Exploring the Universe Using Neutrinos a Search for Point Sources in the Southern Hemisphere Using the Icecube Neutrino Observatory

ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology 117

Exploring the Universe Using Neutrinos A Search for Point Sources in the Southern Hemisphere Using the IceCube Neutrino Observatory

Rickard Ström

Dissertation presented at Uppsala University to be publicly examined in Ångströmlaboratoriet, Polhemsalen, Lägerhyddsvägen 1, Uppsala, Friday, 18 December 2015 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Lawrence R. Sulak (Boston University, Boston, USA).

Abstract Ström, R. 2015. Exploring the Universe Using Neutrinos. A Search for Point Sources in the Southern Hemisphere Using the IceCube Neutrino Observatory. Uppsala Dissertations from the Faculty of Science and Technology 117. 254 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9405-6.

Neutrinos are the ideal cosmic messengers, and can be used to explore the most powerful accelerators in the Universe, in particular the mechanisms for producing and accelerating cosmic rays to incredible energies. By studying clustering of neutrino candidate events in the IceCube detector we can discover sites of hadronic acceleration. We present results on searches for point- like sources of astrophysical neutrinos located in the Southern hemisphere, at energies between 100 GeV and a few TeV. The data were collected during the first year of the completed 86- string detector, corresponding to a detector livetime of 329 days. The event selection focuses on identifying events starting inside the instrumented volume, utilizing several advanced veto techniques, successfully reducing the large background of atmospheric muons. An unbinned maximum likelihood method is used to search for clustering of neutrino-like events. We perform a search in the full Southern hemisphere and a dedicated search using a catalog of 96 pre- defined known gamma-ray emitting sources seen in ground-based telescopes. No evidence of neutrino emission from point-like sources is found. The hottest spot is located at R.A. 305.2° and Dec. -8.5°, with a post-trial p-value of 88.1%. The most significant source in the a priori list is QSO 2022-077 with a post-trial p-value of 14.8%. In the absence of evidence for a signal, we calculate upper limits on the flux of muon-neutrinos for a range of spectra. For an unbroken E-2 neutrino spectrum, the observed limits are between 2.8 and 9.4×10-10 TeV cm-2 s-1, while for an E-2 neutrino spectrum with an exponential cut-off at 10 TeV, the observed limits are between 0.6 and 3.6×10-9 TeV cm-2 s-1.

Keywords: astroparticle physics, neutrino sources, neutrino telescopes, IceCube

Rickard Ström, Department of Physics and Astronomy, High Energy Physics, Box 516, Uppsala University, SE-751 20 Uppsala, Sweden.

ISSN 1104-2516 ISBN 978-91-554-9405-6 urn:nbn:se:uu:diva-265522 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-265522) “The probability of success is difﬁcult to estimate but if we never search the chance of success is zero.”

Cocconi and Morrison [1]

Table of Contents

Page

Acknowledgments ...... 9

About this Thesis ...... 13

Abbreviations and Acronyms ...... 17

1 Introduction ...... 23 1.1 Physics Motivation ...... 24 1.2 The Multi-Messenger Approach ...... 26

2 The Standard Model ...... 29 2.1 Matter Particles and Force Carriers ...... 30 2.2 Interaction Strengths ...... 32 2.3 Symmetries ...... 33 2.4 The Weak Interaction ...... 35 2.5 The Higgs Mechanism ...... 37 2.6 Fermion masses ...... 38 2.7 The Parameters of the Standard Model ...... 39 2.8 Beyond the Standard Model ...... 40

3 The Cosmic Ray Puzzle ...... 47 3.1 Energy Spectrum ...... 50 3.2 The Origin of High-Energy Cosmic Rays ...... 53 3.3 Astrophysical Neutrinos ...... 55 3.4 Atmospheric Backgrounds ...... 60 3.5 Acceleration Mechanisms ...... 63 3.6 Potential Acceleration Sites ...... 67

4 Neutrino Detection Principles ...... 75 4.1 Neutrino Cross-Section ...... 76 4.2 Cherenkov Radiation ...... 78 4.3 Energy Loss Mechanisms ...... 80 4.4 Event Topologies ...... 82

5 The IceCube Neutrino Observatory ...... 85 5.1 The IceCube In-Ice Detector ...... 88 5.2 Optical Properties of the Ice at the South Pole ...... 90 5.3 The Digital Optical Module ...... 93 5.4 Data Acquisition System and Triggering ...... 96 5.5 Processing and Filtering ...... 97

6 Event Simulation ...... 99 6.1 The IceCube Simulation Chain ...... 99 6.2 Neutrino Event Weighting ...... 104

7 Reconstruction Techniques ...... 107 7.1 Noise Cleaning ...... 107 7.2 Particle Direction ...... 108 7.3 Angular Uncertainty ...... 118 7.4 Interaction Vertex ...... 121 7.5 Energy ...... 124

8 Opening Up a Neutrino Window to the Southern Hemisphere ...... 129 8.1 The FSS Filter ...... 132

9 Point Source Analysis Methods ...... 139 9.1 Hypothesis Testing ...... 139 9.2 Likelihood and Test Statistic ...... 141 10 A Search for Low-Energy Starting Events from the Southern Hemisphere ...... 147 10.1 Analysis Strategy ...... 149 10.2 Experimental Data ...... 151 10.3 Simulated Data ...... 154 10.4 Event Selection ...... 154 10.5 Event Selection Summary ...... 189 10.6 Likelihood Analysis ...... 192 10.7 Results ...... 201 10.8 Systematic Uncertainties ...... 209

11 Summary and Outlook ...... 213

Summary in Swedish ...... 217

Appendix A: BDT Input Variables ...... 223

Appendix B: Result Tables ...... 227

References ...... 235 Acknowledgements

During my time as a graduate student at Uppsala University I have had the privilege to work with many dedicated, helpful and experienced scientists. We’ve organized meetings and workshops, had lengthy discussions on peculiar features of fundamental physics, and had a lot of fun during lunches and fika breaks, discussing everything from foreign and domestic politics to candy wrapping and mushroom picking. I’ve enjoyed the company of each one of you, thank you for this great time. Some of you deserve a special mention. First of all I would like to thank my supervisors Allan Hallgren and Olga Botner. Few graduate students have had the privilege to work close to two such excellent and curious physicists, always available to answer questions no matter the scope. Allan was the main supervisor of my thesis and introduced me to the physics potential of the Southern hemisphere at energies below 100 TeV. Together we developed a new data stream for collecting such low-energy events. After the discovery in 2013 of the first ever high-energy astrophysical neutrinos, the interest in this channel has grown dramatically. Allan has a never-ending stream of ideas and taught me how to be daring and bold in my creativity. He also emphasized the need to stay critical to accepted knowledge. How he can successfully calculate and compare areas of histograms with differences as small as 1% solely by judging the shape of lines on a plot located 3 meters away, I will never know. That remains a true mystery to me. Olga helped me organize my work and to prioritize. Olga has the rare gift of making people think in new ways by simply listening and asking the right questions. We’ve had countless discussions about everything from V-A couplings, the Higgs mechanism, and the nature of astrophysical objects. Thank you for taking time to discuss these things with me over the years, although buried in the work that comes by being the spokesperson of IceCube and a member of the Nobel committee. I’d like to extend my thanks also to my co-supervisor Chad Finley. Thank you for taking an interest in my analysis and for all the discussions we’ve had about OneWeight, likelihood algorithms, and hypothesis testing. I would also like to thank Carlos Perez de los Heros. We’ve discussed many topics, ranging from dark matter to statistical methods and art. Whenever you knocked on my door, I knew I was going to learn something new and unexpected. Henric Taavola, we’ve had as fun as I think two people can have. I want to thank you for five fantastic years, and especially that you put up with me singing, dancing, talking politics and doing white-board science in a more than often weird mix and high pace. I will forever remember those days we

9 pretended it was Christmas although June, the days we walked to the gas station to buy falafel because we both forgot to bring lunch, the days we took a walk in the beautiful forest nearby, and the ‘glee’ days where we limited all communication to be done through musical numbers only. All of those days have a special place in my heart and so do you! I would like to send a big thanks the people in the IceCube groups in Up- psala and Stockholm, past and present: Olga, Allan, Carlos, Sebastian, Hen- ric, Lisa, Alexander, Christoph, Leif, Olle, David B., Jonathan M., Chad , Christian, Klas, Jon, Samuel, Martin, Marcel, Matthias, Maryon, and the late Per-Olof. Thank you all for being encouraging and helpful. Per-Olof was an inspiration to all scientists and will continue to be so. I remember him as a very determined and intelligent man with a huge pathos and an open heart. He recommended me for the service work I did on the South Pole and Olga and Allan kindly approved. That was an amazing trip and an absolute highlight of my time as a graduate student. Thank you John, Steve, Larissa, Ben R., Felipe, Blaise, Jonathan D., and Hagar for making this trip unforgettable. I also extend my thanks to everyone in the IceCube Collaboration, in particular to those whom I have worked with. A special thanks goes to Antonia, Zig, Carlos, Kim, Megan, and Olivia. Thank you for making me feel like home in Madison. Thanks also: Kai, Volker, Donglian, Mårten, Mike R., David A., Martin B., Matt, Elisa R., Naoko, Stefan, Jake F. , Jake D., John F., Robert, Claudio, Jason, Mike L., Jan B., Jan K., Ryan, Frank, Jim, Laurel, Sandy, Anna P., Anna B., Sarah, Tania, James, Elisa P., Katherine, Joakim, Michael S., Jakob, Klaus, Ben W., Kurt, Moriah, Gwen, Geraldina, Martin C., and Nancy. You are all great people, and I hope I will have the change to work with all of you again someday. Stefan Leupold, you’re an excellent teacher that takes all questions seri- ously and makes the students feel smart. We have had so many interesting discussions, especially about the theoretical aspects of the Standard Model. Thank you Inger and Annica for providing an escape from physics at times needed and for always being helpful. I would like to thank my mother Maria, you are extraordinary in so many ways that I can’t even begin to describe. You are supportive and believe I can do and achieve anything. Thank you also to my sister Linda, to Bazire, my father Roland, and my late grandparents Evert and Edit. I know you are all very proud of me and I can honestly say that I would not have been able to do this without your support. A big thanks to all my friends: Katarina, Laura, Daniel, Sanna, Mikael, Noel, Anna-Karin, Andreas, Jessica, Maja, Lena, Li, Jim, Tove, Filip, and Anette. A special thanks to Katarina with whom I started the science podcast Professor Magenta. You are exceptionally smart and fun to hang around, and you bring out the best of me. I’m looking forward to much more of all of that in future episodes of both the podcast and my life.

10 My biggest thanks goes to Tony. Thank you for being amazing, for cooking, cleaning, and arranging my life outside of physics. Your encouragement and support means a lot. You are smart and brilliant and I have become a better person because of you. Thank you also to the Lennanders foundation for awarding me one of your scholarships enabling me to finish this project, and to all of you who helped me finish this thesis by providing constructive comments and suggestions on how to improve the text: Olga, Allan, Sebastian, David, Stefan, and Henric. The IceCube Collaboration acknowledge the support from the following agencies: U.S. National Science Foundation Office of Polar Programs, U.S. National Science Foundation Physics Division, University of Wisconsin Al- umni Research Foundation, the Grid Laboratory Of Wisconsin (GLOW) grid infrastructure at the University of Wisconsin - Madison, the Open Science Grid (OSG) grid infrastructure; U.S. Department of Energy, and National Energy Research Scientific Computing Center, the Louisiana Optical Net- work Initiative (LONI) grid computing resources; Natural Sciences and Engi- neering Research Council of Canada, WestGrid and Compute/Calcul Canada; Swedish Research Council, Swedish Polar Research Secretariat, Swedish Na- tional Infrastructure for Computing (SNIC), and Knut and Alice Wallenberg Foundation, Sweden; German Ministry for Education and Research (BMBF), Deutsche Forschungsgemeinschaft (DFG), Helmholtz Alliance for Astropar- ticle Physics (HAP), Research Department of Plasmas with Complex Interac- tions (Bochum), Germany; Fund for Scientific Research (FNRS-FWO), FWO Odysseus programme, Flanders Institute to encourage scientific and techno- logical research in industry (IWT), Belgian Federal Science Policy Office (Belspo); University of Oxford, United Kingdom; Marsden Fund, New Ze- aland; Australian Research Council; Japan Society for Promotion of Science (JSPS); the Swiss National Science Foundation (SNSF), Switzerland; National Research Foundation of Korea (NRF); Danish National Research Foundation, Denmark (DNRF).

Rickard Ström, Uppsala, November 2015

About this Thesis

In this thesis we present an analysis using data from the IceCube Neutrino Observatory to study the neutrino flux from the Southern hemisphere at energies between 100 GeV and a few TeV. In particular, we search for neutrino point sources as indicators for sites of hadronic acceleration where some of the most energetic particles in the Universe are thought to be produced and/or accelerated. The thesis is divided into the following chapters: Chapter 1 is an introduction to high-energy neutrino astrophysics. It also serves as the physics motivation for the analysis. In chapter 2 we discuss the current framework of particle physics, the Standard Model. We focus on the properties of the weak interaction, the only known force (except gravity) that interacts with neutrinos. In chapter 3 we introduce the so-called cosmic ray puzzle and discuss neutrino production in astrophysical sources as well as in the Earth’s atmosphere. Chapter 4 deals with the interaction and energy loss of neutrinos and also introduces the detection principle and the different event topologies seen in IceCube. The IceCube detector, including its optical sensors and data acquisition system is discussed in chapter 5. In chapter 6 we describe the event simulations used to produce the signal and background samples that we use in the analysis. In chapter 7 we go through the noise cleaning algorithms applied to data and all reconstruction techniques used to characterize each observed event in terms of e.g. direction and energy. Chapter 8 defines the online filter used at the South Pole to select the neutrino candidate events that constitute the foundation of the analysis presented in chapter 10. The likelihood analysis method is introduced in chapter 9 and conclusions and discussions of the results are presented in chapter 11.

The Author’s Contribution Inspired by my work as a Master student in the Fermi collaboration, I started off by searching for dark matter from the Galactic center region, but later switched to a search for point sources in the whole Southern hemisphere. These searches both focus on lower energies, where traditional IceCube methods cannot be applied, in particular the southern sky. I developed a new data stream by constructing the so-called Full Sky Starting (FSS) filter described in detail in chapter 8. A lot of time was spent on tests and verification of this filter.

13 The IceCube crew at the Amundsen-Scott South Pole Station during my stay. From left: Felipe Pedreros, Ben Riedel, Rickard Ström, Jonathan Davies, Steve Barnet, Hagar Landsman, John Kelley, Blaise Kuo Tiong, and Larissa Paul.

I have participated in ten IceCube collaboration meetings, including one in Uppsala where I also was a part of the organizing committee. Further, I have had the privilege to participate in several summer and winter schools discussing neutrino theory, phenomenology and experiments as well as dark matter and high-energy physics in general. I also attended the Astroparticle Physics Conference (ICRC) in 2015, where I presented the results of my analysis. The proceedings are pending publication in Proceedings of Science and are attached in the end of this thesis. Other work, not included in this thesis, where I have contributed during my time as a graduate student include: • IceCube service work. I travelled to the South Pole, Antarctica, in Jan- uary 2013 for three weeks of service work on the in-ice detector. I worked together with John Kelley to recover DOMs disconnected due to various problems, such as communication errors, unstable rates, etc. This was not only an opportunity to work hands-on with the detector system at the IceCube Lab but also to get an amazing insight in the detector and the IceCube project as a whole.

14 • IceCube monitoring. In 2013 I did two weeks of monitoring of the IceCube detector, and was later asked to develop educational material for coming monitoring shifters as well as to educate them. • Teaching assistant. During my time as a graduate student I have been a teaching assistant on several courses including: particle physics, nuclear physics, and quantum mechanics. Further I have taken a course in ped- agogic training for academic teachers and worked together with several other teaching assistants to improve the laboratory exercises in nuclear physics. • Outreach activities. I participated in several outreach activities and built a permanent exhibition of IceCube at Ångströmlaboratoriet at Uppsala University together with my colleague Henric Taavola. It contains an event display and monitors showing pictures and a documentary of the construction of the detector. • I participated in ‘Gran Sasso Summer Institute 2014 - Hands-On Exper- imental Underground Physics at LNGS’ (Laboratori Nazionali del Gran Sasso), near the town of L’Aquila, Italy, where I performed PMT investigations in the Borexino test facility, together with Osamu Takachio and Oleg Smirnov. The goal was to characterize a large PMT that might be used in several future neutrino experiments. The results were published in Proceedings of Science with identiﬁcation number PoS(GSSI14)016.

Units and Conventions Throughout this thesis we will use eV (electronvolt) as the standard unit of energy, corresponding to about 1.602 · 10−19 J. It is deﬁned as the energy gained by an electron traversing an electrostatic potential difference of 1 V. Through- out the thesis we also use natural units, i.e., = c = kB = 1, where = h/2π, h is Planck’s constant, c is the speed of light in vacuum, and kB is the Boltzmann constant. This means that we can express particle masses in the same units as energy through the relation E = mc2 = m. Effectively this can be thought of as expressing the masses in units of eV/c2. Throughout this thesis we will use GeV = 109 eV, TeV = 1012 eV, PeV = 1015 eV, and EeV = 1018 eV. When discussing astrophysical objects we sometimes use the erg unit (1 TeV = 1.6 erg).

Cover Illustration The illustration on the cover of this thesis shows the evolution of the Universe from a dense plasma to the structures we see today, such as galaxies, stars, and planets. Credit: European Space Agency (ESA).

15 The author standing on the roof of the IceCube Lab (literally on top of the IceCube detector) at the South Pole, Antarctica. Visible in the background to the left: the 10 m South Pole Telescope (SPT) and the BICEP (Background Imaging of Cosmic Extra- galactic Polarization) telescope. To the right, The Martin A. Pomerantz Observatory (MAPO).

16 Abbreviations and Acronyms

AGILE Astro-rivelatore Gamma a Immagini Leggero AGN Active Galactic Nuclei AHA Additionally Heterogeneous Absorption AMANDA The Antarctic Muon And Neutrino Detector Array AMS Alpha Magnetic Spectrometer ANITA Antarctic Impulse Transient Antenna ANTARES Astronomy with a Neutrino Telescope and Abyss environmental Research project ARA Askaryan Radio Array ARIANNA The Antarctic Ross Ice Shelf Antenna Neutrino Array ASCA The Advanced Satellite for Cosmology and As- trophysics ATLAS A Toroidal LHC ApparatuS ATWD Analog Transient Waveform Digitizer

Baikal-GVD Baikal Gigaton Volume Detector BDT Boosted Decision Tree BDUNT The Baikal Deep Underwater Neutrino Tele- scope

CC Charged Current CERN The European Organization for Nuclear Research (French: Organisation européenne pour la recherche nucléaire) Chandra The Chandra X-ray Observatory CKM The Cabibbo-Kobayashi-Maskawa Matrix C.L. Conﬁdence Level CMB Cosmic Microwave Background CMS The Compact Muon Solenoid COG Center of Gravity CORSIKA COsmic Ray SImulations for KAscade

17 CP Charge Conjugation and Parity Violation CPU Central Processing Unit CR Cosmic Ray CRT Classic RT-Cleaning CTEQ5 The Coordinated Theoretical Experimental Project on QCD

DAQ Data Acquisition System DIS Deep Inelastic Scattering DOM Digital Optical Module DOR DOM Readout DSA Diffusive Shock Acceleration

ESA European Space Agency

fADC fast Analog-to-Digital Converter FSRQ Flat-Spectrum Radio Quasar FSS Full Sky Starting

GC Galactic Center GENIE Generates Events for Neutrino Interaction Ex- periments GPS Global Positioning System GPU Graphical Processing Unit GRB Gamma-Ray Burst GUT Grand Uniﬁed Theories GZK Greisen-Zatsepin-Kuzmin

HESE High-Energy Starting Events HESS High Energy Stereoscopic System HLC Hard Local Coincidence HST The Hubble Space Telescope HV High Voltage

18 IC Inverse Compton IceCube The IceCube Neutrino Observatory ICL IceCube Lab IR Infrared ISM The Interstellar Medium ISS International Space Station

Kamiokande Kamioka Nucleon Decay Experiment KM3NeT Cubic Kilometer Neutrino Telescope KS Kolmogorov-Smirnov

LED Light Emitting Diode LEP The Large Electron-Positron Collider LESE Low-Energy Starting Events LHC The Large Hadron Collider LMC Large Magellanic Cloud

MAGIC Major Atmospheric Gamma Imaging Cheren- kov Telescopes MC Monte Carlo MESE Medium-Energy Starting Events MPE Multi PhotoElectron Mu2e The Muon-to-Electron experiment

NC Neutral Current NH Northern Hemisphere NuGen Neutrino-Generator

PAMELA Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics PAO The Pierre Auger Observatory PDF Probability Density Function

19 p.e. photoelectron PINGU The Precision IceCube Next Generation Up- grade PMNS The Pontecorvo-Maki-Nakagawa-Sakata Ma- trix PMT Photo Multiplier Tube PPC Photon Propagation Code PREM Preliminary Reference Earth Model PROPOSAL PRopagator with Optimal Precision and Opti- mized Speed for All Leptons PTP Punch Through Point PWN Pulsar Wind Nebula

QCD Quantum Chromodynamics QED Quantum Electrodynamics QFT Quantum Field Theory

R.A. Right Ascension RMS Root Mean Square

SED Spectral Energy Distribution SH Southern Hemisphere SLC Soft Local Coincidence SM The Standard Model SMT Simple Majority Trigger SNO The Sudbury Neutrino Observatory SNR Supernova Remnant SPATS South Pole Acoustic Test Setup SPE Single PhotoElectron SPICE South Pole ICE SRT Seeded RT-Cleaning SSC Self-Synchrotron Compton STeVE Starting TeV Events

20 SuperDST Super Data Storage and Transmission Super-K Super-Kamiokande SUSY SUperSYmmetry

TWC Time Window Cleaning

UHE Ultra High-Energy UV Ultra-violet

VERITAS Very Energetic Radiation Imaging Telescope Array System VLA The Very Large Array VLT The European Southern Observatory’s Very Large Telescope

WB Waxman-Bahcall WIMP Weakly Interacting Massive Particle

1. Introduction

“Somewhere, something incredible is waiting to be known.” Carl Sagan

Intergalactic Magnetic Field

Neutrino N

Photon

W E Proton

S Heavy Nucleus

Figure 1.1. Illustration showing the properties of different astrophysical messenger particles. Starting from the top: Neutrinos (blue) only interact with the weak force and are hence the ideal cosmic messenger, photons (yellow) may scatter or become absorbed on their way to Earth, charged particles (green, red) are affected by magnetic ﬁeld and do not necessarily point back to their source. Credit: Jamie Yang/WIPAC.

Astroparticle physics denotes the scientiﬁc study of elementary particles and their interactions, in the context of our Universe. It is a branch of particle physics dealing with cosmic messengers such as neutrinos, cosmic-rays, and high-energy photons, in many cases produced and accelerated in the most violent and extreme environments of the Universe. Historically astroparticle physics sprung out of optical astronomy and the curiosity to understand and reﬂect upon the Universe we live in: a gigantic laboratory for astrophysical environments and high-energy physics, that go beyond what we can produce and measure on Earth. Some of the fundamental questions addressed are: Which are the fundamental building blocks in the Universe and what are their properties? Can the elementary particles and their interactions explain the structures seen in the Universe? What is the origin of cosmic rays? What are the mechanisms behind the acceleration of particles to extremely high energies?

23 In this introductory chapter we will present the physics motivation for this thesis, introduce its main actors - the neutrinos - and discuss their unique role in the exploration of the high-energy Universe. Further we will brieﬂy mention the efforts to connect different kinds of observations of the same astrophysical objects into one uniﬁed description, known as the multi-messenger approach.

1.1 Physics Motivation The first humans studied the Universe with their own eyes looking for an- swers in the optical light emitted by stars and galaxies. In fact almost everything we know today about the Universe is the result of an exploration of the electromagnetic spectra at different wavelengths. As the techniques and methods grew more sophisticated we were able to study the Universe as seen in radio, infrared, X-ray and eventually γ-ray radiation, the latter consisting of extremely energetic particles. Since photons are massless and electrically neutral they are unaffected by the magnetic fields in the Universe and travel in straight lines, in space-time, from the point where they escape their production site to Earth where they can be observed. Indeed they are excellent messenger particles, carrying information about the physics and constituents of other parts of the Universe. However, they may be absorbed in dense environments on the way or at the production site itself, scattered in dust clouds, and captured by ambient radiation and matter in the interstellar medium (ISM). Astronomy is also possible with charged particles, so-called cosmic rays, but their directions are randomized by interstellar and intergalactic magnetic fields for all but the highest energies. Figure 1.2 shows the energy of particles as a function of the observable distance. The blue shaded region illustrates the parameter space where photons are absorbed through interactions with the Cosmic Microwave Background (CMB) and Infrared (IR) background radiation. The red shaded area shows the region where high-energy protons are absorbed by interactions with the CMB. Low-energy protons do not point back to their source, due to magnetic deflection. Further, the upper (lower) horizontal dashed black line indicate the energy of the highest proton (photon) ever observed. The mean free path of photons decreases quickly with increasing energy and above 1 PeV (1015 eV) it is shorter than the typical distances of our own galaxy. The colored bars in the bottom part indicate the position of the Galactic plane, the local galaxy group, some of the closest Active Galactic Nucleis (AGNs), etc. The idea of using neutrinos as cosmic messengers has been around since the late 1930s. They are electrically neutral and about one million times lighter than the electron [2]. Further they only interact with the weak nuclear force and gravitationally. Indeed neutrinos are the perfect astrophysical messenger with the only drawback that the low cross-section also makes them very diffi-

24 Figure 1.2. Particle energy as a function of the observable distance. The blue (red) shaded region illustrates the parameter space where photons (protons) are absorbed by interaction with the CMB and IR background radiation. The upper (lower) horizontal dashed black line indicate the energy of the highest photon (proton) ever observed. Credit: P. Gorham, 1st International Workshop on the Saltdome Shower Array (SalSA), SLAC, (2005). cult to detect. In fact, it turns out that one needs detectors of cubic-kilometer size to see even a handful of astrophysical neutrinos per year. Further, the presence of a large atmospheric background requires neutrino detectors to be built underground. The ﬁrst discovery of astrophysical neutrinos was made in the early 1970s, when Ray Davis and collaborators observed neutrinos coming from the Sun using a detector at the Homestake Gold Mine in South Dakota. Davis was awarded the Nobel Prize in 2002 together with Masatoshi Koshiba who led the design and construction of the Kamiokande (Kamioka Nucleon Decay Ex- periment), a water imaging Cherenkov detector in Japan which later showed that the neutrinos actually pointed to the Sun and was further one of the detectors that observed neutrinos from supernova SN1987A in the Large Magel- lanic Cloud (LMC) in early 1987. These were the ﬁrst neutrinos ever observed from outside the Solar system. Since then, many new experiments have been built and observations show an ever increasing number of peculiar facts about the neutrinos. Most notably they seem to have tiny masses giving rise to so-called neutrino oscillations,

25 responsible for their chameleonic nature: they transform from one type into another as they propagate through space. These observations successfully explained one of the longest standing problems of neutrino astrophysics, namely the presence of a large deﬁcit in the number of observed electron-neutrinos from the Sun, see section 2.8.2. One of the next big breakthroughs in neutrino astrophysics was made in 2013 with the discovery of a diffuse ﬂux of high-energy neutrinos of astrophysical origin by The IceCube Neutrino Observatory (hereafter IceCube) [3]. Localized sources of high-energy neutrinos have not yet been seen outside of our solar system and remain one of the most wished-for discoveries. In particular since neutrinos are indicators for sites of hadronic acceleration where some of the most energetic particles in the Universe are thought to be produced and accelerated.

1.2 The Multi-Messenger Approach With more pieces of the great cosmic puzzle we can build a greater picture. This is the essence of what is called the multi-messenger approach in astronomy: combining observations with different messengers and at various energies to reach a deeper understanding of an event or process in the Universe. In practice this means that traditional observations of electromagnetic radiation are combined with observations of high-energy γ-rays and neutrinos to provide complementary information. In the future gravitational waves may play an equally important role. A stunning example of what can be learned is shown in ﬁgure 1.3 where we present multi-wavelength images of the nearby galaxy Centaurus A, reveal- ing enormous jets of relativistic particles perpendicular to the accretion disc. Localized objects of neutrino emission may reveal other mind-boggling facts about the most energetic sources in the Universe. Further, neutrino ﬂux predictions build upon the close association between the production and acceleration of cosmic rays and the non-thermal photon emission from astrophysical sources. This close connection is covered in more depth in chapter 3.

26 Figure 1.3. Multi-wavelength images of the nearby galaxy Centaurus A. Top right: X- ray data from Chandra. Mid right: Radio data from VLA. Bottom right: Optical data from the ESO’s Wide-Field Imager (WFI) camera at the ESO/MPG 2.2-m telescope on La Silla, Chile. Left: Combined X-ray, radio, and optical data. Credit: X-ray: NASA/CXC/CfA/R.Kraft et al; Radio: NSF/VLA/Univ.Hertfordshire/M.Hardcastle; Optical: ESO/WFI/M.Rejkuba et al.

2. The Standard Model

“Young man, if I could remember the names of these particles, I would have been a botanist.” Enrico Fermi

The visible Universe consists of mainly three elementary particles; the electron, the up-quark and the down-quark. The two latter are the building blocks of the atomic nuclei forming the more familiar proton and neutron, while the electron orbits the nucleus and gives rise to electricity and complex atomic and molecular bonds. These particles are the fundamental constituents of proteins, cells, and humans, but also astrophysical objects such as stars, planets and the vast ISM. When combined with the electromagnetic force we end up with a set of tools that can explain most of the physics of everyday life. But it was realized already in the early 1930s, after careful studies of cosmic-rays (see chapter 3) that more particles and forces were needed to explain the large variety of radiation and phenomena observed [2]. The first major step towards creating a unified standard model in particle physics was taken in the 1960s by Glashow, Weinberg, and Salam [4]. They managed to combine the electromagnetic interaction, Quantum Electrodynam- ics (QED), with the weak interaction, creating a unified electroweak theory in the same spirit as Maxwell in the 1860s, who formulated the theory of the electromagnetic field encompassing the previously separate field theories: electricity and magnetism. The modern Standard Model (SM) of particle physics is a collection of quantum field theories that gives us a unique insight into the structure of matter in terms of a plethora of 301 elementary particles and the interactions among them. Elementary particles are particles thought to be definitive constituents of matter: the smallest building blocks of nature. The SM describes the electroweak force and the strong nuclear force (a.k.a. the strong force), the latter in the theory of Quantum Chromodynamics (QCD). Further the SM provides tools to calculate and predict interactions of combinations of elementary particles, e.g., observed in the incredibly rich zoo of bound quark states, so-called hadrons.

1This number is derived by counting the particles shown in ﬁgure 2.1: 12 fermions, 12 anti- fermions, and 6 bosons (the hypothetical graviton not included).

29 Figure 2.1. The Standard Model of elementary particles. Credit: CERN.

The SM is by far the most accurate theory ever constructed [4] and its crowning achievement was made only years ago in 2012 when the ATLAS (A Toroidal LHC ApparatuS) and CMS (The Compact Muon Solenoid) Col- laborations together announced the discovery of the Higgs particle in data from proton-proton collisions at the Large Hadron Collider (LHC) complex at CERN [5, 6]. In the following sections we will present the constituent particles and ﬁelds of the SM. We will discuss the importance of symmetries in the underlying theories and further explore the weak interaction that is essential in the description of the interactions and phenomena of neutrinos. We conclude the chapter by discussing theories that go beyond the SM.

2.1 Matter Particles and Force Carriers The SM is presented schematically in ﬁgure 2.1 where each square represent the observed particle. Each particle is associated with a set of quantum numbers such as e.g. electric charge, mass2, and spin. These determine the way the

2 Strictly speaking, neutrinos (νe, νμ, and ντ) are not mass eigenstates [4].

30 particles interact and propagate through space. For a thorough introduction to the particles and interactions in the SM see e.g. [4]. The 3 columns on the left hand side of the figure consist of families (also known as generations) of half-integer spin particles called fermions. These are often thought of as the particles that constitute matter. The particles in the first column (u, d, e, and νe) are stable on large time scales, while the 2nd and 3rd column contain particles seen almost exclusively at accelerators or in particle showers resulting from cosmic ray interactions in the Earth’s atmosphere. The three generations are literally copies of the first generation, with the only observable difference being higher mass for the rare particles. The two top rows show the six quarks that all have fractional charges. These are not observed as free particles in nature but rather in bound states of either three quarks, so-called baryons, or a pair consisting of a quark and an anti-quark, so- called meson3. This is a manifestation of a phenomenon called confinement which is a part of QCD. The two bottom rows show the six leptons: three charged leptons (e−, μ−, and τ−) each with a corresponding neutral particle, the neutrino (νe, νμ, and ντ). As indicated in the figure, the fermions also have corresponding antiparticles4. The right hand side of the figure shows integer spin particles called bosons. In the SM a fundamental force is the result of continuous exchange of such force mediating particles. The large rectangles indicate to what extent the forces act upon the fermions. Starting from bottom we have the weak force ± 0 mediators W and Z . These couple to particles with weak iso-spin IW and weak hypercharge Y. In particular, they couple to all fermions and constitute the only SM coupling to neutrinos resulting in their unique role in astroparticle physics. The charged part of the weak force mediated by W± is responsible for radioactive decays of subatomic particles. The γ (photon) is the mediator of the electromagnetic force and couples to all charged particles (incl. W±), while the eight (8) massless color-state gluons (g) only interact with the quarks (and themselves) to give rise to the strong force responsible for the attractive bonds in hadrons and nuclei. As with the quarks, gluons have never been observed free in nature, but hypothetical gluon-only states called glue-balls could exist and might have been observed [8]. The distinction between fermions as the constituents of matter on one side and bosons as force mediating particles on the other, is somewhat simplified. E.g. the valence quarks alone cannot account for the mass or spin in composite particles such as protons. To determine the properties of such bound hadronic states we need to consider the impact of both the quark- and gluon-sea. John Wheeler, a famous theoretical physicist known for his large contributions to the field of general relativity and also for coining the term ’wormhole’

3Indications for the existence of more exotic conﬁgurations have been suggested lately, see [7] for a recent review on the topic. 4Neutrinos might actually be their own antiparticles, but this remains to be seen in experiment.

31 60 U(1) 50

40 SU(2) -1 α 30

10 SU(3)

0 2 4 6 8 10 12 14 16 18 Log10(Q/GeV)

Figure 2.2. The inverse of the gauge couplings as function of energy for the three interactions in the SM (dashed lines) and including SUSY (solid lines), extrapolated to the GUT scale. The two SUSY lines represent different values for the energy scale of the SUSY particles (500 GeV and 1.5 TeV). Figure taken from [9].

(theoretical shortcuts in four-dimensional space-time), once said “Mass tells space-time how to curve, and space-time tells mass how to move”. The interplay between fermions and bosons is very much the same: just like yin and yang, two opposite and contrary forces that work together to complete a wholeness.

2.2 Interaction Strengths The coupling strength between fermions and bosons is determined by dimen- sionless gauge couplings α, so that the probability of an interaction includes a factor α for each interaction vertex. Effectively these couplings are energy dependent, see ﬁgure 2.2 where the inverse gauge couplings (‘strengths’) are shown as function of energy for the three interactions in the SM (dashed lines) and including supersymmetry (SUSY) (solid lines), see section 2.8. The energy dependence can be understood in terms of vacuum polarizations where virtual particle-antiparticle pairs with the charge(s) relevant for each force partially screen the fundamental coupling in the ﬁeld surrounding a central charge. For QED the effect gets smaller the closer we get to the central charge, i.e., the coupling grows with energy. QCD is fundamentally

32 different in that the corresponding gauge bosons, the gluons, themselves carry (color) charge. The polarization of virtual gluons instead augment the field, an effect that in the end wins over the color charge screening caused by virtual quark-antiquark pairs. QCD is therefore referred to as being asymptotically free in that the bonds become asymptotically weaker with increasing energy. A similar balancing act is observed for the weak interaction with the self- interacting W± and Z0, but is less pronounced due to the finite masses of the gauge bosons. Further the number of gauge bosons is smaller leading to an additional weakening of the effect. At energies close to the electroweak scale O(100 GeV), we obtain the following relations between the fundamental forces: α−1 α−1 α−1 ≈ , EM : W : S 128:30:9 (2.1) where all gauge couplings are sufficiently small for perturbation theory to apply. Somewhat lower in energy, at O(1 GeV), perturbation theory breaks down for QCD and we enter the non-perturbative region with bound hadronic states and the final levels of hadronization processes in which hadrons are formed out of jets of quarks and gluons as a consequence of color confinement.

2.3 Symmetries Symmetries play an essential role in modern physics and in particular in the SM. The ﬁrst to understand their signiﬁcance was Emmy Noether who in 1915 proved that continuous symmetries give rise to conserved quantities [10]. The SM is constrained by a set of local and global symmetries. These constraints are motivated by experimental evidence and observations of particles interactions. In section 2.3.2 we describe how local symmetries dynamically give rise to mass-less force carriers and the conservation of so-called good quantum numbers. But we will begin by considering a number of global symmetries in section 2.3.1. In the framework of the SM these are often thought of as accidental in contrast to the local gauge symmetries.

2.3.1 Global Symmetries One of the most important laws of conservation is that of the baryon number B. In particular because it ensures the stability of the proton by prohibiting processes like5: + p e + νe + ν¯e. (2.2) Baryons (anti-baryons) are assigned baryon number B = 1(B = −1) or equivalently quarks (anti-quarks) can be assigned B = 1/3(B = −1/3). Mesons,

5Also forbidden by lepton number conservation.

33 consisting of a quark and anti-quark pair, therefore have baryon number 0 and − − can therefore decay into the lepton sector (e.g. π → μ + ν¯μ)6. Separate quantum numbers can also be defined for the different quark flavors. These are all seen to be conserved separately for both the electromagnetic and strong interaction. We will see below that the weak interaction couples to isospin doublets with mixing between the three families of quarks and can therefore violate the individual quark flavor quantum numbers. To distinguish neutrinos from anti-neutrinos we introduce a total lepton = − number L nl nl¯, where nl(lˆ) is the number of leptons (anti-leptons). This has been observed to be conserved in all known interactions. Further we observe that separate lepton numbers for each family Le, Lμ, and Lτ are also conserved with the exception of considering the oscillations of neutrino eigenstates in the weak sector. Electromagnetic interactions that violate lepton family numbers, e.g., μ± → e± + γ, are searched for but have never been observed. The Mu2e (Muon-to-Electron) experiment at Fermilab (US) began construction in early 2015 and expects preliminary results around 2020 [11]. It will have unprecedented sensitivity for such decays and is particularly interesting since such conversions are expected at low rates in many models of physics beyond the SM, e.g., SUSY discussed briefly in section 2.8.

2.3.2 Local Gauge Symmetries It can be shown that a system described by the Lagrangian L is invariant under local phase transformations if we add terms to L that cancels the ones from the derivatives of the local phase itself. This is called the principle of local gauge invariance [12]. The additional terms introduce matter-gauge ﬁeld interactions, realized by the exchange of massless spin-1 bosons as force mediators. In particular they introduce conserved currents with associated conserved quantum numbers. E.g. the electromagnetic interaction described by the U(1)7 local gauge symmetry is mediated by the massless γ and further leads to the conservation of electric charge8, a quantum number that is non-zero for particles participating in the electromagnetic interaction. Further, the strong force mediated by eight massless gluons acts on particles with quantum numbers called color charge, a consequence of the SU(3)C[4] local gauge symmetry of the terms describing the strong interaction. The weak interaction is discussed in detail below in section 2.4. For a more complete discussion about local gauge symmetries see textbooks in particle physics and quantum ﬁeld theory, e.g., [12] and [4].

6Leptons have baryon number B = 0. 7The Unitary group U(n) with n = 1 consist of all complex numbers with absolute value 1 under multiplication (the so-called circle group) [4]. 8The conservation of charge is in fact a consequence already of global U(1) symmetry.

34 2.4 The Weak Interaction The weak force is unique in the following ways: Two of the three force carri- ≈ . ± ≈ . ers have electric charge, they are all massive (mZ0 91 2 GeV [2], mW 80 4 GeV [2]) unlike the force carriers of QED and QCD, and the interactions do not conserve parity nor charge conjugation. Further, weak interactions can be categorized into two separate processes: Charged Current (CC) interactions mediated by W± and Neutral Current (NC) interactions mediated by Z0. The latter were first identified in the Gargamelle bubble chamber experiment at CERN in 1974 [13] using a beam of muon-neutrinos produced in pion decay. The Gargamelle Collaboration observed two types of NC events: muon-neutrino scattering from a hadron without turning into a muon, as well as events characterized by a single electron track, see figure 2.3. The weak bosons themselves were discovered at the Large Electron-Positron Collider (LEP) at CERN in 1983 [14, 15, 16]. The charge current interactions violate parity (mirror symmetry) and charge conjugation maximally and only interact with left-handed particles and right- handed antiparticles9. This is condensed into a so-called “vector minus axial- vector” (V-A) theory. This chiral theory can be described by an SU(2)L [4] local gauge symmetry where right-handed particles and left-handed antiparticles have been placed in weak-isospin singlet states, i.e., with weak isospin 0:

(ψe)R,(ψμ)R,(ψτ)R and (ψu)R,(ψc)R,(ψt)R,(ψd)R,(ψs)R,(ψb)R. (2.3) Note that there are no right-handed neutrinos in the SM [4]. Left-handed particles (and right-handed antiparticles) are arranged in weak isospin doublets differing by one unit of charge: ψν ψν ψν ψ ψ ψ e , μ , τ and u , c , t . (2.4) ψ ψ ψ ψ ψ ψ e L μ L τ L d L s L b L The ﬂavor eigenstates in the quark sector differ from the corresponding mass states giving rise to so-called quark mixing, parametrized by the Cabibbo- Kobayashi-Maskawa (CKM) matrix. Mixing is also seen in the lepton sector and is described by the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix. While charged leptons are eigenstates of both ﬂavor and mass, neutrinos are not, resulting in neutrino oscillations10. The mass of the neutrinos is discussed is section 2.8.2.

9The handedness of the particles can either refer to the helicity, the projection of the spin onto the direction of momentum or as here chirality, an abstract concept related to helicity (for massless particles they are in fact the same) that describes how particle states transform under Lorentz transformations. 10We consider the weak mixing to take place between the neutrinos and not the charged leptons but this is merely a matter of deﬁnition. However, mixing among the neutrinos is the natural choice since mixing between charge leptons would be unobservable technically due to the large mass splitting.

Figure 2.3. The ﬁrst neutral current event ever detected using the Gargamelle experiment at CERN in 1973. Credit: Picture printed with permission from CERN. Particle trace by Christine Sutton (Editor, CERN Courier).

Complex phases in these matrices give rise to Charge-Parity (CP) violation effects. This has been observed in the CKM matrix and leads to weak processes that occur at different rates for particles and mirrored antiparticles. CP-violations are particularly interesting since they might be connected to the difference between the content of matter and anti-matter in the Universe. CP- violation has yet to be observed in the lepton sector and is the focus of the next generation of long-baseline neutrino oscillation experiments. 1 2 3 SU(2)L has three massless gauge bosons W , W , and W [12]. Linear combinations of the first two can be identified as the charged W-bosons (essentially corresponding to the raising and lowering operators of weak isospin) and it would be tempting to associate the third boson with the observed Z0. The problem is that W3 breaks parity maximally unlike Z0 that does couple to right-handed particles and left-handed antiparticles although with a different strength from left-handed particles and right-handed antiparticles. Hence, following the same procedure as for QED and QCD leads to a theory in tension with experimental observations. The solution came through the unification of the SU(2)L gauge theory and a modified version of the electromagnetic gauge theory, U(1)Y with a new gauge

36 field B0 and an associated weak hypercharge Y. With linear combinations of the fields W3 and B0 we can describe the observed γ and Z0 bosons, with the caveat that the Z0 should still be massless. Note that although the theory is unified it does not follow that the gauge couplings for individual components unite11, see figure 2.2. However, the theory gives relations between the masses of the massive bosons as well as for their gauge couplings. These relations are determined by a parameter, the weak mixing angle θw, experimentally measured to be 28.74◦[2].

2.5 The Higgs Mechanism Both the force carriers and the fermions subject to the weak interaction are massive which is in tension with local gauge symmetry arguments. This means either that the underlying symmetries must be broken below some very high energy not yet accessible or that the theory is wrong. Considering the former, we can introduce a scalar field, the so-called Higgs field, to the SM in a way that spontaneously breaks the underlying SU(2)L ⊗ U(1)Y symmetry of the electroweak interaction. This triggers the so-called Higgs mechanism: a beautiful way of giving mass to the boson fields W± and Z0 through their interaction with the Higgs field. In the SM spontaneous symmetry breaking can happen when a field ac- quires a non-zero vacuum expectation value. Considering a simplified case (following [12]) of a global U(1) symmetry of the Lagrangian, for a complex √1 scalar field Φ= (Φ1 + iΦ2) with the appropriate choice of potential, a so- 2 called ‘Mexican-hat’, it can be shown that we obtain an infinite set of minima along a constant radius. This is depicted in figure 2.4 where the potential is illustrated as a function of the real scalar components Φ1 and Φ2. The vacuum state is the lowest energy state of the field Φ and can be chosen in the real direction (Φ1, Φ2) = (v, 0) without loss in generality. The Lagrangian for the complex scalar field can be rewritten in terms of two new scalar fields (η and ξ) following the expansion around the minimum12. From this we can identify several interaction terms between η and ξ, but more importantly both a massive and a massless scalar field. The latter corresponds to a so-called Goldstone boson predicted by Goldstone’s theorem [17], and can be identified with excitations in the direction along the constant circle of minima. The former instead describes excitations in the radial direction corresponding to a massive gauge boson. These arguments can be promoted to hold for the local gauge symmetry U(1) by replacing the standard derivatives with appropriate covariant derivatives at the cost of introducing a new massless gauge field Bμ. The result is

11 The theory is described by the product group SU(2)L ⊗ U(1). 12In Quantum Field Theory (QFT) we deﬁne particles as excitations of the participating ﬁelds when expanded around the vacuum state.

37 again a massive scalar field η, a massless Goldstone boson ξ and additionally a mass term for Bμ. Hence, spontaneous symmetry breaking can give mass to the gauge boson of the local gauge theory. η can be eliminated from the La- grangian by making an appropriate gauge transformation and it can be shown that the η is “eaten” by the massive gauge boson to provide the longitudinal polarization, see e.g. [12]. For the full electroweak symmetry we introduce a weak isospin doublet of complex scalar fields φ = (φ+,φ0), called the Higgs field. The field φ has four real-valued components φi (i = 1,2,3,4). The Lagrangian is given by:

† μ 2 † † 2 LHiggs = (∂μφ) (∂ φ) − (μ φ φ + λ(φ φ) ) (2.5) where the second term is the Higgs potential. For μ2 < 0 it has an infinite set of degenerate minima. By construction, the Lagrangian is invariant under global transformations of both U(1)Y and SU(2)L. The two components in the doublet differ with one unit of charge just like the left-handed fermion doublets in the weak charge current interaction. Since the photon should remain massless, the minimum of the Higgs potential should be chosen to give a non-zero value in the neutral component φ0 only. The Lagrangian can be made symmetric under the full local gauge symmetry by introducing covariant derivatives i involving both Bμ and Wμ (i = 1,2,3) fields. The spontaneous symmetry breaking of the full electroweak Lagrangian re- 3 sults in the observed mixing of the Bμ and Wμ fields when considering the masses of the physical gauge bosons. Technically the breaking gives a massive scalar and three massless Goldstone bosons. The latter correspond to the longitudinal polarizations of the massive electroweak bosons W± and Z0. The massive scalar is called the Higgs boson. When such a particle was discovered at CERN in 2012, it provided an important missing piece of the electroweak puzzle13. The combination of the unified electroweak theory with the Higgs mechanism is known as the Glashow-Weinberg-Salam model.

2.6 Fermion masses Fermion masses are particularly tricky in the SM since such terms are not invariant under the electroweak gauge symmetry. The Higgs mechanism generates the masses of the massive weak bosons but can also give mass to the fermions. Couplings between the Higgs field and the fermion fields, constructed through combinations of left- and right-handed particle states, can be shown to generate gauge invariant mass terms at the strength of flavor dependent so-called Yukawa couplings proportional to the vacuum expectation value of the Higgs potential (v ∼ 246 GeV) and the fermion masses.

13Note that the actual mass of the Higgs boson was not predicted by the theory. The window of possible masses was rather narrowed down by over three decades of experimental observations.

38 V (φ)

Re(φ) Im(φ)

Figure 2.4. An illustration of the Higgs potential in a simpliﬁed model: the classic shape of a Mexican-hat.

The coupling to a fermion with mass m f can be expressed as [12]:

m f g ∝ . (2.6) f v The couplings to the massive fermions turns out to be quite different in size. E.g. the coupling to taus are in the order of O(1) while the coupling to electrons are O(10−6). Further, without right-handed neutrinos we cannot generate mass to the neutrinos through the Higgs mechanism at all and even if such particles exist, the corresponding Yukawa couplings would be 10−12. This might hint to that the neutrino masses are provided by a different mechanism. The so-called see-saw mechanism is a well-loved possibility for such, see section 2.8.2.

2.7 The Parameters of the Standard Model The expanded SM including also neutrino oscillations has 26 free parameters [12]. These are all measured by experiments and include the twelve (12) Yukawa couplings mentioned in section 2.6 or equivalently the fermion masses

(mν1 , mν2 , mν3 , me, mμ, mτ, mu, ...), the three (3) gauge couplings of the electromagnetic, weak, and strong interactions, the Higgs vacuum expectation value and Higgs mass, four (4) parameters (mixing angles, phases) for each of the CKM and PMNS matrices and ﬁnally a strong CP phase related to a ﬁne-tuning problem in the theory of the strong interaction [12]. The latter is not covered in this thesis, see e.g. [12].

39 We note that the fermion masses (except for the masses of the neutrinos) are of the same order within each family and we have already seen in ﬁgure 2.2 that the coupling strengths of the gauge ﬁelds are similar in size at the electroweak scale. Indeed there seems to be patterns among these parameters and it is tantalizing to think of them as hints of physics and symmetries beyond the SM.

2.8 Beyond the Standard Model Although incredibly successful the SM is not the end of particle physics. A growing number of phenomena cannot be explained within the current framework but requires extensions of the SM: most notably the observation of neutrino masses, the only firm evidence for physics beyond the SM. These topics are discussed below, in particular we discuss the notion of neutrino oscillations and means to give the neutrinos mass. The flavor sector of the SM is a source of several unexplained phenomena. E.g. there is no deeper explanation of why there are exactly three families of fermions and why the PMNS matrix is relatively flat compared to the close to diagonal CKM matrix. Further, the CP violation terms in these matrices are likely too small to explain the observed matter-antimatter asymmetry in the Universe.

Figure 2.5. Tip of the iceberg. Illustration of the energy budget of the Universe. Only about 5% consists of ordinary visible matter such as electrons, protons, and photons. About 25% consist of so-called dark matter and the remaining part of mysterious so- called dark energy. Credit: [18].

40 GUT attempt to unify the electroweak interaction with the strong interaction, i.e., with focus on restoring the apparently broken symmetry between colorless leptons and colored quarks [2]. The simplest GUT would be SU(5) which is the smallest Lie group that can contain all of the symmetries of the SM (U(1)Y ⊗ SU(2)L ⊗ SU(3)C) [2]. This gives rise to twelve (12) colored X-bosons with GUT scale masses, which generally cause problems with the stability of the proton, and predicts a weak angle θW in tension with observations. Note that GUTs lead to a common gauge coupling for all three (3) interactions above some high energy scale O(1016 GeV) where the symmetry is broken. This uniﬁcation of forces becomes even more accurate when the framework of SUSY is included. SUSY is an extension of the SM, building on the success of considering symmetries as a means to understand interactions and derive conservation laws. By incorporating a fundamental symmetry between fermions and bosons, it doubles the number of particles in the SM: each SM particle gets a super-particle companion differing by half a unit in spin. In particular it provides several viable dark matter particle candidates, see section 2.8.1 and references therein. Since we have not yet observed such super-particles at the same mass scale as the SM particles, this symmetry is thought to be broken at some unknown energy scale. The governing force in the Universe is gravity, but at lengths typical for particle physics and relevant at the subatomic scale, it is negligible, with a strength that is 1040 times weaker than the electromagnetic force. There is nothing a priori that says that the strengths should be different, hence this constitutes a so-called hierarchy problem. To solve this, some theories include extra-dimensions into which parts of the initially strong gravitational interaction leak. Attempts to include gravity in the SM include so-called supergravity theories where the quantum world and the general theory of relativity are combined into a single framework. The corresponding gauge particle is called the “graviton” but has never been observed. Another hierarchy problem arises in the Higgs sector where a large ﬁne- tuning is required to obtain the observed bare mass O(100 GeV). The gauge and chiral symmetries of the SM prevent the spin-1 and spin-1/2 particles from getting mass (except for the dynamical creation described in section 2.5) but there is nothing that protects the spin-0 Higgs particle. Since SUSY connects a scalar to a fermion, it can provide such protection by introducing complementary quantum correction terms [4].

2.8.1 The Dark Sector Physics beyond the SM is also found by studying the large-scale structures of the Universe. Measurements of velocity dispersions in clusters of galaxies [19], galaxy rotational curves [20, 21, 22], weak gravitational lensing [23], and

41 Figure 2.6. “Pandora’s cluster” - A collision of at least four galaxy clusters re- vealing a plethora of complex structures and astrophysical effects.. Credit: X- ray: NASA/CXC/ITA/INAF/J.Merten et al, Lensing: NASA/STScI; NAOJ/Subaru; ESO/VLT, Optical: NASA/STScI/R.Dupke.

the CMB [24] provide experimental evidence for a dark sector that dominates the energy budget of the Universe. The CMB reveals tiny fluctuations in the temperature (energy) of photons from different arrival directions. These photons were produced at the time of recombination about 380,000 years after the Big Bang. These fluctuations contain an imprint of the large-scale structures in the early Universe that started as primordial quantum fluctuations and were then amplified during an epoch of rapid expansion known as inflation and further by gravitational forces and the expansion of the Universe. The magnitude and spatial structure of the fluctuations reflect dynamics requiring much more gravitational mass than what can be provided for by the visible Universe. In particular, they show that baryonic non-luminous matter like brown dwarfs cannot make up but a fraction of the dark matter abundance. In fact, ordinary baryonic matter only accounts for about 5% [24] of the total energy density of the Universe. 26% consists of so-called dark matter and the remaining 69% seems to correspond to some kind of dark energy [24]. The two dark components are distinct in that the former originates from the observed mismatch between luminous and gravitational matter while dark energy is introduced to explain the accelerating expansion of the Universe, i.e., dark matter clusters while dark energy does not. In the standard model of cos-

42 mology ΛCDM, dark energy is attributed to a non-zero so-called cosmological constant that emerges in the equations of general relativity. The concept of dark energy is beyond the scope of this thesis, but we’ll say a few words about dark matter since it is potentially closely related to the physics described by the SM. If dark matter consists of some kind of particles these could be a relic density of stable neutral particles that decoupled in the early hot Universe as it expanded and cooled down (for a review of these concepts see e.g. [25]). Particles that were relativistic (non-relativistic) at the time of freeze-out constitute so-called hot (cold) dark matter. Hot dark matter, e.g. SM neutrinos, cannot make up a large fraction of the dark matter content since they would have ‘free-streamed’ out of small density enhancements and suppressed them. Cold dark matter is very interesting and compatible with N-body simulations in which one simulates the large scale formation of the Universe. Particular interest has been directed towards so-called Weakly Interacting Massive Par- ticles (WIMPs). These arise in a large number of theories, such as SUSY and theories with extra curled-up dimensions. Figure 2.6 shows the so-called ‘Pandora’s Cluster’14 located about 3.5 bil- lion light years from Earth. It shows the collision of at least four galaxy clusters in a composite image consisting of X-ray data from Chandra in red tracing the gas content (gas with temperatures of millions of degrees) and gravitational lensing data from the Hubble Space Telescope (HST), the European Southern Observatory’s Very Large Telescope, and the Subaru telescope tracing the total mass concentration in blue on top of an optical image from HST and VLT. The center region shows a separation between gas and matter, where the former slows down as a result of friction in the collisions of the hot gas clouds, induced by the electromagnetic force. The main fraction of the matter only seems to interact gravitationally giving empirical proof of WIMPs.

2.8.2 Neutrino masses and oscillations The neutrinos included in the SM are massless and left-handed. Historically this agreed well with observations and the latter even holds today: only left- handed neutrinos have been observed in nature. But experiments studying neutrino oscillations have confirmed that neutrinos are indeed massive albeit with a tiny mass in the O(1 eV) [2]. Neutrino oscillations have been seen in measurements of neutrinos from the Sun, from nuclear reactors and from neutrinos produced in the atmosphere. The first indication came from a deficit in the flux of solar neutrinos compared to the Standard Solar Model and was measured in Ray Davis’ Homestake Ex- periment in the late 1960s [26]. The concept of neutrino oscillations had been

14Ofﬁcially known as Abell 2744.

43 put forward by Bruno Pontecorvo already in 1957 and was later revised by Pontecorvo, Maki, Nakagawa, and Sakata. The observations of the Super-Kamiokande (Super-K) detector in Japan and the Sudbury Neutrino Observatory (SNO) in the U.S., around the turn of the millennium, provided the first evidence for neutrino oscillations. For this discovery, Takaaki Kajita and Arthur B. McDonald, were rewarded the Nobel prize in physics 2015. Considering vacuum mixing between two flavors: the probability to measure a certain flavor νβ given να is a functions of the total particle energy E and time t. Since neutrinos are close to relativistic we can parametrize t in terms of distance travelled L. The probability is given by [27]: Δ 2 2 2 2 m [eV ]L[km] P(να → νβ) = sin (2θ)sin 1.27 , (2.7) E[GeV] Δ 2 = 2 − 2 θ where m m2 m1 and is the mixing angle. This result can be generalized to three flavors by considering the full PMNS matrix [27]. The results of oscillations with three flavors in vacuum is shown in figure 2.7 given oscillation parameters consistent with current measurements, see figure caption. The plots show the probability for a muon-neutrino to appear in any of the three neutrino flavors as a function of the ratio L/E. The upper plot show a zoom in on small values of L/E relevant for atmospheric oscillations while the lower plot show a larger range relevant for solar oscillations. The effect of neutrino oscillations is only relevant for macroscopic distances and can safely be ignored at the small distances typical for e.g. collider experiments, see equation 2.7. The oscillation probability is dramatically increased if we consider neutrino propagation in matter through the so-called MSW (Mikheyev-Smirnov-Wolfenstein) effect [27]. In particular this effect was crucial for understanding and solving the solar neutrino problem, a deficit in the number of electron-neutrinos arriving at Earth. In order to give mass to the particles through Yukawa couplings to the Higgs field we need terms with mixed Dirac fermion fields (right- and left-handed). ψ = ,μ,τ But even if we were to include right-handed neutrino fields ( νl )R (l e ) (or the corresponding left-handed antineutrino fields) in the SM the Higgs couplings would have to be extremely small to explain the small neutrino masses. These neutrinos would only interact gravitationally and are therefore referred to as ‘sterile’ neutrinos15. Sterile neutrinos can be searched for in neutrino oscillation experiments, where they would mix with the left-handed particles. That effect is particularly strong for propagation in a dense medium such as the Earth [27]. Right-handed neutrinos and left-handed antineutrinos are invariant under the SM gauge symmetries, why we can add terms to the Lagrangian formed

15Technically the term ‘sterile’ neutrino is used to distinguish any non-interacting neutrino from the ‘active’ neutrinos that participate in the SM.

44 Figure 2.7. Probability for a muon-neutrino to appear in any of the three neutrino ﬂavors as a function of the ratio L/E. The upper plot show a zoom in on small values of L/E relevant for atmospheric oscillations while the lower plot show a larger range relevant for solar oscillations. The black line illustrates the probability to observe the particle as an electron-neutrino, blue a muon-neutrino, and red a tau-neutrino. The 2 oscillation parameters used are consistent with current measurements (sin θ13 = 0.10, 2 θ = . 2 θ = . δ = Δ 2 = . · −5 2 Δ 2 ≈ Δ 2 = sin 23 0 97, sin 12 0 861, 0, m12 7 59 10 eV , and m32 m13 2.32 · 10−3 eV2). Normal hierarchy is assumed.

45 by their ﬁelds without breaking the local gauge invariance. In fact, the full neutrino mass Lagrangian can be written as a combination of Dirac (mass terms generated by the spontaneous symmetry breaking) and so-called Majo- rana mass terms. The Majorana term can in principle lead to processes with total lepton number violation that could be searched for in experiments, but since the helicity and chirality is almost identical for neutrinos such processes are suppressed [12]. Instead experiments focus on observing neutrinoless double β-decays, a process that is only possible for so-called Majorana neutrinos, neutrinos that are their own antiparticles. The Lagrangian is deﬁned as: ⎛ ⎞⎛ ⎞ 1 ⎜ 0 m ⎟⎜ νc ⎟ L = − ν νc ⎜ D ⎟⎜ L ⎟ + . . DM L R ⎝ ⎠⎝ ⎠ h c (2.8) 2 mD M νR

= 1 ± + 2 / 2 ν where the eigenvalues are m± 2 (M M 1 4mD M ) and L,R are the left- νc and right-handed neutrino states respectively and R/L is the CP conjugate of νR/L [12]. If mD would be of the same order as the lepton masses and M mD, then m− ≈ mD · (MD/M) and m+ ≈ M, i.e., m− gets suppressed by the scale of M. This way of giving the observed neutrinos light masses is called the see-saw mechanism and typically predicts extremely high masses (in GUT M ∼ 1015 GeV) for the other eigenstate, far above the reach of current experiments [12]. If Majorana mass terms exist, the mechanism predicts one massive neutrino O(M) for each light SM neutrino O(1 eV).

Summary After this review of the SM and in particular of some of the particle physics aspects of the neutrinos, we are ready to introduce neutrinos in a wider context; namely to discuss the important role of neutrinos in the determination of the origin and production of cosmic rays.

46 3. The Cosmic Ray Puzzle

“Thus it is possible to say that each one of us and all of us are truly and literally a little bit of stardust.” William A. Fowler The Quest for the Origin of the Elements, 1984

The Earth’s atmosphere is constantly bombarded by charged particles and nuclei, so-called Cosmic Rays (CRs), at the astonishing rate of 1,000 particles per square meter per second [28]. These are primarily protons and helium nuclei with a small contribution from electrons. In general these particles are relativistic but they arrive with a huge variation of kinetic energies, the most energetic ones with an energy as large as that of a brick falling from a roof. The highest energies observed so far belongs to so-called Ultra High-Energy (UHE) CR that have an energy of O(1020)eV [29]. When CRs where discovered in the early 1910s they provided the first evidence of a more exciting Universe consisting of something more than the stars and gas observed in optical telescopes. The discovery was made through a series of high-altitude balloon flights by Victor Hess (1911-12, < 5.3 km) [30] and subsequently by Werner Kolhörster (1913-14, < 9 km) [30], both measur- ing an increasing flux of ionizing particles with increasing altitude, thus ruling out the Earth itself as a source. Their discovery became one of the biggest breakthroughs in particle physics and started an era of CR experiments that would lead to the discovery of many new particles, most notably the positron (anti-electron) in 1932 [31], the muon in 1936 [32], the pion in 1947 [30], and later kaons and lambdas that were the first particles discovered that contained the strange quark [30]. The majority of the CRs, were confirmed to have positive charge which was illustrated by studies of the so-called east-west effect, the result of deflection in the geomagnetic field [33, 34, 35]. It was also realized in the late 1930s (Rossi, Auger, Bethe, Heitler) that the particles we observe at the ground are in fact so-called secondaries, produced by primary CR interactions with air nuclei causing electromagnetic and hadronic cascades, that propagate like showers in the atmosphere, see figure 3.1.

47 Figure 3.1. Artistic impression of a CR entering Earth’s atmosphere where it interacts with air nuclei to form electromagnetic and hadronic showers. Credit: CERN/Asimmetrie/Infn.

Countless experiments have been built since then and they have provided us with many new clues about the nature of CRs, in particular about their composition and propagation through the ISM. But the most important questions remain partly unanswered: the origin and the production mechanisms are still to a large extent unknown. Two important features of the CR data that can be used to learn more about their origin is their composition, i.e., the relative abundance of different nuclei, and their energy spectra. While the latter may be a characteristic of a particular acceleration mechanism, the former can be used to infer what kind of sources are involved in the acceleration process. This is done by comparing the composition models and data from different astrophysical objects [28]. Further, the identification of a localized source of CRs, either direct of indirect, may provide the most important clue, in particular if the CRs are observed in connection with known emitters of electromagnetic radiation such as X-rays, γ-rays, etc. Galactic CRs are usually modeled by the so-called leaky box model. It assumes that CRs are confined by magnetic fields within the galactic disk (∼ 10−7 G) but gradually leak out. Since the resulting gyro-radii of CRs below 1015 GeV (‘the knee’) are much smaller than the size of the Galaxy, they become trapped for times on the order of 106 years [30]. Scattering on inho- mogeneities in the magnetic fields randomizes their directions and leads to a high degree of isotropy, hence they will have no memory of their origin when reaching Earth. Since CRs above the knee cannot be contained by the galactic magnetic fields they are not trapped for long enough time to accelerate to high energies.

Figure 3.2. CR anisotropy observed by IceCube using 6 years of data. The plots are preliminary and show the relative intensity in equatorial coordinates. The median energy of the primary CR is shown in the upper left corner of each plot. Each map was smoothed using a 20◦ radius. Interestingly the deﬁcit and excess switch positions as we go above ∼ 100 TeV. The reason for this is unknown. Figure is taken from [36].

They are assumed to be extragalactic of origin or alternatively associated with strong local sources. Anisotropies in the arrival directions of CRs can be introduced either through large magnetic fields with significant deviation from an isotropic diffusion (through modified propagation models), by local sources, or by signifiant escape from the Galactic disk1. The predicted anisotropy from these effects features large regions of relative excess and deficit of number of events, with amplitudes on the order of 10−2 to 10−5 [38]. Further there are effects due to the motion of the observer relative to the CRs, e.g. due to the motion of

1At TeV energies propagation effects could give rise to large-scale anomalies [37], but it is not clear if these can also explain observations made at higher energies.

49 the Earth relative to the Sun, and potentially a so-called Compton-Getting effect [39], a dipole anisotropy due to the relative motion of the solar system with respect to the rest frame of the CRs2. However, the predicted amplitude and phase of the latter is not consistent with data from current air shower experiments [40], i.e., if the Compton-Getting effect is present in data it is overshadowed by stronger effects and may be one of several contributions to the CR anisotropy. Indeed, observations of CR arrival directions show a nearly isotropic distribution at most energies [2]. However, energy dependent anisotropies at the level of ∼ 10−3 have been observed by several experiments amongst others: IceCube [40] and Milagro [41] (for median primary CR energies of 6 TeV). Figure 3.2 show the CR anisotropy observed by IceCube using 6 years of data. The plots are preliminary and show the relative intensity in equatorial coordinates for three different median energies. Interestingly the deﬁcit and excess switch positions as we go above ∼ 100 TeV. The reason for this is still unknown. In the following sections we will focus on the observed energy spectra and the possible acceleration mechanisms and sources involved in the production of high-energy CRs. In particular we will investigate the close link between the acceleration of high-energy CRs (> 100 MeV) and the production of high- energy astrophysical neutrinos in section 3.2. For a more complete review of CR, see e.g. [28, 30, 38].

3.1 Energy Spectrum One of the most striking facts about CRs is their enormous span in energy and flux. The spectrum covers several decades in energy, from 108 to 1020 eV, and flux, from 104 to 10−27 GeV−1 m−2 s−1 sr −1. The spectrum approximately3 follows an unbroken power-law E−γ with a slope γ ≈ 2.7 above 1010 eV. Fur- ther it has several interesting features; a knee around 1015 − 1016 eV, a second knee around 1017 eV, an ankle around 1018 − 1019 eV and finally a sharp cut- off above 1020 eV. Figure 3.3 shows the flux of CRs multiplied with E2 as a function of kinetic energy. Further, on the horizontal axis, it illustrates the typical collision energy of man-made accelerators such as the LHC at CERN and Tevatron at Fermilab (Fermi National Accelerator Laboratory). Above the knee we observe roughly 1 particle per m2 per year, while above the ankle we only observe 1 particle per km2 per year. The spectral features can be seen more clearly in figure 3.4 that shows the CR flux multiplied by E2.6. This represents the differential energy spectrum as a function of reconstructed energy-per-nucleus, from direct measurements

2Note that the rest frame of the Galactic CRs is not known. 3The spectral index depends on the compilation of data, in particular the different composition models assumed [29].

50 Figure 3.3. CR particle ﬂux as a function of energy. Credit: Bakhtiyar Ruzy- bayev/University of Delaware.

below 1014 eV and from air-shower events above 1014 eV. The lowest energy CRs can be detected directly, while the flux is so low at high-energies that a direct measurement is no longer feasible and we instead study air-showers produced when CRs interact in the atmosphere. Air-showers are detected using mainly three different techniques: number density and lateral distances of charged particles on the ground are measured in air-shower arrays, Cherenkov radiation from the charged particles as they propagate in the atmosphere, is measured in air Cherenkov detectors, and fluorescence detectors study Ultra-violet (UV) light created as CRs interacts with primarily nitrogen in the atmosphere. In modern facilities these techniques are usually combined, see e.g. the Pierre Auger Observatory (PAO) [42] utilizing 1,600 surface Cherenkov detectors combined with 24 fluorescence detectors, together covering a detection area of 3,000 km2. At low energies, E < 10 GeV, the CR spectrum is largely influenced by the solar wind consisting of electrons and protons with energies in the range

51 1 < E < 10 keV [2, 29]. At even lower energies the spectrum is modulated by Earth’s geomagnetic field. Further, in the event of a solar flare, the spectrum is dominated by particles from the Sun in the range of a few tens of keV to few GeV. The low-energy CR abundance is hence largely dependent on both location and time. While CRs with energies between a few keV to a few GeV are known to be created in large amounts in the Sun, the birthplace of the high-energy CRs (a few GeV to 1020 eV) is still under debate. Indeed, the origin of CRs is a rather complex question mainly because many different processes are likely at play simultaneously throughout the full energy spectrum. One of the key questions is to figure out whether the spectral features are caused by processes happening during creation (acceleration) or propagation through the Universe. Typically we associate events to the left of the knee to the Galaxy. We will see in section 3.5 that shock acceleration in Supernova Remnants (SNRs) can explain particle energies up to PeV (∼ 1015 eV) energies. Further, events to the right of the knee are thought to show the onset of an extragalactic component. Objects such as AGNs and Gamma-Ray Bursts (GRBs) have the necessary power to provide the energy in this region.

Knee 104

Grigorov 2nd Knee ]

-1 JACEE MGU sr 3 -1 10 Tien-Shan s

-2 Tibet07 Ankle

m Akeno 1.6 CASA-MIA 102 HEGRA

[GeV Fly’s Eye Kascade

F(E) Kascade Grande 2.6 IceTop-73 E 10 HiRes 1 HiRes 2 Telescope Array Auger 1 1013 1014 1015 1016 1017 1018 1019 1020 E [eV]

Figure 3.4. CR particle ﬂux as a function of energy-per-nucleus. The data points show the all-particle ﬂux from a number of air-shower experiment. Figure from [2].

52 3.2 The Origin of High-Energy Cosmic Rays Technically CRs are divided into different categories based on their production site, but this division is not sharp and often not decisive4. We will use the following definition: primary CRs denote particles that are accelerated in astrophysical sources: protons, electrons, and nuclei such as helium, carbon, oxygen, and iron. Secondary CRs denote particles that are created through interactions of primary CRs with the gas and dust in the ISM, in the Earth’s atmosphere or in regions close to the accelerators themselves, so-called astrophysical beam dumps. When comparing the composition of CRs with the abundance of elements in the Solar system, we see two main differences. In general there is an en- richment, in the CRs, in the heaviest elements relative to H and He. This is not entirely understood but could be due to a different composition at the sources [28]. Further, we observe two groups of secondaries - Li, Be, B and Sc, Ti, V, Cr, Mn - having a much larger relative abundance among the CRs compared to the relative abundance in the solar system. These two groups of elements are rare end-products of stellar nucleosynthesis, but are present in the CR flux as a result of so-called spallation of primary CRs in the ISM5. Further, the ratio of secondary to primary nuclei is observed to decrease with energy [2]. This is interpreted in terms of high-energy particles escaping the Galaxy to a higher degree. These observations give us a handle on the parameters in propagation models and the lifetime of the CRs in our Galaxy. Another source of secondary CRs is the production of electron-positron pairs, that becomes relevant for protons above 1 EeV, and further dominates the energy loss up to around 70 EeV where pion-production takes over. CRs with energies above 50 EeV may interact with Cosmic Microwave + Background (CMB) photons to produce pions through p + γCMB → Δ → n(p)+π+(π0). This provide the mechanism for the so-called Greisen-Zatsepin- Kuzmin (GZK) cut off [47, 48], potentially the reason for the sharp cut-off in the energy spectra of CRs around 50 EeV [49, 50]. The neutrinos produced through the decay of these charged pions are very highly energetic and are referred to as GZK-neutrinos. The GZK flux prediction is sensitive to the fraction of heavy nuclei present in the UHE CRs. These lose energy through photo-disintegration and hence lower the neutrino production efficiency [51]. The search for GZK-neutrinos has been conducted with a large variety of experiments: large radio telescopes such as e.g. LUNASKA (The Lunar UHE

4E.g. the excess of positrons measured by PAMELA (Payload for Antimatter Matter Explo- ration and Light-nuclei Astrophysics) and later conﬁrmed by Fermi and the AMS-01 (Alpha Magnetic Spectrometer)-01 and AMS-02 experiments at the International Space Station (ISS) has been interpreted as evidence for dark matter [43], in terms of modiﬁed propagation models [44], and as evidence for a nearby astrophysical source [45]. See [29] and references therein for a brief review of the topic. 5In this context spallation refers to the process in which nuclei emit nucleons after being hit by incoming high-energy particles.

53 Neutrino Astrophysics using the Square Kilometer Array) searching for radio pulses from neutrino-induced particle cascades in the Moon [52], balloon experiments such as the ANITA (Antarctic Impulse Transient Antenna), satellite experiments such as FORTE (Fast On-orbit Recording of Transient Events) [53], etc. Future detectors include the ARA (Askaryan Radio Array) [54, 55] and the ARIANNA (Antarctic Ross Ice Shelf Antenna Neutrino Array) [56]. These all search for radio signals created by the so-called Askaryan effect [57]. Further, the SPATS (South Pole Acoustic Test Setup) studies acoustic signals formed in dense neutrino-induced cascades in the Antarctic ice, see e.g. [58] for a review on this topic. In section 3.3 and 3.4, we will show how secondary CRs are produced in regions close to astrophysical sites and the relatively dense environments of the Earth’s atmosphere. These sites also produce high-energy neutrinos, the main topic of this thesis. Figure 3.5 illustrate the sources of neutrinos through-out the Universe. These include both natural sources such as the hypothetical relic neutrinos from the Big Bang (’Cosmological ν’), solar neutrinos, atmospheric neutrinos and neutrinos produced in violent processes related to supernova bursts and AGNs, as well as man-made sources, such as reactor neutrinos produced in radioactive decays of heavy isotopes used for ﬁssion energy generation.

Figure 3.5. Measured and expected neutrino ﬂuxes from several sources, both natural and man-made. The incredible energy range covers both time-dependent and time- independent sources from μeV all the way up to EeV. The ﬁgure is taken from [46] with kind permission from Springer Science and Business Media.

54 Figure 3.6. Cross-section for photo-production of neutral and charged pions. The single-pion production (black solid and red dashed line) is dominated by the resonance + of Δ at mΔ ≈ 1232 MeV [60]. Figure from [60].

3.3 Astrophysical Neutrinos Astrophysical neutrinos can be produced as a result of interactions between accelerated primary CRs and the matter and radiation ﬁelds that surround the acceleration site. The important processes are the hadronic reactions6: p + γ → Δ+ → n(p) + π+(π0) (3.1a) p + p → p + n(p) + π+(π0) (3.1b) where equation 3.1a is commonly referred to as a photo-production process where the protons interact with ambient photons, typically produced by accelerated electrons. Photo-production is the foundation of the so-called Δ- approximation, see ﬁgure 3.6, where we assume that the proton-γ cross-section can be described by an analytic Breit-Wigner resonance at mΔ ≈ 1232 MeV [60]. Equation 3.1b is referred to as an astrophysical beam dump process due to the similarity with accelerator-based experiments [29]. The balance between these reactions is related to the cross-section and number density of each particle present [2]. + + Neutrinos are produced in the decay of charged pions, e.g., π → μ + νμ + + (99.99%) followed by μ → e +νe +ν¯μ (≈100%). The typical energy for each of the three neutrinos is: Eν ∼ 1/4Eπ ∼ 1/20 Ep, i.e., protons at the CR knee creates ∼ 100 TeV neutrinos [61]. γ-rays are produced in the decay of neutral pions π0 → γ +γ (98.82%). Further, escaping neutrons may decay through the

6This set of reactions can also proceed with neutrons and/or higher mass mesons and baryons in the ﬁnal states. Further, see [59] for a review of channels with resonances.

55 − weak interaction n → p + e + ν¯e (100%). All branching ratios are taken from [2]. The energy emission of astrophysical sources consists of escaping high- energy protons, γ-rays, and neutrinos, all with highly correlated continuous non-thermal energy spectra. The pion spectrum from photo-production, and hence the neutrino spectrum, follows closely the primary proton spectrum in case the photons are thermal, but is somewhat steeper if the process proceeds with synchrotron radiation, produced by electrons loosing energy in strong magnetic fields [62]. Note that these arguments require that the sources are transparent enough for protons to interact at least once before decaying and that mesons decay before interacting. For optically thin sources photons are emitted in coincidence with the neutrinos, but for thick sources they avalanche to lower energies until they escape, giving rise to a distribution of sub-TeV photons. In models one typically normalize the expected neutrino flux to the observed flux of γ-rays or CRs given assumptions of the production efficiency and absorption in the sources [63]. The neutrino flux for a generic transparent source of extragalactic CRs is called the Waxman-Bahcall (WB) limit or WB bound [64, 65]. By integrating the energy spectrum from figure 3.4 above the ankle assuming an E−2 spectrum and a GZK cut-off at 50 EeV we arrive at a CR energy density ρ ∼ 3 × 10−19 erg cm−3 [63] or ∼ 3 × 1037 erg s−1Mpc−3 over the Hubble time 1010 years. Converted to power for different populations of sources this gives [66]: • ∼ 3 × 1039 erg s−1 per galaxy, • ∼ 2 × 1042 erg s−1 per cluster of galaxies, • ∼ 2 × 1044 erg s−1 per AGN, or • ∼ 2 × 1052 erg per cosmological GRB. These numbers are of the same order of magnitude as the observed electromagnetic emission from the listed sources [63]. Further, they are consistent with a transparent model where the most important process is the photo-production through the Δ-resonance and the energy emission is approximately equally distributed among the CRs, γ-rays, and neutrinos. These sources have emerged as leading candidates for the extragalactic component of the CRs and the derived neutrino flux is loosely confined in the range [63]:

2 −8 −2 −1 −1 EνdΦWB/dEν = 1 ∼ 5 × 10 GeV cm s sr , (3.2) where ΦWB is the WB bound. The precise value depends on a number of assumptions: the minimum energy considered in the integration of the CR spectrum, details of the production process (in particular the energy distributions), cosmological evolution of the CRs sources, etc. For details see [63], [59] (Δ-approximation), [67] (simulations of pγ processes), and [68] (simulations of pp processes). The Δ-approximation is crucial in order to construct

56 approximate pion-production cross-sections and to determine gross features like the number ratio of γ to neutrinos produced [59]. A similar exercise can be done for the Galactic part of the CR energy spectrum, leading to an energy density ρ ∼ 10−12 erg cm−3 (∼ 1eVcm−3) [28, 63]. Assuming a volume, corresponding roughly to the size of the Galactic disk, V = πR2d ∼ π(15 kpc)2(200 pc) ∼ 4 · 1066 cm3 we can derive the power required to accelerate these galactic CRs [28]: ρ = V ∼ · 40 −1, W τ 5 10 erg s (3.3) where τ is the active time in the source region, typically of the order of 106 years [28]. Interestingly this power estimate is similar to the power provided by typical supernova scenarios, if we assume a supernova rate corresponding to one every 30 years and that roughly 10% of the power produced by supernovae, each releasing 1051 erg, can be used to accelerate new particles through the expanding shock wave [63]. The predicted neutrino rate give a handful of detectable neutrinos per decade of energy per km2 and year [63], assuming that the sources extend to 100 TeV with an E−2 spectrum. The relative ratio of different neutrino flavors produced according to equations 3.1 is 1:2:0 for νe:νμ:ντ. Due to flavor oscillations during propagation this implies that the astrophysical neutrinos arriving at Earth should have the ratio 1:1:1 given the so-called long baseline approximation [69, 70]. The observation of localized neutrinos from known γ-ray emitters would undoubtedly confirm the existence of hadronic accelerators. However, re- cently the Fermi collaboration published results identifying hadronic accelerators solely based on the presence of γ-rays produced from the decay of π0 in the Spectral Energy Distribution (SED) [71]. Assuming an E−2 spectrum the pion-decay bump is characterized by a sharp rise at 70-200 MeV, tracing the parent population above ∼ 1 GeV [72]. The height depends on the maximal proton energy and the fraction of energy transferred to the γ-rays. The standard model for production of high-energy photons is the so-called Self-Synchrotron Compton (SSC) mechanism, see e.g. [73]. This constitutes the basis for leptonic production where high-energy photons are produced through so-called synchrotron emission, caused by the movement of electrons in the strong magnetic fields of jets. The generated photon spectrum is peaked in the IR to X-ray region, and constitute the so-called synchrotron peak. The synchrotron photons subsequently get accelerated by the same parent electron distribution through Inverse Compton (IC) scattering. Further, high-energy photons are also generated through Bremsstrahlung as charged particles are decelerated. These latter two contributions result in photon energies in the range GeV-TeV. The non-thermal emission spectra is hence characterized by a double peak distribution, see e.g. figure 3.7. Note that the SSC model has an intrinsic energy limit set by the decrease of the IC cross-section in the Klein-Nishina regime [74]. This is in contract to the hadronic scenarios where

57 IC 443 10-10 ) -1 s -2

10-11

dN/dE (erg cm Best-fit broken power law 2 Fermi-LAT E VERITAS (30) -12 MAGIC (29) 10 AGILE (31) π0-decay Bremsstrahlung Bremsstrahlung with Break

108 109 1010 1011 1012 Energy (eV)

) 0 decay

-1 π

s Mixed model -2 10-10 Inverse Compton Bremsstrahlung Bremsstrahlung with Break

10-11 dN/dE (erg cm 2

10-12

Gamma-ray flux E 10-13 10-7 10-5 10-3 10-1 10 103 105 107 109 1011 1012 Energy (eV)

Figure 3.7. Spectral Energy Distribution (SED) of SNR ‘IC 443’. The figures show best-fit values to Fermi-LAT data (circles) of both leptonic and hadronic components (the radio band is modeled using synchrotron emission), the upper figure showing a zoom in on the γ-ray band. The solid lines represent the best-fit pion-decay spectrum, and the dashed lines show the best-fit Bremsstrahlung spectrum. The inverse Compton component is shown as a long-dashed line in the lower plot, together with a mixed model (Bremsstrahlung and pion-decay), shown as a dotted line. See details in legend. Figure taken from [71]. Reprinted with permission from AAAS.

58 Figure 3.8. Best-fit neutrino spectra from IceCube global fit paper [77], assuming a single power-law and including all flavors. The red (blue) shaded are correspond to 68% C.L. allowed regions for the astrophysical (atmospheric conventional) flux component, while the green line represent the 90% C.L. upper limit to the prompt atmospheric flux fitted to zero. Figure taken from [77].

the maximal energy is set by the maximum proton acceleration energy of the source. The leptonically produced photons can outnumber the photons from the hadronic production by large amounts, in particular for sources with a very low matter density around the acceleration region. Sources known to be interacting with clouds of dense material therefore provide good targets for where to detect evidence of CR acceleration. SNRs interacting with molecular clouds belong to this class of interesting sources, producing γ-ray via the decay of neutral pions produced in the dense gas surrounding the sources [75]. One of the best examples of such SNR-cloud interactions in the Galaxy is SNR IC-443, with an estimated age of about 10,000 years, located at a distance of 1.5 kpc [76]. The plots in figure 3.7 show the measured energy spectrum for SNR ‘IC 443’. The circles show the best-fit values to Fermi-LAT data of both leptonic and hadronic components. The solid lines denote the best-fit pion- decay γ-ray spectra. See further details in figure caption. The conclusion from this search was that the γ-rays are most likely produced through the hadronic channels, while leptonic production can still account for the synchrotron peak. These models predict a neutrino luminosity that can be searched for by neutrino detectors like IceCube.

59 The IceCube Collaboration reported the detection of a diffuse flux of astrophysical neutrinos in 2013 [3, 78]. Evidence for astrophysical neutrinos were also seen in a separate analysis looking for a diffuse astrophysical neutrino flux using tracks from the Northern hemisphere [79]. The best-fit all-flavor astrophysical neutrino flux calculated using a global fit to six different IceCube searches is given as [77]:

φ = . +1.1 · −18 −1 −2 −1 −1 . (6 7−1.2) 10 GeV cm s sr (at 100 TeV) (3.4) where γ = 2.50 ± 0.09 [77] (valid for neutrino energies between 25 TeV and 2.8 PeV [77]). The atmospheric-only hypothesis was rejected with 7.7 σ assuming a χ2-distribution. Apart from a statistically weak cluster close to the Galactic center, the arrival directions of these neutrinos are consistent with an isotropic distribution, but the actual origin is unknown. Since the events extend to large Galactic latitudes many suggestions include extragalactic sources such as AGNs embedded in molecular clouds, intense star-formation regions, etc. See [80] for a review and references therein. Note that since high-energy photons have a short absorption length such emission is not to be expected in association with the IceCube ﬂux, unless there is a signiﬁcant Galactic contribution [61]. Instead, we can search for association with the possible sub-TeV extension of the signal, as mentioned in the beginning of this section.

3.4 Atmospheric Backgrounds Atmospheric muons constitute the by far most dominant part of the event yield in large-volume underground particle detectors such as IceCube. Analyses searching for astrophysical neutrino-induced muons starting inside of the detector are particularly plagued by atmospheric muons mimicking truly starting events. Further, most analyses also struggle with a close to irreducible background of atmospheric neutrinos. The mimicking muons are particularly troublesome for searches for low-energy neutrinos, relevant for this work, or the diffuse astrophysical flux, but less so when searching for clusters of localized high-energy neutrinos. In this section we discuss these backgrounds and the important interplay between decay and interaction that takes place in the Earth’s atmosphere. The interactions of high-energy nuclei and protons in the Earth’s atmosphere give rise to electromagnetic and hadronic air-showers, see illustration in figure 3.9. The CR flux through the atmosphere can be approximated with a set of coupled cascade equations [2], but Monte Carlo simulations are needed to accurately account for the decay and interactions of the secondary particles as well as the spectral index of the primary CRs.

60 The main reactions generating muons and neutrinos are: p + N → π±(K±) + X ± → μ + νμ(¯νμ) (3.5) ± → e + νe(¯νe) + ν¯μ(νμ), where p is a proton, N is the target nucleus, and X represents the final state hadron(s). The decays of hadrons induce both electromagnetic cascades of high-energy photons, electrons, and positrons as well as highly penetrating muons and neutrinos. The balance between interaction and decay in the atmosphere is energy dependent. The critical energy is defined as the energy where the interaction probability equals the decay probability, under the assumption of an isother- mal atmosphere. The so-called conventional flux of muons and neutrinos is primarily produced in decays of π± or K±7, with critical energies of 115 GeV and 855 GeV [81], respectively. Above the critical energy these particles tend to interact in the atmosphere before they decay, why a steepening (softening) of the muon spectra with about one power relative to the primary spectrum of CRs, is observed above these energies, i.e., γconv. ∼ 3.7 [28]. Note that this effect is less pronounced for zenith angles close to 90◦ since the mesons then travel longer in the low density of the upper atmosphere where they do not interact [2]. The flux from semi-leptonic decays of short-lived charmed hadrons (generally heavy quark particles with lifetimes smaller than 10−12 s) is referred to as prompt and is characterized by a flatter muon spectrum, i.e., relatively more muons at higher energies. This is because the charmed hadrons, in contrast to the conventional component, in general decay before losing energy in interactions. E.g., D± has a critical energy of 3.8 · 107 GeV [29]. Current estimates of the cross-over, from the conventional to the prompt component, predict that it occurs ∼ 1 PeV, see e.g. [82]. Consequently the muon and neutrino spectra below O(100 GeV) where decay dominate follow the CR spectrum and are well described by a power-law spectrum: dΦν ∝ E−γ, (3.6) dEν where γ = 2.7. Above O(100 GeV) the spectra become steeper eventually reaching γ = 3.7. While the conventional production, described in equation 3.5, produces neutrinos and anti-neutrinos with flavor ratio νe:νμ:ντ = 1:2:0, the prompt component yields approximately equal amounts of electron and muon flavored 8 9 neutrinos . Further the ratio of νe/νμ decreases with energy above O(GeV) ,

7The fraction of pion- relative to kaon-induced muons is energy dependent. About 8% (20%) of vertical muons come from decay of kaons at 100 GeV (1 TeV) (27% asymptotically) [28]. 8The large mass of τ suppresses the production of ντ andν ¯τ from atmospheric processes. 9This is in contrast to the lower density environments considered in section 3.3 where the ratio stays constant to much higher energies [28].

61 Figure 3.9. Production of muons and neutrinos in the Earth’s atmosphere.

62 due to the increasing muon decay length [28]. Further, there is an asymmetry in the yield of neutrinos compared to anti-neutrinos. This is due to the excess of positively charged pions and kaons in the forward fragmentation region of proton-initiated interactions, and further due to the larger amount of protons over neutrons in the primary CR spectrum.

Particle Flux at Sea Level Since muons are relatively long-lived (livetime 2.2 μs [2]) some penetrate to sea level and further through kilometers of Earth material such as ice, rock, and water. The muon flux on the surface is around 100 particles m−2s−1sr−1. The abundance of particles in the air-shower as it moves through the atmosphere is shown on the left side of figure 3.10. Muons and neutrinos dominate the picture at sea level and any remaining electrons, hadrons, or photons will be absorbed in the Earth material. At the depths of IceCube the muons outnumber the atmospheric neutrinos by a factor of ∼ 106. The plot on the right side of figure 3.10 shows the vertical intensity of muons as a function of depth expressed in kilometers water equivalent (km w.e.). IceCube is located at a depth of about 1.8 km w.e. and is subjected to a large number of atmospheric muons from the Southern hemisphere. An efficient way to reduce this flux is to only study particles from the Northern hemisphere, where the Earth itself can be used as a filter, blocking most muons. At about 20 km w.e., the muon flux becomes constant, constituting an isotropic neutrino-induced background.

3.5 Acceleration Mechanisms The power-law nature of the CR energy spectrum discussed in section 3.1 is indicative of non-thermal10 processes where a relatively small number of particles is accelerated by a focused energy out-flow from a powerful source [30]. In this section we will discuss mechanisms needed to transfer this macroscopic energy to individual particles, in particular the so-called standard model of CR acceleration: Diffusive Shock Acceleration (DSA). The acceleration of high-energy particles in the Solar system occurs both on large scales, e.g. in interplanetary shock waves associated with the solar wind, and in the vicinity of point sources such as the particle acceleration to GeV energies observed in connection with solar flares [28]. Similarly, both extended and point sources are likely to play a role in the acceleration of Galactic and extragalactic CRs. It is also possible that acceleration (initial or further) takes place during propagation, through interactions with large gas clouds containing magnetic irregularities. In general, acceleration to high-energies (TeV energies and above) requires a massive bulk flow of relativistic charged particles [63]. The

10Emission not described by a black body spectrum with a given temperature.

63 Altitude (km) 15 10 5 3 2 1 0 10000

1000

] _ –1 νμ + νμ sr 100 μ+ + μ− –1 s

–2

10 p + n 11250

1 e+ + e− Vertical ﬂux [m π+ + π− 0.1

0.01 0 200 400 600 800 1000 1 10 100 Atmospheric depth [g cm–2]

Figure 3.10. Left: Vertical CR fluxes in the atmosphere above 1 GeV (displays the integrated flux above 1 GeV for all particles except electrons, for which the threshold Ee > 81MeV applies instead) as a function of atmospheric altitude/depth. Data points show experimental measurements of μ−. Figure taken from [2]. Right: Vertical muon intensity as a function of kilometer water equivalent depth. For data points see caption of figure 28.7 in [2]. The shaded area at large depths shows neutrino-induced muons with an energy above 2 GeV. Figure taken from [2]. presence of relativistic gas in the ISM has been established through mainly two key observations: synchrotron radiation induced by relativistic electrons (and protons) and the presence of γ-rays from the decay of neutral pions. Earth-bound accelerators use electric fields to give energy to particles typically confined in circular orbits by strong magnetic fields. But in most astrophysics environment, such electric fields would immediately short-circuit since the particles are in a plasma state with very high electric conductiv- ity [29]. Instead, we consider so-called shock acceleration where low-energy particles are given higher energies through repeated stochastic encounters with magnetic irregularities. We start by deriving the basic concept of shock acceleration, closely following the discussion in [28]: A test particle undergoing stochastic collisions gains an energy ΔE = ξE in each encounter. After n such collisions the en- n 0 ergy is En = E0(1+ξ) , where E is the initial (injection) energy. Assuming an escape probability, Pesc, from the finite acceleration region per encounter, the proportion of particles with an energy greater than E is [28]:

−γ 1 E N(> E) ∝ , (3.7) Pesc E0

64 where

P 1 Tcycle γ ≈ esc ≡ , (3.8) ξ ξ Tesc where we have introduced Tcycle as the time for each acceleration cycle n and Tesc as the time for escape from the acceleration region. These two parameters are characteristics of the source considered and in general energy dependent. t/T The maximal energy provided Emax = E0(1 + ξ) cycle where t is the total acceleration time. A power-law spectrum emerges from the stochastic nature of this process in combination with the finite probability of escape, but a definite prediction of the spectral index is not provided [28]. Fermi acceleration is a mechanism to transfer macroscopic kinetic energy of moving magnetized plasma to single charged particles, and builds upon the simple model of shock acceleration described above. It requires that particles are magnetically confined to the source region for sufficiently long time to reach the required energies. Further, the encounters have to be collision-less in order for the mechanism to be effective, otherwise collisions with surrounding particles would cause too large energy losses for a net acceleration to take place. In the original version, Fermi considered charged particle interactions with irregularities in dense magnetic clouds, so-called magnetic mirrors, depicted to the right in figure 3.11. Here the scattering angle is uniform and particles can either lose of gain energy depending on the angle. The average energy gain per collision ξ is second-order in the velocity of the cloud, and therefore this is referred to as second-order Fermi acceleration. There are several problems with this type of mechanism. In particular, observations show a too low cloud density and the random velocity of interstellar clouds is very small [29], i.e., this is an inefficient mechanism to accelerate particles to high energies.

Figure 3.11. Left: Fermi acceleration of 1st order. Right: Fermi acceleration of 2nd order.

65 The current baseline model is instead associated with particle acceleration in strong shock waves11, DSA. Evidence for strong shocks has been found, e.g., in the supersonic shells of supernova remnants propagating in the interstellar medium [83].

3.5.1 Diffusive Shock Acceleration In the DSA model we consider a shock wave that moves through a magnetized plasma into which we inject a test particle that traverses the shock wave head- on, entering the shocked region from the unshocked region, see left side of figure 3.11. The particle undergoes repeated elastic scattering on magnetic field irregularities in the region of shocked gas (not due to collisions with other particles) and on average ends up co-moving with the bulk of the shocked gas. A cycle is completed if the particle subsequently scatters back to the unshocked region, gaining the same energy as for the initial transition [28]. In contrast to second-order Fermi acceleration where a particle both can lose and gain energy as it traverses the magnetic mirrors, the collisions with the shock front are always head-on and lead to an increase in energy. The key requirement is the presence of a strong shock wave and that the velocities of the relativistic charged particles in the medium are randomized on either side of the shock so that they are co-moving with the medium. The latter is achieved through the elastic scattering on the magnetic field irregularities. This is the clever aspect of this acceleration mechanism, the same dynamics take place at passage on either side of the shock front. The average energy gain from such a cycle of a non-relativistic shock can be shown to be [28]: 4 ξ ∼ β, (3.9) 3 where β is the relative velocity between the shocked and unshocked gas, i.e., the energy gain is proportional to the initial energy, hence leading to a power- law spectrum as illustrated in the beginning of the section. The acceleration continues in cycles until the particle escapes. The escape probability in this case translates to the probability for particles to scatter away from the shock front. Further, this kind of acceleration predicts a specific spectral index [28]: dN ∝ E−2 (3.10) dE The CR escape probability increases with energy, which leads to the slightly softer spectra γ ∼ 2.7 as observed at Earth [84]. DSA is thought to play an important role for the acceleration of particles up to the knee at 1015 − 1016 eV, but fails to explain the flux above this limit

11A shock wave is formed when the speed of material exceeds the speed of sound in the medium. This propagating disturbance is characterized by a nearly instantaneous drop in pressure, temperature and density.

66 Figure 3.12. Hillas diagram of potential source of acceleration. Crab indicates the Crab nebula and IGM the Intergalactic Magnetic Field. Reprinted by permission from Macmillan Publishers Ltd: Nature [85], copyright 2009.

[29]. In particular, for energies above ∼ 1018 eV, even the most exotic Galactic candidates for acceleration are deemed inefﬁcient [29].

3.6 Potential Acceleration Sites We saw in section 3.3 and 3.5.1 that Galactic SNRs can provide the power needed for accelerating CRs to energies up to 1015 − 1016 eV through DSA. The most prominent candidates for the highest-energy particles ( 1018 eV) include extragalactic sources such as GRBs and the accretion disks and relativistic jets of AGNs. More exotic scenarios (so-called top-down scenarios) include decays of magnetic monopoles and the Z-burst mechanism where neutrinos with extremely high energy interact with relic neutrinos from the Big Bang at the resonance for the neutral weak gauge boson Z0 producing CRs in subsequent decays [86]. The latter has been excluded by neutrino experiments such as ANITA, a radio-balloon experiment in Antarctica [87, 88]. Diffuse fluxes of neutrinos are generally believed to be due to either un- resolved point sources or a truly diffuse flux, i.e., neutrino production that is not localized or limited to a particular source, but that instead may be associated with CR hadrons and electrons interacting with gas and photon fields in the same way as the dominant diffuse γ-ray emission from the Galactic plane [29]. Further, so-called hidden sources may exist, where neutrinos are the only

67 particles escaping and the rest is absorbed in the source. Such sources cannot be the sources of CRs but may still provide insight regarding the interactions in the vicinity of the sources. We saw in the beginning of section 3.5 that the sources of acceleration are generally characterized by their active time and the maximal energy they can produce. In particular, higher energies can be achieved with extreme magnetic fields or a long shock lifetime. Hillas criterion is a way to constrain potential sources by considering the size of the acceleration region and the magnetic field present in it. The maximal attainable particle energy of a CR nucleus of charge Z accelerated in a magnetic field strength B with size L can be written as [29]: B L E ∼ Z · β · · EeV, (3.11) max 1 μG 1 kpc where β is the velocity of the shock front in terms of c. This condition is illustrated in figure 3.12, showing magnetic field strength B as a function of source size L for a large number of potential high-energy accelerators. The solid (dashed) line represent a proton (an iron nucleus) with energy E = 1020 eV. Only source above each line can accelerate the corresponding particle to energies above 1020 eV. In the remainder of this section we will discuss several different source candidates that can provide the power needed to reproduce the CR power-law spectrum from a few GeV to 1020 eV. For a more complete list of candidate sources see e.g. [84] and [89]. The basic assumption for all of the sources presented below is that they are optically thin. This means that we can correlate the predicted neutrino emission with the observed TeV γ-ray emission in the case of a hadronic acceleration scenario as mentioned in section 3.3 [89]. We will briefly mention GRBs in section 3.6.2 but otherwise focus on sources of steady emission, relevant for this thesis.

3.6.1 Galactic Sources

Supernova Explosions/Remnants Scenarios emerging from the event of a supernova include some of the best candidates for neutrino emission in the Galaxy. A supernova is a stellar explosion triggered either by the gravitational collapse of a massive star or through the re-ignition of a degenerate star, e.g., a white dwarf accumulating matter from a companion eventually reaching the point of so-called runaway nuclear fusion [90]. These are extremely bright events that brieﬂy outshine the host galaxy and release a large amount of energy through the emission of MeV neutrinos prior to the optical burst [89].

68 Such neutrinos were detected from supernova SN 1987A12, mentioned in section 1.1. Further, a burst of neutrinos in the TeV range is predicted from proton-nuclei interactions in shock-fronts as they break out of their progenitor star after core collapse [91]. Supernovae are quite rare, and only occur on average every thirtieth year in our Galaxy. Due to their bright emission they have become important in the historical perspective. E.g. the Sumerians discovered the Vela supernova 6,000 years ago and the left-over, the SNR, is clearly visible today, constituting a prime candidate for CR acceleration [92]. Further, in 1054 the Crab supernova was observed by Chinese astronomers [92]. The Crab nebula is particularly important since it has a close to time-independent brightness and hence can be used as a calibration source, a standard candle in γ-ray astronomy. SNRs consist of the remaining structure of ejected material resulting from a supernova explosion. Neutrino emission is expected from shock acceleration in both shell-type SNRs and Pulsar Wind Nebulae (PWNs) [89]. The former is bound by an expanding shock wave driving into the ISM at supersonic velocity, accelerating particles through DSA, and producing radio and X-ray emission via synchrotron radiation. The more energetic emission, at above MeV, can originate from inverse-Compton scattering, Bremsstrahlung or neutral pion decay. Hadronic origin is in general not established.

12Located in the outskirts of the Tarantula Nebula in the Large Magellanic Cloud.

Figure 3.13. Shell of supernova remnant RX J1713.7-3946 revolved at TeV γ-ray energies by HESS (HESS point spread function is shown in the bottom left corner). The black contour show the X-ray surface brightness in the range 1-3 keV observed by ASCA. Credit: HESS Collaboration.

69 The life of a SNR involves mainly two phases that are of interest for γ-ray and neutrino emission. The first phase is the free expansion of the ejected material that lasts typically 2-10 years [74]. Hadronic acceleration and interaction take place in the high density of the expanding envelope [74] as it interacts with the surrounding ISM. This is followed by the so-called Sedov- Taylor phase that can last several hundred years. This is when most of the particles escape the acceleration region and enter the Galaxy as CRs [29]. PWNs also eject material into the ISM, creating a shock wave where particles are accelerated. These objects are believed to be closely connected to the birth and evolution of SNRs. PWNs are thought to be powered by rapidly rotating pulsars with very strong magnetic fields, dissipating their rotational energy over several thousands of years. These pulsars are likely the remnants of old core-collapse supernovae, i.e., rotating neutron stars with a beamed lighthouse-style emission. They are observed in radio, X-rays, and γ-rays. The emission is produced as the pulsar wind interacts with the surrounding material to form a shock front [93]. Many SNRs have now been resolved by γ-ray telescopes such as HESS and we can see the shock fronts as a shell surrounding the source, see figure 3.13. SNRs in regions of dense molecular clouds have confirmed hadronic processes [71] and therefore constitute prime candidates for sources of neutrinos produced in our Galaxy, see figure 3.7 and the discussion in section 3.3.

Microquasars High-energy neutrinos could be produced in the relativistic jets of Galactic microquasars as suggested in [94, 95]. These compact X-ray binary systems consist of a stellar-mass black hole or a neutron star (M > 3Mo) that cannabal- izes a non-compact companion star [84]. The characteristics of microquasars strongly resemble the ones of AGNs with an accretion disk and relativistic jets, 8 but on a much smaller scale (the black holes involved in AGNs have ∼ 10 Mo). Assuming that CRs are accelerated in the jets, neutrinos could be produced through the hadronic processes discussed in section 3.3. The energy could come from either the accretion of matter from the companion star or as magnetic dipole radiation (neutron stars have extremely strong (1012 G) surface magnetic ﬁelds) [84]. The recent detection of TeV γ-rays from such objects has demonstrated that these are indeed sites of effective acceleration of particles up to multi-TeV energies [95]. It remains to be seen if the acceleration is leptonic and/or hadronic in origin.

Molecular Clouds and Diffuse Emission Neutrinos can be produced by the decay of charged pions produced in CR interactions with the Galactic disk, resulting in a diffuse emission. The astrophysical sources themselves may be hidden behind dense regions of matter and radiation. HESS has observed extended regions of γ-rays from known directions of molecular clouds (star formation regions) [96]. The location of

70 these can be traced with e.g. Planck CO observations. This data supports the hadronic hypothesis and suggests that the source is compatible with the emission from an embedded supernova explosion ∼ 104 years ago [96].

3.6.2 Extragalactic Sources We saw already in section 3.6 that many extragalactic sources can contribute to the CR spectrum at the highest energies. These include: AGNs, GRBs, starburst galaxies (galaxies with unusually high star formation rate that can act as calorimeters for CRs produced in SNRs [80]), magnetars (neutrons stars with very strong magnetic ﬁelds), galaxy clusters (where shocks form either through accretion of matter or in termination shocks of galactic winds [97]), etc. In this section we will focus on the two prime source candidates for CR production and acceleration: AGNs and GRBs.

Active Galactic Nuclei AGNs are the most luminous steady sources observed in the Universe. The strong electromagnetic radiation is believed to be caused by matter falling 8 into a super-massive black hole (M ∼ 10 Mo) in the galactic center, forming an accretion disk [62]13. They emit electromagnetic radiation in the form of X-rays, γ-rays and optical light, and many have time-dependent periods of enhanced emission of the order of days or weeks. Due to the wide range of radiation seen, these objects are prime targets for multi-messenger astronomy as discussed in section 1.2. Many AGNs have relativistic jets perpendicular to the accretion disk (collimated outflows of accelerated gas). High-energy neutrinos may be produced as the accelerated particles interact with X-rays or other photons in the core region of the AGN or in the jets, but the relation between the luminosity of these different types of particles is unknown and depends on the models assumed. These models are highly complex. A review including derivations of the maximum energy threshold, various energy losses and normalizations can be found in [84]. The so-called unified AGN model aims to explain the characteristics observed from a large variety of astrophysical objects, as due to different viewing angles of AGNs [98], i.e., the observed electromagnetic emission depend on the orientation of our line of sight to the accretion disk and jet of the super-massive black hole. The unified model is illustrated in figure 3.14. This model seeks to explain a large variety of sources, amongst others: Seyfert galaxies, BL Lacs, and Flat-Spectrum Radio Quasars (FSRQs). For a review of such astrophysical objects and their characteristics, see e.g. [98].

13The luminosity can range from 1040 erg s−1 (nearby galaxies) to 1047 erg s−1 (distant point sources, so-called quasars) [29].

71 Gamma Ray Bursts GRBs are the most luminous transient objects in the Universe and have been proposed as possible candidates for high-energy neutrinos [99]. For the dura- tion of the burst they outshine the entire Universe. They are observed isotrop- ically in the sky with a rate of about 1 per day. They are usually classiﬁed by their burst time: short GRBs on average last 0.3 s and long on average 30 s, and are thought to arise due to somewhat different mechanisms [29]. Short GRBs might be due to the merger of compact binary systems such as neutron stars. They are associated with regions of little or no star formation and have no association to supernovae. Long GRBs have bright afterglows and can be linked to regions of active star formation and in many cases to core-collapse supernovae, black holes with strongly collimated jets [29]. GRBs have non-thermal electromagnetic emission than can be divided into three phases: a less bright precursor phase 10-100 s before the bright so-called prompt phase that is subsequently followed by an afterglow.

Figure 3.14. An illustration of the uniﬁed AGN model, that aims to explain the characteristics observed from a large variety of astrophysical objects, as different viewing angles of AGNs [98]. Credit: ‘Active Galactic Nuclei’, V. Beckmann and C. Shrader, 2012. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

72 The so-called ﬁreball model is a widely used theoretical framework for models of GRBs. A centralized explosion initiates a relativistic blast wave that propagates through the previously ejected material surrounding the source. Electrons, protons, and γ-rays are produced and accelerated in the shocked regions when shells of material moving at different speeds collide [74]. High- energy neutrinos ( 100 TeV) are produced as a result of pγ-interactions. The physics is similar to that of jet acceleration in AGNs, the main difference being the short time scales and much higher boost in energy [74]. IceCube has put strong bounds on the ﬁreball model and excluded large parts of the parameter space, see [100].

Summary We have now reviewed the theoretical background and motivation for neutrino astronomy as well as discussed the primary candidate sources. Before we go on to discuss the details of the analysis and tools used, we elaborate a bit on how neutrinos can be detected, in particular using cubic-kilometer-scale ice/water Cherenkov detectors such as e.g. IceCube. This is discussed in the next chapter.

4. Neutrino Detection Principles

“I have done a terrible thing, I have postulated a particle that cannot be detected.” Wolfgang Pauli

Since neutrinos only interact gravitationally and with the weak force there is a limited way in which they can be detected. Experiments like IceCube and ANTARES detect neutrinos through the charged particles they produce in interactions with atoms in natural ice/water or the nearby bedrock. Similarly, large under-ground detectors such as Super-K detect particles produced in the interactions with puriﬁed water. These interactions proceed either through charged weak interactions where a W± boson acts as force mediator, so-called CC interactions, or through neutral weak interactions where a Z0 boson acts as force mediator, so-called NC interactions. We focus on the semi-leptonic processes whose pictorial form proceed with the interactions:

− + νl(¯νl) + Y → l (l ) + X (CC) (4.1)

νl(¯νl) + Y → νl(¯νl) + X (NC) (4.2) where l is a charged lepton (e,μ,τ), Y represents either a nucleus, nucleon, or quark depending on the kinetic energy of the incoming neutrino and X is the final hadronic state. The corresponding Feynman diagrams for the underlying neutrino-quark interactions are depicted in figure 4.1. Note that lepton flavor conservation imposes that the produced lepton is of the same family as the incoming neutrino. Electron anti-neutrinos may interact directly with electrons through the − − Glashow resonanceν ¯e + e → W . This occurs at neutrino energies close to 6.3 PeV [101], where the center of mass energy ECM ∼ MW , see figure 4.2. The final states may be hadronic and/or electromagnetic showers. Further so- − − − − called pure muon ν¯e + e → ν¯μ + μ and lollipop ν¯e + e → ν¯τ + τ signatures are possible.

75 − + νl l ν¯l l

W± W±

d u u d

νl νl ν¯l ν¯l

Z0 Z0

u,d u,d u,d u,d

Figure 4.1. Feynman diagrams of neutrino-quark interactions through charged (upper row) and neutral (bottom row) currents.

In the following sections we will focus on the topics relevant for neutrino detection in IceCube. We start by discussing the cross-section of neutrinos and then describe how coherent Cherenkov radiation is created as the result of polarization in the detector medium. We saw in section 3.4 that the muons can travel long distances before stopping. The mechanism behind the energy loss of muons is covered in section 4.3.

4.1 Neutrino Cross-Section At the lowest energies, Eν < 1 MeV, neutrino interactions proceed through thresholdless processes such as elastic scattering of free electrons, coherent scattering with nuclei and neutrino capture [101]. Slightly higher, up to Eν ∼ 100 MeV, the neutrinos start to probe the inner structure of the nuclei to interact with individual nucleons. This include pri- + marily inverse beta decayν ¯e + p → e + n but also more complex interactions with collective excitations and bound nuclear states [101]. The description of neutrino scattering becomes increasingly more diverse and complex at even higher energies, Eν ∼ 0.1 − 20 GeV [101], where several different mechanisms compete: elastic and quasi-elastic scattering, resonant pion production, and Deep Inelastic Scattering (DIS). In the ﬁrst two of these, neutrinos scatter off an entire nucleon that may change quark composition

76 Figure 4.2. Neutrino cross-section as a function of energy. Figure taken from [102].

(only in CC interactions) but does not break up. In resonant production neutrinos excite the target nucleon creating baryonic resonances, e.g. Δ or N∗ states, that subsequently decay creating one or several ﬁnal state pions. The neutrino cross-section, averaged over neutron and proton, is illustrated as a function of energy (above 10 GeV) in ﬁgure 4.2. DIS is the process where neutrinos can start to resolve the internal structure of the nucleon targets and interact with individual valence quarks giving rise to hadronic showers as the nucleons break up. The matrix element for antineutrino-quark scattering is different from that of neutrino-quark scattering. This is due to the chiral nature of the weak force, the V-A coupling discussed in section 2.4, as it interacts with the particles of the target material and leads to an interaction that is about a factor two stronger for neutrinos compared to anti-neutrinos1. DIS becomes dominant for energies, Eν ∼ 20 − 500 GeV. The neutron and proton averaged DIS differential cross-section for a target N with mass M is given as [103]: ⎧ ⎪ 2 ⎪ M2 ⎪ W , 2 + , 2 − 2 ⎪ 2 2 2 [xq(x Q ) xq¯(x Q )(1 y) ] (CC) 2 G2 MEν ⎨ Q +M d σ = F ⎪ W , dxdy π ⎪ 2 (4.3) ⎪ M2 ⎪ 1 Z 0 , 2 + 0 , 2 − 2 ⎩ 2 2+ 2 [xq (x Q ) xq¯ (x Q )(1 y) ] (NC) Q MZ

1A naive calculation, see e.g. [4], gives a factor of 3, but when the structure functions of the nucleon are taken into account this amounts to a factor of 2.

77 where x = Q2/2Mκ and y = κ/Eν are the Bjorken scaling variables2 [103], −Q2 is the invariant momentum transfer between the incident neutrino and outgoing lepton, κ is the energy loss in the laboratory frame, MW/Z are the masses of the weak gauge bosons respectively, and GF is the Fermi constant. Due to the universality of the weak interaction, these cross-sections only depend on kinematics and the quark distribution functions q,¯q, q0, andq ¯0. See [103] for more details. The cross-sections at Eν ∼ 1TeV− 1 EeV are basically extensions of the ones for lower energies. The main difference is that above about 10 TeV the propagation term is no longer dominated by the mass of the exchange bosons W± and Z0, leading to a suppression of the cross-section caused by the 1/Q2 term [101]. Further, as interactions with the quark-antiquark symmetric quark-sea become more important, the suppression of anti-neutrino-quark interactions relative to neutrino-quark interactions become less pronounced, see ﬁgure 4.1. At Eν 106 GeV,DIS cross-sections are successfully described in the framework of pQCD (pertubative-QCD), and parameterizations of the nucleon structure functions can be chosen according to e.g. CTEQ5 [102, 104]. But as the neutrino interactions with the quark-sea become more important, the uncertainties in these models increase. At the highest scale, ﬁgure 4.2 shows two models for extrapolating the structure functions: ‘pQCD’ (smooth power-law extrapolation) and ‘HP’ (Hard Pomeron) enhanced extrapolation, see [102] and references therein.

4.2 Cherenkov Radiation When a charged particle traverses a dielectric medium such as ice, photons are produced as a result of polarization of the medium. As this polarization relaxes back to equilibrium, photons are emitted, creating a burst of light. If the particle travels faster than the speed of light in the medium, c/n(λ), constructive interference occurs at an angle θc. This disturbance radiates as a coherent electromagnetic shock wave, similar to the sonic boom produced by an aircraft in supersonic ﬂights. See details in e.g. [105]. We can derive a minimum threshold energy, Eth, the Cherenkov threshold, below which the particle does not emit coherent Cherenkov light: mc2 mc2 Eth = = , (4.4) 1 − β2 1 − n−2(λ) where m is the rest mass of the particle, β = v/c where v is the particle’s velocity, λ the photon wavelength, and n(λ) the wavelength dependent refractive

2 x can be interpreted as the fraction of the nucleon’s momentum that is carried by the target quark, while y is the fraction of the lepton’s energy that is transferred to the nucleon rest frame [2].

78 θc

ct/n ct/n vt vt

Figure 4.3. Illustration of the Cherenkov effect. The left illustration shows the spherical wavefronts for a particle with β = 0.5, where a slight concentration along the direction of travel can be seen. The right illustration shows a particle with β = 1, where the waves interfere constructively to produce the characteristic Cherenkov cone of light. Figure taken from [106]. index of the medium. This gives a threshold of about 0.8 MeV for electrons, 160 MeV for muons, and 2.7 GeV for taus assuming n = 1.33 [106] which corresponds to the refractive index of ice in the range 300-600 nm where IceCube Photo Multiplier Tubes (PMTs) are sensitive [107]. The Cherenkov angle θc, the angle of the coherent wavefront relative to the direction of the velocity of the charged particle, is (see ﬁgure 4.3): 1 cosθ = , (4.5) c n(λ)β ◦ where θc ≈ 41.2 for β = 1 and n = 1.33. Note that the observable photons are not emitted exactly perpendicular to this shock front since they move with the = − λ dn group velocity governed by the group refractive index ng n dλ where n is the phase refractive index mentioned above. Taking this into account has been shown to have a small effect [108]. The number of Cherenkov photons emitted per unit length x and wavelength λ can be estimated from [105]: d2N 2πα 1 = 1 − , (4.6) dxdλ λ2 β2n2(λ) where α ≈ 1/137 is the ﬁne structure constant. Integrating equation 4.6 in the range where IceCube PMTs are sensitive yields about 330 Cherenkov photons

79 /g] + 2 μ on Cu 100 μ Bethe Radiative Anderson- Ziegler Radiative effects Eμc 10

Scharff reach 1%

Lindhard- Radiative Minimum losses ionization Nuclear losses Stopping power [MeV cm Without 1 4 5 0.001 0.01 0.1 1 10 100 1000 10 10

1010.1 100 101 100 101 100 [MeV/c] [GeV/c] [TeV/c] Muon momentum

Figure 4.4. Stopping power of muons in copper. At GeV energies the energy loss is dominated by ionization losses and is nearly constant. Above TeV energies, stochastic radiative losses dominate and the energy loss is approximately proportional to the muon energy. Figure from [2]. per cm of relativistic charged-particle track. The total number of photons resulting from the energy deposition of an entire event is hence largely a function of the total track length. Note further, that the continuous energy loss of the muon and its secondary products from the Cherenkov effect has a negligible contribution to the energy losses we will discuss in the next section. Assuming the loss is due entirely to the emission of ∼ 330 photons per cm, the estimate is O(100) keV/m. This should be compared with e.g., the energy loss by a muon in the so-called minimizing region of O(200) MeV/m.

4.3 Energy Loss Mechanisms Energy loss in matter is due to a number of mechanisms of which the two most important, in the energy range of neutrino telescopes, is ionization and radiative losses, see e.g. ﬁgure 4.4. The former involves ionization of atoms, many interactions but with a small energy transfer each, continuously along the trajectory. Radiative losses can be divided into: e+e− pair production, Bremsstrahlung, and inelastic photonuclear interactions. These are generally stochastic in nature with signiﬁcant losses in single interactions. Figure 4.4 shows the stopping power of muons (μ+) in Copper (Cu) as a function of particle momentum. At energies O(GeV) the stopping power is dominated by ionization losses described by the Bethe-Bloch formula and is

80 102

101

E 100 μ,min 0 1TeV Median range [km10 ice] −1 102 103 104 105 106 107 108 109 Muon energy [GeV]

Figure 4.5. Median range of muons in ice as a function of energy. The solid line shows the median range, while the dotted line shows the range where 50% of the muons at least have a kinetic energy above 1 TeV. Figure from [106]. close to constant, see equation 4.7. This is the so-called minimum ionizing region that manifests itself as a continuous energy loss along the track. The Bethe-Bloch equation describes the mean rate of energy loss of moderately relativistic, charged heavy particles [2]: dE − ∝ 1/β2 · ln const · β2γ2 , (4.7) dx where β = v/c (v is the velocity of the particle) and γ = 1/ 1 − β2. The energy loss of TeV muons is instead dominated by radiative losses approximately proportional to the muon energy. We can parametrize this energy loss as [109]: dEμ − = a + bEμ, (4.8) dx where a ≈ 0.26 GeV mwe−1 (meters of water equivalent) correspond to the ionization losses and b ≈ 3.6 · 10−4 mwe−1 corresponds to stochastic radiative losses for ice [110]. Figure 4.5 shows the median range of muons in ice as a function of energy calculated with PROPOSAL (PRopagator with Optimal Precision and Optimized Speed for All Leptons) [106, 111]. For energies relevant in this analysis, 100 GeV to a few TeV, the muon range goes from a few hundred meters up to about 10 kilometers. Electrons lose energy through the same mechanisms as muons, but due to their relatively small mass, the average fractional energy transfer is much

81 Figure 4.6. Illustration of the event topologies in IceCube. The left ﬁgure shows a muon-neutrino interacting inside the instrumented detector volume creating a charged muon, a so-called track event, as well as an incoming muon, either atmospheric or neutrino-induced, coming in from the right, also producing a track-like event in the detector. The right ﬁgure shows an electron antineutrino interacting inside the detector giving rise to a cascade-like event with a leptonic and hadronic shower component. Cascades are also produced by short-lived taus produced in tau-neutrino interactions. larger. Bremsstrahlung starts to dominate already at ∼ 100 MeV [109] in water, while the corresponding number for muons is ∼ 1 TeV [109]. The Bremsstrahlung photons will themselves create e+e− pairs that can loose energy through the same process. This gives rise to a so-called electromagnetic cascade that continues until the photon drops below the pair production threshold.

4.4 Event Topologies The different ﬁnal state leptons produced in CC and NC interactions give rise to three distinct light-patterns in the detector. All neutrino ﬂavors give rise to an initial hadronic shower with an implicit electromagnetic component from neutral pion decays. For CC interactions, a

82 charged lepton is created with matching lepton flavor. Muons can travel kilometers in ice without stopping giving rise to track-like light-patterns, so-called track topologies. The long lever arm is ideal for determination of direction, hence these events are suitable for point-source analyses and are the type of event considered in this thesis. Electrons only travel a short distance in the detector, giving rise to spherically shaped light-patterns, so-called cascades. Tau leptons are very heavy and further decay fast. In 83% [2] of the cases they produce either an electromagnetic or hadronic cascade, while in 17% [2] of the cases they produce a muon giving rise to a track. For sufficiently high energies, a tau can travel long enough to give rise to a so-called double-bang topology: two spatially separated cascades3. At low energies, the difference between the topologies becomes less clear. Further all NC interactions produce hadronic cascades induced by the break up of the nucleon involved. Figure 4.6 illustrates the different topologies, the left figure showing both a starting and incoming muon track event, while the right figure show a typical cascade event, in this case illustrated by an incoming electron antineutrino interacting inside the detector.

Summary In this chapter we reviewed topics important for neutrino detection, in particular for the detection of neutrinos in large-scale neutrino telescopes such as IceCube. Next, we go on to discuss the actual speciﬁcs needed based on a simple estimation of the level of the astrophysical neutrino ﬂux. We also cover, in depth, the IceCube Neutrino Observatory including its main constituent, the Digital Optical Module (DOM).

3While a 10 TeV tau travels less than 1 m, a 1 PeV tau can travel ∼ 50 m before decaying [2].

5. The IceCube Neutrino Observatory

“We are seeing these cosmic neutrinos for the ﬁrst time.” Francis Halzen, 2013

Why do we need cubic-kilometer scale neutrino telescopes? Predictions of astrophysical neutrino ﬂuxes are available for many source. As a benchmark point source ﬂux for a Galactic source we use:

2 −11 −2 −1 Eν dΦν/dEν ∼ 1 × 10 TeV cm s . (5.1)

The total number of neutrinos, Nd, for a detector livetime T, is given by convolving the flux with the detector acceptance, and is evaluated for a given source declination θ: dΦν(Eν) Nd = T · dEν · · Aeff(Eν,θ), (5.2) Eν dEν where Aeff is the so-called effective area of the neutrino telescope. Techni- cally it is the equivalent geometric area over which the detector is 100% effective for passing neutrinos. Essentially we can think about effective area as a parametrization of the detector performance. It is a particularly valuable quantity when comparing the predicted outcome and sensitivity of different experiments for similar physics. Note however, that it does not say anything about the purity and reconstruction quality of an event sample. The flux dΦν/dEν is given in units GeV−1 cm−2 s−1. The effective area for muon-neutrinos includes the probability that the neutrino survive the propagation through the Earth, interacts close to the detector volume, and induces a secondary muon with enough light to trigger the detector [29]. Following the recipe in [29] it can be parametrized as:

thr −σ(Eν)ρNAZ(θ) Aeﬀ(Eν,θ) = A · Pν→μ(Eν,Eμ ) · · e , where A is the geometrically projected surface area of the detector, and cor- thr responds to fraction of muons with energy Eμ that are detected including triggering, successful reconstruction, and event selection cuts. The exponential factor accounts for the absorption of neutrinos along a given path Z(θ)

85 Figure 5.1. The IceCube Lab located at the surface, in the center of the IceTop air shower array. The bottom part of the picture includes an illustration of a muon event lighting up the optical modules of the in-ice array with Cherenkov photons as it traverses the detector. Credit: IceCube Collaboration.

in the Earth and starts to become important for energies above ∼ 50 TeV [112]. σ(Eν) is the total neutrino cross-section, ρ is the target density, and 23 −1 NA ≈ 6.022 × 10 mol is Avogadro’s constant [2]. Pν→μ is the so-called muon probability, the probability that a neutrino with energy Eν will produce thr a muon with at least energy Eμ on a trajectory through the detector. This quantity is a convolution of the differential neutrino cross-section with the −6 0.8 muon range in ice and can be approximated as ∼ 1.3 × 10 Eν for energies in the range between 1 − 103 TeV [84]. Equation 5.2 can be solved analytically given the benchmark ﬂux of neutrinos from equation 5.1, in the range 1 − 103 TeV, assuming A = 1km2 and = 0.1 (i.e., constant). This gives us roughly 1.5 events per year [29]. By instead using the published effective area for IceCube in the Northern Hemisphere (NH) [113], we get ∼ 13 [29] events per year for an unbroken −2 Eν -spectrum on the level of the benchmark ﬂux. If we assume a source model with a spectrum identical in shape to that measured by HESS for the Southern hemisphere (SH) source RX J1713.7-3946 [29], we get about 2.7 [29] events per year using the same effective area from [113] and assuming Φνμ 1/2 Φγ,

86 where Φγ is given by [29]:

Φγ / 2 d 0 (−Eγ/E )1 2 Eγ =Φγe c , (5.3) dE 0 where Φγ is the benchmark flux from equation 5.1 and Ec = 3.7 TeV. Hence we really need cubic-kilometer sized detectors and very long observation time, preferably both, to detect a significant amount of astrophysical neutrinos, in particular if they originate from source in the SH where the effective area in general is lower due to the huge background of atmospheric muons. To be practical, large volumes of detector material have to be natural occurring in forms that are possible to exploit. These include the transparent materials: air, ice, and water. The natural choice for the detection technique is to use Cherenkov light detection with PMTs. At present there are three large neutrino telescopes in the world that uses either ice or water as the detector medium. The largest by far is the cubic- kilometer-sized (∼ 109 m3) IceCube, located in the Southern hemisphere (South Pole, Antartica). ANTARES (Astronomy with a Neutrino Telescope and Abyss environmental Research project) is located in the Northern hemisphere (in the Mediterranean Sea, off the coast of Toulon, France) and consists of 12 strings of optical modules, a total of ∼ 900 PMTs. It has an instrumented volume ∼ 107 m3 and was completed in 2008. ANTARES provide the best limits in the SH at low energies and is a predecessor for the larger Cubic Kilometer Neutrino Telescope (KM3NeT). The Baikal Deep Underwater Neutrino Tele- scope (BDUNT) is located in Lake Baikal, Russia. This observatory is under expansion and the new Baikal Gigaton Volume Detector (Baikal-GVD) will have a projected total volume of ∼ 5 · 108 m3 when completed in 2020 [114]. The construction of IceCube began in 2004 and was completed in 2010. Due to the weather conditions on Antarctica, the IceCube detector deployment work was only possible during a couple of months in the austral summer. IceCube is located roughly one kilometer away from the Amundsen-Scott station and the geographical South Pole. It is a multi-use observatory with a large range of scientific goals, a primary goal is to improve our understanding of the origin of CRs. The IceCube observatory includes the main instrument IceCube, a cubic- kilometer in-ice neutrino detector with a dense central subarray called Deep- Core, a surface air-shower array called IceTop, and the IceCube Lab (ICL) at the glacial surface to which all cables from both IceCube and IceTop are connected. The ICL is depicted in figure 5.1 including an illustration of a muon- like event in the in-ice detector. Further, figure 5.2 shows the whole facility including also The Antarctic Muon And Neutrino Detector Array (AMANDA)- II, the predecessor of IceCube. These are all shown in relation to the Eiffel Tower, illustrating their enormous size. IceTop consists of 162 large tanks with purified water frozen to clear ice in a controlled process to avoid bubbles formation. Each tank contains two optical

87 Figure 5.2. The IceCube Neutrino Observatory. The in-ice neutrino detector (‘IceCube array’), the denser subarray DeepCore, the surface air-shower array Ice- Top, and IceCube Lab centered in the middle of the IceTop array, are all indicated. Also shown is the precursor to IceCube, the AMANDA-II array which was decom- missioned in 2009. Credit: IceCube Collaboration. sensors each, one at high-gain and one at low-gain. IceTop detects atmospheric showers through signals induced by muons, electrons, and photons. These emit Cherenkov radiation as they pass through the tank. IceTop is used for calibration, veto, and CR studies, above a primary energy of ∼ 102 TeV. One of the key measurements so far is that of the anisotropy of the arrival directions of CRs discussed in chapter 3. In the analysis described in chapter 10, we use IceTop as a coincidence shield for in-ice events.

5.1 The IceCube In-Ice Detector IceCube instruments a cubic-kilometer of deep glacial ice and is the world’s largest neutrino telescope. It is located under the ice cap at the geographic South Pole, Antarctica. It consists of 5160 optical sensors arranged in a three- dimensional grid between 1450 and 2450 m beneath the surface [107], see ﬁgure 5.2. The ultra-transparent ice at such depths is ideal for observations of Cherenkov light from charged particles. The in-ice array is sensitive to energies above 100 GeV [115], hence covering everything between atmospheric neutrinos and GZK neutrinos. However,

88 at the highest energies, the flux is so low that no or at most very few events are expected. Further, the effect of absorption of neutrinos at UHE energies limits the possibilities to detect EeV neutrino events. The denser DeepCore subarray enables searches down to 10 GeV [116], important in particular for dark matter and neutrino oscillation analyses. The lower energy bound of IceCube can be lowered further for searches of bursts of neutrinos from supernova explosions, giving rise to a collective increase in the photoelectron (p.e.) count rate. The detector was constructed using a hot water drill making 2.5 km deep holes, about 60 cm wide into which optical modules, so-called DOMs, were lowered on a total of 86 strings [117]. To penetrate the first 50 m of compact snow, a so-called firn drill was used since this low density layer does not hold water [117]. Each string is supported by a cable that provide power and communication with the Data Acquisition System (DAQ) on the surface. For details concerning the construction of IceCube, see [107, 117] and references therein. The DOMs constitute the fundamental building blocks of IceCube [118]. Each of the 5160 DOMs operates as an individual detector and were designed to operate for at least 15 years [107]. Out of the 86 strings, 78 are arranged on a hexagonal grid with an average string spacing of 125 m [119]. These constitute so-called standard IceCube strings. Each of these strings hosts 60 DOMs evenly spaced over a length of 1 kilometer, with an average DOM-to- DOM spacing of about 17 m [117]. The remaining 8 strings also host 60 DOMs each distributed over two regions, one at the bottom of the detector consisting of 50 DOMs with a DOM- to-DOM spacing of about 7 m, and one slightly above the so-called dust layer discussed in section 5.2, consisting of 10 DOMs with a DOM-to-DOM spacing of about 10 m [116]. The latter can be used as a veto against down-going muons penetrating towards the veto. These strings were inserted between the standard strings at the center of IceCube and have an average string spacing of ∼ 55 m. They define, together with the 12 surrounding standard strings, the DeepCore subarray1,2.

5.1.1 Coordinate System The coordinate system used has its origin close to the geometrical center of the in-ice detector. The z-axis points to the surface and z = 0 corresponds to a depth of 1946 m. The y-axis points toward longitude 0◦ and the x-axis lies perpendicular to the plane spanned by the y- and z-axis, altogether deﬁning a

1The actual number of surrounding standard strings included in analyses dedicated to DeepCore, depends on the application. Typically, either 1, 2, or 3 layers of the closest surrounding strings are included. 2Note that most of the DOMs used for these 8 additional strings have PMTs with a higher quantum efﬁciency [116].

89 z

Surface

Source θ

Longitude 0◦

φ y

Figure 5.3. Coordinate system. right-handed system. To indicate a source position in the sky we use spherical coordinates θ ∈ [0,π] (zenith) defined from the direction of the z-axis and φ ∈ [0,2π) (azimuth) defined counter-clockwise starting from the x-axis, see figure 5.3.

5.2 Optical Properties of the Ice at the South Pole To detect the faint Cherenkov light the detector medium needs to be highly transparent and in a dark environment. For this purpose IceCube uses the ultra-transparent glacial ice deep under the surface of the South Pole. The ice consists of layers with varying age, including traces from climatic changes and geological events. The ice just above the bedrock at a depth of about 2800 m is close to 165,000 years old [122]. The ice properties are observed to vary throughout the detector and the overall picture is complex including dust layers, air bubbles, anisotropies, and an overall tilt [121]. To accurately reconstruct the light patterns we need a deep understanding of the medium in which the light propagates. The ice is studied by using Light Emitting Diodes (LEDs) from so-called ﬂasher-boards in the DOMs, see section 5.3. Ice properties were also studied during construction: a so-called dust logger, a combination of camera equipment and lasers was lowered into a few holes, scanning the ice prior to the deployment of strings. Further, a permanent camera, the so-called Sweden

90 Figure 5.4. The effective scattering length λe and absorption length λa (see y-axis on right-hand side) as a function of depth for a wavelength of 400 nm. The gray area represents the tolerated range in a global ﬁt to in-situ data while the black solid line shows the SPICE-Mie [120] ice model, the benchmark model used in this thesis. The AHA model shown is a previous ice model based on separate ﬁts to data for individual pairs of emitters and receivers [121]. Credit: Figure 16 from reference [120].

91 camera, was deployed at the bottom of string 80 at the center of the array. The results revealed the presence of a central core of ice with air bubbles in the hole, over roughly 1/3 of its diameter. This so-called hole ice affects the angular sensitivity of the DOMs, making it more isotropic, due to the short scattering length. The Cherenkov light will be scattered and/or absorbed as it propagates through the ice. In particular, scattered light will arrive later to the DOMs. We define an absorption length λa corresponding to the distance where only a fraction 1/e of the photons remain. We also define a scattering length λs corresponding to the average distance between scatters. To a first order these are considered as functions of depth and wavelength. When the glacier is formed from compressed snow, air is entrapped in bubbles. For ice that has reached depths of 1,300 m [121], the air is under higher pressure and diffuse into the surrounding ice, forming non-scattering air hy- drate crystals, so-called clathrates [121]. Hence, in the region where IceCube is located we are mainly concerned with dust particles, pre-dominantly min- eral dust but also salt, acids, and volcanic soot. We typically record light that has been scattered several times. Further, these scatter-centers in general lead to an anisotropic distribution of the scattered light with a strong preference in the forward direction [121]. Following the definition in [121], we define an effective scattering length λe:

λ λ = s , (5.4) e 1− < cosθ> in terms of the average cosine of the angle θ for single scatters, < cosθ>≈ 0.94 (representing an average over relevant wavelengths) [121]. Similarly we define the effective scattering coefficient be = 1/λe and the absorption coefficient a = 1/λa. The top (bottom) plot of figure 5.4 shows the effective scattering length λe (the absorption length λa) as a function of depth for a wavelength of 400 nm. On the opposite axes we show the corresponding coefficient. The figure shows the presence of several large dust peaks corresponding to cold periods from the last glacial period in the late Pleistocene [122]. In particular, the large dust peak in the middle of the detector correlates to an interglacial period about 65,000 years ago [122]. In this main dust layer, the absorption length is as a small as 20 m, while on average it is closer to 100 m (200 m) in the shallower (deeper) parts of the detector. Further the effective scattering length above the main dust layer is about 25 m while below, where the ice becomes clearer, it is as long as 70 m. For the analysis presented in this thesis we use the SPICE-MIE ice model [120]. It is shown in figure 5.4 as a black solid line and corresponds to a global fit to data from in-situ light sources as described in the beginning of this section. The tolerated range of the global fit is illustrated in the gray area.

92 Figure 5.5. The Digital Optical Module (DOM) can be considered the smallest building block of IceCube and is essentially autonomous. It includes a PMT, digitizer electronics, and calibration LEDs. The DOMs are deployed on 86 strings, with 60 DOMs each, and are lowered into the South Pole ice down kilometer-long holes made using a hot water drill. Credit: Figure 2 from reference [118].

The AHA model shown in black dashed lines is a previous ice model based on separate ﬁts to data for individual pairs of emitters and receivers [121]. The parameters used in the SPICE-MIE ice model are be and a, both evaluated at 400 nm, the temperature δτ for each 10 m layer of ice plus additional parameters [121]. The column of re-frozen ice in the drill hole is modeled by including a modiﬁcation of the effective angular sensitivity of the DOMs as mentioned above.

5.3 The Digital Optical Module Each DOM in IceCube consists of a downwards oriented PMT, digitization electronics (the DOM mainboard), and calibration LEDs. All is housed in a pressure-resistant 13 mm thick glass sphere, see figure 5.5. The glass sphere is sealed with dry nitrogen gas at 0.5 atm and can withstand a pressure of 70 MPa [119]. The material is transparent in the operating range of the PMTs, between 300 nm to 650 nm, with a maximum transparency at 410 nm. The PMT is supported and optically coupled to the glass sphere by a flexible sili- con gel [119]. A penetrator links the interior of the DOM to the cable outside and a so-called mu-metal grid partly shields the PMT against the Earth’s magnetic field [118]. A single twisted-pair of ∼ 1 mm copper conductor carries communications, power, and timing signals to the DOMs from the surface.

93 Once the modules are frozen in, they are operated remotely from the ICL on the surface. Each DOM is an autonomous data acquisition module including full digitization of the signals. IceCube uses a decentralized time-stamping procedure, the waveforms in each DOM receives a local time-stamp from its onboard 20 MHz oscillator. The local time is continuously monitored in relation to a Global Positioning System (GPS) reference time from a master clock at the ICL. The timing resolution, following this procedure, is 2 ns [119]. Note that the limiting factor for reconstructions is dominated by the scattering of photons in the ice. The PMTs are of type HAMAMATSU R7081-02, approximately 25 cm (10 inch) in diameter and contain 10 dynodes giving a total amplification factor of about 107 at the operating voltage3, hence enabling detection of single photons. The quantum efficiency, the probability that a photon striking the photocathode will results in the ejection an electron, is about 25% at 390 nm [119]. The DOMs used for the DeepCore array and a few standard strings have PMTs with a higher quantum efficiency (R7081MOD), about 35% higher than for standard IceCube PMTs [116]. These are denoted HQ-DOMs. The PMT response is affected by both pre-pulses (∼ 1% of the Single Pho- toelectron (SPE) rate [119]), either due to electrons taking shortcuts in the multiplication (avalanche) region or photo-production on the first dynode, late pulses due to inelastic scattering on the first dynode, and so-called after-pulses associated with ionization of residual gas [119]4. Additionally, PMT dark noise is caused by thermal electrons evaporating from the photocathode and/or individual dynodes, ∼ 300 Hz [119]. Further, by including also the noise from radioactive decays in the glass housing, the total noise rate is about ∼ 650 Hz5 [107]. These features are all simulated in the Monte Carlo (MC), see chapter 6. The analog signals from the PMTs are digitized if they are above a discriminator threshold representing 25% of the average signal of one photoelectron. When two neighboring or next-to-neighboring DOMs on the same string both cross the threshold within a 1 μs time window, the signals qualify as a Hard Local Coincidence (HLC). Conversely hit DOMs that do not qualify are defined as having a Soft Local Coincidence (SLC). The HLC are used in the trigger criterions, see section 5.4, to reduce the influence of noise from individual DOMs on the trigger rate. To cover a large time range of signals from the PMT we use two separate digitizing chains including both a fast Analog-to-Digital Converter (fADC) and two Analog Transient Waveform Digitizers (ATWDs). The ATWDs are working in so-called ping-pong mode to avoid dead-time. This means that one

3The voltage is set individually for each DOM and tuned to provide the same gain. It is typically in the range 1100-1500 V. 4Late pulses give rise to photo-electrons delayed tens of ns, while after pulses are typically delayed several μs. 5High-Quantum Efﬁciency DOMs has a total noise rate of about 900 Hz [107].

Figure 5.6. Bird’s eye view of IceCube showing the position of all 86 strings. Gray filled circles indicate standard IceCube strings, while white filled circles indicate strings with HQ-DOMs. Strings marked with a black border constitute the so-called DeepCore fiducial volume used for one of the primary triggers in this analysis. The gray outer area indicates the main veto region as defined in the analysis presented in this thesis. Credit: Illustration by Henric Taavola, modified by including a veto layer, shown in gray. unit is always available to capture signal while the other might be digitizing a previous signal. The ATWDs cover a large dynamical range and have three digitizing channels each, with amplitudes: 16x, 2x and 0.25x6. They collect 128 samples at a rate of 300 MHz resulting in a bin width of 3.3 ns over totally 422 ns [118]. Further, the ATWD chip has a fourth channel used for calibration and monitoring [118]. The fADC collects 256 samples at a rate of 40 MHz resulting in a bin width of 25 ns over totally 6.4 μs, hence a longer window particularly useful for bright events. The DOM mainboard contains a so-called flasherboard with 12 evenly spaced LEDs peaking around 410 nm that are directed outwards at different angles (6 are directed horizontally and 6 are tilted upwards at an angle of 48 degrees. These are used to calibrate the detector and for the in-situ calibrations mentioned in section 5.2. Some of the DOMs have LEDs with different

6The amplitude of the waveform decides what channels should be used.

95 colors, with wavelengths 340 nm, 370 nm, 450 nm, and 505 nm. These are used to obtain a more detailed understanding of the wavelength dependence of the optical properties of the ice. See [119] and [107] and references therein for more details on the calibration of IceCube.

5.4 Data Acquisition System and Triggering Since signals are digitized in the DOM and only digital information is sent to ICL, the following parts of the DAQ is based on processors and software. Each string is connected to a so-called DOMHub at ICL that controls the power and physics data transfer through so-called DOM Readout (DOR) cards7. Digitized signals are sent from each DOM with signal above the discriminator threshold to the surface in data packages called DOMLaunches. They consist of locally generated timestamps, coarse fADC info in case of SLC and the full fADC and available ATWD waveforms in case of HLC [118]. The coarse fADC contains the amplitude of the highest bin and two neighboring bins together with a timestamp [118]. To reduce the total noise rate from the DOMs we apply a coincidence trigger criterion, based on the information in the DOMLaunches. The leading trigger condition, Simple Majority Trigger (SMT)-8, is formed when at least 8 DOMs has HLCs pulses within a 5 μs time window. In the analysis presented in this thesis we also use events from a trigger dedicated to catching almost vertical events, the so-called StringTrigger, demanding HLC from 5 out of 7 adjacent DOMs on the same string within 1 μs. Further, we use a trigger with a lower effective energy threshold active in the so-called DeepCore fiducial volume.It consists of the lowest 50 DOMs on the 6 DeepCore strings as well as the lowest 22 DOMs on the 14 surrounding standard strings, and requires 3 HLC DOMs within 2.5 μs [116]. The strings involved are marked with black borders in figure 5.6. Each trigger in the system is considered globally when forming the so- called event trigger hierarchy. This consists of all DOMLaunches within the time window defined by merging all overlapping triggers plus an additional 10 μs readout window. The total trigger rate considered is ∼ 2,500 Hz, but is influenced by atmospheric conditions and seasonal variations, an effect of ∼ 10%. The online filtering system, discussed in section 5.5, reduces the overall rate by about a factor of 10.

7Control of DOM operation, ﬁrmware updates, time synchronization, restarts, High Voltage (HV) calibration, ﬂashed operation, etc., are also handled by the DOMHubs over the DOR cards.

96 5.5 Processing and Filtering Each IceCube event is processed in the ICL, so-called online processing, where the raw waveforms are calibrated, baselines are subtracted, and so-called droop correction is made8. This is done individually for each DOM using baselines measured in in-situ calibration data. SPE pulses are extracted from the waveforms using an iterative unfolding algorithm with pre-defined templates measured in the laboratory. The extracted pulses consists of the leading edge time9 and charge, and define a so-called pulse-series for each event. A hit in IceCube can be referred to as either a DOMLaunch, i.e., when a DOM detects one or more photons that cross the discriminator threshold, or a pulse extracted from the waveform using the feature extraction mentioned above. The definition used for a particular case will be made clear from the context. The SLC pulses are particularly useful to improve the reconstruction of low-energy muon tracks by increasing the number of hits and the lever arm between first and last hit in time, and to get an additional efficiency on vetoing incoming background tracks. However, the majority of the SLC pulses are due to pure noise. Therefore, the pulse-series needs thorough cleaning before they can be used for reconstruction of event variables. The different cleaning algorithms are described in detail in the beginning of chapter 7. Only keeping HLC pulses removes almost 30% of the hits connected to particles traversing the detector. First reconstructions of direction and energy are done online and made available for the filtering scheme that defines the samples used for analyses. The filtering used for the data presented in this thesis is covered in depth in chapter 8. Data that pass at least one filter is sent north via satellite for further processing (so-called offline processing). This is typically customized for each analysis. The offline processing and events selection for the sample used in this thesis is presented in chapter 10.

Summary In this chapter we introduced the detectors used to collect data for the analysis presented in this thesis. The IceCube in-ice detector is the world’s largest neutrino detector and consists of over 5,000 optical modules collecting Cherenkov radiation in the ice. In the next chapter we will discuss the event simulations used to deﬁne the astrophysical signal.

8The tail of the waveform undershoot due to saturation in a transformer between the HV supply and the PMT. This only effected the ﬁrst part of the DOMs, the transformer was exchanged in the latter part of the DOM production. 9Deﬁned as the intersection between the baseline and the tangent of the segment of fastest ascent.

6. Event Simulation

“If a little dreaming is dangerous, the cure for it is not to dream less but to dream more, to dream all the time.” Marcel Proust

Monte Carlo (MC) simulations are an essential tool to verify the detector response and efﬁciency. Further, in many analyses, e.g., searches for a diffuse ﬂux of astrophysical neutrinos, MC is used to determine the level of background and is hence critically important. In the analysis presented in this thesis we search for a clustering of neutrino events and use scrambled experimental data as background. However, a simulation of the background is still important to verify the simulation chain since large parts of it is also used for the signal simulation of astrophysical neutrinos. In each step of the analysis, we carefully investigate the agreement between the measured data and the simulated background. In particular, we avoid using variables or regions of variables where large discrepancies are found. In this chapter we present the simulation chain including event generation, propagation, and detector response. Further, we discuss how to weight generated events into a desired spectrum which is different from the generated spectrum.

6.1 The IceCube Simulation Chain The simulation chain used in IceCube is encoded in the software framework IceSim that mainly consists of three parts: particle generation, propagation, and detector simulation (detection), see figure 6.1. Starting from the top of the figure, following the arrow, events of a specified type are generated with an energy, direction, and position relative to the detector. We simulate atmospheric muons and neutrinos resulting from air showers of primary CRs but also so- called signal neutrinos of astrophysical nature. Each event is injected in a region close to IceCube to ensure that it has a chance to trigger the detector. The primary and secondary particles are propagated through the Earth’s atmosphere, rock and ice including energy losses and further particle generation

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Figure 6.1. IceCube simulation chain. Following the arrow, we start by generating particle of a given type, energy, direction, and position relative to the detector. The primaries and their secondary particles are propagated through the atmosphere, matter and ice including energy losses and further particle production. The ﬁnal step includes the detector response with hit reconstruction, PMT simulation, etc.

from interactions, see section 4.3. Particles that travel faster than the speed of light in the ice give rise to Cherenkov photons, see section 4.2. These are also propagated. The ﬁnal step includes the full detector response and is simulated for each event. Note that we only keep triggered events. Particle generation and detection is optimized to result in large statistics in a given desired energy interval, i.e., the simulations are biased to oversample interesting events. To be able to change the generation spectrum a posteriori each event is given a weight, a so-called OneWeight, that takes all simulation steps into account. Using these weights, the sample can be re-weighted to correspond to any desired particle ﬂux. This is very convenient, since it allows generic simulations, useful for many different analyses, to be made with very large statistics. For more details, see section 6.2.

100 6.1.1 Event Generation For this analysis we used two different event generators: CORSIKA (COs- mic Ray SImulations for KAscade) [123] to generate extensive air showers and NuGen (Neutrino-Generator) [102] to generate neutrinos including their propagation through Earth. Both are generated using IceCube simulation soft- ware1, and are further described in the next set of paragraphs.

Atmospheric Muon Background Downgoing atmospheric muons created in extensive air showers constitute the largest background for this analysis. These can enter through the veto regions of the detector without leaving a trace and hence effectively mimic neutrino- induced muons truly starting inside the instrumented volume. Primary nuclei in the range from protons to iron are injected at the top of the Earth’s atmosphere creating air showers as a result of interactions with air nuclei. Each of these particles is tracked in the CORSIKA framework that includes both single and coincident air showers as well as hadronic interactions described by SIBYLL (an event generator for simulation of high-energy CR cascades) [124]. Secondary particles are tracked through the atmosphere until they interact with air nuclei, decay in the case of unstable secondaries, or go below a pre-set energy threshold. Since muons are the only charged particle that can reach the in-ice detector the rest of the shower is manually stopped as it reaches the surface. In figure 6.2 we show the results of CORSIKA simulations for various primary nuclei and energies. These plots are taken from [125]. The vertical axis represents the first interaction height at 30 km (top) and surface at 0 km (bottom). The events used in this thesis are generated with a so-called 5-component model where 5 different primary nuclei (H, He, N, Al, and Fe) are injected according to specified individual generation spectra, see table 10.2 for details. For the analysis, we re-weight these events to a polygonato model according to Hörandel [126] where the primary CR flux is treated as a superposition of fluxes from protons to uranium nuclei, and the individual cutoffs at the knee are rigidity-dependent, resulting in ∼ E−2.7. Note that this model does not include an extragalactic component and hence does not describe UHE CR.

Neutrinos Neutrinos are generated with NuGen that is based on the ANIS (All Neutrino Interaction Simulation) event generator [102]. The events are injected at the surface of the Earth pointing towards the detector with an isotropic distribution as seen from IceCube (isotropic in local coordinates cosθ and φ). The neutrinos are propagated through the Earth considering both CC and NC interactions and assuming the Preliminary Reference Earth Model (PREM) [127].

1Software release V03-03-02

101 (a) Proton 1 TeV (b) Proton 10 TeV (c) Iron 1 TeV (d) Iron 10 TeV

Figure 6.2. Air-showers simulated using CORSIKA conﬁgured with different primary nuclei and energy. The vertical shower axis represents the ﬁrst interaction height at 30 km (top) and surface at 0 km (bottom). The horizontal shower axis shows ±5km around the shower core. The plots only show tracks above 0.1 MeV for e−, e+, and γ (red lines), and above 0.1 GeV for muons (green lines) and hadrons (blue lines). Credit: [125].

One flavor (νe, νμ,orντ) is chosen for the entire simulation run including a 50% probability for the particle to be ν orν ¯. NuGen is configured with parton function Probability Density Functions (PDFs) from CTEQ5 [104] using cross-section from [103], and in principle assumes DIS only. Technically it can simulate neutrinos with energies in the range from 10 GeV to 109 GeV, the region where DIS is dominant, see figure 4.2 and the discussion in section 4.1. Below 100 GeV, where other processes become important, IceCube uses a generator called GENIE (Generates Events for Neutrino Interaction Experiments) [128] that incorporates the dominant scattering mechanisms from several MeV to several hundred GeV [128]. The events are generated with an E−2 spectrum. To arrive at a sample representing astrophysical neutrinos the events are re-weighted to various power law spectra some including exponential cut-offs at TeV-scale. The spectra considered are presented in detail in chapter 10. The conventional flux component of the atmospheric neutrino background is modeled by re-weighting the events to the Honda flux model2 [129]. The prompt flux component is not modeled in this thesis. It is predicted to start to dominate at ∼ 1 PeV (see section 3.4 and references therein) and does not need to be considered in this analysis, focusing on energies ≤ 10 TeV. In fact, the

2The Honda model assumes an atmosphere that is a climatological average referred to as the U.S. Standard Atmosphere 1976

102 plots in ﬁgure 10.23 clearly display a transition in experimental data between an atmospheric muon and atmospheric neutrino component, the latter well described by conventional atmospheric muon-neutrinos only.

6.1.2 Propagation All relevant particles, primary and secondary, are propagated through the ice. This includes both charged leptons and photons.

Lepton propagation The propagation of charged particles through ice and rock is done using a software package called PROPOSAL (PRopagator with Optimal Precision and Optimized Speed for All Leptons) which is a C++ re-implementation of the java program MMC (Muon Monte Carlo) [110]. The software accounts for both stochastic and continuous energy losses, see section 4.3. It uses a homo- geneous ice model with properties from [2, 130]. For further details about the parametrization of energy losses and structure of the code see [110].

Photon propagation Photons are propagated using PPC (Photon Propagation Code) [131], a direct photon propagation code using Graphical Processing Units (GPUs) and splined tables of local ice properties from the conﬁgured ice model, in this analysis SPICE-Mie [120]. This direct propagation is very computer intensive and unpractical for the creation of PDFs of the arrival times of photons to be used in the event reconstructions described in detail in chapter 7. For this purpose, we use look-up tables created using a faster, Central Processing Unit (CPU) based, software called Photonics [132]. It propagates photons from an injection point to the arrival at the DOMs using a statistical approach rather than following individual photons. The Photonics tables consist of PDFs of the arrival times of photons for different depths and various light sources, photons from starting, stopping, and through-going muons, as well as from electromagnetic cascades. The actual number of expected photons used in the reconstructions is sampled from a Poisson distribution with the mean corresponding to the tabulated values. Fur- ther, Photonics uses tabulated values of the local ice properties: the scattering and absorption are parametrized as functions of wavelength and depth. The general agreement between PPC and Photonics is good, in particular at energies above ∼ 100 GeV, i.e. the agreement is good in the full energy range considered in this analysis. For lower energies, linear interpolation between bins leads to a systematic overestimation of the expected number of photons, i.e., Photonics overestimates the light yield, in particular for light emitters far from the receiving DOM.

103 6.1.3 Detector Response The simulation of the detector’s response to Cherenkov photons includes several steps: PMT output, detector electronics, DOM logic and triggering. The PMT simulation includes dark noise, pre-pulses and after-pulses generated using a so-called noise-generator. Further, we also include thermal noise according to a Poisson distribution (uncorrelated noise for each DOM). The mainboard response is simulated including the digitizing steps of the ATWDs and fADC. Waveforms are generated in an inverse procedure compared to the unfolding done for the feature extraction, described in section 5.5. DOMLaunches are formed and sent to the trigger simulation algorithm including the local coincidence logic assigning ﬂags for HLC and SLC. Pulses are extracted from the DOMLaunches using a feature extraction similar to the one used for experimental data.

DOM Efficiency DOM efficiency is a collective term describing a number of local DOM properties related to the light collection efficiency, such as properties of local hole ice, transmittance of the glass housing and optical gel, the quantum efficiency of individual PMTs, and the PMT threshold. While some of these properties can be calibrated in the laboratory prior to deployment in the ice [119], others can only be inferred through in situ calibrations (see section 5.3) of the DOMs after deployment. The DOM efficiency level is used as a handle in simulations and can be tuned to fit calibration data. Deviations from the baseline is used as a tool to evaluate the systematic uncertainty of the analysis, see section 10.8.

6.2 Neutrino Event Weighting In the beginning of chapter 5 we discussed the expected event rate in kilometer- sized neutrino detectors, see equation 5.2, where the expected number of events is given as a convolution of the neutrino ﬂux with the effective area. The latter can simplistically be calculated as:

Nd Aeff = Agen · , (6.1) Ngen where Agen is the generation area inside which we generated a total of Ngen events. Nd is the number of detected events in the detector at the level of the event selection where Aeff is evaluated. Our simulations are biased in many different ways to make them more efficient, in particular to save computing time. E.g. we force the neutrinos to interact in the vicinity of IceCube, so that the secondaries will trigger the detector, and we generate events according to a spectrum E−γ some times different from the desired one. Equation 6.1 does not take any of these factors

104 into account and hence needs to be modified to accurately represent the effective area. The total number of generated particles, Ngen, corresponds to Ngen unbiased particles. In a bin ( j,k) in energy and zenith angle, respectively, this is defined as: E + j 1 E−γ dE ( j,k) Ngen E j 2π · [cosθk − cosθk+1] Ngen = · · , (6.2) ( j,k) Emax Ω P E−γ dE int Emin ( j,k) where Pint is the neutrino propagation and interaction probability for bin ( j,k), Emin and Emax are the minimum and maximum generation energy, respectively, γ is the spectral index of the generation spectrum, and Ω is the solid angle from which events were generated. Replacing Ngen with Ngen in equation 6.1 gives us the effective area for each event i (among Nd), in a bin ( j,k) in energy and zenith angle, respectively: Emax −γ , Agen , E E dE Ω A( j k)(E,θ) = · P( j k) · min · eff int E + π · θ − θ Ngen j 1 E−γ dE 2 [cos k cos k+1] E j (6.3) OneWeight = i , Ngen · Ωk · (E j+1 − E j) ej+1 −γ −γ where E dE ≈ E · (E j+1 − E j), Ωk = 2π · [cosθk − cosθk+1], and ej j ( j,k) P Emax = int · −γ · · Ω. OneWeighti −γ E dE Agen (6.4) Ei Emin ‘OneWeight’ is given in the units GeV cm2 sr1. The effective area for an event sample as function of energy is then formed by a weighted sum in each energy bin, where each event i is weighted according to equation 6.3. A similar construction can be made for the so-called effective volume, i.e., the effective volume is the equivalent geometric volume over which the detector is 100% effective for interactions occurring inside. This quantity is particularly interesting for an analysis of particles starting inside a detector, since it also take into account the finite length of the tracks. Additionally, for a given neutrino flux model dΦν(Eν)/dEν, we can calculate the number of expected events Nd, see equation 5.2, by re-weighting the simulation using the individual event weights ‘OneWeight’, introduced in equation 6.4. The detector efficiency for a neutrino with a given energy and direction is included in these weights, and to represent the desired spectral distribution, these only have to be combined with the right amplitudes. The number of expected events is therefore calculated as: Nd = T · wi, (6.5)

105 where Φ OneWeighti d ν(Eν) wi = · , (6.6) Ngen dEν T is the integrated livetime and the sum runs over all remaining events at the level where Nd is evaluated. The ﬂux dΦν(Eν)/dEν is given in the units GeV−1 cm−2 s−1 sr−1.

Summary In this chapter we discussed the IceCube simulation chain used to produce the samples of atmospheric and astrophysical neutrinos, as well as atmospheric muons, for the analysis presented in chapter 10. In the next chapter we will describe the reconstructions and methods used to determine the interaction vertex, incoming direction, and energy for each event. These quantities are the foundation of the point source likelihood introduced in chapter 9.

106 7. Reconstruction Techniques

“Nothing happens until something moves.” Albert Einstein

To estimate the characteristics of an event such as its direction, energy and type (lepton ﬂavor, topology, interaction, etc.) we perform several reconstructions based on the hit1 pattern in the detector using e.g. the time, position, and charge of the individual pulses. These reconstructions are based on noise cleaned pulse-series, as described in section 7.1.

7.1 Noise Cleaning The noise cleaning tries to identify pulses related to a potential particle in the detector and remove pulses created by noise. This is typically tailored for specific applications: we use different cleaning algorithms to reconstruct the neutrino interaction vertex and direction, respectively. Angular reconstructions are quite sensitive to noise hits and therefore require rather strict cleaning. On the other hand, semi-isolated hits of low quality can be crucial for determining whether a track starts within the detector or came from outside. Through- going tracks may sometimes ‘leak in’, with very few hits recorded in the outer parts of the detector array. In order to make a correct event classification those remote hits should definitely not be removed by cleaning. The pulse-series used for the reconstruction of the neutrino interaction vertex described in section 7.4 is cleaned in two steps, first by applying a so-called Time Window Cleaning (TWC), rejecting pulses outside the range [-4, 6] μs relative to the first trigger window in time. Causality information of the pulses is used in the second step consisting of a so-called Classic RT-Cleaning (CRT) algorithm where all pulses (HLC and SLC) within a radius (R) of 150 m and a time (T) of 1 μs from each other are kept while pulses not falling into this

1Note that in this chapter we will use the word pulse and hit interchangeably. They will both refer to a pulse as the entity extracted using the pulse extraction processes discussed in section 5.5.

107 category, are rejected. This cleaning keeps roughly 96% of the physics hits and about 18% of the noise hits. The pulse-series resulting from this cleaning will be denoted RTTWOfflinePulsesFR. For the angular reconstructions we instead start by applying a so-called Seeded RT-Cleaning (SRT) algorithm which is inspired by the CRT algorithm. It initially only considers an already quite clean subset of pulses, a seed consisting of a so-called core of HLC hits. This core consists of those HLC hits which fulfill a stronger version of the RT criterion, namely that have not just one but at least two other HLC hits within the RT range. Starting from the core, pulses (HLC and SLC) within the RT-conditions from any pulse in the seed set are added to the seed set. This adding procedure is iterated two more times. After this we apply a TWC rejecting pulses outside the range [-4, 10] μs relative to the first trigger window. This cleaning is slightly stricter than the cleaning used to reconstruct the vertex, it keeps roughly 92% of the physics hits, while rejecting all but 3% of the noise hits. The pulse-series resulting from this cleaning will be denoted TWSRTOfflinePulses. The upper row of figure 7.1 shows a simulated muon-neutrino event before (left) and after (right) the cleaning process used for the angular reconstructions.

7.2 Particle Direction Precise determination of the direction of an event is very important in a point source analysis since the algorithm, described in chapter 9, is looking for a clustering of event directions with respect to an almost isotropic background. We use a number of different algorithms to determine the direction, varying both in accuracy and computing time. The goal of the track reconstruction is to estimate the most likely direction and position of the muon in the detector, assuming that most of the recorded pulses in the event were indeed due to Che- renkov light emitted by a muon. The timing and location of the participating DOMs provide the most important handle on the determination of these parameters. Note that energy is kept fixed during the directional reconstructions and considered separately in section 7.5. A simpler first guess algorithm is used as starting points, seed, to more complex ones in a consecutive chain of reconstructions. The more advanced and time-consuming algorithms can only be applied at a high level of the analysis, where the number of events has been reduced significantly. In many branches of astronomy they use a so-called standard candle,a celestial object of known location and brightness, to calibrate their equipment. See e.g., the discussion in 3.6.1. Since such a localized astrophysical neutrino source has yet to be discovered we cannot calibrate the angular reconstruction and pointing capabilities of the detector directly. However, studies of the so- called cosmic ray Moon shadow as predicted by Clark already in 1957 [133]

108 Figure 7.1. Illustration of noise cleaning and reconstruction in IceCube. All of the panels illustrate the same simulated muon-neutrino event with interaction inside the instrumented volume. The color indicates the time of the event (from red to blue) and is adjusted to ﬁt the timing of the cleaned event shown in the upper right panel. The applied cleaning corresponds to the algorithms used for the angular reconstructions. The upper left panel shows the uncleaned event. The size of the spheres is approximately proportional to the charge observed. The lower panels show the true muon track in gray, with a matching dot indicating the neutrino interaction point. The left illustration also displays the ﬁrst guess, so-called Improved LineFit, reconstruction discussed in section 7.2.1 (in red). The lower right plot shows the full likelihood reconstruction denoted SPEFit2 in blue, including an illustration of the Cherenkov-cone hypothesis. This event was successfully reconstructed by SPEFit2 and constitutes a prime example of a typical starting track-like event.

109 can be used as a first approximation. Figure 7.2 shows the observed position of the Moon shadow, denoted μ, measured using one year of data when IceCube operated in a partial configuration with 59 strings prior to completion [134]. The horizontal axis shows the difference in right ascension (αμ −αMoon)·cosδμ relative to the Moon position, while the vertical axis shows the corresponding difference in declination, δμ − δMoon. The position of the observed shadow agrees with the position of the Moon with a high statistical significance. The conclusion from this study is that the systematic uncertainty of the absolute pointing is smaller than ∼ 0.2◦. In this thesis we focus on the detection of neutrino-induced muons. These are detectable and distinguishable from cascade type events above an energy of ∼ 100 GeV. This limit is primarily set by the geometrical parameters of the IceCube detector. A muon in the minimum ionizing energy range can travel about 5 m per GeV in ice, see figure 4.4. With a horizontal string spacing of 125 m and a vertical DOM-to-DOM spacing of 17 m, this implies a minimum neutrino energy of about 50 − 100 GeV if the final state muon is to be reconstructed. To further distinguish muon tracks from cascades, a slightly higher energy is required.

0.4

0.2 ] ° [

Moon 0 δ - μ δ -0.2 1σ 2σ -0.4 3σ

-0.4 -0.2 0 0.2 0.4 α α δ ° ( μ - Moon) cos( μ) [ ]

Figure 7.2. The cosmic ray Moon shadow as measured by IceCube [134]. The black dot indicates the best-fit position of the shadow from a maximum-likelihood analysis, while the white circle show the position after including effects of geomagnetic deflection. The contour illustrates the uncertainty of the position at the 1, 2, and 3 σ level. Reprinted figure 9 with permission from [134]. Copyright 2014 by the American Physical Society.

110 Neutrino-induced muons, although highly boosted in the forward direction, will be produced with an angle relative to the direction of the primary neutrino. ◦ . The mean scattering angle can be approximated with ψνμ≈0.7 /(Eν/TeV)0 7 [62]. For the energy range considered in this analysis this means the angle is roughly between 0.1◦ and 3◦. This constitutes a minimum kinetic bound to the reconstruction capability. However, the reconstructed muon direction is still the best available proxy for the neutrino arrival direction, and will be used as such for the remainder of this thesis.

7.2.1 First Guess The Improved LineFit algorithm [135] is used as a ﬁrst guess track reconstruction. It is an approximative hypothesis that ignores the geometry of the Cherenkov cone as well as the detector medium, i.e., photons travel on straight lines without scattering or absorption in the ice. Instead, every hit is used as an independent measurement of the position of a straight moving particle at the time of the hit. The algorithm minimizes the distance between the moving particle and the hit DOMs for each event through a least-square ﬁt [136]:

N 2 2 χ = (ri −r0 −vLineFit · (ti − t0)) , (7.1) i=1 where N is the number of pulses, ri and ti is the DOM position and time of each pulse (leading edge time), vLineFit is the muon track velocity as it passes through a point r0 at an arbitrarily chosen time t0. The χ2 is modified to be robust against outliers by applying a so-called Hu- ber penalty function. Further, the Improved LineFit algorithm also filters out hits likely to be scattered by studying the arrival times of pulses in neighboring DOMs. The modified χ2 can be solved analytically and is therefore very fast with a resulting median angular resolution of about a few degrees. The drawback is the simple description that does not take into account the full complexity of the Cherenkov cone or the scattering and absorption effects in the ice. In fact, photons can move around for over 1 μs before being detected [135], corresponding to a muon traveling ∼ 300 m. The magnitude of the resulting velocity vector, the so-called LineFit speed, is close to the speed of light for track-like events, while it is close to zero for cascade-like events due to the spherically symmetric hit pattern. The LineFit speed and the individual components of the LineFit velocity vector all constitute variables used in the offline event selection presented in chapter 10.

111 Figure 7.3. Deﬁnition of variables used to calculate the time residuals of each event.

7.2.2 Likelihood-Based Reconstructions The advanced directional reconstructions use a maximum-likelihood algorithm2 where the hit pattern is assumed to be caused by a relativistic (β = 1) infinite muon track traversing the detector, causing emission of Cherenkov light. The likelihoods are maximized numerically using Minuit [137] and the solution depends on the expected photon arrival times at the DOMs and the optical properties of ice. The infinite track is defined by a = (r0, p,t0) where r0 = (x0,y0, x0) corresponds to an arbitrary point along the track, t0 is the time at r0, and p = (θ,φ) defines the incoming direction of the track in spherical coordinates, see the definition of the coordinate system in section 5.1.1. The experimental data for each event consists of a pulse-series with DOM positions ri and corresponding leading edge times ti. We introduce the so- called residual time tres,i for each pulse i. It is defined as the time difference between the observed arrival time ti and the hypothetical arrival time, tgeo,i,ofa so-called direct photon, emitted under the Cherenkov angle, traveling straight to the receiving DOM at position ri without scattering or absorption:

tres,i ≡ ti − tgeo,i, (7.2) where tgeo,i is defined using the geometrical construction illustrated in figure 7.3. p · (ri −r0) + d tanθc t , = t + , (7.3) geo i 0 c where the Cherenkov angle θc is the fixed angle under which the Cherenkov photons are emitted along the track3 and d is the closest distance from the track to the DOM, i.e., unscattered Cherenkov photons are expected to arrive

2For practical reasons we often equivalently perform a minimization on the −logL instead of maximizing L. 3For the sake of clarity we neglect the effect of the small difference between group velocity and phase velocity, see section 4.2.

112 to a DOM i located at ri at time tgeo,i, see ﬁgure 7.3. That is only true for photons emitted from the Cherenkov emission point (see gray circle in ﬁgure 7.3). Photons which are emitted before or after that point and somehow land at ri will arrive later than tgeo,i, even if they travel in a straight line. The strongest effect on the photon arrival times tres,i is scattering and absorption in the ice but also the orientation of the DOM axis relative to the track. The unknown track parameters of a are determined from experimental data by minimizing the expression [136]:

N − logL(tres|a) = − log p(tres,i|a), (7.4) i where L is the likelihood function and p(tres,i|a) is the PDF representing the probability of observing the experimentally measured values tres,i at ri given a. Equation 7.4 is correctly defined as long as p(tres,i,ri) is provided and the sum runs over all detected pulses. Typically however, we approximate this relation by only using the time of the first recorded pulse on each DOM. Indeed the first p.e. is likely to be the least scattered and hence carry most information about the true track direction, i.e., we use the so-called SPE PDF, p1(tres,i), describing the photon arrival time of a detected p.e. in the case when only one photon is observed at each DOM. This approximation is sufficient for events with low energies, but at higher energies, where the light output is large enough to produce several direct or semi-direct photons in each DOM, the likelihood becomes distorted. This is due to the fact that the arrival time distribution for an arbitrary photon is much wider than the distribution for the first photon. The latter is more strongly peaked at smaller time residuals than the former. The Multi Photoelectron (MPE) PDF modifies the SPE PDF to account for the total charge observed in each DOM. The arrival time distribution of the first out of N photons is [136]:

∞ (N−1) 1 = · · pN(tres,i) N p1(tres,i) p1(t) dt (7.5) tres,i

The PDF p1 is determined with simulations of photon propagation in the medium using two different approaches: an approximative description using the analytic Pandel function [138] as described in [136] and splined look-up tables created using Photonics (see section 6.1.2). The MPE description is very important for high-energy analyses, but it will only give a modest improvement over SPE in the low-energy events typical for the analysis presented in this thesis. We deﬁne direct hits by considering different classes of pulses based on their individual tres value, see table 7.1. Variables based on hits of a particular class are used in the ofﬂine event selection described in chapter 10.

113 0.0030 d 0.0025 Perpendicular distance [m] 50 200 ]

1 0.0020 − 100 250 0.0015 150 0.0010 PDF [ns 0.0005 0.0000 0 500 1000 1500 2000 2500 3000 3500 4000 tres [ns]

Figure 7.4. Pandel time-residual PDFs for an inﬁnite track hypothesis. The different lines show the distribution for various values of the perpendicular distance d. The distributions are smoothed using a Gaussian with a width of ∼ 15 ns set to match the jitter time of the PMT [139]. Figure adapted from [106].

The Pandel Distribution The probability to detect a photon with a given tres is given by [136]: −(d/λ) (d/λ−1) c 1 τ · t − t · 1 + medium + d p(t ) ≡ res · e res τ λa λa , (7.6) res N(d) Γ(d/λ)

−d/λ − /λ τ · c N(d) = e d a · 1 + medium , (7.7) λa where d is the perpendicular distance between the track and the DOM (indicated in ﬁgure 7.3), λa is the average absorption length, cmedium = c/n is the

Table 7.1. Deﬁnition of classes of direct hits used to construct several event selection variables that is applied in chapter 10. The classes are based on the tres distribution deﬁned in equation 7.2.

Class tres interval [ns] A [-15, 15] B [-15, 25] C [-15, 75] D [-15, 125]

114 speed of light in ice, and λ and τ are parameters determined empirically by MC simulations. These PDFs parametrize the average characteristics of the arrival times of photons and are further modified to include the effects of PMT jitter [139] and dark noise. Although the function is only directly dependent on the so-called source-receiver distance d, there is an implicit dependence on the parameters a through the definition of tres. Figure 7.4 shows the Pandel PDFs for an infinite track hypothesis at various source-receiver distances as a function of tres.

Spline Parametrization A more accurate description of the photon arrival PDFs can be achieved by using the look-up tables created with the Photonics software as described in section 6.1.2. These tables contain the expected number of photons (at a distance away from the track), and the PDF for the time residual at which each of these photons arrives. The numbers in this table have been obtained from extensive photon transport simulations using depth dependent optical properties.

7.2.3 Reconstructions and Performance The minimization of equation 7.4 yields a set of best-fit parameters for a hy- pothesisa ˆ. The so-called reduced log-likelihood rlogl is introduced as a quality parameter of the reconstruction, and corresponds to the reduced χ2 for a Gaussian probability distribution. It is defined as the minimum value of the negative log-likelihood, −logL, divided by the number of degrees of freedom (the number of data points (hits) minus the number of free parameters in the fit). For the track reconstructions we maximize the likelihood numerically to find the best-fit five parameter solution consisting of the vertex point (x ˆ0,yˆ0,zˆ0), and direction (θ,ˆ φˆ). The numerical minimizer finds its result in an iterative manner. The likelihood function and its gradient are evaluated in a few phase space points. New phase space points are selected based on the results of the first set, hopefully closer to the minimum. The likelihood function and its gradient are evaluated for these new phase space points, and new points are selected based on the results, etc. These minimizer-iterations are performed, on average 100 − 200 times (maximally 10,000 times), in order to approach the minimum within the configured tolerance. The likelihood space can be quite complex and contain several local minima. The minimizer will typically land in the one that is the easiest to reach by just rolling downhill in the 5-dimensional −logL landscape. To avoid getting stuck in such local minima, each reconstruction is performed with several so-called iterations. The seed to each iteration is partly based on the previous successful iteration, but rotated around its vertex position by picking pseudo- random directions (θ,φ) on a unit sphere. The vertex point is allowed to be

115 shifted along the track both before and after the rotation. It is typically moved to the position of the smallest perpendicular distance to the so-called Center of Gravity (COG) where the hits are spatially accumulated. The COG is de- ﬁned as the charge weighted mean of DOM positions. Further, the time at the vertex is transformed accordingly. The goal of these shifts is to modify the tres distribution to better agree with a Cherenkov model (the minimizer has a hard time to get unstuck if given a seed with too many negative time residuals).

SPEFit2 and MPEFit One of the main reconstructions used in the analysis is denoted SPEFit2, an iterative fit with a single iteration, performed according to the prescription above. It is constructed using the SPE PDFs and the approximative Pandel function. The result from the Improved LineFit reconstruction is used as seed. The reconstruction is used in the online data pre-selection described in chapter 8 and when forming the veto criteria for the offline event selection described in chapter 10. MPEFit is an iterative fit using the MPE function in equation 7.5, and is based on the Pandel function just like SPEFit2. It is constructed with a single fit based on the SPEFit2 as input seed.

MPEFitSpline The MPEFitSpline reconstruction is an infinite track reconstruction using MPE PDFs, see equation 7.5, now based on splined tables of the arrival times of the photons. It is used in the final likelihood analysis to search for clustering of signal-like events. MPEFit is used as a seed to this reconstruction. Figure 7.5 shows the likelihood space of the MPEFitSpline reconstruction for six simulated muon-neutrino events at the final analysis level, see section 10.5. The plot in figure 7.6 shows the median likelihood space of simulated events at the final analysis level. Each bin in the represents the weighted median of lnL using 282 events, weighted to a neutrino spectrum proportional to −2 −Eν/10 TeV Eν e .

Performance The performance of the different reconstructions is evaluated using the so- called space angle ψ defined as the opening angle between two directional vectors on a three-dimensional sphere. Using the spherical coordinates defined in section 5.1.1 it is defined as:

cosψ = cosθ1 cosθ2 + sinθ1 sinθ2 cos(φ1 − φ2), (7.8) where index 1,2 refers to the two vectors compared. Figure 7.7 shows the space angle distributions for simulated neutrino events at ﬁnal level of the event selection for various reconstructions. All events used in the calculations are truly starting inside the instrumented detector volume, using criterion p = 0.8 and z ≤ 300 deﬁned in chapter 8. Further, they are truly

116 Figure 7.5. These figures show examples of the highly complex likelihood space of the MPEFitSpline directional reconstruction for six simulated muon-neutrino events. They are shown in local coordinates (θ, φ) at the final analysis level. The primary neutrino energy is indicted in the upper left corners of each plot. The colors represent the value of lnL and the intersection of the dotted black lines shows the reconstructed best-fit direction. When the true muon position is located within the plot boundaries it is illustrated with a white circle.

117 Figure 7.6. The figures illustrates the median likelihood space lnL of the MPEFit- Spline directional reconstruction. It is shown in local coordinates (θ, φ) for 282 simulated muon-neutrino events at final level, weighted to a neutrino spectrum proportional −2 −Eν/10 TeV to Eν e spectrum. The best-fit point of each event was moved to the coordinates (0,0). down-going (i.e., originate from the SH), and interacts through CC interaction producing a charged muon. The gray solid line represents the kinematic limit, i.e., the scattering angle between the direction of the primary neutrino and the produced muon track. The black solid, dashed, and dotted lines show the angle between the direction of the primary neutrino and the SPEFit2, MPEFit, and MPEFitSpline reconstruction, respectively. As expected, they all perform about the same, with a small improvement using MPEFitSpline, see table 7.2. MPEFitSpline is therefore chosen for the final point source likelihood. Nev- ertheless, the median angular resolution of the final signal sample is 1.7◦ for −2 −Eν/ 10 TeV a neutrino spectrum given by Eν e with a central 90% energy range roughly between 100 GeV and 10 TeV.

7.3 Angular Uncertainty To search for neutrino point sources within an almost isotropic distribution of background events it is important to not only have a good reconstruction but also a good handle on its uncertainty, even more so when dealing with potentially quite weak sources. During the ofﬂine event selection, we explicitly select events with good reconstruction quality and small estimated angular

118 100

10−1 . −2 u

. 10 a

10−3

10−4 0 5 10 15 20 Space Angle ψ [◦]

1.0

0.8

0.6 . u . a 0.4

0.2

0.0 0 5 10 15 20 Space Angle ψ [◦]

Figure 7.7. Space angle distribution of the reconstructions used in the analysis. The plots show simulated neutrino events at ﬁnal level of the event selection, with event −2 −Eν/10 TeV weights corresponding to a neutrino spectrum proportional to Eν e . The gray line represents the kinematic limit, deﬁned as the scattering angle between the primary neutrino and the produced muon. The black solid, dashed, and dotted lines show the angle between the primary neutrino and the SPEFit2, MPEFit, and MPEFit- Spline reconstruction, respectively.

119 Table 7.2. Median space angle of the reconstructions used in the analysis, calculated using equation 7.8. Values are calculated using simulated neutrino events at final level of the event selection, see section 10.4. All events are truly starting inside the instrumented detector volume, using criterion p = 0.8 and z = 300 defined in chapter 8. Further, they are truly down-going (i.e., originate from the SH), and interact through CC interaction producing a charged muon. The kinematic limit represents the scattering angle between the direction of the primary neutrino and the produced muon track. As small improvement is seen for the MPEFitSpline reconstruction relative to LineFit, SPEFit2 and MPEFit, why it is chosen for the final point source likelihood.

−2 −2 −Eν/ 10 TeV Eν Eν e Kinematic 0.17◦ 0.41◦ LineFit 4.3◦ 4.4◦ SPEFit2 2.1◦ 2.0◦ MPEFit 1.7◦ 1.9◦ MPEFitSpline 1.4◦ 1.7◦ uncertainty. The angular reconstruction uncertainty is estimated individually for each event from the likelihood function used in the reconstruction. Two different algorithms are used in the event selection, each presented below.

Cramér-Rao The Cramér-Rao reconstruction uses the Fisher information matrix of the reconstruction SPEFit2 to estimate the angular uncertainty. It is a relatively simple analytic calculation without iterative numerical approximations, and is hence fast and can be computed for many events at an early level of the analysis. The estimated angular uncertainty is defined as: 2 2 2 σθ + sin θ · σφ σ − = , (7.9) Cramer Rao 2 where σθ and σφ are the estimated directional uncertainties of θ, φ, respectively. The uncertainties are derived using the so-called Cramér-Rao bound, stating that the inverted Fisher information matrix gives a lower bound to the true resolution. The matrix is based on the behavior of the per-DOM PDFs near the final fit results.

Paraboloid The paraboloid ﬁt is a numerical method that uses the actual likelihood space of the reconstruction considered to estimate the angular uncertainty. This ﬁt is used at level 7 of the event selection, see section 10.4.7, to provide the angular uncertainty of the MPEFitSpline reconstruction.

120 The estimated angular uncertainty is defined as: σ2 + σ2 σ = 1 2 , (7.10) Reco 2 where σ1(2) is the major (minor) axis of an ellipse that constitutes the section at constant log-likelihood, the value of −log(L) has changed by 1/2 with respect to the best-fit value, of a paraboloid fitted to the likelihood space around the reconstruction minimum [140]. This construction corresponds to a 1 σ confidence region (39% containment) for the the reconstructed zenith and azimuth. The paraboloid algorithm often underestimates the true angular uncertainty. Therefore, we apply an energy dependent correction based on the median of the pull. This is presented in detail in chapter 10. The pull itself is defined as the ratio of the true angular error ψTrue to the estimated angular error σReco for each event: ψ Pull = True . (7.11) σReco Events with a corrected value above 5◦ were rejected after optimization studies of the final sensitivity. The paraboloid fit was used as the angular uncertainty estimator in the final likelihood analysis.

7.4 Interaction Vertex For a given directional reconstruction, we now reconstruct the length of the track in the detector, while keeping the direction fixed. We use the finiteReco algorithm [141] and the pulses in RTTWOfflinePulsesFR. The SPEFit2 result is used as a seed. The goal of the algorithm is to calculate the starting and/or stopping point using a finite track hypothesis. The starting point is used as a proxy for the true neutrino interaction vertex in several steps of the event selection. In particular, it is one of the most important variables in the creation of the initial veto that makes it possible to select events from the full SH at low-energies, see chapter 8. In a simple first-guess approach it calculates the first emission point by pro- jecting all hits within 200 m of the seed track , onto the seed track under the Cherenkov angle, and returning the first point of emission in time, see illustration in figure 7.8, where the dashed lines represent a cylinder with radius 200 m surrounding the track. A more advanced algorithm is performed at a higher level of the analysis. It minimizes a likelihood that estimates the starting and stopping point of the muon by considering the so-called no-hit probability of DOMs, the probability to not observe photons, given a infinite/finite track hypothesis. This is illustrated in figure 7.9. The DOMs in the shaded regions, marked ‘Selected DOMs’, before and after the starting and stopping point respectively, did not

121

Figure 7.8. Illustration of the first-guess construction in the finiteReco algorithm. Fig- ure adapted from [142]. detect hits, and are considered in the likelihood. The time of the vertex is allowed to shift to provide Cherenkov-like time residual distributions. Note that through the seed reconstruction, there is an implicit dependence on the hit probability for the DOMs located between the shaded regions. The probabilities are defined as follows: • p(noHit | Track) is the probability of the so-called ‘Track’ hypothesis, i.e., the probability to not observe a hit under the assumption of an infinite track, and • p(noHit | noTrack) is the probability of the so-called ‘noTrack’ hypothesis, i.e., to not observe a hit under the assumption of a track starting and stopping at the reconstructed starting and stopping point, respectively. Several different topologies can be distinguished: starting track, through- going track, stopping track, and fully contained track. The photon arrival time PDFs, used for the ‘Track’ hypothesis, are taken from the look-up tables created using Photonics as described in section 6.1.2. From these tables we extract the expected number of photoelectrons λ, as a function of depth in the ice as well as the perpendicular distance and orientation of the DOMs relative to the specified track hypothesis. For the ‘noTrack’ hypothesis, λ is sampled from a noise hit distribution. The general no-hit probability is defined as [141]:

0 λ −λ −λ pλ(noHit) = pλ(0) = e = e . (7.12) 0! 122 The likelihood L is defined by multiplying the individual contributions from each selected DOM i [141]: L(noHit|Track) = pi(noHit|Track), (7.13) i L(noHit|noTrack) = pi(noHit|noTrack). (7.14) i The likelihood ratio between the starting track (‘noTrack’) hypothesis and the infinite track hypothesis is maximized with respect to the starting and stopping position respectively. Technically, the stopping point is calculated first, keeping the starting point fixed at the position given by the first-guess algorithm. The resulting stopping point is then kept fixed in a similar determination of the starting point. The likelihood is used as a quality parameter to estimate the statistical confidence in the fit. We also derive a so-called reduced log-likelihood (rlogl) value similar to the one defined in section 7.2.3. Furthermore, the individual likelihood for different track hypotheses can be computed through equation 7.13 and 7.14. In this case no minimization is done, but the probability is calculated based on the starting and stopping point from the first-guess algorithm. The ratio between the probability under a starting and infinite track hypothesis, respectively, defines one of the variables used in event selection.

Figure 7.9. Illustration of the advanced finiteReco reconstruction. The DOMs in the shaped region are selected for the calculation of no-hit probability under either a ‘no- Track’ or ‘Track’ hypothesis. The reconstructed starting and stopping points are evaluated one at a time for technical reasons. These reconstructions are seeded with the points from the first-guess algorithm illustrated in figure 7.8. Illustration adapted from [142].

123 7.5 Energy High-energy muons lose most of their energy in multiple stochastic processes along the track, see figure 4.4. This leads to large fluctuations in the energy deposition pattern between muons of the same energy. Muon-neutrinos that interact via a CC process inside the detector volume are characterized by the lack of energy depositions before the interaction vertex, a hadronic cascade at the interaction vertex and subsequent stochastic losses along the muon track, i.e., the energy loss pattern deviates significantly from the assumption of a constant average energy loss along the track. Figure 7.10 shows a comparison between the primary neutrino energy and the muon energy for simulated events. These are highly correlated although the range of neutrino energies corresponding to a given Eμ is larger for lower Eμ. Moreover, since low-energy starting events are typically approximately contained in the detector, the reconstructed energy can be used as a proxy for the true neutrino energy.

7.5.1 Millipede The energy loss pattern is reconstructed using an algorithm called Millipede.It ﬁts hypothetical cascade-like energy depositions along the reconstructed track [143]. The depositions are modeled by dividing up the track in 15 m track segments and treating each segment as a cascade with a direction equal to that of the track and an energy that is completely independent from the energies deposited at the other segments.

Figure 7.10. Muon energy as a function of primary neutrino energy. The plot is shown −2 −Eν/10 TeV for events weighted to a Eν e signal spectrum.

124 Figure 7.11. An illustration of the results from the Millipede energy unfolding algorithm. This particular event has a large reconstructed deposition outside of the instrumented volume of the detector. The size of the spheres indicate the DOM charge and the energy depositions in logarithmic scale. The timing of the pulses in TWSRTOf- ﬂinePulses are shown in gray scale (white = early, black = late). The orange spheres, positioned along the track (MPEFitSpline, black arrow), represent the positions of the reconstructed energy depositions. Depositions that appear outside the detector border are rejected when constructing the ﬁnal energy proxy.

Millipede is based on a Poissonian likelihood L with mean value λ = ρ + i EiΛi, for the number of photoelectrons k observed in a DOM, given ρ expected noise hits and the expected numbers of photoelectrons per unit energy Λi for track segments i with energy Ei [143]: lnL = kln(λ) − λ − ln(k!) (7.15) The likelihood can be rewritten as [143]: lnL = kln E · Λ+ ρ − E · Λ − ρ − ln(k!). (7.16) The ﬁnal energy deposition pattern is solved numerically for the energy losses E by minimizing the likelihood via a linear unfolding [143]:

k −ρ = Λ · E. (7.17)

125 Millipede solves the energy loss distribution and returns the charge and location of each reconstructed energy loss. For further details see [143]. The result of such a calculation for a simulated starting neutrino event is shown in figure 7.11. The spheres in gray scale indicate the size and timing of pulses in TWSRTOfflinePulses, while the orange spheres, positioned along the track are the energy depositions fitted by the Millipede algorithm. An example of an energy loss reconstructed to have occurred outside of the instrumented detector volume is clearly visible on the left side of the figure. Such depositions, so-called outliers, are removed and a final estimate of the deposited energy is formed by summing up all remaining depositions. Although Millipede reconstructs the visible energy of a muon track in the detector, the final value is used as an energy proxy for the true neutrino energy. The correlation for simulated neutrino events, before and after removal of the outliers can be seen in figure 7.12. The upper plot shows the sum of energy depositions reconstructed with Millipede (including outliers), while the bottom plot shows the final energy proxy. Both are plotted as a function of the true neutrino energy. As seen in the top plot, large depositions outside the detector shift the energy proxy to values far away from the true. These overestimates are thought to be caused by the fact that the implementation of the algorithm used, cannot distinguish between a larger deposition outside of the detector producing a small signal on the edge, and a small noise hit on that same edge. By only including depositions that appear inside the geometrical volume (defined as 100% of the distance from string 36 to the outer layer corner DOMs and within ±500 m in z-coordinate, see figure 8.1) we can improve the correlation. This energy proxy is useful all the way down to 100 GeV.

Summary In this chapter we have discussed the different event reconstructions used in this thesis to quantify each event in terms of direction, energy, and quality. In the next chapter we describe the initial online ﬁlter developed exclusively for the Low-Energy Starting Events (LESE) analysis. This analysis is described in detail in chapter 10.

126 Figure 7.12. The upper plot shows the sum of all energy depositions reconstructed with Millipede, while the bottom plot shows the ﬁnal energy proxy. Both are plotted as a function of the true neutrino energy. Note that the plots show weighted distributions −2 −Eν/ 10 TeV corresponding to a neutrino signal spectrum of Eν e .

127

8. Opening Up a Neutrino Window to the Southern Hemisphere

“The real voyage of discovery consists not in seeking new lands but seeing with new eyes.” Marcel Proust

Rejection of the atmospheric muon background is of prime interest for most IceCube analyses, particularly for the ones targeting the Southern hemisphere (SH), where the Earth cannot be used as a filter. The traditional online filters for the SH are effectively using a charge cut, focusing on keeping events above 100 TeV, as a means to reduce the background of atmospheric muons. To reach lower energies, where the background is large, a new filter had to be developed utilizing parts of the detector as veto for incoming muon events. This chapter describes the development of the so-called Full Sky Starting (FSS) filter, a filter selecting starting events. It is designed to optimize the event collection at neutrino primary energies < 100 TeV, for a wide range of analyses such as: studies of the Galactic Center (GC) and the Sun as sources of neutrinos from WIMP interactions, SH neutrino point source analyses (both time dependent (transients) and time independent), and studies of the galactic plane and other extended astrophysical objects. The FSS filter has been used successfully in two point source analysis dedicated to events below 100 TeV. One, operating in the region between 100 GeV and a few TeV, is the main topic of this thesis and is covered in chapters 9 and 10. The other focuses on energies in the range from a few TeV to about 100 TeV and is presented in [144]. Studying neutrino emission from the region of the Galactic plane would be a natural extension once a multi-year sample exist, but this analysis has not yet been designed. Since the main background of muons is produced in the atmosphere, they always enter the detector from the outside. However, due to the sparsely distributed DOMs some muons, especially at low energies, may “leak” in without leaving a detectable signal in the outer detector layers. The filter utilizes the outermost parts of the IceCube detector to construct vetoes against incoming atmospheric muons, searching for starting events. At the same time we try to

129

Figure 8.1. Bird’s eye view of IceCube illustrating the definition of the vetoes used in the event selection. The outermost (light gray) polygon represents the full distance (p = 1.0) between each of the eight (8) corner strings (1, 31, 75, 78, 72, 74, 50, 6) and string 36. The dark gray polygon illustrates the cut region defined by p = 0.9, i.e., defined by 90% of the distance from string 36 to each of the outermost corner strings. Similarly the dashed gray polygon represents p = 0.8, the region used to define truly starting signal events. See figure 5.6 for further details. Credit: Illustration by Henric Taavola, modified by including polygon shapes to indicate cut and fiducial regions used in the analysis.

maximize the active, so-called fiducial, volume, not only utilizing the denser DeepCore sub-array but also large parts of the standard in-ice strings. Historically, simpler starting event filters have been running with partial detector configurations even during the construction of IceCube. However, these targeted specific regions of interest, such as the Galactic Center, or focused on low-energy events appearing primarily in the DeepCore array. The first implementation of the FSS filter ran in the first year of the completed 86-string detector. Today it constitutes one of the standard IceCube filters with an accumulated livetime of more than 4 years. Since the filter accepts events also from the SH it has a very high passing rate and was made simpler to implement through the development of a compact data storage format called SuperDST (Super Data Storage and Transmission). Prior to and during the first year of

130 Figure 8.2. Zenith angle distributions before the FSS filter. The green line represents the true neutrino direction, for a simulated assumed isotropic signal neutrino −2 −Eν/1TeV −2 −Eν/10TeV flux, weighted to the following signal spectra: Eν e (solid), Eν e −3 (dashed), and Eν (dotted). All other distributions show the reconstructed zenith angle (SPEFit2). Experimental data is shown as black dots and is further illustrated by the gray shaded area. Signals are shown as blue (orange) lines, following the same style as the green lines for the corresponding spectrum, and illustrate neutrino signal spectra with (without) cuts on the true direction and true interaction vertex position as described in section 10.4. All signal distributions are normalized to experimental data. operation, intense tests were made to ensure the stability and implementation of both the filter algorithm and the new data format. Figure 8.1 shows a bird’s eye view of IceCube and illustrates the definition of some important parameters used to define the vetoes used in the event selection. The fractional distance from string 36 to the outermost corner strings (1, 31, 75, 78, 72, 74, 50, 6) is denoted p, and define the corners of a polygon shaped region. The outermost light gray polygon represents the full distance (p = 1.0). The dark gray polygon illustrates the cut region, defined by p = 0.9, e.g., used in the third step of the FSS filter as described in section 8.1. Sim- ilarly the dashed gray polygon represents p = 0.8, the region used to define truly starting signal events in the analysis. The Low-Energy Starting Events (LESE) analysis presented in chapter 10 builds upon the development of the FSS filter and would not have been possible without it. The event distribution for the final event sample is significantly different in terms of energy and direction compared to classic point source analyses in IceCube using through-going muons, see figure 10.2.

131 The zenith distributions, before the application of the FSS filter, are shown in figure 8.2. The green line represents the true neutrino direction, for a simulated assumed isotropic signal neutrino flux, weighted to signal spectra: −2 −Eν/1TeV −2 −Eν/10TeV −3 Eν e (solid), Eν e (dashed), and Eν (dotted). These are all peaked at the horizon due to the integration over space angle. All other distributions show the reconstructed zenith angle (SPEFit2). Experimental data (dominated by atmospheric muons) is shown as black dots and is further illustrated by the gray shaded area. Signals are shown as blue (orange) lines, following the same style as the green lines for the corresponding spectrum, and illustrate neutrino signal spectra with (without) cuts on the true direction and true interaction vertex position as described in section 10.4. These cuts are made to illustrate the distribution of neutrinos truly starting inside the detector volume. Hence, the blue distribution with θ>90◦ corresponds to mis-reconstructed events from the Southern sky (θ ≤ 90).

8.1 The FSS Filter The FSS filter consists of several consecutive steps, both hit pattern based vetoes as well as cuts on the reconstructed interaction vertices. The former are based on a map of uncleaned HLC pulses. The filter algorithm is applied to each event and can be described in the following steps: i. A hit pattern based top veto rejects events with HLC pulses in any of the DOMs in the five topmost DOM layers. This veto is applied to DOM with numbers 1-5 among the 78 standard strings1. ii. A hit pattern based side veto rejects events where the first HLC pulse occurs in a DOM on any of the strings of the outermost string layer. The string layers are conveniently defined using the bird’s eye view of IceCube, see figure 8.1. This veto is applied for strings in layer 12. iii. The neutrino interaction vertex is reconstructed using the simple finiteReco algorithm illustrated in figure 7.8. iv. A cut on the reconstructed vertex in the (x, y)-plane is performed. The event is rejected if the interaction vertex is reconstructed to be outside of the polygon shaped region defined by p = 0.9. v. A cut on the reconstructed z-position of the vertex is performed. The event is rejected if the z-coordinate of the interaction vertex is reconstructed above 400 m. The filter acceptance rate varies around 190 Hz and is dominated by atmospheric muons leaking in through the veto layers. Note that the filter does not

1The standard IceCube strings contain 60 DOMs each, deployed at roughly the same depth. The DOMs on each string are numbered starting from the top with number 1. 2The outermost layer, layer 1, consists of strings 1-7, 13, 14, 21, 22, 30, 31, 40, 41, 50, 51, 59, 60, 67, 68, 72-78.

132 (a) Experimental data before FSS. (b) Experimental data after FSS.

(e) Signal E−3 before FSS. (f) Signal E−3 after FSS.

Figure 8.3. The plots show the reconstructed interaction vertex distributions in the (x, y)-plane before (after) application of the FSS ﬁlter in the left (right) column. The upper row shows experimental data (color shows the rate), while the second and third −2 −Eν/10 TeV −3 row illustrate the distributions for signal weighted to Eν e and Eν respectively (color shows the rate normalized to exp. data). The string positions are shown as black dots, while the polygon shape represents the containment criteria (p = 0.9) applied in the side veto of the FSS ﬁlter. See text for further explanation of events outside the polygon. 133 (a) Experimental data before FSS. (b) Experimental data after FSS.

(e) Signal E−3 before FSS. (f) Signal E−3 after FSS.

Figure 8.4. The plots show the reconstructed interaction vertex distributions before (after) application of the FSS ﬁlter in the left (right) column. The upper row shows experimental data (color shows the rate), while the second and third row illustrate the −2 −Eν/10 TeV −3 distributions for signal weighted to Eν e and Eν respectively (color shows the rate normalized to exp. data). The z-coordinate is shown as a function of the radius r = x2 + y2. The applied cut is shown as a horizontal black line at z = 400 m. The effect of cutting is seen clearly in the plots in the right column. See text for further explanation of events above 400 m.

134 Figure 8.5. finiteReco z-coordinate, before (upper) and after (lower) the FSS filter. Experimental data is shown as black dots and is further illustrated by the gray shaded area. The background simulation of atmospheric muons is presented in solid red line −2 −Eν/1TeV (only in lower plot). Signals are shown as blue lines: (solid) Eν e , (dashed) −2 −Eν/10TeV −3 Eν e , (dotted) Eν . Signal distributions are normalized to experimental data. In the upper plot we also show orange lines representing simulated signal without cuts on true direction and true interaction vertex position, as well as green lines representing the true primary neutrino vertex distribution. For further details, see text and legend definitions in section 10.4.

135 contain explicit cuts on energy-related variables. However, there are implicit cuts due to the starting requirement since high-energy background events are more likely to leave traces in the veto regions. Events that pass the filter are sent north for further processing (∼ 4,700 MB/day)3. Figure 8.3 shows the distributions of reconstructed interaction vertices in the (x, y)-plane, before and after the FSS filter. The upper row shows experimental data, while the second and third row illustrate the distributions for −2 −Eν/10 TeV −3 simulated signal weighted to Eν e and Eν respectively. For experimental data, color indicates the rate at the given level, while for signal the color corresponds to the rate of signal events normalized to the total rate of experimental data. The plots in the left column are generated using events captured by a so-called minimum bias filter selecting every 1,000th event that triggers the detector. The right column shows the results of a second round of vertex reconstructions performed offline after the application of the filter and transfer to the North. The whole reconstruction chain is re-applied for technical reasons. Random components in the chain (picking seed etc.) result in that a few events are reconstructed to start outside of the border defined by the filter. These are rejected at level 2 as described in section 10.4.2. Similarly, figure 8.4 shows the distributions of reconstructed interaction vertices in the (z, r)-plane, where r = x2 + y2 is the geometrical radius in the (x, y)-plane. Note the accumulation of events in the dense DeepCore array, −3 especially for the Eν spectrum. Further, we observe a deficit at the location of the main dust layer, discussed in section 5.2. This region is less sensitive to optical light due to increased absorption and scattering for photons. A consequence of the dust layer is that the distributions slightly below -150 m has a concentration of found vertices. This is due to events that interact in the dust layer but remain unobserved until the track reaches the sensitive region below the dust. The effect of the dust layer is clearly visible in figure 8.5, where the projected distribution of the z-coordinate is shown, before (upper) and after (lower) the FSS filter. Due to lack of processed simulated background data at trigger level, the upper plot is missing the red solid line representing atmospheric muons seen in the lower panel. In the upper plot we show orange lines representing the different signal spectra without cuts on true direction and true interaction vertex position (these cuts are described in section 10.4). The peak at z ∼ 500 m mainly consists of events starting above the instrumented region, while the leftmost peak is due to truly upgoing events. Further, the upper plot also show green lines representing the true primary neutrino interaction position.

3The total allocation for all IceCube ﬁlters is ∼ 100 GB/day

136 Summary In this chapter we introduced the FSS ﬁlter and discussed its implementation including vetoes based on both the hit pattern of pulses in the detector as well as cuts on the reconstructed interaction vertices. This ﬁlter is the corner stone of the analysis presented in chapter 10 and enables point source searches to be extended to low energies in the full SH.

137

9. Point Source Analysis Methods

“Look up at the stars and not down at your feet. Try to make sense of what you see, and wonder about what makes the universe exist. Be curious.” Stephen Hawking

We look for point sources by searching for a spacial clustering of signal-like events in a distribution of background events, uniform in declination bands. We follow a procedure similar to that developed in [113, 145], where the final sample is analyzed using an un-binned maximum likelihood function where the events contribute individually, with a reconstructed position, reconstructed energy and an estimate of the angular uncertainty. This approach uses the event-by-event information including a precise estimate of the detector angular resolution. Further, the energy can be used as a means to separate signal from the background, in particular if the signal events are predicted to follow a slightly harder spectrum than that of atmospheric muons or atmospheric neutrinos. The event times can be used to study neutrino bursts or periodic emission but in this analysis we focus on steady sources of neutrino emission probing the time-integrated neutrino flux. In this chapter we discuss the hypotheses and likelihood functions used to characterize the background and signal samples. Further, we define the test statistic used for the hypothesis tests applied in chapter 10.

9.1 Hypothesis Testing The goal of the analysis is to say something about the presence of a signal from low-energy neutrino point sources. We formalize these statements using so-called hypothesis tests where we compare a null hypothesis H0, without the presence of signal, to an alternative hypothesis HS , including the signal description. These tests are designed for discovery and will either accept or reject the null hypothesis at some conﬁdence level depending on the observed experimental data.

139 p-value

TS TSobs

Figure 9.1. The PDF of the test statistic TS for the null hypothesis H0. Such PDF can be constructed using thousands of pseudo-experiments where the directions of the events in the experimental data sample have been scrambled in right ascension, providing a background-like distribution of events, uniform in each declination band. The one-sided p-value corresponds to the probability of obtaining a TS equal or higher than TSobs in the observed data.

The data in this analysis is modeled using two different hypotheses:

• Null hypothesis H0: The data is described by a distribution of mainly atmospheric muons which is uniform in right ascension (R.A.). • Alternative hypothesis HS : The data is described by a distribution of mainly atmospheric muons which is uniform in R.A. plus a localized source of astrophysical neutrinos. The degree of confidence in a given hypothesis can be quantified using a so- called test statistic TS that compares the observed data with what is expected under the null hypothesis. The TS is defined as the ratio of the likelihood for the best fit of the parameters to the likelihood of the null hypothesis. It is defined so that a large value indicates poor agreement with the null hypothesis. The TS distribution is established by conducting 10,000 pseudo-experiments of the null hypothesis where we scramble the directions of each event in the experimental sample in right ascension and calculate the TS-value after each scrambling. We further define a so-called p-value, the probability to observe an outcome as large or larger given that the null hypothesis is true. This p- value is illustrated in figure 9.1, where the PDF represents the distribution of TS-values for the null hypothesis. Note that this figure only serves as an illustration of the method. The actual PDFs for the data in this analysis look quite different, see e.g. figure 9.4 and the discussion in section 10.6.2.

140 Hypothesis tests with injected signal are used as a way to establish the level of signal the analysis is sensitive to. Hypothesis tests using the observed data is used to calculate limits on the existence of signal if no signal was found, and to establish the amount of signal found if present in the ﬁnal sample. This is further explained in section 10.6.1.

9.2 Likelihood and Test Statistic The likelihood function L models the outcome of the experiment and is a function of two fit parameters: the number of signal events nS and the spec- −γ tral index γ assuming an unbroken power-law spectrum (i.e., Eν ). The final likelihood function is a sum over the N events in the final sample: N n n L(n ,γ) = S S(x ,σ ,E ;x ,γ) + 1 − S B(δ ;E ) , (9.1) s N i i i S N i i i where xi = (δi,αi)(δ denotes declination, α R.A.), σi, and Ei are the position, angular uncertainty and energy for each event i, xS is the position of a source S with parameters nS and γ, and S and B represent the probability for an event to be signal- or background-like, respectively. The likelihood is for simplicity configured with an unbroken power-law. Broken spectra with exponential cut- offs are to some extent represented by spectra with large values of γ. The signal PDF S consists of two separate parts: one modeling the spacial distribution as a two-dimensional Gaussian distribution centered on the source position with a standard deviation σi, one modeling the calorimetric information (covered in detail after equation 9.6):

S = S (|xi − xS|,σi) × E(Ei,δi,σi;γ), (9.2) where |xi − xS| is the space angle difference between the source and an event i (see equation 7.8), and S i is deﬁned as:

| − |2 − xi xS 1 2σ2 S (|x − x |,σ ) = e i . (9.3) i S i πσ2 2 i

The background PDF B also consists of two separate parts, a spacial S bkg and a calorimetric Ebkg (covered in detail after equation 9.6):

B = S bkg(δi) × Ebkg(Ei,δi,σi,γ), (9.4) where the spacial part is described by a spline fit, Pexp, to the full experimental data sample at final level, depending on the declination of each event only. S bkg is easily described since IceCube has a uniform acceptance in right ascension due to its location at the South Pole. 1 S = P (δ). (9.5) bkg 2π exp 141 Figure 9.2. The declination distribution of experimental data at final level is shown in the black histogram. A spline fit to this histogram is shown as a red dashed line. Further, we show the distributions of a number of signal hypotheses in blue. All histograms are normalized so that the integral is equal to 1. The red line is used as the spacial PDF Pexp.

Figure 9.2 shows the background spline Pexp for the final event sample in red. This is fitted to the histogram of experimental data shown in black, binned using 40 equidistant bins in sinδ in the range −1.0 ≤ sinδ ≤ 0.0. As a comparison we also show the distributions for three different neutrino signal hypotheses in blue. To estimate the significance of an observation we define the test statistic TS 1 as the likelihood ratio with respect to the null hypothesis (nS = 0) : L(ˆnS,γˆ) nS S i TS = 2ln = 2 ln 1 + Wi − 1 (9.6) L(n = 0) N S , S i bkg i where Wi = Ei/Ebkg,i is the ratio of the calorimetric parts of the signal- and background-probability,n ˆS andγ ˆ denote the best-fit values. Note that S i, S bkg,i, Ei, and Ebkg,i represent the distributions defined in equation 9.2 and 9.4, respectively, evaluated for an event i. W is constructed by fitting a spline to the ratio of the calorimetric parts in the three dimensions defined by the reconstructed energy E (‘Energy Proxy’), declination δ, and angular uncertainty σ. The angular uncertainty was not used in [145] but is included in this analysis to form a complete likelihood

1The factor 2 is included in concordance with Wilks theorem.

142 expression avoiding biases as discussed in [146]. The splines are functions of the source spectral index γ and are recalculated for each signal hypothesis considered in the likelihood. Figure 9.3a and 9.3b show the background and signal distributions at final level of the event selection as a function of the reconstructed energy and direction (for all σ). The binning used here represent the binning used to define the spline. The third dimension, σ, is binned using the bin edges (0.0, 0.5, 1.0, 3.0, 5.0). Note that the distributions shown in figure 9.3a and 9.3b are scaled in each declination bin so that the sum of bin-counts along the axis of the energy proxy, equals one. This is also done for each distribution when forming the ratio, to ensure that no extra spacial weights are applied other than the ones from the spacial part S/S bkg. When constructing the ratio, bins outside of the domain of experimental data, but inside the signal domain, are mapped to the most signal-like value, calculated as the 99% percentile of the ratios above 1. This is due to practical reasons, when injecting signal MC events there is a certain probability to inject events outside the region of experimental data, and results in fast evaluation of the injected trials without having to redefine the background sample including the signal for each injection. The impact of this procedure was shown to be negligible. Vice-versa, for bins in the experimental data sample where there are no corresponding signal estimation, the ratio is set to 1, i.e., the calorimetric part of the likelihood has no preference for either signal or background. Figure 9.3c and 9.3d show spline fits to the ratio of signal over background evaluated on a grid of 100×100 equal sized pixels in E and sinδ, respectively, −2 evaluated for Eν and two of the bins used in the third dimension, σ. 2 The likelihood ratio in equation 9.6 is maximized with respect to nS and γ. We only fit for positive values of nS, i.e., nS ≥ 0. Additionally, we constrain γ to be in the range -1 to -6, seeded with the value -3. The significance of the observation is quantified by comparing the best-fit TS-value with the distribution from the null hypothesis, i.e., from data sets of randomized events in right ascension. The latter correspond to the probability of the observation occurring by chance, given the measured data sample. It can be shown that the TS distribution, defined in equation 9.6, approximately follows a χ2 distribution with n degrees of freedom in the limit of infinite statistics. This is a consequence of the so-called Wilks theorem [147, 148]. In this analysis n ∼ 2 since both nS and γ are allowed to float freely. However, the actual number of degrees of freedom is typically less mainly since energy is not very helpful at low energies. This discrepancy is clearly seen in figure 9.4 showing the test statistics distribution for the null hypothesis (nS = 0) at ◦ δ = −50 over 100,000 trials. The single sided p-value for an observed TSobs, see figure 9.1, can be found from this distribution. A χ2 distribution for n = 2 (‘Theory’) is shown as a dotted line. This theoretical line does not always

2 For practical reasons we perform a minimization of −2ln(L(ˆnS,γˆ)/L(nS = 0)).

143 7.0 100 7.0 100

6.0 6.0 ) ) 10−1 10−1 5.0 5.0

4.0 4.0 10−2 10−2 3.0 3.0 Energy Proxy Energy Proxy ( ( 10 10 2.0 2.0 10−3 10−3 log log 1.0 1.0

0.0 10−4 0.0 10−4 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 sin δ sin δ −2 (a) Experimental data (b) Signal Eν

7.0 102 7.0 102

6.0 6.0 ) ) 101 101 5.0 5.0

4.0 4.0 100 100 3.0 3.0 Energy Proxy Energy Proxy ( (

10 2.0 10 2.0 10−1 10−1 log log 1.0 1.0

0.0 10−2 0.0 10−2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 sin δ sin δ (c) Evaluated ratio spline (σ = 0.75◦) (d) Evaluated ratio spline (σ = 2◦)

Figure 9.3. The top row shows the background (left) and signal (right) distributions at ﬁnal level of the event selection as a function of the reconstructed energy and direction. −2 The signal is weighted to an Eν spectrum. These plots are scaled in each declination bin so that the sum of bin-counts along that axis of the energy proxy, equals one. The bottom row illustrate the three-dimensional spline ﬁts of the ratio of signal over background, used in the calorimetric part of the likelihood. The left (right) plot shows the spline evaluated in the bin including σ = 0.75◦ (σ = 2.0◦), respectively. The splines are based on the ratio formed from the distributions in the upper row.

144 100 χ2 Fit 10−1 χ2 Theory

Null hypothesis (nS =0) 10−2

10−3 PDF

10−4

10−5

10−6 0 10 20 30 Test statistic TS

Figure 9.4. The test statistic distribution for the null hypothesis, nS = 0, evaluated at δ = −50◦, is shown in the histogram. A χ2 distribution for n = 2 (‘Theory’) is shown as a dotted line. The dashed line shows a fit to the histogram using a combination of a χ2 and a Dirac delta-function at TS = 0. The latter will be used to calculate the final p-values for this particular declination. See section 10.6.1 for more details. agree with the distribution of TS-values and often overestimates the height of the distribution leading to a bias towards a higher p-value given an observation TSobs. A procedure is developed to reduce this bias and will be presented in section 10.6.1. It builds on fits of the observed TS distribution for a number of declinations as illustrated by the dashed line shown in figure 9.4.

Summary Hypothesis testing is a way to compare different hypotheses and provide a quantitive way of rejecting or accepting models at pre-defined confidence levels. In this chapter we have introduced the hypotheses and test statistic used in the analysis as well as the constituent likelihood PDFs, both spacial and calorimetric. The application of the method is presented in chapter 10, including detailed TS distributions and a review of the actual number of degrees of freedom in the likelihood fit.

145

10. A Search for Low-Energy Starting Events from the Southern Hemisphere

“We don’t receive wisdom; we must discover it for ourselves after a journey that no one can take for us or spare us.” Marcel Proust

Classic IceCube point source analyses study the Northern Hemisphere (NH) using the Earth as a filter, effectively eliminating up-going atmospheric muons to provide a nearly pure sample of atmospheric neutrinos (misreconstructed muons can be removed to a high degree). IceCube’s sensitivity is unrivaled in this part of the sky as can be seen on the right hand side of figure 10.1 (sinδ 0). IceCube’s limits and sensitivities are shown as black dots and lines −2 and are calculated for an Eν -spectrum. The results are computed for a joint analysis between the classic through-going sample [149] and a starting track sample, denoted Medium-Energy Starting Events (MESE), for energies above 100 TeV [150]. The former is using 4 years of data1, while the latter is using 3 years2. The event selection used for the through-going analysis is sensitive in the entire NH and extends into the Southern hemisphere (SH), up to δ ∼−5◦, where the Earth and Antarctic glacier still provide an efficient filter. In the main part of the SH3, δ −5◦, down-going atmospheric muon bun- dles4 constitute a significant background and it is very challenging to isolate a pure neutrino sample. Instead the background is reduced by exploiting variables connected to event topology and energy loss pattern. Hence, the so- called through-going event sample mainly consists of atmospheric neutrinos in the NH and atmospheric muons in the SH. Note further that since high-energy neutrinos are absorbed in the Earth the effective area for neutrinos reaches its maximum close to the horizon. The MESE sample utilizes the veto method

1Using data from the 40, 59, 79, and the first year of the 86-string configuration of IceCube. 2Using data from the 79, and the first two years of the 86-string configuration of IceCube. 3Southern hemisphere is defined as δ ≤ 0◦. 4Muon bundles consist of many low-energy muons that typically have a smoother energy loss distribution while the energy loss of individual high-energy muons is dominated by stochastic losses.

147 Figure 10.1. IceCube muon-neutrino upper limits at 90% C.L. (black dots) shown for 38 pre-defined sources in the SH. Limits for the NH are not shown but are consistent with the sensitivity [149]. Further, we show the sensitivities as a function of declina- −2 tion for an unbroken Eν spectrum (black solid line), with hard cut-offs at 1 PeV (black dashed line) and 100 TeV (black dashed-dotted line). The limits and sensitivities are all calculated for the classic point source analysis in IceCube using through-going muon tracks [149] in combination with a starting track sample [150]. The latter uses three years of IceCube data and improves the limits in the SH (for δ ≤−30◦)bya factor of ∼ 5 − 20 (∼ 2 − 3) for fluxes ending at 100 TeV (1 PeV). Also shown are the point source sensitivities (red lines) and upper limits (red crosses) from ANTARES [151] using 4 years of data. Figure taken from [150]. developed for the so-called High-Energy Starting Events (HESE) analysis [3] in which a significant number of astrophysical neutrinos was first observed. However, the effective energy cut applied in the HESE analysis is lowered to a level corresponding to ∼ 100 TeV5. This sample improves the limits for δ ≤−30◦ relative to the through-going sample by a factor of ∼5-20 (∼2-3) for fluxes with a so-called hard cut-off 6 at 100 TeV (1 PeV). Note that the MESE sample only extends to a declination of −5◦. The joint analysis is unchanged with respect to the through-going sample above this declination [150]. The cuts used to reduce the background in the SH also remove a significant part of

5An explicit cut is set to remove events with less than 1,500 p.e. in the detector. 6The spectrum is cut-off at this maximum value but otherwise follows an unbroken power-law.

148 the low-energy signal. The sensitivity is then significantly worse for spectra predicting neutrinos of low-energy. This is clearly seen in figure 10.1 as we −2 apply a hard cut-off to the Eν -spectrum. The dashed-dotted and dashed black −2 lines show the sensitivity for an Eν -spectrum with a hard cut-off at 100 TeV and 1 PeV, respectively. The SH is of particular interest since it contains both the GC and the main part of the Galactic plane, two of the most probable neutrino source candidates (regions). The Low-Energy Starting Events (LESE) analysis described in this chapter is a search for low-energy point sources of astrophysical neutrinos in the SH. It focuses on neutrinos in the energy range from 100 GeV to a few TeV. The analysis was made possible by the development of the Full Sky Starting (FSS) data filter, described in chapter 8. Figure 10.2 shows the central 90% energy ranges as a function of declination for event samples for the through-going analysis (upper) and LESE analysis (lower), each for a number of different spectra ranging from hard to soft. The distributions are shown for the final event selection of each analysis. The LESE analysis is the only IceCube analysis so far that can explore the low-energy regime (100 GeV - few TeV) for muon-neutrinos, in the entire SH. Further, as we will see in section 10.6.1, it provides the best IceCube point source sensitivity all the way up to ∼ 10 TeV. The energy threshold for the LESE analysis was lowered significantly utilizing veto techniques, i.e., by selecting events starting inside the detector volume as a way to distinguish the signal from the large background of atmospheric muons, see figure 10.3. In this chapter we will present the event selection leading to the final sample of 6191 neutrino-like candidate events and the following likelihood analysis looking for a clustering of such events. We will present the results using the first year of IceCube data from the completed array as well as an estimate of the systematic uncertainties.

10.1 Analysis Strategy The event selection focuses on identifying starting events, see figure 10.3, building upon the stream of events that pass the FSS filter. Initially we apply overall data quality cuts ensuring that we have enough charge and participating strings for directional reconstructions. Several different veto prescriptions are applied in the subsequent steps. Further, a machine-learning algorithm is applied that simultaneously analyzes several variables, creating a score based on whether the events are signal- or background-like. At the higher levels of selection, when the number of events is smaller, more advanced and time-consuming reconstructions are performed. The final analysis uses the standard IceCube point source likelihood method to look for so-called hot-spots of neutrinos anywhere in the SH and additionally in a pre-

149 Figure 10.2. Signal distributions at ﬁnal level in a Eν-sinδ plane. The ﬁgures show central 90% energy ranges for various spectra. The classic through-going analysis is shown in the upper panel, and the LESE analysis is shown in the lower panel.

150 deﬁned list of candidate neutrino sources. Scrambled experimental data are used as background for these searches.

Blindness To avoid confirmation bias during development and optimization of the event selection, we blind the R.A. of each event until the final analysis chain, including all cuts, has been fully developed and approved. Note that since IceCube is located at the South Pole, we can use the azimuthal angle defined in detector local coordinates for each event without violating blindness. However, the event timestamp needed to convert this position into R.A. is kept blind.

10.2 Experimental Data This analysis uses data taken with the completed 86-string configuration of IceCube, denoted IC86-17, between May 2011 and May 2012. IceCube DAQ divides data into so-called runs. If successful, each run contains ∼ 8 hours of data from the whole in-ice array and the IceTop air shower array at the surface. Some runs are cut short due to temporary malfunctions or during detector maintenance periods. The DAQ then automatically starts a new run, potentially with a partial configuration, i.e., with one or several DOMs or even entire strings removed. Since this analysis is strongly dependent on the presence and operation of the outermost layers of DOMs which are used in the veto, we remove all partial runs with gaps in these critical regions. This selection of so-called good runs is described in detail in section 10.2.2. Several different samples of experimental data are defined. In particular, we develop the whole event selection on the so-called burnsample.

10.2.1 Burnsample The burnsample consists of a total of 12 runs grouped in sets of 3 consecutive runs (hence about 24 consecutive hours in each set), spread out evenly throughout the data taking period. This dataset was defined at an early stage of the analysis and consists of runs marked good by the detector monitoring system. Note that all but one of these runs (118209) failed the good run selection (see section 10.2.2), but follow-up investigations showed no apparent cause. Nonetheless, such runs were excluded from the final sample. The impact on the event selection is minimal at most, since each step was carefully checked and verified against simulated muon background. A larger burnsample, denoted Burnsample-BIG, consisting of every 10th run (all runs with a run number ending at 0), was defined at higher levels where more statistics were needed.

7The ‘1’ indicate that it is data from the 1st year of the ﬁnal conﬁguration. Subsequent years are denoted IC86-2, IC86-3, etc.

151 (a) High-energy muon (b) Low-energy muon at level 1 of the event selection at level 1 of the event selection

(c) High-energy signal event (d) Low-energy signal event at level 8 of the event selection at level 8 of the event selection

Figure 10.3. Illustration of the different event topologies considered in the analysis. The color coding of the hits are illustrative of the timing of the event with red meaning earlier hits and blue later hits. The top row shows the light pattern in the detector from two simulated atmospheric muon-bundle events. The bottom row shows the light pattern from two simulated muon-neutrinos interacting inside the detector volume.

152 Table 10.1. Deﬁnition of the different experimental datasets used in the LESE analysis, presented in this thesis.

Dataset Runs Livetime [s] IC86-1 [118175, 120155] 28435423 (∼ 329 d) Burnsample-BIG Runs ending with 0 in [118175, 120155] 2652273 (∼ 31 d) Burnsample 118209-11, 118589-91, 118971-73, 119671-73 28801.27 (∼ 0.3d)

10.2.2 Good Run Selection All runs marked good by the detector monitoring system were used as a baseline for the good run selection. This list of runs was comprised by removing runs containing either manual overrides due to e.g. calibration conditions or ‘Sweden camera’ runs (i.e., light in detector), runs with significant trigger and filter rate variations or runs where very large parts of the detector were not taking data. As mentioned above, partial runs constitute a problem for analyses dependent on the construction of vetoes. If a dropped-out string is located in the veto region, incoming muon events may leak in through the hole it creates, appearing starting inside the detector. To address this issue we manually checked the status of the detector through a series of tests. The rate of each run at level 5 (the livetimes of the runs were extracted at level 2) is illustrated by a dot in figure 10.4. Runs with a deviation within ±5% of the so-called running mean, constructed using a sliding window of 15 runs, were used in a polynomial fit to determine the average rate. For this calculation we divided the data into two separate regions clearly distinguishable in the figure. The shift occurring at run 118494, in the end of July 2011, was caused by a change in DOM firmware. The selected runs before (after) the shift were fitted using a 2nd (4th) order polynomial. Runs outside ±5% of the fit results, indicated with dashed lines in each region, were rejected (black dots), while runs inside the regions were kept (gray dots). Further we checked the individual detector configuration for each run making sure that the number of configured DOMs in the veto regions defined by the FSS filter (5 top layers, outermost side veto layer), as well as in the full in-ice array, was not lower than 97% of the deployed number of DOMs in each region. This run selection discards about 4 (11)% of the livetime (number of runs) initially considered. The total good livetime is finally about 329 days out of 342 days initially considered. Figure 10.4 also shows the seasonal variations in IceCube due to changes in the atmospheric temperature and pressure. This has an impact on the development of CR air showers in the atmosphere as discussed in section 3.4.

153 Figure 10.4. Rate at level 5 for each run in IC86-1 considered good by the detector monitoring system. The dashed black lines show the level at ±5% relative to two fitted polynomials, one in each of the two regions defined by run 118494 at the end of July 2011. Runs with a rate outside these lines are marked with black dots and are excluded from the final likelihood analysis. Further we exclude runs where less than 97% of the deployed DOMs are configured.

10.3 Simulated Data The simulation datasets used throughout the event selection are presented in table 10.2. The atmospheric muons are simulated using CORSIKA datasets 9622 and 10309. These are combined in all plots to provide enough statistics at both low and high energies. The neutrino signal as well as the atmospheric neutrinos were simulated using NuGen dataset 10602 containing muon neutrinos only. These are weighted to the desired spectrum using the scheme presented in section 6.2.

10.4 Event Selection The event selection is illustrated in ﬁgure 10.5 and consists of several consecutive steps of cuts and data processing. Each of these steps focuses on a different task and is referred to as a level. These are discussed extensively in the following sections. All cuts up to level 5 were carefully studied to ensure that the sample re- mained as unbiased as possible towards any true direction on the sky or a particular energy region. This is important to avoid an early bias towards

154 &/*' (& **+,-

& ' (&)*+,-

! " ) # (&*# .+,-

$ % !

Figure 10.5. The LESE event selection and analysis chain.

155 Table 10.2. Simulation datasets used in the analysis. CORSIKA events are generated using a 5-component model where 5 different primary nuclei are injected according to the speciﬁed generation spectrum. For details, see 6.1.1.

Generator Type Dataset Generation spectrum Angles θ [◦] Energy [GeV] − NuGen νμ 10602 E 2 [0, 180] [101,109] CORSIKA 5-component 9622 E−2.6 a [0, 89.99] [600, 105] CORSIKA 5-component 10309 E−2 [0, 89.99] [105,1011] aProton spectrum is generated as E−2.65. well-reconstructed high-energy events or certain parts of the SH. Further, in each step of the event selection we monitored the agreement between simulated background of atmospheric muons and the experimental data. Cuts were only made for variables and in regions with good agreement. The event selection was optimized for a neutrino signal described by a −2 −Eν/10 TeV power-law spectrum with an exponential cut-off at 10 TeV: Eν e . Several other spectra were studied in parallel to verify the behavior of each variable in the selection. The optimization√ was made by maximizing the sig- niﬁcance approximated as S/ B (unless stated otherwise), where S and B represent the number of signal- and background-like events respectively. As previously mentioned, we use burnsamples of experimental data as represen- tatives for the full IC86-1 data sample.

Figure Legends Throughout the event selection we will use plots to illustrate the variables used to separate signal- and background-like events. Unless stated otherwise, the plots contain the following: • Experimental data shown in black dots and further illustrated by a gray shaded area. The statistical uncertainty is illustrated with black error bars. Note however, that the statistical errors are very small, in particular for the ﬁrst levels, why clear error bars may not always be visible. • The total background simulation including both atmospheric muons μ and atmospheric muon-neutrinos νμ are shown using a red solid line. The individual contributions are shown in red dashed and dotted lines, respectively. Further a red shaded area is used to indicate the spread in the statistical uncertainty of the total background sample. Note that the rate of atmospheric muon-neutrinos initially is several orders of magnitude lower than the rate of atmospheric muons. That is why atmospheric neutrinos are only visible in the plots as we reach the higher levels. −2 −Eν/1TeV • Neutrino signal events are shown in blue lines: Eν e (solid), −2 −Eν/10TeV −3 Eν e (dashed), Eν (dotted). All simulated signal events shown are truly starting inside the instrumented detector volume (unless stated

156 otherwise). The containment criteria used is p = 0.8 and z ≤ 300 m, de- ﬁned in chapter 8 (see ﬁgure 8.1). Further, events are truly down-going (i.e., originate from the SH), interact through the CC interaction producing a charged muon, and are normalized to the total rate of experimental data (black dots).

10.4.1 Level 1 The IceCube triggers described in section 5.4 are applied at level 1. We apply three different triggers to data, each aimed at catching events of slightly different character: SMT-8, SMT-3, and StringTrigger. Several reconstructions are applied online to the triggered data before it is sent through the ﬁltering process described in chapter 8.

10.4.2 Level 2 Events that pass the FSS filter are sent north via satellite. The processing and filtering of subsequent levels is then performed offline, either on computers at UW-Madison or in Uppsala. Note that all filters and reconstructions performed online are re-done offline as data arrive to the data farm. These new reconstructions are used in the event selection from level 2. Due to the use of random numbers in the reconstruction chains, offline reconstruction results may differ somewhat from the results obtained online, at the Pole. At level 2 we also reject events with an SPEFit2 reconstruction in the NH, see figure 10.6 showing the distribution of reconstructed zenith angles after the FSS filter. Note that the neutrino signal distributions in blue shows truly downgoing tracks, hence the part of the distribution reconstructed as up-going represents so-called mis-reconstructed events.

Level 2 Requirements • Passed the FSS ﬁlter (see chapter 8), • Reconstructed direction (SPEFit2) is in the SH (θ ≤ 90◦).

10.4.3 Level 3 Level 3 focuses on general data quality, removing events with very few hits (too low charge for reconstructions), too few strings to resolve the azimuthal direction, and events with bad reconstruction quality (high values of rlogl). Further we cut on the z-coordinate of the finiteReco reconstruction of the neutrino interaction vertex. This cut significantly lowers the event rate and shows strong separation between signal- and background-like events as can be seen in figure 10.7a. The level 3 requirements are summarized in the list below. The corresponding distributions are also shown in figure 10.7.

157 Figure 10.6. Zenith angles from the SPEFit2 reconstruction after application of the FSS ﬁlter at level 2.

Level 3 Requirements • z-coordinate of finiteReco interaction vertex ≤ 250 m, • Total charge in TWSRTOfflinePulses ≥ 10 p.e., • Number of hit strings in TWSRTOfflinePulses ≥ 3, • rlogl of SPEFit2 ≤ 15. Note that the cut on rlogl only removes the worst tail of the distribution. The variable correlates strongly with energy and the cut was chosen to keep a large part of the low-energy (E < 1 TeV) events, see figure 10.7e.

10.4.4 Level 4 Level 4 focuses on the improvement of the angular resolution, which is crucial for the point source likelihood where we search for a clustering of events. It also includes variables that exploit the difference between signal- and background- like events. The plots in ﬁgure 10.8 show the pointing resolution as a function of true neutrino energy before (upper row) and after (lower row) level 4, for an −2 −Eν/10 TeV Eν e signal spectrum. The black lines indicate the median in each energy bin, showing a clear improvement especially at the lower energies, ◦ Eν 300 GeV (ﬁgure 10.8b and 10.8d). The global median (all events) is 3.1 after level 4 compared to 4.3◦ before, i.e., an improvement of roughly 30%.

158 (a) z-coordinate of reconstructed (b) Total charge of interaction vertex TWSRTOfﬂinePulses

(e) rlogl of SPEFit2 as a function of primary neutrino energy

Figure 10.7. All plots show level 3 variables before level 3 cuts are applied. The plot on the bottom row shows the dependence of rlogl on the primary neutrino energy Eν. As expected, higher energy events are easier to reconstruct and hence have lower rlogl values. The cut at 15 mainly removes low-energy events with a bad angular reconstruction. 159 (a) After level 3 (b) Zoom: After level 3

Figure 10.8. True space angle resolution distribution before (upper row) and after (lower row) application of the level 4 cuts. Plots show ψTrue as function of the primary −2 −Eν/10 TeV neutrino energy Eν for an Eν e -spectrum. The black line goes through the ◦ ◦ median of ψTrue in each energy bin. The median over all energies is 3.1 (4.3 ) after (before) level 4, hence an improvement with roughly 30%.

160 Several variables related to the pointing accuracy of the events are used at this level, e.g., σCramer−Rao defined in section 7.3 and the length between the reconstructed interaction vertex8 and the COG of the 25% latest pulses of TWSRTOfflinePulses denoted ‘Length fR-COG4:4’. The variables σCramer−Rao and ‘Length fR-COG4:4’ are shown in figure 10.9. The latter is proportional to the lever arm of hits in the detector and strongly correlates with the true angular uncertainty, see figure 10.9d. Further, we introduce so-called Δ-angles, the space angle between two reconstructions calculated using equation 7.8. Δ1 denotes the space angle between the SPEFit2 reconstruction and a line that goes from the COG of the 25% earliest (in time) pulses to the COG of the 25% latest pulses (using TWSRTOfflinePulses). Δ3 denotes the angle between the SPE- Fit2 reconstruction and a line starting at the reconstructed interaction vertex and ending at the COG of the 25% latest pulses (using TWSRTOfflinePulses). The Δ-angles are illustrated in figure 10.10. We also introduce the so-called Punch Through Point (PTP) as the point where the SPEFit2 track reconstruction penetrates an imaginary outer border of IceCube defined using p = 1 (see figure 8.1) and z ± 500 m. The distance between this PTP point to the earliest hit DOM in TWSRTOfflinePulses defines one of the variables used. The idea behind this variable is that short distances indicate activity close to the outer borders of the instrumented volume. This may indicate that a muon track entered from the outside leaking through the initial vetoes. This variable is divided into two regions, one for PTP points where the z-coordinate is equal to 500 m, i.e., where the extension of the infinite track reconstruction passes through the topmost DOM layer of IceCube and one where it is located below 500 m, i.e., where the infinite track reconstruction enters the detector through the outermost side layer9. The final cut is the same for both of these regions, but the distributions are significantly different, why they are displayed separately in figure 10.11. We introduce and make cuts on the two variables denoted ‘ZTravel’ and ‘Accumulation’, illustrated in figure 10.12. ‘ZTravel’ is defined as the mean deviation of the z-coordinate of all hit DOMs to the mean value of the z- coordinate of the first quantile in time,z ¯q1 : n zi − z¯q ZTravel = 1 , (10.1) n i where q z z¯ = i . (10.2) q1 q i=1

8Calculated using the simple finiteReco algorithm as described in section 7.4 and illustrated in figure 7.8. 9Since all tracks are reconstructed to be down-going, no events will enter through the bottom layer, i.e., no tracks will have a PTP located at z = −500 m. Further, due to the definition of the PTP, no events can have z > 500morz < −500 m.

161 and q is the total number of hits in the first quantile. ‘ZTravel’ is constructed using the pulses in TWSRTOfflinePulses. This variable is highly correlated with the zenith angle of the events and can be described as its upward tendency. To avoid cutting away signal from a particular part of the SH we therefore apply a soft cut. The variable ‘Accumulation’ is defined as the time until 75% of the total charge in TWSRTOfflinePulses has been collected. In figures 10.9 - 10.12 all variables used at level 4 are shown together with their correlation with the true space angle resolution. Further, all plots show −2 −Eν/10TeV the distribution of events from a signal simulation weighted to Eν e and normalized to experimental data. All plots are constructed using the containment criterion in ‘Figure Legends’ in section 10.4. The cuts made at level 4 are summarized below. They select events with a small true angular uncertainty, at the same time avoiding variables that are strongly correlated with the true neutrino energy.

Level 4 Requirements ◦ • σCramer−Rao ≤ 10 (deﬁned in section 7.3), • Length fR-COG4:4 ≥ 100 m., ◦ • Δ1 ≤ 40 , ◦ • Δ3 ≤ 20 , • Distance between ﬁrst hit and the PTP ≥ 200 m (for PTP-z < 500 m and PTP-z = 500 m), • ZTravel ≥−200 m, • Accumulation ≤ 2,000 ns.

162 ψ σ (a) Reconstruction uncertainty (b) True as a function of Cramer−Rao proxy σCramer−Rao

Figure 10.9. Level 4 variables - The upper (lower) row shows the distribution of σCramer−Rao (‘Length fR-COG4:4’). The plots in the left column show the distribution of the events prior to level 4. The right column shows the variables as function of the true space angle ψTrue, color indicating the rate of signal events weighted to −2 −Eν/10TeV Eν e and normalized to experimental data.

163 ψ Δ (a) Reconstruction uncertainty proxy Δ1 (b) True as a function of 1

ψ Δ (c) Reconstruction uncertainty proxy Δ3 (d) True as a function of 3

Figure 10.10. Level 4 variables - Δ-angles. The upper (lower) row shows the distribution of Δ1 (Δ3). The plots in the left column show the distribution of the events prior to level 4. The right column shows the variables as function of the true −2 −Eν/10TeV space angle ψTrue, color indicating the rate of signal events weighted to Eν e and normalized to experimental data.

164 ψ < (a) PTP-z < 500 m (b) True dependence (PTP-z 500 m)

Figure 10.11. Level 4 variables - PTP-based variables. The distance between ﬁrst hit and the PTP for events with PTP-z < 500 m (PTP-z = 500 m) is shown in the upper (lower) plots. The left column shows the distribution of the events prior to level 4. The right column shows the variables as function of the true space angle ψTrue, −2 −Eν/10TeV color indicating the rate of signal events weighted to Eν e and normalized to experimental data.

165 (b) ψ as a function of ZTravel (a) ZTravel True

Figure 10.12. Level 4 variables. The upper (lower) row shows the distribution of ZTravel (Accumulation). The plots in the left column show the distribution of the events prior to level 4. The right column shows the variables as function of the true −2 −Eν/10TeV space angle ψTrue, color indicating the rate of signal events weighted to Eν e and normalized to experimental data.

166 10.4.5 Level 5 In level 5 we focus on and apply additional veto requirements for incoming muons. We also apply a cut on the total charge of direct pulses in TWSRT- OfflinePulses using category C (see table 7.1). The events are reconstructed using the advanced likelihood-based finiteReco algorithm described in section 7.4. Cuts are then applied to the resulting interaction vertex, as well as to the likelihood ratio between a starting and infinite track hypothesis (LLHR Starting Track), see list of requirements below. Figure 10.13 shows the distribution of some of the variables used at level 5, including the ‘LLH Veto’ and ‘Causality Veto’ discussed below. Level 5 also includes a veto based on the possible coincidence between pulses in the in-ice detector and pulses recorded by the surface air-shower array IceTop. This is further discussed in the section ‘IceTop Veto’ below.

LLH Veto This veto algorithm is based on the calculation of rlogl for early pulses in a cylindrical region surrounding the track reconstruction SPEFit2, on the incoming side, see illustration in figure 10.14. The calculation is performed on a pulse series of uncleaned hits considering pulses on the outermost string layer of IceCube only. The idea is that neutrinos interacting inside the detector would only have uncorrelated noise hits in this region while events impinging from the outside may have left faint traces in the form of individual SLC hits. The radius of the veto cylinder was optimized in steps of 50 m, by considering the number of remaining√ signal S in relation to the number of background events B through S/ B. The optimal value of 350 m was chosen for the final cut. The rlogl values from the LLH Veto are presented in figure 10.13e. The bin corresponding to a value above 19 is added manually and represent events without pulses in the veto region (i.e., where the calculation of rlogl failed). Events with a rlogl less than 18 are rejected.

Causality Veto The Causality Veto algorithm investigates whether potential noise hits in two distinct veto regions (one top veto and one side veto), are causally connected to hits in the ‘active’ region of the detector. This veto does not explicitly rely on a track reconstruction but investigates the causal (time and space) connection between hits in the veto region and the ﬁrst HLC hit in a reference volume. If a causal connection exists the hits are expected to line up approximately along the so-called light-cone describing a particle traveling at the speed of light. PDFs are established for two hypotheses. The background hypothesis (B) is described by experimental data using the ‘Burnsample-BIG’, and the signal hypothesis (S ) is described by a simulated signal sample weighted to −2 −Eν/10TeV Eν e . The likelihood ratio between these two hypotheses is calcu-

167 (a) xy-plane of reconstructed interaction (b) xy-plane of reconstructed interaction −2 −Eν/10 TeV vertex, showing experimental data vertex, showing signal Eν e

(e) rlogl from the LLH Veto (f) Total charge of direct pulses of category C

Figure 10.13. Level 5 variables.

168

Figure 10.14. LLH Veto: The rlogl value is calculated for pulses located in a cylinder around the track reconstruction, on the incoming side. The idea is that lower rlogl values indicate some coincidence with hits in the veto region which may be interpreted as due to a particle entered from outside, leaking through previous vetoes.

Figure 10.15. Causality Veto: PDFs are calculated based on the causality of hits in a veto region (dark gray box) relative to the ﬁrst HLC in a reference, so-called ‘active’ volume. Two different veto topologies are used. The top veto (left) uses the twelve top DOM layers of IceCube while the side veto (right) consists of the two outermost string layers of IceCube excluding all DOMs used in the top veto.

169 lated for all events and is used to distinguish between signal- and background- like patterns in the detector. The top veto consists of the twelve (12) top DOM layers of IceCube (corresponding roughly to the finiteReco cut at level 3). The side veto consists of the two outermost string layers of IceCube, excluding all DOMs used in the top veto, i.e., these veto regions are completely separated in space. Fur- ther, we define a reference so-called ’active’ volume as the complement of the DOMs considered in each veto. Causality is studied for hits in the veto regions in relation to the first HLC hit in the corresponding ’active’ volume, denoted reference hit. Figure 10.15 shows an illustration of the veto construction. The top veto is only applied to events that enter through the top of IceCube (PTP > 300 m). Similarly, the side veto is only applied to events that enter through the side (PTP ≤ 300 m). The background and signal PDFs are constructed following the same division. Note that there is an implicit dependence on the track reconstruction, since the PTP is calculated using SPEFit2. The PDFs for signal events are constructed from events that are truly down- going (SPEFit2) and that have a reconstructed vertex inside the region defined by p = 0.8 and z ≤ 300 m. The distributions of veto hits relative to the reference hit, expressed in the time difference δt and spacial distance δr are shown in figure 10.16. These quantities are defined for each pulse i (note the sign of δt where a negative value identifies early veto hits):

2 2 2 δr = (xi − xref) + (yi − yref) + (zi − zref) , (10.3a)

δt = ti − tref. (10.3b) Each plot in the figure also shows the light-cone as two solid black lines con- verging at (δt,δr) = (0,0), the location of the reference hit. Since incoming background-like events cause early hits that are consistent with the speed of light with respect to the reference point, these are expected to cluster close to the light-cone line for δt < 0. On the opposite side δt > 0 we see traces of particles leaving the detector through the side veto as well as faint back-scattered light produced close to the neutrino interaction vertex for both vetoes. The edge at -4 μs is caused by the different pre-trigger window definitions used for the two main triggers, see section 5.4. A so-called box cut is used to select hits to use in the likelihood calculation, see black dashed borders in figure 10.16. Note that the boxes applied are different for the side and top veto10. The shape is determined manually to extract regions where possible veto hits are located, at the same time avoiding vetoing events by coincidence, this is particularly important for the tracks leaving the detector through one to the side veto layers. A band is clearly visible in the

10 The top veto box is deﬁned as: δt ≤ 0 ns, 120 <δr < 850 m and −150 m <δr + cδt < 450 m. The side veto box is deﬁned as: δt ≤ 0 ns, 200 <δr < 600 m and −150 m <δr + cδt < 450 m.

170 region roughly between 200 m and 1,000 m. This corresponds to the range of DOM-to-DOM distances between DOMs in the veto region and DOMs used as reference points, for each veto respectively.

PDFs The construction of the PDFs is challenging, especially due to the limited statistics in the signal sample. Instead of constructing multi-dimensional PDFs from the information in the boxes we construct several one-dimensional PDFs. δ δ We define the so-called decorrelated distance r and decorrelated time t by a rotation in the two-dimensional space defined by δr and δt. ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜δ⎟ ⎜cosω −sinω⎟ ⎜δ ⎟ ⎜ r⎟ = ⎜ ⎟ · ⎜ r⎟, (10.4) ⎝δ⎠ ⎝ ω ω ⎠ ⎝δ ⎠ t sin cos t where ω = tan−1(1/c) is the angle between the vertical axis and the line representing an incoming particle√ traveling at c. We also define the so-called ‘Dis- tance offset’ (d)asd = δr + cδt, with the corresponding PDFs pd. Further we count the number of pulses within the boxes and define the corresponding PDFs denoted pN. PDFs are established for both signal and background-like events. They are constructed by fitting splines to the variable distributions presented in the two upper rows of figure 10.17 (top veto) and 10.18 (side veto). The total background simulation is shown using a red solid line while the red shaded area indicates the spread due to its statistical uncertainty. Atmospheric muons μ are shown as red dashed lines and atmospheric muon neutrinos νμ are shown as red dotted lines. Since the distributions for different signal spectra (blue −2 −Eν/10TeV lines) do not differ much from each other, we use one model, Eν e , to represent generic signal events.

Likelihood Ratio The likelihood of an event to be described by signal or background is calculated for each of the four PDFs used, for both the top and side veto. The final likelihood ratio, denoted ‘Causality Veto LLHR’ (R), is defined in equation 10.5, as the product of individual likelihood ratios between the signal and background hypotheses. The resulting ratios for the top and side veto are presented in the bottom rows of figure 10.17 and 10.18, respectively. Value 13 is reserved for events without hits in the veto region, while -13 is reserved for events without a reference hit in the fiducial volume.

N N N p (N|S ) p (δ |S ) pt(δ |S ) p (d|S ) R = log N · r r · t · d , (10.5) p (N|B) p (δ|B) p (δ|B) p (d|B) N i r r i t t i d where the ﬁrst ratio is deﬁned once for each event given the total number of δ δ hits N and pr and pt are the PDFs for r and t , respectively. Large positive

171 (a) Top veto: Experimental data (b) Side veto: Experimental data

−2 −Eν/10TeV −2 −Eν/10TeV (e) Top veto: Signal Eν e (f) Side veto: Signal Eν e

Figure 10.16. ‘Causality Veto’ distributions for top veto (left column) and side veto (right column). The box cuts used in each veto is indicated as the dashed contours.

172 Figure 10.17. The distributions used to construct the PDFs used in the ‘Causality Top Veto’ are shown in the two upper rows. The bottom row shows the distribution of the corresponding likelihood ratio.

173 Figure 10.18. The distributions used to construct the PDFs used in the ‘Causality Side Veto’ are shown in the two upper rows. The bottom row shows the distribution of the corresponding likelihood ratio.

174

Figure 10.19. Illustration of the IceTop Veto. values of R correspond to signal-like events, while large negative values correspond to background events. Cuts are made at 0 for both the top and side vetoes, excluding events with a value ≤ 0.

IceTop Veto A so-called ‘IceTop Veto’ is designed to study coincidence between hits in the in-ice detector and hits in the IceTop air-shower array, see figure 5.2. For each pulse in IceTop, the algorithm calculates the time and lateral distance relative to the shower axis of a moving shower plane defined (curvature not included) by the direction and timing of the event track reconstruction (SPEFit2) performed on hits in the in-ice detector, see illustration in figure 10.19. A true correlation will occur on-time, i.e., when the shower plane passes IceTop, and is only expected for vertically downgoing events that pass through or close-by the IceTop array. We use the lateral distance between each IceTop

175 pulse and the reconstructed shower axis (track reconstruction) as an indicator for hit probability. The integrated number of IceTop pulses (SLC and HLC) is shown as function of time to the shower plane for various cuts on the lateral distance in the plots of figure 10.20. A sharp peak of on-time pulses is clearly seen for all lines and occurs on top of a general noise hit distribution with tails formed due to the mismatch in overlapping trigger windows as discussed for the ‘Causal- ity Veto’. The peaks consist of pulses very close to the shower axis. In fact we can limit the region of interest to lateral distances below ∼ 400 m without loosing efficiency for discarding coincident events. Further, by only considering pulses below a certain lateral distance, we can lower the random coincidence rate. To illustrate this, we show the number of IceTop pulses as a function of the time and lateral distances in the upper plot of figure 10.21. An on-time region is defined as the range from -400 ns to 100 ns and an off-time region is defined prior to this window in time, between -2,500 ns and 2,000 ns. The lower plot of figure 10.21 shows the projection of the time distribution on the horizontal axis for the pulses in the on-time (black) and off-time (gray) region respectively. The final analysis considers pulses within 400 m of the shower axis. An event is discarded if it has 1 or more pulses in the on-time region. This criterion removes 0.77% of the events in the experimental data sample. The random coincidence rate was determined by imposing the same criterion on the off-time region leading to an expected loss of about 0.13% for signal events −2 −Eν/10 TeV weighted to Eν e . This small loss of signal neutrinos is addressed in section 10.8, discussing the systematic uncertainties of the analysis.

Level 5 Requirements • (x,y)-coordinate of advanced finiteReco interaction vertex is inside the polygon defined by p = 0.9 (shown with a black line in figures 10.13a and 10.13b), • z-coordinate of advanced finiteReco interaction vertex ≤ 150 m, • LLHR Starting Track ≥ 5 (see section 7.4), • rlogl from LLH Veto ≥ 18 (see ‘LLH Veto’ above), • Total charge of direct pulses (using TWSRTOfflinePulses and category C, see table 7.1) ≥ 3 p.e., • LLHR Causality Veto TOP/SIDE > 0 (paired with z-coordinate of PTP, see ‘Causality Veto’ above), • No coincident hits in the IceTop air-shower array (see ‘IceTop Veto’).

176 3000 oﬀ-time on-time All 2500 d ≤ 2000 m d ≤ 1500 m 2000 d ≤ 1000 m d ≤ 500 m 1500

1000

500 Number of IceTop pulses

0 -10 -5 0 5 10 15 20 Time to the shower plane [μs]

500 d ≤ 500 m d ≤ 400 m 400 d ≤ 300 m d ≤ 200 m 300 d ≤ 100 m

200

100 Number of IceTop pulses

0 -0.4 -0.3 -0.2 -0.1 0.0 0.1 Time to the shower plane [μs]

Figure 10.20. Time to the shower plane in the IceTop Veto. The upper and lower plot show the number of IceTop pulses as a function of the time to the shower plane for a number of different lateral distances. The sharp peak of on-time pulses is clearly seen for all lines and occurs on top of a general noise hit distribution. The peak consists of pulses very close to the shower axis, in fact we can limit the region of interest to lateral distances below ∼ 400 m without loosing efficiency for discarding coincident events. In this way we can also lower the random coincidence rate. The gray shaded areas show the definitions of the on-time (off-time) region. Note that the time range of the lower plot corresponds to the definition of the on-time. Events with at least one IceTop pulse on-time within 400 m of the shower axis are rejected.

177 20 103 μ s] 15

10 102

0 101

-5 Number of IceTop pulses

Time to the-10 shower plane [ 100 0 500 1000 1500 2000 2500 Lateral distance to track [m]

800 on-time 700 oﬀ-time 600

500

400

300

200

100 Number of on-time IceTop pulses 0 0 500 1000 1500 2000 2500 Lateral distance to track [m]

Figure 10.21. The upper plot shows the number of IceTop pulses as a function of the time and lateral distances. A band consisting of on-time pulses is clearly seen on the left side for distances up to about 700 m. The upper plot shows the projection of the time distribution on the horizontal axis for the pulses in the on-time (black) and off-time (gray) region respectively.

178 10.4.6 Level 6 In level 6 we use a so-called machine learning algorithm to exploit the separation between signal- and background-like events for variables that might be nested. The algorithm used is a combination of a so-called Boosted Decision Tree (BDT) [152] and a so-called random forest. In general, we will refer to it as a BDT throughout this thesis. The BDT algorithm simultaneously analyzes all input variables in a multi- dimensional space, producing a final score for each event indicating whether it is signal- or background-like. The BDT is developed using a training sample consisting of both signal and background events. In this thesis, we use half of the experimental data in ‘Burnsample-BIG’ as background and half −2 −Eν/10TeV of all simulated muon-neutrino events weighted to Eν e as signal. The procedure used consists of two consecutive BDTs. The initial one uses all 22 variables considered, while the final only uses the 14 most important according to the results of the initial training. This is done to reduce the di- mensionality of the phase space of the BDT as a mean to lower the risk for so-called overtraining, see discussion below. Decision trees are classifiers that use a binary tree structure, splitting the data sample in several consecutive steps by applying linear cuts on the participating variables at each split point, so-called node. Each cut is chosen to increase the signal-to-background separation of the sample. The splitting continues until a stop criterion is fulfilled. Each resulting so-called end node is classified (scored) as either signal- or background-like based on whether it is dominated by events from the simulated signal or background sample. The stop criterion consists of several conditions. Either the specified maximum so-called depth (number of splits) is reached, a node is completely pure (i.e., only signal or background events remain), or the best cut results in a node with less than the specified minimum number of events remaining. A BDT consists of many consecutive decision trees. Typical for a classic BDTs is that a boosting weight is applied to all events when moving from tree to tree. These weights are determined by whether the previous tree classified the events correctly or not. Characteristic for random forests are instead processes of randomization. In the implementation used in this thesis, we allow each node to pick 5 (10) random variables out of the 22 (14) provided in the initial (final) BDT. Further, each tree is only allowed to use 40% of the data in the training samples, also selected randomly. The final BDT score for each event is calculated as the weighted average score from the individual trees (including boost weights). The score ranges from +1 to -1, indicating whether the event was signal- or background-like respectively. BDTs can easily be overtrained, either by being tuned to classify every single event in the training sample correctly, i.e., so that the division between signal and background is perfect, or by being tuned to find differences be-

179 tween the imperfect simulation and experimental data instead of differences in the physics parameters, so-called MC overtraining. To verify the training we therefore use the other half of each data sample, not used in the training, as a dedicated testing sample. A good agreement between the BDT scores of the training and the testing sample is expected if overtraining is low. We quantify this by making a so-called Kolmogorov-Smirnov (KS) test, providing a p-value based on the statistical probability that two compared samples are drawn from the same distribution. In general, a smaller KS p-value indicates greater overtraining. MC overtraining will not show up in a KS test but can be studied visually. If MC overtraining is present it is typically characterized by a small excess of events in the experimental data sample relative to the number of simulated events, in the region where the signal and background samples meet. Introducing random components, as described above, is another tool to minimize the overtraining of the sample. Further, we apply so-called pruning where the deeper nodes of each tree are removed 11.

Initial BDT The initial BDT uses 22 candidate variables that all show good separation power on visual inspection. These are shown in appendix A and presented in the list below. We made a large scan of hundreds of different combinations of BDT settings for the number of trees, node depth, prune strength, etc. The BDT that provided the highest p-value from the KS test ( 10−3) was selected. Settings used: 450 trees, each with a node depth of 4. The boost parameter was set to 0.3 and the pruning strength to 20.

List of initial variables: Initially we considered 22 variables for the BDT. These are presented in the list below and shown in appendix A. Variables based on the reconstructed interaction vertex are calculated using the advanced algorithm described in 7.4. COG is calculated using TWSRTOfflinePulses. PTP is calculated using SPEFit2. • Reconstructed interaction vertex: – z-coordinate, – distance in xy-plane r = x2 + y2, – LLHR Starting Track (defined in section 10.4.5), – rlogl of finiteReco fit (defined in section 7.4). • LineFit reconstruction (see section 7.2.1): – Magnitude of vLineFit, – x-component of vLineFit, – y-component of vLineFit,

11While the nodes close to the first node do most of the classification, deeper nodes are important for classifying less frequent types of events. These deeper nodes are also more sensitive to statistical fluctuations in the training sample

180 – z-component of vLineFit. • SPEFit2 reconstruction (see section 7.2.2): – zenith (θ), – rlogl, – z-coordinate of PTP, – PTP distance in xy-plane r = x2 + y2. • Pulse-map variables (based on TWSRTOfflinePulses): – Total charge, – Accumulation (see section 10.4.4), – ZTravel (see section 10.4.4), – Track hit smoothness (see below), – Total charge of late pulses (tres > 15 ns), – Number of direct pulses (category D, see table 7.1). • Miscellaneous – Distance between first hit and the PTP (see section 10.4.4), – Length fR-PTP, i.e., distance between the interaction vertex and the PTP, – z-coordinate of COG, 12 – σz of COG, i.e., RMS of the z-coordinate of COG. The track hit smoothness is a measure of how smoothly the pulses (TW- SRTOfflinePulses) are distributed along the track reconstruction (SPEFit2). The algorithm only considers the first pulse of every DOM within a cylinder surrounding the track with radius of 150 m. The distance from the first hit to each of the following hits is projected onto the tracks and ordered in time. The resulting vector is compared with a uniform hit distribution. Tracks with all hits clustered in the beginning or end of the track receive a value +1 and -1 respectively, while a perfectly uniform distribution corresponds to 0.

Results from the initial BDT: The 14 most important variables of the initial BDT are shown in table 10.3 ranked starting from 1 (most important). Importance is a measure on how often a variable is used to discriminate between signal and background events.

Final BDT The 14 most important variables of the initial BDT are used in the final BDT, see table 10.3. Again we made a scan of hundreds of different combinations of BDT settings. The BDT output with the highest p-value from the KS test ( 10−1) was selected. Settings used: 350 trees, each with a node depth of 6. The boost parameter was set to 0.3 and the pruning strength to 20. The result is shown in figure 10.22 and 10.23a where both training and testing samples have been merged. The plots follow the figure legend introduced in section 10.4.

12Root Mean Square (RMS)

181 Table 10.3. Variable importance of the ﬁnal BDT

Importance Ranking Variable Name 1 Charge of late pulses 2 Total charge 3 Hit distribution smoothness

4 σz of COG 5 z-coordinate of ﬁniteReco 6 z-coordinate of COG 7 Distance between earliest hit DOM and PTP

8 Magnitude of vLineFit 9 Zenith (θ) 10 ﬁniteReco xy-distance 11 ﬁniteReco rlogl 12 rlogl 13 z-coordinate of PTP 14 Number of direct pulses (D)

Figure 10.22 also show a comparison between experimental data and the total simulated background (atmospheric muons and atmospheric neutrinos) in the bottom panel. Figure 10.23b, 10.23c, and 10.23d show the BDT score divided into three bands using the zenith angle. The atmospheric muons are generally overestimated in the region 0.66 < cos(θ) ≤ 1.00 and underestimated in 0.00 < cos(θ) ≤ 0.33, but the overall shape is consistent with the experimental data up to statistical fluctuations. The transition from atmospheric muons to atmospheric neutrinos is clearly visible in the plots in figure 10.23, and occurs at BDT scores slightly above 0.5. The transition is most clear in the zenith band 0.00 < cosθ ≤ 0.33, i.e., for horizontal and close to horizontal events with θ ∼ 70◦ − 90◦. The KS p-value is 0.73 for the signal sample and 0.99 for the background sample. These values translate into a very high similarity between the testing and training samples, respectively. No visual discrepancies are observed other than statistical. Further, no hints of overtraining were found in the region where the signal and background distributions meet, BDT score ∼ 0.0. The correlations between the input variables are shown in figure 10.24 for experimental data (left) and signal (right), respectively. There is a clear correlation between a couple of variables, e.g., ‘Total charge’ and ‘Charge of late pulses’, ‘finiteReco rlog’ and ‘rlogl’ (SPEFit2), and ‘zenith (θ)’ and ‘z-coord. of PTP’. We therefore tested a new BDT by removing one variable in each pair of strongly correlated variables. The results got slightly worse, i.e., lower KS

182 14 0.00 < cos θ ≤ 1.00 12 10 8 6 mHz per bin 4 2 0 1.2 1.0 MC ratio

/ 0.8

Data -1.00 -0.50 0.00 0.50 1.00 BDT Score

Figure 10.22. BDT scores from the final BDT with events from the whole SH. The plots follow the figure legend introduced in section 10.4. The bottom panel show a comparison between experimental data and the total simulated background (atmospheric muons and atmospheric neutrinos). p-values, indicating higher degree of overtraining. Therefore, we decided to use the BDT score from the 14-variable BDT as the final one in the analysis. The final BDT cut was optimized in relation to the final sensitivity of the −2 analysis. The sensitivity for signal, described by an Eν spectrum with a hard cut-off at 10 TeV, was calculated for a range of different BDT cuts. The final cut is placed at 0.40. See section 10.6.1 for more details. Further, studies were made on the dependence of the BDT score on the zenith angle of the events. No improvement was found by making a zenith angle dependent cut instead of using one cut value for all zenith angles, why the latter was chosen.

Level 6 Requirements • BDT score ≥ 0.4.

183 102 102 0.00 < cos θ ≤ 1.00 0.00 < cos θ ≤ 0.33 101 101

100 100

10−1 10−1

10−2 10−2 mHz per bin mHz per bin

10−3 10−3

10−4 10−4 -1.00 -0.50 0.00 0.50 1.00 -1.00 -0.50 0.00 0.50 1.00 BDT Score BDT Score (a) BDT score, 0.00 < cosθ ≤ 1.00 (b) BDT score, 0.00 < cosθ ≤ 0.33

102 102 0.33 < cos θ ≤ 0.66 0.66 < cos θ ≤ 1.00 101 101

100 100

10−1 10−1

10−2 10−2 mHz per bin mHz per bin

10−3 10−3

10−4 10−4 -1.00 -0.50 0.00 0.50 1.00 -1.00 -0.50 0.00 0.50 1.00 BDT Score BDT Score (c) BDT score, 0.33 < cosθ ≤ 0.66 (d) BDT score, 0.66 < cosθ ≤ 1.00

Figure 10.23. BDT scores from the final BDT with events from the whole SH (upper left) (same as figure 10.22 but in logarithmic scale). All plots follow the figure legend introduced in section 10.4. The upper right panel and the panels in the bottom row show the BDT score for events divided into three bands using the zenith angle. The transition from atmospheric muons (red dashed line) to atmospheric neutrinos (red dotted line) can be seen for BDT scores slightly above 0.5. This transition is most clear in the zenith band 0.00 < cosθ ≤ 0.33 (upper right), i.e., for horizontal and close to horizontal events.

184 185 it / s i n PTP and hit 1st b/w Dist. o fdrc uss(D) pulses direct of No. -or.o finiteReco of z-coord. hreo aepulses late of Charge i it smoothness dist. Hit ntRc xy-dist. finiteReco eghof Length -or.o COG of z-coord. -or.o PTP of z-coord. ntRc rlogl finiteReco oa charge Total iue10.24. Figure σ eih( zenith z − fCOG of v 1. LineFit 0 rlogl θ − ) 0 . 8 Charge of late pulses −

No. of direct pulses (D) 0. 6

orlto arcsfrteﬁa D o xeietldt lf)adsga (right). signal and (left) data experimental for BDT ﬁnal the for matrices Correlation z-coord. of PTP − 0.

Hit dist. smoothness 4

rlogl − 0 . zenith (θ) 2

Dist. b/w 1st hit and PTP 0. 0 z-coord. of COG

σz of COG 0. 2 finiteReco rlogl 0 . finiteReco xy-dist. 4 z-coord. of finiteReco 0.

Length of vLineFit 6 Total charge 0. 8 1. 0 it / s i n PTP and hit 1st b/w Dist. o fdrc uss(D) pulses direct of No. -or.o finiteReco of z-coord. hreo aepulses late of Charge i it smoothness dist. Hit ntRc xy-dist. finiteReco eghof Length -or.o COG of z-coord. -or.o PTP of z-coord. ntRc rlogl finiteReco oa charge Total σ eih( zenith z − fCOG of v 1 . LineFit 0 rlogl θ − ) 0 . 8 Charge of late pulses − 0

No. of direct pulses (D) . 6 z-coord. of PTP − 0 . Hit dist. smoothness 4

rlogl − 0 . zenith (θ) 2

Dist. b/w 1st hit and PTP 0 . 0 z-coord. of COG

σz of COG 0 . 2 finiteReco rlogl 0 . finiteReco xy-dist. 4 z-coord. of finiteReco 0.

Length of vLineFit 6 Total charge 0. 8 1. 0 10.4.7 Level 7 At level 7 we perform several advanced reconstructions considering direction, angular uncertainty and energy, see chapter 7 for details. All of the reconstructions are required to succeed and the resulting directions are used to reject events from the NH. A cut on the LineFit speed is included to reject cascade-like events (see section 4.4). Further, a cut is applied to the corrected paraboloid uncertainty, σRescaled, deﬁned in the section ‘Angular Uncertainty - Pull Correction’ below. The cut was optimized in relation to the sensitivity at ﬁnal level of the analysis, see details in section 10.6.1. The cut is placed at 5◦.

Level 7 Requirements • Reconstructed MPEFitSpline point to the SH (θ ≤ 90◦), • Magnitude of vLineFit, ≥ 0.175 m/ns, see ﬁgure 10.25, ◦ • Paraboloid σRescaled ≤ 5 , see ﬁgure 10.26b.

Angular Uncertainty - Pull Correction The angular uncertainty is estimated using the paraboloid algorithm discussed in section 7.3. The performance is evaluated using simulated signal events −2 weighted to an Eν spectrum. Figure 10.26a shows the paraboloid σReco, calculated using equation 7.10, as a function of the true space angle between the track reconstruction and the simulated neutrino direction. The black diagonal shows the 1:1 correspondence. Ideally, the points would cluster around the line, but for unknown reasons the algorithm more often underestimates the angular uncertainty, a bias that becomes worse for higher energies.

. 30 0 07

0.06 25 0.05 20 0.04 15 0.03 Rate [Hz] Rate [Hz] 10 0.02

5 0.01

0 0.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Magnitude of vLineFit [m/ns] Magnitude of vLineFit [m/ns]

Figure 10.25. The left plot shows the magnitude of vLineFit at Level 2, while the right plot shows the magnitude of vLineFit at the ﬁnal level of the analysis. Both plots follow the ﬁgure legend introduced in section 10.4, with additional green lines representing electron-neutrinos. The green lines follow the same weighting scheme as for muon- neutrinos, and are normalized to the experimental data. A cut at 0.175 effectively removes the majority of the cascade-like events.

186 10 10−2 10 10−2 9 9 8 8

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10 ] 10 ◦ ] [

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4 Rescaled 4 σ − − 10 4 σ 10 4 3 3 2 2 1 1 0 10−5 0 10−5 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 ◦ ◦ ψTrue [ ] ψTrue [ ]

(a) Paraboloid σ (b) Corrected paraboloid, σRescaled

20 10−2 20 10−2 18 18 16 16

) 14 ) 14 10−3 10−3

/σ 12 /σ 12

True 10 True 10 ψ ψ 8 8 10−4 10−4

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10−2 10−2

101 101

) 10−3 ) 10−3 /σ /σ True True

ψ 100 ψ 100 10−4 10−4 Pull ( Pull (

10−1 10−5 10−1 10−5 1 2 3 4 5 1 2 3 4 5 log10(Energy Proxy) log10(Energy Proxy) (e) Pull distribution (f) Corrected pull distribution

Figure 10.26. The upper row shows the estimate of the angular uncertainty σReco as a function of the true space angle before (left) and after (right) the pull correction. The second row (linear scale) and third row (log scale) show the pull defined according to equation 7.11 as a function of reconstructed energy. The correction function is constructed by fitting a 4th degree polynomial (black dashed line) to the median pull in each bin and returning it to the ideal median equal to one (red dashed line). All −2 plots in this figure show simulated signal events weighted to Eν , normalized to the experimental data rate at the same analysis level.

187 0.008

0.007

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0.003 Rate [mHz] 0.002

0.001

0.000 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 log10(Eν) [GeV]

Figure 10.27. Event distributions for several signal spectra at the ﬁnal level of the −2 event selection. Neutrino signal hypotheses are shown in blue lines: Eν (light blue, −2 −Eν/10TeV −2 −Eν/1TeV −3 solid), Eν e (dashed), Eν e (solid), and Eν (dotted). All signal events are truly down-going CC events that truly interact within the detector (using criteria p = 0.8 and z ≤ 300 m). Atmospheric muon-neutrinos νμ are shown as a red dotted line, and correspond to the rate predicted by the Honda model, given a livetime of 329 days. The red solid line shows atmospheric muon-neutrinos νμ contained using the same deﬁnition as for signal. All signal lines are normalized to the red solid line.

To quantify the discrepancy we define the pull distribution according to equation 7.11. Figure 10.26c (linear scale) and 10.26e (logarithmic scale) show the pull as a function of the reconstructed energy (denoted ‘Energy Proxy’). The desired ideal pull value of 1 is shown as a red dashed line. The correction function consists of a 4th degree polynomial fit (black dashed line) to the median pull in each energy bin (black dots). Also shown is the standard deviation in each bin (gray shadow). The correction function is derived for a −2 signal spectrum of Eν but will be applied generally to all signal hypotheses. A biased estimator of the angular uncertainty can lead to a clear degrada- tion of the performance of the final point source likelihood results why the correction is applied to all events in the final sample in order to return the median pull to one throughout the energy spectrum. The result is shown in figure 10.26d (linear scale) and 10.26f (logarithmic scale). The pull corrected paraboloid value, σRescaled, is used as an estimate of the angular uncertainty in the following sections.

188 10.5 Event Selection Summary Table 10.4 shows a summary of the event rates at different cut levels of the analysis. The values represent the rates for experimental data and the simulated atmospheric background (μ and νμ), and the signal retention for various signal hypotheses. All values are calculated after the cuts on the corresponding level have been applied and are subject to statistical variations as well as uncertainties in the models assumed. The final level of experimental data consists of 6191 events for a livetime of 329 days. All signal events are truly down-going CC events that interact within the detector (using criteria p = 0.8 and ≤ 300 m). At final level, level 7, we expect about a factor of two more events from atmospheric muons, compared to atmospheric neutrinos. The sig- −2 nal efficiency is presented relative to level 2. For an Eν -spectrum it is about 7.5%, and slight lower for the softer spectra. The neutrino simulations used for the analysis in this thesis do not include the accompanying muons from the CR shower. Such events are likely to be vetoed by the analysis, if the muons reach the detector with sufficient energy. The effect of this so-called self-vetoing is expected to be more pronounced at neutrino energies 10 TeV [153, 154], i.e., above the energies relevant for this analysis. Note that the rate estimates of atmospheric muons and atmospheric neutrinos do not exclude a contribution from signal events.

10.5.1 Signal Figure 10.27 shows the event distributions for several signal spectra at the final level of the event selection. Atmospheric muon-neutrinos νμ are shown as a red dotted line, and correspond to the rate predicted by the Honda model. Neutrino signal hypotheses are shown in blue lines. All signal events are truly down-going CC events that truly interact within the detector (using criteria p = 0.8 and z ≤ 300 m). The red solid line shows atmospheric muon-neutrinos νμ contained using the same definition. The neutrino effective area for the final level sample is shown in the upper panel of figure 10.28. It is calculated using equation 6.3 in section 6.2. The effective area shown is the average of the area for νμ andν ¯μ. The solid line shows the distribution averaged over the whole SH, while the dashed, dotted, and dash-dotted lines show the distribution in declination bands of the true neutrino direction. The effective area is shown for the energies relevant to this analysis. The lower panel of figure 10.28 shows the effective target mass, based on the effective volume of the detector, defined in section 6.2, with target density 0.92 g cm−3 [2]. The target mass represents the efficiency to detect a muon created inside the detector. This is in contrast to the definition of effective area which also includes the neutrino interaction probability in order to obtain the event rate directly from a flux model. The target mass is roughly 0.1-20 MTon

189 190

Table 10.4. Summary of the event rates after different levels of the event selection. The values shown represent the rate for experimental data and the simulated atmospheric background (μ and νμ), and signal retention for four different spectra ranging from hard to soft. All signal events are truly down-going, truly interacting (through CC) inside p = 0.8 and z ≤ 300 m (see ﬁgure 8.1). The livetime of the experimental data is 329 days.

−2 −2 −Eν/10TeV −2 −Eν/1TeV −3 Level Exp. data Atmo. μ Atmo. νμ Eν Eν e Eν e Eν Level 1 ∼ 2,500 Hz Level 2 171 Hz 158 Hz 5.3 mHz 100% 100% 100% 100% Level 3 32 Hz 29 Hz 3.4 mHz 80.0% 83.1% 82.5% 76.8% Level 4 5.2 Hz 5.1 Hz 1.1 mHz 45.5% 47.2% 42.9% 31.2% Level 5 270 mHz 279 mHz 0.46 mHz 18.2% 21.0% 19.8% 14.9% Level 6 0.43 mHz 0.30 mHz 0.13 mHz 11.3% 10.0% 6.0% 4.0% Level 7 0.22 mHz 0.16 mHz 0.08 mHz 7.5% 6.3% 3.8% 2.0% 100

10−1 ] 2 10−2

10−3

10−4 Eﬀective area [m −90◦ ≤ δ<0◦ − ◦ ≤ δ<− ◦ −5 90 60 10 ◦ ◦ −60 ≤ δ<−30 −30◦ ≤ δ<0◦ 10−6 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

log10(Eν) [GeV]

102

101

100

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10−2 −90◦ ≤ δ<0◦ −90◦ ≤ δ<−60◦ Eﬀective target mass [MTon] −3 10 ◦ ◦ −60 ≤ δ<−30 −30◦ ≤ δ<0◦ 10−4 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

log10(Eν) [GeV]

Figure 10.28. Effective area (upper) and effective target mass (lower) at ﬁnal level.

191 for the LESE analysis, depending on energy. As a comparison, the HESE analysis, has an effective target mass of roughly 10 MTon for 10 TeV, and 500 MTon for energies above 100 TeV [3].

10.6 Likelihood Analysis We search for point sources using the un-binned maximum likelihood method presented in chapter 9, for the first year of data from the 86-string configuration of IceCube. We fit two parameters: the number of signal events nS and the spectral index γ of an unbroken power-law. The likelihood requires three observables for each event: a reconstructed direction (MPEFitSpline), an estimate of the angular uncertainty (σRescaled), and an estimate of the neutrino energy (sum of Millipede depositions contained in the instrumented volume). Two different searches are performed. One is looking for evidence for a neutrino source anywhere in the SH and is not motivated by any prior information of where such a source might be located. The other searches for an excess of signal-like emission at coordinates from a pre-defined list of known sources of electromagnetic radiation.

10.6.1 Sensitivity The performance of the analysis is estimated by observing the response of so- called pseudo-experiments, sets of randomized experimental data where signal events from an astrophysical spectrum at a pre-defined location and with a configured strength can be included. The test statistic TS defined in equation 9.6 is maximized for each pseudo-experiment. The sensitivity of the analysis is defined as the flux level at which 90% of pseudo-experiments without injected signal, i.e., nS = 0, give a p-value less than 0.5. This corresponds to the median upper limit in the absence of signal, i.e., from background fluctuations only. Further, discovery potential is defined by injecting signal events up to a the flux level at which 50% of all pseudo-experiments give a p-value corresponding to a 5σ discovery. For the declination shown in figure 9.4 this means we demand that 50% of the pseudo-experiments are above TS ∼ 19, where only ∼ 0.00003% (2.85 · 10−5%) [2] of the background-only experiments are expected. As mentioned in section 10.4.6 we optimize the cut on the BDT score to achieve the best sensitivity over the whole SH. The upper panel in figure 10.29 −2 shows the sensitivity for an Eν with a hard cut-off at 10 TeV and with different cuts applied to the BDT score. We found that a cut at 0.40 results in the best sensitivity considering the full range of declinations. The same cut also −2 −2 provides the optimal sensitivity for an unbroken Eν spectrum and an Eν spectrum with a hard cut-off at 1 TeV. Note that this investigation was done without a cut on σRescaled as discussed next. The cut on σRescaled was optimized

192 10−8 BDT score cut 0.30 BDT score cut 0.50 BDT score cut 0.40 BDT score cut 0.60 ] 1 − s 2 −

−9

[TeVcm 10 0 Φ

−1.0 −0.8 −0.6 −0.4 −0.2 0.0 sin δ

◦ ◦ σRescaled =1 σRescaled =4 ◦ ◦ σRescaled =2 σRescaled =5 −8 ◦ ] 10 σRescaled =3 no cut 1 − s 2 − [TeVcm 0 10−9 Φ

−1.0 −0.8 −0.6 −0.4 −0.2 0.0 sin δ

Figure 10.29. The plot in the upper panel shows the sensitivity for different cuts on the BDT score. The plot in the lower panel shows the sensitivity for different cuts −2 on σRescaled. Both plots are constructed for an Eν spectrum with a hard cut-off at 10 TeV.

193 to achieve the best sensitivity after application of a cut on the BDT score at −2 0.40. The lower panel in figure 10.29 shows the sensitivity for an Eν with a hard cut-off at 10 TeV and different cuts applied to σRescaled. The orange line represent the sensitivity without a cut. A small improvement was found ◦ −2 cutting at 5 . This was also investigated for an unbroken Eν spectra and −2 an Eν with a hard cut-off at 1 TeV, where the same conclusion was made. Note that both optimizations described above were done before a model with exponential cut-off was implemented in the likelihood algorithm. However, the difference in sensitivity between a model with a hard cut-off at an energy Ecut and a model with an exponential cut-off at the same energy is observed to be small. Figure 10.30 shows the median sensitivity of the LESE analysis for four −2 −Eν/1TeV −3 −2 −Eν/10 TeV signal hypotheses, dΦ/dEν =Φ0 · Eν e ,Φ0Eν , Φ0 · Eν e , −2 and Φ0 · Eν , as a function of declination, and corresponding to 1 year of data. Φ90% Further, it shows the upper limits νμ+ν¯μ (markers) at 90% C.L., for sources in a pre-defined list, see section 10.6.4. Note that the vertical axis show the (γ−1) −2 −1 flux in terms of Φ0 in units TeV cm s , where γ is the spectral index for each hypothesis, respectively. The upper panel in figure 10.31 shows the differential sensitivity of the −2 LESE analysis, created by simulating point sources with an Eν spectrum over quarter-decades in energy. The lower panel illustrates the joint efforts within the IceCube collaboration towards lowering the energy threshold for point source searches. It is also calculated by simulating point sources with an

−7 10 IceCube Preliminary E−2e−E/ 1TeV −3

] E 1 E−2e−E/ 10 TeV − −2

s E 2 − 10−8 cm 1) − ( γ

10−9 [TeV 0 Φ

Livetime: 329 d 10−10 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 sin δ

Figure 10.30. Median sensitivities of the LESE analysis as a function of declination (line) and source upper limits (markers) at 90% C.L., for four different signal spectra.

194 10−5 δ = −10◦ ] 1 δ − ◦

− = 40

s −6 ◦ 2 10 δ = −70 −

10−7 dE [TeVcm / 10−8 dN 2 E

10−9 102 103 104 105 106 Eν [GeV]

10−6

LESE (3y∗) ] IceCube Preliminary ∗ 1 STeVE (3y ) −

s −7 MESE (3y)

2 10 Through–going (3y∗) −

*scaled from 1y

10−8 dE [TeVcm / 10−9 dN 2 E δ = −60.0◦ 10−10 102 103 104 105 106 107 108 109 Eν (GeV)

Figure 10.31. The upper panel shows the differential sensitivity (solid lines) and discovery potential (dashed lines) for the LESE analysis at three different declinations in the SH, corresponding to 1 year of operation. The lower panel shows differential sensitivities at δ = −60◦, for four different IceCube analysis targeting the SH, corresponding to 3 years of operation.

195 −2 Eν spectrum over quarter-decades in energy. It shows the differential sensitivity at δ = −60◦ for four different analyses: the LESE analysis optimized in the energy range 100 GeV-afewTeV,theSTeVE(Starting TeV Events) analysis optimized at slightly higher energies (a few TeV - 100 TeV) [144], the MESE analysis which focused on energies in the region 100 TeV - 1 PeV [150], and the classic through-going point source analysis in black [149]. The sensitivities in this ﬁgure correspond to 3 years of operation and were estimated by simulating events with the livetime corresponding to the MESE analysis. To- gether these analyses cover an unprecedented energy range from about 100 GeV to EeV, almost 8 decades.

10.6.2 Test Statistic The test statistic, TS, PDFs are shown in figures 10.32 and 10.33, for several declinations. The red histogram represents the TS-values obtained for the null hypothesis, i.e., without injection of signal events. The orange and green histograms show the distribution obtained for the sensitivity and discov- −2 −Eν/10TeV ery potential, respectively. The two latter are calculated for an Eν e spectrum. Also shown, as dotted black lines, are the theoretical χ2 function with two degrees of freedom, discussed in section 9.2. The dashed lines show functional fits to the observed TS distributions for the null hypothesis. The function consists of a χ2 distribution plus a Dirac delta distribution at zero. The function is defined as: 2 TS = η · χ (nS;ndof), (10.6) where η is the ratio of pseudo-experiments with TS > 0 to pseudo-experiments with TS = 0, a correction factor caused by the restriction nS ≥ 0, and ndof is the number of effective degrees of freedom. Figure 10.34 show the two parameters of the function fitted to the TS distributions of the null hypothesis, as a function of declination. The ndof parameter is shown in black open circles. The horizontal line at 2.0 represent the theoretical value of ndof. It is clear from this figure that the actual ndof used in the likelihood is closer to 1.25, around which it fluctuates. A spline is fitted to the data points of each distribution and used as a template for all declinations when calculating the pre-trial p-values of the observed data sample. In the edge regions sinδ<−0.9 and sinδ>−0.1, we use the default value of 1.25. A similar spline construction is made for the η parameter shown as gray open circles. This value fluctuates around 0.5, i.e., 50% of the pseudo-experiments for the null hypothesis generate an over fluctuation (TS > 0). The default value used for the spline in the edge regions, is 0.5. All p-values are calculated using equation 10.6 with the values given by the parametrization of the η and ndof distributions. The p-values are robust against systematic uncertainties since they are calculated using thousands of pseudo-experiments on datasets randomized in right ascension.

196 100 100 ◦ χ2 Fit ◦ δ =0 (sin δ =0.00) χ2 Theory δ = −10 (sin δ = −0.17) − − 10 1 Discovery Potential 10 1 Sensitivity Background 10−2 10−2

10−3 10−3 PDF PDF

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100 100 δ = −20◦ (sin δ = −0.34) δ = −30◦ (sin δ = −0.50) 10−1 10−1

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10−6 10−6 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 Test statistic TS Test statistic TS

Figure 10.32. TS PDFs for declinations in the range from 0◦ to −50◦, in steps of 10◦. The TS-values for the null hypothesis are shown in red. The values obtained for the ﬂux corresponding to the sensitivity and discovery potential is shown in orange and −2 −Eν/10TeV green, respectively. The two latter are calculated for an Eν e spectrum. The theoretical χ2 function with two degrees of freedom is shown as dotted black lines, while the functional ﬁt to the observed TS distribution, using equation 10.6, for the null hypothesis is shown as a dashed line.

197 100 100 δ = −60◦ (sin δ = −0.87) δ = −70◦ (sin δ = −0.94) 10−1 10−1

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10−5 10−5

10−6 10−6 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 Test statistic TS Test statistic TS

Figure 10.33. TS PDFs for declinations −60◦ and −70◦. The TS-values for the null hypothesis are shown in red. The values obtained for the ﬂux corresponding to the sensitivity and discovery potential is shown in orange and green, respectively. The −2 −Eν/10TeV 2 two latter are calculated for an Eν e spectrum. The theoretical χ function with two degrees of freedom is shown as dotted black lines, while the functional ﬁt to the observed TS distribution, using equation 10.6, for the null hypothesis is shown as a dashed line.

Figure 10.34. The parameters of equation 10.6, ﬁtted to the TS distributions for the null hypothesis, as a function of declination. The ndof (η) parameter is shown in black (gray) open circles. The horizontal line at 2.0 (0.5) represent the theoretical value of ndof (η). A spline is ﬁtted to the data points of each distribution and used as a template for all declinations when calculating the pre-trial p-values of the observed data sample.

198 10.6.3 Sky Search An all sky search is performed, looking for an excess of neutrino candidate events in the SH, excluding a circle of 5◦ around the pole13. This search is not motivated by any prior knowledge regarding the position of the sources, instead we are limited by the large number of trials performed, which together with the angular resolution gives a limit on the effective number of individual points tested. The search is done on a HEALPix14 [155] grid corresponding to a resolution of about 0.5◦. The most interesting points are followed up with a finer binning. The so-called pre-trial p-values are calculated for each spot on the grid, using equation 10.6 with the parameters extracted from the spline fit shown in figure 10.34. The p-values represent the probability of compatibility with the background-only hypothesis. The most significant spot, the so-called hotspot, is reported from this search. A so-called trial correction is performed to take into account the number of trials (searches) performed on the sky. This is done by repeating the sky search on the entire SH for pure background samples, i.e., where the R.A. directions are scrambled. The distribution of pre-trial p-values for the hottest spot in the SH, for 10,000 randomized trials, is used to calculate a final so-called post-trial p-value. It is defined as the fraction of trials which give a p-value equal or greater than the observed pre-trial p-value.

10.6.4 Search in a List of 96 Candidate Sources We also perform a search at positions in a pre-deﬁned source list of 96 astrophysical objects: all 84 TeVCat15 [156] sources in the SH (δ ≤ 0◦) (as of May 2015) and in addition 12 sources in the standard IceCube point source list: • GX 339-4, Cir X-1, PKS 0426-380, PKS 0537-441, QSO 2022-077, PKS 1406-076, PKS 0727-11, QSO 1730-130, PKS 0454-234, PKS 1622-297, PKS 1454-354, ESO 139-G12. The TeVCat listing consists of sources seen by ground-based γ-ray experiments, such as Very Energetic Radiation Imaging Telescope Array System (VERITAS), MAGIC (Major Atmospheric Gamma Imaging Cherenkov Tele- scopes), and HESS. Here we consider sources from the catalogs ‘Default Cata- log’ and ‘Newly Announced’, stable sources published or pending publication in refereed journals. The Galactic sources include e.g. SNRs, PWNs, star formation regions, and compact binary systems, while the extragalactic sources include e.g. AGNs and Radio Galaxies. Figure 10.35 shows all 96 sources in a sky map using Galactic (Equatorial) coordinates in the upper (lower) panel. The sources are categorized as they appear in the TeVCat listing. Many of

13The likelihood algorithm is not efﬁcient close to the pole, since we run out of disjoint scrambling sets. 14http://healpix.sourceforge.net 15http://tevcat.uchicago.edu

199 Galactic Plane Binary BL Lac Globular cluster SNR Not identiﬁed Fanaroﬀ-Riley I FSRQ Superbubbles DARK Galactic Center XB/mqso PWN Massive Star Cluster Starburst Seyfert

+75◦

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5◦ 0◦ -5◦ -90◦ -75◦ -60◦ -45◦ -30◦ -15◦ 0◦ 15◦ 30◦ 45◦ 60◦ 75◦ 90◦

(a) Galactic coordinates

+75◦

+45◦

+15◦

24h 0h

−15◦

−45◦ Equatorial −75◦

(b) Equatorial coordinates

Figure 10.35. Sky map of the 96 sources considered in the source list scan. The map is shown in galactic (a) and equatorial (b) coordinates (J2000). The source position of each of the sources is indicated, divided into categories as they appear in the TeVCat listing. The Equatorial (Galactic) plane is shown as a curved black line in the upper (lower) plot.

200 these sources have small angular distances from each other, smaller than the angular uncertainty of the analysis. This effect of correlation is included in the TS evaluation as the scrambling is done using the actual, unaltered, source list. The p-values are calculated for each of the 96 sources in the source list, using equation 10.6 with parameters shown in ﬁgure 10.34. The p-value for the most signiﬁcant source is trial corrected using background-only scrambled datasets. The procedure follows the one described in section 10.6.3, but only considers the hotspot among the 96 sources in each trial.

10.7 Results The events in the final sample of experimental data were unblinded, i.e., the true event timestamps were used to convert the local coordinates to equatorial coordinates (α, δ). The resulting p-values from the sky search are shown in figure 10.36, where the hotspot is marked with a black circle. The figure is shown in equatorial coordinates. The hotspot, is located at α = 305.2◦ and δ = −8.5◦, with best fit −4 parametersn ˆS = 18.3 andγ ˆ = 3.5. It has a pre-trial p-value of 1.6 · 10 . The distribution of pre-trial p-values from scrambled trials is shown in figure 10.37. The vertical lines represent the 1, 2, and 3 σ limits, respectively, calculated from the pre-trial p-value distribution. The observed pre-trial p-value is indicated with a solid vertical line. The corresponding post-trial p-value equals 88.1%, i.e., the search is well compatible with the expectation from background. The best-fit values,n ˆS andγ ˆ are shown for all bins in the sky scan in the upper and lower panel of figure 10.38, respectively. Figure 10.39 showsn ˆS as function of the number of injected events, and is constructed from trials with signal at varying strengths injected on top of a randomized experimental data sample at the declination of the hottest spot, i.e., δ = −8.5◦. The number of fitted signal eventsn ˆS for the hotspot is shown as a black horizontal line. The observed value ofn ˆS = 18.3 corresponds roughly to about 15 injected events. Note that this illustrates the situation before trial correction is applied. In the upper panel of figure 10.40 we show a zoom-in on the TS distribution in the area surrounding the hottest spot in the sky search. The position of the hottest spot is illustrated with a red open circle with a cross. The hottest source in the a priori source list is shown with a red open circle without a cross. The individual event positions in the final sample are illustrated as black dots. The lower panel of figure 10.40 shows a zoom-in on the same coordinates, with color indicating the so-called individual event weight ln(1 + nSχi) for each event contributing to the test statistic at this particular position and with the best-fit parameters of the hottest spot (see equation 9.6),

201 202

Figure 10.36. Pre-trial significance sky map in equatorial coordinates (J2000) of the sky search in the SH. The black line indicates the Galactic plane. The position of the most significant position is indicated with a black circle. where χ is defined as: i 1 S i χi = Wi − 1 . (10.7) N S bkg,i The most significant source in the a priori list was QSO 2022-07716, located at α = 306.5◦ and δ = −7.6◦, a FSRQ with a pre-trial p-value of 2.5·10−3. The p-value distribution for the scrambled trials using the pre-defined source list is shown in gray in figure 10.41. The vertical lines represent the 1, 2, and 3 σ limits, respectively. Note that the scale of the p-values is significantly lower than the corresponding values in figure 10.36 for the sky scan. This is due to the much lower number of effective trials in the search using a pre-defined source list. The observed pre-trial p-value for the hottest source is indicated with a solid vertical line. The post-trial p-value equals 14.8%, and is compatible with a pure background scenario. For the sources in the list, we calculate the upper limit at 90% Confidence Level (C.L.), based on the classical approach [157], −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 for the signal hypotheses: Eν ,Eν e ,Eν e , and Eν , see figure 10.30. The limits of the five most significant sources are presented in table 10.5 along with the best-fit parametersn ˆS andγ ˆ. Note that we do not consider under-fluctuations, i.e., for observed values of TS below the median TS for the background-only hypothesis, we report the corresponding median upper limit.

16Alternate name: 2EG J2023-0836

0.07 1 σ 0.06 2 σ 3 σ 0.05 Observed p − value Scrambled trials 0.04

0.03

Fraction of trials 0.02

0.01

0.00 2.0 3.0 4.0 5.0 6.0 7.0 8.0 − log10(p-value)

Figure 10.37. The distribution of the smallest p-value in the Southern hemisphere, obtained from randomized data. The vertical lines represent the 1, 2, and 3 σ limits, respectively. The observed pre-trial p-value is indicated with a solid vertical line.

203 Figure 10.38. The upper (lower) plot shows the distribution of the best-ﬁt valuesn ˆS (ˆγ) of the observed data sample in the sky search in the SH. The sky maps are shown in equatorial coordinates (J2000). The black line indicates the Galactic plane. The position of the most signiﬁcant position is indicated with a black circle. The sky map forγ ˆ illustrates the distribution of values for directions withn ˆS > 0.

204 80 10−1

60 10−2 50

30 10−3 20

10 Number of Fitted Events

0 10−4 0 10 20 30 40 50 Number of Injected Events

Figure 10.39. Distribution of the number of fitted signal eventsn ˆS as function of the number of injected events at the declination of the hottest spot, i.e., δ = −8.5◦. The plot −2 is constructed from trials where signal events from an unbroken Eν neutrino spectra with a hard cut-off at 10 TeV, are injected at a fixed position, on top of a randomized experimental data sample. For zero injected events we used 100,000 trials, while for the others we used 10,000 trials. The entries in each bin on the horizontal axis (the number of injected events) are normalized so that the sum in each column equals 1. The horizontal black line show the observed best-fitn ˆS for the hottest spot in the Southern hemisphere sky search.

205 Figure 10.40. The upper panel shows a zoom-in on the test statistic TS distribution in the area surrounding the hottest spot (red circle with red cross). The lower panel shows the individual event weights χi defined in equation 10.7, normalized so that the highest weight corresponds to 1. The black dots show the individual event positions of the final sample. The position of the hottest source in pre-defined source list is shown with a red open circle without a cross.

206 Table 10.5. Results for the 10 most significant astrophysical sources in the a priori search list. Sources are shown in descending order of p-value. The p-values are pre-trial probability of compatibility with the background-only hypothesis. The nˆS and γˆ columns give the best-fit values for the number of signal events and spectral index of an unbroken power-law, respectively. The last four columns show the 90% C.L. γ−1 − − upper flux limits for νμ + ν¯μ, based on the classical approach [157], for different source spectra normalizations in units TeV cm 2 s 1.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν QSO 2022-077 306.5 -7.6 2.61 17.3 3.5 6.74·10−10 1.56·10−9 5.81·10−9 1.27·10−9 HESS J1718-385 259.5 -38.5 1.58 5.9 3.4 7.62·10−10 2.80·10−9 3.21·10−8 5.58·10−9 HESS J1841-055 280.3 -5.5 1.48 5.0 2.4 5.01·10−10 1.19·10−9 4.52·10−9 9.88·10−10 KUV 00311-1938 8.4 -19.4 1.40 7.1 3.4 8.25·10−10 2.47·10−9 1.33·10−8 2.65·10−9 30 Dor-C 83.9 -69.1 1.04 2.3 3.6 9.14·10−10 3.65·10−9 5.35·10−8 7.92·10−9 HESS J1026-582 156.6 -58.2 1.04 2.0 3.0 6.67·10−10 2.61·10−9 3.37·10−8 5.39·10−9 LMC N132D 81.3 -69.6 1.03 2.1 3.7 9.41·10−10 3.64·10−9 5.38·10−8 7.85·10−9 LHA 120 84.3 -69.1 1.01 2.2 3.6 9.19·10−10 3.56·10−9 5.33·10−8 7.78·10−9 PKS 1510-089 228.3 -9.1 1.00 6.3 4.5 4.53·10−10 1.02·10−9 3.79·10−9 8.16·10−10 NGC 253 11.9 -25.3 1.00 5.3 3.3 7.10·10−10 2.83·10−9 2.05·10−8 3.88·10−9 207 0.08 1 σ 0.07 2 σ σ 0.06 3 Observed p − value 0.05 Scrambled trials

0.04

0.03 Fraction of trials 0.02

0.01

0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 − log10(p-value)

Figure 10.41. The distribution of the smallest p-value out of the 96 objects in the pre- deﬁned source list, obtained from randomized data. The vertical lines represent the 1, 2, and 3 σ limits, respectively. The observed pre-trial p-value is indicated with a solid vertical line.

208 Table 10.6. Datasets used in the evaluation of systematic uncertainties.

Generator Type Dataset Notes

NuGen νμ 10602 Baseline

νμ 10039 Absorption +10%

νμ 10040 Scattering +10%

νμ 10041 Scattering and absorption -10%

νμ 10437 DOM efﬁciency -10%

νμ 10438 DOM efﬁciency +10%

10.8 Systematic Uncertainties The analysis described in this chapter uses scrambled experimental data to estimate the background. The p-values are not sensitive to theoretical uncertainties on fluxes of atmospheric neutrinos and muons, and are robust against uncertainties in the simulation of the detector. The sensitivity and upper limits however are calculated using simulated neutrino events, including simulations of the detector response, detector medium, etc. These are therefore affected by the systematic uncertainties on these quantities. The systematic uncertainties of main importance in this analysis are the ones related to the detector efficiency such as the ice model used, uncertainties in the neutrino-nucleon cross-sections, and the absolute light detection efficiency of the DOM (DOM efficiency). The impact of systematic uncertainties is evaluated by studying the change in sensitivity when injecting signal events from a model different from the so-called baseline model (dataset 10602) used in the analysis up to this point. Note that the analysis chain including all cuts is unchanged during these studies. We use a set of five signal simulations, each modified with respect to one of the systematic uncertainties considered, see table 10.6. Each row in the table specifies the neutrino flavor, dataset number, and change in the configuration.

Ice Properties One of the largest uncertainties comes from the uncertainty in the modeling of the ice in the detector. Two parameters, the scattering and absorption lengths, see section 5.2, were varied with respect to the baseline values. Note that the uncertainties in these parameters are correlated through the ice model. We study three different datasets: dataset 10039 and 10040 have a 10% increase in the absorption and scattering length, respectively, while dataset 10041 has a 10% decrease in both the scattering and absorption lengths. This leads to a

209 −2 systematic uncertainty of 4% on the sensitivity for an Eν spectrum, and 15% on the sensitivity for a spectrum with an exponential cut-off at 10 TeV.

Detector Properties The uncertainty on the absolute efficiency of the optical modules, the so-called DOM efficiency (see section 6.1.3), is studied using a conservative estimate of ±10%. This is a linear scaling of how well the light is converted to electrical signals in the DOMs, including PMT quantum efficiency, transmittance of the optical gel and glass housing, local hole ice, etc. The 10% roughly corresponds to the standard deviation of this quantity as measured in the laboratory and again after deployment. The effect for all spectra considered is about 10%, see table 10.7.

Cross-Section As mentioned in section 6.1.1, the baseline simulation of muon-neutrinos is conﬁgured with CTEQ5 [104] PDFs of the parton functions and cross-sections from [103]. Another cross-section model used in IceCube is CSMS (Cooper- Sarkar, Mertsch and Sarkar) [158]. It yields a slightly lower event rate, ≤5%, compared to CTEQ5. This value is used to represent the systematic uncertainty in the cross-section for all neutrino spectra considered.

Analysis Method The ﬁnal likelihood depends on a few random components (scrambling of dataset, Poisson selection from number of signal events, etc.). The effect of this randomness was estimated by calculating the sensitivity for the baseline dataset with different input seeds. This calculation shows that is it less than 0.5%, and is hence negligible compared to the other systematic uncertainties considered. Further, there is a probability that the IceTop Veto applied in the event selection, see section 10.4.5, will veto signal neutrinos by random coincidence. This effect was estimated to roughly 0.13% and can hence also be neglected in comparison to the impact of other uncertainties.

Results The results from the systematics studies are shown in table 10.7 and figure 10.42, illustrating the resulting uncertainty on the sensitivity for four different signal spectra. The numbers presented in the table represent the square-root of the sum of quadratic contributions from each of the categories of systematics considered. These are rough estimates, and subject to statistical uncertainties due to the limited number of simulated events in the datasets used. The total uncertainty on each flux model is also illustrated as bands in figure 10.42. The band widths correspond to the values in the bottom line of table 10.7, for each flux model.

210 10−7 E−2e−E/ 1TeV E−3 ] 1 E−2e−E/ 10 TeV −

s −2

2 E − 10−8 cm 1) − ( γ

10−9 [TeV 0 Φ

10−10 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 sin δ

Figure 10.42. Systematics impact on sensitivity shown for four different neutrino spectra. Each band represents the square-root of the quadratic sum of the contributions from all systematics considered, for each ﬂux model.

Table 10.7. A summary of the systematics considered and the impact on the ﬁnal sensitivities for various neutrino spectra. The total is the square-root of the quadratic sum of each contribution, for each column, respectively.

−2 −2 −Eν/10TeV −2 −Eν/1TeV −3 Systematic Uncertainty Eν Eν e Eν e Eν Absorption & scattering 4% 15% 15% 13% DOM efﬁciency 12% 8% 9% 7% Cross-section ≤ 5% ≤ 5% ≤ 5% ≤ 5% Total 14% 18% 18% 16%

211

11. Summary and Outlook

"Neutrino physics is largely an art of learning a great deal by observing nothing." Haim Harari

In this thesis we presented the results of searches for astrophysical point sources of neutrinos in the Southern hemisphere (SH) using data from the first year of the completed 86-string configuration of IceCube, the so-called Low-Energy Starting Events (LESE) analysis. The analysis builds on an event selection of low-energy neutrino candidates, tracks starting inside the instrumented volume, and is sensitive to neutrinos in the range from 100 GeV to a few TeV. Background rejection is achieved by using several advanced veto techniques. The final sample of experimental data consists of 6191 events and corresponds to a livetime of 329 days. The median angular resolution at final ◦ −2 −Eν/10 TeV level is 1.7 for an Eν e spectrum and slightly better for an unbroken −2 Eν spectrum. The events in the final sample were used in searches for spacial clustering in the SH: one search scanning the whole SH and another targeting a list of 96 pre-defined sources. The latter were selected from a list of known γ-ray emitters seen by ground-based experiments such as VERITAS, MAGIC, and HESS. No evidence of neutrino emission from point-like sources in the SH at low-energies (100 GeV - few TeV) was found. The most significant spot in the sky search has a post-trial p-value of 88.1% and was fit with 18.3 signal −3.5 events with an Eν spectrum. The most significant source in the source list has a post-trial p-value of 14.8% and was fit with 17.3 signal events with an −3.5 Eν spectrum. Upper limits at 90% C.L. were calculated for all sources for a number of signal hypotheses, see figure 10.30 and the tables in appendix B (the 10 most significant sources are also shown in table 10.5). These searches are quite model-independent. An increased sensitivity can be achieved when targeting models specific for a source or a source class, i.e., by adding model-dependent information in the likelihood. E.g. one can study catalogs of similar object using so-called stacking of sources, see e.g. [159] and [160]. Further, many astrophysical objects have time-dependent

213 ] 18 1 − s 16 δ = −60◦ 2 √ − 14 t @1year δ = −15◦ 12 √ t @1year

TeV cm 10

10 8 − 6

4 / dE [10 2 dN 2

E 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Years of IceCube

−2 −Eν/10 TeV Figure 11.1. LESE point source sensitivity at two declinations for an Eν e spectrum, as a function of years of√ data-taking. Due to the low background rate, the sensitivity improves faster than the t limit (dashed line). Adding four more years of data will lead to a sensitivity that is a factor 3-4 times better than the results presented in this thesis.

emission. By limiting the sample to a specific time interval the background can be suppressed substantially. Plans also exist to use the LESE event sample to search for extended point sources and for neutrino emission in the Galactic plane. Ultimately, more data are needed to identify astrophysical objects with neutrino emission. Three more years of IceCube data with the 86-string configuration are ready to be incorporated into this analysis. The sensitivity is expected to improve slightly faster than square-root of time, due to the relatively low background rate. This is illustrated for two different declinations in figure 11.1. The improvement can be accelerated by developments in background rejection techniques and improvements in the angular reconstruction for low- energy events. Further, a small gain can be achieved by expanding the likelihood description to include the individual probability for events to be starting inside the detector volume, determined from reconstructions. Although IceCube’s observation of a diffuse flux of astrophysical neutrinos marks the beginning of neutrino astronomy, it seems IceCube is not yet sensitive to the neutrino point source flux levels expected on the basis of γ-ray experiments, particular at the lowest energies. The limits presented in this thesis are about one order of magnitude higher than what is achieved with the ANTARES neutrino telescope in the Mediterranean. For studies in the SH,

214 Figure 11.2. Proposed IceCube extension, IceCube Gen-2.

ANTARES benefits by using the Earth to remove atmospheric muons. Fur- ther, photons in sea water scatter less than in glacial ice but are more rapidly absorbed. This lack of late scattered photons results in improved reconstruction accuracy for ANTARES. The joint efforts of the IceCube collaboration in the Southern hemisphere now give us sensitivities for point sources in the energy range from about 100 GeV to EeV, getting closer to the ANTARES sensitivities. Currently plans exist to expand the IceCube Neutrino Observatory in several ways. Figure 11.2 shows an illustration of the proposed IceCube Gen-2 facility [161], including both a low-energy extension, The Precision IceCube Next Generation Upgrade (PINGU) shown in purple (inside the green region), which is an even denser central sub-array inside DeepCore, and a high- energy extension surrounding IceCube reaching an instrumented volume of O(10) km3, shown in blue. The current IceCube (DeepCore) detector is shown in red (green). The physics goals for PINGU include determining the neutrino mass hierarchy, studying neutrino oscillations, and dark matter. The high- energy extension will focus on energies above 100 TeV to characterize the observed diffuse flux of neutrinos as well as to continue the search for astrophysical point sources of neutrinos. Plans also exist to add an extended surface veto that will help in the rejection of the atmospheric background for the searches in the SH. Further, the proposed KM3NeT Neutrino Telescope in the Mediterranean sea, hopes to reach the sensitivity required to observe TeV Galactic sources in the SH within a couple of years of livetime [162]. The origin of the high-energy cosmic rays remain a mystery, but it continues to be an exiting period for neutrino astronomy, as we continue to search for the first point source of high-energy neutrinos.

215

Summary in Swedish Sammanfattning på svenska

Avhandlingens titel: En upptäcksfärd i Universum med hjälp av neutriner - En jakt på punktkällor på södra stjärnhimlen i data från neutrinoteleskopet IceCube

Neutriner är unika eftersom att de bara interagerar med andra partiklar genom den s.k. svaga växelverkan. Det gör dem särskilt lämpliga att använda som budbärare av kosmisk information. Instrumentet IceCube är unikt i sitt slag och har ett brett forskningsområde som omfattar forskning både på den största skalan i Universum där vi ﬁnner bl.a. den mörka materian och källorna till kosmisk strålning samt på den minsta skalan där vi undersöker egenskaperna hos naturens minsta beståndsdelar som t.ex. neutriners oscillationer. I denna avhandling undersöker vi förekomsten av neutriner från södra stjärn- himlen av lägre energi än tidigare (vi bortser här från neutriner i MeV-området) och är den första i sitt slag. De källor som producerar kosmisk strålning vid intermediära energier bör även kunna producera neutriner som skulle ha mis- sats av tidigare analyser men skulle kunna observeras med de metoder som beskrivs i denna avhandling. Neutrinerna kan tydligt visa var denna del av den kosmiska strålningen bildas och/eller accelereras, en fråga som har intresserat det vetenskapliga samfundet i över 100 år.

Var kommer den kosmisk strålningen ifrån? Jorden bombarderas ständigt av laddade partiklar, s.k. kosmiska partiklar, främst protoner, som produceras någonstans ute i Universum. Deras energier kan uppgå till ﬂera miljoner gånger högre än vad vi själva kan åstadkomma på Jorden, t.ex. vid acceleratorn LHC vid CERN. Trots att förekomsten av dessa partiklar upptäcktes redan 1912 av den österrikisk-amerikanska fysikern Vic- tor Hess, vet vi väldigt lite om hur och var de skapades. Det beror främst på att partiklarna är elektriskt laddade och därför böjer av i de magnetiska fälten i Universum (och därmed inte länge pekar tillbaka till den plats där de skapades och/eller accelererades) samt att antalet partiklar som når Jorden snabbt avtar med stigande partikelenergi.

217 I Universum ﬁnns en mängd olika fenomen som i det närmaste kan beteck- nas som extrema: kolliderande galaxer, svarta hål, exploderande stjärnor, m.m. Vid dessa frigörs en ofantlig mängd energi som i teorin skulle kunna skapa och accelerera kosmiska partiklar. Det råder ingen brist på potentiella kandidater men än har man inte på ett övertygande sätt lyckats påvisa en sådan miljö där detta sker. Svaret på var de laddade partiklarna kommer ifrån och hur de accelereras är en av de mest intressanta och uppmärksammade frågorna inom fysik idag.

Vad gör neutriner så intressanta? Neutriner är unika budbärare av information. Eftersom de saknar elektrisk laddning kan de färdas utan att böja av i Universums magnetfält. Dessutom har de en väldigt svag växelverkan med annan materia, vilket gör att de inte absorberas eller växelverkar på annat sätt under sin resa igenom Universum. De färdas i en rak linje från den plats de skapas rakt ut i Universum. Genom att observera de neutriner som når Jorden kan vi därför för första gången få en bild av vad som sker i några av Universums mest extrema och energitäta platser. Neutriner fungerar dessutom som ett lackmustest för att skilja på två olika typer av acceleration, s.k. leptonisk och hadronisk. Den senare till skillnad från den första är nämligen garanterad att ge ett stort ﬂöde av neutriner som re- sultatet av en kedja av sönderfall av tunga mesoner, främst pioner och kaoner. Genom att lokalisera neutrinostrålning kan vi alltså utforska platser där protoner och tyngre hadroner skapas och/eller accelereras. En observation av neutriner möjliggör också bildandet av en unik helhets- bild där vi kan knyta samman kunskap från olika kanaler (t.ex. med obser- vationer som gjorts i det elektromagnetiska spektrat (Röntgen-, mikrovågs-, radiostrålning, etc.)) för att på så vis skapa oss en större förståelse för redan bekanta fenomen som t.ex. aktiva galaxkärnor (AGNs). IceCube-kollaborationen publicerade 2013 en artikel i Science Magazine om upptäckten av de första högenergetiska neutrinerna med ursprung någon- stans utanför vårt solsystem. Upptäckten väckte stor uppmärksamhet och blev prisad som årets fysikgenombrott av den brittiska tidskriften Physics World samt gav upphov till hundratals publicerade vetenskapliga artiklar som vidare försökte förklara deras ursprung. Analysen som presenteras i denna avhandling rör neutriner av något lägre energi, vilka är särskilt svåra att fånga då de lätt förväxlas med partiklar från bakgrundsprocesser i Jordens atmosfär.

Hur detekterar vi neutriner? Eftersom neutriner endast växelverkan med den svaga växelverkan är de väldigt svåra att påvisa. Oftast krävs enorma detektorer och mätningar i ﬂera år. ‘The

218 Figure 11.3. En illustration av ‘The IceCube Neutrino Observatory’ belägen i glaciären under den geograﬁska Sydpolen på Antarktis. Credit: Credit: Jamie Yang/WIPAC.

IceCube Neutrino Observatory’ är ett unikt neutrinoteleskop beläget på 1,5 till 2,5 km djup under ytan vid den geografiska Sydpolen på Antarktis. Det består av totalt 5160 optiska moduler som tillsammans med isen skapar en ku- bikkilometer stor instrumenterad volym i tre dimensioner, se illustrationen i figur 11.3. Det internationella projektet IceCube inkluderar runt 300 forskare från ca 40 institutioner i 12 länder. I Sverige finns det två forskningsgrupper: en vid Uppsala universitet och en vid Stockholms universitet. Utöver de resurser som finns på universiteten, stöds projektet av NSF (National Science Foundation) i USA samt bl.a. Vetenskapsrådet och Knut och Alice Wallenbergs Stiftelse. De optiska modulerna i IceCube, s.k. DOM, detekterar ljus (s.k. Cherenkov- strålning) som skapas då elektriskt laddade partiklar färdas igenom isen med en hastighet över ljusets hastighet i is. Sådana laddade partiklar skapas bl.a. då neutriner växelverkar med atomkärnor i isen. Men laddade partiklar skapas också då kosmisk strålning växelverkan med partiklar i Jordens atmosfär. Till stor del handlar avhandlingen om att skilja på dessa två olika typer av händelser i detektorn genom att konstruera variabler och algoritmer som väljer ut de händelser som liknar signal som har sitt ursprung utanför solsystemet.

219 Detta görs genom att analysera vilka av de optiska modulerna som träffats, vid vilken tidpunkt samt hur mycket energi som deponerades i modulens om- givning. Med hjälp av den informationen kan vi återskapa den ursprungliga neutrinens riktning och energi. Analysen är mycket komplex då bakgrunden av ointressanta händelser är ﬂera miljoner gånger högre än antalet intressanta signalhändelser.

Analysmetod och Resultat I analysen har vi fokuserat på händelser som startar i en inre delmängd av detektorn. Detta görs genom att utnyttja de yttersta lagren av optiska moduler som ett veto. På så vis kan vi skilja ut händelser där en neutrino växelverkar och bildar en laddad partikel inuti detektorn från händelser där en laddad partikel åker igenom vetolagret och där avger spår i form av ljus som fångas upp av modulerna. Tidigare analyser har fokuserat på högre energier för att därigenom kunna reducera den kvarvarande bakgrunden av laddade partiklar från atmosfären men har då förlorat all känslighet för neutriner vid lägre energier. Analysen involverar flera olika steg i vilka vi fokuserar på olika egenskaper, bl.a. kvalitén på riktningsinformationen samt sannolikheten för s.k. läckage, där en laddad partikel smiter in igenom vetot utan att där lämna några spår efter sig, och därmed härmar en startande signalhändelse. Ett av stegen involverar en s.k. maskininlärningsalgoritm av typen BDT som kan tränas att känna igen signal och bakgrund genom att kombinera flera olika variabler och behandla dem simultant. För att välja ut de variabler som vi använder för att separera signalen från bakgrunden av laddade partiklar, främst myoner (tunga elektronliknande partiklar), har vi använt oss av mycket detaljerade simuleringar av både signal och bakgrund. Den simulerade bakgrunden har dessutom jämförts med ett litet urval av experimentell data för att verifiera simuleringens tillförlitlighet. Simuleringen tar bl.a. hänsyn till partiklarnas växelverkan, ljusets spridning i isen samt detektorernas reaktion på ljuset samt deras brus. Selektionen av händelser är unik också i det att vi accepterar signalhän- delser från hela södra halvklotet istället för som i tidigare analyser vid lägre energier fokusera på mindre lokaliserade områden. En av de stora utmaningarna här har varit att kunna hantera den enorma mängd data som då samlas in. För att klara av den mängden händelser har ett nytt dataformat skapats vilket kom- primerar all insamlad data, med en minimal förlust av information. Tillsam- mans med det filter som vi utvecklat för ändamålet kunde händelserna samlas in och sparas i en gigantisk händelsebank med drygt 6 miljarder händelser per år (2011-). Ett flertal forskare inom IceCube har uttryckt intresse för att använda denna händelsebank och en analys vid något högre energier har sitt ursprung i samma selektion av händelser.

220 I analysens sista steg använder vi händelsernas riktning i kombination med deponerad energi i ett stort sannolikhetstest som testar om den experimentella datamängden har en komponent från punktlika neutrinokällor mot hypotesen att den är isotropt fördelad och således inte innehåller neutrinokällor starkare än vad vår känslighet kan påvisa. Känsligheten för flera olika typer av signal beräknades och hela analysen genomgick en rigorös kontroll inom IceCube- kollaborationen innan vi fick tillåtelse att titta på den slutgiltiga fördelningen av händelser med en livstid av ca 329 dagar. Ingen lokaliserad källa av neutriner kunde påvisas i händelsebanken varför gränser beräknades för dess möjliga flöde av partiklar som funktion av dess koordinater på södra stjärnhimlen. Dessutom beräknades gränser för 96 st för-definierade källor som valts ut då de observerats i mycket högenergetisk elektromagnetisk strålning av andra experiment. Analysen som presenteras i denna avhandling ger banbrytande bevis för att den metoden som användes fungerar. Genom att utnyttja de yttre delarna av den instrumenterade volymen av ljuskänsliga detektorer kan vi nå en mycket hög grad av känslighet för neutriner från den södra stjärnhimlen även vid låga energier. Ytterligare tre år av data från IceCube finns att tillgå och ger en faktor 3-4 gånger högre känslighet.

221

Appendix A. BDT Input Variables

This appendix contains plots of all 22 variables considered in the initial BDT described in section 10.4.6. The legend is described in section 10.4. Data from ‘Burnsample-BIG’ is used to represent experimental data.

30 16

14 25 12 20 10

15 8

Rate [mHz] 10 Rate [mHz] 4 5 2

0 0 −600 −400 −200 0 200 400 600 0 100 200 300 400 500 600 ﬁniteReco z − coord. [m] ﬁniteReco xy − distance [m] (a) z-coordinate of reconstructed (b) Distance in xy-plane of interaction vertex reconstructed interaction vertex

45 25

35 20

30 15 25

20 10

Rate [mHz] 15 Rate [mHz]

10 5 5

0 0 10 20 30 40 50 60 0 2 4 6 8 10 LLHR Starting Track ﬁniteReco rlogl (c) LLHR Starting Track (d) rlogl of reconstructed interaction vertex

Figure A.1. BDT variables

223 25 20

20 15

15 10 10 Rate [mHz] Rate [mHz] 5 5

0 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 −0.4 −0.2 0.0 0.2 0.4 v / Magnitude of LineFit [m ns] x − component of vLineFit [m/ns] (a) Magnitude of vLineFit (b) x-component of vLineFit

20 25

20 15

15 10 10 Rate [mHz] Rate [mHz] 5 5

0 0 −0.4 −0.2 0.0 0.2 0.4 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.10.2 − v / y − component of vLineFit [m/ns] z component of LineFit [m ns] (c) y-component of vLineFit (d) z-component of vLineFit

14 35

12 30

10 25

8 20

6 15 Rate [mHz] Rate [mHz] 4 10

2 5

0 0 0 10 20 30 40 50 60 70 80 90 6 7 8 9 10 11 12 13 14 15 θ [◦] rlogl (e) zenith angle of SPEFit2 (f) rlogl of SPEFit2

Figure A.2. BDT variables cont.

224 102 40

101 30

100 20

15 Rate [mHz] Rate [mHz] − 10 1 10

−2 10 0 −400 −200 0 200 400 0 100 200 300 400 500 600 z − coord. of PTP − point [m] xy − distance of PTP − point [m] (a) z-coordinate of PTP (b) Distance in xy-plane of PTP

101 20

15 100

10 Rate [mHz] Rate [mHz] 10−1 5

10−2 0 0 500 1000 1500 2000 0 20 40 60 80 100 Total charge [p.e.] Accumulation [ns] (c) Total charge (d) Accumulation time of pulses (TWSRTOfﬂinePulses) (TWSRTOfﬂinePulses)

20 30

25 15 20

10 15 Rate [mHz] Rate [mHz] 10 5 5

0 0 −200 −150 −100 −50 0 50 100 −1.0 −0.5 0.0 0.5 1.0 ZTravel [m] Hit distribution smoothness (e) ZTravel (f) Smoothness of pulses in (TWSRTOfﬂinePulses)

Figure A.3. BDT variables cont.

225 30 60

25 50

20 40

15 30

Rate [mHz] 10 Rate [mHz] 20

5 10

0 0 0 20 40 60 80 100 0 20 40 60 80 100 Charge of late pulses [p.e.] No. of direct pulses (D) [p.e.] (a) Total charge of late pulses (b) Number of direct pulses (tres > 15 ns) (tres category D)

40 101

35 0 30 10

25 −1 20 10 Rate [mHz]

Rate [mHz] 15 10−2 10

5 10−3 0 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 − Dist. between ﬁrst hit and PTP − point [m] Length fR PTP [m] (c) Distance between ﬁrst hit (d) Distance between PTP and and PTP reconstructed interaction vertex

25 30

25 20

20 15 15 10

Rate [mHz] Rate [mHz] 10

5 5

0 0 −500 −400 −300 −200 −100 0 100 200 0 50 100 150 200 250 z − coord. of COG [m] σz of COG [m] (e) z-coordinate of COG (f) Spread in z-coordinate of COG (TWSRTOfﬂinePulses) (TWSRTOfﬂinePulses)

Figure A.4. BDT variables cont.

226 Appendix B. Result Tables

This appendix contains the tabulated results for sources in the a priori search list of 96 astrophysical objects1, see section 10.6.4.

1Note that the point source likelihood algorithm did not converge for ‘SNR G015.4+00.1’ and ‘SHBL J001355.9-185406’. No limits are reported for these sources.

227 228

Table 11.1. Results for astrophysical sources in the a priori search list. Sources are shown in descending order of declination. The p-values represent the pre-trial probability of compatibility with the background-only hypothesis. The nˆS and γˆ columns give the best-ﬁt values for the number of signal events and the spectral index of an unbroken power-law, respectively. When nˆS < 0.05, no p-value or γˆ are reported. The last four columns show the 90% C.L. upper ﬂux limits for νμ +ν¯μ, based on the classical approach [157], for different source spectra normalizations in units TeVγ−1 cm−2 s−1. This table continues on the following pages.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν IGR J18490-0000 282.2 0.0 - 0.0 - 9.36·10−10 2.00·10−9 7.07·10−9 1.62·10−9 HESS J1848-018 282.0 -1.8 - 0.0 - 5.12·10−10 1.08·10−9 3.80·10−9 8.55·10−10 HESS J1846-029 281.6 -2.9 - 0.0 - 3.53·10−10 7.38·10−10 2.63·10−9 5.91·10−10 HESS J1843-033 280.8 -3.3 - 0.0 - 3.01·10−10 6.59·10−10 2.38·10−9 5.32·10−10 HESS J1841-055 280.3 -5.5 1.48 5.0 2.4 5.01·10−10 1.19·10−9 4.52·10−9 9.88·10−10 3C 279 194.1 -5.8 0.46 3.1 2.7 2.80·10−10 6.35·10−10 2.38·10−9 5.14·10−10 HESS J1837-069 279.4 -6.9 0.61 4.2 2.6 3.26·10−10 7.41·10−10 2.76·10−9 5.77·10−10 QSO 2022-077 306.5 -7.6 2.61 17.3 3.5 6.74·10−10 1.56·10−9 5.81·10−9 1.27·10−9 PKS 1406-076 212.2 -7.9 0.55 1.5 2.0 3.12·10−10 6.88·10−10 2.60·10−9 5.55·10−10 HESS J1834-087 278.6 -8.8 0.53 3.6 3.5 3.36·10−10 7.22·10−10 2.54·10−9 5.72·10−10 PKS 1510-089 228.3 -9.1 1.00 6.3 4.5 4.53·10−10 1.02·10−9 3.79·10−9 8.16·10−10 HESS J1832-093 278.3 -9.4 0.50 3.3 3.4 3.41·10−10 7.66·10−10 2.63·10−9 5.65·10−10 Table 11.2. Results for astrophysical sources on the a priori search list. Table continued.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν HESS J1831-098 277.8 -9.9 0.42 2.7 3.0 3.30·10−10 6.97·10−10 2.47·10−9 5.54·10−10 PKS 0727-11 112.6 -11.7 0.20 0.2 3.8 2.99·10−10 6.67·10−10 2.59·10−9 5.50·10−10 1ES 0347-121 57.3 -11.9 0.43 2.6 3.9 3.68·10−10 8.12·10−10 3.13·10−9 6.60·10−10 QSO 1730-130 263.2 -13.1 0.56 2.7 4.5 4.28·10−10 1.04·10−9 4.08·10−9 8.68·10−10 HESS J1825-137 276.4 -13.9 - 0.0 - 3.13·10−10 7.56·10−10 3.14·10−9 6.35·10−10 LS 5039 276.6 -14.8 - 0.0 - 3.08·10−10 8.10·10−10 3.51·10−9 7.14·10−10 SNR G015.4+00.1 274.6 -15.5 - 0.0 - -- -- HESS J1813-178 273.3 -17.8 - 0.0 - 3.43·10−10 9.60·10−10 4.56·10−9 8.91·10−10 SHBL J001355.9-185406 3.5 -18.9 - 0.0 - -- -- HESS J1809-193 272.6 -19.2 0.59 1.5 4.6 5.57·10−10 1.57·10−9 8.33·10−9 1.63·10−9 KUV 00311-1938 8.4 -19.4 1.40 7.1 3.4 8.25·10−10 2.47·10−9 1.33·10−8 2.65·10−9 HESS J1808-204 272.2 -20.4 0.62 2.1 4.5 5.59·10−10 1.68·10−9 9.60·10−9 1.86·10−9 HESS J1804-216 271.1 -21.7 0.51 2.1 4.3 5.30·10−10 1.66·10−9 9.75·10−9 1.89·10−9 W28 270.4 -23.3 0.83 3.0 4.3 7.18·10−10 2.36·10−9 1.59·10−8 3.02·10−9 PKS 0454-234 74.3 -23.5 0.72 1.2 4.9 6.79·10−10 2.23·10−9 1.47·10−8 2.79·10−9 1ES 1101-232 165.8 -23.5 0.32 0.1 5.3 4.28·10−10 1.33·10−9 8.70·10−9 1.63·10−9 229 230

Table 11.3. Results for astrophysical sources on the a priori search list. Table continued.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν HESS J1800-240A 270.4 -24.0 0.55 1.6 4.3 5.94·10−10 1.96·10−9 1.29·10−8 2.46·10−9 HESS J1800-240B 270.2 -24.1 0.54 1.5 4.3 5.91·10−10 1.94·10−9 1.34·10−8 2.45·10−9 PKS 0301-243 45.8 -24.1 0.33 0.1 4.0 4.48·10−10 1.40·10−9 9.45·10−9 1.79·10−9 AP Lib 229.4 -24.4 - 0.0 - 4.32·10−10 1.42·10−9 9.49·10−9 1.78·10−9 Terzan 5 266.9 -24.8 0.40 0.4 4.2 4.59·10−10 1.63·10−9 1.11·10−8 2.03·10−9 NGC 253 11.9 -25.3 1.00 5.3 3.3 7.10·10−10 2.83·10−9 2.05·10−8 3.88·10−9 SNR G000.9+00.1 266.8 -28.2 - 0.0 - 4.39·10−10 1.61·10−9 1.38·10−8 2.47·10−9 Galactic Centre 266.4 -29.0 0.41 0.1 2.3 4.34·10−10 1.64·10−9 1.48·10−8 2.66·10−9 PKS 1622-297 246.5 -29.8 - 0.0 - 3.92·10−10 1.51·10−9 1.43·10−8 2.55·10−9 PKS 2155-304 329.8 -30.3 - 0.0 - 3.90·10−10 1.51·10−9 1.46·10−8 2.55·10−9 HESS J1741-302 265.3 -30.3 0.96 2.4 2.2 5.82·10−10 2.54·10−9 2.56·10−8 4.44·10−9 HESS J1745-303 266.2 -30.3 0.63 1.4 2.3 4.84·10−10 1.98·10−9 1.96·10−8 3.47·10−9 H 2356-309 359.8 -30.6 - 0.0 - 3.75·10−10 1.46·10−9 1.43·10−8 2.58·10−9 1RXS J101015.9-311909 152.6 -31.3 - 0.0 - 3.67·10−10 1.47·10−9 1.42·10−8 2.55·10−9 PKS 0548-322 87.6 -32.3 - 0.0 - 3.80·10−10 1.43·10−9 1.43·10−8 2.57·10−9 HESS J1729-345 262.4 -34.5 0.36 0.1 3.8 3.36·10−10 1.26·10−9 1.40·10−8 2.37·10−9 HESS J1731-347 263.1 -34.8 - 0.0 - 3.36·10−10 1.24·10−9 1.33·10−8 2.32·10−9 Table 11.4. Results for astrophysical sources on the a priori search list. Table continued.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν PKS 1454-354 224.4 -35.7 - 0.0 - 3.13·10−10 1.17·10−9 1.27·10−8 2.25·10−9 SNR G349.7+00.2 259.5 -37.5 0.74 4.2 3.4 5.07·10−10 1.92·10−9 2.25·10−8 3.89·10−9 PKS 0426-380 67.2 -37.9 0.54 2.0 2.5 4.40·10−10 1.60·10−9 1.89·10−8 3.26·10−9 CTB 37B 258.5 -38.1 0.72 4.0 3.2 5.14·10−10 1.90·10−9 2.20·10−8 3.83·10−9 HESS J1718-385 259.5 -38.5 1.58 5.9 3.4 7.62·10−10 2.80·10−9 3.21·10−8 5.58·10−9 CTB 37A 258.6 -38.6 0.94 4.9 3.3 5.84·10−10 2.22·10−9 2.44·10−8 4.18·10−9 RX J1713.7-3946 258.4 -39.7 0.67 3.0 2.4 4.85·10−10 1.79·10−9 2.01·10−8 3.59·10−9 HESS J1708-410 257.1 -41.0 0.69 2.0 2.1 5.12·10−10 1.86·10−9 2.10·10−8 3.68·10−9 SN 1006-SW 225.5 -41.1 - 0.0 - 3.70·10−10 1.25·10−9 1.36·10−8 2.41·10−9 SN 1006-NE 226.0 -41.8 0.51 1.4 3.4 4.40·10−10 1.56·10−9 1.74·10−8 3.04·10−9 HESS J1702-420 255.6 -42.0 0.63 1.2 2.1 4.97·10−10 1.78·10−9 2.02·10−8 3.54·10−9 1ES 1312-423 198.7 -42.6 0.50 0.9 3.3 4.56·10−10 1.60·10−9 1.72·10−8 3.02·10−9 Centaurus A 201.3 -43.0 0.83 1.2 4.3 5.80·10−10 2.07·10−9 2.34·10−8 4.09·10−9 PKS 0447-439 72.3 -43.8 - 0.0 - 3.96·10−10 1.30·10−9 1.39·10−8 2.51·10−9 PKS 0537-441 84.8 -44.1 0.77 3.1 3.3 5.70·10−10 2.04·10−9 2.18·10−8 3.96·10−9 HESS J1708-443 257.0 -44.3 0.62 0.9 1.8 5.16·10−10 1.76·10−9 1.94·10−8 3.51·10−9 Vela Pulsar 128.9 -45.2 - 0.0 - 4.11·10−10 1.31·10−9 1.44·10−8 2.62·10−9 231 232

Table 11.5. Results for astrophysical sources on the a priori search list. Table continued.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν Vela X 128.8 -45.6 - 0.0 - 4.11·10−10 1.34·10−9 1.49·10−8 2.64·10−9 Westerlund 1 251.8 -45.9 0.43 0.2 1.9 4.18·10−10 1.43·10−9 1.55·10−8 2.77·10−9 HESS J1641-463 250.2 -46.3 - 0.0 - 3.98·10−10 1.33·10−9 1.48·10−8 2.60·10−9 RX J0852.0-4622 133.0 -46.4 0.48 0.5 3.9 4.49·10−10 1.54·10−9 1.73·10−8 3.09·10−9 HESS J1640-465 250.2 -46.5 - 0.0 - 4.00·10−10 1.35·10−9 1.46·10−8 2.62·10−9 HESS J1634-472 248.8 -47.4 - 0.0 - 4.04·10−10 1.38·10−9 1.52·10−8 2.72·10−9 HESS J1632-478 248.0 -47.7 - 0.0 - 4.08·10−10 1.40·10−9 1.49·10−8 2.73·10−9 GX 339-4 255.6 -48.7 - 0.0 - 4.23·10−10 1.47·10−9 1.56·10−8 2.76·10−9 PKS 2005-489 302.3 -48.8 - 0.0 - 4.17·10−10 1.43·10−9 1.57·10−8 2.78·10−9 HESS J1626-490 246.5 -49.1 0.95 1.8 3.0 6.37·10−10 2.36·10−9 2.58·10−8 4.74·10−9 HESS J1616-508 244.1 -51.0 0.55 0.9 2.7 4.77·10−10 1.75·10−9 1.92·10−8 3.55·10−9 HESS J1614-518 243.5 -51.8 0.62 1.1 2.7 5.03·10−10 1.87·10−9 2.22·10−8 3.77·10−9 SNR G327.1-01.1 238.6 -55.0 - 0.0 - 4.18·10−10 1.48·10−9 1.67·10−8 2.96·10−9 Cir X-1 230.2 -57.2 - 0.0 - 4.55·10−10 1.62·10−9 1.99·10−8 3.32·10−9 Westerlund 2 155.8 -57.8 0.96 1.6 2.9 6.46·10−10 2.51·10−9 3.19·10−8 5.16·10−9 HESS J1503-582 225.9 -58.2 - 0.0 - 4.67·10−10 1.67·10−9 2.12·10−8 3.45·10−9 HESS J1026-582 156.6 -58.2 1.04 2.0 3.0 6.67·10−10 2.61·10−9 3.37·10−8 5.39·10−9 Table 11.6. Results for astrophysical sources on the a priori search list. Table continued.

Φ90% × γ−1 −2 −1 ◦ ◦ νμ+ν¯μ TeV cm s Source R.A. [ ] dec. [ ] −log (p-val.) nˆS γˆ 10 −2 −2 −Eν/10 TeV −2 −Eν/1TeV −3 Eν Eν e Eν e Eν HESS J1018-589 154.3 -59.0 0.73 1.0 2.7 5.77·10−10 2.18·10−9 2.89·10−8 4.61·10−9 MSH 15-52 228.5 -59.2 - 0.0 - 4.72·10−10 1.74·10−9 2.12·10−8 3.51·10−9 SNR G318.2+00.1 224.5 -59.4 - 0.0 - 4.69·10−10 1.72·10−9 2.13·10−8 3.63·10−9 ESO 139-G12 264.3 -59.9 - 0.0 - 4.62·10−10 1.66·10−9 2.13·10−8 3.49·10−9 Kookaburra (PWN) 215.1 -60.7 - 0.0 - 4.72·10−10 1.70·10−9 2.26·10−8 3.61·10−9 HESS J1458-608 224.6 -60.8 - 0.0 - 4.73·10−10 1.71·10−9 2.27·10−8 3.63·10−9 HESS J1427-608 217.0 -60.9 - 0.0 - 4.75·10−10 1.70·10−9 2.28·10−8 3.64·10−9 Kookaburra (Rabbit) 214.5 -61.0 - 0.0 - 4.73·10−10 1.70·10−9 2.28·10−8 3.64·10−9 SNR G292.2-00.5 169.7 -61.4 - 0.0 - 4.91·10−10 1.71·10−9 2.25·10−8 3.59·10−9 HESS J1507-622 226.7 -62.3 - 0.0 - 4.60·10−10 1.70·10−9 2.26·10−8 3.51·10−9 RCW 86 220.6 -62.5 - 0.0 - 4.63·10−10 1.70·10−9 2.30·10−8 3.55·10−9 HESS J1303-631 195.6 -63.2 0.33 0.1 3.4 4.75·10−10 1.76·10−9 2.39·10−8 3.71·10−9 PSR B1259-63 195.7 -63.8 0.51 1.2 3.2 6.35·10−10 2.48·10−9 3.41·10−8 5.23·10−9 HESS J1356-645 209.1 -64.5 - 0.0 - 4.81·10−10 1.74·10−9 2.38·10−8 3.70·10−9 30 Dor-C 83.9 -69.1 1.04 2.3 3.6 9.14·10−10 3.65·10−9 5.35·10−8 7.92·10−9 LHA 120 84.3 -69.1 1.01 2.2 3.6 9.19·10−10 3.56·10−9 5.33·10−8 7.78·10−9 LMC N132D 81.3 -69.6 1.03 2.1 3.7 9.41·10−10 3.64·10−9 5.38·10−8 7.85·10−9 233

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244 ICRC 2015 CONTRIBUTION

Author’s contribution to the Astroparticle Physics Conference (ICRC) in 2015. The proceedings are pending publication in Proceedings of Science2.

2Minor edits: A factor of 2 is missing after the second and third equal sign in equation 4.2. The values in the eight and ninth column in table 1, should switch place, see table 10.5 in this thesis. The binning in the effective area plot on the right hand side of figure 1 is not correct which leads to an underestimation of the effective area. This is purely a visual effect and does not affect the results. The corrected effective area is shown in figure 10.28 in this thesis. The vertical axis of the left plot in figure 2 should read Φ0, see figure 10.30 in this thesis.

Low-energy (100 GeV - few TeV) neutrino point source searches in the southern sky with IceCube

The IceCube Collaboration† † http://icecube.wisc.edu/collaboration/authors/icrc15_icecube

E-mail: [email protected]

IceCube searches for neutrino point sources in the southern sky have traditionally been restricted to energies well above 100 TeV, where the background of down-going atmospheric muons becomes sufﬁciently low to be tolerated in searches. Recent developments of a data stream dedicated to the study of low-energy neutrinos from the Southern Hemisphere enable searches to be extended far below this threshold. This data stream utilizes powerful veto techniques to reduce the atmospheric muon background, allowing IceCube for the ﬁrst time to perform a search for point-like sources of neutrinos in the southern sky at energies between 100 GeV and a few TeV. We will present the event selection along with the results obtained using one year of data from the full detector.

Corresponding authors: R. Ström1∗, 1 Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden

The 34th International Cosmic Ray Conference, 30 July- 6 August, 2015 The Hague, The Netherlands

∗Speaker.

c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Low-energy neutrino point source searches with IceCube R. Ström1

1. Introduction

Neutrinos interact through gravity and the weak interaction only and can therefore, unlike other messenger particles like photons and protons, travel astronomical distances without experiencing significant absorption or deflection in magnetic fields. Further, they constitute a unique probe for distances larger than 50 Mpc and from extremely dense environments. This makes neutrinos ideal as cosmic messengers that can be used to explore the most powerful accelerators in the Universe, in particular the mechanisms for producing and accelerating cosmic rays to incredible energies. By studying clustering of neutrino candidate events in the IceCube Neutrino Observatory (Ice- Cube) we can discover sites of hadronic acceleration where neutrinos are produced in the decay of charged pions created when primary cosmic ray protons and nuclei interact with radiation and matter in the vicinity of the acceleration site. The Southern Hemisphere is particularly interesting, containing both the Galactic Center and the main part of the Galactic plane. For IceCube this means we are studying down-going tracks in a much larger background of muons created as cosmic rays enter the Earth’s atmosphere. The traditional workaround has been to study only the highest energy neutrinos well above 100 TeV, where the background of atmospheric muons is sufficiently low. In the LESE (Low Energy Starting Events) analysis presented in this contribution we have lowered the energy threshold significantly utilizing several veto techniques, i.e. by looking for starting events in the detector. In particular we study neutrinos from soft spectra with cut offs in TeV-scale as observed for Galactic γ-ray sources, see e.g. [1, 2, 3], and references therein.

2. Data and Simulation

IceCube instruments a cubic-kilometer of ice and is the world’s largest neutrino telescope, located under the ice cap of the geographic South Pole, Antarctica [4]. It consists of 5160 optical modules deployed on 86 cables, called strings, and arranged in a three-dimensional grid between 1450 and 2450 m beneath the surface. The ultra pure ice at such depths is ideal for observations of Cherenkov light from charged leptons created when neutrinos interact with molecules in the ice or in the nearby bedrock. Each optical module operates as an individual detector, a so-called DOM (Digital Optical Module), and consists of a photomultiplier tube, digitizer electronics and calibration LEDs, all housed in a pressure-resistant glass sphere. When two neighboring or next-to-neighboring DOMs on the same string both cross the 0.25 photoelectron discriminator threshold of the PMT within a 1 μs time window, the signals qualify to be in Hard Local Coincidence (HLC). The leading trigger condition is formed when at least eight DOMs with HLCs trigger within a 5 μs time window. In this analysis we also use events from a trigger dedicated to catching almost vertical events as well as one with a lower effective energy threshold active in a denser central subarray called DeepCore [5]. The total trigger rate considered is around 2.8 kHz. The data is reduced via a series of straight cuts dedicated to reconstruction and calorimetric quality and a cut on an event score calculated using a machine learning algorithm. We present the analysis and results for data taken between May 2011 and May 2012, the ﬁrst year of the completed 86-string IceCube detector. Runs were carefully selected to ensure that the Low-energy neutrino point source searches with IceCube R. Ström1

101 14 12 100

10 −1

) 10 8 2 −2 6 10 mHz per bin 4 − 10 3 2 −4 0 Eﬀective Area (m 10 −90◦ ≤ δ<0◦ 1.2 −90◦ ≤ δ<−60◦ ◦ ◦ −5 −60 ≤ δ<−30 1.0 10 ◦ ◦ MC ratio −30 ≤ δ<0

/ 0.8 10−6 Data -1.00 -0.50 0.00 0.50 1.00 2.0 2.5 3.0 3.5 4.0 4.5 5.0 BDT Score log10(Eν) (GeV)

Figure 1: Left: BDT score distribution where experimental data is shown in black dots with error bars showing the statistical uncertainty (too small to be seen on this scale) and is further illustrated by the gray shaded area. Simulated atmospheric muons are presented in the solid red line. Signal hypotheses are shown −2 −2 −Eν /10 TeV −2 −Eν /1TeV in blue lines normalized to experimental data: Eν (dash-dotted), Eν e (dashed), Eν e −3 (solid) and Eν (dotted). Simulated signals are defined as starting inside the instrumented detector volume. Right: Neutrino effective area as a function of neutrino energy. majority of the DOMs used in vetoes were active, by both requiring a certain fraction of active DOMs overall and individually in the two different veto regions applied at the filter level, but also by studying the event rates at higher analysis levels. The final livetime considered is 329 days. The true right ascension directions of the data were kept blind until the last step of the analysis to keep the event selection and the final likelihood implementation as unbiased as possible.

3. Selecting Low-Energy Starting Events

The event selection is optimized for neutrinos in the energy region between 100 GeV to a few TeV. The outermost parts of the instrumented detector are used as a veto towards incoming muons. The triggered data is reduced by both real-time filtering at the South Pole, as well as subsequent offline CPU-intensive processing. The development of a real-time full sky filter with a low energy threshold was crucial to reach lower energies, since many of the traditional IceCube real-time filters for the Southern Hemisphere were effectively using a charge cut, focusing on keeping events from 100 TeV and up. The filter consists of two steps: a hit pattern based part, that rejects events with recorded hits in any of the 5 top DOMs or with the first HLC hit on any of the outermost strings, followed by a rejection of events with a reconstructed interaction vertex outside of the fiducial volume1. About 170 Hz pass the filter and is sent North for offline processing. To ensure that we have enough information in the events for advanced angular and energy reconstructions we begin by considering overall quality cuts, such as a minimum required number of photoelectrons. We further reject events with a poor reconstruction quality. Several advanced vetoes are used to reduce the number of muons leaking in. In particular we are studying causality

1A polygon shaped region deﬁned by connecting lines that go through points at 90% of the distance from the center string (string 36) to the outermost strings at the position of the 8 corners of the detector (as seen from the top) and the region below the 5 topmost DOMs. Low-energy neutrino point source searches with IceCube R. Ström1

10−6 −7 10 −2 −E/ 1TeV ∗ IceCube Preliminary E e LESE (3y ) −3 IceCube Preliminary E ∗

] STeVE (3y ) 1 E−2e−E/ 10 TeV − ] −7 MESE (3y) s −2 1

2 E 10 ∗

− Through–going (3y ) − s 2 − cm −8 *scaled from 1y

1) 10 − ( γ 10−8 dE [TeVcm / dE [TeV − / 10 9 dN

2 −9 dN

E 10 γ E

◦ Livetime: 329 d Dec. = −60.0 − 10 10 10−10 −1.0 −0.8 −0.6 −0.4 −0.2 0.0 102 103 104 105 106 107 108 109 sin δ Eν (GeV)

Figure 2: Left: Median sensitivities as a function of declination (line) and source upper limits (markers) at 90% C.L. Right: Differential median sensitivity corresponding to 3 years of operation (at -60◦ and 90% C.L.). Created by simulating point sources with an E−2 spectrum over quarter-decades in energy. of hits in an extended veto region, consisting both of the outer regions of IceCube and the IceTop surface array [6]. As a major step in the event selection we apply a machine learning algorithm: a Boosted Decision Tree (BDT) is programmed to exploit the remaining separation between signal and background. In particular, it focuses on directional and calorimetric information. The BDT event score is shown in figure 1. We make a cut at 0.40 which was found to be optimal or close to optimal for a wide range of signal hypotheses. The angular reconstruction uncertainty σ is estimated individually for each event as σ 2 = (σ 2 + σ 2)/ σ 1 2 2 where 1,2 are the major/minor axes of an ellipse that constitute the conic section of a paraboloid fitted to the likelihood space around the reconstruction minimum [7]. The ellipse is located at a level corresponding to 1σ indicating 68% containment. This quantity often underestimates the angular uncertainty, which is why we apply an energy dependent correction to the pull as seen in simulation, defined as the ratio of the true reconstruction error to the estimated reconstruction error, based on the median angular resolution. Events with a corrected value above 5◦ were rejected after optimization studies of the final sensitivity. The median angular resolution of the signal sample is about 2◦. The energy loss pattern for each event is estimated using an algorithm fitting hypothetical cascade-like energy depositions along the input track reconstruction [8]. An energy proxy for the neutrino energy is constructed by adding the contributions that are reconstructed inside the instrumented volume. The final sample consists of 6191 events, a rate of about 0.2 mHz, and is still dominated by atmospheric muons leaking in through the veto layers, effectively mimicking starting events. The effective area for the full southern sky as well as in three declination bands is shown in figure 1.

4. Search for Clustering of Events

We look for point sources by searching for spacial clustering of events in the Southern Hemi- sphere. Hypotheses are tested using an unbinned maximum likelihood method [9] where the events Low-energy neutrino point source searches with IceCube R. Ström1

in the final sample contribute individually with their reconstructed position xi, reconstructed energy Ei and an estimation of the angular uncertainty σi. The likelihood L is a function of two fit parameters: ns (the number of signal events) and γ (spectral index of a source S located at position xS with an unbroken power law spectrum) and contains the probability for an event to be signal- or background-like. The final likelihood function is a sum over N events and is maximized with respect to ns and γ where ns is constrained to be non-negative: ns ns L(ns,γ)=∏ Si(x,xS;σ,E,γ)+ 1 − Bi(δ;E) . (4.1) i N N The signal PDF S contains a spacial part parametrized with a two-dimensional gaussian profile with extension σi and since Icecube, due to its location, has a uniform acceptance in right ascension, the spacial part of the background PDF B is represented with a spline fit to the full sample of experimental data depending on the declination δ only. The calorimetric parts of these PDFs consist of two-dimensional spline fits to the reconstructed energy Ei and declination δi. The test statistic TS used is the likelihood ratio Λ taken with respect to the null hypothesis (ns = 0): S TS = Λ = + ns i W − ≡ ( + χ ), 2log ∑log 1 B i 1 ∑log 1 ns i (4.2) i N i i where χi is the individual event weight evaluated for a point source hypothesis at a particular location. An all sky search is performed looking for an excess of neutrino candidate events in the South- ern Hemisphere (declination range -85◦ to 0◦) on a HEALPix2 [10] grid corresponding to a resolution of about 0.5◦. In a second iteration we zoom in on the most interesting regions. This search is not motivated by any prior knowledge regarding the position of the sources, instead we are limited by the large number of trials performed, which together with the angular resolution gives a limit on the effective number of individual points tested. The pre-trial p-values obtained are converted into post-trial p-values by counting the fraction of times we get an equal or greater pre-trial p-value from an ensemble of 10000 pseudo-experiments where the right ascension directions were scrambled, see figure 3. We also perform a search at the position of 96 pre-defined sources: all 84 TeVCat3 [11] sources in the Southern Hemisphere (as of May 2015) and in addition 12 sources traditionally tested by IceCube (’GX 339-4’, ’Cir X-1’, ’PKS 0426-380’, ’PKS 0537-441’, ’QSO 2022-077’, ’PKS 1406-076’, ’PKS 0727- 11’, ’QSO 1730-130’, ’PKS 0454-234’, ’PKS 1622-297’, ’PKS 1454-354’, ’ESO 139-G12’). The TeVCat listing consists of sources seen by ground-based gamma-ray experiments, such as VERITAS, MAGIC, and H.E.S.S. and from these we consider sources from the catalogs ’Default Catalog’ and ’Newly Announced’, stable sources published or pending publication in refereed journals. Figure 2 shows the median sensitivity of the LESE analysis for four different signal hypotheses as a function of declination. Further we illustrate the joint effort within the IceCube collaboration towards lowering the energy threshold for point source searches by showing the differential sensitivity for four different analyses: the LESE analysis, the STeVE (Starting TeV Events) analysis optimized at slightly higher energies (few TeV - 100 TeV) [12], and the classic through-going point

2http://healpix.sourceforge.net 3http://tevcat.uchicago.edu Low-energy neutrino point source searches with IceCube R. Ström1

0.07 0.08

. 0.06 IceCube Preliminary 0 07 IceCube Preliminary 0.06 0.05 Post − trial p − value : 0.881 Post − trial p − value : 0.148 0.05 0.04 0.04 0.03 0.03 Fraction of trials 0.02 Fraction of trials 0.02 1 σ Observed p − value 1 σ Observed p − value σ σ 0.01 2 Scrambled trials . 2 Scrambled trials 3 σ 0 01 3 σ

0.00 0.00 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 − − log10(p-value) log10(p-value)

Figure 3: Pre-trial p-value distribution from 10000 scrambled trials for the sky scan (left) and the source list scan (right). The red line indicates the observed best p-values for the hottest spot and hottest source respectively, while the black vertical lines represent the 1, 2, and 3σ signiﬁcance levels. source analysis in black [13]. The sensitivities shown correspond to 3 years of operation and where estimated by simulating events with the livetime corresponding to the MESE (Medium-Energy Starting Events) analysis focusing on energies in the region 100 TeV - 1 PeV [14].

5. Results

The pre-trial p-value distribution for the all sky search is shown in figure 4. The hottest spot is located at right ascension 305.2◦ and declination -8.5◦ with a pre-trial p-value of 1.6 · 10−4 and a post-trial p-value of 88.1% (best fit parametersn ˆs = 18.3 and γˆ = 3.5). In figure 5 we show a zoom in on the TS distribution in the area surrounding the hottest spot and further a zoom in on the individual event weights log(1 + nsχi) that contribute to the test statistic at the position and with the best fit parameters of the hottest spot. The most significant source in the pre-defined list was QSO 2022-0774, a Flat-Spectrum Radio Quasar (FSRQ), with a pre-trial p-value of 2.5 · 10−3. The post-trial p-value is 14.8%. For the sources in the list, we calculate the upper limit at 90% confidence level (C.L.) based on the classical −2 −2 −Eν /10 TeV −2 −Eν /1TeV −3 approach [15] for the signal hypotheses: dΦ/dEν ∝ Eν ,Eν e ,Eν e , and Eν ,

Table 1: The most significant sources in the pre-defined list. The p-values are the pre-trial probability of being compatible with the background-only hypothesis. Then ˆs and γˆ are the best-fit values from the likelihood optimization. We further show the flux upper limit Φ at 90% C.L. for a number of neutrino flux γ−1 − − models. These are shown for the combined flux of νμ and ν¯μ in units TeV cm 2s 1.

Φ90% × TeVγ−1cm−2s−1 Source R.A. [◦] dec. [◦] −log (p-val.) nˆ γˆ νμ +ν¯μ 10 s −2 −2 −Eν /10 TeV −2 −Eν /1TeV −3 Eν Eν e Eν e Eν QSO 2022-077 306.5 -7.6 2.61 17.3 3.5 6.74 · 10−10 5.81 · 10−9 1.56 · 10−9 1.27 · 10−9 HESS J1718-385 259.5 -38.5 1.58 5.9 3.4 7.62 · 10−10 3.21 · 10−8 2.80 · 10−9 5.58 · 10−9 HESS J1841-055 280.3 -5.53 1.48 5.0 2.4 5.01 · 10−10 4.52 · 10−9 1.19 · 10−9 9.88 · 10−10 KUV 00311-1938 8.4 -19.4 1.40 7.1 3.4 8.25 · 10−10 1.33 · 10−8 2.47 · 10−9 2.65 · 10−9 30 Dor C 83.9 -69.1 1.04 2.3 3.6 9.14 · 10−10 5.35 · 10−8 3.65 · 10−9 7.92 · 10−9

4Alternate name: 2EG J2023-0836 Low-energy neutrino point source searches with IceCube R. Ström1

Figure 4: Pre-trial significance skymap in equatorial coordinates (J2000) showing the LESE analysis result on data from the first year of the full 86-string configuration of IceCube. The location of the Galactic plane is illustrated with a black solid line and the position of the most significant fluctuation is indicated with a black circle. The hottest spot is located at R.A. 305.2◦ and dec. -8.5◦ with a pre-trial p-value of 1.6 · 10−4. The corresponding post-trial p-value is 88.1%.

Figure 5: Zoom on the hottest spot (red circle + cross) and hottest source (red circle) in equatorial coordinates R.A. and dec. The reconstructed position of each event is shown in black dots. Left: The color transparency indicates the test statistic value at each pixel in the sky. Right: The radii of the circles are equal to the estimated angular uncertainty of each event. Color transparency indicate the strength of the individual likelihood weights log(1 + nsχi) that contribute to the test statistic at the position and with the best fit parameters of the hottest spot. Low-energy neutrino point source searches with IceCube R. Ström1 see figure 2. The limits of the five most significant sources are presented in table 1 along with the best fit parameters ns and γ. Note that we do not consider under fluctuations, i.e. for observed values of TS below the median of TS for the background-only hypothesis we report the corresponding median upper limit.

6. Summary and Outlook

No evidence of neutrino emission from point-like sources in the Southern Hemisphere at low- energies (100 GeV - few TeV) was found in the first year of data from the 86-string configuration of IceCube. The most significant spot in the sky has a post-trial p-value of 88.1%. Further we tested the presence of signal from 96 sources in a pre-defined source list of known γ-ray emitters seen in ground-based telescopes. The results are consistent with the background-only hypothesis. The most significant source has a post-trial p-value of 14.8%. Upper limits at 90% C.L. were calculated for these sources for a number of signal hypotheses, see figure 2 and table 1. Three more years of IceCube data with the full configuration exist and are ready to be incorporated into this analysis. We expect the sensitivity to improve slightly faster than the square-root of time limit, due to the relatively low background rate. Further, we have plans of performing a search for extended point sources and for neutrino emission in the Galactic plane.

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