Unveiling Dark Matter through Gamma Rays: Spectral Features, Spatial Signatures and Astrophysical Backgrounds Dissertation with the aim of achieving a doctoral degree at the Faculty of Mathematics, Informatics and Natural Sciences Department of Physics of Universitat¨ Hamburg and Department of Physics of Universita` degli Studi di Torino submitted by Francesca Calore Hamburg 2013 { corrected version { Day of oral defense: 18th of September, 2013 The following evaluators recommend the admission of the dissertation: Dr. Torsten Bringmann Dr. Fiorenza Donato Zusammenfassung Obwohl die Existenz der Dunklen Materie (DM) durch zahlreiche un- abh¨angige Ergebnisse auf verschiedenen Skalen gestutzt¨ wird, sind die De- tails ihrer eigentlichen Beschaffenheit weit davon entfernt, durch gegenw¨artige M¨oglichkeit der Detektion offengelegt zu werden. Die vorliegende Arbeit kon- zentriert sich auf die indirekte Suche nach DM schwach wechselwirkenden massiven Teilchen (Weakly Interacting Massive Particles - WIMPs) mithilfe der γ-Strahlung. Um die spektrale DM-Verteilung sorgf¨altig zu modellieren, fuhren¨ wir die erste allgemein gultige¨ Berechnung der fuhrenden¨ elektroschwachen Korrek- turen zur Paarvernichtungsrate supersymmetrischer Neutralino-DM durch und zeigen, dass diese Korrekturen die totale Photonenausbeute signifikant erh¨ohen, was zum Teil dadurch bedingt wird, dass einige der Beitr¨age bis- her nicht beachtet worden sind. Ferner erwartet man, dass DM neben den spektralen Signaturen auch spezifische r¨aumliche Besonderheiten bewirkt, da Ergebnisse von N-K¨orper-Simulationen vorhersagen, dass der prim¨are ga- laktische Halo DM-Subhalos unterschiedlicher Gr¨oße und Masse beherbergt. Wir berechnen das winkelabh¨angige Leistungsspektrum der γ-Strahlung ga- laktischer DM unter Ausnutzung der neuesten Ergebnisse von N-K¨orper- Simulationen. Zus¨atzlich heben wir die theoretischen Unsicherheiten dieser Berechnung, die sich als relevant fur¨ gegenw¨artige Suchen nach DM mithilfe von Anisotropien der γ-Strahlung herausstellen kann, hervor. Eine angemessene Strategie zur Detektion von DM sollte sowohl die Methoden als auch die Auswahl der Zielobjekte optimieren. Wir zeigen, dass traditionelle Methoden der Spektralliniensuche fur¨ γ-Strahlung, die die auf astrophysikalische Hintergrundflusse¨ zuruckzuf¨ uhrenden¨ Unsicher- heiten stark reduziert, erfolgreich erweitert werden k¨onnen, um spezifische Merkmale des Spektrums fur¨ Energien nahe der Masse der DM-Teilchen zu entdecken und dass die projizierten Einschr¨ankungen des Wirkungsquer- schnitts der DM-Paarvernichtung in Hinblick auf die Tscherenkow-Teleskope der n¨achsten Generation im Vergleich zur heutigen Eingrenzung erheblich verbessert werden k¨onnen. Außerdem weisen wir nach, dass der isotrope dif- fuse γ-Strahlungshintergrund (isotropic diffuse γ-ray background - IGRB) eines der vielversprechendsten Objekte ist, um DM indirekt nachzuweisen, sobald die Unsicherheiten des unvermeidbaren astrophysikalischen Hinter- i ii grunds durch weitere Messdaten reduziert worden sind. Tats¨achlich k¨onnen wir zeigen, dass der wichtigste astrophysikalische Beitrag zum IGRB von der unbekannten Menge der sogenannten schlecht ausgerichteten aktiven galaktischen Kerne stammt. Unter Beachtung dieses zus¨atzlichen Beitrags k¨onnen thermisch produzierte WIMPs mit Massen von bis zu einigen TeV stark eingeschr¨ankt werden. Abstract Although the existence of Dark Matter (DM) is supported by multi- ple unrelated evidences at different scales, its intimate nature is far from been unveiled by current detection strategies. This thesis focuses on indi- rect searches of DM Weakly Interacting Massive Particles (WIMPs) through γ-rays. In order to accurately model the spectral DM distribution, we perform the first fully general calculation of leading electroweak corrections to the annihilation rate of supersymmetric neutralino DM and we demonstrate that these corrections significantly enhance the total photon yield, partially because of contributions that have been overlooked so far. Besides spectral signatures, DM is expected to show distinctive spatial features because of DM subhalos of various sizes and masses hosted by the main galactic halo as predicted by N-body simulations. We compute the γ-ray angular power spectrum of galactic DM by exploiting the results of recent N-body simula- tions. Notably, we emphasize the theoretical uncertainty associated to such a calculation which may turn out to be relevant for current DM searches by means of γ-ray anisotropies. A good DM detection strategy should optimize methods and choice of targets. We demonstrate that traditional methods for γ-ray line searches, which greatly reduce the uncertainties related to astrophysical background fluxes, can successfully be extended to look for any spectral feature at photon energies close to the DM particle mass and that projected constraints on the DM annihilation cross section by means of the next generation of Cherenkov telescopes turn out to be considerably improved with respect to current lim- its. Moreover, we prove the isotropic diffuse γ-ray background (IGRB) to be one of the most promising targets for testing the WIMP hypothesis once the uncertainties on the unavoidable astrophysical background will be reduced by further data. We indeed show that the most important astrophysical con- tribution to the IGRB is due to the unresolved population of mis-aligned active galactic nuclei. Taking into account this additional contribution to the IGRB, thermally produced WIMPs may be severely constrained for masses up to several TeV. iii iv Acronyms AGN Active Galactic Nuclei APS Angular Power Spectrum BB Back-to-Back (system) BL Lacs BL Lacertae objects CDM Cold Dark Matter CMB Cosmic Microwave Background CMS Center of Mass System CR Cosmic Ray DM Dark Matter EBL Extragalactic Background Light EC External Compton EM Electromagnetic EW Electroweak FR (I/II) Fanaroff Riley (I/II) FSR Final State Radiation FSRQ Flat Spectrum Radio Quasar GC Galactic Center IACT Imaging Atmospheric Cherenkov Telescope IC Inverse Compton ID Indirect Detection IGRB Isotropic (Diffuse) γ-ray Background ISR Initial State Radiation KK Kaluza Klein LHC Large Hadron Collider LSP Lightest Supersymmetric Particle MAGN Mis-Aligned Active Galactic Nuclei MSP Milli-second Pulsar MSSM Minimal Supersymmetric Standard Model SF Star Forming SM Standard Model SSC Self Synchrotron Compton SUSY Supersymmetry VIB Virtual Internal Bremsstrahlung WIMP Weakly Interacting Massive Particle UED Universal Extra-Dimensions v vi Contents List of Publications xii List of Figures xix List of Tables xxiii 1 Introduction 1 2 Dark Matter Primer 5 2.1 The matter-energy content of the universe . .5 2.2 The density parameter and evidence for Dark Matter . .7 2.3 Summary: Dark Matter properties . 10 2.4 Particle Dark Matter . 13 2.4.1 Weakly Interacting Massive Particles . 14 2.4.2 Neutralino Dark Matter . 17 2.4.3 Kaluza Klein Dark Matter . 20 2.5 Hunting Dark Matter . 21 2.5.1 Direct Detection . 21 2.5.2 Indirect Detection . 23 2.5.3 Dark Matter searches at colliders . 26 2.5.4 Complementarity . 27 3 Dark Matter indirect detection: a closer look to γ-rays 29 3.1 γ-ray production from Dark Matter annihilation . 30 3.2 Astrophysical and cosmological Dark Matter distribution . 33 3.2.1 Galactic Dark Matter distribution . 34 3.2.2 Enhancement factor I: galactic Dark Matter substruc- tures . 37 3.2.3 Enhancement factor II: extragalactic Dark Matter . 38 3.3 Dark Matter searches through γ-rays . 38 3.3.1 γ-ray experiments . 39 3.3.2 Promising targets and astrophysical backgrounds . 40 3.4 The Fermi-LAT isotropic γ-ray background . 42 3.5 Current results . 50 vii viii Contents 4 Particle physics content: the role of radiative corrections 55 4.1 The importance of radiative corrections . 55 4.2 Computing EW corrections to neutralino DM annihilation . 61 4.2.1 From Feynman rules to amplitudes . 61 4.2.2 From amplitudes to the squared matrix element . 62 4.2.3 Cross sections and particles yields . 65 4.3 Results . 67 4.3.1 Spectra of final state particles . 67 4.3.2 Spectra of final stable particles: the differential photon yield . 70 4.3.3 Cross sections and total photon yields . 73 5 Astrophysical distribution: the role of galactic substructures 77 5.1 The galactic Dark Matter distribution . 78 5.2 Dark Matter anisotropy signal . 83 5.2.1 The angular power spectrum of γ-ray anisotropies . 85 5.2.2 Sky-maps generation . 85 5.2.3 Uncertainties on the angular power spectrum of galac- tic Dark Matter . 89 6 MAGN: a new relevant contribution to the IGRB 99 6.1 MAGN as γ-ray emitters . 100 6.2 Radio and γ-ray luminosity correlation . 102 6.3 Upper limits on unresolved MAGN γ-ray flux . 107 6.4 The γ-ray luminosity function . 115 6.5 The source count distribution . 118 6.6 The contribution to the IGRB . 121 7 Dark Matter constraints and potential detection 127 7.1 Constraining Dark Matter through the IGRB . 127 7.1.1 Modeling the astrophysical background . 128 7.1.2 Modeling the Dark Matter contribution . 129 7.1.3 Updated constraints and future potential . 132 7.2 The relevance of Dark Matter spectral features . 138 7.2.1 Looking for spectral features . 139 7.2.2 A concrete example: prospects for IACTs . 140 8 Conclusions and Outlook 151 Appendices 155 A Four-spinors in Dirac representation 157 B Initial state projector for Majorana particles 161 Contents ix C The helicity amplitude method 165 C.1 From Dirac bilinears to helicity vectors . 165 D Kinematics of three-body final state 171 D.1 Vector-contractions . 173 D.2 Kinematical boundaries . 175 E Supersymmetry, a brief compendium 179 F Statistics 185 F.1 The method of Maximum Likelihood . 185 F.2 Statistical Tests . 187 F.3 The Profile Likelihood . 188 Bibliography 189 List of Publications My research activity during the former three years has been focused on Astroparticle Physics, namely on the indirect detection of Dark Matter (DM) through γ-rays. My main contribution in this field deals with the modeling of the expected spectral and angular DM signal as well as with the possibility to constrain the DM annihilation cross section by means of targets as different as the isotropic diffuse γ-ray background and the galactic center region.