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Observational Probes of Dark Matter Halos

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Observational Probes of Dark Matter Halos Observational probes of dark matter halos Submitted for the Ph.D.-degree Copenhagen, August 26, 2009 Ole Høst Supervisor: Steen H. Hansen Dark Cosmology Centre, Niels Bohr Institute Faculty of Science, University of Copenhagen Observational probes of dark matter halos Ole Høst August 26, 2009 Dark Cosmology Centre Niels Bohr Institute The Graduate School of Science Faculty of Science University of Copenhagen Denmark ABSTRACT Dark matter constitutes six times more of the mass in the Universe than ordinary baryonic matter. The halos formed by dark matter are fundamental to the formation of structure, yet the properties of these halos are not well understood theoretically or observationally. In the first part of this thesis, I review the evidence for the existence of dark matter and its role in cosmology and astrophysics, and I discuss the particle nature of dark matter and how that nature can be identified. Then, I summarize the predicted properties of collisionless dark matter halos from fundamental theory and from numerical simulations of the formation of structure. In particular, I focus on the possibility of an anisotropic velocity dispersion tensor where the typical velocity in one direction can be different from that in another direction. This anisotropy demonstrates the fundamental difference between collisionless dark matter systems and collisional gases. In the second part of the thesis, I investigate how the properties of halos can be constrained obser- vationally, and what these constraints imply about dark matter. First, I analyze how accurately the velocity anisotropy parameter can be measured in a dark matter detector which is sensitive to the direc- tion of the measured dark matter particles. The anisotropy parameter turns out to be measurable, but I find that a very large number of events are necessary to reject isotropy at high statistical significance. Second, using x-ray observations of a sample of galaxy clusters, I carry out a first measurement of the radially-varying velocity anisotropy profile of dark matter. The measured profile is found to be non-zero and radially increasing, which is in good agreement with the predictions of numerical simulations. The measurement implies that dark matter is in fact effectively collisionless in clusters and it sets an upper limit on the dark matter self-scattering cross section. Finally, I again use a sample of clusters observed in x-ray to constrain the mass distribution of dark matter in the halos of the clusters. I compare the measured mass profiles with a number of parametrized mass models in a detailed statistical analysis. I find moderate evidence that the observed mass profiles are not strictly universal but require a shape parameter to be fitted to each halo. Mørkt stof udgør seks gange s˚ameget af massen i universet som almindeligt, baryoniskt stof. Haloer dannet af mørkt stof spiller en grundlæggende rolle i dannelsen af struktur, men alligevel er den teoretiske og observationelle forst˚aelseaf haloernes egenskaber mangelfuld. I denne afhandlings første del gennemg˚arjeg beviserne for eksistensen af mørkt stof, og jeg diskuterer mørkt stofs egenskaber som partikel, samt hvorledes denne partikel kan identifceres. Derefter beskriver jeg egenskaberne ved en kollisionsløs halo af mørkt stof, som forudsagt teoretisk og udfra numeriske simu- leringer. Jeg fokuserer p˚ahastighedsfordelingens dispersionstensor, som kan være ellipsoidisk, s˚aledesat middelhastigheden i ´enretning er forskellig fra middelhastigheden i en anden retning. Denne anisotropi er et eksempel p˚aden grundlæggendel forskel mellem kollisionsløst mørkt stof og vekselvirkende gas. I afhandlingens anden del undersøger jeg, hvorledes haloers egenskaber kan bestemmes gennem ob- 6 Abstract servationer, samt hvad disse egenskaber betyder for mørkt stof. Først undersøger jeg, hvor nøjagtigt anisotropiparameteren kan m˚alesi en partikeldetektor, som kan bestemme retningen af de m˚altemørkt stof partikler. Det viser sig, at der kræves et meget stort antal vekselvirkninger af mørkt stof i detek- toren for at afvise med statistisk signifikans, at hastighedsfordelingen er isotrop. Derefter anvender jeg observationer af galaksehobe i røntgenspektret til, for første gang nogensinde, at m˚aleanisotropiparam- eteren og dennes radiale variation i hobenes haloer. Den m˚alteprofil er forskellig fra nul og vokser med radius i god overensstemmelse med forudsigelser baseret p˚anumeriske simuleringer. M˚alingenbetyder, at mørkt stof i galaksehobe m˚aopføre sig som kollisionsløse partikler, og at der kan sættes en øvre grænse for tværsnittet af det mørke stofs egenvekselvirkning. Til sidst bruger jeg igen røntgenobservationer af galaksehobe til at undersøge massefordelingen i hobene. Jeg sammenligner de m˚altefordelinger med forskellige parametriserede masseprofiler p˚agrundlag af en detaljeret statistisk analyse. Jeg p˚aviser, at der er moderat evidens for, at masseprofilen ikke er strengt universel, men derimod kræver, at en formbestemmende parameter tilpasses hver hobs halo. CONTENTS 1. Introduction & Objectives :::::::::::::::::::::::::::::::::::::: 9 2. Cosmology ::::::::::::::::::::::::::::::::::::::::::::::: 11 2.1 The evolution of the Universe . 11 2.2 Growth of perturbations . 12 2.3 Evidence for dark matter . 15 3. Particle nature of dark matter :::::::::::::::::::::::::::::::::::: 19 3.1 Theoretical candidates . 19 3.2 Indirect detection . 21 3.3 Direct detection . 23 3.4 Present status . 26 3.5 Establishing a detection . 28 4. Dark matter halos ::::::::::::::::::::::::::::::::::::::::::: 29 4.1 Theory . 29 4.2 Numerical simulations . 30 4.3 Observational probes . 36 5. Summary & discussion of Paper I-III :::::::::::::::::::::::::::::::: 41 5.1 Paper I: Host & Hansen (2007) . 41 5.2 Paper II: Host et al. (2009) . 43 5.3 Paper III: Host & Hansen (2009) . 45 Appendix 49 A. Paper I: A fundamental difference between dark matter and baryons: the halo velocity anisotropy :::::::::::::::::::::::::::::::::::::::::::::::: 51 A.1 Introduction . 52 A.2 Modelling . 52 A.3 Results . 54 A.4 Discussion . 59 B. Paper II: Measurement of the dark matter velocity anisotropy in galaxy clusters ::::::: 61 B.1 Introduction . 62 B.2 The temperature of dark matter . 62 B.3 Solving the dark matter dynamics . 63 B.4 Cluster simulations . 64 B.5 Observations . 66 8 Contents B.6 Results . 67 B.7 Summary and discussion . 70 C. Paper III: A detailed statistical analysis of the dark matter mass profiles of galaxy clusters 73 C.1 Introduction . 74 C.2 Density profile models . 75 C.3 Data analysis . 75 C.4 Statistical analysis . 76 C.5 Biases . 83 C.6 Mass{concentration relation . 83 C.7 Summary & discussion . 84 1. INTRODUCTION & OBJECTIVES Dark matter is one of the main unsolved myster- matter, how dark matter can appear in particle ies in modern physics and cosmology. The notion physics theories beyond the standard model, and that the majority of matter in the Universe is of a the various possibilities for identifying dark mat- so far unknown nature humbles our perception of ter. In section 4, dark matter halos are discussed, the physical world. The investigation of dark mat- with an emphasis on how they can be studied in ter, its particle nature, and its role in the Universe observations. Finally, section 5 is a summary and encompasses efforts from the fields of cosmology, comment on the papers. astrophysics, high energy physics, experimental nu- The actual accounts of the research, i.e. the sci- clear physics, and so on. So far the nature of dark entific papers on which the thesis is based, are in- matter is unknown, but a large and diverse experi- cluded in manuscript as appendices. The papers mental effort gives hope that this situation may be are about to change. Identifying dark matter will be a major breakthrough in high energy physics, as • Paper I: Host & Hansen (2007), published a signpost for physics beyond the standard model, in Journal of Cosmology and Astro-particle and in cosmology, as the dominant form of matter. Physics, Issue 06, pp. 016 (2007). Historically, dark matter was first suggested as • Paper II: Host et al. (2009), published in The unobserved missing matter in galaxy clusters. To- Astrophysical Journal Volume 690, Issue 1, pp. day we know that dark matter halos play a crucial 358-366 (2009). role in the formation of structure in the Universe. The purpose of this thesis is to constrain the prop- • Paper III: Host & Hansen (2009), submitted to erties of dark matter halos observationally. This The Astrophysical Journal, preprint available includes the distribution of mass in the halos and from arXiv:0907.1097. the dynamics of the dark matter particles. Out The appended manuscripts are identical to the pub- of several possible observational probes, I focus on lished or submitted versions, except that the refer- two: x-rays from the intracluster medium of galaxy ences have been merged into a single bibliography clusters, which traces the distribution of mass in for the whole thesis and are updated where neces- the dark matter halo, and `dark matter telescopes' sary. in the form of direction-sensitive dark matter de- tectors, that may be able to detect Galactic dark matter particles. Acknowledgments The present thesis takes the form of a synop- I am thankful to my supervisor, Steen H. Hansen, sis, which means that the main body of the thesis for three years of guidance and instruction in the presents a review of the dark matter field and a field of dark matter and its characters, always with summary of the research in relation to that context. a glint in the eye, and for drinking my coffee. To my By necessity, this review is concise and, in some secondary supervisor, Kristian Pedersen, for being cases, quite selective in the topics covered, and the available when others were not, and for good port bibliography is perhaps exemplifying rather than wine. And to my other colleagues at the Dark Cos- exhaustive. In section 2, the modern picture of cos- mology Centre, for merriment, discussions, good mology is summarized, including a brief discussion will, and making the centre a fun place to be. of structure formation with dark matter, and the evidence for dark matter in astrophysics is intro- duced.
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