ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology

116

Dark Matter in the Galactic Halo A Search Using Neutrino Induced Cascades

in the DeepCore Extension of IceCube

Henric Taavola

Dissertation presented at Uppsala University to be publicly examined in Polhemsalen,Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 4 December 2015 at 09:15 forthe degree of Doctor of Philosophy. The examination will be conducted in English. Facultyexaminer: Associate Professor Jodi Cooley (Southern Methodist University, Texas, USA).

AbstractTaavola, H. 2015. Dark Matter in the Galactic Halo. A Search Using Neutrino InducedCascades in the DeepCore Extension of IceCube. Uppsala Dissertations from theFaculty of Science and Technology 116. 133 pp. Uppsala: Acta Universitatis Upsaliensis.ISBN 978-91-554-9377-6.

A search for Weakly Interacting Massive Particles (WIMPs) annihilating in the dark matterhalo of the Milky Way was performed, using data from the IceCube Neutrino Observatoryand its low-energy extension DeepCore. The data were collected during one year between2011 to 2012 corresponding to 329.1 days of detector livetime. If WIMPs in the dark matterhalo undergo pairwise annihilation they may produce a neutrino signal detectable at the Earth.Assuming annihilation into bb, W+W-, τ+τ-, μ+μ-, νν and a neutrino flavor ratio of 1:1:1 at thedetector, cascade events from all neutrino flavors were used to search for an excess of neutrinosmatching a dark matter signal spectrum. Two dark matter density profiles for the halo wereused; the cored Burkert profile and the cusped NFW profile. No excess of neutrinos from theGalactic halo was observed, and upper limits were set for the thermally averaged product of theWIMP self-annihilation cross section and velocity, <σAv>, in the WIMP mass range 30 GeV to10 TeV. For the bb annihilation channel and the NFW halo profile, the 90% C.L. upper limitsare 9.03×10-22 cm3 s-1 for the mass WIMP 100 GeV and 4.08×10-22 cm3 s-1 for the WIMP mass3000 GeV. The corresponding upper limits for the μ+μ- annihilation channel are 4.40×10-23 cm3

s-1 and 3.20×10-23 cm3 s-1.

Keywords: dark matter, WIMP, neutralino, MSSM, neutrino telescope, IceCube, DeepCore,Galactic halo

Henric Taavola, Department of Physics and Astronomy, High Energy Physics, 516, UppsalaUniversity, SE-751 20 Uppsala, Sweden.

© Henric Taavola 2015

ISSN 1104-2516ISBN 978-91-554-9377-6urn:nbn:se:uu:diva-264079 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-264079)

To my parents, Jan and Gunilla,for always cheering me on.

Table of Contents

Page

Abbreviations and Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1 Dark Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.1 The Mystery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.1.1 Rotational Curves of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.1.2 The Bullet Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.1.3 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.1.4 Shortcomings of the Standard Model . . . . . . . . . . . . . . . . . . . . . . 25

1.2 Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.2.1 The WIMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.3 Dark Matter Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.3.1 Direct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.3.2 Indirect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.3.3 Collider Based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.4 Halo Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2 Neutrino Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2 Energy Losses of Charged Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.2.1 Muon Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.2.2 Electron Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.3 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3 The IceCube Neutrino Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2 The Digital Optical Module (DOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3 The Ice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4 The In-Ice Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.4.1 DeepCore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.5 Data Acquisition and Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.5.1 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.5.2 The Hit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.5.3 Local Coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5.4 Triggering and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 Signal and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.1 The Signal - Neutrinos from WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1.1 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3 Event Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3.1 The Simulation Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Simulation Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 The Signal Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.3.4 The Background Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.1 Hit Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.1.1 Static Time Window Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.1.2 Seeded Radius-Time Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2 First-Guess Reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2.1 Improved LineFit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2.2 Tensor of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2.3 CLast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 Likelihood Reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.3.1 TrackLLH (SPE32) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.3.2 CascadeLLH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.3.3 Monopod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.4 Angular Reconstruction Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6 Event Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.1 Blindness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776.2 Level 1 and 2 - The DeepCore Trigger and Filter . . . . . . . . . . . . . . . . . 78

6.2.1 The DeepCore Trigger - SMT3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.2.2 The DeepCore Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.2.3 Level 2′ - Quality Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.3 Level 3 - Straight Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.3.1 Level 3 Cut Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4 Level 4 - BDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846.4.1 The BDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846.4.2 Level 4 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.4.3 BDT Performance and Final Selection . . . . . . . . . . . . . . . . . . . . 88

6.5 Event Selection Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7 The Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.1 PDFs for Signal and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.2 The Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.3 Creating a Confidence Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.4 Determining the Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

8 Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

8.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.2.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Summary in Swedish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Abbreviations and Acronyms

ΛCDM Lambda Cold Dark Matter

ATWD Analog Transient Waveform Digitizer

BDT Boosted Decision Tree

CMB Cosmic Microwave BackgroundCOG Center Of GravityCORSIKA COsmic Ray SImulations for KAskade

DAQ Data AcQuisition systemDOM Digital Optical ModuledSph dwarf Spheroidal galaxy

fADC fast Analog-to-Digital Converter

GENIE Generates Events for Neutrino Interaction Ex-periments

GPU Graphics Processing Unit

HLC Hard Local Coincidence

IACT Imaging Air Cherenkov TelescopeISM InterStellar Medium

LC Local CoincidenceLED Light Emitting DiodeLSP Lightest Supersymmetric Particle

MaCHO Massive Compact Halo ObjectMCHits Monte Carlo HitsMoND Modified Newtonian DynamicsMSPS Mega Samples Per SecondMSSM Minimal Supersymmetric Standard Model

NFW Navarro-Frenk-White (dark matter halo profile)NuGen Neutrino Generator

11

PDF Probability Density FunctionPMT Photo Multiplier TubePnF Processing and FilteringPPC Photon Propagation CodePROPOSAL PRopagator with Optimal Precision and Opti-

mized Speed for All Leptons

RAPCal Reciprocal Active Pulsing CalibrationRTV Room Temperature VulcanizationRTVeto Radius-Time Veto

SLC Soft Local CoincidenceSMT Simple Multiplicity TriggerSNO Sudbury Neutrino ObservatorySNR Super Nova RemnantSPE Single Photo ElectronSRT Seeded Radius-Time (event cleaning)STW Static Time Window (event cleaning)SUSY SUperSYmmetrySVM Support Vector Machine

TPC Time Projection Chamber

UED Universal Extra Dimensions

WIMP Weakly Interacting Massive ParticleWMAP Wilkinson Microwave Anisotropy Probe

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List of Figures

Page

1 The author posing with a Wedell seal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Adelie penguins at Beaufort Island. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 The Oden bridge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 The Oden docked at McMurdo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.1 Rotation curve of the Andromeda galaxy (M31). . . . . . . . . . . . . . . . . . 221.2 The Bullet cluster.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.3 The Standard Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.4 Results from DAMA/LIBRA-phase1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.5 Summary of upper limits on the SI WIMP-nucleon cross section. 311.6 Summary of the SD WIMP-nucleon cross section. . . . . . . . . . . . . . . . 321.7 Projected 2σ constraints on dark matter annihilations channels

μ+μ− and τ+τ− for DeepCore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.8 Comparison of upper limits of 〈σAv〉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361.9 Line-of-sight integral for the Burkert and NFW halo profiles. . . . 382.1 Illustration of Cherenkov light emission. . . . . . . . . . . . . . . . . . . . . . . . . . . 402.2 Illustration of the development of an electromagnetic cascade. . . 412.3 Illustration of charged-current and neutral-current interactions. . 432.4 The neutrino and antineutrino cross sections on nucleons and

electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.1 Overview of the IceCube Neutrino Observatory. . . . . . . . . . . . . . . . . . . 463.2 Illustration of an IceCube DOM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3 Schematic description of a PMT.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.4 An example ATWD waveform of a single photoelectron. . . . . . . . . 483.5 Effective scattering and absorption in IceCube as a function of

depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.6 The local coordinate system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.7 Schematic overview of the IceCube string layout. . . . . . . . . . . . . . . . . 523.8 Simulated track and cascade events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.9 Two simulated cascade events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.1 Illustration of the variables used to calculate the line-of-sight

integral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2 Example neutrino spectra from annihilating WIMPs. . . . . . . . . . . . . . 614.3 Particle fluxes from cosmic rays and vertical muon intensity. . . . . 625.1 Illustration of hit cleaning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 The angular resolution distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.1 Illustration of the DeepCore veto algorithm. . . . . . . . . . . . . . . . . . . . . . . 79

13

6.2 Level 3 variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.3 Level 3 variables (continued). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826.4 Level 4 variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.5 Level 4 variables (continued). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876.6 BDT score distribution for the low-energy event sample. . . . . . . . . 896.7 BDT score distribution for the high-energy event sample. . . . . . . . . 896.8 The neutrino effective area as a function of neutrino energy. . . . . . 916.9 Sky maps of the true and reconstructed event distributions for

signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.1 Examples of signal and background PDFs. . . . . . . . . . . . . . . . . . . . . . . . . 967.2 Distribution of upper and lower limits from 104 pseudo-experiments

with no injected signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.3 Sensitivities to 〈σAv〉 as a function of the WIMP mass. . . . . . . . . . . 1018.1 Distributions of the ψ angles of the unblinded event samples.. . . . 1038.2 Resulting upper limits of 〈σAv〉 for the Burkert halo profile. . . . . . 1058.3 Resulting upper limits of 〈σAv〉 for the NFW halo profile. . . . . . . . 1068.4 Comparison of final upper limits to other experiments. . . . . . . . . . . . 111

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List of Tables

Page

1.1 Measured values of the cosmological parameters. . . . . . . . . . . . . . . . . 241.2 A summary of particles and fields in the MSSM. . . . . . . . . . . . . . . . . . 281.3 The dark matter halo parameters used in this work.. . . . . . . . . . . . . . . 385.1 Summary of the angular resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.1 Summary of data rates for the different cut levels. . . . . . . . . . . . . . . . . 938.1 Summary table of the results for the χχ→ bb annihilation chan-

nel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078.2 Summary table of the results for the χχ→ μ+μ− annihilation

channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088.3 Summary of systematic uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

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Introduction

This thesis is a presentation of a dark matter search using neutrino inducedcascades in the DeepCore extension of the IceCube Neutrino Observatory. Itis not known what the dark matter is, but indirectly we can infer its presencein our Universe and it seems to be roughly five times more abundant than thenormal matter we are familiar with. Current popular theories suggest that thedark matter is a new elementary particle that has gone unnoticed due to itsunwillingness to interact with normal matter. The focus of the work presentedhere is to look for signals from such particles as they might annihilate pairwiseto produce neutrinos that we can detect.

The structure of this thesis is as follows: We start by setting the dark matterstage with a brief introduction in chapter 1, including a general presentation ofdifferent methods of detection and how the dark matter might be distributed inour galaxy. In chapter 2, the principles of neutrino detection using a Cheren-kov detector are discussed. The IceCube Neutrino Observatory is presented inchapter 3 and a description of what the signal and background look like is pre-sented in chapter 4, along with how they are simulated. Chapter 5 presents thevarious data reconstruction techniques used in the data analysis, while chapter6 details the data selection. Chapter 7 describes the analysis method used andthe results are presented along with conclusions and outlook in chapter 8.

The Author’s ContributionDuring my time as a graduate student at Uppsala University I have had theprivilege to work with many of the skilled people in the IceCube Collabora-tion. Apart from developing the analysis presented in this thesis, I also adaptedand tested the trigger and filter used by DeepCore to expand its fiducial vol-ume so it could take full advantage of the completed 86 string in-ice array.This trigger and filter was used as data taking with the full detector began inMay 2011, which is the start of the one year data set used in this analysis.I was also part of the effort to run IceCube data simulation on the Swedishnational grid infrastructure, SweGrid. I have had the privilege to attend nineIceCube Collaboration meetings, several workshops and summer schools allover Europe and North America, presenting my work and having very fruit-ful discussions. When Uppsala University hosted the IceCube CollaborationMeeting in 2011, I was part of the organizing committee.

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Some other work not included in this thesis where I have contributed duringmy time as a graduate student include:

• Guiding school children, aged 10-12, in the physics exhibition AugustaÅngström at Ångströmlaboratoriet, Uppsala University. It was a veryenriching experience and I recommend it to any graduate student, if evergiven the chance to do something similar.

• Building a permanent outreach exhibition of IceCube together with mycolleague Rickard Ström. It is placed outside our department in Ång-strömlaboratoriet at Uppsala University and has screens mounted insidecustom made “ice” blocks showing IceCube event views and a docu-mentary about the detector.

• Doing field work for two months onboard the Swedish icebreaker Odenas it made its way from Montevideo, Uruguay, to the McMurdo researchstation at the coast of Antarctica. I was running an experiment onboardtogether with Samantha Jakel, a U.S. undergraduate student, measur-ing the cosmic ray flux as a function of geographical latitude. We useda modified version of an IceTop tank as our detector (see chapter 3),housed inside a freezer container. To say that this was an amazing ex-perience would be a massive understatement and for any doubters, evi-dence of this are presented in figures 1, 2, 3 and 4.

Units and ConventionsThroughout this thesis natural units will be used, meaning � = c = kB = 1,where � is the reduced Planck constant, c is the speed of light in vacuum andkB is the Boltzmann constant. Particle masses will be given in electronvolt(eV) and cross sections in cm2.

Cover IllustrationThe illustration on the cover is an event view of a simulated 1.6 TeV electronneutrino that has interacted in the detector volume and created a cascade. Theoptical modules that detected the light from this cascade are indicated withcolored spheres and colors represent the timing, where red is early and violetare late detections. The size of the spheres indicate how much light eachmodule registered.

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Figure 1. The author posing with a Wedell seal on the ice sheet outside McMurdostation, Antarctica, on January 9, 2010.

Figure 2. Picture of Adelie penguins and their chicks taken while visiting a largepenguin colony on Beaufort Island, Antarctica, on January 29, 2010.

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Figure 3. The Oden bridge, January 11, 2010.

Figure 4. The Oden docked alongside the tankship Paul Buck at McMurdo station,Antarctica, on January 26, 2010.

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1. Dark Matter

There seems to exist much more matter in the Universe than what can be ex-plained by visible matter such as stars, planets, gas and dust clouds. Thequestion why this is so, along with why there also seems to exist a dark energycomponent, is one of the greatest unsolved mysteries in the field of physicstoday.

This chapter will cover the background of the dark matter story along withthe observational evidence, the Weakly Interacting Massive Particle (WIMP)as a candidate to offer an explanation of said evidence and different techniquesfor detecting such WIMPs. Also, a presentation of the different models de-scribing how the dark matter could be distributed in the Galaxy is given.

1.1 The MysteryThe problem of the “missing matter”, as it was initially called, was discoveredin the early 1930’s. Fritz Zwicky studied galaxy clusters and found that thegalaxies of the Coma cluster had such large velocity dispersions that the grav-ity exerted by the visible matter in these galaxies could not, by itself, explainhow the cluster could stay together [1]. For the measurements to add up, therehad to be a larger invisible gravitating mass mixed in among the galaxies.

In those early days the problem was noted, but not much happened in thefield until the 1960’s and 1970’s, when studies of how galaxies rotate startedto become more detailed.

1.1.1 Rotational Curves of GalaxiesIn the late 1960’s, Vera Rubin studied the rotation of the Andromeda galaxy bydetermining the velocities of 67 H-II regions (large clouds of partially ionizedhydrogen) distributed between 3 and 24 kpc from the galaxy’s core [2]. Thiswas done using spectroscopy to detect the red and blue shift of the prominentspectral lines from the ionized hydrogen. If the galaxy only consisted of thevisible matter we would expect the orbital speed of its stars and gas to decreasewith increasing radial distance as v ∝ 1/

√R, where v is the orbital speed and

R is the radial distance to the center of the galaxy. Much like how the planetsorbit the Sun. However, Rubin did not see this kind of behavior. In fact, hermeasurements showed a quite high and flat velocity distribution at larger radii.

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Figure 1.1. The rotation curve of the Andromeda galaxy (M31) is shown along withoptical measurements (triangular markers) by Rubin and Ford [2] and 21 cm radiowavelength measurements by Roberts and Whitehurst [4]. The lines for the surfacedensity and cumulative mass are derived from the best fit of a model of the galaxy.Credit: Figure 16 from reference [4].

This suggests there being more mass present in the Andromeda galaxy thancan be detected. However, no mention of such an explanation was made in herpaper from 1970 and the measurements did not extend far enough from thegalaxy’s center to prove the existence of dark matter. It was shown in a paperby Kenneth Freeman, also from 1970, that the rotational curve of the outerpart of the luminous disk agrees with a Keplerian rotation [3]. In 1975 MortonRoberts and Robert Whitehurst published a paper that extends the rotationalcurve data of the Andromeda galaxy using radio measurements (21 cm wave-length). These measurements extend out to 30 kpc and show an almost flatrotational curve indicating a large mass beyond the optical disk [4], see figure1.1. In a later paper Rubin wrote together with W. Kent Ford, Jr, and NorbertThonnard published in 1980, where they studied 21 additional galaxies, theywrite: “The conclusion is inescapable that non-luminous matter exists beyondthe optical galaxy.” [5]. This is not conclusive evidence for what we today calldark matter, but Rubin’s studies together with measurements done in radiowavelengths (21 cm) certainly suggest there is a large mass present in thesegalaxies not readily detectable in the electromagnetic spectrum.

Recently, measurements of the rotational curves of our own galaxy havebecome accurate enough to provide evidence for the existence of dark mattereven within the Sun’s orbit around the Galactic center [6].

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Figure 1.2. The merging galaxy cluster 1E 0657-558, also known as “the Bullet clus-ter,” in optical (left) and X-ray (right). The green contours in both panels, obtainedfrom gravitational lensing measurements, trace the lines of gravitational equipotentialin the cluster and show where the dark matter is located. The gray contours denotethe 68.3%, 95.5% and 99.7% confidence levels of the peaks of the gravitational po-tential, while the plus signs mark the center of the X-ray emitting plasma clouds. Thestraight white lines indicate 200 kpc at the distance of the cluster. Credit: Figure 1from reference [7], c© AAS. Reproduced with permission.

1.1.2 The Bullet ClusterIn most cases when making observations of galaxies or clusters of galaxies,the baryonic and dark matter overlaps which makes it difficult to separate theeffects of one or the other component in measurements. But this is not the casefor the merging galaxy cluster 1E 0657-558, or “the Bullet cluster,” which isone of the clearest evidence for the existence of dark matter [7]. It is a regionwhere two galaxy clusters have collided and passed through each other.

Using images from the Chandra X-ray Observatory and combining themwith gravitational lensing measurements from optical images, it has been seenthat the X-ray emitting intracluster plasma have collided and interacted, caus-ing it to slow down. The dark matter component have passed through virtuallyunhindered, causing a clear separation between the center of the plasma andcenter of mass of the clusters, as can be seen in figure 1.2. In this kind ofevent the galaxies in the cluster behave as collisionless particles. Since theX-ray emitting plasma makes up 5-15% [8, 9] of the mass and the stellar com-ponent of the cluster’s galaxies makes up about 1-2% [10], this is a clear signof a large, invisible, gravitating mass present in the cluster. If no dark matterwould be present, the plasma would be the dominant mass contribution in thecluster and the gravitational potential would follow the plasma distribution.This kind of measurement is independent of many assumptions and proves theexistence of dark matter as long as one can assume standard gravity.

The measurement of the gravitational potential in the Bullet cluster done byClowe et al. [7] was made using the technique called weak lensing, where onelooks at how distorted objects in the background appear due to the light beingbent by the gravity of the cluster in the foreground. Since this distortion is very

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small, statistical methods are used by observing several background objects,measuring components of their distortions. These measured quantities are thencompared to a statistical average of all the observed objects of the same typeto deduce the properties of the gravitational lens.

As a clarifying contrast, strong lensing is an effect that manifests when thegravitational potential of the foreground object is stronger and the backgroundobject is close enough for it to appear as multiple images or distorted into anarc.

1.1.3 CosmologyTo get a picture of the dark matter content for the Universe as a whole, weneed to look to the cosmological theories for answers. From the Friedmannequations we can obtain an expression for the critical density for a flat universeas

ρcrit =2H2

0

8πGN, (1.1)

where H0 is the Hubble constant and GN is Newton’s gravitational constant.This critical density is the combined average density of energy and matterneeded to get the flat geometry that we observe. The density parameter isconstructed such that

Ωi =ρi

ρcrit, (1.2)

where ρi is the energy density contribution of any particular component ofthe critical density. In the Lambda Cold Dark Matter (ΛCDM) model, thesecomponents are baryonic matter Ωb, dark matter ΩDM and dark energy ΩΛ.Since a flat universe requires thatΩtot =

∑Ωi = 1, the value of each component

also represent the fraction of that component [12].From the latest measurements of the Cosmic Microwave Background

(CMB), made by the Planck satellite [11], we can conclude that the Universeseems to have a flat geometry with about 5% baryonic matter, 26% dark matterand 69% dark energy. See table 1.1 for more details. The 7-year data from the

Table 1.1. The measured values of the baryon densityΩb, the cold dark matter densityΩc, the dark energy density ΩΛ and the Hubble constant H0 [11]. h is the Hubbleparameter defined as h ≡ H0/(100 km s−1 Mpc−1).

Ωbh2 Ωch2 ΩΛ H0(km s−1 Mpc−1)

0.02205±0.00028 0.1199±0.0027 0.685+0.018−0.016 67.3±1.2

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Figure 1.3. Schematic description of the particle content of Standard Model of particlephysics. The gray fields in the background indicate the possible interactions betweenthe particles. Though not indicated in the figure, the Higgs boson can interact with theW± and Z0 bosons, the quarks and the charged leptons. Image credit: [15].

Wilkinson Microwave Anisotropy Probe (WMAP) [13] are also compatiblethe Planck data.

There are also highly accurate measurements of supernovae that support theexistence of dark matter. In the data from the Supernova Cosmology Project,where 557 type Ia supernovae with high redshifts were studied, there was anexcellent agreement to the ΛCDM model [14].

1.1.4 Shortcomings of the Standard ModelThe Standard Model of particle physics describes the properties of the knownelementary particles and the possible interactions between them except forgravity. See figure 1.3 for a schematic overview.

Many aspects of the model have been confirmed through experiments withhigh precision and the model was successful in predicting the existence of, forexample, the bosons of the weak interaction and Higgs particle before theywere discovered experimentally [16]. In spite of this, none of the particles inthe Standard Model can provide a satisfactory explanation to the dark matterproblem. Also, the Standard Model does not account for the non-zero masses

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of the neutrinos and the resulting neutrino oscillations. These facts are bothclues to physics beyond the Standard Model.

1.2 CandidatesThere are several theories trying to explain the observations described in theprevious sections. Some try to keep the Standard Model unchanged and sug-gest that the force of gravity changes at large length scales. One such theoryis Modified Newtonian Dynamics (MoND). While it has been successful inexplaining the rotational curves of galaxies and the velocity dispersions ofgalaxy clusters, it has not been able to explain observations such as the Bulletcluster (described in section 1.1.2) and the anisotropy of the CMB [17].

Non-luminous baryonic matter such as black holes, brown dwarfs, neutronstars, white dwarfs and unassociated planets collectively know as MassiveCompact Halo Objects (MaCHOs), have also been suggested as a candidatefor dark matter. They would all be too dim to detect over the large distancesinvolved when observing other galaxies and galaxy clusters. However, theseobjects can only account for a small fraction of the dark matter, as a search forthe gravitational microlensing effects these objects should cause did not findenough instances of this effect to explain the dark matter observations [18].

The most popular and widely used theories today involve a class of hy-pothetical elementary particles called Weakly Interacting Massive Particles(WIMPs). The reason for them being so popular is because they fit in verywell into theories for physics beyond the Standard Model, as well as in cos-mological models as a candidate for dark matter. The focus of this thesiswill be on the neutralino, which is the lightest supersymmetric particle of thesupersymmetric extension of the Standard Model, but there are other WIMPmodels. For example, some theories makes use of Universal Extra Dimen-sions (UED) where extra, curled up, dimensions are added to our familiarfour. When standard model particles are allowed to move through these UEDsan infinite number of so-called Kaluza-Klein states are created. The lightestof these states are believed to be stable, and is therefore a candidate for beingthe dark matter [19].

Another particle candidate for dark matter is the axion. It is a hypotheticalparticle that arises as a natural solution to the strong CP problem, and will bebriefly discussed as there are a few experiments looking for it.

1.2.1 The WIMPThe WIMP, as the name suggests, must interact with normal matter onlythrough a force with similar strength as the weak force (and gravity), be mas-sive and stable (i.e. have a lifetime larger than the age of the Universe). Thereason for this is that any particle interacting through any of the other forces

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would probably have been detected already. The lifetime must be long enoughfor WIMPs created just after the Big Bang to survive to the present day. Itshould also be massive, since it would make it non-relativistic, or “cold,” atfreeze-out in the young Universe. This is desirable since a non-relativisticparticle can explain both the small and large scale structures observed in theUniverse. Relativistic particles struggle with explaining the small scale struc-tures as they would not clump together due to their high speed.

The “WIMP Miracle”

Any particle candidate for dark matter must have been created in the earlyUniverse in sufficient amounts to account for the observations described inprevious sections. It also needs to have decoupled from ordinary matter as theUniverse expanded and cooled. After the Big Bang, the temperature was highenough for reactions of the type

χχ↔ xx (1.3)

to occur and reach an equilibrium, where χ is a WIMP and x is a Standardmodel particle. When the temperature drops below the WIMP mass mχ thereaction can only go in one direction, which means equation (1.3) becomes

χχ→ xx (1.4)

and no more WIMPs will be produced. As the Universe continued to expand,the WIMPs soon became too diluted to annihilate at any significant rate. Atthis “freeze-out” point, the dark matter decoupled from normal matter and thisrelic density co-evolved with the other components so thatΩχ has stayed moreor less constant up to this day.

If one assumes that the WIMPs interacted with Standard Model particlesin the primordial soup of the early Universe with standard weak interactionstrength, one finds that a good approximation of the current relic density onlydepends on the annihilation cross section σA and velocity v as

Ωχh2 ≈ 3×10−27 cm3 s−1

〈σAv〉 , (1.5)

where h is the Hubble parameter defined as h ≡ H0/(100 km s−1 Mpc−1) [20].〈 〉 denotes thermal averaging, usually assuming a Maxwellian velocity distri-bution of the WIMPs. If the mass of the WIMP is of the same order as W± andZ0 we get a relic density close to the one observed today. Since a particle withthese properties are predicted by supersymmetric extensions of the Standardmodel, this is sometimes referred to as the WIMP miracle [21].

Supersymmetry

Supersymmetry, or SUSY for short, is a collective name for models that extendthe Standard Model by adding a fermion-boson symmetry that results in all the

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Table 1.2. A collection of particles and fields and their supersymmetric counterpartsin the MSSM. Note that there are only evidence for one neutral Higgs and no chargedHiggs in the Standard Model. Table adapted from reference [22].

Particles/Fields Supersymmetric partners

Interaction eigenstates Mass eigenstatesSymbol Name Symbol Name Symbol Name

q = u, d, c, s, t, b quark qL, qR squark q1, q2 squark� = e, μ, τ lepton �L, �R slepton �1, �2 sleptonν = νe, νμ, ντ neutrino ν sneutrino ν sneutrinog gluon g gluino g gluinoW± W-boson W± wino

⎫⎪⎪⎪⎬⎪⎪⎪⎭ χ±1,2 charginoH−}

charged Higgs H−1}

higgsinoH+ H+2B

}γ, Z0 B-field B bino

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭χ0

1,2,3,4 neutralinoW3 W3-field W winoH0

1⎫⎪⎪⎪⎬⎪⎪⎪⎭ neutral Higgs H0

1

}higgsinoH0

2 H02H0

3

Standard Model particles getting a supersymmetric partner. Each fermion hasa supersymmetric partner called a sfermion, which is a boson. Also, eachboson has a supersymmetric partner called gauginos or higgsinos, which arefermions. See table 1.2 for an overview of the particles in the so-called Mini-mal Supersymmetric Standard Model (MSSM). Many SUSY models, such asthe MSSM, impose a conserved quantity called R-parity defined as

R ≡ (−1)3B+L+2S , (1.6)

where B is the baryon number, L is the lepton number and S is the spin of aparticle. This quantity should be conserved in a particle reaction 1 2→ 3 4such that R1 ·R2 = R3 ·R4. Thus, all Standard Model Particles have R = 1 andtheir supersymmetric partners have R = −1, meaning that the lightest super-symmetric particle (LSP) has to be stable since it has no lighter particle withthe same quantum number to decay into. In many versions of the MSSM thisLSP is the neutralino χ0

1 which is the kind of WIMP we want as our candidatefor dark matter. From now on we simply denote this with χ.

1.3 Dark Matter DetectionThere are many experiments, current and planned, trying to detect dark matterand they utilize many different approaches and detection principles. They cantry to detect WIMPs directly by observing the expected interactions between

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them and the normal matter in the detector. Another approach is searchingindirectly, by observing expected signals resulting from WIMPs annihilating(or decaying if the model permits) and producing standard model particles thatcan be detected.

1.3.1 DirectDirect detection experiments use different techniques to look for nuclear re-coils caused by a WIMP scattering off a nucleon in the detector material.Due to the weak-scale interaction, these WIMP-scattering events are very rarewhich demands that these types of detectors are heavily shielded from back-grounds, or have very efficient veto mechanisms. The backgrounds can beatmospheric muons or radioactive decays in the surrounding environment. Itis also important that the detector material is as free from radioactive isotopesas possible. Most of the shielding from atmospheric muons is obtained byinstalling the detectors in laboratories that are deep underground, such as inabandoned mines. Since the WIMP-nucleon cross section is expected to betiny, the WIMPs are only expected to produce single-scatter events in the de-tectors. Many detectors can therefore reject events with multiple scatteringsfrom, for example, neutrons. Consequently, this means that the backgroundsthat are most difficult to reject are nuclear recoils from spontaneous fissionreactions, reactions induced by muons or single scatter neutron events from(α,n) reactions. If the detector has the ability to determine the interactionvertex of the event, this can also be used to reject background since mostbackground events are expected to occur closer to the edges of the detectormaterial. Some detectors can also reject background by being able to differ-entiate the recoils of the atomic electrons from the desired nuclear recoils.These electronic recoil events are induced by environmental γ-backgroundsand by β-particles. Apart from being deep underground the detectors are usu-ally shielded with dense materials such as copper or lead to protect from γ-raysand water or polyethylene to shield against neutrons.

Direct detection experiments are sensitive to the spin independent or spindependent WIMP-nucleon cross sections, which depend on the spin of thenuclei in the detector material. Since direct detection experiments depend oninteractions between dark matter and normal matter, they have no sensitivityto the WIMP self-annihilation cross section.

There are experiments that claim to see a dark matter signal. The mostprominent of these claims is the DAMA/NaI experiment, which searched forthe annual modulation of the expected signal using a NaI(Tl) scintillator. Themodulation stems from the variation in relative velocity to the Galactic darkmatter halo that the Earth experiences due to its orbit around the Sun. Theypublished their results of the full seven years of the experiment in 2003 wherethey claim a discovery of an annual modulation due to WIMPs at 6.3σ sig-

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Figure 1.4. DAMA/LIBRA-phase1 residual rate of the single-hit scintillation events(counts per day) in the 2-6 keV energy range. The dots with error bars are the time-binned data points and the curve is a cosine with a period of 1 year and amplitudethat has the best fit to the data. The dashed vertical lines correspond to when the darkmatter signal is at its maximum (June 2nd) and the dotted lines mark the expectedminimum. Image credit: Figure 2 from reference [23].

nificance [24]. This result has been followed up by the DAMA/LIBRA-phase1experiment, which is the successor to DAMA/NaI and their result seems to standas the upgraded detector finds the signal at 7.5σ in another seven annual cy-cles, see figure 1.4. Combining the data from the two experiments results ina significance of 9.3σ in a total of 14 annual cycles [23]. However, these re-sults remain controversial since there has been no clear confirmation of theseresults and several other experiments have produced limits that exclude themby several orders of magnitude. The experiments with the strongest limitsare XENON100 [25] and LUX [26], which are both dual-phase Time ProjectionChambers (TPCs) using liquid xenon as detector medium.

The DM-Ice project [27] is using the same kind of NaI crystals as DAMAand currently have a prototype detector deployed at the South pole beneaththe IceCube in-ice array, which serves as a veto for the atmospheric muons.If the full-size DM-Ice detector is deployed, it will have the power to probethe finding by DAMA. Due to its location in the southern hemisphere, it has aunique opportunity to check if the DAMA signal is due to seasonal variationsin the atmospheric background. DM-Ice should see an opposite modulation ifthis is the case.

There have also been weaker claims of evidence for dark matter fromCDMS-Si, which is the Silicon detector of the CDMS-II experiment. Theyreported three signal events with a p-value of 0.19% [28], but at a lower crosssection than DAMA/LIBRA. However, this result is in conflict with the limit setby the successor of the same experiment, SuperCDMS, which is almost oneorder of magnitude lower [29].

The experiments mentioned above are most sensitive to the spin indepen-dent WIMP-nucleon cross section, but some of them also have sensitivity to

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Figure 1.5. Summary of various results on the spin-independent WIMP-nucleon crosssection from experiments indicated in the plot. Figure taken from reference [34] weremore details can be found.

the spin dependent cross section. This is due to some, or all, of their targetnuclei having either unpaired protons or unpaired neutrons. The target nu-clei making detectors most sensitive to the spin dependent cross section is19F [30]. Therefore, there are experiments that select their detector materialdue to its content of 19F to maximize their sensitivity to the WIMP-protoncross sections. The experiments that have the strongest limits in this parame-ter space are PICASSO [30], SIMPLE [31] and COUPP [32], for WIMP massesranging from O(1) to O(104) GeV. The COUPP detector is a bubble chambersusing CF3I as its medium while PICASSO and SIMPLE are using C4F10 andC2CIF5 respectively. The latter two detectors have their mediums enclosedas superheated droplet in a gel where the formations of bubbles are detectedacoustically. When it comes to the WIMP-neutron spin-dependent cross sec-tion, the best limit comes from XENON100 [33]. A summary of recent directdetection results for the spin-independent and spin-dependent WIMP-nucleoncross sections are available in figures 1.5 and 1.6 respectively.

There are a few direct detection experiments actively looking for axions.Some are experiments that are primarily looking for WIMPs but have somesensitivity to the axio-photon coupling constant �Aγ and the axio-electric cou-pling constant �Ae. DAMA [35] and EDELWEISS [36] are examples of such exper-iments. Experiments with a liquid detector medium have no sensitivity to �Aγsince they lack a strictly oriented magnetic field. However, these experimentscan still look for axions “indirectly” by detecting electrons that are due to theaxio-electric effect and are therefore sensitive to �Ae. This kind of searches

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Figure 1.6. Summary of various results on the spin-dependent cross section fromexperiments indicated in the plot assuming WIMPs would couple only to proton (left)or neutron (right) spins. Figure taken from reference [34] were more details can befound.

have been performed by, for example, XMASS [37] and XENON100 [38], wherethe latter reported the better limit. There are dedicated axion searches, suchas ADMX [39] that uses a microwave cavity inside strong magnets. When ax-ions encounter a magnetic field perpendicular to its momentum, a photon iscreated. This is known as the Primakov effect.

1.3.2 IndirectIn indirect searches, one looks for the annihilation (or decay) products ofWIMPs. These products need to be stable enough to allow them to travelover the vast distances in space, such as γ, e±, νe,μ,τ, etc. Indirect detectionexperiments can be sensitive both to the WIMP self annihilation cross sectionas well as the WIMP-nucleon cross sections depending on the source beinglooked at.

Sources

When searching indirect signals from dark matter, one can tailor the search tothe different sources where dark matter is expected to be concentrated. Somesources such as dwarf galaxies and the Galactic center and halo can be utilizedby most signal channels, while some are only useful for neutrino searches.

The Galactic center and halo are interesting targets for indirect dark mattersearches. As earlier described, the visible part of galaxies seem to sit at thecenters of much larger halos of dark matter. We therefore expect the WIMPconcentration to be largest at the Galactic center. The precise distribution ofdark matter in the halos is an active field of research and there are several com-peting models. More on these models in section 1.4. Since our own galaxyprovides us with a large amount of dark matter close by, it is an excellentsource to look for a signal from annihilating WIMPs. One can either con-

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centrate on the Galactic center region where the dark matter concentration isbelieved to be largest, or one can look for signals from the entire halo. The lat-ter is the strategy selected for the analysis described in this thesis. The reasonfor this is that this analysis is optimized for low-energy cascades for which theangular resolution is not as good as for tracks. Also, one of the most favoredhalo profiles (Burkert) is not very peaked at the Galactic center resulting in thata higher fraction of the potential signal would come from outside the Galacticcenter region. This strategy also avoids a potential contamination from thevery active central parts of the Milky Way.

Dwarf spheroidal galaxies (dSphs) such as Segue 1 are also interestingsources when considering WIMP signals. The reason for this is that theyhave very large mass-to-light ratios, suggesting they are dark matter domi-nated [40]. Many dwarf galaxies would also appear as point sources due totheir distance from Earth. Even though their distance from us makes the sig-nal weaker one can reach high sensitivities by stacking multiple dwarf galax-ies statistically. This approach is also what has given us the strongest limits todate, at least for lower range WIMP masses.

When looking at the Sun and the Earth the idea is to look for WIMPs thathave been captured in the gravitational wells of these objects. This can happenif the WIMPs scatter off the nuclei in these massive bodies and loose enoughenergy to become trapped. This allows for a higher WIMP concentration tobuild up which would boost the self annihilation rate at the centers of thesebodies. There are models [41] that describe the balance between the captureand annihilation rates so an expected signal rate can be calculated. Most ofthese assume that a steady state have been reached. These sources are onlyinteresting for neutrino searches since neutrinos are the only particles able toescape from the interiors of the Sun and the Earth.

Experiments

Neutrinos are very attractive as cosmic messengers since they are electri-cally neutral and are not affected by magnetic fields present in and outsideour Galaxy. They thus point back to their sources. Also, they only interactthrough the weak force making them the only particles that can escape fromvery dense objects and regions virtually unhindered and keep traveling unim-peded through dust and gas. These features, although desirable, also makeneutrinos quite challenging to detect (see ch. 2) and require very large detec-tors. The two largest experiments currently searching for dark matter usingneutrinos are IceCube located in the ice cap of the South pole (see ch. 3)and ANTARES [42] located in the Mediterranean sea off the coast of Toulon,France. Both are Cherenkov detectors using ice and water as their detectormedium respectively. Other, smaller, neutrino detectors producing competi-tive results, especially in the lower WIMP mass range are Super-Kamiokande[43], Baksan and Baikal [44]. The neutrino experiments are also the only de-tectors that can search the same WIMP-nucleon cross section parameter space

33

as direct detection experiments do by looking for neutrino signals from WIMPannihilations inside the Sun. Even though this signal comes from pair-wiseannihilating WIMPs, it is directly connected to the capture process which in-volves the WIMP-nucleon cross section. IceCube currently have the strongestlimits for the spin dependent WIMP-proton cross section in the higher part ofthe WIMP mass range [45], see left plot of figure 1.6. Apart from the Sunand other massive objects, such as the Earth [46], neutrino signals have beensearched for from other sources such as the Galactic center [47], Galactic halo[48] and nearby extra-galactic sources, such as dwarf galaxies [49].

The γ-ray channel can be used to look at most of the potential sources justmentioned, except for the Sun and the Earth. In the GeV to TeV energy rangeγ-rays do not scatter much during their journey through space and generallypoint back to their origin. Also, for sources relevant to dark matter searches theabsorption can generally be neglected as well. This makes γ-rays a very goodchannel for dark matter searches. The relative ease in detecting high energyphotons together with a long history of technical development results in γ-experiments producing the strongest limits we currently have on the WIMPself-annihilation cross section for masses up to about 10 TeV.

There are two main methods to detect γ-rays, where satellite based pair-conversion telescopes such as Fermi Large Area Telescope (Fermi-LAT) [50]are most sensitive at the lower energy range (up to a few hundred GeV). Abovethat ground-based Imaging Air Cherenkov Telescopes (IACTs), such as MAGIC[51], VERITAS [52] and H.E.S.S. [53] become more sensitive, although theirfield of view is generally more limited at around 5◦ compared to ∼120◦ for theFermi-LAT. An advantage of satellite-based experiments is that the ambientbackground is very low. This is not the case for IACTs that have a significantbackground from charged cosmic rays. As previously mentioned, the strongestlimits for annihilating WIMPs comes from γ-experiments where Fermi-LATdominates the lower mass range (up to ∼ 500 GeV) with upper limits reachingall the way down to the so-called natural scale for the lowest WIMP masses[54]. These limits were obtained by using four years of data and combiningthe observations of 25 dSphs that are satellite companions to the Milky Way.At the higher mass range (up to 10 TeV) the best limits comes from HESS [55],where they observed the Galactic center searching for a residual γ-ray fluxconsistent with dark matter.

There have been claims of a dark matter signal in γ-ray data from the di-rection of the Galactic center. In 2012 Bringmann et al. found a weak spectralline at ∼130 GeV in the publicly available data from Fermi-LAT with a sig-nificance of 3.1σ [56]. This claim was followed up with an analysis by theFermi-LAT Collaboration where they used 3.7 years of data that had been re-processed with updated instrument calibrations. The best fit for a spectral linewas found at 133 GeV but only with a global significance of 1.5σ [57].

Other measurements have also provided interesting hints, although nothingas prominent as a spectral line. These are measurements of the electron and

34

Figure 1.7. Projected 2σ constraints on dark matter annihilations producing μ+μ−(left) and τ+τ− (right) for DeepCore from [62]. The blue solid lines represent 1 and3 years of cascade events, while the dashed blue line show 5 years of track evens forcomparison. The red and orange areas indicate the region allowed by the electronand positron data from Fermi and PAMELA respectively. Credit: Figure 3 from [62].Copyright (2010) by the American Physical Society.

positron fluxes from Fermi-LAT [58] and PAMELA [59]. Their measurementsshow an unexpected excess in the combined flux of electrons and positrons aswell as a much higher positron-to-electron ratio than what can be explainedby existing theories, such as secondary production from cosmic rays interact-ing with matter and radiation in the interstellar medium (ISM). The positronfraction measurements have also been confirmed and improved upon by theAMS experiment [60, 61] located on the International Space Station. Thesemeasurements are very interesting from a dark matter point of view since theirspectra might be due to WIMPs annihilating or decaying.

Mandal et al. suggest the use of DeepCore and neutrinos of all three fla-vors (cascade-like events) to look for a signal from dark matter matching thePAMELA and Fermi-LAT anomalies [62]. This paper is also what inspired theanalysis described in this thesis since it predicts superior performance com-pared to using only charged-current νμ interaction (track-like events) whenprobing the WIMP annihilation cross section parameter space allowed by thePAMELA and Fermi-LAT data, see figure 1.7. There are also suggestions thatthese anomalies are due to positron production in pulsars, either one or twothat are relatively close to us [63, 64] or by a combined diffuse flux frompulsars throughout the Milky Way [65]. If it is the former case, this wouldbe testable by trying to detect dipoles in the positron flux consistent with thedirection of the closest pulsars [66]. There are also suggestions that tradi-tional sources of cosmic rays, such as Super Nova Remnants (SNRs), canactually produce the observed positrons directly [67, 68]. These hypotheses

35

Figure 1.8. Comparison of upper limits from several IceCube analyses (designated byICXX, where XX is the number of strings) and limits from gamma-ray searches ofdSphs by VERITAS, MAGIC and Fermi-LAT. Also included are the preferred regionsof the dark matter interpretation of the electron and positron observations by PAMELA,Fermi-LAT and H.E.S.S. Figure taken from reference [47] where more details canbe found.

are testable by measuring proton/anti-proton and B/C (boron-to-carbon) ratios[69], for example with the AMS which has such capabilities.

A summary of results from indirect dark matter searches are presented infigure 1.8, where upper limits from IceCube [70, 48, 49, 47] are presentedalong with limits from gamma-ray searches from dSphs by Fermi-LAT [54],MAGIC [71] and VERITAS [72, 73].

1.3.3 Collider BasedParticle accelerators can be used to collide particles (e.g. e± or p) and lookfor signatures of dark matter particles being created. Typically one looks forevents in the detectors with large amounts of missing energy, which is theterm used for particles escaping the detector without any detectable interac-tion. For supersymmetric dark matter one looks for events that have missingenergy together with high jet multiplicity and unbalanced momenta. The mostproblematic backgrounds for these searches are events involving neutrinos,such as (Z0→ νν) + jets or tt which have high jet multiplicity.

Even if WIMPs are created and detected in collider experiments, these par-ticles cannot be confirmed to be what makes up the dark matter we see inthe Universe. Since these particles will escape the detectors without leaving a

36

trace it will also be impossible to determine if their lifetimes are large enoughto build up the relic density we see today. However, evidence or discoveriesfrom collider experiments will help direct and indirect dark matter searchestune their detectors and analyses by narrowing down the parameter space. Ofcourse, any evidence or discovery of a supersymmetric particle would be veryinteresting for the entire field of dark matter research since it would constrainthe theories and perhaps point us in the right direction.

1.4 Halo ProfilesHow the dark matter is distributed in the Universe and within galaxies is avery active field of research. Most models suggest that the visible parts ofgalaxies are embedded within a spherically symmetric halo of dark matter thatis much larger than the visible parts. In the outer parts of the halo the differenthalo models roughly agree with each other, but closer to the center the story isquite different. Models derived from observations prefer a more cored profile,where the dark matter density reaches its maximum quite far from the Galacticcenter and does not increase further with decreasing radii. On the other handmodels derived from computer simulations generally prefer a cusped profilewith an exponential increase in dark matter density with decreasing radii. Thisdiscrepancy between observation and simulation is sometimes referred to asthe core/cusp problem. In this thesis we use two different density profiles todescribe the dark matter distribution in the Milky Way; one cored and onecusped profile. For the cored profile we use the Burkert model [74] and for thecusped profile we use the Navarro-Frenk-White (NFW) model [75] that has theadded advantage of having been used in the community as a de facto standardin the past, and can serve as a benchmark for comparisons with previous work.

In this work a parametrization is used that can handle both cusped and coredprofiles, modified from [76],

ρDM(r) =ρ0(

δ+ rrs

)γ · (1+ ( rrs

)α)(β−γ)/α , (1.7)

where ρDM(r) is the dark matter density at radius r from the Galactic center,ρ0 is the normalization parameter while α, β and γ are the shape parametersof the halo. α and β describe the outer slope of the density profile while γdescribes the inner slope. The transition region between the inner and outerslope is determined by the scale radius rs. The δ parameter allows for a coredhalo profile if set to 1 and a cuspy halo profile if set to 0. The normalizationparameter ρ0 is determined by demanding that the dark matter density is equalto the local density ρlocal at the radius of the solar circle RSC,

ρDM(RSC) = ρlocal. (1.8)

37

Table 1.3. The dark matter halo parameters used in this work. From reference [77].

Parameter Burkert NFW

(α, β, γ, δ) (2, 3, 1, 1) (1, 3, 1, 0)

ρ0 [107M /kpc3] 4.13+6.2−1.6 1.40+2.90

−0.93

rs [kpc] 9.26+5.6−4.2 16.1+17.0

−7.8

ρlocal [GeV/cm3] 0.487+0.075−0.088 0.471+0.048

−0.061

Figure 1.9. Line-of-sight integral for the Burkert and NFW halo profiles plottedagainst ψ, the angle between the line-of-sight and the Galactic center. Credit: Fig-ure 1 from [47]

In table 1.3 the halo parameters used in this work are presented. They havebeen taken from reference [77] and represent the best fit of observational datato the Burkert and NFW halo profiles. The values for the local density pre-sented in the table are consistent with the value ρlocal = 0.43 which was deter-mined by using the local equation of centrifugal equilibrium and observationaldata [78], making it independent of the shape of the halo density profile.

The differences between the two profiles are illustrated in figure 1.9, wherethe line-of-sight integral Ja is plotted against ψ, the angle between the line-of-sight and the Galactic center. Details on Ja are presented in section 4.1.

38

2. Neutrino Detection

Neutrinos are neutral leptons with very small masses making them ideal as-tronomical messengers. Because of their small masses they always move withspeeds close to the speed of light. Since they do not have any electric charge,they are unaffected by the magnetic fields that permeate interstellar and in-tergalactic space. This is a very desirable property as it means that the pathof the neutrino generally points back to its origin which is not the case forcharged cosmic rays. Neutrinos only interact through the weak force andgravity, which allow them to escape from virtually any dense body and arealso impervious to the dust and gas scattered throughout space. This propertyunfortunately also makes neutrinos very hard to detect and to do so very largedetectors are needed. There are several ways to detect neutrinos, but this chap-ter will focus on the use of Cherenkov detectors using ice or liquid water asthe detector medium.

2.1 Cherenkov RadiationBefore discussing how neutrinos are detected using Cherenkov radiation, itmakes sense to first describe what Cherenkov radiation is and how it is created.

When a charged particle moves through a dielectric medium, electromag-netic radiation is created. This happens because the medium is polarized by thepassing particle and the radiation is emitted when the medium relaxes. If thecharged particle moves slower than the speed of light in the medium, the emis-sions from the different parts of the track interfere destructively to quickly dimwith increasing distance. However, if the charged particle exceeds the speedof light in the medium a shockwave of constructive interference is created atan angle θc to the direction of travel given by

cosθc =1

nβ, (2.1)

where n is the index of refraction for the medium and β = v/c is the speed ofthe particle v relative to the speed of light in vacuum c. The two cases areillustrated in figure 2.1. For ice with refractive index n ≈ 1.32 and β ≈ 1 theCherenkov angle becomes θc ≈ 41◦.

The spectrum per unit path length of the emitted Cherenkov photons isgiven by [80]

d2Ndxdλ

=2παλ2

(1− 1β2n2(λ)

), (2.2)

39

ct/nvt

ct/nvt

θc

Figure 2.1. Left: A charged particle moving with β = 0.5. Right: A charged particlemoving with β ≈ 1 resulting in a Cherenkov cone moving at angle θc relative to thetrajectory of the charged particle. Credit: Figure 3.4 from reference [79].

where λ is the wavelength of the emitted photons and α ≈ 1/137 is the fine-structure constant. If this equation is integrated over the sensitivity range ofthe Photo Multiplier Tubes (PMTs) used in IceCube (300–600 nm) it resultsin ∼32,600 photons per meter for an ultra-relativistic particle [79]. The Che-renkov wavelength spectrum in water peaks at around 360 nm [81]. Usingthis to estimate how much of a particle’s energy is lost through Cherenkovemission can be done by simply multiplying the energy of one such photonwith the number of emitted photons. For 32,600 photons per meter at the peakwavelength 360 nm results in an energy loss rate of O(100) keV m−1, which isnegligible compared to the overall energy loss of relativistic charged particles.

The threshold energy Ec for a charged particle to produce Cherenkov radi-ation is dependent on the mass of the particle. Taking equation (2.1) togetherwith the condition cosθc ≤ 1 we have v ≥ c/n. Using the relativistic energyrelation, we can obtain the Cherenkov energy threshold expressed in terms ofthe refractive index of the medium as

Ec = mc2 n√n2−1

. (2.3)

For the charged leptons in ice (n = 1.32), this means a Cherenkov thresholdenergy of 0.8 MeV for the electron, 162 MeV for the muon and 2.72 GeV forthe tau.

40

2.2 Energy Losses of Charged Leptons2.2.1 Muon Energy LossApart from the emission of Cherenkov photons, muons with energies of theorder of TeV lose energy through several different processes, such as brems-strahlung, ionization, electron-positron pair production and inelastic photo-nuclear interactions. The average energy loss rate can be approximated as

−⟨

dEμdx

⟩= a+bEμ, (2.4)

where a and b are coefficients that can be approximated to a = 0.246 GeV m−1

and b = 4.31 · 10−3 m−1 for muon energies between 20 and 1011 GeV in ice[82].

The mass of the muon (105.7 MeV [16]) allows it to be quite penetrating,while still having a long enough mean lifetime to allow it to survive passingstraight through several kilometers of ice at TeV-scale energies.

2.2.2 Electron Energy LossFor electrons, the process of losing energy in matter is much the same as formuons. The main difference is that electrons are much less massive, whichmakes them lose much more of their energy with each interaction. For elec-tron energies above 79 MeV (in ice) the dominating process for the energyloss is through bremsstrahlung [83]. The photons created through this processwill themselves create electron-positron pairs and these will in turn producebremsstrahlung, see figure 2.2. This is what is referred to as an electromag-

e−

γ

e−

γ

e+

e−

e−

Figure 2.2. Illustration of the development of an electromagnetic cascade.

41

netic cascade, which continues until the emitted bremsstrahlung photons donot have enough energy to create an electron-positron pair and the cascadestops.

As long as the electrons are in this bremsstrahlung regime their mean energyloss rate can be approximated as

−⟨

dEe−

dx

⟩=

Ee−

X0, (2.5)

where X0 = 0.39 m is the radiation length in ice [83]. The radiation length isdefined as the length where, on average, a particle has lost all except 1/e of itsinitial energy.

At the energies discussed here, all the electron and positron tracks are closeto parallel to the initial electron. This means that the collected Cherenkovradiation emission from the cascade is peaked at the Cherenkov angle θc = 41◦relative to the initial electron’s direction of travel.

The longitudinal distribution of an electromagnetic cascade can be de-scribed by a gamma distribution

dEdu= E0b

bua−1e−bu

Γ(a), (2.6)

where u is defined as the distance traveled in units of the radiation lengthu ≡ x/X0, a = 2.03+0.604log10(E0/GeV), and b = 0.633 [84].

2.3 Neutrino InteractionsNeutrinos can only be seen indirectly as they interact with matter to produceother particles that we can readily detect. Cherenkov detectors utilize the lightemitted by charged particles traveling faster than the speed of light in a trans-parent medium, as discussed previously. Fortunately, charged particles areproduced when a neutrino interacts with an atomic nucleon N in the detec-tor medium through deep inelastic scattering. This can happen either by acharged current interaction (the exchange of a W−(+) boson),

ν�(ν�)+N→ �−(�+)+X, (2.7)

or a neutral current interaction (the exchange of a Z0 boson),

ν�(ν�)+N→ ν�(ν�)+X, (2.8)

where � is a charged lepton and X is a hadronic component, see figure 2.3.Neutrinos can also interact with the electrons in the detector medium. How-ever, the cross sections for these interactions are negligible compared to thecross sections on the nucleons for the energies relevant for the work presentedin this thesis (10 GeV - 10 TeV) [85]. Only for electron anti-neutrinos with

42

d(u)

W+(−)

u(d)

N

νl(νl)

X

l−(+)

q

Z0

q

N

νl(νl)

X

νl(νl)

Figure 2.3. Left: Charged-current interaction between a neutrino and a nucleon re-sulting in a charged lepton and a hadronic cascade. Right: Neutral-current interactionbetween a neutrino and a nucleon where the neutrino remains, but transfers some ofits energy to the nucleon resulting in a hadronic cascade. Adapted from figure 3.1 inreference [79].

energies around 6.3× 106 GeV does the electron cross section matter, sinceat this energy resonant production of W− takes place, known as the Glashowresonance [86], see figure 2.4.

Both the neutrino-nucleon interaction types above produce a hadronic cas-cade, with particle speeds above the Cherenkov threshold resulting in de-tectable photon emissions. In the case of the charged current interaction, acharged lepton with a flavor matching the incident neutrino is also created. Ifthis lepton is an electron (or positron) we also get Cherenkov radiation fromthe electromagnetic cascade that is produced. This results in a light patternthat does have some elongation but, in detectors similar to IceCube, appearsroughly spherical and can, at least to leading order, be approximated as comingfrom a point source in the detector.

If the incident neutrino is a muon neutrino, the resulting muon will tra-verse the detector in a straight line emitting photons forming a Cherenkovcone along its path. This causes muons to appear as tracks in detectors suchas IceCube.

If the incident neutrino is a tau neutrino, the charged lepton will be a tau.Since the tau has a very short lifetime (∼ 3× 10−13 s) [16], it will only travela very short distance in the ice before decaying. At least for the energiesrelevant for this work (<10 TeV). When it decays it will produce a cascade in83% of the cases (either a hadronic or electromagnetic one) or a muon trackin 17% of the cases [16]. Since it will not have traveled far before decaying,the second cascade will overlap with the initial hadronic cascade to such anextent that they will be indistinguishable from each other, effectively causingthe tau neutrino to have the same appearance as an electron neutrino. At higherenergies, when the tau is highly boosted, it will have time to travel a significant

43

Figure 2.4. The neutrino and antineutrino cross sections on nucleons N and electronse as a function of energy. The sharp peak in the center is the Glashow resonance. Atthe highest energies, two models for extrapolating the structure functions have beenused: A smooth power-law extrapolation (pQCD) and the enhanced Hard Pomeron(HP) extrapolation, see [85] and references therein. Credit: Figure 1(a) from reference[85].

distance before decaying. This may produce a very distinctive “double-bang”signature where the two cascades will have a significant separation.

For a neutral current event, only the initial hadronic cascade is seen, so forthis interaction all three neutrino flavors have the same appearance. A hadroniccascade has a similar appearance to the electromagnetic cascade, but has morecomplicated process for losing energy in the medium. There are more particlestypes involved, both charged and neutral, which ultimately makes it appeardimmer since neutral particles will not produce any Cherenkov light. Energyis also lost to nuclear binding and since the produced hadrons are heavierthan both the electron and the muon, they require more energy to reach theCherenkov threshold. However, energy can escape from the hadronic to theelectromagnetic sector through π0 → γγ and this component becomes morepronounced with increasing energy, since more π0 are created. Overall, thelight yield from a hadronic cascade compared to an electromagnetic one withthe same initial energy is about 70%-85% for the energy range of this work[79].

44

3. The IceCube Neutrino Observatory

3.1 OverviewThe IceCube Neutrino Observatory [87] is a Cherenkov particle detector com-prised of an in-ice array and a surface air shower array located in Antarc-tica about one kilometer from the geographical South Pole. The main part ofIceCube utilizes one cubic kilometer of the ultra-clear glacial ice 1.5-2.5 kmbeneath the surface as its detector medium. This volume is instrumented with5,160 Digital Optical Modules (DOMs) that register the Cherenkov photonsfrom the particles interacting with the ice, as described earlier in chapter 2.The DOMs are distributed over 86 strings that go down into the ice. Out ofthese, 78 are placed in a triangular grid evenly spaced over the volume, and arereferred to as IceCube strings. The remaining 8 strings are placed in betweenthe central IceCube strings and have a denser DOM spacing, with the majorityof the DOMs located in the bottom part of the IceCube volume. These stringsare the DeepCore strings. At the surface, the observatory also includes a cos-mic ray air shower array called IceTop [88]. It consists of 81 stations placedclose to where 81 of the strings go down into the ice. Each station has two3 m3 tanks of ice with two DOMs frozen into each. Also at the surface, allcables from all the strings and IceTop stations come together and connect tothe central data acquisition system (DAQ) housed in the IceCube Laboratorylocated at the center of the array. See figure 3.1 for an overview of the entireobservatory.

The construction took place during the austral summers between 2004 and2010. Each string was installed by first drilling a hole in the ice using a hotwater drill [89] followed by a rapid deployment of the string. Once a stringwas in place, the water in the drill hole was allowed to re-freeze and lock theDOMs into place. The freezing process takes a couple of weeks starting fromthe top and working its way down. After the string has frozen into place it iscommissioned into the DAQ and is then ready to detect the Cherenkov photonscaused by particle interactions.

3.2 The Digital Optical Module (DOM)The DOM [90] is the most basic unit of IceCube in the sense that it is a fullyself-contained optical sensor. It contains a Photo Multiplier Tube (PMT), high-voltage supply, digitizing electronics, communication hardware, a set of LEDs

45

Figure 3.1. Overview of the IceCube Neutrino Observatory.

used for calibration and a clock circuit for local time-stamping. See figure 3.2for an overview of the different components.

The main component of the DOM is a 25 cm diameter PMT made by Hama-matsu [91] that is powered by the 2 kV on-board high-voltage supply. When aphoton hits a thin conducting layer called the photocathode (deposited on theinside of the evacuated glass enclosure) of the PMT, an electron referred to asa photoelectron is released from the conducting surface due to the photoelec-tric effect. How “easy” a photon can kick out an electron is referred to as thequantum efficiency of the PMT. The photoelectron is accelerated by a high-voltage field and focused towards the electron multiplier consisting of multi-ple dynodes, each with a higher electric potential than the previous one. Whenthe photoelectron hits the first dynode, several electrons are ejected throughsecondary emission. These electrons are accelerated towards the next dynodedue to the potential difference and the process is repeated several times untilreaching the final anode. This results in a massive multiplication (∼ 107) of asingle initial photoelectron which can be read out as a pulsed increase in theoutput voltage of the PMT. See figure 3.3 for a schematic overview.

46

Figure 3.2. Illustration of an IceCube DOM. Credit: Figure 2 from reference [90].

The signal from the PMT is fed to the two types of digitizers housed on theDOM mainboard; the Analog Transient Waveform Digitizer (ATWD) and thefast Analog-to-Digital Converter (fADC). The ATWD uses an analog memoryof 128 sampling capacitors with a sampling rate set to 300 Mega Samples PerSecond (MSPS), which translates to a sampling time of ∼ 3.3 ns/sample. Thismeans that the ATWD can capture a waveform that is at most 427 ns long. Seefigure 3.4 for an example of an ATWD waveform of one single photoelectron.To reduce downtime of the DOM when a signal is being digitized, there are

two identical ATWDs on the DOM mainboard so that one is ready for a newtrigger if the other one is busy. The signal capture from the PMT is triggeredwhen the output voltage surpasses 25% of the average voltage generated byone photoelectron. Since the ATWDs need to be triggered to start a signalreadout, the signal from the PMT is passed through a serpentine strip line lo-cated on a separate board in the DOM to create a 75 ns delay. This is enough toallow the ATWDs to capture the very beginning of the waveform. The fADCcontinuously digitizes the output signal from the PMT, but at a lower sam-pling rate of 40 MSPS. This provides a coarser, but longer waveform readout,which is needed since some waveforms can be significantly longer than whatthe ATWDs can record. The length of the raw fADC record is set to 6.4 μs.For all triggered DOMs, a very compact representation of the fADC, knownas a coarse charge stamp, is calculated. This charge stamp is constructed by

47

Figure 3.3. Schematic description of a PMT. Credit: [92].

taking the highest fADC sample among the first 16 samples, along with thesamples directly before and after [90].

The PMT and the other components of the DOM are enclosed in a 13 mmthick glass sphere, which can withstand the pressure of the 2.5 km of waterduring deployment and the re-freezing of the hole. The glass sphere is filledwith dry nitrogen at 0.5 atmospheres of pressure, to make sure the seal remainssecure before and during deployment. An onboard pressure sensor can detectif there is a leak in the seal or if the PMT vacuum is compromised. Inside theglass, the PMT is surrounded by a Mu-metal grid to shield it from the Earth’smagnetic field. To secure and optically couple the PMT to the glass enclosurea Room Temperature Vulcanization (RTV) silicone gel is used. The power andcommunication cable enters the DOM via a penetrator located close to the topof the sphere [90].

Figure 3.4. An example ATWD waveform of a single photoelectron. Credit: Figure 6from reference [90].

48

The temperature the DOMs are exposed to in the ice is in the range -40◦Cto -10◦C depending on depth, where deeper is warmer. At these temperaturesthe average dark noise rate of the PMTs is around 650 Hz, which is in partdue to the thermal background of the photocathode [93]. Another componentcomes from radioactive isotopes in the material of the glass enclosure whichcan cause noise hits as these isotopes decay. Sometimes the radioactive decaycan give rise to scintillation in the glass. This scintillation causes correlated“bursts” of noise in the DOM and when the timing of these bursts overlap inseveral DOMs they can give rise to noise-induced triggers of the detector [94].

3.3 The IceThe Antarctic glacial ice sheet at the South Pole has formed over thousands ofyears from accumulating snow that has slowly been compressed into solid ice.At shallow depths the ice contains trapped air bubbles, making the ice quiteopaque. However, with the increasing pressure further down, at depths around1,350 m, these bubbles become so compressed that they become integratedinto the crystal structure of the ice. These small-scale structures are calledair-ice clathrates and have an index of refraction that is very close to pure, airfree, ice. For photons of optical wavelengths, this means that the ice becomeshighly transparent [95]. At depths between 1,450 and 2,450 m, where IceCubeis instrumented, the main source of impurities causing scattering and absorp-tion in the ice is due to dust deposited by the wind. The amount and verticaldistribution of the dust have been measured in eight of the IceCube boreholeswith a “dust logger” utilizing a technique called laser particulate stratigraphy[96]. This dust was mixed in with the snow that fell at least 25,000 years ago[97] and comes from volcano eruptions and large dust storms taking place atother parts of the Earth. The amount of scattering and absorption depends onthe amount of dust present in the ice. This amount is correlated to the globalclimate and is therefore similar for all ice layers created around the same time[95].

Since detailed knowledge of the optical properties of the ice is needed to beable to perform accurate reconstructions of the detected particle interactions,models of the ice based on in situ measurements are used. These measure-ments have been made using the LED flashers present in the optical modules ofAMANDA [95] and IceCube [98]. The complex interplay between the absorptionand scattering in the ice makes an analytical description problematic. Insteadthe photon propagation must be treated numerically through Monte Carlo sim-ulation [98]. Such simulations have resulted in the ice model called SPICE-Mie (South Pole ICE with Mie scattering) used in this work. To build themodel, LED flasher data was recorded throughout the entire array of DOMs.The light flashes were then simulated [99] with a set of model parameters anda global fit of these was made so that the simulated detections of the flashes

49

Figure 3.5. Effective scattering (top) and absorption (bottom) as a function of depth.The solid line is the global fit of the ice parameters to the SPICE-Mie model to LEDflasher data. The gray band is an estimate of the systematic uncertainties. The dashedline represents AHA [95] which is an older ice model developed for the AMANDA de-tector extrapolated to cover the full IceCube volume. Credit: Figure 16 from reference[98].

50

x

y

z

Surface

Greenwich

Source

φ

θ

Figure 3.6. The local coordinate system. Its origin is located in the center of the in-icearray with the z axis pointing towards the local zenith and the y axis pointing towardsGreenwich. The angles θ and φ are referred to as zenith and azimuth respectively.

matched the true recorded ones. The result of this global fit with respect toabsorption and effective scattering length can be seen in figure 3.5. Worth not-ing is the large peak just below 2,000 m, where the absorption and scatteringis significantly more pronounced. This is due to a larger accumulation of dustand is referred to as the dust layer. Also, the measurements showed that theice layers are slightly tilted which is not taken into account in the SPICE-Miemodel.

3.4 The In-Ice ArrayThe major part of the in-ice array of IceCube consists of the 78 IceCube stringsmentioned earlier. These strings with 60 DOMs each are deployed so that theDOMs are distributed between 1,450 and 2,450 m below the surface of the icesheet. The vertical spacing of the DOMs is 17 m and the distance betweenthe strings is about 125 m. This configuration results in a neutrino energythreshold of about 100 GeV [87].

The local coordinate system used is Cartesian and has its origin at the centerof the in-ice array. The z-axis points towards the local zenith and the y-axispoints towards Greenwich, United Kingdom. A directional vector is given bythe zenith angle θ from the positive z-axis and the azimuth angle φ in the x-yplane counting counter-clockwise from the positive x-axis, see figure 3.6.

51

12

34

567

89

1011

1213

1415

1617

18

19 2021

2223

2425

2627

2829

30

3132

3334

3536 37

38 39

40

4142

4344

4546

47 48 49

50

5152

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6263

6465

6667

6869

7071

7273

7475

7677

78

79 80

81 82

83

84

85

86

y

x100 m

Figure 3.7. Schematic overview of the IceCube string layout seen from above. Graymarkers indicate IceCube strings and white markers indicate DeepCore strings withdenser DOM spacing. All strings marked with a black border are included in thedefinition of DeepCore. The numbers indicate the identification number of each stringand the indicated coordinate system refers to the local coordinate system visualized infigure 3.6. Note that the coordinate system has its origin in the center of the array.

3.4.1 DeepCoreDeepCore [100] is the low-energy extension of IceCube. It is located in thebottom center of the main in-ice array and is defined as the bottom 22 DOMsof the 12 innermost IceCube strings1 along with eight DeepCore strings thathave a denser DOM spacing than the standard IceCube strings. See figure 3.7for a schematic overview. The DeepCore strings have 60 DOMs each with50 of them below the dust layer (see section 3.3) where the ice is the mosttransparent. These DOMs have a vertical separation of 7 m. The remaining 10

1Different analyses in IceCube can have different definitions of which strings make up the Deep-Core fiducial volume. This work includes IceCube strings 25, 34, 44, 47 and 57 in DeepCore(see figure 3.7), a configuration known as Extended DeepCore.

52

DOMs have a vertical separation of 10 m and are placed above the dust layer toserve as an enhanced atmospheric muon veto. The inter-string spacing of theDeepCore strings is roughly half that of the IceCube strings, about 55 m. Apartfrom the denser DOM spacing, most of the DeepCore strings also have DOMswith higher quantum efficiency PMTs. Strings 79 and 80 are the exception,having a mix of standard DOMs and DOMs with higher quantum efficiency.The denser DOM spacing together with the higher quantum efficiency resultsin a reduction of the neutrino energy threshold to about 10 GeV [100].

3.5 Data Acquisition and Processing3.5.1 Timing CalibrationTo be able to accurately reconstruct the direction of the detected particles, ac-curate timing information of the detected Cherenkov photons is needed. Thisis a challenge for a detector the size of IceCube, where the DOMs can beplaced over 1 km from each other and still need to be synchronized in timedown to a few nanoseconds. To overcome this challenge, IceCube employs adecentralized time-stamping procedure where the waveforms receive a time-stamp locally in the DOM from its onboard 20 MHz oscillator. Every twoseconds, this oscillator is calibrated to a GPS-controlled master oscillator atthe surface. The calibration procedure is called reciprocal active pulsing cali-bration (RAPCal) [93], where a fast bipolar pulse is sent from the surface to aDOM that responds with an identical pulse after a short pre-determined delay.The pulses are created by the same type of communication hardware at bothends and the signal travels through the same wire. This means the pulses willhave the same shape and by comparing them at the surface the round-trip timecan be extracted with high accuracy. The resolution of the round-trip time isgenerally below 2 ns. Using this information connects the local time-stampsof the DOMs to the master clock with a very high accuracy.

3.5.2 The HitA hit in IceCube generally refers to a DOM being triggered locally to record awaveform from the PMT output. This can either be a single pulse from a singlephotoelectron, as can be seen in figure 3.4, or a much more complex waveformof several pulses partly superimposed on each other. When processing theraw waveforms at the surface, all pulses and their corresponding times areextracted. These individual pulses can be referred to as just “pulses” but it isequally common, and sometimes more convenient, to refer to them as “hits”since they are close to the same thing for most purposes.

In this work, a “hit” or the phrase “hit DOM” refers to a DOM with arecorded waveform and “first hit” refers to only the first extracted pulse of thefirst waveform in a DOM.

53

3.5.3 Local CoincidenceApart from being able to communicate with the DAQ at the surface, eachDOM can also communicate with its nearest and next-to-nearest neighborson the same string. This makes it possible to use local coincidence (LC) toreduce noise and thereby reduce data traffic. When a DOM detects a hit, itsends information about this to its four closest neighbors. If at least one ofthem also detect a hit within 1 μs, the LC criterion is met. The in-ice arrayas a whole can be set to use the LC information in different ways, but themain mode of operation is called Soft Local Coincidence (SLC). In this mode,triggered DOMs without LC only send their coarse charge stamp along withits associated time stamp. These hits are referred to as SLC hits. DOMs thatparticipate in an LC will send their coarse charge stamp along with both thefADC and the more detailed ATWD waveform data. These are referred to asHard Local Coincidence (HLC) hits.

3.5.4 Triggering and FilteringTo capture interesting data related to physics and reject as much noise as pos-sible, a set of trigger conditions and subsequent filters is used. These triggersand filters are designed and optimized for different physics scenarios and runsimultaneously in the DAQ.

The simplest trigger algorithm is called Simple Multiplicity Trigger (SMT)and works by looking at the time-ordered stream of hits from the DOMs with a5 μs sliding time window. When this time window contains a preset number ofHLC hits, the algorithm “fires” and creates a readout time window around thetrigger time, which is the time of the first hit satisfying the trigger criteria. Aglobal trigger window is created and is defined as the logical OR of all readoutwindows of all firing triggers with an additional ±10 μs added. All hits withinthis global trigger window are assembled into an event hit map and sent onto the Processing and Filtering (PnF) system. At this point, some basic noisecleaning is performed along with calculations of general observables and basicreconstructions needed by the filtering algorithms.

The filters are more specialized than the triggers and aim to select goodphysics candidate events, while rejecting as much background induced eventsas possible. There are several different filters focusing on different candidatessuch as track-like or cascade-like events, high or low energy events, up-goingevents or events starting in DeepCore. The specific trigger and filter used inthis work will be presented in chapter 6. For an example of a typical track-like and cascade-like events in IceCube, see figures 3.8 and 3.9. Note that theevents shown are simulated and cleaned from noise hits.

For the year when the data used in this work was collected (May 2011– March 2012) the global trigger rate of IceCube was about 2.3 kHz. All

54

Figure 3.8. A simulated 27 TeV atmospheric muon bundle track event (top) and acascade event from a 1.6 TeV electron neutrino (bottom). Time is indicated with thecolors of the rainbow with red being the earliest and violet being the latest hits. Thesizes of the DOMs indicate the amount of light detected.

55

Figure 3.9. Two simulated cascade events from electron neutrinos with energies108 GeV (top) and 26 GeV (bottom). Time is indicated with the colors of the rainbowwith red being the earliest and violet being the latest hits. The sizes of the DOMsindicate the amount of light detected.

56

triggered events were written to data tapes while all events that passed at leastone of the filters were packaged and sent north via satellite.

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4. Signal and Background

4.1 The Signal - Neutrinos from WIMPsThe neutrino flux from self-annihilating WIMPs is dependent on the line-of-sight from the observer through the dark matter halo. To account for this aJa-factor is used that integrates the squared dark matter mass density along theline-of-sight. Following the procedure in [101, 102], it can be defined as

Ja(ψ) =∫ lmax

0ρ2

DM

(√l2+R2

SC−2 l RSC cosψ)

dl, (4.1)

where ρDM(r) is the dark matter mass density as defined in equation (1.7), ψis the angle from the line-of-sight to the Galactic center, l is the distance fromthe observer, RSC ≈ 8.5 kpc is the radius of the solar circle and lmax is themaximum distance from the observer. lmax is defined as

lmax = RSC cosψ+√

R2MW−R2

SC sin2ψ, (4.2)

where RMW is the radius of the dark matter halo of the Milky Way, here as-sumed to be ≈ 50 kpc. A schematic overview of the variables used in thecalculation of the Ja-factor is presented in figure 4.1. Generally contributionsto Ja from radii larger than the scale radius rs can be neglected. Recall thescale radii used in this work from table 1.3.

The differential neutrino flux is given by

dφνdE=〈σAv〉

21

4πm2χ

dNνdE

Ja(ψ), (4.3)

where 〈σAv〉 is the thermally averaged product of the self-annihilation crosssection σA and the velocity v of the WIMPs, mχ is the WIMP mass anddNν/dE is the neutrino energy spectrum from the WIMP annihilations.

Realistic neutrino energy spectra are highly model dependent with a mix ofbranching ratios for the particles produced after the WIMPs annihilate. Insteadof considering just one or a few of these models, a set of annihilation chan-nels are considered, assuming a 100% branching ratio to each respectively;χχ→ bb, W+W−, μ+μ−, τ+τ− and νν. These channels serve as benchmarks,effectively bracketing the spectra from more realistic models. For the chan-nel χχ→ νν, neutrinos are produced directly from the WIMP annihilation.The neutrinos will each have an energy equal to the WIMP mass, resultingin a spectral line at this energy. In the signal simulation (presented in sec-tion 4.3.3), this spectral line is approximated by only including neutrinos with

59

GC Sun

RMWlmax

RSC

Figure 4.1. Illustration of the variables used to calculate the line-of-sight integral. Thedistances are not to scale.

energies that are ±10% of the WIMP mass weighted to a flat spectrum. Inthe remaining channels neutrinos are produced as secondary particles, such asthrough the decay of charged pions and kaons resulting in a continuous neu-trino spectrum. These spectra were calculated using PYTHIA (version 8.175)[103] by setting up a generic resonance having the energy of twice the consid-ered WIMP mass. The resonance was forced to produce only the particle pairof the channel being calculated. From here the standard PYTHIA implementa-tion can handle the remaining calculations, such as hadronizations and decays.In figure 4.2 example neutrino spectra are shown for the bb, W+W− and μ+μ−annihilation channels.

A consequence of using a generic resonance is that the spin of the annihi-lating WIMPs is not taken into consideration. This makes the assumed WIMPmodel more generic than models described by supersymmetry were the light-est neutralino is the WIMP candidate [104]. In the more generic model, theinitial annihilation products decay isotropically which would not be the casefor the gauge boson channels such as W+W− in the supersymmetric models.Since the supersymmetric WIMPs would have spin 1/2 it would lead to theW-bosons being transversely polarized, which in turn would affect the neu-trino energy spectrum from this channel [105]. The effect on the differentialneutrino yield is about ±40% between the two cases [47] depending on theneutrino energy and the WIMP mass.

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Figure 4.2. Example neutrino spectra from annihilating WIMPs calculated usingPYTHIA8 [103] for WIMP mass mχ = 500 GeV. Credit: Figure 1 from [47]

4.1.1 Neutrino OscillationsNeutrino oscillations were discovered around the turn of the millennium bySuper-Kamiokande [106] and Sudbury Neutrino Observatory (SNO) [107].This discovery indicates that not all neutrinos are massless. Super-Kamioka-nde found a deficit in the flux of atmospheric muon neutrinos dependent on thedistance traveled, which was consistent with the oscillation hypothesis. TheSNO made their measurement by detecting solar neutrinos of all three flavorsand the measured ratios between the flavors were fully consistent with oscil-lations. IceCube has confirmed the Super-Kamiokande measurement usingatmospheric neutrinos [108, 109].

In this work, the signal is assumed to have a flavor ratio of

νe : νμ : ντ = 1 : 1 : 1

at Earth due to the very long oscillation baseline, where the distance from theemission point always will be long enough for the neutrinos to become wellmixed, even if the flavor ratio is different at the source.

4.2 BackgroundThe main sources of background for most analyses in IceCube are muons andneutrinos created through cosmic rays interacting with nucleons in the upperatmosphere. A typical example of such reactions is

p+N→ π±(K±)+X

↪→ μ+(−)+ νμ(νμ)

↪→ e+(−)+ νe(νe)+ νμ(νμ),

(4.4)

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15 10 5 3 2 1 0

0 200 400 600 800 10000.01

0.1

1

10

100

1000

10000

Atmospher ic depth [g cm–2]

Ver

tica

l fl

ux

[m

–2 s

–1 s

r–1 ]

Alt itude (km)

e e

p n

_

1 10 100

Figure 4.3. Left: Particle fluxes from cosmic rays in the atmosphere with energiesabove 1 GeV as a function of decreasing altitude above the Earth’s surface. The linesrepresent an analytical approximation and the data points are measurements of μ−.Right: Vertical muon intensity plotted against depth (in km water equivalent). Thehorizontal shaded part represents atmospheric neutrino-induced muons. Credit: Fig-ures 28.8 and 28.7 from [16], where more details are available.

where N is a nucleon in the atmosphere and X represents the rest of thehadronic component produced in the interaction. Apart from these reactionsinvolving pions and kaons producing the so-called conventional flux of at-mospheric neutrinos, there are also reactions producing short-lived charmedhadrons. The neutrino flux produced by charmed hadrons is referred to asprompt and has a flatter energy spectrum due to these short-lived particles de-caying before having time to interact.

The particle flux from cosmic rays that reaches the surface of the Earth isdominated by neutrinos and muons, see figure 4.3 (left plot). The muons rep-resent the largest background to any neutrino signal since they can penetrateseveral kilometers of ice and rock. This is illustrated in the right plot of figure4.3 showing the muon flux vs depth in km.w.e. (km water equivalent). As areference, the center of the IceCube in-ice array is located at about 1.8 km.w.e.The atmospheric muons will penetrate at most about 20 km, meaning thatthey will be effectively stopped by the Earth, preventing them from reachingIceCube if they are produced below the horizon at the South Pole. This is notthe case for the atmospheric neutrinos, which have little problems penetratingthe Earth at energies relevant to this work. Since the flux of cosmic rays isnearly isotropic, so is the flux of atmospheric neutrinos. As mentioned in sec-tion 3.5.4, the trigger rate of IceCube is about 2.3 kHz, out of which the vastmajority is due to atmospheric muons. The trigger rate for atmospheric neu-

62

trinos is O(106) lower. The overall trigger rate is also affected by a seasonalvariation of ±10% that is due to variations in atmospheric density. This affectsthe number of muons able to penetrate all the way down to IceCube [110].

4.3 Event SimulationSimulations of physical processes in IceCube are created through a chain ofconnected Monte Carlo programs. The individual pieces model primary parti-cle interactions, propagation of particles through ice, creation and propagationof light through the ice and the detector response to that light.

4.3.1 The Simulation ChainThe simulation chain starts with a particle generator which hands the gen-erated particles off to a particle propagator that takes care of the propagationthrough the ice. The Cherenkov photons created by the charged particles mov-ing through the ice are handled by a photon propagator. If such a propagatedphoton hits a DOM the detector response generator simulates the output a realDOM would generate and this response is your simulated data.

Particle Generators

To simulate the atmospheric muons in IceCube, CORSIKA (COsmic RaySImulations for KAskade) [111] is used. CORSIKA can simulate the entireair shower produced when a cosmic ray primary particle interacts with a nu-cleon in the atmosphere. It handles primaries such as photons, electrons andnuclei ranging from protons to iron. These primaries are injected at the top ofthe atmosphere and are propagated towards the Earth until they interact with anucleon. CORSIKA can handle hadronic and electromagnetic interactions, aswell as particle decay. IceCube uses the hadronic interaction model SIBYLL[112] and has its own custom implementation of CORSIKA. This implementa-tion has adaptations specific for the IceCube software framework and focuseson the muons by tracking all secondaries from the cosmic ray interactions andsaving the muons created. If and when the shower reaches the surface, allother particles are stopped and only the stored muons are handed over to theparticle propagator for further “transport” down to the in-ice array.

For this work, two particle generators for neutrinos are used. One is calledNuGen (Neutrino Generator) [85] and the other is called GENIE (GeneratesEvents for Neutrino Interaction Experiments) [113].

NuGen calculates the neutrino-nucleon cross sections for deep inelasticscattering, discussed in section 2.3, using parton distribution functions fromCTEQ5 [114]. The neutrino interaction energy range handled by NuGen is10 GeV to 109 GeV, but for energies below about 200 GeV other interaction

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processes, such as resonances and quasi-inelastic scattering, become impor-tant. This is where GENIE comes in since it takes these effects into consider-ation when calculating the neutrino-nucleon interactions.

The Particle Propagator

The Monte Carlo simulation that takes care of the propagation of the chargedleptons through the ice (and bedrock) is called PROPOSAL (PRopagator withOptimal Precision and Optimized Speed for All Leptons) [115]. It is written inC++ to optimize it for speed as opposed to its predecessor MMC (Muon MonteCarlo) [82] which was written in Java. PROPOSAL models energy losses asthe charged lepton travels through the ice such as the continuous minimumionizing losses, but it also handles stochastic processes such as bremsstrah-lung.

The Photon Propagator

The Cherenkov photons created by the charged leptons traveling through theice are all tracked by PPC (Photon Propagation Code) [99]. Propagating everysingle photon requires a significant amount of computing power. Fortunately,the propagation of one photon does not depend on the next, making the pro-cessing highly parallelizable. In fact, PPC has been written to be able to run onGraphics Processing Units (GPUs), which are specialized in massive parallelprocessing of independent calculations that do not require a large amount ofmemory. An added bonus is that GPUs are inexpensive since they are availableon off-the-shelf graphics cards used for computer games.

The Detector Response

If one or more of the propagated photons reaches a DOM, hits are created bya program called Monte Carlo Hits (MCHits). On top of this, a simulation ofthe noise hits is added and all hits are then passed on to the PMTResponseS-imulator. Here, a full physics simulation of the PMT is done and the output isa waveform that is close to identical to the real PMT output. The waveform ispassed on to a simulation of the local coincidence logic, followed by a simu-lation of the waveform digitization by the fADC and ATWD. At this point wehave output data that has the same format as what the real detector producesand from here on it can be treated in much the same way. The last part that issimulated is the triggering of the full detector. The subsequent filtering can beapplied as well.

4.3.2 Simulation WeightsEvent simulation requires considerable computing resources due to the sheernumber of particles to track for each event. On top of the actual simulationcomes much of the same processing and reconstruction that is done on real

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data. To avoid wasting computing resources, the IceCube Collaboration em-ploys a scheme to simulate events that are the most relevant and then applyweights that will make the simulated dataset correspond to a natural spectrum.

For the simulation of the atmospheric muons using CORSIKA, the naturalspectrum has the largest flux at energies that are too low to trigger the detector.It would therefore be very wasteful to generate events according to that naturalspectrum. Instead a flat generation spectrum is used to get high statistics of thetypes of events that would be seen in the in-ice array. This flat spectrum canthen be weighted to any desired model of the natural spectrum. In this workthe cosmic ray energy spectrum by Hörandel [116] is used.

The simulation of neutrinos takes on a similar approach, but here the mainissue is the low probability of a neutrino interacting in IceCube at all. To avoidsimulating a massive amount of neutrinos where the vast majority pass throughundetected, all neutrinos are forced to interact within a volume surroundingthe in-ice array. A weight is calculated for each event to reflect the actualprobability of detection. The event weight w is defined so that the event ratein the detector can be calculated as

Rν =∑

i

(dφνdE

)i

wi

Ngen, (4.5)

where dφν/dE is the differential neutrino flux calculated for event i and Ngenis the number of generated events in the simulation dataset used. The units ofw are GeV cm2 sr.

4.3.3 The Signal SimulationThe neutrino signal simulation used in this work is isotropic and has a genera-tion spectrum of E−2 that has been created using both GENIE and NuGen. Thegenerated events are then weighted using the spectra calculated using PYTHIAand the correct distribution over the sky is achieved by applying weights cal-culated from the Ja-factor, as discussed in section 4.1. The GENIE simulationranges in energy from 10 GeV to 195 GeV and NuGen ranges from 10 GeV to109 GeV. To take advantage of the higher accuracy of the GENIE simulationat lower energies, 100% of the events come from GENIE in the energy rangefrom 10 GeV to 185 GeV. From there a linear transition is made to reach 100%NuGen events at 195 GeV.

The simulations are made for one neutrino flavor at a time containing 50%neutrinos and 50% anti-neutrinos. The difference in cross section is includedin the event weight. For GENIE, all three flavors are available with similarstatistics. For NuGen, high statistics datasets are available for νe and νμ, but forντ the statistics are limited and the simulated dataset starts at around 300 GeV.This will affect dark matter annihilation channels with neutrinos in the range

65

185 GeV to 300 GeV, but the effect is small enough to be negligible in thefinal sensitivity plots.

For the event selection, only the NuGen νe simulation was used togetherwith the WIMP self-annihilation neutrino energy spectrum dNν/dE calculatedby DarkSUSY [117]. The isotropic distribution was cut down so the true arrivaldirections of the neutrinos were limited in zenith to be ±20◦ around the zenithof the Galactic center. These two differences from the final signal definitionhave been investigated and the effect on the event selection was on the orderof 1%-3% on the number of events passing all cuts.

4.3.4 The Background SimulationThe analysis presented in this work does not use the CORSIKA atmosphericmuon simulation as background. Instead, real scrambled data is used, whichhas the advantage of reducing the systematic uncertainties. The CORSIKAsimulation is used to verify the accuracy of the simulations overall. Since thevast majority of the events captured by IceCube are atmospheric muons, theCORSIKA simulation should match the real data fairly well at all but the finallevel of event selection. At this point the data sample should have a significantfraction of neutrinos. At the earlier levels, the CORSIKA simulation serves toverify the accuracy of the signal simulation.

The atmospheric neutrino background, again for comparative purposesonly, is created by using the same isotropic neutrino simulation as for thesignal, but weighted to an atmospheric neutrino energy spectrum. To calculatethe weights, the model by Honda et al. [118] is used.

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5. Event Reconstruction

5.1 Hit CleaningMany reconstruction techniques, especially first guess reconstructions, requirethat the recorded hits in an event are created by an interacting particle and notnoise, such as random hits induced by the PMT dark current and radioactivity(see section 3.2). Therefore the hits due to noise need to be cleaned out asefficiently as possible. To achieve this two types of noise cleaning were usedin this analysis; Static Time Window (STW) cleaning and Seeded Radius-Time(SRT) cleaning.

5.1.1 Static Time Window CleaningThe STW cleaning removes all hits (HLC and SLC alike) outside a pre-definedtime window around the trigger time of the event. This analysis uses a timewindow from -5 to +4 μs. The time window was determined in tandem withthe development of the DeepCore filter to make sure enough time was allowedbefore the trigger to preserve any hits from atmospheric muons sneaking in,as well as having enough time after the trigger to allow the light of any signalto fully propagate in the detector. The time interval has been verified to besuitable for the event sample used in this work. The reason for wanting topreserve early hits from muons sneaking in, is to use this information later onto try to remove such events altogether.

5.1.2 Seeded Radius-Time CleaningAfter the STW cleaning has been applied to remove the most obvious noisehits, a more sophisticated cleaning algorithm is used. The SRT cleaning al-gorithm, as it has been implemented in this analysis1, is given all hits (HLCand SLC) that are left after the STW cleaning and starts by looking at all theremaining HLC hits. Each HLC hit is evaluated for coincidence with the otherHLC hits by checking if it has other HLC hits within a radius R = 150 m andwithin the time interval T = 1000 ns. If these criteria are not met by at leasttwo of the other HLC hits, the evaluated hit is discarded. The HLC hits thatpass this cut make up a set of seed hits that are used in the next part of the

1The employed hit cleanings and their settings are the IceCube standard for the offline process-ing of the DeepCore filter event sample.

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Figure 5.1. A simulated 1.6 TeV νe cascade event before (left) and after (right) hitcleaning. Time is indicated with the colors of the rainbow with red being the earliestand violet being the latest hits.

algorithm. They are also added to a list of hits to keep. The reason for thisinitial selection is to remove isolated HLC pairs and thereby only selecting the“core” of the HLC hits. If no HLC hit passes this cut, all of them are addedto the list of hits to keep and are used as seed hits. The previously mentionedR and T criteria are applied to the hits on the list and any new SLC/HLC hitsthat are included by these criteria are added to the list as well. This processis repeated for a maximum of three iterations or until no more hits are addedto the list. Note that HLC hits previously excluded when selecting the seedhits may be re-included in the following iterations since they can be causallyconnected to the seed hits via an SLC hit included in an intermediate iteration.

After running the SRT cleaning algorithm most SLC hits that are due tonoise have been removed, leaving only hits with a high probability of beingrelated to the particle interaction of interest. In figure 5.1 an example eventcan be seen before and after hit cleaning has been performed.

5.2 First-Guess ReconstructionsFirst-guess reconstructions are developed to give a first interpretation of therecorded events while still being fast enough to run on all events comingthrough one or more filter streams. Since they are developed for speed, theiraccuracy might be lower than more advanced reconstructions. Their results areprimarily used for event selection and as seeds for more advanced reconstruc-tions. All first-guess reconstructions described in this section use hit maps thathave been cleaned from noise as described in section 5.1.

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5.2.1 Improved LineFitThe improved LineFit reconstruction [119] is one of the fast standard recon-structions that are run online at the South Pole on all triggered events. It isprimarily a muon track reconstruction algorithm that serves as a seed for moreadvanced algorithms, but is also a good tool when trying to differentiate track-like events from cascade-like events. The LineFit algorithm finds a track thatmatches the hits in the detector by disregarding the Cherenkov cone and in-stead regards every hit as an independent measurement of the position of aparticle moving in a straight line through the detector. Consider N hits wherethe ith hit is at position �xi at time ti and the reconstructed track passes throughthe point �x0 at time t0 having velocity �v. Using this information, the LineFitalgorithm solves the least-squares optimization problem that can be written as

mint0, �x0, �v

N∑i=1

ρi(t0, �x0, �v)2, (5.1)

where

ρi(t0, �x0, �v) = || �v · (ti− t0)+ �x0− �xi ||. (5.2)

This represents the classic LineFit reconstruction which has the disadvantageof ignoring that hits might be due to scattered photons. These photons mightbe detected long after the muon has passed the position where the photonswere detected. Also, using the least squares model described in equation (5.1)will give outliers a quadratic weight, whereas we would like them to be zero.Addressing these two points is what makes improved LineFit improved. Tomitigate the effects from scattered photons, the hit map is cleaned by iteratingthrough the hits and removing those that deviate too much in time in relationto their closest neighbors. This improves performance by almost a factor oftwo in terms of median angular resolution. To resolve the issue of quadraticweights for outliers, an intermediate Huber fit [120] is introduced which mod-ifies equation (5.1) by switching the quadratic dependence to a linear one if ρis larger than 153 m. This distance was determined by analyzing a simulateddataset of typical muon tracks. The switch to a linear dependance makes theHuber fit more robust to noise and at the same time tags all outliers after thefit has converged, enabling us to remove them altogether. Running LineFit onthe hit map that has hits from highly scattered photons and outliers removedresults in an overall improvement on median angular resolution of 57.6%. Fordetails on the improvements of LineFit, see reference [119].

5.2.2 Tensor of InertiaThe tensor of inertia reconstruction borrows an analogy from classical me-chanics by treating the ensemble of hit DOMs as a rigid body of N point

69

masses, where the amplitude of a hit serves as virtual mass assigned to eachDOM. As the origin for the reconstruction, the center of gravity (COG) of thevirtual masses is calculated as

�xCOG =

∑Nchi=1 mi�xi∑Nch

i=1 mi, (5.3)

where mi is the virtual mass of the DOM at position �xi and Nch is the numberof hit DOMs. Using these virtual masses along with their positions, the re-construction calculates the eigenvalues of the tensor of inertia for this systemof “masses.” The three eigenvalues represent the three principal axes of anellipsoid spanned by the virtual masses. The smallest one of these eigenvaluescorresponds to the longest principal axis of the ellipsoid which is selected todetermine the direction of the event. Since the direction along the selectedaxis is ambiguous, the hit times are projected onto this axis, from latest to ear-liest, to decide the reconstructed direction so that it points towards where theincident particle is believed to have come from.

The tensor of inertia reconstruction is generally only suitable as a first guessof the direction for track-like events, since for cascade-like events the threeeigenvalues, and hence the three principal axes of the ellipsoid, will be close toequal in size. However, this property can be leveraged to discriminate betweentracks and cascades and is further discussed in section 6.3.1.

5.2.3 CLastCLast is a first guess reconstruction for cascades. It uses the COG as an esti-mate of the neutrino interaction vertex position and then proceeds to estimatethe corresponding vertex time. To do this we begin by defining the geometricaltime tgeo as the time it would take an un-scattered Cherenkov photon emittedat the COG to reach a certain DOM or

tgeo ≡ || �xDOM− �xemit ||cice

, (5.4)

where cice is the speed of light in ice, while �xDOM and �xemit are the positions fora hit DOM and the point of emission respectively. We also define the shiftedtime tshift as

tshift ≡ tfirst− tgeo, (5.5)

where tfirst is the time of the first hit of the considered DOM. tshift is calculatedfor all hit DOMs within 300 m of the COG and it represents each hit DOM’sestimate of the vertex time. If several DOMs have their tshift close to eachother, it suggests that they all have hits that are causally connected to the COG.Starting from the hit with the lowest tshift a time window of 200 ns is extendedand other hits with tshift within this window are counted. If at least three hits

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fall within this window (first hit included), the time of the first hit is used asthe vertex time. If the criterion of three hits is not met, the time window ismoved up to the next hit until the criterion is fulfilled. CLast is a modifiedversion of CFirst [121] with only one difference: If there is no cluster of hitswith tshift within 200 ns of each other, the earliest hit is used instead.

5.3 Likelihood ReconstructionsOnce the sample of events is small enough to run the more advanced and timeconsuming reconstructions on all events, their power and higher accuracy canbe used to further develop the analysis.

In general one wants to determine a set of unknown parameters

�a = (�x0, t0, θ,E0), (5.6)

where �x0 is an arbitrary point along the track in the case of a track hypothesis.For a cascade hypothesis �x0 represents the vertex position, t0 is the event timeat position �x0, θ is the direction of the incoming particle and E0 is the depositedenergy of the event. For a cascade reconstruction there are seven degrees offreedom, while track reconstructions have only six since the point �x0 can bechosen arbitrarily along the track provided that t0 is shifted accordingly.

A likelihood reconstruction aims to determine or estimate a set of param-eters �a given a set of measured data points {�di} (e.g. hits in an event with aposition and time) by using a likelihood function, such as

L(�a | {�di}) =N∏

i=1

p(�di | �a), (5.7)

where p(�di | �a) represents the Probability Density Function (PDF) of measur-ing the datapoint �di given the set of parameters �a and N is the number of datapoints in the event. The reconstruction is performed by finding the values of �afor which − logL is minimal.

To determine the direction, track position or neutrino interaction vertex ofan event, only the times and positions of the recorded hits are used. Scatteringand absorption play a role in when or if an emitted Cherenkov photon is de-tected at a DOM, since scatterings will change the photon’s path and therebyaffect its arrival time. The absorption limits the amount of scatterings a pho-ton will do and therefore affects the timing distributions at the DOMs. Theseeffects needs to be taken into account along with the distance r from, and theDOM’s orientation η relative to, the emission point. It is convenient to definethe residual time as

tres ≡ thit− (t0+ tgeo), (5.8)

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where thit is the recorded time of the hit, t0 is the time when the detected photonwas emitted and tgeo is the same as previously defined in equation (5.4). tgeocan also be modified to account for a specific emission hypothesis such asCherenkov emission along a track or from a cascade. By using a PDF of tres,here denoted as p(tres | r, η), the time based likelihood can be written as [122]

LT =

Nhits∏i=1

p(tres,i | ri, ηi). (5.9)

There are different approaches to how the arrival time PDF is constructed.Depending on the accuracy needed and the computing resources available,one can try to define an analytical function that is computationally efficient,or go for a more complex description that provides a higher accuracy. Thereconstructions used in this work utilize both approaches.

The faster reconstructions use the Pandel function as the PDF which is moti-vated by laser light measurements conducted in the BAIKAL project [122, 123].The Pandel function, as used in IceCube reconstructions, parameterizes thedistribution of tres by way of a gamma function convoluted with a gaussianrepresenting the detector timing resolution [124, 125]. This makes the func-tion piece-wise analytically integrable, which in turn makes it computationallyefficient. This efficiency comes at a price since the Pandel function assumesbulk ice with constant values for scattering and absorption lengths. The op-tical properties of the Antarctic ice that make up IceCube has been measuredin situ and has been shown to have scattering and absorption lengths that varywith depth, see section 3.3. To take full advantage of these measurements, thePhotonics [126] software package is used to simulate photons propagatingthrough the ice using a detailed model of its optical properties. Since thesesimulations are very computationally intensive the results are saved into ta-bles for quick access during event reconstructions. To save time, these tablesinclude interpolated values that have been calculated from a 5-dimensional B-spline surface fitted to the points calculated using Photonics [127]. The finalPDFs, whether they come from the Pandel function or the Photonics tables,have also been adjusted to take jitter from the PMTs and the dark noise rate ofthe DOMs into account.

Energy reconstruction is performed simultaneously with the other param-eters in some of the reconstructions described in this chapter. The expectednumber of detected photons λ from a particle depositing the energy E in icefollows a Poisson distribution [128]. The energy likelihood for the full detec-tor can therefore be written as

LE =λk

k!e−λ, (5.10)

where k is the actual number of detected photons and λ is given by

λ = ΛE+ρ, (5.11)

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where Λ is the number of photons produced per unit energy, E is the depositedenergy and ρ is the expected noise. Substituting equation (5.11) into equation(5.10) and taking the logarithm yields

logLE = k · log(ΛE+ρ)− (ΛE+ρ)− log(k!), (5.12)

which is the expression used in the reconstructions by minimizing − logLE . Itis also possible to make use of DOMs that were not hit and add them into thelikelihood by including the complement of the probability of a certain DOMbeing hit, pno hit = 1− phit. This option is called HitNoHit.

Common for all likelihood reconstructions is that they return the final neg-ative log-likelihood as (− logL)min for each event. Along with this, each re-construction calculates the reduced log-likelihood defined as

(logL)r ≡ (− logL)min

Nch−NDoF, (5.13)

where Nch is the number of hit DOMs and NDoF is the number of degrees offreedom in the fit. (logL)r tends to correlate with the reconstruction error andcan be used as a goodness-of-fit parameter.

5.3.1 TrackLLH (SPE32)The TrackLLH reconstruction, or SPE32 as it is also called, uses the Pandellikelihood with an infinite track hypothesis. SPE stands for single photo elec-tron which means that the reconstruction only uses the first hit in each DOM.The number 32 indicates the number of iterations that the algorithm runs. Thereason to do it more than once is to overcome the issue of the minimizer con-verging on local minima instead of the global one. First, a regular likelihoodfit is performed, seeded with the direction from a first guess reconstruction. Inthis case improved LineFit is used. Each of the following 32 iterations startby creating a new seed based on the result from the last successful fit. Firstthe point x0 is moved along the direction of the result of the previous iterationto the point closest to the COG of the hits. Then a quasi-random direction isselected and the fit is run again. The iteration with the highest overall like-lihood is used. The TrackLLH reconstruction does not fit the energy, onlydirection. The time is chosen arbitrarily based on numerical convenience andthe position on the track is then calculated to match the particle’s position atthat time.

5.3.2 CascadeLLHThe CascadeLLH reconstruction also uses the Pandel likelihood, but with acascade hypothesis. It does only one iteration and fits all reconstruction pa-rameters simultaneously. It uses the CLast reconstruction as its seed. Cas-

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Table 5.1. Summary of the angular resolution distributions for the three signal chan-nels shown in figure 5.2.

Median 90th percentile

bb 100 GeV 33◦ 100◦W+W− 300 GeV 15◦ 49◦μ+μ−μ+μ−μ+μ− 1000 GeV 14◦ 50◦

cadeLLH is slower than CLast, but is fast enough to be run on quite a largedata sample if needed.

5.3.3 MonopodThe Monopod reconstruction [79, sec. 3.4.3] is the most advanced reconstruc-tion used in this work. It uses the full description of the Antarctic ice throughthe Photonics tables discussed previously. Since Monopod is a cascade re-construction, it uses tables that were created using a cascade as the emitter forthe simulated photons. All reconstruction parameters are fitted simultaneouslyand the combined time and energy likelihood is maximized (by minimizing− logL). The full, uncleaned hit map is used and non-hit DOMs are also takeninto account with a HitNoHit term added to the energy likelihood.

In this work, Monopod was set to 16 iterations and was seeded with Cas-cadeLLH. Similar to the case for the SPE32 reconstruction the result of theprevious iteration is used to create a new seed. Since x0 cannot be chosenarbitrarily as it is the interaction vertex point of the incoming neutrino, it isnot moved as is the case for SPE32. Instead a new pseudo-random directionis chosen as the seed following iterations using the x0 result from the previousiteration. The iteration with the highest overall likelihood is selected as thefinal result.

5.4 Angular Reconstruction PerformanceThe main goal of using the likelihood reconstructions is to be able to recon-struct the arrival direction of the detected particles. To investigate how goodthe final angular resolution is, signal simulation was used since we know thetrue neutrino direction for those events. Unsurprisingly, Monopod providedthe best angular resolution by far. The full angular resolution distribution forthree benchmark signal channels can be seen in figure 5.2 as well as summa-rized by median and 90th percentile in table 5.1. The resolution is given asmedian of the distribution of the space angles, defined as the angle betweenthe reconstructed and true direction for each event.

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Figure 5.2. The angular resolution distribution obtained from the Monopod recon-struction (16 iterations) for three signal channels at final event selection level. Shownvalues are the space angle between the reconstructed direction and the true directionof the incoming neutrino.

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6. Event Selection

The work presented in this thesis is the first dark matter analysis in IceCubeusing neutrino-induced cascade events, as opposed to tracks. Although it isharder to reconstruct the direction of cascades due to their spherical shape,they have the advantage of being produced more often in the deep inelasticscattering reactions described in section 2.3. Neutrino-induced muon tracksare only produced through the charged current interaction of a muon neutrino,while cascades are produced in all electron neutrino and 83% of tau neutrinocharged current interactions. On top of this, all neutrino flavors produce cas-cades if undergoing neutral current interactions. The event selection presentedin this chapter is therefore aimed at finding cascade-like events that match adark matter signal while rejecting track-like events, as the main background istracks from atmospheric muons. This is done in several stages, or levels, asthey will be called throughout this chapter.

The logic of the different cut levels is best described by an example. Thelevel 3 data sample is obtained by cutting on the variables called level 3 vari-ables. Therefore the level 3 variables are calculated using the level 2 datasample. This process is then repeated to reach level 4.

6.1 BlindnessTo avoid any unintentional bias from the analyzer, most IceCube analyses areblinded while being developed. For an analysis such as the one presented inthis work, where the arrival direction of the neutrinos are of importance, thetimes of the events are kept blind. Due to IceCube’s position at the South Pole,this means that the azimuthal directions are blinded as well.

The event selection and analysis is done using simulated signal and back-ground along with a small sample of scrambled data to verify that the simula-tions behave correctly for each calculated variable. After the event selectionand analysis method have been finalized, there is an internal review processwithin the IceCube Collaboration to straighten out any questions before look-ing at the real data. During this process everyone in the collaboration is giventhe opportunity to comment and ask questions. Once all questions and is-sues have been addressed, the analysis is approved for “unblinding” and theanalyzer is allowed to run the analysis on the real data sample. After the un-blinding no part of the event selection can be changed without first presentingany changes to the collaboration for review.

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6.2 Level 1 and 2 - The DeepCore Trigger and FilterLevel 1 and 2 are the automated triggering and filtering that is done at theIceCube Laboratory at the South Pole before the data is sent north via satel-lite. There are several different triggers and filters running in IceCube thataim to find events suitable for the large range of different analyses being per-formed by the IceCube Collaboration. This section is dedicated to describingthe DeepCore trigger and filter stream which is the only one being used in theanalysis described in this thesis.

6.2.1 The DeepCore Trigger - SMT3The trigger running in the DeepCore fiducial volume is the Simple MultiplicityTrigger (SMT) with the condition that at least 3 HLC hits are registered within2.5 μs of each other. This trigger creates a readout window of ±6 μs centeredaround the trigger time, which is defined as the time of the first of the threeHLC hits. All hits in the full in-ice array, both SLC and HLC, within this timewindow are saved as an event. More hits than those selected by the SMT3trigger can be added to the event if another trigger fires within the readoutwindow and the new trigger has a readout window extending beyond the onefor SMT3. If the DeepCore trigger fires, the IceTop array is also read out, butwith a time window of ±10 μs around the trigger time. Note that no IceTophits were used in the analysis presented here. The average trigger rate of theSMT3 is about 260 Hz.

6.2.2 The DeepCore FilterThe DeepCore filter is applied to all events triggered by SMT3. It selectsevents that appear to be starting within the DeepCore fiducial volume withthe aim of removing as many events as possible triggered by the atmosphericmuons. This is achieved by using the remaining IceCube DOMs surroundingDeepCore as a veto for incoming tracks.

The algorithm works by using the HLC hits in the DeepCore region to cal-culate a COG as defined in equation (5.3), along with a corresponding time,i.e., the mean hit time of all hits included in the COG. Assuming that thereare hits in the veto region and that those hits are caused by un-scattered pho-tons from a passing charged particle, the particle’s speed can be calculated bycomparing the hit times and distances of each HLC hit in the veto region withthe COG position and time. If the speed calculated from the hits in the vetoregion is close to the speed of light, it is an indication that the hit pattern wasthe result of an incoming muon. The DeepCore filter allows no more than oneHLC hit matching this criterion. See figure 6.1 for an illustration of the Deep-Core filter algorithm. The average passing rate of the DeepCore filter is about28 Hz.

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Figure 6.1. Illustration of the DeepCore veto algorithm. A COG with a correspondingmean time is calculated using all HLC hits in the DeepCore volume. For each HLC hitin the veto region, the hit time and position are used to calculate the speed of a particletraveling from the hit to the COG. If this speed is consistent with the speed of light itsuggests that the hit was caused by an incoming muon. The colors represent the timeof the hit from red (early) to blue (late). Credit: Figure 10 from reference [100].

6.2.3 Level 2′ - Quality CutsSince the analysis presented here depends on the pointing resolution of thereconstructions, some initial quality cuts are made to remove events that wouldbe difficult to reconstruct. These cuts are made on the number of hit DOMsafter event cleaning Nch:A, demanding this number to be at least eight or more.Also, the number of strings with hits after cleaning Nstr:A should be at leastfour or more. Another strong motivation for these cuts is that the correlatednoise hits discussed in section 3.2 cause a spike in the rate of events withNch:A around 6. At the time when this part of the event selection was made,the nature of this peak in data was not well understood or simulated. A cut atNch:A ≥ 8 removes the discrepancy between data and simulation. The peak is

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now understood as being due to the correlated noise bursts and this effect isincluded in the simulations used for calculations done after the event selection.

6.3 Level 3 - Straight CutsThe event selection to reach level 3 is based on variables from reconstructionsthat are simple to calculate and therefore do not require a large amount of com-puting power or time. This is important since the event sample is quite largeat this point. Once it has been reduced, more advanced and time consumingreconstructions can be applied.

The main aim of this cut level is to quickly remove the most obvious back-ground events while keeping as many of the signal events as possible. There-fore the cuts made on the variables described below were made “by eye.”

Many variables were investigated and the ten that showed the best separa-tion between signal and background were chosen to be used for cutting downthe size of the data sample. Plots of all the variables presented in this sectionare shown in figures 6.2 and 6.3. Apart from an overall rate difference of 7%between experimental data and background simulation, the shapes agree wellacross all variables.

6.3.1 Level 3 Cut VariablesLineFit Speed

The speed parameter calculated by the improved LineFit reconstruction, de-scribed in section 5.2.1, is the speed of a particle that best fits the timing ofthe cleaned hit map of an event. For a muon track this speed will be aroundthe speed of light, while the spherical light pattern of a cascade will result inLineFit speeds close to 0. The cut is placed at 0.22 m/ns, keeping all eventswith that speed or lower.

Tensor of Inertia Eigenvalue Ratio

The Tensor of Inertia reconstruction, described in section 5.2.2, calculatesthree eigenvalues corresponding to the principal axes of an ellipsoid represent-ing the hit map of the event. The magnitudes of the eigenvalues correspond tothe length of the principal axes. By constructing a ratio where the smallest ofthe eigenvalues are divided by the sum of all three, one obtains a variable thatis 0.33 for spherical, cascade-like, events and close to 0 for more elongated,track-like, events. The exact definition of the variable as used in this analysisis

RToI =min([I1, I2, I3])∑3

i=1 Ii, (6.1)

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(a) LineFitSpeed (b) Tensor-of-Inertia eigenvalue ratio

(c) Radius-Time veto (d) NVetoAbove

(e) COGSplitDiff (f) COGzSplitDiff

Figure 6.2. Level 3 variables. Signal is represented by bb 100 GeV (thin blue solidline), W+W− 300 GeV (thick green solid line) and μ+μ− 1000 GeV (thick red dottedline). Background simulation of atmospheric muons (thin black solid line) is showntogether with experimental data (gray shaded area). The signal simulation is normal-ized to the experimental data rate and the cut value is indicated (dashed vertical line).

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(a) | FirstHit - COG | (b) ZFirst

(c) QR6 (d) FillRatio

Figure 6.3. Level 3 variables (continued). Signal is represented by bb 100 GeV (thinblue solid line), W+W− 300 GeV (thick green solid line) and μ+μ− 1000 GeV (thickred dotted line). Background simulation of atmospheric muons (thin black solid line)is shown together with experimental data (gray shaded area). The signal simulation isnormalized to the experimental data rate and the cut value is indicated (dashed verticalline).

where I1,2,3 are the three eigenvalues from the Tensor-of-Inertia reconstruc-tion. The cut is placed at RToI ≥ 0.10.

Radius-Time Veto (RTVeto)

RTVeto looks for hits that are clustered in space and time in the veto regionaround DeepCore. Only hits with times before the first hit in the cleaned hitmap of the event are investigated. The RTVeto algorithm goes through all theearly hits in the veto region, that are not part of the cleaned hit map, tryingto find causally connected clusters of hits. It returns the number of hits in thelargest causally connected cluster it finds. The cut is placed to allow for nomore than two hits in such a cluster.

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NVetoAbove

The NVetoAbove variable describes the number of hits in the veto regionabove the position of the first trigger hit and before the trigger time. Thecut is placed to allow for three or fewer such hits.

COGSplitDiff

The COGSplitDiff variable is a measure of how far apart the early hits arefrom the late hits. The algorithm sorts all the hits of the cleaned hit map bytime and the list is split in half. If there is an odd number of hits, the list of latehits will have one more than the list of early ones. A charge weighted COGis calculated for both the early and late half of the hits and the COGSplitDiffvariable is simply the distance between these two COGs. For cascades thisdistance should be small due to the point source-like emission. The cut is setto allow no more than a 100 m separation of the two COGs.

COGzSplitDiff

The COGzSplitDiff is defined in the same way as COGSplitDiff above, excepthere only the z component1 between the two COGs is considered. The cut isset to allow at most a 70 m separation in the z (vertical) direction.

| FirstHit - COG |

This variable is the distance between the position of the first hit and the COGfor the cleaned hit map. This quantity should be smaller for cascades than fortracks. The cut is set to keep events where this distance is shorter than 175 m.

ZFirst

ZFirst is the vertical (z) position of the first hit in the cleaned pulse map. If thishit is above the DeepCore fiducial volume it is very likely to be an atmosphericmuon. The cut is placed at z = −150 m, keeping events with its first hit belowthis value.

QR6

QR6 is the ratio between the charge accumulated during the first 600 ns overthe total charge of the event. It is defined as

QR6 =∑i @ 600 ns

i=0 Qi

Qtot, (6.2)

where Qi is the charge of each individual pulse extracted from the PMT wave-forms in the event and Qtot is the total charge of the event. This ratio is usuallylarger for cascades, since they generally deposit their energy faster than tracks.The cut is set to QR6 > 0.45.

1See section 3.4 and figure 3.6 for a description of the local coordinate system.

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FillRatio

FillRatio is calculated by drawing the smallest possible sphere that containsall the hits of the cleaned hit map inside. Then the ratio is taken between thenumber of hit DOMs and the total number of DOMs contained within thatsphere. A large fill ratio indicates that the event is highly spherical in its shapeand therefore more cascade-like than track-like. The cut is set to keep allevents with a FillRatio larger than 0.03.

6.4 Level 4 - BDTFor this cut level a machine learning algorithm is used to help classify theevents as signal-like or background-like. There are several kinds of machinelearning algorithms, such as Support Vector Machines (SVMs) and artificialneural networks to mention a few. The algorithm used in this analysis is calleda Boosted Decision Tree (BDT) [129]. It considers multiple variables at onceand produces an overall score for each event, ranging from -1 (background-like) to 1 (signal-like). The reason for this choice of algorithm is due to itsproven effectiveness and ease of use. The specific implementation, PyBDT,used in this analysis provides a software module that integrates with the stan-dard IceCube software framework, IceTray. This speeds up the processingsince the scoring of the events can be done at the same time as the rest of thedata processing.

Apart from the BDT, a cut on the zenith of the reconstructed direction isalso made. This cut removes events reconstructed within 5◦ of the poles (5◦≤ zenith ≤ 175◦) to avoid problems later in the analysis when oversamplingand scrambling. Scrambling is done by assigning a random azimuth angleto the reconstructed event. Events close to the poles will not get sufficientlyscrambled due to the limited phase space, hence the cut on the zenith angle.

6.4.1 The BDTAs is the case for many machine learning algorithms, a BDT works by firsttraining it on known samples of signal and background. Each event in thesesamples has an identical set of pre-calculated variables that all show promise tobe able to differentiate signal from background. The signal events can eithercome from a sample of known signal recorded by the detector, or be simu-lated events as is the case for this analysis. The background training samplehere comes from scrambled experimental data. Along with these datasets,a simulated background sample was used to verify the accuracy of the sig-nal simulation, but was not included in the training. The selection of sevenvariables included in the BDT for this analysis was narrowed down from alarger selection of 14. This selection was made by training the BDT using all14 variables and evaluating the BDT’s performance. The performance metric

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used was the background supression when placing a cut on the BDT score re-sulting in a signal efficiency of exactly 60%. The variable that got the lowestranking, meaning it was rarely used to discriminate signal from background,was removed. The BDT was then trained again and its performance was eval-uated. As long as the performance did not decline significantly, the lowestranked variable was removed and the procedure was repeated. This resultedin a seven variable BDT with as good performance as the initial 14 variableBDT, but with less complexity.

The BDT is trained by having it find the variable that has the best separationbetween the signal and background training samples. It then makes a cut onthat variable separating out the most signal-like or background-like events. Forthe rest of the events, another evaluation of which variable is most powerfulis done and a cut on this new variable is made, creating another sub-samplethat has a high purity in either signal or background. When using the trainedBDT to score events, the cut values determined during training and the orderthe cuts were applied are used to calculate an event’s score. This is done basedon in which sub-sample of the tree the event ends up in and the signal puritythat sub-sample had during training.

The distribution of the output score from the BDT has a better separationbetween background and signal than any of the input variables had on theirown. The BDT also handles correlations between the variables, so if usingone variable makes another variable more or less powerful, this is taken intoaccount.

Overtraining

Even though a BDT is a powerful tool, the resulting decision tree used toscore the data needs to be carefully checked, so that it is not overtrained. Ifthe training process is allowed to continue too many levels the resulting de-cision tree will become overtrained, since it will start to split the remainingpart of the training set based on differences that are not describing the data ingeneral. Instead it starts splitting based on differences valid only for the spe-cific training sets. This can be compared to using a polynomial fit on a set ofdata points with a clearly linear relationship. To avoid overtraining a randomforest was used, where many BDTs are allowed to train using a random subsetof the seven variables and only with a limited number of internal cut levels.In this analysis, only three levels were allowed for each BDT. The resultingtrees are weighed together based on their separation performance to produceone final tree that is less likely to be overtrained. To check for overtraining,only half of each training data set was used to actually train the random forest.Then both halves of the data sets were scored using the final tree and the scoredistributions were compared, both visually and using a Kolmogorov-Smirnovtest. The score distributions of both the training and testing samples should bevery similar if the BDT is not overtrained.

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6.4.2 Level 4 VariablesIn this section the final variables used in the BDT are presented. Some ofthe variables are based on the results of reconstructions that were not possibleto run on the full data sample due to the amount of processing time needed.Other variables are simple geometric ones that were not considered for theprevious level. Plots of all the variables are shown in figures 6.4 and 6.5. Asfor level 3, there is a difference on the overall rate between experimental dataand simulated background that is 9% for level 4, while the shapes still agreewell across all the variables.

(a) L3QR6 (b) RatioLH

(c) RatioRLogL (d) RhoL4

Figure 6.4. Level 4 variables. Signal is represented by bb 100 GeV (thin blue solidline), W+W− 300 GeV (thick green solid line) and μ+μ− 1000 GeV (thick red dottedline). Background simulation of atmospheric muons (thin black solid line) is showntogether with experimental data (gray shaded area). The signal simulation is normal-ized to the experimental data rate.

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(a) TrackRLogL (b) DeltaCOGz

(c) L3ZFirst

Figure 6.5. Level 4 variables (continued). Signal is represented by bb 100 GeV (thinblue solid line), W+W− 300 GeV (thick green solid line) and μ+μ− 1000 GeV (thickred dotted line). Background simulation of atmospheric muons (thin black solid line)is shown together with experimental data (gray shaded area). The signal simulation isnormalized to the experimental data rate.

L3QR6

This is the same variable as QR6 for level 3, described in section 6.3.1. It stillshows good separation between signal and background after the level 3 cut,which is why it is included in the BDT.

RatioLH

RatioLH is the ratio between the likelihoods calculated by the CascadeLLHand TrackLLH (SPE32) reconstructions. The two reconstructions are de-scribed in sections 5.3.2 and 5.3.1 respectively. The precise definition of thevariable is

RLH = log(Lcascade

Ltrack

), (6.3)

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where Lcascade and Ltrack are the likelihood values calculated by the cascadeand track reconstructions just mentioned.

RatioRLogL

RatioRLogL is the ratio between the reduced log-likelihoods from the Cas-cadeLLH and TrackLLH (SPE32) reconstructions. The definition of reducedlog-likelihood is given in equation (5.13) and the definition of RatioRLogL is

RrLLH =(logL)r:cascade

(logL)r:track, (6.4)

where (logL)r:cascade and (logL)r:track are the reduced log-likelihood values ofthe corresponding reconstructions.

RhoL4 (ρL4)

RhoL4 is the distance in the x-y plane of the local coordinate system (cf. figure3.6) between the central string (number 36) and the first hit of the cleaned hitmap.

TrackRLogL

This variable is the reduced log-likelihood (logL)r:track from the TrackLLH(SPE32) reconstruction, which is the quantity used in denominator of equation(6.4). From visual inspection of the signal and background distributions ofTrackRLogL (fig. 6.5a), it is not immediately evident that it can yield a goodseparation between the two distributions. However, it comes out as highlyranked by the BDT meaning that it will gain in separation power when cuttingin combination with some of the other variables.

DeltaCOGz

To calculate DeltaCOGz, the ensemble of hits in the cleaned hit map is split intwo by a plane. This plane is placed at the COG (of all the cleaned hits) andis perpendicular to the improved LineFit reconstruction. The COGs of eachhalf of the hits are calculated and the DeltaCOGz variable is the vertical (z)component of the distance between them.

L3ZFirst

L3ZFirst is identical to the ZFirst variable used in level 3 and is described insection 6.3.1. As it still has good separation between signal and background,as well as being ranked highly by the BDT, it is included again at this cut level.

6.4.3 BDT Performance and Final SelectionIn total, three different BDTs were trained and investigated in this analysis.The first one was trained on the signal spectrum of the bb 100 GeV anni-hilation channel and it was trained on all of the 14 initial variables before

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bb 100 GeV

CORSIKA

Data

Atm. nue

Atm. numu

Total MC

Figure 6.6. The score distribution for the BDT trained on the bb 100 GeV signal chan-nel. The final cut was made at BDT score 0.25 (red vertical line) and keeping eventsabove that value, resulting in the low-energy event sample. The signal simulation isnormalized to the experimental data rate.

CORSIKA

WW 300 GeV

Atm. nue

Atm. numu

Data

Total MC

Figure 6.7. The score distribution for the BDT trained on the W+W− 300 GeV signalchannel. The final cut was made at BDT score 0.35 (red vertical line) and keepingevents above that value, resulting in the high-energy event sample. The signal simula-tion is normalized to the experimental data rate.

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they were narrowed down to the final seven, using the method discussed ear-lier in this section. The other two BDTs were trained on the signal fromthe W+W− 300 GeV and μ+μ− 1000 GeV channels respectively. The BDTtrained on the μ+μ− 1000 GeV signal channel produced a very similar eventselection as the BDT trained on the W+W− 300 GeV channel and was there-fore abandoned. The final BDT score distributions for the bb 100 GeV andW+W− 300 GeV channels are presented in figures 6.6 and 6.7 respectively.

To decide on the final cut value for the two BDTs, a systematic study wasdone by running the resulting event selections from a range of BDT scorecut values through the full shape likelihood analysis, presented in the nextchapter, to produce a signal sensitivity. The BDT score cut value producing thebest sensitivity for the two signal channels for which the BDTs were trainedwas selected. For the BDT trained on the bb channel, the final cut value onthe BDT score is 0.25 and the corresponding value for the BDT trained onthe W+W− channel is 0.35. These two event samples are referred to as thelow-energy (LE) and high-energy (HE) sample respectively. The LE samplecontains 5,892 events, the HE sample contains 2,178 events and the overlapbetween them is 664 events.

6.5 Event Selection SummaryThe event selection presented in this chapter aims to produce a final eventsample sufficiently free from the background to look for a neutrino signalfrom annihilating WIMPs. Starting from a data rate of about 260 Hz fromthe SMT3 trigger that was reduced to about 28 Hz by the DeepCore filter, thetwo final selections end up with a data rate of 2.06×10−4 Hz for the LE sam-ple and 7.61×10−5 Hz for the HE sample. At the final level, the atmosphericneutrinos are estimated to contribute with a rate of 1.03×10−4 Hz (50%) and3.58× 10−5 Hz (47%) to the LE and HE samples respectively, while the cor-responding rates for the atmospheric muon simulation are 4× 10−5 Hz and2×10−5 Hz. Note that the statistics for the simulated atmospheric muons arevery low at final level, making the relative errors on their rates large. Thatsaid, the total rate of the simulated backgrounds is consistent with there beingroom for signal in the final events samples.

The signal efficiency compared to level 2′ (after the quality cuts, see section6.2.3) is about 8% for the bb 100 GeV channel in the LE event sample andabout 6% and 11% for the W+W− 300 GeV and μ+μ− 1000 GeV respectivelyin the HE event sample. A more extensive summary of the event selectionis available in table 6.1. Also, a plot of the effective area for the two eventsamples can be found in figure 6.8. The effective area is defined as the area a100% efficient detector would have, i.e., if DeepCore was able to detect everyneutrino passing through it. This quantity is a measure of how efficient thedetector is for a certain event selection.

90

Figure 6.8. The neutrino effective area as a function of neutrino energy. Each line hasall three neutrino flavors included.

In figure 6.9, sky maps show the true and reconstructed event distributionsfor signal at final level. To illustrate the range of the event distributions fromdifferent signal channels, a wide distribution is represented by the bb 100 GeVchannel in combination with the Burkert profile and the LE event sample. Amore peaked distribution is represented by the μ+μ− 1000 GeV channel incombination with the NFW profile and the HE event sample.

91

(a) Burkert, bb 100 GeV,true directions.

(b) Burkert, bb 100 GeV,reconstructed directions.

(c) NFW, μ+μ− 1000 GeV,true directions.

(d) NFW, μ+μ− 1000 GeV,reconstructed directions.

Figure 6.9. Sky maps of the true and reconstructed event distributions for signal atfinal level. A wide distribution is represented by the bb 100 GeV channel in combina-tion with the Burkert profile and the LE event sample. A more peaked distribution isrepresented by the μ+μ− 1000 GeV channel in combination with the NFW profile andthe HE event sample. The distribution within each plot is normalized to one. The scaleis logarithmic, in arbitrary units and have the same range for all the plots. The coor-dinates in the plots are local zenith an azimuth at a defined time where the Galacticcenter is located in the center of the red part of the true distributions.

92

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93

7. The Analysis Method

The analysis described in this thesis uses a maximum likelihood method totest the signal hypothesis against the background-only hypothesis. The signaland background hypotheses are represented by Probability Density Functions(PDFs) constructed from the distributions of the space angle ψ, which is theangle between the reconstructed direction of an event and the direction of theGalactic center. This is the same angle as used to describe the dark matter haloprofiles in figure 1.9 and the line-of-sight integral when discussing the signalin section 4.1. In the PDFs, the ψ angle is allowed to be in the full range 0◦ to180◦, thereby covering the full sky and the entire Galactic halo.1

7.1 PDFs for Signal and BackgroundThe space angle ψ is calculated from the relation

cosψ = cosθ cosθGC+ sinθ sinθGC cos(φ−φGC), (7.1)

where θ and φ are the reconstructed zenith and azimuth angles of the eventrespectively (local coordinates, cf. figure 3.6), while the corresponding anglesfor the Galactic center are θGC and φGC.

The signal PDF, fS, is constructed from signal simulation, while the back-ground PDF, fB, is a weighted sum of scrambled data and scrambled signalsimulation. The combined PDF is defined as

f (ψ | μ) = μnobs

fS(ψ)+(1− μ

nobs

)fB(ψ | μ), (7.2)

where μ is the number of signal events present among the total number ofobserved events, nobs. Note that fB, apart from ψ, also depends on μ as

fB(ψ | μ) = μnobs

fss(ψ)+(1− μ

nobs

)fsd(ψ), (7.3)

where fss is the PDF for scrambled signal and fsd is the PDF for scrambleddata. This addition of scrambled signal to the background is needed becausethe background only can be scrambled in azimuth, since the detector accep-tance varies with zenith. This makes the effectiveness of the scrambling vary

1Except for the 5◦ around the poles, due to the cut made to facilitate scrambling and oversam-pling. See section 6.4.

95

(a) Burkert, bb 100 GeV (b) NFW, bb 100 GeV

(c) Burkert, μ+μ− 1000 GeV (d) NFW, μ+μ− 1000 GeV

Figure 7.1. PDFs for two signal channels and two halo profiles. In each panel thesignal PDF fS(ψ) (thick black line) is shown together with the two components ofthe background PDF; the scrambled data fsd(ψ) (gray shaded area) and the scrambledsignal fss(ψ) (thin black line).

across different zeniths. Also, the effectiveness of the scrambling is reduced ifthe signal source is extended in azimuth. Adding scrambled signal to the dataresolves these issues, but introduces a bias if true signal is present in the data.This bias, however, is easy to understand and control. See figure 7.1 for exam-ples of all three PDFs for different signal channels and halo models. As canbe seen, the addition of scrambled signal to the background has an increasedeffect when moving towards a harder signal spectrum (e.g., μ+μ− 1000 GeV)and when switching from the flatter Burkert halo profile to the cuspier NFWprofile.

The signal PDFs were created using the signal simulation described in sec-tion 4.3.3. Apart from using the event simulation weight w, the weight for theneutrino spectrum dNν/dE and the halo weight in the form of the Ja-factorare used. To compensate for the limited event statistics available, all eventswere oversampled 50 times by rotating each event’s true and reconstructed di-

96

rections together to a new random azimuthal angle, preserving their relativepositions to each other. After the rotation a new Ja-factor and ψ angle werecalculated based on the new true and reconstructed directions of the event re-spectively. The ψ angles were histogrammed along with their weights and asmoothing in the form of a five bin moving average was applied before nor-malizing the histogram to unity to produce a PDF. The PDFs for the scrambledsignal were produced using the oversampled signal sample just described, in-cluding all their weights. The only difference is that new random values forthe reconstructed azimuth angles were assigned to the events before calculat-ing the ψ angles.

The two background PDFs (one for the LE and one for the HE sample)were created by scrambling and oversampling the event samples. The eventswere oversampled until exceeding 200,000 events, meaning 34 times for theLE sample and 92 times for the HE sample. Each oversampling calculateda ψ angle for the reconstructed direction using a random time and therebyrandomizing the position of the Galactic center (in local coordinates). Allψ angles were histogrammed and the resulting histogram was normalized tounity. No smoothing was applied to the background PDFs.

7.2 The LikelihoodWith the PDFs defined, we can go on and define the likelihood as

L(μ) =nobs∏i=1

f (ψi | μ). (7.4)

The test statistic used is the rank R, following the method developed by Feld-man and Cousins [130]. It is defined as

R(μ) =L(μ)L(μ)

, (7.5)

where μ is the value of μ that maximizes the likelihood, L(μ). A nice feature ofthis method is that it allows the data to decide if we quote a confidence intervalor an upper limit (if the confidence interval contains 0). This is accomplishedwhile keeping the number of possible signal events within the physical bound-aries μ ∈ [0,nobs] and still avoiding over-coverage in the confidence interval.

7.3 Creating a Confidence IntervalWe want to find the best fit and obtain a confidence interval (C.I.) for the un-known parameter μ. The best fit μ is obtained by finding the maximum ofthe likelihood function (eq. 7.4). The confidence interval for μ is obtained

97

by finding the acceptance interval of our observable test statistic R(μ). Sincewe are using a frequentist approach, we want to create a confidence interval[μlower, μupper] with confidence level α such that N repeated, identical, exper-iments will have a fraction α of their confidence intervals covering the truevalue of μ. If we know the distribution of μ for each true value of μ, we candetermine the acceptance interval of R(μ). R is called the rank since it is con-nected to the unified ordering principle [130]. It is the number that determinesthe order in which we add values of μ to the confidence interval until we havereached the desired confidence level α. Since R ≤ 1 the acceptance intervalwill have the form [Rαcrit(μ), 1].

To calculate Rαcrit(μ) we performed 104 pseudo-experiments for each valueof μ ∈ [0,nobs] by sampling nobs values of ψ from the distribution f (ψ | μ)(eq. 7.2) and calculate R(μ) for each pseudo-experiment. Rαcrit(μ) is then sim-ply the quantile 1−α of the R(μ) distribution obtained from the 104 pseudo-experiments. Since R(μ) is closer to 1 the closer the best fit μ is to the truevalue of μ, we have thereby selected the fraction α of the pseudo-experimentswith μ closest to the true value μ.

In practice, the calculations were made the following way:

1. for each μ ∈ [0, 0.2 ·nobs]2 using step size Δμ = (0.2 ·nobs)/100

a) for each pseudo-experiment k = 1 . . .104

i. using eq. (7.2), given μ, sample nobs space angles to obtain aset {ψ}k

ii. using eq. (7.4), calculate the likelihood distribution Lk(μ′) forμ′ ∈ [0, nobs]

iii. using the previous step, find the best fit μ′ that maximizes thelikelihood Lk(μ′)

iv. calculate the rank distribution lnRk(μ′) using eq. (7.5)

b) lnRαcrit(μ) is the value of lnR for which a fraction α of the 104

pseudo-experiments satisfies lnRk(μ) ≥ lnRαcrit(μ)

2. smoothen and fit the distribution of lnRαcrit(μ) with a spline

To determine the confidence interval for an experiment, we simply include thevalues of μ that satisfy the condition

lnR(μ) ≥ lnRαcrit(μ). (7.6)

2To avoid doing unnecessary and time-consuming calculations we do not go all the way up tonobs. The value 0.2 was chosen through a qualified guess. If this value would have been insuffi-cient, the calculations down the line would not have produced any results since any comparisonto Rαcrit(μ > 0.2 ·nobs) is set up to fail.

98

In this thesis we will use α = 90%.

7.4 Determining the SensitivityTo find the sensitivity to the various signal channels we perform one additionalrun of 104 pseudo experiments, but this time we only sample nobs space anglesψ from the combined PDF (eq. 7.2) having no signal present. That is, μ = 0making equation (7.2) together with equation (7.3) reduce to

f (ψ | μ = 0) = fsd(ψ), (7.7)

leaving the background, i.e., the scrambled experimental data, as the only con-tribution to the combined PDF.

For each of the 104 pseudo-experiments we construct a 90% confidenceinterval by using R90%

crit (μ) calculated in section 7.3 and the expression in equa-tion (7.6). The sensitivity μ90 is defined as the median upper limit, i.e., themedian of the upper value of these 104 confidence intervals for the case whereno signal is present. In figure 7.2 histograms of the lower and upper limits arepresented for the W+W− 300 GeV signal channel using the high energy BDTselection. As is indicated in the figure, the median upper limit on the numberof signal events μ90 in this specific annihilation channel is 132 events. Thiscan be interpreted as needing at least 132 signal events to be able to see theW+W− 300 GeV signal at 90% confidence level with 50% probability.

Figure 7.2. Histograms for the lower limits (thin line) and upper limits (thick line)for 104 pseudo-experiments containing no signal tested against the W+W− 300 GeVsignal channel. The median of the upper limits (dashed line) is the sensitivity for thischannel.

99

To use μ90 to calculate a median upper limit of the thermally averaged prod-uct of the WIMP annihilation cross section and velocity 〈σAv〉90, the simulatedevents used to construct the signal PDFs are needed. Combining equations(4.5) and (4.3), we have

Rν =〈σAv〉2 Ngen

14πm2

χ

∑i

(dNνdE

)iJa, i wi. (7.8)

Since the neutrino rate is given by Rν = μ/T , where T is the detector live-time, we can use the sensitivity for the numer of signal events μ90 to obtainthe corresponding sensitivity for the thermally averaged product of the WIMPself-annihilation cross section and velocity, 〈σAv〉90. Using equation (7.8),substituting Rν = μ90/T and rearranging, we have

〈σAv〉90 =μ90

T

2 Ngen 4π m2χ∑

i

(dNνdE

)iJa, i wi

. (7.9)

The detector livetime for the collected event sample used in this analysisis 329.1 days. Using equation (7.9), the final sensitivities 〈σAv〉90 were cal-culated for all previously mentioned annihilation channels for WIMP massesranging from 30 GeV to 10 TeV. They are presented for both the Burkert andNFW halo profiles in figure 7.3, where the resulting sensitivities from the LEand HE event samples have been selected so that only the best value from eachsample is shown at each mass value.

100

(a) Burkert profile

(b) NFW profile

Figure 7.3. Sensitivities to the thermally averaged product of the WIMP self-annihilation cross section and velocity 〈σAv〉 as a function of the WIMP mass forthe annihilation channels indicated in the plots.

101

8. Results and Conclusions

After the analysis had been reviewed by the IceCube collaboration, accordingto the procedure described in section 6.1, it was approved for “unblinding.”The true event times were used to calculate the position of the Galactic centerin local coordinates, which in turn made it possible to calculate the real ψangles for the events. The true ψ distributions for both the LE and HE eventsamples are presented in figure 8.1.

Using the Feldman & Cousins method described in section 7.3, 90% con-fidence intervals were calculated for all combinations of WIMP annihilationchannels and masses previously discussed, using the unblinded event samples.The confidence intervals for the best fit of the number of signal events μ in-clude zero for all investigated signal channels and we therefore report upperlimits on 〈σAv〉. The upper limits are presented along with their correspondingsensitivities in figures 8.2 and 8.3 for the Burkert and NFW profiles respec-tively. For each combination of annihilation channel and WIMP mass, onlythe limit from the event selection with the best sensitivity is presented. Forthe bb and μ+μ− annihilation channels, the limits (both μ90 and 〈σAv〉90) arealso presented in tables 8.1 and 8.2 respectively. There, the upper limits arepresented along with their corresponding sensitivities μ90, 〈σAv〉90 and best fitfor the number of signal events μ.

As can be seen, the resulting upper limits all lie slightly above the sensi-tivity, compatible with a statistical over-fluctuation within one standard devi-ation. Since such fluctuations are correlated within an event sample and the

(a) LE event sample, nobs = 5,892. (b) HE event sample, nobs = 2,178.

Figure 8.1. Distributions of the ψ angles of the final, unblinded, event samples.

103

two event samples used in this analysis have an overlap of 664 events, it is notsurprising that the fluctuations would be in the same direction.

8.1 Systematic UncertaintiesTo estimate the systematic uncertainties affecting the resulting upper limitspresented in this chapter, a combination of two approaches was used: For asmany sources of systematic uncertainties as possible Monte Carlo simulationstudies were done to investigate the effect of varying the input parametersof the signal simulation. Where possible, previous studies were used if theirresults were general enough to be applicable to this analysis.

All systematic uncertainties considered for this analysis are summarized intable 8.3 together with their total (quadratic sum) for the low and high-energyselections for both halo profiles. Some of the entries in the table are correlatedso the total represents a conservative estimate of the combined systematic un-certainty.

For parameters where simulated Monte Carlo datasets are available withdifferent settings, studies could be done for the specific analysis chain pre-sented in this thesis. These datasets were processed with the same scripts andtools as the baseline datasets that produced the sensitivity presented earlierin section 7.4. Once the “systematic” datasets were processed, we could cal-culate a corresponding “systematic” sensitivity that was compared with thebaseline to get a measure of the uncertainty of the considered parameter.

Ice Properties

For most IceCube analyses one of the largest uncertainties comes from the iceitself. The parameters, absorption and scattering length, were investigated byvarying the baseline settings by ±10%, individually. Their contribution to theuncertainties on the sensitivity is in the range 8%-12%.

Another source for uncertainty is the so-called hole ice that forms as thewater in the hole drilled for the string deployment re-freezes. This new icecontains residual air bubbles that alters the optical properties of this ice com-pared to the glacial bulk ice surrounding it. These bubbles result in a shorterscattering length, causing light to scatter both away from and in towards aDOM. In the baseline datasets the scattering length of the hole ice is set to50 cm. Varying this parameter between 30 cm and 100 cm yields a 10%-24%effect on the sensitivity.

The baseline model used in this analysis to describe the ice in the in-icearray of IceCube is called SPICE-Mie [98]. As an extra check, sensitivitieswere also calculated for the more recent model, SPICE-Lea, which also takesthe slight tilt of the ice layers into account (see section 3.3). The differencesfound on the sensitivity, 〈σAv〉, when switching between the to ice modelswere up to 25% for the lowest WIMP masses and up to 5% for masses over

104

(a) χχ→ bb (b) χχ→W+W−

(c) χχ→ τ+τ− (d) χχ→ μ+μ−

(e) χχ→ νν

Figure 8.2. Resulting upper limits (90% C.L., solid black line) of the thermally aver-aged product of the WIMP self-annihilation cross section and velocity 〈σAv〉 for theBurkert halo model together with the corresponding sensitivities (dashed black line)and their 1σ (green) and 2σ (yellow) statistical uncertainties. No systematic uncer-tainties included. The local dark matter density used was ρlocal = 0.487 g/cm3, seetable 1.3.

105

(a) χχ→ bb (b) χχ→W+W−

(c) χχ→ τ+τ− (d) χχ→ μ+μ−

(e) χχ→ νν

Figure 8.3. Resulting upper limits (90% C.L., solid black line) of the thermally aver-aged product of the WIMP self-annihilation cross section and velocity 〈σAv〉 for theNFW halo model together with the corresponding sensitivities (dashed black line) andtheir 1σ (green) and 2σ (yellow) statistical uncertainties. No systematic uncertaintiesincluded. The local dark matter density used was ρlocal = 0.471 g/cm3, see table 1.3.

106

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108

∼300 GeV. Since the difference between these two models do not bracket abaseline value in the same way as the other investigated uncertainties, it mightnot be considered a systematic effect in the same way. However, the differencestill quantifies the effect ot the uncertainty of our understanding of the ice andwill therefore be added to the total systematic uncertainty along with the effectof other investigated parameters.

Detector Properties

The overall efficiency of how well the detector converts the Cherenkov lightinto a detectable electrical signal is another major source of uncertainty. Theeffect of this was investigated by changing the so-called DOM efficiency ofthe signal simulation by ±10%. This is a linear scaling of how well light isconverted to electrical signals in the DOMs and the 10% spread is roughly thestandard deviation of this quantity as measured in a laboratory and again afterdeployment. The effect on the sensitivity compared to the baseline is 10%-35% depending on the combination of halo profile and event selection. Thereason for this effect varying depending on halo model, is due to reconstruc-tion quality being affected when the detector detects more or less light. TheNFW profile is more sensitive to this since more peaked towards the Galacticcenter. As expected, we see a higher effect on the low-energy events since theredundancy of hits in the detector is lower than for events with higher energy.

The noise simulation was investigated in the same way as the ice model. Bychanging the noise model used in the simulation from the one called Vuvuzelato NoiseGenerator a 5%-10% effect was noted on the sensitivity.

The effects of detector calibration accuracy on hit timing and the uncer-tainties on the geometrical DOM positions have not been investigated for thisspecific analysis, but for other IceCube dark matter searches. The effect was

Table 8.3. Summary of systematic uncertainties for both the low-energy (LE) andhigh-energy (HE) event selections presented for both halo profiles used in this thesis.The total is the quadratic sum of each individual contribution.

Burkert Profile NFW Profile

LE Selection HE Selection LE Selection HE Selection

Absorption & scattering 8% 8% 12% 12%Hole ice 24% 15% 24% 10%Ice model 25% 5% 25% 5%

DOM efficiency 17% 10% 35% 12%Noise model 10% <5% 8% 10%Calibration <5% <5% <5% <5%

Analysis method 2% 2% 2% 2%

Total 41% 22% 52% 23%

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found to be less than 5% (see, e.g., [131]) and should be similar for this anal-ysis.

Analysis Method

This analysis depends on several random components, which makes each runthrough all the calculations involved produce a slightly different result. Therandom steps include the scrambling of the signal and experimental data touse as background, the oversampling when creating the PDFs for signal andbackground and the many pseudo-experiments used to calculate the criticalrank Rαcrit and the sensitivity. The effect of this randomness was investigatedby recalculating the baseline sensitivity several times. The variation was about2% across all signal channels and event selections.

Astrophysical Uncertainties

To cover a wide range of the astrophysical uncertainties, two different modelsfor the density profile of the dark matter halo have been used throughout theanalysis presented in this work; Burkert and NFW. They represent two differ-ent approaches of trying to identify the true distribution of dark matter in ourgalaxy, namely observation and simulation (see section 1.4). Within each pro-file, the uncertainties of the parameters are still large, but cannot be considereda systematic uncertainty of the experimental results presented in this chapter.In order to keep the experimental results separated from the uncertainties cou-pled to the choice of halo model, they will not be added to the total systematicuncertainties of the results presented here.

In a recent IceCube dark matter analysis using track-like events comingfrom the direction of the Galactic center [47], this effect was investigated byvarying the scale radius rs and local dark matter density ρlocal within the uncer-tainties stated in table 1.3. They estimated the effect on 〈σAv〉 to be 60%-100%for their low-energy analysis and 60%-200% for their high-energy analysis.

8.2 ConclusionsIn this thesis we have used data recorded by the IceCube Neutrino Observa-tory, and its low-energy extension DeepCore, to set new limits on the thermallyaveraged product of the WIMP self-annihilation cross section and velocity〈σAv〉. To put these new results into context, figure 8.4 shows a comparisonto a recent analysis from ANTARES [132] along with previous IceCube anal-yses [70, 48, 49, 47]. Also shown are limits from searches for gamma-raysignals from Dwarf spheroidal galaxies (dSphs) by Fermi [54], MAGIC [71]and VERITAS [72, 73]. The comparison is shown for the NFW halo profileand the χχ→ τ+τ− annihilation channel. Along with the experimental lim-its, preferred regions for the dark matter interpretation of the positron fluxexcess seen by PAMELA and the e+ + e− flux excess seen by Fermi-LAT and

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Figure 8.4. Comparison of upper limits (including systematic uncertainties) of theannihilation channel χχ→ τ+τ−. This work (IC86 Halo Cascades) is compared toANTARES [132] and other IceCube searches (IC + string number) for dark matterWIMP annihilations [70, 48, 49, 47]. Also, upper limits from gamma-ray searchesfrom dSphs by Fermi-LAT [54], MAGIC [71] and VERITAS [72, 73] are presented.The three diagonal shaded regions are dark-matter interpretations of the e+ + e− fluxexcess seen by Fermi-LAT and H.E.S.S. (3σ in dark green, 5σ in light green) andthe positron excess seen by PAMELA (in gray). The data for the shaded regions aretaken from [133]. The data for IC22 and the shaded regions have been rescaled tothe local dark matter density ρlocal = 0.471 GeV/cm3 used for the NFW profile in thiswork. The natural scale denotes the region of 〈σAv〉 needed for WIMPs to be thermalrelics of the Big Bang [134].

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H.E.S.S. [133] are shown. The data from the IceCube 22-string halo anal-ysis [70] and the shaded regions have been rescaled to the local dark matterdensity ρlocal = 0.471 GeV/cm3 used for the NFW profile in this work. Alsoindicated in the figure is the unitarity bound [135] as well as the natural scale,which is the region of 〈σAv〉 needed for WIMPs to be thermal relics of the BigBang [134].

For dark matter masses between 200 GeV and 10 TeV, the analysis pre-sented in this thesis improves on all previous IceCube analyses. It can almostcompletely exclude the preferred region of the dark matter interpretation of thee+ + e− flux excess seen by Fermi-LAT and H.E.S.S. It also shows that cas-cade events are a resource that is a competitive option for dark matter searches.

Comparisons to the results of direct detection experiments are not easilydone without making model specific assumptions for the WIMPs composi-tion and interactions. However, if the claims of detection from DAMA [23] andCDMS-II [28] are interpreted as being due to WIMP scatterings, the resultstranslate into preferred ranges in WIMP mass. CDMS favours a WIMP massof around 10 GeV, while the DAMA results are compatible with a mass around∼ 10 GeV if scattering on Na and 70 GeV if scattering on I (see figure 1.5).Only the 70 GeV result would lie within the mass range of the analysis pre-sented in this thesis. Since no indication of a neutrino signal from a WIMPwith this mass was seen in this analysis the results would seem to be in ten-sion with DAMA. There are however, many caveats to take into account whencomparing direct and indirect results, from the structure of the halo to the char-acteristics of the WIMPs. For example, a WIMP producing a signal in DAMAmight have an annihilation cross section below the sensitivity of this analysis,or no annihilations at all [136], or the dark matter halo may have substructurethat enhances local direct detection over indirect methods.

8.2.1 OutlookThe fields of dark matter physics and neutrino astronomy have reached a veryexciting stage. In the dark matter research community, there have been un-verified claims of evidence from direct detection experiments that suggestWIMPs might be what makes up the mysterious matter holding galaxies to-gether [23, 28]. When it comes to indirect searches, the upper limits are finallystarting to probe the most interesting parts of the dark matter parameter space.For neutrino astronomy there was a breakthrough when IceCube discoveredthe existence of high-energy neutrinos originating outside of our solar system[137].

IceCube is planning detector extensions to reach more of both sides of theneutrino energy spectrum as a part of IceCube-Gen2 [138]. For the low-energy side another in-fill array called PINGU (Precision IceCube Next Gen-eration Upgrade) [139] will lower the energy threshold one order of magnitude

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from DeepCore’s 10 GeV to about 1 GeV. This will be very beneficial for darkmatter searches such as the one presented in this thesis. On the high-energyside an extension is planned to increase the instrumented volume in the icefrom 1 km3 to ∼10 km3 in order to capture more of the high-energy neutrinos.

There are several possibilities to improve on the work presented in this the-sis by investigating the new promising reconstruction techniques that are beingdeveloped in IceCube. Improved angular resolution would be beneficial for ananalysis such as this one. Further, there are four more years of data that couldbe used to extend the event selection and provide more statistics. There is alsoprogress being made in making better models of the ice, which would reducethe systematic uncertainties. There seems to be a bright future for dark mattersearches using neutrinos, especially for searches using cascades.

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Acknowledgements

The work presented in this thesis does not only reflect the effort of one grad-uate student. It is the result of a collaboration with many skilled minds andexperts.

I would, first of all, like to express my gratitude to my supervisors OlgaBotner, Allan Hallgren and Carlos Perez de los Heros for giving me the oppor-tunity to work on such an amazing project like IceCube and for their guidancealong the way. A special thank you goes to Olga, for always being availableto answer questions, give advice, suggestions and encouragement. Anotherspecial thanks goes to Allan, for lending me your fast-paced mind to inspireideas, give suggestions and constructive criticism. A third special thanks goesto Carlos, for helping me unravel some of the mysteries surrounding dark mat-ter, analysis techniques and statistics.

I’ve had the opportunity to travel the world, for which I am very grateful.Apart from seeing much of Europe and North America, I got to go to Antarc-tica onboard an icebreaker, which is an experience that I will always cherish.

I would also like to thank the people from the Uppsala IceCube group thatI have had the pleasure of working with: Olle, for many nice discussions andfor introducing me into the jungle of IceCube-related software; Jon, for yourmany helpful suggestions on how to compile code that does not want to do so;David, for resolving many code-related issues and for helping me understandthe inner workings of IceCube’s event reconstructions; Sebastian, for answer-ing my questions on low-energy related matters in IceCube; Lisa, for yourhelpful comments on the early drafts of this thesis and your ever high spirits;Alex, for reading and providing helpful comments on this entire thesis. Lastbut not least, I would like to thank my office mate Rickard. For all the amazingdiscussions over the years, for the music and the theatrics, for the laughs, forall your patient help with the theoretical mysteries of particle physics and forencouraging me when I felt overwhelmed.

The IceCube group in Stockholm has also had a large influence on thiswork. Thank you for all the helpful comments and suggestions throughoutthe years. A special thank you to Samuel and Martin for helping me use yoursoftware and making my analysis better.

Thank you to my fellow graduate students and colleagues at the department,for many funny and interesting discussions over lunch and coffee. EspeciallyMaja, Lena, Li, Jim, Karin, Elin, Aila, Hazhar, Carla, Walter, Max, Elisabetta,Daniel, Dominik, Patrik and Bo.

I would also like to thank the amazing people of the IceCube Collaboration,for many fruitful discussions and great company. There are too many of you

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to mention everyone, but I would like to mention a few. Antonia, you are asawesome as they come and I’m grateful that I can call you my friend. All ofyou who made the collaboration meetings an event to really look forward to:Zig, Donglian, Klaus, Matt, Carlos, Tania, Kai, Kim, Mike, Jan K., Jan B.,Jake D., Jake F., Rob, James, Megan and Laurel.

I wouldn’t be writing this thesis if it wasn’t for the encouragement from myparents, brother, friends and extended family, who have always supported mein my studies and cheered me on along the way.

Finally, I would like to express my gratitude to Tommy, who has been withme on most of this journey. Your encouragement and support mean so muchto me and it’s a great comfort knowing that you are there cheering me along.Thank you.

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Summary in Swedish - Sammanfattning påsvenska

Avhandlingens titel: Mörk materia i Galaxens halo - En undersökning medneutrino-inducerade kaskadhändelser i IceCubes DeepCore

IntroduktionEtt av vår tids största mysterier inom fysiken är gåtan om vad den mörka ma-terian är och hur den beter sig. Mindre än fem procent av all massa och en-ergi i universum utgörs av den typ av materia som vi är bekanta med, alltsåde atomer som bygger upp allt från en bakterie eller en stol till planeter ochstjärnor. Resten utgörs av mörk materia (ca. 25%) och mörk energi (ca. 70%).Den mörka energin är det som verkar driva den ständigt accelererande expan-sionen av universum. Den mörka materian sänder inte ut något mätbart ljus,därav namnet, utan har bara observeras genom sin gravitationella påverkan påstjärnor och galaxer. Denna gravitationella växelverkan är vad som håller ihopgalaxer och galaxhopar.

Partikelfysikens standardmodell är en av de mest väletablerade vetenska-pliga teorierna och är experimentellt verifierad med mycket hög precision.Ändå finns det frågor som inte kan förklaras med standardmodellen så somden ser ut idag. Till exempel kan ingen av standardmodellens partiklar förk-lara vad den mörka materian är. Det har gjorts utvidgningar av standardmod-ellen, exempelvis de så kallade supersymmetriska modellerna. Där får varjepartikel i standardmodellen en supersymmetrisk partner, bland vilka man kanhitta partiklar som kan uppfylla kraven för att förklara den mörka materian.En sådan partikel måste ha lång livslängd, vara elektriskt neutral, tillräckligtmassiv och begränsad till växelverkan genom gravitation och en interaktionav samma styrka som den svaga växelverkan. Denna klass av partiklar brukargenerellt kallas Weakly Interacting Massive Particles (WIMPs) och inom desupersymmetriska modellerna kallas dessa för neutraliner. Det som gör neu-tralinon särskilt intressant som kandidat för mörk materia, är att dess egen-skaper passar väl in med de modeller vi har för det tidiga Universum. Närdessa partiklar "krockar" förintar de varandra och producerar partiklar somkan detekteras, däribland neutriner. Det är just dessa neutriner som analysen iden här avhandlingen är ute efter att hitta med IceCube och DeepCore.

På grund av neutrinernas svaga växelverkan kan de ta sig fram, nästintillobehindrat, från täta områden där elektromagnetisk strålning sprids eller ab-sorberas. Till skillnad från kosmisk strålning (elektroner, protoner och joner)

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saknar neutrinerna även elektrisk laddning vilket gör dem till idealiska as-tronomiska budbärare eftersom de, på sin färd, inte böjs av i magnetfältensom genomsyrar universum och därmed pekar tillbaka direkt till källan därde skapades. Dessa attraktiva egenskaper gör också att neutriner är svåra attregistrera och mäta, vilket betyder att man behöver en mycket stor detektor.

IceCube är ett neutrinoteleskop som konstruerats genom att borra ner 5 160optiska moduler i glaciärisen på den geografiska sydpolen. Modulerna ärfördelade på 86 strängar och är utspridda inom en total volym av en kubikkilo-meter klar is på ca 1,5 till 2,5 km djup. Detektionsprincipen bygger på attinkommande neutriner kan växelverka med atomkärnorna i isen. De laddadepartiklar som då bildas har hastigheter över ljusets hastighet i is, varpå ljus(tjerenkovstrålning) sänds ut när de rör sig genom isen. Detta ljus kan de-tekteras av de optiska modulerna. Genom att analysera vilka moduler somträffats, och vid vilken tidpunkt, går det att rekonstruera den ursprungliga neu-trinens riktning och energi. I den nedre halvan, i mitten av den instrumenteradevolymen, har en del av strängarna ett tätare avstånd mellan de optiska mod-ulerna och mellan de angränsande strängarna. Denna del kallas DeepCore ochhar en lägre energitröskel för detektion än vad resten av detektorn har.

Vid de, för IceCube, låga neutrinoenergier som används för analysen i denhär avhandlingen, kan en neutrino som detekteras ge en ljusbild i två olika for-mer; spår eller kaskad. Det finns tre neutrinotyper och dessa växelverkar medmateria på två sätt; via utbyte av en W-boson eller en Z-boson. Detta resulterari sex olika sluttillstånd. Endast en av dessa ”kanaler” ger upphov till spårlik-nande registrering av ljus (spårhändelse) i detektorn, medan de övriga fem re-sulterar i mer klotlika ljusregistreringar (kaskadhändelser). Under antagandetatt de inkommande neutrinerna är jämt fördelade över de tre olika neutrino-typerna, genom oscillationer över astronomiska avstånd, betyder det, någotförenklat, att kaskadhändelser bör vara fem gånger så vanliga som spårhän-delser för signaler från mörk materia.

Bilden på avhandlingens framsida föreställer hur en simulerad kasdadhän-delse producerad av en inkommande neutrino med energin 1 600 miljarderelektronvolt ser ut när den detekteras av IceCube och DeepCore. Färgernaanger när de optiska modulerna såg ljuset från interaktionen där rött är tidigtoch violett är sent. Storleken på kloten anger hur mycket ljus en modul reg-istrerade.

SyfteSyftet med analysen som presenterats i den här avhandlingen är att användadata från IceCube för att söka efter en neutrinosignal från den stora halo avmörk materia som vår galax ligger inbäddad i. Mer specifikt fokuserar analy-sen på WIMP-massor i intervallet 30-10 000 GeV/c2, där det finns många teo-retiska modeller som inte har uteslutits experimentellt. Analysen är den första

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av sitt slag inom IceCube eftersom den använder kaskadhändelser. Anlednin-gen till att en mörk materia-analys med kaskadhändelser inte gjorts tidigare ärför att det är betydligt svårare att rekonstruera riktningen på kaskader jämförtmed spår, speciellt vid låga energier. På senare tid har våra rekonstruktionsal-goritmer förbättrats avsevärt, vilket möjliggör en analys av det här slaget. Idagsläget uppnår vi en medianvärde av riktningsupplösningen på ca 14◦-33◦vid de energier som är relevanta för den här analysen, vilket är tillräckligt föratt kunna se ett överskott av neutriner från området kring Vintergatans centrumjämfört med övriga stjärnhimlen.

Analys och resultatAnalysproceduren har utvecklats genom att använda simulerad data och sig-nal tillsammans med ett litet urval mätdata för att verifiera att simuleringarnaär tillförlitliga. Dessa simuleringar är mycket detaljerade och tar hänsyn tillhur partiklarna växelverkar, hur mycket ljus som bildas, hur detta ljus spridsgenom isen, samt hur detektorn reagerar på ljuset. Även brus finns med för attkunna representera den faktiska mätdatan så exakt som möjligt. Inom IceCubeutvecklas de flesta analyser med simulerad data för att hålla oss så objek-tiva som möjligt under utvecklingsfasen. När analysen är helt färdigutveck-lad presenteras den för hela kollaborationen, varav två personer är särskilt ut-valda granskare, som kritiskt granskar de metoder som använts under utveck-lingsprocessen. Det är först när granskarna, tillsammans med resten av kollab-orationen, ger klartecken som man får applicera sin analys på den komplettamätdatan. I det här skedet får inget i analysen ändras utan att be om en nygranskning.

Den största källan till bakgrund för denna analys är atmosfäriska myoner,tunga elektronliknande partiklar, som når ner till detektorn. Dessa bildas närkosmisk strålning interagerar med atmosfären och är över 1 miljon gånger flerän neutriner från atmosfären eller den potentiella signalen från mörk materia.När man tittar på den norra stjärnhimlen med IceCube används Jorden som ettfilter för att bli av med myonbakgrunden. Myonerna stoppas då efter någrakilometers färd, medan neutrinerna passerar obehindrat och kan nå IceCube.Eftersom den här analysen tittar i riktning mot Vintergatans centrum, som lig-ger på den södra stjärnhimlen, fungerar inte denna metod. Istället används denmindre DeepCore-volymen för att registrera kaskadhändelser som startar där,medan resten av IceCube-volymen används som ett veto för inkommande my-oner. För att ytterligare reducera den störande bakgrunden har många variablerundersökts för att hitta de som bäst kan separera den från signalen. Variablernabeskriver allt från formen händelserna har i detektorn till tidsdistributioner avenskilda ljusregistreringar. I en första omgång valdes tio variabler ut och dessabeskars för att förkasta så mycket av bakgrunden som möjligt utan att offra förmycket av signalen. I en andra omgång utvärderades fler variabler och sju

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av dessa valdes ut att ingå i en så kallad maskininlärningsalgoritm av typenBoosted Decision Tree (BDT). En BDT-algoritm kan lära sig separera sig-nal från bakgrund genom en simultan analys av flera variabler. Resultatet geren sammanfattande poängvariabel med betydligt större separation än de in-gående variablerna har var för sig, förutsatt att det ingående variablerna intekorrelerar starkt med varandra. I mitt fall gav BDTn en mycket bra separationoch det slutgiltiga dataurvalet visar att återstående signal är cirka 6%-11% ochåterstående bakgrund är ungefär en miljondel relativt detektorns filternivå förDeepCore-volymen, som i sin tur är en tiondel av alla händelser som triggadedetektorn. Relativt triggernivån för DeepCore motsvarar detta en total reduk-tion av datan i storleksordningen 107.

När dataurvalet är färdigt och vi sållat ut de registrerade partikelhändelser idetektorn som mest liknar den svaga signal vi söker, kan vi göra den slutligajämförelsen för att testa vår hypotes. Denna jämförelse görs i form av enstatistisk beräkning som ger ett mått på hur förenligt det vi ser i datan är medhypotesen att ingen signal har observerats. Resultatet är att inget signifikantöverskott av neutriner från halon av mörk materia kunde hittas.

SlutsatsDå ingen neutrinosignal från mörk materia kunde hittas kan vi sätta en övregräns på hur stort detta flöde av neutriner kan vara. När experimenten ochanalyserna utvecklas, kan vi sätta allt starkare gränser och på detta sätt utes-luta eller bekräfta de teoretiska modellerna av vad mörk materia är och hurden beter sig. Hittills har inget experiment presenterat bevis för existensen avWIMPs som kunnat bekräftas.

Resultatet från analysen som presenterats i den här avhandlingen har sattstarkare gränser än tidigare IceCube-analyser för WIMP-massor mellan 200och 10 000 GeV/c2. Jämfört med andra neutrinoexperiment är gränserna fråndenna analys starkast i intervallet 200 till 1 000 GeV/c2. Utvecklingen avanalysmetoden gör att mer data från IceCube snabbt kan analyseras för atthitta en signal eller stärka gränserna ytterligare.

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Acta Universitatis UpsaliensisUppsala Dissertations from the Faculty of ScienceEditor: The Dean of the Faculty of Science

1–11: 1970–197512. Lars Thofelt: Studies on leaf temperature recorded by direct measurement and

by thermography. 1975.13. Monica Henricsson: Nutritional studies on Chara globularis Thuill., Chara zey-

lanica Willd., and Chara haitensis Turpin. 1976.14. Göran Kloow: Studies on Regenerated Cellulose by the Fluorescence Depolar-

ization Technique. 1976.15. Carl-Magnus Backman: A High Pressure Study of the Photolytic Decomposi-

tion of Azoethane and Propionyl Peroxide. 1976.16. Lennart Källströmer: The significance of biotin and certain monosaccharides

for the growth of Aspergillus niger on rhamnose medium at elevated tempera-ture. 1977.

17. Staffan Renlund: Identification of Oxytocin and Vasopressin in the Bovine Ade-nohypophysis. 1978.

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19. Thomas C. Amu: Diffusion in Dilute Solutions: An Experimental Study with Special Reference to the Effect of Size and Shape of Solute and Solvent Mole-cules. 1978.

20. Lars Tegnér: A Flash Photolysis Study of the Thermal Cis-Trans Isomerization of Some Aromatic Schiff Bases in Solution. 1979.

21. Stig Tormod: A High-Speed Stopped Flow Laser Light Scattering Apparatus and its Application in a Study of Conformational Changes in Bovine Serum Albu-min. 1985.

22. Björn Varnestig: Coulomb Excitation of Rotational Nuclei. 1987.23. Frans Lettenström: A study of nuclear effects in deep inelastic muon scattering.

1988.24. Göran Ericsson: Production of Heavy Hypernuclei in Antiproton Annihilation.

Study of their decay in the fission channel. 1988.25. Fang Peng: The Geopotential: Modelling Techniques and Physical Implications

with Case Studies in the South and East China Sea and Fennoscandia. 1989.26. Md. Anowar Hossain: Seismic Refraction Studies in the Baltic Shield along the

Fennolora Profile. 1989.27. Lars Erik Svensson: Coulomb Excitation of Vibrational Nuclei. 1989.28. Bengt Carlsson: Digital differentiating filters and model based fault detection.

1989.29. Alexander Edgar Kavka: Coulomb Excitation. Analytical Methods and Experi-

mental Results on even Selenium Nuclei. 1989.30. Christopher Juhlin: Seismic Attenuation, Shear Wave Anisotropy and Some

Aspects of Fracturing in the Crystalline Rock of the Siljan Ring Area, Central Sweden. 1990.

31. Torbjörn Wigren: Recursive Identification Based on the Nonlinear Wiener Model. 1990.

32. Kjell Janson: Experimental investigations of the proton and deuteron structure functions. 1991.

33. Suzanne W. Harris: Positive Muons in Crystalline and Amorphous Solids. 1991.34. Jan Blomgren: Experimental Studies of Giant Resonances in Medium-Weight

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Optimisation Methods. 1992.36. Liqi Fang: Dynamic Light Scattering from Polymer Gels and Semidilute Solutions.

1992.37. Raymond Munier: Segmentation, Fragmentation and Jostling of the Baltic Shield

with Time. 1993.

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56. Esteban Damián Avendaño Soto: Electrochromism in Nickel-based Oxides. Color-ation Mechanisms and Optimization of Sputter-deposited Thin Films. 2004.

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what, why, how and where. 2005.63. Barbara Piechocinska: Physics from Wholeness. Dynamical Totality as a Concep-

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96. Liselott Dominicus van den Bussche. Getting the Picture of University Physics. 2010.

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