun’s core temperature and gravitational potential. Because the WIMPs are locally bound to the Sun’s core where the total matter density is roughly constant, the annihilation rate follows the simple analytical form of

3/2 57 m 1 C = 2.8 10 s , (2.14) a ⇥ GeV ⇣ ⌘ using a solar core temperature of 1.57 107 K and mass density of 150 g/cm3 [55]. ⇥

2.1.3 Thermalisation

The thermalisation time is the time it takes between a WIMP’s first scattering event that binds it to the Sun’s gravitational field, to having reached thermal equilibrium with the Sun’s core after down-scattering through subsequent collisions. As mentioned in Section 2.1.2 and used in Equations (2.4) and (2.5), this time is commonly assumed to be negligible. However, if the thermalisation time is large, in the sense of being comparable to other time-scales 2.1. Dark matter capture by the Sun 21 of interest (in this case the age of the Sun, primarily), the expressions in Equations (2.4) and (2.5) are invalid, because captured WIMPs will not significantly contribute to the annihilation rate until they have been thermalised. In Paper I, the median thermalisation time is calculated with Monte-Carlo integration. I sample a large number of WIMP trajectories, from the first scattering event, to subsequent WIMP-nucleus collisions, until an energy equal to the time-averaged energy of thermalised WIMPs is reached. I account for the thermal motions of all relevant species of nuclei and take full account of the 3D kinematics of the interactions. A useful simplification comes from the spherical symmetry of the Sun, such that a WIMP’s orbit is fully described by its energy and angular momenta, analogous to how the capture rate was calculated in Section 2.1.2. Details of this calculation is provided in Paper I. The following two assumptions are tested for WIMPs within a mass range of 10–1000 GeV, and interactions governed by one of the operators of Table 2.1, with isoscalar or isovector couplings: (1) thermalised WIMPs follow a thermal profile fully described by the Sun’s core temperature and gravitational potential; (2) the thermalisation time of captured WIMPs is much shorter than the age of the Sun. I find that both assumptions are valid in the parameter space of interest, although the thermalisation time can be on the order of a billion years for masses higher than 1 TeV. Thermalisation time scales are shown in Figure 2.1, where the coupling strengths are normalised to a fixed capture rate. The thermalisation is inversely proportional to the capture rate Cc (equivalently, inversely proportional to the WIMP-nucleon cross section), as long as we remain in the optically thin regime. The thermalisation time scales di↵er by several orders of magnitude, depending on what operator governs the interaction. Another interesting result is that for most operators, the majority of the thermalisation process is actually spent in the solar interior. Exceptions to this are spin-dependent operators such as ˆ , which collide almost exclusively with hydrogen and therefore lose a small amount of O4 momentum per collision event. For these types of interactions, the WIMP typically spends most of its time on its first few bound orbits, with very large major orbital axes.

2.1.4 Conclusion

In Paper II, I tested and verified the common assumption of instantaneous thermalisation for the process the dark matter capture by the Sun, up to a WIMP mass of 1 TeV. Although the thermalisation time is small compared to the age of the Sun, it could have an e↵ect in one of the following scenarios. The Sun could pass through substructures in the Galaxy that are large enough to cause fluctuations in the capture rate, due to increased dark matter densities or even comoving structures that supply a flux of low velocity WIMPs that are more easily captured. This can also cause fluctuations in the annihilation rate, but only if the equilibration time, roughly t (C C ) 1/2, is comparable to or short with respect to eq. ' c a such fluctuations in the capture rate. In this case the thermalisation time must also be taken into consideration, as it could modify the response of the annihilation rate with respect to the capture rate. Varying capture rates have been considered [56], but has recently been shown to be very unlikely [57]. 22 2. Dark matter particle phenomenology

Figure 2.1: Thermalisation time medians for operators ˆ , with isoscalar (upper panel) and Oi isovector (lower panel) couplings. The coupling strength is normalized to a capture rate such that the equilibration time (t (C C ) 1/2) is equal to the current age of the Sun. eq. ' c a Using this capture rate and the current age of the solar system, significant annihilation has come into e↵ect. This is Figure 4 in Paper I. 2.2. Spin-dependent dark matter and 21 cm cosmology 23

If the WIMP is self-interacting, the capture rate can be significantly amplified, as captured WIMPs would constitute a second scattering target [50]. This introduces another time-scale, related to the rate at which captured WIMPs interact with the flux of halo WIMPs. If this self-interaction time scale is short with respect to the thermalisation time, it means that any captured population of WIMPs will be heated up by the halo wind faster than they are cooled by interactions with solar nuclei. In such a case a higher equilibrium temperature could be reached, or deplete the Sun of captured WIMPs altogether. Within current limits for self-interaction of a dominant dark matter component, the self-interaction time scale of WIMPs in the Sun could be roughly a billion years, in which case the thermalisation time scale is short in comparison. Only for a sub-dominant dark matter component with stronger self-interaction can this become important.

2.2 Spin-dependent dark matter and 21 cm cosmology

This section is a summary of Paper II, with the aim of explaining its core ideas and results in a more accessible manner. I present a brief background on 21 cm cosmology and how it can be used to probe the epoch of reionisation in Section 2.2.1. I discuss the alluring results of the EDGES low-band experiment and how it could be related to dark matter in Section 2.2.2. I present a novel idea for how spin-dependent dark matter can a↵ect the 21 cm signal in Section 2.2.3, as well as the exclusion limits that constrain such a model in Section 2.2.4. In Section 2.2.5, I conclude.

2.2.1 Reionisation and 21 cm cosmology

When the Universe was 380,000 years old, it had cooled enough for the primordial plasma of electrons and protons (and some other light nuclei) to bind in the form of neutral atoms – an event somewhat counter-intuitively referred to as recombination. Quite suddenly, at least from a cosmic perspective, the Universe went from opaque to transparent. After at least another 150 million years, structure formation via gravitational collapse gave birth to the first stars. This reheated the hydrogen gas, returning it to a plasma state, a phase transition known as reionisation. The interim between recombination and reionisation is known as the cosmic dark ages. As the name suggests, almost nothing can be seen from this era. An exception to the Universe’s transparency at this time is the 21 cm signal, associated with the hyperfine structure of the hydrogen atom. The ground state of the hydrogen atom, in which the electron is sitting in the lowest energy orbital, is actually split into two states with a very small energy di↵erence. This splitting corresponds to the proton and electron spins being aligned or anti-aligned, giving a total spin of one or zero, also known as the triplet and singlet states. The singlet state has a lower energy, di↵ering by E? = 5.9 µeV (roughly six orders of magnitude lower than the 13.6 eV hydrogen ionisation energy). This energy corresponds to a radio photon with a wavelength of 21 cm. Interactions with the hyperfine structure, without high energy excitations to higher electron orbitals, is very weak. The average time of spontaneous decay from the triplet to 24 2. Dark matter particle phenomenology singlet state, whereby spin and excess energy is carried away by a 21 cm photon, is roughly 100,000 years. Although feeble, a 21 cm signal can be used to probe the distribution of atomic hydrogen in the Milky Way or nearby Universe, and even the epoch of reionisation, observed as an absorption or emission feature in a radio background. Apart from spontaneous decay, hyperfine transitions of the hydrogen atom are caused by interactions with CMB photons, collisions with other gas and free plasma particles, and Lyman-↵ radiation. Lyman-↵ radiation causes hyperfine transitions via an intermediate excited electron state. This high-energy radiation is produced by the first stars, and is not present during the cosmic dark ages. The relative abundance of triplet and singlet states of the hydrogen gas, unless already in equilibrium, will imprint a feature with respect to the CMB we observe today, at a wavelength of 21 (1 + z) cm,wherez is the cosmological ⇥ redshift.

The relative abundance of triplet and singlet states, written n1 and n0, can be parametrised in terms of a spin temperature Ts, according to

n T 1 =3exp ? . (2.15) n T 0 ✓ s ◆ where T? = kBE? = 0.068 K is the temperature associated with the hyperfine transition energy, and the factor 3 comes from the multiplicity of the triplet state. Because the processes that influence the spin temperature are fast with respect to the spontaneous decay rate, we can relate the spin temperature to the the relative rates of excitation and deexcitation via the following steady state equation [58, 59],

T P + P K + P ↵ 3exp ? = 01 01 01 = T P + P K + P ↵ ✓ s ◆ 10 10 10 T T T 3A +3exp ? P K +3exp ? P ↵ (2.16) 10 T T 10 T 10 = ? ✓ K ◆ ✓ K ◆ , T A 1+ + P K + P ↵ 10 T 10 10 ✓ ? ◆ where the quantities P01 and P10 are the excitation and deexcitation rates for interactions with the CMB (), gas collisions (K), and Lyman-↵ radiation (↵), and A = 2.85 10 15 s 1 10 ⇥ is the spontaneous deexcitation rate. The final expression is found through thermodynamic relationships between the excitation and deexcitation rates, parametrised by the CMB and kinetic gas temperatures (T and TK ; the temperature of the Lyman-↵ radiation is strongly coupled to TK .). The spin temperature will tend to the temperature associated with its most dominant interaction. A more detailed description of how the spin temperature is calculated can be found in Paper II and references therein. Given the standard scenario described above, we show the evolution of the spin tempera- ture in Figure 2.2, from the time soon after recombination to the epoch of reionization. For high redshifts (early times soon after recombination) there is still a small number of free electron and protons, which couple the kinetic temperature of the hydrogen gas to that of the CMB. At a redshift of z 200, the gas temperature decouples and cools adiabatically ' at a rate of T (1 + z)2, while the CMB continues to cool at a rate of T (1 + z). K / K / 2.2. Spin-dependent dark matter and 21 cm cosmology 25

Figure 2.2: CMB temperature (T), kinetic hydrogen gas temperature (TK ), and spin temperature (Ts), as a function of redshift (z). Because the redshift decreases with time, time goes from right to left in this figure. This is figure 1 in Paper II.

Down to z 100, the spin temperature is strongly coupled to the gas temperature, due to ' gas collisions. As the universe cools and expands, such collisions become increasingly rare, and the spin temperature tends to the CMB temperature instead. At some point, around a redshift of z = 15–20, the onset of star formation heats the hydrogen gas, and produces Lyman-↵ radiation that once again couples the spin temperature to its kinetic temperature. The details of the start of star formation are highly uncertain, in terms of when and how quickly the gas is heated, how much Lyman-↵ radiation is produced, and the relative order of the two [60].

2.2.2 The EDGES measurement

In early 2018, the EDGES low-band experiment published an observation of an absorption feature in the radio tail of the CMB spectrum [61], corresponding to a 21 cm signal at redshift z 17. The depth of this absorption feature suggests a spin temperature of roughly ' Ts =3K. Such a low spin temperature is remarkable, as both the gas and CMB temperatures are significantly higher. Adiabatic cooling of the gas since its decoupling from the CMB will result in a temperature of T 7 K. The unexpectedly low spin temperature is measured to K ' 26 2. Dark matter particle phenomenology high statistical significance, but the measurement is dicult and the validity of the EDGES analysis and result has been debated [62]. Ultimately, it should be regarded with skepticism before confirmed by other independent experiments, which should produce results within the next few years (see for example Philip et al. [63]). If entertaining the thought that the EDGES result is accurate, it becomes necessary to explain the low spin temperature with some form of new physics. One proposed solution is to cool the hydrogen gas through interactions with a dark matter particle. Dark matter, thanks to its early decoupling from Standard Model particles, would be significantly colder than the hydrogen gas. If the hydrogen-dark matter interaction is mediated via a low mass mediator, its cross section would be strongly enhanced at low velocities (proportional to 4 v ), and could potentially cool the hydrogen gas in the epoch of reionisation. It is not trivial to accomplish this given the constraints on dark matter, but can be done with milli-charged dark matter [64, 65, 66, 67], which carries a small electric charge. Such models have been constrained to a small window of parameter space, where this dark matter particle constitutes one per cent of the total dark matter abundance. Such a dark matter model would reduce the kinetic temperature of the hydrogen gas, which in turn would couple to the spin temperature via Lyman-↵ radiation. For this to work, Lyman-↵ radiation from the first stars would have to be produced in significant quantity before the very same stars heats the hydrogen gas. While not an impossible scenario, this additional fine-turning might prompt the question – is it possible for a cold dark sector to couple to the spin temperature directly?

2.2.3 Spin-dependent dark matter

The essential idea of Paper II is that a spin-dependent coupling with dark matter can a↵ect the spin temperature directly, via spin-flipping inelastic collisions, without a↵ecting the kinetic temperature of the hydrogen gas. I consider a dark matter fermion with a mass (m) between 1 keV to 10 MeV, and a pseudo-vector mediator V with a mass (mV ) between 1 meV and 10 eV, coupling to nucleons (Paper II also includes the analogous case for coupling to electrons). The interactions terms of this model’s Lagrangian are written

g V ¯ µ5 + g V N¯µ5N, (2.17) L µ N µ where g and gN are coupling constants. For the dark fermion’s interactions with hydrogen, the spin flip mechanism can either excite the hydrogen atom from a singlet to a triplet state, or deexcite it from triplet to singlet. At low velocities, the inelastic cross section for interactions between the dark fermion and hydrogen is

2 2 2 ggN m ±H (v)=F (v, E?) 2 2 2 , (2.18) ± 4⇡[(mv/c) + mV ] where µv2 µv2/2 E F (v, E )=⇥ E ± ? (2.19) ± ? 2 ± ? µv2/2 ✓ ◆ 2.2. Spin-dependent dark matter and 21 cm cosmology 27

Figure 2.3: Form factor F (v, E ) for excitation and deexcitation as a function of collisional ± ? velocity. The dark fermion mass is set to m =1MeV in this figure. The constant form factor of elastic collision is also shown. This is figure 2 in Paper II.

is the inelastic form factor, equal to the ratio of ingoing and outgoing volumes of phase-space. The quantity µ m m /(m + m ) is the reduced mass of the hydrogen atom and dark ⌘ H H matter fermion, and ⇥is the Heaviside step function. The form factor is illustrated in Figure 2.3, as a function of collisional velocity. For comparison, the root mean square velocity of hydrogen at 7 K is about 0.4 km/s. 4 Low velocity enhancement of the cross section is in part due to the v factor associated with the light mediator and in part to the form factor of deexcitation. For low temperatures, deexcitation is enhanced and excitation is suppressed. The spin temperature does not couple directly to the temperature of the dark fermion gas, denoted T, but rather to an e↵ective temperature of dark fermion-hydrogen collisions, denoted T˜. The dark matter and hydrogen gases are not in thermal equilibrium, so T˜ is a mass weighted mean of their temperatures, according to ˜ 1 1 1 1 T (mH + m )=TK mH + Tm . (2.20) The two terms on the right hand side of this equation are proportional to the velocity dispersions of the respective gases. In the limit where the dark fermion velocity dispersion and mass are small, the e↵ective temperature is equal to

m T˜ = TK . (2.21) mH

In order to compute the spin temperature evolution, we now need to modify Equation (2.16) to include the excitation and deexcitation rates of dark sector interaction (P01 and P10). Further details on how this is calculated is found in Paper II. In Figure 2.4, we show how the spin temperature evolves under the influence of the dark 28 2. Dark matter particle phenomenology

sector. This is for a specific choice of masses (although the result is the same for most parts of the considered range of dark sector masses), and coupling constants that are normalised

to produce a spin temperature of Ts =3K at redshift z = 17. In order to evade dark matter self-interaction bounds, the dark fermion is assumed to be a dark matter sub-component constituting 10 % of the total dark matter abundance (see Section 2.2.4 for further details). The spin temperature is plotted for three di↵erent cases. In an idealised case, the dark

fermion gas is (a) perfectly cold (T =0K) and does not heat up through interactions with the hydrogen gas. This is an idealised case, because the dark fermion gas is absorbing energy from deexciting the hydrogen triplet states and can actually heat up to a significant degree. In a more realistic case, the dark fermion gas is (b) cold initially, but heats up with time through its interactions with hydrogen. In a third case, the dark fermion gas is (c) warm from the very beginning, such that heating via interactions with hydrogen is negligible. The three cases have di↵erent spin temperature evolutions. Cases (a) and (b) have a knee at z 200, as the e↵ective temperature T˜ follows the gas temperature T . Case ' K (c) di↵ers, because T˜ is dominated by the temperature of the dark fermion gas, which has a higher velocity dispersion than the hydrogen gas. For case (b), the dark fermion gas starts to heat up significantly at z . 80, producing a very wide and deep troth in the spin temperature evolution, with a minimum around z 60. The importance of the heating ' e↵ect that causes this troth varies depending on the abundance of the dark fermion, which was assumed to be 10 % of the total dark matter abundance. If this fraction is higher, then heating of the dark fermion gas has a smaller e↵ect, and vice versa. Only for case (c) does the spin temperature have a narrow troth with walls on both sides around z = 17, similar to what was measured by the EDGES experiment [61]. A reduction of the spin temperature down to 3 K at redshift z = 17 can be achieved if the coupling constants fulfil that

2 11 mV g g 10 . (2.22) N . ⇥ eV ⇣ ⌘ Exclusion limits to these quantities are described in the next section.

2.2.4 Bounds and exclusion limits

In this section, we discuss the limits that apply to the dark sector, and discuss whether we can fulfil the condition expressed in Equation (2.22). The dark sector considered here is of relatively low mass, both for the dark fermion (compared to the canonical mass range of WIMPs) and the dark mediator. Limits that apply to such sub-GeV models are reviewed by Green and Rajendran [68] and Knapen et al. [69].

The coupling constant g is constrained by dark matter self-interaction limits, coming mainly from the Bullet Cluster. However, a dark matter sub-component constituting less than approximately a third of the total dark matter abundance can essentially have arbitrarily

strong self-interactions [70]. For this reason we can set g = 1. Very low mediator masses are excluded by fifth force constraints [71], but for most 2.2. Spin-dependent dark matter and 21 cm cosmology 29

Figure 2.4: CMB temperature (T), kinetic hydrogen gas temperature (TK ), and spin temperature (Ts), as a function of redshift, where the spin temperature is a↵ected by dark matter interactions. The spin temperature is plotted for three di↵erent cases of heating of the dark fermion gas. The dark fermion is assumed to constitute 10 % of the total dark matter abundance and the masses are m = 10 MeV and mV =1eV. The dark sector coupling constants of the three cases are independently normalised, such that all give rise to Ts = 3 K at z = 17. This is figure 4 in Paper II. 30 2. Dark matter particle phenomenology

of the mass range considered, the coupling constant gN is most strongly constrained by stellar cooling limits of horizontal branch stars and red giants. A light mediator could be produced in the interior of such stars and escape – a cooling e↵ect that would a↵ect the stars’ evolution with time. For the largely analogous case of a scalar mediator with 12 spin-independent interactions, the coupling constant limit is gN . 10 [72, 73], where the dominant mode of cooling is the Compton process with helium: + He He + V .Ifthe ! mediator V couples to spin, this process will be suppressed due to destructive interference (He4 has zero total spin), and soften this limit. On the other hand, production of the pseudo-vector mediator is enhanced in the low energy regime, due to enhanced production of its longitudinal mode. This gives a significantly stronger limit (not accounting for the e↵ect of destructive interference) of g 10 17 (m /eV). The nature of this low-energy N . ⇥ V enhancement is contingent on the complete particle model and how the mass of the mediator is generated. Although beyond the scope of Paper II, maybe a more complete dark sector model can soften the strong bounds that arise from longitudinal mode enhancement. In summary, it seems challenging to fulfil the condition expressed in Equation (2.22). 11 Only with some fine-tuned model building can a coupling constant of gN = 10 be allowed, if at all possible.

2.2.5 Conclusion

This project contains a great variety of interesting physics, from collisional mechanism and particle physics, to the expansion of the Universe and birth of the first stars. It is based on the alluring result of the EDGES low-band experiment which, if taken seriously, is an indication of new physics. The conservative interpretation is that the EDGES result is incorrect, and that future experiments will favour a more standard scenario for the spin temperature’s evolution. If the result persists, on the other hand, it might be a first non-gravitational indication of dark matter. In Paper II, I explored the possibility that the spin temperature is a↵ected by spin- dependent dark matter interactions. For the simple dark matter model I considered, su- ciently strong interactions are excluded. Perhaps these bounds can be softened by a more complete particle model, although probably at the cost of being very fine tuned. Perhaps a similar model can reduce the spin temperature by the same mechanism, for example by dark matter particles in an even lower mass range. I look forward to seeing future measurements of the 21 cm signal from the epoch of reionisation. Chapter 3

Dynamical mass measurements of the Galactic disk

This chapter is based on Paper III, Paper IV, and Paper V, which are about determining the total matter density of the Galactic1 disk using the Gaia space telescope. Gaia is an astrometric mission, meaning it measures the position and velocity of stars in the Milky Way. This data can be used to perform dynamical mass measurements. This chapter contains a background on the Gaia mission in Section 3.1, a summary of dynamical mass measurement theory in Section 3.2, its application to the Galactic disk in Section 3.3, and an outlook for future work in Section 3.4.

3.1 Gaia

The Gaia mission is an astrometric space telescope that was launched by the European Space Agency in December 2013. It had its first data release (DR1) in September 2016 [74], its second data release (DR2) in April 2018 [75], and is scheduled for its fifth and final data release in early 2022.2 The telescope measures angular position, parallax, proper motion, and two-band photometry of stellar objects. For a subset of bright stars it also measures the radial velocity (or line-of-sight velocity), inferred from the redshift of stellar emission lines observed with a near-infrared spectrograph [76]. Gaia has an end-of-mission limiting magnitude of m 21. The limiting magnitude for radial velocities is m 13 for DR2, G ' G ' and the projected end-of-mission limit is m 14.5. G ' The parallax, denoted $, is a way of measuring distance by triangulation. This is illustrated in the schematic of Figure 3.1. The angular position of a star is measured from di↵erent positions of the Earth’s orbit around the Sun, giving rise to a small angular shift. This shift corresponds to the parallax, which is related to the distance (s) to the star, according to R $ 1 s = pc, (3.1) sin($) ' arcsecond ⇣ ⌘ where R is Earth’s orbital radius. The final expression on the right hand side uses the 1When writing “Galaxy” or “Galactic” with a capital G, it refers to our own Milky Way. 2More information about the Gaia mission can be found at https://sci.esa.int/web/gaia

31 32 3. Dynamical mass measurements of the Galactic disk

Figure 3.1: Parallax of a star. In the special case that the angles ✓ and ✓0 are equal, they also correspond to the parallax angle (✓ = ✓0 = $). The relative scales of this figure are not representative for actual stars. small angle approximation. The angular position of a star is given by longitude l and latitude b in right-handed

Galactic coordinates, where (l, b)=(0,0) corresponds to the direction towards the Galactic centre, and b = 90 is the direction of Galactic north. The proper motions, denoted µl and µb, are the angular velocities in the longitudinal and latitudinal directions, which are proportional to the star’s velocities perpendicular to the line-of-sight. For the subset of Gaia data that includes radial velocity measurements, full 6d phase-space information is available. Already with Gaia DR2, the catalogue boasts a total of 1.3 billion stars with astrometric data, and 720,000 stars with radial velocity information. The end-of-mission precision for bright stars will be on the order of 0.01 milliarcseconds (mas) for the parallax and 1 0.01 mas yr for proper motions. For a star at a distance of 1 kpc, the parallax uncertainty corresponds to about 10 pc in distance. Given a fixed distance of 1 kpc, the proper motion uncertainty corresponds to 0.05 km/s in velocity. The radial velocity has an uncertainty of 0.3 km/s. This can be compared to Hipparcos, the state-of-the-art astrometric mission of ⇠ the 1990’s, which had a parallax precision of 1 mas and contained roughly 100,000 stars ⇠ [77]. The Gaia DR1 catalogue contained only angular position and photometry, but was cross-correlated with the Hipparcos and Tycho-2 catalogues, to produce the Tycho-Gaia Astrometric Solution (TGAS) catalogue containing 2.5 million stellar objects with parallax and proper motion [78]. This catalogue was used in Paper III, where systematics, such as severe selection e↵ects, constituted a major challenge. The more precise and complete DR2 3.2. Dynamical mass measurements 33 catalogue was used in Paper IV. Paper V is a demonstration of a method on mock data, which was generated using the projected Gaia end-of-mission observational uncertainties.

3.2 Dynamical mass measurements

The mass of astronomical objects can be determined by studying their dynamics. For example, the mass of the Sun can be measured from the orbits of the planets, given that the gravitational constant G is independently determined. Indeed, any gravitational potential can be probed by following the trajectories of objects travelling through it. However, large scales makes it impossible to observe an object for long enough to trace its trajectory or even measure its acceleration. Under the assumption of steady-state, the mass of a system of self-gravitating bodies can still be determined from their phase-space distribution (meaning its joint six-dimensional distribution in space and velocity). A simple example of this is the virial theorem, which relates the spatial extent (Rcl.) and velocity dispersion (v)tothe mass (Mcl.) of a cluster, according to

GMcl. 2 v. (3.2) Rcl. '

In this expression, the left and right hand sides are proportional to a cluster object’s average potential and kinetic energy, respectively. In more precise terms, a collision-less fluid with phase-space density f(x, v), sitting in a gravitational potential , evolves according to the collision-less Boltzmann equation,

@f + f v f = 0. (3.3) @t rx · rv ·rx

In a steady-state system, the partial derivative with respect to time is zero (or at least close to zero for a quasi-steady-state system that changes slowly with time), such that the potential can be inferred by measuring the phase-space distribution f. The matter density ⇢ is then found via Poisson’s equation,

2 =4⇡G⇢. (3.4) rx

Stars in a gravitational potential can be seen as tracers of an underlying collision-less phase-space fluid. This tracer population is often a small subset of all stars, for example within some range in absolute luminosity, which only constitutes a small fraction of the total matter density. For the purposes of a steady-state dynamical mass measurement, the size of this fraction is insignificant – the dynamical mass measurement always informs us of the total matter density (tracer population included). In practice, measuring the phase-space derivatives of the distribution function ( f and rx f) to obtain the gravitational force ( ) is dicult due to its high dimensionality – a rv rx set of a million stars would correspond to only ten data points per phase-space dimension. For this reason, it is useful to make some further simplifications, in addition to the steady-state assumption, in order to reduce the dimensionality of the problem. Such an assumption 34 3. Dynamical mass measurements of the Galactic disk could be spherical symmetry or separability of the gravitational potential in di↵erent spatial dimensions.

3.2.1 Jeans modelling

A common mass measurement method is based on the Jeans equations, expressed in terms of the moments of the distribution function. Although this method is not used in this thesis, it is instructive in terms of the general principles of dynamical mass measurements. We can reformulate Equation (3.3), still neglecting the time derivative, in cylindrical coordinates (radius R, height z, and angle ),

@f v @f @f @ v2 @f 1 @ @f @ @f v + + v v v + = 0. (3.5) R @R R @ z @z @R R @v R R @ @v @z @v ! R ✓ ◆ z When considering a spiral galaxy like the Milky Way, the potential and phase-space distri- bution are commonly assumed to be axisymmetric, meaning that they do not vary with the azimuthal angle . Under this assumption, any derivatives with respect to can be neglected. Even in the case where the global potential is not axisymmetric, it can still be a good approximation locally, as long as the neglected terms are subdominant. By multiplying this expression by a velocity in some direction and integrating over all velocities, we obtain the Jeans equations. For example, using vz gives

1 @(R⌫ ) @(⌫2) @ Rz + z + ⌫ = 0, (3.6) R @R @z @z where the ’s are velocity dispersions (or second degree velocity moments, equivalently), and ⌫ = f d3v (3.7) Z is the spatial number density. The first term of Equation (3.6) is called the tilt term, and couples the velocities in the radial and vertical directions. Under mirror symmetry of the Galactic plane, the tilt term is zero in the Galactic mid-plane. It can also be measured directly, and has been shown to be small in the local neighbourhood, and negligible to heights perhaps as high as z = 1 kpc [79, 80, 81]. | | We can infer the gravitational force in the vertical direction using the Jeans method in the following way. We group a set of observed stars into di↵erent bins in height (z), and 2 measure the stellar number density (⌫) and vertical velocity dispersion (z ) for each bin. Using Equation (3.6), neglecting the tilt term, the variation in the summary statistics of the tracer stellar population gives an estimate of @/@z. The total matter content is then found via Poisson’s equation, which in the axisymmetric potential is

@2 1 @ @ + R =4⇡G⇢(z). (3.8) @z2 R @R @R ✓ ◆ The second term on the left hand side is called the radial term or rotational curve term, which amounts to a few per cent of the total matter density for local mass measurements. 3.2. Dynamical mass measurements 35

The advantages of Jeans modelling lie in its simplicity – it is computationally fast and does not require making any assumptions on the exact form of f. This also has drawbacks, because some information is disregarded. While the Jeans equations hold for any distribution function, second order moments give a complete description only in the special case where the velocity distribution is perfectly Gaussian. In some cases, the shape of the velocity distribution is highly informative. It is possible to consider also higher moment Jeans equations in order to account for this, although there are some distributions that cannot be described by a finite series of moment equations. Another important loss of information lies in the binning of data, which disregards observational uncertainties on individual stars as well as small scale variations. It is possible to estimate the e↵ects of observational uncertainties using Monte Carlo sampling of mock data, although this sampling does require assuming a shape for f.

3.2.2 Distribution function modelling

In this section, I describe the distribution function method, in which the phase-space distribution is fitted to data directly. The same fundamental principles hold as for Jeans modelling, and we make the same assumptions of steady-state, axisymmetry, mirror symmetry across the plane, and separability in the directions perpendicular and parallel to the Galactic disk. The assumption of separability can be stated like

(x)= (R)+ (z), k ? (3.9) f(x, v)=f (R, , vR, v) f (z, vz), k ⇥ ? thus reducing the dynamical problem to only the vertical dimension. The assumption of separability should be valid to heights of at least 500 pc, according to simulations ⇠ performed by Garbari et al. [82]. Under assumption of steady-state, f is in equilibrium ? 2 and is fully described by a distribution in vertical energy per mass: Ez (z)+vz /2. In ⌘ ? other words, the density of states with the same energy is spatially invariant, so the velocity distribution at some fixed height is related to the mid-plane velocity distribution according to

f (z, vz)dEz = f (0, vz0 )dEz. (3.10) ? ? 2 where vz0 = vz + 2 (z). The di↵erential relationship between energy and velocity is ? dEz = vz dvzp= vz0 dvz0 , so we can rewrite Equation (3.10) to read

f (z, vz)vzdvz = f (0, vz0 )vz0 dvz0 (3.11) ? ? or vz0 f (0, vz0 )vz0 f (z, vz)dvz = f (0, vz0 ) dvz0 = ? dvz0 . (3.12) ? ? 2 vz vz0 2 (z) ? The fraction vz0 /vz can be understood as the fractionalp increase in time that a star spends at a certain height, due to the star travelling at a lower velocity compared to when it passed through the Galactic mid-plane. 36 3. Dynamical mass measurements of the Galactic disk

The total number density of stars at a certain height can be calculated by integrating the distribution function over velocity, like

1 1 f (0, vz0 )vz0 ⌫(z)=2 f (z, vz)dvz =2 ? dvz0 . (3.13) ? 2 0 p2 (z) vz0 2 (z) Z Z ? ? p The factor 2 comes from using mirror symmetry f (z, vz)=f (z, vz) and integrating ? ? over only positive velocities. In the right-most expression, the lower bound of the integral corresponds to the minimum mid-plane velocity that is necessary to reach height z.Inthe special case where the mid-plane velocity distribution is described by a sum of Gaussians

with amplitudes ai and dispersions i, according to

2 vz exp 2 2i f (0, vz)= ai ✓ ◆, (3.14) ? 2 i 2⇡ X i q the stellar number density as a function of height becomes

(z) ⌫(z) ai exp ?2 . (3.15) / i Xi  We can construct our model such that its free parameters determine the mid-plane

velocity distribution f (0, vz), and the gravitational potential (z). Thus the distribution ? ? function f (z, vz) is completely described at all heights, according to the above equations. ? The distribution function can then be fitted to data by varying the model parameters, while considering the velocity information of all stars or for only a subset of stars. The matter density is given by the parameters that determine the gravitational potential via Poisson’s equation, as in Equation (3.8). The method described in this section is used in Paper III and Paper IV. A similar method is used in Paper V, in which the weight of the Galactic disk is inferred using streams. In this case, all stream stars have approximately the same vertical energy per mass, such that measuring the vertical velocity as a function of height is enough to constrain the potential (independent of variations in the stellar number density). This method is described in more detail in Section 3.3.3.

3.3 Weighing the Milky Way disk

Dynamical mass measurements of the Milky Way is a window to understanding its kinematics, history, composition and matter distribution [83, 84, 85, 86, 87, 88, 89, 90, 91, 92]. It can also give clues about the particle nature of dark matter, for example by the abundance of dark matter subhalos which can place constraints on warm or fuzzy dark matter [93, 94, 95], or kinematic signatures of self-interacting dark matter [96, 97]. On large scales, the Milky Way is dominated by dark matter. The solar neighbourhood and the Galactic disk, on the other hand, are dominated by baryons, with roughly equal quantities of stars and gas [98, 99, 100]. The matter density distribution of baryons in the 3.3. Weighing the Milky Way disk 37 solar neighbourhood is visible in Figure 3.2, where the di↵erent components are measured separately (not dynamically, but by direct observation). The largest uncertainties are associated with the cold gas components, which also have small scale heights, meaning that their densities decrease quickly with height. Understanding the baryonic content is interesting in its own right – for example, the local gas density is important for constraining models of star formation [101]. Dark matter is expected to constitute roughly 10 % of the total matter density in the Galactic disk, and is therefore dicult to measure precisely. The local dark matter density is important for direct and indirect dark matter searches (for example dark matter capture by the Sun, as discussed in Chapter 2.1 and Paper I), which are sensitive to the local dark matter density and velocity distribution. It is also possible that the Galactic disk contains a surplus of dark matter with respect to the Galactic halo, called a dark disk scenario. Such a structure could be formed by cold dark matter through the accretion of satellites, giving rise to a dark disk with a scale height of at least 200 pc [102], or with a dark matter sub-component with strong dissipative self-interaction, potentially giving rise to a thin dark disk with a scale height of only a few tens of parsecs [70, 103]. Measurements of the local matter density started already in the 1920s and 30s, with measurements by Kapteyn and Oort, whose results were remarkably consistent with current estimates. In the late 90s, great progress was made due to the Hipparcos mission, suggesting 3 3 that the total matter density of the solar neighbourhood is ⇢0 0.1 M pc [104, 105]. A ' more detailed historical account of this can be found in the introduction of Paper III or a review by Read [106]. With Paper III and especially Paper IV, we made significant progress in terms of statistical modelling, with respect to other similar studies. We account for the full error covariance matrix of astrometric observables of all stars; we perform a joint fit of the vertical velocity distribution and stellar number density distribution; we fit relatively model- independent distributions for the stars’ vertical velocities and the total matter density (e.g. not relying on any underlying model for the baryonic distribution); and we use more samples and significantly higher number of stars that any other similar study. To a large part, mass measurements of the Galactic disk is a game of controlling systematics. It is a problem of precise statistics – a bias in the stellar number density of only a few per cent can severely alter the inferred result. It is critical that the selection function and data systematics are well understood, and that the tracer population is uniform over the considered volume. For example, unknown data systematics could introduce variability in the tracer population, such that properties of the stellar sample varies with distance. This type of bias could also arise due to physical reasons, such as dust extinction or multiple stellar systems that are angularly resolved only for small distances. In Sections 3.3.1 and 3.3.2 below, I summarise the method and results of Paper III, based on TGAS, and Paper IV, based on Gaia DR2. A brief summary of Paper V, about an alternative way of weighing the Galactic disk with stellar streams, is presented in Section 3.3.3. There are some di↵erences in nomenclature of this chapter and the individual

3 3 3 The conversion factor to a unit more familiar for particle physicists is M pc =37.97GeV/cm . 38 3. Dynamical mass measurements of the Galactic disk

0.10 All baryons Stars and dwarfs Cold atomic gas Molecular gas 0.08 Warm and hot gas

0.06 ) 3 pc M ( r 0.04

0.02

0.00 0 50 100 150 200 Z (pc)

Figure 3.2: Baryonic densities in the solar neighbourhood, as a function of height with respect to the Galactic plane (Z). The coloured regions correspond to the 1- bands for the sum total, the stars and dwarfs, and three di↵erent gas components. This is figure 3 from Paper III. 3.3. Weighing the Milky Way disk 39

Sample Abs. mag. # of stars $ (mas) Dist. (pc)

S1 3–5 19,350 6.25–12.5 80–160 S2 4–5.5 9,737 8–20 50–125 S3 4–4.5 11,781 5–20 50–200 S4 3–4 28,614 4–12.5 80–250

Table 3.1: Stellar samples of Paper III. The columns are: sample name, the interval of observed absolute magnitude in the Tycho-2 V-band, the number of stars, the interval of observed parallax, the distance range corresponding to this parallax interval. articles found in Part II – the definitions given in respective articles should be considered when comparing mathematical expressions.

3.3.1 Weighing the disk with TGAS

In order to weigh the Galactic disk in the solar neighbourhood, we need to measure the velocity distribution and number density distribution of a tracer stellar population. Because there is no radial velocity information in the TGAS catalogue, the only velocity information comes from proper motion measurements, corresponding to the velocities perpendicular to the line-of-sight. Since we are interested in the vertical velocity, perpendicular to the Galactic plane, this can only be measured for stars close to the plane. In Paper III, we considered the velocity information for stars with Galactic latitudes b < 20 , and added a | | vertical velocity uncertainty of sin b 40 km/s in order to account for the proper motion | |⇥ contribution of velocities parallel to the Galactic plane. The velocity distribution in the Galactic mid-plane was modelled as a sum of three Gaussians with di↵erent widths and amplitudes, as written in Equation (3.14).Wemodelled the matter density distribution as parabola,

k ⇢(z)=⇢ + z2, (3.16) 0 2 parametrized by ⇢0 and k, corresponding to the density in the mid-plane and its (strictly negative) curvature with respect to z. In addition to the mid-plane velocity distribution and the matter density distribution, the height and vertical velocity of the Sun with respect to the Galactic plane constitute two free parameters of the model. We constructed four samples of tracer stars, using cuts in observed parallax and observed absolute magnitude (given by the observed apparent magnitude and observed parallax). Because TGAS su↵ers from severe incompleteness e↵ects in both the bright and dim end, we limited ourselves to construct samples of stars with apparent magnitudes within

7.5

Figure 3.3: Completeness as a function of angular position on the sky, in a Mollweide projection. The horizontal and vertical axes correspond to Galactic longitude and latitude (increasing to the left and upwards), where the centre point is (l, b) = (0, 0). The completeness is modelled as the ratio of stars included in TGAS versus Tycho-2, where the latter is assumed to be perfectly complete. Masked regions of the sky are white. This is figure 2 in Paper III.

measurement errors. For example, some stars that are at a distance slightly greater than 160 pc can still be included in sample S1, which produces a bias if not accounted for. Furthermore, the TGAS catalogue is not complete, meaning that stars that are in principle bright enough to be included are actually missing. Due to a complicated scanning law for the Gaia telescope, some areas of the sky have significantly worse completeness than others. In order to avoid severe systematic errors, we mask parts of the sky where completeness is especially poor (< 85%), which largely corresponds to the ecliptic where the Sun has been in the way of observation. The completeness function can be seen in Figure 3.3. All these selection e↵ects are summarised in a selection function, corresponding to the probability of being included in a stellar sample. The nine population parameters are inferred in a framework of a Bayesian hierarchical model, using a Metropolis-within-Gibbs Markov chain Monte Carlo algorithm. This is a powerful way to calculate the posterior density of the population parameters, while taking full account of individual uncertainties for all stars, as well as the selection function. This is described in detail in Paper III. The samples are ordered in terms of trustworthiness – especially sample S4 is expected to su↵er from severe systematics. First of all, the form of the matter distribution, as expressed in Equation (3.16), can only be expected to be valid close to the Galactic plane – the observed baryonic distribution has heavier tails than a simple parabola, as seen in Figure 3.2. 3.3. Weighing the Milky Way disk 41

Furthermore, dust extinction e↵ects become more severe with distance and a↵ect the stellar sample construction. The e↵ects of parallax errors, and systematics associated with it, become more severe with distance, as the parallax angle approaches zero. These potential systematic biases are all worsened with greater distance, and sample S4 is the most distant – it has a distance limit of 250 pc, which extends to at least 300 pc if we include the most severe parallax uncertainties. We considered sample S1 most trustworthy, because its upper distance limit is 160 pc, and it also contains a high number of stars. The inferred total matter density is presented in Figure 3.4, for samples S1–S4. It shows the posterior distribution of the mid-plane matter density (⇢0) and the density’s second order curvature with respect to height above the plane (k), as defined in Equation (3.16). Samples S1, S2, and S3 agree to within statistical errors, while S4 is in tension with S1 and S3. Sample S2, which only extends to about 125 pc in distance and contains the fewest number of stars of all samples, does not constrain the dynamical density very well. Sample

S4 yields a flat and low matter density distribution (small ⇢0 and k close to zero), which can be explained by the assumed parabolic shape of the matter density profile – at these distances, the tails of density distribution are more dominant (such that a flat distribution is preferred), and we are also averaging the matter density over greater heights from the mid-plane (yielding lower ⇢0). For other samples, there is a slight degeneracy between the density parameters, where larger negative curvature k correlates with a higher mid-plane density ⇢0. For sample S1, this degeneracy corresponds to a constant integrated surface density within 100 pc of the plane. ⇠ +0.015 3 Using the results of sample S1, we find a local matter density of ⇢0 = 0.119 0.012 M pc . In the low end of the posterior, this corresponds to the expectation given the baryonic distri- 3 bution, as illustrated in Figure 3.2, and a local halo dark matter density of 0.01 M pc . ⇠ The method we have used is very similar to that of previous studies using Hipparcos data 3 by Cr´ez´eet al. [104] and Holmberg & Flynn [105], who find ⇢0 = 0.076 0.015 M pc ± 3 and ⇢0 = 0.102 0.010 M pc respectively. In terms of the Sun’s position and velocity ± with respect to the disk, our results are consistent between samples. For sample S1, we infer a height of 15.3 2.2 pc and a vertical velocity of 7.19 0.18 km/s, which agrees well with ± ± other previous publications [107, 108]. A comparison with the results of Paper IV is found in the end of Section 3.3.2.

3.3.2 Weighing the disk with Gaia DR2

Compared to the TGAS catalogue, Gaia DR2 has improved tremendously. For stars of similar apparent magnitude to what was used in Paper III, astrometric uncertainties have decreased by almost one order of magnitude, radial velocities is available for a majority of those stars, and completeness is evaluated to at least 99 %. The statistical method of Paper IV is similar to that of Paper III, although somewhat more sophisticated. The model contains a more flexible total matter distribution, includes dust extinction, accounts for the 3d velocity information of all stars, and is applied to eight separate samples containing roughly 25,000 stars each. In Paper IV, the volume considered is the same for all samples, with an upper distance 42 3. Dynamical mass measurements of the Galactic disk

Figure 3.4: The lower panel shows the joint posterior probability density for the total dynamical matter density in the plane (⇢0) and the density’s second order curvature with respect to height above the plane (k), for samples S1–S4 (in order green, blue, red, black). The region enclosed by the solid (dashed) line contains 68 % (90 %) of the total posterior density. The upper panel shows a histogram over ⇢0 only. This is figure 5 in Paper III. 3.3. Weighing the Milky Way disk 43

Name Abs. mag. # of stars RV % ˆRV < 3km/s% S1 3.0–3.7 27,010 81.2 75.7 S2 3.7–4.2 25,812 85.1 80.2 S3 4.2–4.6 23,895 88.5 83.8 S4 4.6–5.0 26,847 90.5 85.8 S5 5.0–5.35 25,568 91.2 86.3 S6 5.35–5.7 27,591 90.3 84.7 S7 5.7–6.0 24,730 89.9 83.3 S8 6.0–6.3 25,531 88.5 80.5

Table 3.2: Stellar samples of Paper IV. The columns are: sample name, range of observed absolute magnitude in the Gaia G-band, number of stars in the sample, the percentage of stars with available radial velocity measurements, and the percentage of stars with radial velocity uncertainties smaller than 3 km/s.

bound of 200 pc. The total matter distribution is modelled as a sum of sech2 functions with di↵erent scale heights, according to

z z z ⇢(z)=⇢ sech2 + ⇢ sech2 + ⇢ sech2 + ⇢ . (3.17) 1 30 pc 2 60 pc 3 120 pc 4 ✓ ◆ ✓ ◆ ✓ ◆

The densities ⇢ 1,2,3,4 are free parameters of the model, giving it quite large freedom to { } vary in shape in the considered volume, although constrained by assumptions of mirror symmetry across the plane and being monotonically decreasing with height. Further details about the statistical model can be found in Paper IV. As in Paper III, the samples are constructed in terms of the observed parallax and observed absolute magnitude. Properties of the eight stellar samples of Paper IV are listed in Table 3.2. The range of absolute magnitudes of the eight samples correspond to F and G type stars. The range in observed parallax is the same for all samples, corresponding to a distance between 100 and 200 pc. The innermost 100 pc is excluded because of systematic issues with very bright objects in Gaia. Furthermore, excluding stars at small distances lessens the potential bias coming from multiple stellar systems – for example, a binary system might be angularly resolved and seen as two separate objects at a distance of 20 pc, but seen as a single object at a distance of 200 pc, which can cause a bias due to an inhomogeneous tracer population. The main result is summarised in Figure 3.5, showing the inferred matter density as a function of height with respect to the Galactic plane. The matter density is shown in three coloured bands, where each band is a summary statistic over the eight stellar samples. The upper and lower limits of the bands at a given height correspond to the 16th and 84th percentile of a distribution which is constructed by sampling – in this sampling, each set of density parameters is a random realisations of the posterior density for a randomly 44 3. Dynamical mass measurements of the Galactic disk chosen stellar sample. In this manner, the width of the bands represents both the statistical variance within the stellar samples, as well as the variance between stellar samples. The three colours correspond to three di↵erent ways of handling the velocity information: in the first case, the velocity information of all stars is considered; in the second case, only the velocity information of stars that have good radial velocity measurements (RV < 3 km/s)is considered; in the third case, only stars with Galactic latitude b < 5 is considered (similar | | to Paper III). If the velocity information of a star is ignored, its position is space is still used in the inference. The grey band in Figure 3.5 corresponds to the baryonic distribution, as discussed in the beginning of Section 3.3. This distribution is not used in the inference itself, as the total matter density is modelled according to Equation (3.17). Instead, it is used only post-inference, in order to compare the inferred result with what is expected. 3 Given a halo dark matter density of roughly 0.01 M pc , the expected total matter density would be only slightly higher than the grey band of the baryonic distribution. The striking results seen in Figure 3.5 is that the inferred matter density has a large surplus 2 close to the mid-plane of approximately 5–9 M pc in surface density, compared to what is expected. This surplus is seen in all eight samples, for all three cases of velocity information cuts. There is some variation between samples and di↵erent velocity information cuts, which is unlikely to be explained by statistical variation alone. This indicates that there are some unmodelled systematic e↵ects that influence the inferred density distribution. However, these discrepancies are not large enough to discredit the overall result and do not indicate a large bias. See Paper IV for more detailed information. The power of inference has improved greatly with respect to the analysis performed with TGAS. In Paper III, the matter distribution was less constrained, especially in terms of its shape. There was a degeneracy between the shape and the mid-plane density, corresponding roughly to a constant surface density within 100 pc of the mid-plane. For the results of Paper 3 IV, the average matter density of within 100 pc of the plane is inferred to be 0.122 M pc , 3 with a posterior standard deviation of roughly 0.006 M pc within the stellar samples, 3 and a variance of 0.011 M pc between samples. This is in agreement with the results of 3 Paper III, in the sense that an average matter density of 0.122 M pc within 100 pc of the plane is consistent with the 68 % confidence region of sample S1 in Figure 3.4. 2 The inferred surplus surface density of 5–9 M pc is in mild tension with two other recent studies, using TGAS [109] and Gaia DR2 [110], who both set an upper bound of 2 about 7 M pc . In both of these studies, they only use the velocity information of stars with small Galactic latitudes, and they use significantly smaller and fewer stellar samples compared to the analysis of Paper IV. For the height of the Sun, the inferred result of the eight samples agree well, with an average height of 4.6 pc above the plane, with posterior standard deviations below 2 pc for all samples. This is in tension with the results of Paper III (15.3 2.2 pc), which could ± be explained by a mis-modelled TGAS completeness function. We agree well with other similar studies [110, 109], although studies that go to greater distances typically infer larger values for the Sun’s height with respect to the mid-plane, closer to Z 20 pc [107, 111, ' 3.3. Weighing the Milky Way disk 45

0.25 Full velocity information Radial velocity stars only Mid-plane velocities only 0.20 Baryonic model ) 3 0.15 pc M (

r 0.10

0.05

0.00 0 50 100 150 200 Z (pc)

Figure 3.5: Inferred total matter density (⇢) as a function of height with respect to the Galactic plane (Z), in terms of a summary statistic over all eight samples. The three coloured bands correspond to three di↵erent ways of handling the velocity information. The grey band is the expected baryonic distribution, corresponding to the black band in Figure 3.2. This is figure 4 in Paper IV. 46 3. Dynamical mass measurements of the Galactic disk

112]. This discrepancy is probably, at least in part, due to a broken symmetry across the Galactic plane at heights larger than 200 pc [112]. For the vertical velocity, the average result of the eight samples is 7.24 km/s, with posterior standard deviations of 0.1 km/s ⇠ for all samples. The variation between samples is somewhat larger than what would be expected from statistical variance. The most extreme cases are samples S3 and S8, which have posterior means of 7.45 km/s and 6.86 km/s, respectively. Overall, the inferred vertical velocity is in good agreement with other studies [108, 109, 110]. In the inferred posterior densities, there are no strong correlations between the height and vertical velocity of the Sun and other free parameters of the model. The main result of Paper IV is curious, and could be influenced by systematic biases. To begin with, the method itself is based on a few assumptions. The fundamental assumption is that the population of tracer stars is in equilibrium, such that their phase-space distribution is in a steady-state, or at least changes very slowly with time. Other important assumptions are mirror symmetry with respect to the Galactic plane, and separability of the Galactic potential in the vertical direction (I also assume separability of the vertical velocity distribution, but was able to test the validity of this assumption by di↵erent ways of handling the velocity information). According to recent studies using Gaia DR2, there are no significant bending or breathing modes (symmetric or anti-symmetric disk oscillations) in the solar neighbourhood [113]. At heights suciently far from the Galactic plane, it is clear that the distribution of stars is perturbed with respect to a symmetric, steady-state phase-space distribution, for example in the form of phase-space ridges and spirals [112, 114, 115]. These patterns are observed to be shared between all stellar populations (with di↵erent ages, metallicities and masses), indicating that they are due to an external perturbation. Stars with lower vertical energies, more confined to the Galactic plane, are probably less sensitive to external perturbations and have a shorter equilibration time (which is inversely proportional to the vertical oscillation frequency). In summary, for the small volume considered in Paper IV, there is no strong evidence for significant breaking of the assumed symmetries or a steady-state configuration. Such e↵ects could still be present and it is an open to question how and to what extent they would bias this kind of dynamical mass measurements of the Galactic disk. An important potential source of systematics is associated with the survey’s completeness. The completeness of Gaia DR2 has been evaluated to over 99 % in the considered range of apparent magnitude, which is based on a cross-match with another independent survey called 2MASS [116]. By assuming that the probability of observing a star in one survey is independent from observing a star in the other, the completeness of the two surveys can be calculated by comparing the intersecting and disjoint sets of observed stars. However, this evaluation becomes biased if some stars are intrinsically dicult to measure, for example due to stellar crowding, which breaks the assumption of independent observation in the two surveys. For this reason, it could be that the completeness function of Gaia DR2 is biased, with a dependence on Galactic latitude, which would produce a bias in the inferred matter density distribution. A completeness function that is incorrect by only a few percent can have a significant e↵ect, comparable to the surplus density discussed above. Other data 3.3. Weighing the Milky Way disk 47 systematics, for example associated with underestimated observational uncertainties, are likely negligible in terms of biasing the inferred result – this is discussed in more detail in Paper IV. A surplus matter density in the Galactic plane could be due to either an underestimated density of baryons, or a surplus associated with the dark sector. In case of the former, it is most likely an underestimated density of cold gas. Cold gas is the baryonic component with the most uncertain total matter density, and also has a small scale height in accordance with the inferred surplus surface density. In order to fully explain the result of Paper IV, the amount of cold gas would need to be quite severely underestimated [99, 100]. The latter case of a dark disk is arguably more exotic. As explained in the beginning of Section 3.3, there could be a dark disk, aligned with stellar disk of the Milky Way, with significantly higher density than the dark matter halo. The inferred shape of the matter distribution suggests a small scale height, which would favour the thin dark disk scenario. However, the exact shape of the surplus matter density is highly uncertain and especially sensitive to systematic errors. The results of Paper IV warrants further study. Some further discussion about future work and upcoming Gaia data releases can be found in Section 3.4.

3.3.3 Weighing the disk with streams

This section is a summary of Paper V, in which we present an alternative method for inferring the Galactic disk matter density using stellar streams. A stellar stream is an elongated structure of stars, formed through the tidal disruption of an accreted globular cluster or dwarf galaxy as it orbits its host galaxy’s gravitational potential. Both leading and trailing arms of stars are formed from the disrupting satel- lite, which to first order are all aligned to the same orbit. Because all stream stars have approximately the same energy per mass, their kinematics can be used to constrain the gravitational potential of the Milky Way. So far, stellar streams have provided the best constraints on the integrated Galactic halo mass and shape [117, 118, 119]. In Paper V, we demonstrate that a stream passing through or close to the Galactic mid-plane can be used to measure the disk’s integrated surface density. Not only is this measurement precise and competitive with respect to the method using disk tracer stars (as used in Paper III and Paper IV), but it is also complementary for the following reasons. The method using stellar streams does not depend on any equilibrium assumption for stars in the Galactic disk, and is also insensitive to completeness and selection function systematics that a↵ect the observed stellar number density distribution. It also opens a window to precise measurements of the disk’s matter density at distances up to a few kilo-parsec from the Sun, wherever a suitable stellar stream can be identified. The method utilises the fact that the stars of a stellar stream have approximately the same vertical energy per mass. Therefore, the gravitational potential can be probed by considering the vertical velocity of stars at di↵erent heights with respect to the Galactic mid-plane. A fundamental di↵erence with respect to the method using disk tracer stars is that this measurement does not depend on the stellar number density. 48 3. Dynamical mass measurements of the Galactic disk

To first order, the vertical velocity (w) of a stellar stream passing through the Galactic plane follows the relation 2 2 w (z)=w0 + 2 (z), (3.18) ? where w0 is the vertical velocity of the stream at its mid-plane passage, and the ? gravitational potential, following the definition of Equation (3.9) and the assumption of separability. In theory, measuring the matter density of the Galactic disk is simply a matter of fitting a curve to the stream stars in the space of height (z) and vertical velocity (w). In practice, this is more complicated. Due to the stream’s intrinsic phase-space dispersion, observational uncertainties, and missing radial velocity information, it becomes necessary to model the stellar stream’s full six-dimensional trajectory. Only by taking all of this into account can the total surface density of the Galactic disk be constrained to good precision. In Paper V, we generate mock data stellar streams, with realistic intrinsic phase-space dispersion as well as Gaia end-of-mission observational uncertainties and magnitude-limited radial velocity information, in order to test our method of inference. Each stream contains a total of 300 observed stars, located at an approximate distance of one kilo-parsec. Our model fully accounts for the intrinsic phase-space dispersion of a stellar stream, as well as observational uncertainties, and uncertainties associated with the phase-space position of the Sun in the Galactic rest frame. A fit of our model with respect to one of our mock data stellar streams, shown in the space of observables, is visible in Figure 3.6. We demonstrate that the integrated surface density within 240 pc from the Galactic mid-plane can be measured accurately and precisely, to an uncertainty as low as 6 % for the realistic mock data stellar streams that we consider. 3.3. Weighing the Milky Way disk 49

Figure 3.6: Data and model fit of a mock data stellar stream. The observables are parallax ($), Galactic longitude and latitude (l and b), proper motion in the longitudinal and latitudinal directions (µl and µb), and radial velocity (vRV ). The dots correspond to the observed values of the respective observables (including observational errors), while the solid line is the inferred orbit of the stream, using the median values for all model parameters of the inferred posterior density. The radial velocity (vRV ) is plotted only for the subset of stars for which it is available (60 out of 300). This is figure 4 from Paper V. 50 3. Dynamical mass measurements of the Galactic disk

3.4 Outlook

The local matter density of the Galactic disk was measured in Paper III and Paper IV. The results indicate a significant surplus matter density with respect to the observed baryonic distribution and extrapolated dark matter halo density. This result could be due to systematic e↵ects such as a poorly modelled completeness function or non-equilibrium dynamics, or correspond to an actual matter density surplus of baryonic and/or dark components. The observed surplus matter density warrants further study. In future projects on measuring the local density of the Galactic disk, I plan to perform similar studies of disk star kinematics, but in volumes that are not in the immediate vicinity of the Sun. This will give better control of potential systematic e↵ects, and could inform us about possible non- equilibrium dynamics and how to model them. The third data release of Gaia is scheduled for an early release in the third quarter of 2020, and a complete release in the second half of 2021.4 The quality of the data will improve, including the Gaia completeness function which could shed light on a potential biases associated with it in previous data releases. Furthermore, the prospects for finding a stellar stream passing through the Galactic disk will improve with future data releases. With a suitable stellar stream, we could make an independent measurement of the Galactic disk matter density, which is not relying on the same assumptions as the method using disk tracer stars. Overall, a robust and precise measurement of the Galactic disk matter density seems within reach. In the larger picture, it is becoming all the more interesting to reach beyond the steady- state modelling of dynamics and mass measurements performed under an equilibrium assumption. A first step could be to include first order time-dependent perturbations, such as bending or breathing modes of the Galactic disk, for which an analytical formulation of the inference problem is still possible. However, if we are to perform inference on more complicated dynamical systems, it will eventually be necessary to do so in a simulation based manner. This constitutes a significant methodological and computational challenge, especially when applied to something as complicated as the Milky Way. There are fantastic developments for statistical inference based on forward simulation, especially in the field of cosmology [120, 121]. Such methods would not only be relevant and applicable to Gaia data and our own Galaxy, but also future surveys such as LSST and extra-galactic stellar bodies. Simulation based dynamical inference will be the main focus of my upcoming scientific work.

4For the moment, it looks like these data releases are going to be delayed, due to the current outbreak of covid-19. Chapter 4

Conclusion

There is evidence that dark matter constitutes a majority of the Universe’s total matter content. As described in Chapter 1, this evidence is purely gravitational, despite large-scale e↵orts to detect it by other means. For many proposed models of particle dark matter, the strongest constraints to its properties do not come from particle collider or direct detection experiments on Earth, but from the vast laboratory of space. This thesis focuses on such extra-terrestrial probes. In particular, it concerns three di↵erent indirect signatures of dark matter. (1) Section 2.1 and Paper I are about the process of dark matter capture by the Sun. Specifically, the dark matter candidate known as the Weakly Interacting Massive Particle (WIMP) can collide with atomic nuclei in the Sun. If the WIMP loses enough kinetic energy in such a collision, it will be bound to the Sun’s gravitational field. With further collisions, a captured WIMP will eventually settle to thermal equilibrium in the Sun’s core. As the population of captured WIMPs builds up in the core, they will begin to annihilate and produce Standard Model particles. While most such particles are trapped, neutrinos can escape the solar interior due to their weak interactions. This process could potentially be detectable in neutrino telescopes on Earth. In my work, I studied the thermalisation process for captured WIMPs, meaning the process of a WIMP’s down-scattering, from first bound orbit to reaching thermal equilibration with the Sun’s interior. It is commonly assumed that a captured WIMP thermalises quickly, such that the process of thermalisation can be neglected altogether. I was the first to thoroughly test this assumption, and found that it was valid, with the exception of some fine-tuned cases. (2) Section 2.2 and Paper II concern a radio signal associated with the epoch of reionisation, when the first stars were born. The EDGES low-band experiment has measured an absorption feature in the cosmic microwave background, connected to the ratio of hyperfine states of the hydrogen gas during this epoch. The depth of this absorption feature indicated a hydrogen gas temperature that was too low to be explained by standard cosmology. While the EDGES result is highly uncertain, there have been speculations that the measurement could be explained by cooling via milli-charged dark matter interactions. In my work, I proposed an alternative and qualitatively di↵erent cooling mechanism via spin-dependent dark matter interactions. While bounds coming from stellar cooling excluded significant

51 52 4. Conclusion cooling for the simple model I considered, perhaps the same cooling mechanism is allowed in an alternative dark matter model. (3) Chapter 3 is about dynamical mass measurements of the Milky Way disk. In Paper III and Paper IV, this is performed by analysing disk stellar populations in the solar neighbourhood, using data from the astrometric Gaia mission. I made significant progress in terms of statistical modelling, for example by accounting for the observational uncertainties of every individual star in my stellar samples. With my model of inference, I found a surplus matter density in the Galactic disk, with respect to the observed baryonic and extrapolated dark matter halo densities. This result could be due to data systematics, non-equilibrium e↵ects, or indeed an actual matter density surplus. For example, dark matter could form a dark disk that is co-planar with the stellar disk, arising either from the Galactic accretion of in-falling satellites or by a strongly self-interacting dark matter subcomponent. In Paper V, we developed an alternative method for weighing the Galactic disk, using stellar streams. This method is complementary to the method using disk stars, especially because it does not rely on any equilibrium assumption for the disk stellar populations. These three di↵erent indirect probes of dark matter span a great range of spatial scales, from interactions with stars relevant to our own solar system, to the matter distribution of the Milky Way, and even cosmological signals from the epoch of reionisation. Through its macroscopic phenomenology, the microscopic particle nature of dark matter can be constrained. Doing so is a window into new physics and a deeper understanding of the Universe we live in. Bibliography

[1] Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, et al. “Planck 2018 results. VI. Cosmological parameters”. In: arXiv e-prints, arXiv:1807.06209 (July 2018). arXiv: 1807.06209 [astro-ph.CO]. [2] Lars Bergstr¨om. “Nonbaryonic dark matter: Observational evidence and detection methods”. In: Rept. Prog. Phys. 63 (2000), p. 793. doi: 10.1088/0034-4885/63/5/2r3. arXiv: hep-ph/0002126 [hep-ph]. [3] J. Silk et al. Particle Dark Matter: Observations, Models and Searches.Ed.by Gianfranco Bertone. Cambridge: Cambridge Univ. Press, 2010. isbn: 9781107653924. doi: 10.1017/CBO9780511770739. url: http: //www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521763684. [4] Gianfranco Bertone and Dan Hooper. “History of dark matter”. In: Reviews of Modern Physics 90.4, 045002 (Oct. 2018), p. 045002. doi: 10.1103/RevModPhys.90.045002. arXiv: 1605.04909 [astro-ph.CO]. [5] Popular astronomi. D¨arfor gl¨omde alla Knut Lundmarks stora uppt¨ackt. 2015. url: http://www.popularastronomi.se/2015/06/darfor-glomde-alla-knut- lundmarks-stora-upptackt-den-morka-materian/ (visited on 04/09/2020). [6] H. Andernach and F. Zwicky. “English and Spanish Translation of Zwicky’s (1933) The Redshift of Extragalactic Nebulae”. In: ArXiv e-prints (Nov. 2017). arXiv: 1711.01693 [astro-ph.IM]. [7] V. C. Rubin, N. Thonnard, and W. K. Ford Jr. “Rotational properties of 21 SC galaxies with a large range of luminosities and radii, from NGC 4605 /R = 4kpc/ to UGC 2885 /R = 122 kpc/”. In: Astrophys. J. 238 (1980), p. 471. doi: 10.1086/158003. [8] K. C. Freeman. “On the Disks of Spiral and S0 Galaxies”. In: Astrophys. J. 160 (June 1970), p. 811. doi: 10.1086/150474. [9] Robert N. Whitehurst and Morton S. Roberts. “High-Velocity Neutral Hydrogen in the Central Region of the Andromeda Galaxy”. In: Astrophys. J. 175 (July 1972), p. 347. doi: 10.1086/151562. [10] D. H. Rogstad and G. S. Shostak. “Gross Properties of Five Scd Galaxies as Determined from 21-CENTIMETER Observations”. In: Astrophys. J. 176 (Sept. 1972), p. 315. doi: 10.1086/151636. [11] M. S. Roberts and A. H. Rots. “Comparison of Rotation Curves of Di↵erent Galaxy Types”. In: A&A 26 (Aug. 1973), pp. 483–485.

53 54 Bibliography

[12] K. G. Begeman, A. H. Broeils, and R. H. Sanders. “Extended rotation curves of spiral galaxies - Dark haloes and modified dynamics”. In: MNRAS 249 (Apr. 1991), pp. 523–537. doi: 10.1093/mnras/249.3.523. [13] Douglas Clowe, Anthony Gonzalez, and Maxim Markevitch. “Weak-Lensing Mass Reconstruction of the Interacting Cluster 1E 0657–558: Direct Evidence for the Existence of Dark Matter”. In: The Astrophysical Journal 604.2 (2004), p. 596. url: http://stacks.iop.org/0004-637X/604/i=2/a=596. [14] Dorothea Samtleben, Suzanne Staggs, and Bruce Winstein. “The Cosmic microwave background for pedestrians: A Review for particle and nuclear physicists”. In: Ann. Rev. Nucl. Part. Sci. 57 (2007), pp. 245–283. doi: 10.1146/annurev.nucl.54.070103.181232. arXiv: 0803.0834 [astro-ph]. [15] S. Weinberg. Cosmology. Cosmology. OUP Oxford, 2008. isbn: 9780191523601. url: https://books.google.se/books?id=nqQZdg020fsC. [16] Planck Collaboration, P. A. R. Ade, N. Aghanim, C. Armitage-Caplan, et al. “Planck 2013 results. XV. CMB power spectra and likelihood”. In: A&A 571, A15 (Nov. 2014), A15. doi: 10.1051/0004-6361/201321573. arXiv: 1303.5075 [astro-ph.CO]. [17] Gerard Lemson. “Halo and Galaxy Formation Histories from the Millennium Simulation: Public release of a VO-oriented and SQL-queryable database for studying the evolution of galaxies in the Lambda-CDM cosmogony”. In: (2006). arXiv: astro-ph/0608019 [astro-ph]. [18] Mary K. Gaillard, Paul D. Grannis, and Frank J. Sciulli. “The standard model of particle physics”. In: Rev. Mod. Phys. 71 (2 1999), S96–S111. doi: 10.1103/RevModPhys.71.S96. url: https://link.aps.org/doi/10.1103/RevModPhys.71.S96. [19] Leszek Roszkowski, Enrico Maria Sessolo, and Sebastian Trojanowski. “WIMP dark matter candidates and searches—current status and future prospects”. In: Reports on Progress in Physics 81.6, 066201 (June 2018), p. 066201. doi: 10.1088/1361-6633/aab913. arXiv: 1707.06277 [hep-ph]. [20] Marcus T. Grisaru, W. Siegel, and M. Rocek. “Improved Methods for Supergraphs”. In: Nucl. Phys. B 159 (1979), p. 429. doi: 10.1016/0550-3213(79)90344-4. [21] Nathan Seiberg. “Naturalness versus supersymmetric non-renormalization theorems”. In: Physics Letters B 318.3 (Dec. 1993), pp. 469–475. doi: 10.1016/0370-2693(93)91541-T. arXiv: hep-ph/9309335 [hep-ph]. [22] Gary Steigman, Basudeb Dasgupta, and John F. Beacom. “Precise Relic WIMP Abundance and its Impact on Searches for Dark Matter Annihilation”. In: Phys. Rev. D86 (2012), p. 023506. doi: 10.1103/PhysRevD.86.023506. arXiv: 1204.3622 [hep-ph]. [23] Jonathan M. Cornell, Stefano Profumo, and William Shepherd. “Dark matter in minimal universal extra dimensions with a stable vacuum and the “right” Higgs boson”. In: Phys. Rev. D 89.5, 056005 (Mar. 2014), p. 056005. doi: 10.1103/PhysRevD.89.056005. arXiv: 1401.7050 [hep-ph]. Bibliography 55

[24] Gianfranco Bertone, Dan Hooper, and Joseph Silk. “Particle dark matter: Evidence, candidates and constraints”. In: Phys. Rept. 405 (2005), pp. 279–390. doi: 10.1016/j.physrep.2004.08.031. arXiv: hep-ph/0404175 [hep-ph]. [25] Jessica Goodman, Masahiro Ibe, Arvind Rajaraman, William Shepherd, Tim M. P. Tait, and Hai-Bo Yu. “Constraints on dark matter from colliders”. In: Phys. Rev. D 82.11, 116010 (Dec. 2010), p. 116010. doi: 10.1103/PhysRevD.82.116010. arXiv: 1008.1783 [hep-ph]. [26] Michael Klasen, Martin Pohl, and G¨unter Sigl. “Indirect and direct search for dark matter”. In: Prog. Part. Nucl. Phys. 85 (2015), pp. 1–32. doi: 10.1016/j.ppnp.2015.07.001. arXiv: 1507.03800 [hep-ph]. [27] E. Aprile, J. Aalbers, F. Agostini, M. Alfonsi, et al. “First Dark Matter Search Results from the XENON1T Experiment”. In: Phys. Rev. Lett. 119 (18 2017), p. 181301. doi: 10.1103/PhysRevLett.119.181301. url: https://link.aps.org/doi/10.1103/PhysRevLett.119.181301. [28] R. Agnese, A. J. Anderson, T. Aramaki, I. Arnquist, et al. “Projected sensitivity of the SuperCDMS SNOLAB experiment”. In: Phys. Rev. D 95.8, 082002 (Apr. 2017). doi: 10.1103/PhysRevD.95.082002. arXiv: 1610.00006 [physics.ins-det]. [29] G. Angloher, A. Bento, C. Bucci, L. Canonica, et al. “Results on light dark matter particles with a low-threshold CRESST-II detector”. In: European Physical Journal C 76, 25 (Jan. 2016), p. 25. doi: 10.1140/epjc/s10052-016-3877-3. arXiv: 1509.01515 [astro-ph.CO]. [30] N. Du, N. Force, R. Khatiwada, E. Lentz, et al. “Search for Invisible Axion Dark Matter with the Axion Dark Matter Experiment”. In: Phys. Rev. Lett. 120 (15 2018), p. 151301. doi: 10.1103/PhysRevLett.120.151301. url: https://link.aps.org/doi/10.1103/PhysRevLett.120.151301. [31] L. Zhong, S. Al Kenany, K. M. Backes, B. M. Brubaker, et al. “Results from phase 1 of the HAYSTAC microwave cavity axion experiment”. In: Phys. Rev. D 97 (9 2018), p. 092001. doi: 10.1103/PhysRevD.97.092001. url: https://link.aps.org/doi/10.1103/PhysRevD.97.092001. [32] Toby Falk, Keith A. Olive, and Mark Srednicki. “Heavy sneutrinos as dark matter”. In: Physics Letters B 339.3 (1994), pp. 248 –251. issn: 0370-2693. doi: https://doi.org/10.1016/0370-2693(94)90639-4. url: http://www.sciencedirect.com/science/article/pii/0370269394906394. [33] Lawrence J. Hall, Takeo Moroi, and Hitoshi Murayama. “Sneutrino cold dark matter with lepton-number violation”. In: Physics Letters B 424.3 (1998), pp. 305 –312. issn: 0370-2693. doi: https://doi.org/10.1016/S0370-2693(98)00196-8. url: http://www.sciencedirect.com/science/article/pii/S0370269398001968. [34] Chiara Arina and Nicolao Fornengo. “Sneutrino cold dark matter, a new analysis: Relic abundance and detection rates”. In: JHEP 11 (2007), p. 029. doi: 10.1088/1126-6708/2007/11/029. arXiv: 0709.4477 [hep-ph]. 56 Bibliography

[35] Teresa Marrod´anUndagoitia and Ludwig Rauch. “Dark matter direct-detection experiments”. In: J. Phys. G43.1 (2016), p. 013001. doi: 10.1088/0954-3899/43/1/013001. arXiv: 1509.08767 [physics.ins-det]. [36] W. B. Atwood et al. “The Large Area Telescope on the Fermi Gamma-ray Space Telescope Mission”. In: Astrophys. J. 697 (2009), pp. 1071–1102. doi: 10.1088/0004-637X/697/2/1071. arXiv: 0902.1089 [astro-ph.IM]. [37] I. Sushch. “The Galactic sky through H.E.S.S. eyes”. In: 22nd Young Scientists’ Conference on Astronomy and Space Physics (YSC 2015) Kyiv, Ukraine, April 20-25, 2015. 2016. arXiv: 1604.00229 [astro-ph.HE]. url: http://inspirehep.net/record/1439749/files/arXiv:1604.00229.pdf. [38] A. U. Abeysekara et al. “Sensitivity of HAWC to high-mass dark matter annihilations”. In: Phys. Rev. D90.12 (2014), p. 122002. doi: 10.1103/PhysRevD.90.122002. arXiv: 1405.1730 [astro-ph.HE]. [39] Lisa Goodenough and Dan Hooper. “Possible Evidence For Dark Matter Annihilation In The Inner Milky Way From The Fermi Gamma Ray Space Telescope”. In: (2009). arXiv: 0910.2998 [hep-ph]. [40] Dan Hooper and Tim Linden. “On The Origin Of The Gamma Rays From The Galactic Center”. In: Phys. Rev. D84 (2011), p. 123005. doi: 10.1103/PhysRevD.84.123005. arXiv: 1110.0006 [astro-ph.HE]. [41] M. Ajello, A. Albert, W. B. Atwood, G. Barbiellini, et al. “FERMI-LAT OBSERVATIONS OF HIGH-ENERGY-RAY EMISSION TOWARD THE GALACTIC CENTER”. In: The Astrophysical Journal 819.1 (2016), p. 44. doi: 10.3847/0004-637x/819/1/44. url: https://doi.org/10.3847%2F0004-637x%2F819%2F1%2F44. [42] Kevork N Abazajian. “The consistency of Fermi-LAT observations of the galactic center with a millisecond pulsar population in the central stellar cluster”. In: JCAP 2011.03 (2011), pp. 010–010. doi: 10.1088/1475-7516/2011/03/010. url: https://doi.org/10.1088%2F1475-7516%2F2011%2F03%2F010. [43] Kevork N. Abazajian and Manoj Kaplinghat. “Detection of a Gamma-Ray Source in the Galactic Center Consistent with Extended Emission from Dark Matter Annihilation and Concentrated Astrophysical Emission”. In: Phys. Rev. D86 (2012). [Erratum: Phys. Rev.D87,129902(2013)], p. 083511. doi: 10.1103/PhysRevD.86.083511,10.1103/PhysRevD.87.129902. arXiv: 1207.6047 [astro-ph.HE]. [44] P. Picozza, A.M. Galper, G. Castellini, O. Adriani, et al. “PAMELA – A payload for antimatter matter exploration and light-nuclei astrophysics”. In: Astroparticle Physics 27.4 (2007), pp. 296 –315. issn: 0927-6505. doi: https://doi.org/10.1016/j.astropartphys.2006.12.002. url: http://www.sciencedirect.com/science/article/pii/S0927650506001861. [45] M. Paniccia. “The Alpha Magnetic Spectrometer on the International Space Station”. In: Astroparticle, particle and space physics, detectors and medical physics Bibliography 57

applications. Proceedings, 10th Conference, ICATPP 2007, Como, Italy, October 8-12, 2007. 2008, pp. 896–900. doi: 10.1142/9789812819093_0150. [46] M. G. Aartsen et al. “Search for neutrinos from decaying dark matter with IceCube”. In: (2018). arXiv: 1804.03848 [astro-ph.HE]. [47] M. G. Aartsen, M. Ackermann, J. Adams, J. A. Aguilar, et al. “Search for annihilating dark matter in the Sun with 3 years of IceCube data”. In: European Physical Journal C 77.3, 146 (2017), p. 146. doi: 10.1140/epjc/s10052-017-4689-9. arXiv: 1612.05949 [astro-ph.HE]. [48] A. Liam Fitzpatrick, Wick Haxton, Emanuel Katz, Nicholas Lubbers, and Yiming Xu. “The E↵ective Field Theory of Dark Matter Direct Detection”. In: JCAP 1302 (2013), p. 004. doi: 10.1088/1475-7516/2013/02/004. arXiv: 1203.3542 [hep-ph]. [49] Nikhil Anand, A. Liam Fitzpatrick, and W. C. Haxton. “Weakly interacting massive particle-nucleus elastic scattering response”. In: Phys. Rev. C89.6 (2014), p. 065501. doi: 10.1103/PhysRevC.89.065501. arXiv: 1308.6288 [hep-ph]. [50] Riccardo Catena and Axel Widmark. “WIMP capture by the Sun in the e↵ective theory of dark matter self-interactions”. In: JCAP 1612.12 (2016), p. 016. doi: 10.1088/1475-7516/2016/12/016. arXiv: 1609.04825 [astro-ph.CO]. [51] Andrew Gould. “WIMP Distribution in and Evaporation From the Sun”. In: Astrophys. J. 321 (1987), p. 560. doi: 10.1086/165652. [52] Raghuveer Garani and Sergio Palomares-Ruiz. “Dark matter in the Sun: scattering o↵electrons vs nucleons”. In: JCAP 2017.05 (2017), pp. 007–007. doi: 10.1088/1475-7516/2017/05/007. url: https://doi.org/10.1088%2F1475-7516%2F2017%2F05%2F007. [53] Andrew Gould. “Resonant Enhancements in Weakly Interacting Massive Particle Capture by the Earth”. In: Astrophys. J. 321 (1987), p. 571. doi: 10.1086/165653. [54] Gary Steigman, Basudeb Dasgupta, and John F. Beacom. “Precise relic WIMP abundance and its impact on searches for dark matter annihilation”. In: Phys. Rev. D 86.2, 023506 (July 2012), p. 023506. doi: 10.1103/PhysRevD.86.023506. arXiv: 1204.3622 [hep-ph]. [55] John N. Bahcall, M. H. Pinsonneault, and Sarbani Basu. “Solar models: Current epoch and time dependences, neutrinos, and helioseismological properties”. In: Astrophys. J. 555 (2001), pp. 990–1012. doi: 10.1086/321493. arXiv: astro-ph/0010346 [astro-ph]. [56] Savvas M. Koushiappas and Marc Kamionkowski. “Galactic Substructure and Energetic Neutrinos from the Sun and Earth”. In: Phys. Rev. Lett. 103.12, 121301 (2009), p. 121301. doi: 10.1103/PhysRevLett.103.121301. arXiv: 0907.4778 [astro-ph.CO]. [57] Alejandro Ibarra, Bradley J. Kavanagh, and Andreas Rappelt. “Impact of substructure on local dark matter searches”. In: JCAP 2019.12, 013 (2019), p. 013. doi: 10.1088/1475-7516/2019/12/013. arXiv: 1908.00747 [hep-ph]. 58 Bibliography

[58] G. B. Field. “Excitation of the Hydrogen 21-CM Line”. In: Proceedings of the IRE 46 (Jan. 1958), pp. 240–250. doi: 10.1109/JRPROC.1958.286741. [59] Jonathan R. Pritchard and Abraham Loeb. “21-cm cosmology”. In: Rept. Prog. Phys. 75 (2012), p. 086901. doi: 10.1088/0034-4885/75/8/086901. arXiv: 1109.6012 [astro-ph.CO]. [60] A. Cohen, A. Fialkov, R. Barkana, and M. Lotem. “Charting the parameter space of the global 21-cm signal”. In: MNRAS 472 (Dec. 2017), pp. 1915–1931. doi: 10.1093/mnras/stx2065. arXiv: 1609.02312. [61] Judd D. Bowman, Alan E. E. Rogers, Raul A. Monsalve, Thomas J. Mozdzen, and Nivedita Mahesh. “An absorption profile centred at 78 megahertz in the sky-averaged spectrum”. In: Nature 555.7694 (2018), pp. 67–70. doi: 10.1038/nature25792. [62] Richard Hills, Girish Kulkarni, P. Daniel Meerburg, and Ewald Puchwein. “Concerns about modelling of the EDGES data”. In: Nature 564.7736 (Dec. 2018), E32–E34. doi: 10.1038/s41586-018-0796-5. arXiv: 1805.01421 [astro-ph.CO]. [63] L. Philip, Z. Abdurashidova, H. C. Chiang, N. Ghazi, et al. “Probing Radio Intensity at High-Z from Marion: 2017 Instrument”. In: Journal of Astronomical Instrumentation 8.2, 1950004 (2019). doi: 10.1142/S2251171719500041. arXiv: 1806.09531 [astro-ph.IM]. [64] Asher Berlin, Dan Hooper, Gordan Krnjaic, and Samuel D. McDermott. “Severely Constraining Dark-Matter Interpretations of the 21-cm Anomaly”. In: Phys. Rev. Lett. 121, 011102 (July 2018). doi: 10.1103/PhysRevLett.121.011102. arXiv: 1803.02804 [hep-ph]. [65] Julian B. Mu˜noz and Abraham Loeb. “A small amount of mini-charged dark matter could cool the baryons in the early Universe”. In: Nature 557.7707 (2018), p. 684. doi: 10.1038/s41586-018-0151-x. arXiv: 1802.10094 [astro-ph.CO]. [66] Julian B. Mu˜noz, Cora Dvorkin, and Abraham Loeb. “21-cm Fluctuations from Charged Dark Matter”. In: Phys. Rev. Lett. 121.12 (2018). doi: 10.1103/PhysRevLett.121.121301. arXiv: 1804.01092 [astro-ph.CO]. [67] Rennan Barkana, Nadav Joseph Outmezguine, Diego Redigolo, and Tomer Volansky. “Strong constraints on light dark matter interpretation of the EDGES signal”. In: Phys. Rev. D98.10 (2018). doi: 10.1103/PhysRevD.98.103005. arXiv: 1803.03091 [hep-ph]. [68] Daniel Green and Surjeet Rajendran. “The Cosmology of Sub-MeV Dark Matter”. In: JHEP 10 (2017), p. 013. doi: 10.1007/JHEP10(2017)013. arXiv: 1701.08750 [hep-ph]. [69] Simon Knapen, Tongyan Lin, and Kathryn M. Zurek. “Light dark matter: Models and constraints”. In: Phys. Rev. D 96, 115021 (Dec. 2017). doi: 10.1103/PhysRevD.96.115021. arXiv: 1709.07882 [hep-ph]. [70] JiJi Fan, Andrey Katz, Lisa Randall, and Matthew Reece. “Double-Disk Dark Matter”. In: Phys. Dark Univ. 2 (2013), pp. 139–156. doi: 10.1016/j.dark.2013.07.001. arXiv: 1303.1521 [astro-ph.CO]. Bibliography 59

[71] Jiro Murata and Saki Tanaka. “A review of short-range gravity experiments in the LHC era”. In: Class. Quant. Grav. 32.3 (2015), p. 033001. doi: 10.1088/0264-9381/32/3/033001. arXiv: 1408.3588 [hep-ex]. [72] J. A. Grifols and E. Mass´o.“Constraints on finite-range baryonic and leptonic forces from stellar evolution”. In: Physics Letters B 173.3 (1986), pp. 237–240. doi: 10.1016/0370-2693(86)90509-5. [73] Edward Hardy and Robert Lasenby. “Stellar cooling bounds on new light particles: plasma mixing e↵ects”. In: JHEP 02 (2017), p. 033. doi: 10.1007/JHEP02(2017)033. arXiv: 1611.05852 [hep-ph]. [74] Gaia Collaboration, T. Prusti, J. H. J. de Bruijne, A. G. A. Brown, et al. “The Gaia mission”. In: A&A 595, A1 (2016). doi: 10.1051/0004-6361/201629272. arXiv: 1609.04153 [astro-ph.IM]. [75] Gaia Collaboration, A. G. A. Brown, A. Vallenari, T. Prusti, et al. “Gaia Data Release 2. Summary of the contents and survey properties”. In: A&A 616, A1 (Aug. 2018), A1. doi: 10.1051/0004-6361/201833051. arXiv: 1804.09365 [astro-ph.GA]. [76] D. Katz, P. Sartoretti, M. Cropper, P. Panuzzo, et al. “Gaia Data Release 2. Properties and validation of the radial velocities”. In: A&A 622, A205 (2019). doi: 10.1051/0004-6361/201833273. arXiv: 1804.09372 [astro-ph.IM]. [77] M. A. C. Perryman, L. Lindegren, J. Kovalevsky, E. Hog, et al. “The Hipparcos Catalogue.” In: A&A 500 (1997), pp. 501–504. [78] D. Michalik, L. Lindegren, and D. Hobbs. “The Tycho-Gaia astrometric solution . How to get 2.5 million parallaxes with less than one year of Gaia data”. In: A&A 574, A115 (2015), A115. doi: 10.1051/0004-6361/201425310. arXiv: 1412.8770 [astro-ph.IM]. [79] S. Garbari, J. I. Read, and G. Lake. “Limits on the local dark matter density”. In: MNRAS 416 (Sept. 2011), pp. 2318–2340. doi: 10.1111/j.1365-2966.2011.19206.x. arXiv: 1105.6339 [astro-ph.GA]. [80] A. B¨udenbender, G. van de Ven, and L. L. Watkins. “The tilt of the velocity ellipsoid in the Milky Way disc”. In: MNRAS 452 (Sept. 2015), pp. 956–968. doi: 10.1093/mnras/stv1314. arXiv: 1407.4808. [81] S. Sivertsson, H. Silverwood, J. I. Read, G. Bertone, and P. Steger. “The localdark matter density from SDSS-SEGUE G-dwarfs”. In: MNRAS 478.2 (2018), pp. 1677–1693. doi: 10.1093/mnras/sty977. arXiv: 1708.07836 [astro-ph.GA]. [82] Silvia Garbari, Justin I. Read, and George Lake. “Limits on the local dark matter density”. In: MNRAS 416.3 (2011), pp. 2318–2340. doi: 10.1111/j.1365-2966.2011.19206.x.eprint: /oup/backfile/content_public/journal/mnras/416/3/10.1111/j.1365- 2966.2011.19206.x/2/mnras0416-2318.pdf. url: http://dx.doi.org/10.1111/j.1365-2966.2011.19206.x. 60 Bibliography

[83] Walter Dehnen and James Binney. “Mass models of the Milky Way”. In: MNRAS 294.3 (1998), pp. 429–438. doi: 10.1046/j.1365-8711.1998.01282.x. arXiv: astro-ph/9612059 [astro-ph]. [84] Anatoly Klypin, HongSheng Zhao, and Rachel S. Somerville. “Lambda CDM-based models for the Milky Way and M31 I: Dynamical models”. In: Astrophys.J. 573 (2002), pp. 597–613. doi: 10.1086/340656. [85] Lawrence M. Widrow, Brent Pym, and John Dubinski. “Dynamical Blueprints for Galaxies”. In: Astrophys.J. 679 (2008), pp. 1239–1259. doi: 10.1086/587636. arXiv: 0801.3414 [astro-ph]. [86] M. Weber and W. de Boer. “Determination of the local dark matter density in our Galaxy”. In: A&A 509, A25 (2010). doi: 10.1051/0004-6361/200913381. arXiv: 0910.4272 [astro-ph.CO]. [87] Paul J. McMillan. “Mass models of the Milky Way”. In: MNRAS 414 (2011), pp. 2446–2457. doi: 10.1111/j.1365-2966.2011.18564.x. arXiv: 1102.4340 [astro-ph.GA]. [88] Prajwal Raj Kafle, Sanjib Sharma, Geraint F. Lewis, and Joss Bland-Hawthorn. “On the Shoulders of Giants: Properties of the Stellar Halo and the Milky Way Mass Distribution”. In: Astrophys. J. 794.1, 59 (2014), p. 59. doi: 10.1088/0004-637X/794/1/59. arXiv: 1408.1787 [astro-ph.GA]. [89] Paul J. McMillan. “The mass distribution and gravitational potential of the Milky Way”. In: MNRAS 465.1 (2017), pp. 76–94. doi: 10.1093/mnras/stw2759. arXiv: 1608.00971 [astro-ph.GA]. [90] Maria Selina Nitschai, Michele Cappellari, and Nadine Neumayer. “First Gaia dynamical model of the Milky Way disc with six phase space coordinates: a test for galaxy dynamics”. In: arXiv e-prints, arXiv:1909.05269 (2019). arXiv: 1909.05269 [astro-ph.GA]. [91] Marius Cautun, Alejandro Benitez-Llambay, Alis J. Deason, Carlos S. Frenk, Azadeh Fattahi, Facundo A. G´omez, Robert J. J. Grand, Kyle A. Oman, Julio F. Navarro, and Christine M. Simpson. “The Milky Way total mass profile as inferred from Gaia DR2”. In: arXiv e-prints, arXiv:1911.04557 (2019). arXiv: 1911.04557 [astro-ph.GA]. [92] Zhao-Zhou Li, Yong-Zhong Qian, Jiaxin Han, Ting S. Li, Wenting Wang, and Y. P. Jing. “Constraining the Milky Way Mass Profile with Phase-Space Distribution of Satellite Galaxies”. In: arXiv e-prints, arXiv:1912.02086 (2019). arXiv: 1912.02086 [astro-ph.GA]. [93] Rachel Kennedy, Carlos Frenk, Shaun Cole, and Andrew Benson. “Constraining the warm dark matter particle mass with Milky Way satellites”. In: MNRAS 442.3 (2014), pp. 2487–2495. doi: 10.1093/mnras/stu719. arXiv: 1310.7739 [astro-ph.CO]. [94] Oliver Newton, Marius Cautun, Adrian Jenkins, Carlos S. Frenk, and John C. Helly. “The Milky Way?s total satellite population and constraining the mass of the warm Bibliography 61

dark matter particle”. In: Proceedings of the International Astronomical Union 14.S344 (2018), pp. 109–113. doi: 10.1017/S1743921318006464. [95] Stephon Alexander, Jason J. Bramburger, and Evan McDonough. “Dark disk substructure and superfluid dark matter”. In: Physics Letters B 797, 134871 (2019). doi: 10.1016/j.physletb.2019.134871. arXiv: 1901.03694 [astro-ph.CO]. [96] Sean Tulin and Hai-Bo Yu. “Dark matter self-interactions and small scale structure”. In: Physics Reports 730 (2018), pp. 1–57. doi: 10.1016/j.physrep.2017.11.004. arXiv: 1705.02358 [hep-ph]. [97] K. Pardo, H. Desmond, and P. G. Ferreira. “Testing self-interacting dark matter with galaxy warps”. In: Phys. Rev. D 100 (12 2019). doi: 10.1103/PhysRevD.100.123006. url: https://link.aps.org/doi/10.1103/PhysRevD.100.123006. [98] Chris Flynn, Johan Holmberg, Laura Portinari, Burkhard Fuchs, and Hartmut Jahreiss. “On the mass-to-light ratio of the local Galactic disc and the optical luminosity of the Galaxy”. In: MNRAS 372 (2006), pp. 1149–1160. doi: 10.1111/j.1365-2966.2006.10911.x. arXiv: astro-ph/0608193 [astro-ph]. [99] C. F. McKee, A. Parravano, and D. J. Hollenbach. “Stars, Gas, and Dark Matter in the Solar Neighborhood”. In: Astrophys. J. 814, 13 (Nov. 2015), p. 13. doi: 10.1088/0004-637X/814/1/13. arXiv: 1509.05334. [100] Eric David Kramer and Lisa Randall. “Interstellar Gas and a Dark Disk”. In: The Astrophysical Journal 829.2 (2016), p. 126. url: http://stacks.iop.org/0004-637X/829/i=2/a=126. [101] Robert C. Kennicutt and Neal J. Evans. “Star Formation in the Milky Way and Nearby Galaxies”. In: Annual Review of Astronomy and Astrophysics 50.1 (2012), pp. 531–608. doi: 10.1146/annurev-astro-081811-125610.eprint: https://doi.org/10.1146/annurev-astro-081811-125610. url: https://doi.org/10.1146/annurev-astro-081811-125610. [102] J. I. Read, G. Lake, O. Agertz, and Victor P. Debattista. “Thin, thick and dark discs in ⇤CDM”. In: MNRAS 389.3 (Sept. 2008), pp. 1041–1057. issn: 0035-8711. doi: 10.1111/j.1365-2966.2008.13643.x.eprint: https://academic.oup.com/mnras/article- pdf/389/3/1041/3318673/mnras0389-1041.pdf. url: https://doi.org/10.1111/j.1365-2966.2008.13643.x. [103] JiJi Fan, Andrey Katz, Lisa Randall, and Matthew Reece. “Dark-Disk Universe”. In: Phys. Rev. Lett. 110.21 (2013), p. 211302. doi: 10.1103/PhysRevLett.110.211302. arXiv: 1303.3271 [hep-ph]. [104] M. Creze, E. Chereul, O. Bienayme, and C. Pichon. “The distribution of nearby stars in phase space mapped by hipparcos: I. the potential well and local dynamical mass”. In: A&A 329 (1998), p. 920. arXiv: astro-ph/9709022 [astro-ph]. [105] J. Holmberg and C. Flynn. “The local density of matter mapped by Hipparcos”. In: MNRAS 313 (2000), pp. 209–216. doi: 10.1046/j.1365-8711.2000.02905.x. eprint: astro-ph/9812404. 62 Bibliography

[106] J. I. Read. “The Local Dark Matter Density”. In: J. Phys. G41 (2014), p. 063101. doi: 10.1088/0954-3899/41/6/063101. arXiv: 1404.1938 [astro-ph.GA]. [107] J. M. Yao, R. N. Manchester, and N. Wang. “Determination of the Sun’s o↵set from the Galactic plane using pulsars”. In: MNRAS 468 (July 2017), pp. 3289–3294. doi: 10.1093/mnras/stx729. arXiv: 1704.01272 [astro-ph.SR]. [108] R. Sch¨onrich, J. Binney, and W. Dehnen. “Local kinematics and the local standard of rest”. In: MNRAS 403 (Apr. 2010), pp. 1829–1833. doi: 10.1111/j.1365-2966.2010.16253.x. arXiv: 0912.3693. [109] Katelin Schutz, Tongyan Lin, Benjamin R. Safdi, and Chih-Liang Wu. “Constraining a Thin Dark Matter Disk with Gaia”. In: Phys. Rev. Lett. 121.8 (2018), p. 081101. doi: 10.1103/PhysRevLett.121.081101. arXiv: 1711.03103 [astro-ph.GA]. [110] Jatan Buch, John Shing Chau Leung, and JiJi Fan. “Using Gaia DR2 to Constrain Local Dark Matter Density and Thin Dark Disk”. In: preprint (2018). arXiv: 1808.05603 [astro-ph.GA]. [111] Mario Juric et al. “The Milky Way Tomography with SDSS. 1. Stellar Number Density Distribution”. In: Astrophys. J. 673 (2008), pp. 864–914. doi: 10.1086/523619. arXiv: astro-ph/0510520 [astro-ph]. [112] Morgan Bennett and Jo Bovy. “Vertical waves in the solar neighbourhood in Gaia DR2”. In: MNRAS 482 (Jan. 2019), pp. 1417–1425. doi: 10.1093/mnras/sty2813. arXiv: 1809.03507 [astro-ph.GA]. [113] M. L´opez-Corredoira, F. Garz´on, H. F. Wang, F. Sylos Labini, R. Nagy, Z.ˇ Chrob´akov´a,J. Chang, and B. Villarroel. “Gaia-DR2 extended kinematical maps. II. Dynamics in the Galactic disk explaining radial and vertical velocities”. In: A&A 634, A66 (2020), A66. doi: 10.1051/0004-6361/201936711. arXiv: 2001.05455 [astro-ph.GA]. [114] Lina Necib, Mariangela Lisanti, and Vasily Belokurov. “Dark Matter in Disequilibrium: The Local Velocity Distribution from SDSS-Gaia”. In: arXiv e-prints, arXiv:1807.02519 (July 2018). arXiv: 1807.02519 [astro-ph.GA]. [115] T. Antoja, A. Helmi, M. Romero-G´omez, D. Katz, et al. “A dynamically young and perturbed Milky Way disk”. In: Nature 561 (Sept. 2018), pp. 360–362. doi: 10.1038/s41586-018-0510-7. arXiv: 1804.10196 [astro-ph.GA]. [116] M. F. Skrutskie, R. M. Cutri, R. Stiening, M. D. Weinberg, et al. “The Two Micron All Sky Survey (2MASS)”. In: Astron. J. 131.2 (2006), pp. 1163–1183. doi: 10.1086/498708. [117] S. E. Koposov, H.-W. Rix, and D. W. Hogg. “Constraining the Milky Way Potential with a Six-Dimensional Phase-Space Map of the GD-1 Stellar Stream”. In: Astrophys. J. 712 (Mar. 2010), pp. 260–273. doi: 10.1088/0004-637X/712/1/260. arXiv: 0907.1085 [astro-ph.GA]. [118] J. Bovy, A. Bahmanyar, T. K. Fritz, and N. Kallivayalil. “The Shape of the Inner Milky Way Halo from Observations of the Pal 5 and GD–1 Stellar Streams”. In: Astrophys. J. 833, 31 (Dec. 2016), p. 31. doi: 10.3847/1538-4357/833/1/31. arXiv: 1609.01298. Bibliography 63

[119] Khyati Malhan and Rodrigo A. Ibata. “Constraining the Milky Way halo potential with the GD-1 stellar stream”. In: MNRAS 486.3 (2019), pp. 2995–3005. doi: 10.1093/mnras/stz1035. arXiv: 1807.05994 [astro-ph.GA]. [120] Justin Alsing, Tom Charnock, Stephen Feeney, and Benjamin Wand elt. “Fast likelihood-free cosmology with neural density estimators and active learning”. In: MNRAS 488.3 (2019), pp. 4440–4458. doi: 10.1093/mnras/stz1960. arXiv: 1903.00007 [astro-ph.CO]. [121] J. Jasche and G. Lavaux. “Physical Bayesian modelling of the non-linear matter distribution: New insights into the nearby universe”. In: A&A 625, A64 (2019), A64. doi: 10.1051/0004-6361/201833710. arXiv: 1806.11117 [astro-ph.CO].

Part II

INCLUDED PAPERS

65