On the Detection of Subrelativistic Magnetic Monopoles With the ...

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Subrelativistic magnetic monopoles from the GUT era are predicted by theory. Utilizing the Rubakov effect these monopoles can induce nucleon decay along ...

On the Detection of Subrelativistic Magnetic Monopoles with the IceCube Neutrino Observatory von Thorsten Glüsenkamp Diplomarbeit in P H Y S I K vorgelegt der

Fakultät für Mathematik, Informatik und Naturwissenschaften der Rheinisch-Westfälischen Technischen Hochschule Aachen im Oktober 2010 angefertigt am III. Physikalischen Institut B Prof. Dr. Christopher Wiebusch

Abstract

Subrelativistic magnetic monopoles from the GUT era are predicted by theory. Utilizing the Rubakov effect, these monopoles can induce nucleon decay along their path. This thesis investigates the capabilities of the IceCube Neutrino Observatory at the South Pole to detect the Cherenkov light from such decays and thus detect magnetic monopoles. The sensitivity using the standard trigger configuration of IceCube is evaluated and prevailing disadvantages are demonstrated. This leads to the development of a dedicated Slow Monopole Trigger which increases the overall sensitivity by more than an order of magnitude while triggering on muons and noise is suppressed. A 30-minute test run of this trigger at the South Pole demonstrates it is working properly and can be integrated into the DAQ system.

Contents Abstract

i

List of Figures

v

List of Tables

vii

1 Introduction

1

2 Historical overview 2.1 Maxwell Equations and Dirac’s Formula . . . . . . . . . . . . . . . . . . . 2.2 The 1970’s and 1980’s - Emergence of the GUT Picture . . . . . . . . . . .

3 4 5

3 Properties of Magnetic Monopoles 3.1 Synthesis of Magnetic Monopoles . . . . . . . . . . . . 3.2 Expected Mass and Velocity Spectrum . . . . . . . . . 3.3 The Rubakov/Callan Mechanism . . . . . . . . . . . . 3.4 Interaction with Matter and Energy Loss . . . . . . . . 3.4.1 Excitation and Ionization Losses . . . . . . . . . 3.4.2 Other Energy Losses . . . . . . . . . . . . . . . 3.4.3 Implications for the Expected Monopole Flux in 3.5 Flux Limits . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 The Parker Bound . . . . . . . . . . . . . . . . 3.5.2 Other Astrophysical Bounds . . . . . . . . . . . 3.5.3 Experimentally obtained Limits . . . . . . . . . 4 The 4.1 4.2 4.3

4.4 4.5

4.6

IceCube Neutrino Observatory Astrophysical Motivation . . . . . . . . . . . . . . . . . Principle of Particle Detection - Cherenkov Radiation . Design of the Detector . . . . . . . . . . . . . . . . . . 4.3.1 Geometric Layout . . . . . . . . . . . . . . . . . 4.3.2 Design and Purpose of a Digital Optical Module 4.3.3 Optical Ice Properties . . . . . . . . . . . . . . Particle Signatures in the Detector . . . . . . . . . . . 4.4.1 Lepton Signatures . . . . . . . . . . . . . . . . . 4.4.2 Subrelativistic Monopole Signatures . . . . . . . Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Data Acquisition . . . . . . . . . . . . . . . . . 4.5.2 Triggering . . . . . . . . . . . . . . . . . . . . . 4.5.3 Filtering . . . . . . . . . . . . . . . . . . . . . . Simulation of Monopoles and the Detector Response . . 4.6.1 The IceTray Framework . . . . . . . . . . . . . 4.6.2 Slow Monopole Generation and Propagation . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IceCube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (DOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 8 8 11 14 14 15 18 19 19 21 22

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25 26 28 29 29 31 32 34 34 37 39 39 41 43 43 45 45

iii

CONTENTS

4.6.3 4.6.4 4.6.5

General Remarks on Background Simulation . . . . . . . . . . . . . 47 Simulation of Cherenkov Light and Photon Propagation . . . . . . 47 Simulation of the Detector Response . . . . . . . . . . . . . . . . . 47

5 Sensitivity of the Full Detector (IC-86 Configuration) 5.1 Performance with Standard Triggers . . . . . . . . . . . 5.2 The SLOP-filter . . . . . . . . . . . . . . . . . . . . . . . 5.3 The Effective Area . . . . . . . . . . . . . . . . . . . . . 5.3.1 Definition and usage . . . . . . . . . . . . . . . . 5.3.2 Simulation and Results . . . . . . . . . . . . . . . 6 Development of a Dedicated Trigger for Slow 6.1 Motivation and Goal . . . . . . . . . . . . . . 6.2 Trigger Concept . . . . . . . . . . . . . . . . . 6.3 Simulations . . . . . . . . . . . . . . . . . . . 6.3.1 Simulation of Background . . . . . . . 6.3.2 Simulation of Signal . . . . . . . . . . 6.4 Optimization of the Trigger Parameters . . . . 6.4.1 “First stage” Parameters . . . . . . . . 6.4.2 “Second stage” Parameters . . . . . . . 6.5 IC-86 Background Rates . . . . . . . . . . . . 6.6 Effective Areas on Trigger Level . . . . . . . . 6.7 Impact on IC-86 SLOP Effective Area . . . .

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Magnetic Monopoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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49 50 54 55 55 58

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63 64 64 67 67 71 72 72 74 81 82 83

7 DAQ SlowMPTrigger Testrun 89 7.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.2 Investigations on the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 8 Conclusion

99

A Systematic Effects

101

B Effective Detection Radius of a Magnetic Monopole

103

C Event Displays

109

D Parameter Distributions for Different Signal/Background Mixtures

113

Acknowledgements Erklärung / Declaration References

iv

I III V

List of Figures 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 5.1 5.2 5.3 5.4 5.5 5.6 5.7 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14

Synthesis of magnetic monopoles . . . . . . . . . . . . . . . . . . . . . . . Structure of a SU-5 GUT monopole . . . . . . . . . . . . . . . . . . . . . . Simplest induced positronic decay mode of the proton . . . . . . . . . . . . Energy loss of a slow magnetic monopole due to ionization . . . . . . . . . Expected arrival flux of magnetic monopoles at IceCube . . . . . . . . . . The revised parker limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flux limits for subrelativistic monopoles from the Amanda-II experiment . Flux limits for subrelativistic monopoles from the MACRO detector . . . . Flux limits for highly relativistic monopoles . . . . . . . . . . . . . . . . . Illustration of neutrinos as cosmic messengers . . . . . . . . . . . . . . . . Illustration of the Cherenkov effect . . . . . . . . . . . . . . . . . . . . . . 3-d sketch of the IceCube Observatory . . . . . . . . . . . . . . . . . . . . Sketch of the top view of the IceCube Observatory . . . . . . . . . . . . . Sketch of an IceCube DOM . . . . . . . . . . . . . . . . . . . . . . . . . . Ice properties (scattering/absorption) . . . . . . . . . . . . . . . . . . . . . Sketch of the signature of a magnetic monopole . . . . . . . . . . . . . . . Different stages in Data Acquisition (DAQ) . . . . . . . . . . . . . . . . . . Illustration of the trigger hierarchy . . . . . . . . . . . . . . . . . . . . . . Monopole generation with IceTray . . . . . . . . . . . . . . . . . . . . . . . Average HLC launch rate of magnetic monopoles . . . . . . . . . . . . . . Maximum event lengths with the Cluster Trigger (track along string 36) . . Time difference between successive DomLaunches . . . . . . . . . . . . . . Hit rate distributions of two example events that pass the SLOP-filter . . . Effective area on SLOP filter level without DeepCore strings . . . . . . . . Effective area on SLOP filter level (SMT-8/Cluster) . . . . . . . . . . . . . Effective area on SLOP filter level (SMT-3/SMT-8/Cluster) . . . . . . . . Schematic of a sample of HLC pairs . . . . . . . . . . . . . . . . . . . . . . Illustration of a 3-tuple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic depiction of muon mixing . . . . . . . . . . . . . . . . . . . . . Schematic depiction of background generation . . . . . . . . . . . . . . . . Trigger lengths for different values of t_max . . . . . . . . . . . . . . . . . delta_d (all 3-tuples) distribution with cut . . . . . . . . . . . . . . . . . delta_d (best 3-tuples) distribution with cut . . . . . . . . . . . . . . . . rel_v (all 3-tuples) distribution with cut . . . . . . . . . . . . . . . . . . . rel_v (best) distribution with cut . . . . . . . . . . . . . . . . . . . . . . num_tuples distribution with cut . . . . . . . . . . . . . . . . . . . . . . . Trigger reduction factors for different trigger levels . . . . . . . . . . . . . . Trigger efficiency for trigger levels 0-3 . . . . . . . . . . . . . . . . . . . . . Trigger length for different monopole velocities . . . . . . . . . . . . . . . . Effective area on SLOP filter level (SMT3/SMT8/Cluster/SlowMPTrigger lvl 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 10 12 16 18 21 22 23 24 27 28 30 31 33 35 39 40 44 46 51 52 53 56 59 60 61 65 66 69 70 73 75 76 77 78 79 80 84 85 86

v

LIST OF FIGURES

6.15 Effective area on SLOP filter level with Rubakov relation for different values of σ0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Number of SMT-8 triggers per SlowMpTrigger . . . . . . . . . . . . . . . . 7.2 Trigger length distributions - before fix . . . . . . . . . . . . . . . . . . . . 7.3 n-channel distributions - before fix . . . . . . . . . . . . . . . . . . . . . . 7.4 Trigger length distributions - after fix . . . . . . . . . . . . . . . . . . . . . 7.5 n-channel distributions - after fix . . . . . . . . . . . . . . . . . . . . . . . 7.6 delta_d distribution from the test run (retriggered) . . . . . . . . . . . . B.1 Schematic of a the effective monopole detection radius . . . . . . . . . . . B.2 2d-histogram of the distance at which the first DomLaunch happens . . . . B.3 Example probability distribution for λcat = 1cm . . . . . . . . . . . . . . . B.4 Probability distributions for all simulated mean free paths λcat . . . . . . . C.1 Event display of a simulated monopole with λcat = 100 cm and β = 10−3 . C.2 Event display of a triggered event from the test run . . . . . . . . . . . . . C.3 Event display of a the longest triggered event from the test run . . . . . . D.1 delta_d (all 3-tuples) - background . . . . . . . . . . . . . . . . . . . . . D.2 delta_d (best 3-tuples) - background . . . . . . . . . . . . . . . . . . . . D.3 delta_d (all 3-tuples) - λcat = 100 cm and β = 10−2 . . . . . . . . . . . . D.4 delta_d (best 3-tuples) - λcat = 100 cm and β = 10−2 . . . . . . . . . . . D.5 delta_d (all 3-tuples) - λcat = 100 cm and β = 10−3 . . . . . . . . . . . . D.6 delta_d (best 3-tuples) - λcat = 100 cm and β = 10−3 . . . . . . . . . . . D.7 rel_v (all 3-tuples) - background . . . . . . . . . . . . . . . . . . . . . . . D.8 rel_v (best 3-tuples) - background . . . . . . . . . . . . . . . . . . . . . . D.9 rel_v (all 3-tuples) - λcat = 100 cm and β = 10−2 . . . . . . . . . . . . . . D.10 rel_v (best 3-tuples) - λcat = 100 cm and β = 10−2 . . . . . . . . . . . . . D.11 rel_v (all 3-tuples) - λcat = 100 cm and β = 10−3 . . . . . . . . . . . . . . D.12 rel_v (best 3-tuples) - λcat = 100 cm and β = 10−3 . . . . . . . . . . . . . D.13 num_tuples - background . . . . . . . . . . . . . . . . . . . . . . . . . . . D.14 num_tuples - λcat = 100 cm and β = 10−2 . . . . . . . . . . . . . . . . . . D.15 num_tuples - λcat = 100 cm and β = 10−3 . . . . . . . . . . . . . . . . . .

vi

87 90 92 93 95 96 98 104 105 105 106 110 111 112 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128

List of Tables 3.1 3.2 3.3 4.1 6.1 6.2 6.3 6.4 6.5 6.6 7.1 7.2 7.3

Rubakov/Callan parameters β0 and γ for different atoms . . . . . . . . . . Minimum masses for which the arrival flux of magnetic monopoles at IceCube is expected to be isotropic . . . . . . . . . . . . . . . . . . . . . . . . Dimensionless quantities for the calculation of the refined parker bound . . Summary of the configuration of the three IC-79 triggers . . . . . . . . . . Abbreviations for different simulated backgrounds . . . . . . . . . . . . . . Transit times of prominent distances for different monopole velocities . . . Trigger level definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IC-86 background trigger rates (simulated) . . . . . . . . . . . . . . . . . . Effective areas on different trigger levels - β = 0.01 and λcat = 100 m . . . Effective areas on different trigger levels - β = 0.001 and λcat = 100 m . . . IC-79 background trigger rates (simulated) . . . . . . . . . . . . . . . . . . IC-79 test run trigger rates (retriggered) . . . . . . . . . . . . . . . . . . . IC-79 background trigger rates (simulated) - with NoiseGenerator fix . . .

13 19 20 42 71 72 81 81 82 82 91 94 97

vii

LIST OF TABLES

viii

CHAPTER I Introduction Magnetic monopoles are among those predictions that are demanded by theory but have yet lacked experimental verification. Models predict that they originate from the earliest stages of the universe as topological defects during GUT symmetry breaking. They posses an exceptionally high mass on the order of 1017 GeV and predominantly move subrelativistically. In contrast to relativistic magnetic monopoles, detection via energy loss is not very promising. Due to this fact, early experiments in the 1970’s primarily looked for magnetic induction signals. This changed when Rubakov and Callan in the beginning of the 1980’s proposed a mechanism by which a monopole induces nucleon decays in matter[1]. These decays would occur along the monopole track. The decay products are charged particles containing the rest energy of the nucleon. Experiments shortly thereafter began to look for typical decay signatures. Until now, monopoles successfully eluded detection. Cherenkov detectors like the IceCube Neutrino Observatory may offer detection of the charged particles from such nucleon decays. IceCube has the largest instrumented volume of all existing Cherenkov detectors. It is worthwhile to investigate which sensitivity for subrelativistic monopoles is expected. The huge volume is not necessarily to be seen as only positive. The Cherenkov modules have a certain module spacing which may turn out to be to high. The DeepCore subdetector with its denser module spacing may counterbalance this effect. The aim of this thesis is to investigate the prospects of subrelativistic monopole detection with IceCube. For this, the sensitivity using the existing trigger/filter system is analyzed. Afterwards, development and testing of a dedicated slow monopole trigger is described and the sensitivity gain is evaluated. Chapter 2 gives a short overview over the historical development of this subject. Chapter 3 summarizes the properties of magnetic monopoles and gives an overview of the experimental status. Chapter 4 introduces the IceCube Neutrino Observatory and the terminology to understand the subsequent chapters. Chapter 5 then discusses the current status of IceCube’s cababilities for monopole detection. Chapter 6 describes the development of a dedicated trigger for subrelativistic monopoles and explains the advantages of an implementation of such a dedicated trigger. Chapter 7 presents results from a trigger testrun that was conducted at the South Pole. Finally, chapter 8 summarizes the results and gives a short outlook.

1

1 INTRODUCTION

2

CHAPTER II Historical overview This chapter provides a short historical overview of the milestones that took place in the 20th century concerning the understanding of magnetic monopoles.

3

2 HISTORICAL OVERVIEW

2.1

Maxwell Equations and Dirac’s Formula

Ever since Maxwells equations had been known to science, people could use those to understand light and the interplay between electric and magnetic fields. Electricity and Magnetism had been seen as two different phenomena before, and now they appeared as intertwined entities. The Maxwell Equations can be written in the following way1 :

div E = 4πρ 1 ∂B rot E = − c ∂t

div B = 0 1 ∂E 4π rot B = + j. c ∂t c

(2.1)

Physicists have always been tempted to include a magnetic elementary charge and a magnetic current to make them look more symmetric. Then, the equations would change to

div E = 4πρe 1 ∂B − jm rot E = − c ∂t

div B = 4πρm 1 ∂E 4π rot B = + j. c ∂t c e

(2.2)

je and ρe now denote electric current and charge density and jm and ρm denote magnetic current and charge density. Suppose M refers to the magnetic quantities like ρm , jm , B and E refers to the electric quantities like ρe , je and E. Then the following transformation leaves the generalized Maxwell equations invariant:

E → E · cos(θ) + M · sin(θ) M → M · cos(θ) − E · sin(θ).

(2.3) (2.4)

This symmetry can be exploited mathematically. For example, it may be used to derive the laws of energy and momentum conservation for classical electrodynamic systems, even if there is no magnetic charge present [2]. Additionally, the angle can be chosen such that ρm = 0 and jm = 0 and the standard Maxwell Equations are obtained [3] (eq. 2.1). A magnetic elementary charge had never been observed though, and there was also no real need for it. This symmetry transformation is nice to have but it can not be used to predict entirely new phenomena. 1

4

in gaussian units

2.2 The 1970’s and 1980’s - Emergence of the GUT Picture

In 1931, however, Paul Dirac wrote a famous paper [4] where he derived a formula for the quantization condition of a magnetic charge 2 .

e·g n = (n = ±1, ±2, ...) 4π~ 2

(2.5)

If the magnetic charge has a specific quantized value, g, it follows that the electric charge has to be quantized, too. Based on this formula he came to the conclusion that if there is at least one magnetic monopole in the universe, there exists a mathematical explanation for the quantized nature of electric charge. Similar to the fine structure constant α=

1 e2 ≈ 4π0 ~c 137

(2.6)

one can define a “magnetic fine structure constant” αm =

g2 137 2 ≈ ·n 4πµ0 ~c 4

(2.7)

using equation 2.5. A particle with “magnetic fine structure constant” αm magnetic charge g is also called a “Dirac Monopole”. The Dirac Monopole can be thought of as a pointlike particle like the electron with a quantized magnetic charge instead of an electric one. It is obvious that the coupling constant is much larger than for the electric case, making its interaction and detection in matter easier (it will be shown that this is only the case for relativistic monopoles, see section 3.4). From equation 2.5 one can also see that g is an for n = 1. This minimal magnetic charge integer multiple of the minimum value gD = 2π~ e 3 is called “Dirac Charge” .

2.2

The 1970’s and 1980’s - Emergence of the GUT Picture

Electroweak unification is a fundamental part of the current standard model of particle physics. When it was formulated in the late 60’s, it did not take long for physicists to go one step further and try to unite the electroweak force with the strong force at even higher energies. In 1974 Howard Georgi and Sheldon Glashow[5] formulated the first Grand Unified Theory (GUT), which accomplishes this “grand unification”. They used the SU(5) as the symmetry group, which is the smallest simple Lie group to contain the standard model subgroup (see eq. 2.8). 2

A simple derivation can be found in Jackson’s “Classical Electrodynamics” [3] In Lorenz-Heavyside units, combined with natural units (~ = c = 1), the Dirac Charge takes the e simple form gD = 2α 3

5

2 HISTORICAL OVERVIEW

SU (5) ⊃ SU (3) × SU (2) × U (1)

(2.8)

In the same year Polyakov [6] and ’t Hooft [7] were able to determine Monopole solutions for this simplest GUT. It was now possible to predict important properties of the corresponding monopoles. For example, the mass of the monopole is closely related to the masses of the gauge bosons in the theory and could be calculated. This had been an impossible challenge in the Dirac picture. Magnetic monopoles are in fact inherent in every GUT: In any unified gauge theory, it can be demonstrated that electric charge is quantized. If one reverses Dirac’s argument, that the pure existence of a magnetic monopole implies charge quantization, one comes to the conclusion that every GUT implies magnetic monopoles. Joseph Polchinski presented this argumentation chain in detail in a talk he gave at the Dirac Symposium in 2002 [8], calling the existence of magnetic monopoles “one of the safest bets one can make about physics not yet seen”. With the advances in understanding magnetic monopoles that came with unified gauge theories, the first true era of monopole research was set in motion. During the end of the 70’s and early 80’s numerous experiments were conducted that marked the first period of experimental search for magnetic monopoles.

6

CHAPTER III Properties of Magnetic Monopoles This chapter covers the current understanding of magnetic monopoles. Their origin, their propagation through the universe as well as their properties and possible interaction with matter are discussed. Most important for this work is the “Rubakov/Callan Mechanism” which is described in its own subsection. At last the latest flux limits from recent experiments are compared and discussed.

7

3 PROPERTIES OF MAGNETIC MONOPOLES

3.1

Synthesis of Magnetic Monopoles

Magnetic monopoles are thought to be originated as topological defects in spacetime from a GUT-symmetry breaking shortly after the Big Bang (see figure 3.1). At this instant, the GUT force is thought to have split up into the electroweak and the strong force. For the simplest GUT (SU(5)), the mathematical description of this process can be described by equation 3.1. SU (5) → SU (3) × SU (2) × U (1)

(3.1)

SO(10) and other GUTs consist of more complicated breakdown chains [9] (eqs. 3.2,3.3) SO(10) → SU (5) → SU (3) × SU (2) × U (1) SO(10) → SU (4) × SU (2) × SU (2) → SU (3) × SU (2) × U (1) .. .

(3.2) (3.3)

It has been calculated [10] [11] that too many monopoles would have been produced in this scenario to be consistent with a firmly established astrophysical bound, known as the “parker limit” (see section 3.5.1). This has become known as the “Monopole Problem“. Inflation provides a solution to this overabundance of monopoles. It states that shortly after the GUT epoch, the universe underwent a short and very rapid expansion, thus diluting the existing monopole density. Since the monopoles are predicted to be stable, they went on traversing the universe until today and may eventually be detected in an earthbound detector. In contrast to the pointlike nature of the Dirac Monopole (see section 2.1) ,these GUT monopoles have an onion-like structure of virtual particles, as illustrated in figure 3.2.

3.2

Expected Mass and Velocity Spectrum

The mass of a monopole depends on the underlying unified gauge group which is used. For the simplest SU(5) GUT, for instance, masses are on the order of 1017 GeV. The next simple SO(10) GUT predicts masses in the range from 1010 GeV to 1016 GeV. The lightest and heaviest monopoles with masses 107 GeV and 1019 GeV respectively are predicted by supersymmetric models [13] [14]. The true underlying symmetry group, if grand unification is correct, is not known and remains speculative, though. Magnetic monopoles gain energy in a magnetic field in the same way as electrons do in an electric field by

8

3.2 Expected Mass and Velocity Spectrum

time after big bang

10−36 s 10−32 s

GUT-Phase

Inflation

GUT symmetry breaking

Planck scale Big Bang

scale factor of the universe

10−43 s

Electro-Weak Phase

magnetic monopoles freeze out

Figure 3.1: Schematic depiction of the first phases after the big bang. At ∼ 10−36 s monopoles freeze out as a consequence of the GUT-symmetry breaking. Inflation then drastically dilutes their density.

9

3 PROPERTIES OF MAGNETIC MONOPOLES

Internal structure of a SU-5 GUT monopole magnetic field lines

q q¯ γ f f¯ g

W W+

f f¯



GUT Core g

γ

Z0

g

γ q q¯

10−15 cm 10−13 cm

10−29 cm 10−16 cm

Figure 3.2: Schematic depiction of the internal onion like structure of a SU-5 GUT monopole (copied from [12]). The inner core consists of a GUT symmetric vacuum. At 10−29 cm the so called electroweak region begins, containing virtual gauge bosons. Between 10−16 cm and 10−15 cm virtual photons and gluons dominate (the so called confinement region). The outside layer consists of a fermion-antifermion condensate. To the outside the monopole has the same magnetic appearance as a Dirac Monopole - a pointlike particle with outwards oriented magnetic field lines.

10

3.3 The Rubakov/Callan Mechanism

∆E = g ·

Z

B · dl ≈ g · B · L,

(3.4)

where g denotes the monopole charge, B the magnetic field strength and L the coherence length of the field. The maximum energy that can be transfered to monopoles by cosmic magnetic fields in this way is estimated to be on the order of 1014 GeV [15]. Therefore, monopoles with masses lower than ∼ 1014 GeV have a probability of being relativistic which increases when going to even smaller masses. On the contrary, standard SU(5)Monopoles can only reach subrelativistic speeds. For example, a 1017 GeV monopole with 14 + 1 = 1.001. kinetic energy 1014 GeV would have a gamma factor of only γ = 10 1017 Since the mass spectrum that is predicted by GUT theories spans more than 12 orders of magnitudes, it is not clear whether the monopole flux consists of mainly relativistic or sub-relativistic particles. Since high masses > 1014 GeV are favored by most GUTs, it is likely that the first monopoles to be detected are subrelativistic. A hypothetical gas of thermal relic monopoles would have cooled down to about ∼ 10 mK until now. Due to the their high masses this corresponds to mean velocities of less than 10−20 c with respect to the restframe of the Cosmic Microwave Background[16]. Their infall velocity into the milky way galaxy and into the solar system would then be on the order of the peculiar motion of the galaxy with respect to the CMB restframe[11], which is β ∼ O(10−3 ). They can of course also be accelerated by magnetic fields and be gravitationally captured by a mass distribution like our galaxy, for instance. If that is the case, their expected velocities here on earth are on the order of the virial velocity of our galaxy which is also β ∼ O(10−3 ) [11]. Sufficiently slow monopoles could even be captured by the solar system [17]. −5

To summarize, high monopole masses > 1014 GeV are predicted by many GUT’s. It is likely that these heavy monopoles move with subrelativistic velocities (β ∼ 10−3 ) with respect to Earth.

3.3

The Rubakov/Callan Mechanism

Valeri Rubakov [1] and independently Callan [18] showed that a GUT monopole can induce nucleon decay while traversing matter. This mechanism became known as the ”Rubakov/Callan Effect“. They predicted that the cross section of those decays is on the order of strong interactions and therefore, they can be searched for experimentally. Typical decay channels of the nucleons (proton or neutron) due to the monopole catalysis

11

3 PROPERTIES OF MAGNETIC MONOPOLES

are: M +p→M M +p→M M +p→M .. . M +n→M M +n→M .. .

+ e+ + π 0 + µ+ + K 0 + e+ + µ+ + µ− + K 0

(3.5) (3.6) (3.7)

+ e+ + π − + µ+ + K − .

(3.8) (3.9)

Many more combinations are possible which is denoted by the dots. Figure 3.3 illustrates the simplest positronic decay of the proton.

e+

Monopole

u u d

d¯ d π0

p

Figure 3.3: Depiction of the simplest positronic decay mode of the proton induced by a GUT monopole.

The original formula for the calculation of the cross section was given by Rubakov as σcat =

σ0 . β

(3.10)

σ0 is a parameter which is expected to be on the order of 10−32 cm2 − 10−24 cm2 . Rubakov later remarked that at sufficiently low velocities the catalysis cross section may even behave like σcat ∼ β −2 . Further work by Arafune et. al [19] confirmed this behavior for hydrogen. They concluded that for a certain threshold velocity β0 , a factor has to be

12

3.3 The Rubakov/Callan Mechanism

added to the formula. It takes into account the extra angular momentum carried by the magnetic-charge/electric-charge system of the monopole and atomic nucleus. This can be written like

  σ0

β > β0 σcat =  σβ0 · F (β) β < β0 β

(3.11)

with the correction factor F (β) =

β β0



(3.12)

,

where γ and β0 are dependent on the properties of the different atomic nuclei. Table 3.1 lists the parameters for some elements. Hydrogen is the only case for which this factor enhances the cross section. For all higher elements it acts as a suppression factor. Table 3.1: Parameters β0 and γ for different atoms. Taken from [19].

nucleus H He 12 C 16 O 28 Si 1

4

Z

β0

γ

1 0.175 −1 4 0.0275 1.236 12 0.00636 2.605 16 0.00434 3.123 28 0.00206 4.385

Another important and more concrete quantity is the mean free path between two consecutive decays λcat . It is closely related to the cross section σcat by λcat =

1 σcat · n

(3.13)

where n denotes the particle density of the traversed material. Bernreuther and Craige [20] made an effort to calculate the inclusive cross section for the proton decay M + p → M + e+ + pions

(3.14)

using a non-relativistic quark model. They calculated σcat to be ∼ 0.1 mb = 10−28 cm2 . No other direct calculations have been made since then. However, the branching ratios of different channels have been estimated by Bais et al. [21] to be

13

3 PROPERTIES OF MAGNETIC MONOPOLES

1 + e + pions

: :

O(10−1 − 10−3 ) µ+ + kaons

: :

O(10−5 ) e+ + µ+ + µ− + kaons

The Rubakov/Callan mechanism is not uncontroversial. There have been claims that the typical cross sections are not on the order of the strong, but of the weak interactions. Some have even presented arguments that nucleon decay is impossible in unified field theories [22].

3.4

Interaction with Matter and Energy Loss

There are several mechanisms by which a magnetic monopole can loose energy when traversing matter. Most of these interactions take place in gas clouds of interstellar or intergalactic space. At some point a monopole may also hit a star or a planet and will loose energy while traversing its interior. A good understanding of the underlying processes is especially vital for possible detection signatures (see section 4.4.2) or flux estimates (see section 3.4.3).

3.4.1

Excitation and Ionization Losses

It has been shown that the mean energy loss of a relativistic magnetic monopole traversing a nonconducting material can in principle be described by a modified Bethe-Bloch formula [23], which is the standard formula for ionization/excitation losses of charged particles (see section 4.4.1). It writes out to 4πN e2 g 2 2me c2 β 2 γ 2 dE = · ln − dX me c2 Im

!

1 δm K(|g|) − − − B(|g|) + , 2 2 2 !

(3.15)

where Ne is the electron number density of the material, me is the electron mass, Im is the mean Ionization potential,  0.406

K(|g|) = 

|g| = gD 0.346 |g| = 2 · gD

is the Kazama cross section correction [24],  0.248

|g| = gD B(|g|) =  0.672 |g| = 2 · gD

14

3.4 Interaction with Matter and Energy Loss

is the Bloch correction for magnetic monopoles and δm is the density correction for high energies. This formula is accurate to within ±3% when β ≥ 0.2 [23] One can see that the formula basically resembles the standard Bethe-Bloch formula with the substitution z · e → g · β, except the Bloch and Kazama corrections which are monopole specific. For a monopole with one Dirac charge g = gD and speed close to the speed of light (β ≈ 1) this means its energy loss is increased by a factor ( g2 )2 ∼ 4700, thus, in principle



dE dE ≈ · 4700. dX m dX e

(3.16)

Extremely relativistic magnetic monopoles begin to loose energy by so called “radiative energy losses”. These include bremsstrahlung, pair production and photonuclear interactions, which are not covered by the above formula. For the highest boost factors γ > 104 pair production and photonuclear interactions dominate the total energy loss. For the subrelativistic case, which is important for this work, the situation is more difficult. Bethe-Bloch approximations do not apply for monopoles with β < 0.1 [25] and different approaches have been used. There have been several papers about the energy loss of sub-relativistic monopoles with β < 10−2 since the 1970’s. Many had made different assumptions and contradicted themselves until the standard work on this topic was provided by Ahlen and Kinoshita [25] who also depicted the inconsistencies of previous approaches. Their method is based on similarities to the energy loss of subrelativistic protons. Ritson [26] shortly therafter investigated the case for insulators, whose energy gap has an effect on the ionization energy loss. From figure 3.4 one can see that for a monopole with one Dirac charge and a velocity of β ∼ 10−2 the energy loss is on the order of 100 GeVcm2 g−1 . For β ∼ 10−3 it is around 20 GeVcm2 g−1 and for β ∼ 10−4 it has already dropped below the barrier of minimum ionizing particles of around 2 GeVcm2 g−1 . Drell et. al [27] have published a paper in which the energy loss is calculated to be one order of magnitude higher than the values obtained by Ahlen and Kinoshita, but for atomic hydrogen and helium. They conclude that helium-based detectors with a Penning mixture could be used to measure the released energy.

3.4.2

Other Energy Losses

Energy Loss due to the Rubakov/Callan Mechanism The energy loss due to nucleon decay can be estimated by some simple calculations. The upper bound for momentum transfer away from the monopole has been shown to be ∆p < 1 GeV/c[29]. Since the Rubakov mechanism applies to subrelativistic monopoles, the

15

3 PROPERTIES OF MAGNETIC MONOPOLES

Figure 3.4: Energy loss of a slow magnetic monopole of one Dirac charge due to excitation and ionization of atoms is depicted as the solid line in the shaded area (below β = 0.01). It gets extend below β = 10−3 by the calculation of Ritson [26] until it reaches the barrier of minimum ionizing particles. The energy loss for a relativistic monopole, calculated by Ahlen [23], is also plotted which breaks down below β = 0.1. Proton energy loss calculations are depicted for the subrelativistic and relativistic case using the Bethe-Bloch formula and an approach by Lindhard [28]. Dots depict experimental values for protons. The figure is adapted from [16].

16

3.4 Interaction with Matter and Energy Loss

kinetic energy can be approximated to the nonrelativistic case Ekin =

p2 2·m

(3.17)

A momentum transfer ∆p would thus change the energy accordingly by ∆Ekin ≈

∆p · p = v · ∆p = β · c · ∆p. m

(3.18)

If one now includes the mean free path of two nucleon decays λcat one arrives at the following formula for the maximal energy loss. ∆Ekin β · c · ∆p = ∆x λcat

(3.19)

Inserting typical values like β ∼ 10−3 and λcat ∼ 1 m yields ∆E < 1 MeVm−1 using ∆x the above mentioned upper bound for the momentum transfer. [29]. In comparison to Ionization losses this is negligibly small. Energy loss due to Elastic Collisions with Atoms L. Bracci et. al [30] have shown that it is possible for slow monopoles with β ∼ 10−5 −10−1 to loose energy on the order of 50 MeVcm−1 in liquid hydrogen and helium by elastic collisions with the atoms. From that they conclude that the magnitude of this energy loss is probably independent of the atomic species. The energy would be released in the form of acoustic oscillations or infrared radiation. Cherenkov Radiation Relativistic particles passing through matter emit Cherenkov radiation when they move faster than the velocity of light in that material (see section 4.4.1). For normal charged particles the energy loss due to Cherenkov radiation is negligibly small. On the contrary, for monopoles there is a significant enhancement of the radiated energy. The energy loss ∆Em due to Cherenkov radiation evaluates to [31] g 2 n2 4π 2 z 2 e2 Z ∆Em = 2 · e c2

1 1− 2 2 β ·n

!

· ν dν ≈ ·4700 · n2 · ∆Ee

(3.20)

where n is the refractive index of the medium and g the magnetic charge. ∆Ee denotes the Cherenkov energy loss of an electrically charged particle. The enhancement of the energy loss is at least by a factor of 4700 for g = 1 · gD like for the ionization loss (see eqation 3.16), but will in reality even be higher due to the refractive index. The whole mechanism of course only applies for particles whose β > βc where βc is the Cherenkov velocity threshold (see section 4.2).

17

3 PROPERTIES OF MAGNETIC MONOPOLES

3.4.3

Implications for the Expected Monopole Flux in IceCube

As has been pointed out previously in section 3.2, the monopole flux arriving at earth is expected to be isotropic. When coming from below the horizon, interaction with the matter in the earths interior can lead to a non isotropic flux, viewing from the position of IceCube. J. Derkaoui et. al [32] have calculated the energy loss of monopoles through earth over a broad velocity and mass range . They use a simplified model of the earths density profile and apply energy loss calculations for different arrival directions. Depending on the mass, velocity and magnetic charge, they get an estimate for the isotropy of an arriving flux at an underground detector. Figure 3.5 demonstrates the results. Table 3.2 summarizes the minimum masses for which an isotropic flux is expected.

Figure 3.5: Expected fraction of the 4π solid angle for the arrival flux of magnetic monopoles at an underground observatory like IceCube. a), b), c), d) denote different velocities. Taken from [32].

Two jumps are generally visible in the plots. They reach from 0 to 2π and from 2π to 4π. This means that it depends on the mass of the monopole wheter it reaches the detector, if the velocity and charge are fixed,. Light monopoles can not traverse the earth layer above the detector so their flux is 0. Intermediate mass monopoles may enter from above but not from below the horizon, which means their fraction is 2π. For the highest masses around 1017 GeV and velocities β ∼ 10−2 − 10−3 the flux is isotropic.

18

3.5 Flux Limits

Table 3.2: Minimum masses for which the arrival flux of magnetic monopoles at IceCube is expected to be isotropic. Values are given for 3 different velocities and for different multiples of the Dirac charge. Taken from [32].

magn. charge β = 0.01 β = 0.001 β = 0.0001 gD 2gD 3gD

3.5 3.5.1

2 · 1013 8 · 1013 2 · 1014

2 · 1014 9 · 1014 2 · 1015

2 · 1017 9 · 1017 2 · 1018

Flux Limits The Parker Bound

Magnetic monopoles get accelerated by galactic magnetic fields. In this process energy is being transfered which depletes the field strength. At the same time astrophysical sources replenish it. In 1970 an upper limit was derived for the monopole flux requiring it is consistent with the survival of the galactic magnetic field of B ≈ 3 · 10−6 G [33]. This limit is also called ”Parker Bound“ and calculates to Φ = 10−15 cm−1 s−1 sr−1

(3.21)

It was revised again in 1982 [11] by Turner et. al. taking into account the different monopoles masses, their velocity distribution and properties of the magnetic field. They wanted to understand how a monopole behaves when it enters a galaxy with a certain initial velocity. For their studies, they divided the galaxy into cells of coherent magnetic field. The diameter of such magnetic cell in the galaxy is on the order of 300 pc. Dimensionless parameters help to simplify the calculations. They are summarized in table 3.3: In principle, two different flux limits were published. Important for differentiating which limit is valid, one has to know about two quantities. The first is the initial velocity vi of the monopole when it enters the galaxy. The second is vmag = 10

−4

l21 · B3 · m19

!

which describes the velocity a monopole reaches in a cell of coherent magnetic field when it is initially at rest. The first limit (eq. 3.22) is valid for monopoles with vi < vmag , which means they get easily deflected and accelerated by interactions with the field until they reach vmag . It is obvious that this limit only depends on the attributes of the galaxy. B3 Φ1 = 10−15 cm−1 s−1 sr−1 · · t15

s

r23 l21

(3.22)

19

3 PROPERTIES OF MAGNETIC MONOPOLES

Table 3.3: Dimensionless quantities for the calculation of the refined parker bound: a) mass of the monopole in terms of 1019 GeV, b) magnetic field strength in terms of the standard field strength in the galaxy, c) coherence length in terms of the standard coherence length (1021 cm ∼ 300pc) of the galactic magnetic field, d) regeneration time of the magnetic field in terms of the standard regeneration time of the galactic magnetic field, e) distance from the center of the galaxy in units of the radius of the Milky Way galaxy (1023 cm ∼ 30kpc), f) infall velocity into the galaxy in units of a standard infall velocity (∼ 10−3 c) - Taken from [11].

name

formula

standard value

m19 a) B3 b) l21 c) t15 d) r23 e) v3 f )

M = m19 · 1019 GeV B = B3 · 3 · 10−6 G lc = l21 · 1021 cm treg = t15 · 1015 s r = r23 · 1023 cm vi = v3 · 10−3 c

0.01 1 1 1 1 1

For the case v1 > vmag another limit is more appropriate. It is now dependent on the infall velocity and the mass because the monopole will only marginally be influenced by the galactic magnetic field. Instead, the monopole parameters get higher significance.

Φ2 = 10−13 cm−1 s−1 sr−1 ·

m19 · v3 2 t15 · l21

(3.23)

Both flux limits are combined and plotted in dependence of the mass in figure 3.6. The standard values of table 3.3 are used for the dimensionless parameters and the infall velocity of the monopole has been chosen to be vi = 10−3 c. The limit is constant up to 1017 GeV and gets less restrictive for higher monopole masses. Extensions of the Parker Bound There have been two further extensions in 1993 by Turner et al. [34] and in 2000 by M.J. Lewis et al.[35]. They both investigate the influence and survival of an early or even protogalactic field on the parker bound. It has also been shown by Raphaeli and Turner [36] that intra-cluster magnetic fields set limits that are 3 orders of magnitude more stringent than those set by the galactic magnetic field. In all those papers the authors stress that the uncertainties are severe and the resulting bounds have to be taken with care.

20

3.5 Flux Limits

Figure 3.6: Plot of the revised parker limits. Φ1 is valid as long as the infall velocity is smaller than the velocity vmag . Φ2 is plottet with an infall velocity of 10−3 and intersects this bound at a mass of 1017 GeV. With increasing mass it gets less restrictive.

3.5.2

Other Astrophysical Bounds

Dense astrophysical objects like white dwarfs or neutron stars have been used to infer limits on the monopole flux, assuming the monopoles would catalyze nuclear decay by the Rubakov effect [37]. It is likely to happen in stars rich of hydrogen, as for hydrogen the effect is enhanced rather than suppressed (see Section. 3.3). The idea is that monopoles cluster within the star during its lifetime. Induced nucleon decay in the interior would release a certain amount of energy. This energy would visible in increased UV and XRay radiation for neutron stars or increased luminosity for white dwarfs. The amount of measured radiation can be used to infer a limit. The same can be done for the Jovian planets in our solar system: Jupiter, Saturn, Uranus and Neptune [38]. They are much closer to earth but get illuminated by the sun, which makes it much harder to infer flux limits based on their intrinsic heat. All those limits are well below the parker bound and seem beyond the reach of earthbound experiments (see section 3.5.3 on experimental limits). Careful interpretation hints that these limits should not be taken as stringent as they seem and detectors on earth could still be able to detect monopoles by nucleon decay[39].

21

3 PROPERTIES OF MAGNETIC MONOPOLES

3.5.3

Experimentally obtained Limits

Experimental upper limits of slow magnetic monopoles have decreased by several orders of magnitude and are now well below the parker bound. These limits were mostly set by recent experiments from the 1990’s and 2000’s, but direct searches with supraconducting magnetic coils and SQUIDS were the first ones in the late 1970s to perform searches. They looked for changes in the magnetic flux when a monopole passes through detector. No positive signals have been found to date although a candidate event has been reported by Cabrera[40]. Furthermore, nucleon decay candidates have been seen by the KGF[41] and Nusex[42] experiments. All these results are inconclusive though and are not interpreted as discovery. Among the recent experiments that were able to obtain limits for subrelativistic monopoles were searches with the MACRO detector [43] and the Amanda-II Neutrino Telescope [44] which both relied on the Rubakov/Callan effect (section 3.3). Since their results are valid for different intervals of β, both are depicted in individual figures. See 3.7 and 3.8.

Figure 3.7: Flux limits for subrelativistic monopoles from the Amanda-II experiment[31]. The Best MACRO limit is also plottet. Depicted are limits for different values of σ0 .

There are also limits derived analyzing mica crystals [45]. The idea is that a magnetic monopole captures 27 Al, 55 Mn or another nucleus into a bound system by a magnetic-

22

3.5 Flux Limits

Figure 3.8: Flux limits for subrelativistic monopoles from the MACRO detector[43]. Depicted are limits for different values of σ0 .

dipole - magnetic monopole resonance. When this bound system traverses the crystal lattice this leaves a trail of lattice defects which can be searched for with a microscope. Absence of these traces and the old age of those crystals (on the order of 400 million years) can be used to derive even more stringent monopole flux limits in the velocity range of approximately β = 10−3 −10−4 . This excludes the possibility of the Rubakov/Callan-effect though, and cannot be compared to limits obtained using that effect. Although, as described in section 3.2, the likelihood that monopoles are massive and slow is high, light and fast monopoles can not be excluded. Recently, the most stringent limits for those intermediate mass monopoles could be set by the RICE [46] and AnitaII[47] experiment, which could constrain the upper flux limit about 4 orders of magnitude below the parker bound for extremely high gamma factors of γ > 107 . For lower gamma factors the AMANDA-II limits [31] are the most stringent to date. Figure 3.9 summarizes these limits. Particle accelerators have also looked for very light monopoles from particle collisions and could set limits on the minimum monopole mass. Currently the results from the DZero collaboration are the most restrictive [48] with lower mass limits (95 % CL) of m > 610, 870 and 1580 GeV/c2 for monopoles with spin 0, 21 , 1 respectively. With experiments running soon at the LHC [49] these mass limits will be improved. .

23

3 PROPERTIES OF MAGNETIC MONOPOLES

Figure 3.9: Flux limits for highly relativistic monopoles. Taken from [47].

24

CHAPTER IV The IceCube Neutrino Observatory IceCube is a cubic kilometer Neutrino Observatory located at the geographic South Pole. This chapter covers the motivation behind it, its structural design and the way it can detect particles. Expected signatures from subrelativistic monopoles are specifically explained. In the last section the simulation framework is described.

25

4 THE ICECUBE NEUTRINO OBSERVATORY

4.1

Astrophysical Motivation

IceCube has been built to detect galactic and extragalactic neutrinos up to the highest energies of 1020 eV. Neutrinos are interesting for high energy astrophysics because of their interaction behavior. They do not possess charge and are not affected by magnetic fields. Thus, their direction points back directly to their origin. Additionally, they only interact via the Weak Force and penetrate interstellar matter and heavy bodies like the Earth with ease. The detector is embedded deep into the Antarctic ice (see section 4.3.1 for a description of the detector layout). Neutrinos will typically interact with the nuclei in the ice, either by mediating a Z 0 or a W ± boson. The cross section for the interaction with the electrons is orders of magnitudes smaller. If the exchanged boson is a Z 0 , the reaction is called a NC (Neutral Current) reaction. The neutrino will basically scatter off a nucleus and initiate a hadronic cascade (eq. 4.1). να + Nucleus ⇒ να + hadronic cascade

α ∈ {e, µ, τ }

(4.1)

In case of a W ± exchange the reaction is called a Charged Current (CC) reaction. Charged currents are more interesting for neutrino detection, because the cross section is about one order of magnitude higher than for neutral currents. Furthermore, they produce leptons lα corresponding to the neutrino generation which interact with the ice (eq. 4.2). να + Nucleus ⇒ lα + hadronic cascade

α ∈ {e, µ, τ }

(4.2)

These charged leptons can be detected via Cherenkov radiation (see section 4.2) and allow to draw conclusions on the primary neutrinos. Depending on the neutrino flavor, different Cherenkov signatures are expected (see section 4.4.1). Examples for potential galactic neutrino sources are supernovae , microquasars, dark matter annihilations in the galactic halo or the supermassive black hole in the center of the galaxy . Examples for potential extragalactic neutrino sources are Active Galactic Nuclei (AGN) or Gamma Ray Bursts (GRBs). In addition to neutrinos originating from outer space, one can observe secondary neutrinos produced from collisions of cosmic rays with the atmosphere. They traverse earth and may interact near IceCube, leaving a similar signature in the detector. These ”atmospheric neutrinos“ are thus usually accounted for as background and have to be distinguished from extraterrestrial ones. The main background, however, comes from charged cosmic rays that produce muons which enter the detector from above. The Earth is used as a veto for these particles, since only a neutrino can reach IceCube from below. Figure 4.1 illustrates the different scenarios.

26

4.1 Astrophysical Motivation

neutrino

Source

charged cosmic ray muon

Atmosphere

magnetic field lines interaction

ISM/IGM 2 1

Earth

1

direct neutrino

2

atmospheric neutrino

3

cosmic ray background

IceCube

3 Figure 4.1: Illustration of neutrinos as cosmic messengers. Depicted is the primary neutrino signal and possible other signals from an atmospheric neutrino or cosmic ray interaction in the atmosphere. ISM/IGM denotes interstellar matter/intergalactic matter. Note that the neutrino interaction could also produce an electron or a tau depending on the flavor (see section 4.4.1).

27

4 THE ICECUBE NEUTRINO OBSERVATORY

4.2

Principle of Particle Detection - Cherenkov Radiation

When a charged particle traverses a non-conducting medium it polarizes the atoms in the material. When the electrons fall back into equilibrium photons are released which destructively interfere with each other. If the charged particle is faster than the speed of light in that medium, these photons will instead interfere constructively and form a light front which has a distinctive orientation compared to the direction of the charged particle. This light is called ”Cherenkov radiation“. Its existence was first observed by P. Cherenkov in 1934 [50] and is the fundamental concept on which all particle detection within IceCube is based on. The process is depicted in figure 4.2.

Cherenkov light front

θ Cherenkov angle

charged particle

c n

·t β·c·t

Figure 4.2: Illustration of the Cherenkov effect. A charged particle with relative velocity β = vc moves through a medium with refractive index n. During a time interval t, photons traverse a length of nc ·t while the charged particle moves the longer distance β ·c·t. Elementary waves depict the photons which originate from the particle track and form the Cherenkov wave front.

Within a certain time t light will travel a distance of c xlight = · t. n c is the speed of light in vacuum and n is the refractive index of the medium. In the meanwhile, the particle will have travelled xparticle = β · c · t.

28

4.3 Design of the Detector

From the Huygens principle one comes to the conclusion that a light front with the angle cos(θc ) =

1 , n·β

(4.3)

with respect to the particle direction is formed. In three dimensions this corresponds to a light cone around the track. θc is called ”Cherenkov angle“. In the Antarctic ice the refractive index is n ≈ 1.32 and thus θc ≈ 41◦ for particles close to the speed of light. The critical velocity at which this effect takes place is called the Cherenkov velocity βc = n1 which evaluates to approximately βc = 0.76. The spectrum of Cherenkov light extends over all visible wavelengths down to the ultra violet. Thus, an optical transparent medium like the Antarctic ice is necessary to exploit Cherenkov radiation for particle detection.

4.3 4.3.1

Design of the Detector Geometric Layout

The geometric layout of the detector is depicted in figure 4.3. It consists of 86 strings which are placed in several deep drill holes in the Antarctic ice. Each string has 60 Digital Optical Modules (DOMs) (section 4.3.2) attached to it. These modules are the Cherenkov light detection units for the experiment. They are aligned like bubbles on a string, most of them with 17 m spacing, starting at a depth of about 2450 m ranging down to 2450 m. Additionally to the subterranean “InIce“ strings there are ice tanks at the surface which form the so called ”IceTop“ surface air shower detector [51]. IceTop consists of 160 tanks distributed over an area of a square kilometer filled with clear ice and 2 DOMs each which detect Cherenkov radiation from cosmic ray showers. This surface array can act as a veto for the ”InIce“ part on atmospheric muons, which are often accompanied by air showers, as well as an independent cosmic ray detector for the intermediate TeV-PeV energy range. For the topic of slow magnetic monopole searches only the sub-surface detector is relevant. As depicted in figure 4.4, the detector has been upgraded in different stages. Because of the harsh conditions in Antarctica these extensions of the detector have to take place during the 3 months of the Antarctic summer (from Nov. to Feb.) where temperatures allow airplanes to land at the site. In its current layout, the detector consists of 79 strings. In the 2010/2011 season the last 7 strings will be deployed and the final IceCube86 configuration will be established. A central part of the detector is furnished with a denser string packing (figure 4.4). These inner strings have an average spacing of only 75 m instead of the standard spacing of 125 m. Additional so called ”DeepCore strings“ are filled into the gaps. These contain more sensitive DOMs than standard strings and

29

4 THE ICECUBE NEUTRINO OBSERVATORY

Figure 4.3: 3-d sketch of the IceCube Observatory. The lower part of the strings is populated with DOMs. DeepCore is highlighted in green. The Eifel Tower is drawn to get an idea of the proportions. Taken from [52]

30

4.3 Design of the Detector

IceCube − top view season 06/07 season 07/08

season 05/06 season 09/10 season 04/05

season 10/11

season 08/09 DeepCore

Figure 4.4: Sketch of the top view of the IceCube Observatory. The different deployment stages are color marked. DeepCore strings have thicker borders. The circle marks all strings that belong to the DeepCore subdetector.

a different geometrical module arrangement. The 50 lower DOMs have a 7 m spacing and comprise the lower 350 m of the string, while the 10 upper ones are situated in the upper detector region with 10 m spacing. Together with the lower 21 modules of the 6 surrounding standard strings and the string in their middle this region of modules forms a subdetector called “DeepCore” (see figure 4.4). DeepCore has been constructed with the intent to be sensitive to low-energy muons down to ∼ 10 GeV [53]. As it turns out, in addition to provide a much lower energy threshold for standard particles, DeepCore also raises sensitivity for subrelativistic monopoles (see chapter 5).

4.3.2

Design and Purpose of a Digital Optical Module (DOM)

The purpose of a DOM is to detect Cherenkov light from charged particles (see section 4.2). Its design is depicted in figure 4.5. The three major hardware components are a PMT (Photomultiplier Tube), the DOM mainboard containing the important electronics and a LED flasher mainboard. All components are housed inside a 32.5 cm diameter glass sphere. The Photomultplier is a Hamamatsu Photomultiplier [54] optimized for optical wavelengths between 300 − 600 nm with a peak quantum efficiency of ∼ 25% at 405 nm. DeepCore DOMs contain PMTs which reach 33 % quantum efficiency. The Photomultiplier is operated at a gain of 107 . For optical coupling to the glass it is embedded into an

31

4 THE ICECUBE NEUTRINO OBSERVATORY

RTV (Room-Temperature Vulcanizing) gel. When photons hit the PMT they produce photoelectrons that get amplified and produce an analog PMT waveform. Integrating over this waveform yields a charge, which is measured in units of PE (Photo Electrons). The DOM mainboard contains several chips which digitize the analog signal from the PMT. The high resolution digitizers are two ATWD (Analog Transient Waveform Digitizer) chips, called ATWD-A and ATWD-B, which have a very fine sampling resolution of 3.3 ns per channel. Because each chip comprises 128 channels it can digitize ∼ 422 ns of signal. Every ATWD has a dead time of about 29 µs which is the time needed for the digitization process. ATWD-A and ATWD-B run in “ping pong mode”, which means they alternate to reduce dead time. A low resolution FADC (Fast Analog To Digital Converter) chip digitizes simultaneously. It has a lower sampling resolution of only 25 ns per channel but a longer sampling interval of 6400 ns in total. Additionally, the FADC chip has no dead time. A waveform is only digitized, if both the ATWD and FADC run together. Thus, if both ATWD chips are in “dead time mode”, the FADC will not start digitizing alone. This has implications for the hit pattern and triggering of slowly moving monopoles, see section (5.1). The LED flasher board contains 12 individually controllable LEDs each capable of emitting up to 1010 photons per pulse at a wavelength of 405 nm. They are aligned in pairs of 2 in 60◦ intervals covering the whole circle. One looks into the upper hemisphere, tilted at about 40circ and the other one is mounted horizontally. They are used for geometrical calibration as well as to determine the optical ice properties in different depths (section 4.3.3). Contaminations of potassium-40 within the glass sphere undergo beta decay and can potentially trigger the PMT. This results in a characteristic noise rate. The rate of the standard DOMs has been measured individually to about 500 Hz. High-QE-DOMs measure a noise rate up to 650 Hz.

4.3.3

Optical Ice Properties

Unlike other particle physics detectors, IceCube uses naturally formed ice as the detection medium. Actually, it makes up over 99% of the detector volume. The ice is structured in layers that have formed over thousands of years and contain different impurities based on fluctuating atmospheric conditions of the past millennia. It is important to understand these ice properties in detail for the simulation of the propagation of Cherenkov photons. Wrong assumptions about the scattering and absorption length in different layers can produce systematic errors (see appendix A). Photon propagation in ice is determined by two properties: scattering on dust particles and absorption in the ice.

32

4.3 Design of the Detector

Figure 4.5: Sketched lateral cut of an IceCube DOM. Taken from [55].

The scattering process is mathematically described by Mie Scattering [56]. Mie Scattering describes the scattering of light on small pointlike particles like dust impurities. An important quantity in this respect is the mean scattering angle between the path before and after the scattering process, usually depicted as hcos(θ)i. The average path length that a photon travels between two scattering processes is called the scattering length λs . One can now define an “effective“ scattering length λe which sums over all the individual scatter processes and is a measure at which length scale the photon direction has become isotropic. It is defined as λe := lim λs n→∞

n X

hcos(θ)ii =

i=0

λs . 1 − hcos(θ)i

(4.4)

The absorption process is defined by the mean absorption length λa . This is the length after which the intensity of a photon beam has dropped to 1/e of the initial value. One can also define a ”propagation length“ s

λp =

λe · λa 3

which combines both quantities and is used to describe the diffuse transport of photons from a point source. At distances d & 5 · λe the photon fluence N behaves like N∼

1 −d · e λp . d

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4 THE ICECUBE NEUTRINO OBSERVATORY

The elementary quantities λe and λa can be determined in-situ with flasher LED measurements. These measurements have been done by the predecessor of Icecube, the AMANDA-II neutrino telescope in 2005 [57]. The results are the basis of the ice model that is used for simulation in this thesis (the AHA2 ice model, see section 4.6.4). Therefore, these results are presented here rather than newer IceCube flasher data. Figures 4.6 a) and b) illustrate the inverse mean scattering length (scattering coefficient) and inverse absorption length (absorption coefficient/absorptivity) in dependence of the depth and wavelength. A high coefficient means high scattering/absorption and in turn a short scattering/absorption length. It should be mentioned that the data in the deepest ice layers is an extrapolation because Amanda’s deepest string only reaches to a depth of 2138 m. In the very shallow region the optical properties are bad because of residual air bubbles. Towards deeper layers they vanish because of the higher environmental pressure. Several peaks appear nonetheless because of dust deposits in the ice. The dominant one is located at ∼ 2100 m depth. The high dust concentration is this region was given the name ”dust layer“. It is hardly optically penetrable, with λe , λa on the order of a few meter. Towards deeper layers bubble and dust free ice provides the best ”seeing“ conditions of λe ∼ 50 m, λa ∼ 200 m. This is the reason why DeepCore in this depth. It should be mentioned that the scattering and absorption were assumed to be horizontally homogeneous. New measurements indicate that there is slight tilting in the ice layers which is implemented in recent ice models [58].

4.4

Particle Signatures in the Detector

This section describes the particle interactions and resulting Cherenkov signatures of the three charged leptons as well as the expected signature of a subrelativistic monopole. 4.4.1

Lepton Signatures

Electron Signature: A high energetic electron will loose energy dominantly via bremsstrahlung. The bremsstrahlung photons will quickly form e+ e− pairs which themselves produce bremsstrahlung again. This process will go on until the resulting photons have less energy than 2 · me or the electrons are below a critical energy Ec = 81 MeV for which ionization losses become dominant. This exponential increase in particle numbers results in an electromagnetic shower. Shower lengths can vary from a few meter for a 1 PeV electron up to L ∼ 200 m for the highest expected energies of 10 EeV. The Cherenkov light emission profile of from an electromagnetic shower (with energy > ∼ 10 MeV) is peaked around the Cherenkov angle with respect to the direction of the

34

4.4 Particle Signatures in the Detector

(a) Inverse mean scattering length vs ice-depth and wavelength

(b) Inverse absorption length vs ice-depth and wavelength

Figure 4.6: Ice properties measured by the AMANDA-II experiment. Taken from [57].

35

4 THE ICECUBE NEUTRINO OBSERVATORY

incident electron [59]. Since the light emission happens in a compact region, it is quite hard to measure the direction. On the contrary, the energy can be estimated quite well when the electromagnetic cascade is contained within the instrumented volume. Several such cascades with an energy of a few 100 MeV which are aligned on a line are the expected signature of a subrelativistic monopole (see section 4.4.2). Muon Signature: The critical energy up to which a muon will loose energy dominantly via ionization/excitation losses in ice is Ec ≈ 580 GeV. Above that energy radiative losses like pair production, bremsstrahlung and photonuclear interactions take over. These are of stochastic nature. To consider both types, it is useful to parameterize the total energy loss via −

dE ≈ a(E) + b(E) · E dx

(4.5)

where a and b are slowly varying functions of the energy. The a-term contains the ionization loss, which is basically the Bethe-Bloch formula [60]. The b-term includes radiative losses. Assuming that a and b are fairly constant, an approximation for muons yields [61] −

dE ≈ 0.2 GeVm−1 + 3.4 · 10−4 m−1 · E. dx

(4.6)

One is then allowed to approximate the estimated track length L by L≈

1 E · ln(1 + ) b Ec

(4.7)

a b

(4.8)

with Ec ≡ which corresponds to L ≈ 2900 m · ln(1 +

E ) 580 GeV

(4.9)

for a muon. Because of their mass mµ ≈ 105 MeV muons are already highly relativistic at GeV-energy scales which corresponds to Lorenz factors γ > 10 and velocities β ≈ 1. The mean track length of a muon without energy loss can be calculated via Lmin = vµ · γ · τµ and evaluates to ∼ 6.6 km for a muon with γ = 10 using the mean lifetime τµ ≈ 2.2 µs, which is already much larger than the detector diameter.

36

4.4 Particle Signatures in the Detector

Thus, if compared to eq. 4.9, the propagation length expected from energy loss is more important than the decay time. One can also see from eq. 4.9 that a ∼ 1 TeV muon should already be able to traverse the whole IceCube detector. Since scattering is negligible , it has a straight track along which Cherenkov light is emitted with an emission profile much higher peaked around the Cherenkov angle than for an electromagnetic cascade [59]. Together with the long track length this permits a much easier reconstruction of the muon direction than for the electron.

Tau Signature: A tau will decay much faster than a muon because of its shorter mean lifetime ττ ≈ 29 ps, but the general energy loss behavior is similar to the muon. The main contributor to the radiative losses is now due to photonuclear interactions. Bremsstrahlung and pair production have slightly less impact [62]. Basically, the Cherenkov emission profile is fainter than from the electron. Expected decay lengths of the tau are around 50 m per PeV. This means a tau of 20 PeV can already traverse IceCube [63]. By virtue of the tau’s wide variety of decay modes and strongly varying decay lengths in the range between 1 PeV and 50 PeV it can have many possible Cherenkov Signatures. For TeV energies the point of tau creation happens geometrically close to the tau decay cascade. Thus it is hard to see a tau track at all. For energies of a few PeV the decay length is a few hundred meter. It is accompanied by two cascades, one at the start from the generation of the tau and the other one at the end from its decay. The Cherenkov profile from involved hadronic cascades are comparable to electromagnetic ones. If both cascades lie within the instrumented volume it would be a clear signature for a tau, also called ”double bang“.

4.4.2

Subrelativistic Monopole Signatures

When a subrelativistic monopole traverses IceCube, it will not emit Cherenkov light. Thus, one has to investigate which energy losses involve relativistic particles that could be detected. Into consideration come ionization losses and induced nucleon decay, while others can be ruled out (see section 3.4). Concerning the ionization loss, it is important to know if the monopole can transfer enough energy to an electron in the ice so that it emits Cherenkov radiation. One can estimate the maximum energy transfer from a monopole to an electron, if one assumes a degenerate electron gas [25]. It turns out to be Emax = 2 · me · vF · vM P = 2 · me · βF · βMP · c2

(4.10)

where me is the electron mass, vF the Fermi velocity of the electron gas and vMP the monopole velocity. Since ice is an insulator, a certain energy has to be subtracted, too.

37

4 THE ICECUBE NEUTRINO OBSERVATORY

Neglecting the energy gap in ice, one finds that Emax . 10 keV  Ecrit ≈ 235 keV 4 , where Ecrit denotes the critical kinetic energy at which an electron starts to emit Cherenkov radiation. Therefore, ionization losses of the monopole are not detectable by Cherenkov light. The signature of a monopole is assumed to originate from induced nucleon decay along the monopole track. As described in section 3.3 these nucleon decays can result in electronic (e+ , e− ), muonic (µ+ , µ− ), pionic (π 0 , π + , π − ) and kaonic components (K 0 , K + , K − ). Electrons and the neutral pion will induce electromagnetic cascades which have a distinctive Cherenkov emission profile (see section 4.4.1). Muons will only possess a few 100 MeV kinetic energy which they will loose within a few meters [60]. Then they decay into an electron and neutrinos. The resulting electromagnetic cascade produces less Cherenkov light since the neutrinos will carry away some energy. A charged pion will decay into a muon and neutrino (99 % branching ratio) , which means the resulting Cherenkov signature is even fainter. The charged Kaons will mainly decay into muons (∼ 63% branching ratio) and the neutral kaons into different pions and leptons. The resulting electromagnetic component of the kaonic channels is thus comparable to the charged pionic channels. As described in section 3.3, the decay channel with the highest branching ratio ( ΓΓtot > 90 %) for protons and neutrons is

p, n → e+ + pions

(4.11)

The simplest decay in this channel produces an e+ and π 0 which completely transfers the nucleon rest energy into an electromagnetic component. Thus, it is the optimum decay mode to be detected via Cherenkov radiation. To summarize, the signature expected from a subrelativistic monopole are electromagnetic and hadronic cascades along the monopole track. These vary in energy content because energy gets transferred away by neutrinos. These cascades are separated on average by the mean free path λcat which can be calculated according to equation 3.11. Each of them produces Cherenkov light, which can potentially be detected, see figure 4.7. The velocity β and the mean free path λcat are the characterizing properties of a subrelativistic monopole and will be used throughout this thesis.

4

38

This calculation uses βMP < 0.01

4.5 Data Flow

strings

nucleon decay cascades

monopole track ∼ λcat

Figure 4.7: Illustration of the nucleon catalysis signature by a subrelativistic monopole traversing IceCube. On average, cascades are separated by λcat .

4.5 4.5.1

Data Flow Data Acquisition

When a photon hits an IceCube DOM there is a chance it is detected by the PMT. The result is an analog waveform which is digitized in the DOM-mainboard (see section 4.3.2). This process is called a ”DomLaunch”. Thus, each DOMLaunch has a corresponding digitized waveform, which contains information on the deposited charge in the PMT. It is possible that a second photon hits shortly after the first one and falls into the same digitization time window. This will still count as the same DOMLaunch5 . Domlaunches are the basis upon which the trigger logic is built up. For simplicity and computing time purposes only minimal information is used: time of the DomLaunch and position of the optical module. The whole DAQ software system is written in Java and consists of many different modules which have their specific tasks. These modules are installed in different computers at the South Pole for reasonable computing power. A schematic of the involved components is depicted in figure 4.8. The process of data taking is built up hierarchically. The in-situ variant of this whole system of hardware and software components is also called SPS (South Pole System). For software testing purposes there also exists a test system called SPTS (South Pole Test System) which is located in Madison, Wisconsin. It has exactly the same structure except that ”fake DOMLaunches” are inserted instead of real data. 5

The term ”DOMLaunched“ may be interchanged forth and back with the term ”hit“ from now on. They are both used synonymously.

39

4 THE ICECUBE NEUTRINO OBSERVATORY

form event Global Trigger / Event Builder

Events

send trigger information request all hits within the event window

InIce Trigger (forms one timeordered stream of DOMLaunches and runs trigger modules)

StringHub no. 1

cable

StringHub no. 79

IceTop Trigger

IceTop Data

send hit information to the corresponding StringHubs

DOMs photons "launch" the DOMs

Figure 4.8: Schematic of the different stages in Data Acquisition (DAQ). Hardware components are colored blue. Data are colored red. At the physical level photons launch the DOMs. This hit information is collected in the StringHubs and then transfered to the InIceTrigger component. A time ordered hit stream is built up and passed on to trigger modules. All triggered events get eventually merged by the Event Builder, which requests the hit information from the StringHubs, once an event has been formed. This includes IceTop.

40

4.5 Data Flow

The first step in the chain begins with a DOMLaunch. If another module within the two upper or two lower neighbors also registers a photon within 1 µs, both launches get flagged as so called ”HLC“ (Hard Local Coincidence) launches. If the first launch is isolated, it gets flagged as an ”SLC“ (Soft Local Coincidence) launch instead. Noise hits (see section 4.3.2) will almost entirely produce SLC hits, since it is very unlikely that two nearby DOMs launch within 1µs from 40 K decay 6 . Since later in the chain, only HLC hits will be used in trigger formation, this prevents noise hits from taking part in triggering. The DOMLaunch information is then transported to a corresponding ”StringHub“ at the surface. A StringHub is a computer at the surface that handles communication with all the modules on the string. It buffers the received DomLaunch information for a few seconds. In certain time intervals the latest HLC hits are sent from the StringHub to the ”InIceTrigger” computer. It forms a time ordered stream out of all HLC-hit streams from the StringHubs. This single stream serves as an input for various trigger modules (section 4.5.2) that are also hosted within this computer. Once a trigger condition is met, the “InIceTrigger” sends a readout request for a certain time window to the “GlobalTrigger/EventBuilder“. This computer manages all trigger requests, including the ones from IceTop triggers. It merges different readouts if they overlap in time and requests specific DOMLaunch information from the StringHubs including SLC Hits for the full readout time (see section 4.5.2). The complete hit information forms an event and is then stored in binary DAQ format. 4.5.2

Triggering

As described in the previous section, the first step of triggering involves the InIceTrigger computer. It runs different software modules that get a time ordered DOMLaunch stream as an input. For each DOMLaunch the trigger module decides whether a trigger condition is fulfilled. If so, it sends a readout request to the GlobalTrigger which handles all readout requests from different triggers and merges them if they overlap. The GlobalTrigger is not a trigger itself, it acts as the trigger handler. When a trigger fires, it has a trigger length associated with it. This is not the same as the readout request time, since certain time windows are added to the front and to the back. (see. figure 4.9). In the current IC-79 configuration 3 triggers are operational. Each of these has a certain readout window associated with it, a certain set of DOMs (domset) on which it operates on and a certain part of the detector that is read out if the trigger is fired. Their configurations are summarized in table 4.1. 6

In fact, this occasionally happens. These ”noise pairs“ are the main background signal for the trigger developed in this thesis, see section (6.3.1)

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4 THE ICECUBE NEUTRINO OBSERVATORY

Table 4.1: Summary of the configuration of the three IC-79 triggers. SMT-8 is operating on all DOMS, thus there is no specific domset defined. The Cluster Trigger operates on all strings, excluding the 6 DeepCore strings (domset 2). The SMT-3 trigger operates on the 50 lower modules of the 6 DeepCore strings and on the 21 lower modules of the 7 standard strings that are also part of DeepCore (domset 5). The whole detector including IceTop is read out in each case. Longer readout windows associated with the SMT-3 have an effect in the global trigger process (see figure 4.9).

name

readout window (before)

readout window (after)

domset

readout part

SMT-8 Cluster SMT-3

−4 µs −4 µs −10 µs

+6 µs +6 µs +10 µs

NONE 2 5

InIce+IceTop InIce+IceTop InIce+IceTop

The SMT-8 trigger (Simple Multiplicity Trigger-8) is the standard trigger in IceCube and is based on hit-time information only. It fires if 8 hits from anywhere in the whole detector fall within 5 µs. Since this trigger is based on a sliding time window, it will include hits that follow afterwards until the latest hit fails to take part in an ”8 in 5 condition“. The trigger length is then determined by the time difference of the last and the first hit for which such a condition could be found. Typically, a muon with an energy of ∼ 100 GeV produces enough light output to meet these conditions. Since the muon traverses IceCube with the speed of light, which means in ∼ 3.3 µs, typical trigger lengths are ∼ 3 − 4 µs. The Cluster Trigger looks for clustered DOMLaunches within a single string. It was specifically designed to capture muons that traverse almost vertically. It fires if 5 out of 7 consecutive DOMs on one string register a DOMLaunch within 1.5 µs. Each cluster can also extend with a sliding time window like for the SMT-8. Additionally, if such a condition is met on several strings and their trigger-lengths overlap, it will count as one trigger. The trigger length is then determined by the time difference between the last and the first hit of all 5/7 string conditions that overlapped. Since this is rarely the case, most trigger lengths are below 1.5 µs. In the rare cases the muon passes exactly along the string or another muon travels through IceCube at the same time, it can extend by a few microseconds. The SMT-3 Trigger has the same trigger logic as the SMT-8. It was designed to capture low energetic muons because of its lower multiplicity threshold of 3. The condition here is 3 hits within 2.5 µs, with the additional difference that the participating DOMs are different (see table 4.1). ”Low energetic“ for the muon means its energy is around 10 GeV which corresponds to a velocity of v > 0.99 · c. This means that 2.5 µs is more

42

4.6 Simulation of Monopoles and the Detector Response

than its passing time through DeepCore, which is roughly 1 µs. The three IC-79 triggers are also called ”InIce” triggers. When the GlobalTrigger component receives a readout request from the InIceTrigger (see figure 4.8), it forms a so called “Throughput Trigger”. This is basically another terminology for a time window information from a specific trigger, which is used for merging different trigger readout requests. The throughput window always starts 10 µs before the InIce trigger fires. The length of this window can vary. If the InIce Trigger length is smaller than 4 µs the throughput window length is 20 µs. Otherwise the throughput window length is 16 µs plus the InIce trigger length. This only holds true for the SMT-8/Cluster Trigger, though. For the SMT-3 the throughput window length is always 10 µs + InIce trigger length. “Throughput Triggers” are eventually merged if they overlap and released as events. This whole procedure from “InIce“ trigger to an event is a hierarchical process illustrated in figure 4.9 with two schematic examples. An important fact which is depicted is that not all DOMLaunches within the eventwindow are read out. Only all hits within the readout window around the individual InIce Trigger are. This can have implications for SMT-8 and Cluster triggered events, but not so for the SMT3-trigger because its readout windows are identical with the throughput time window. It should be noted that the event length is defined as the total length of the merged Throughput Triggers. This means that events can not be shorter than 20 µs . Since the readout windows that get appended to the trigger time window do not contain hits that took part in triggering, it is likely that no hits of interest fall into these (−4/ + 6 or −10/ + 10) microseconds. Thus, a ”physical“ event length would most likely be defined subtracting these additional windows. For the case of subrelativistic monopoles yet another event length definition is used (see section 5.2).

4.5.3

Filtering

Once an event is triggered, it has to be decided if it should be transferred via satellite. For this purpose, filter are applied to all events that are coming from the GlobalTrigger. These look for interesting physical signatures that are relevant for different analysis. A filter looking specifically for events that could be interesting for slow magnetic monopoles has been installed since the 79 string configuration of IceCube has been taking data. More on the properties of this filter can be found in section 5.2.

4.6

Simulation of Monopoles and the Detector Response

Simulation is a vital component in present experiments. Large scale Monte Carlo simulations offer statistical power that helps to analyze complex processes which would be

43

4 THE ICECUBE NEUTRINO OBSERVATORY

time Event

Event

Throughput

Throughput

layer 3 - events detector readout ”hit gaps” intermediate layer 2 ”throughput” -4 SMT-8 µs

physical layer 1 - ”InIce”

+6 µs

-10 µs

SMT-8

SMT-3

+10 µs

SMT-3

event length

trigger length

(a) A SMT-8 and a SMT-3 are fired. Their readout windows do not overlap and two separated events are formed. Notice that the SMT-8 contains hit gaps, while the SMT-3 event does not because of its longer readout window. time Event layer 3 - events detector readout ”hit gaps”

1 0 0 1 0 1 0 1 0 1

Throughput intermediate layer 2 ”throughput”

overlap -4 SMT-8 µs

physical layer 1 - ”InIce”

Throughput

+6 µs

-4 Cluster µs

SMT-8

+6 µs

Cluster

event length

(b) Instead of the SMT-3 a Cluster Trigger fires close to the SMT-8. Their corresponding Throughput Triggers overlap and one long event is formed. A hit gap appears in the middle because the readout windows are shorter than the full throughput window.

Figure 4.9: Illustration of the trigger hierarchy.

44

4.6 Simulation of Monopoles and the Detector Response

impossible to do with pen and paper alone. Usually, the simulation process involves three different stages: • signal and background simulation, • particle propagation and physical interactions, • response of the detector.

4.6.1

The IceTray Framework

The IceTray framework is a simulation environment written in C++. It provides a workflow framework which allows the consecutive execution of specific modules. Each module has access to a data stream, can extract information or manipulate it, and release it for the next module. This offers an easy and straightforward way to process simulation data. Python scripts can be used as steering scripts by simply adding the modules needed for the simulation chain. The modular structure of this framework allows the user to write his own module and directly integrate it into the simulation data flow. The modules described in this section can be found in [64]. IceTray uses its own data format where the data is stored in containers called frames. Basically, each frame contains data from one event. Typical data stored in frames are event time and length, DOMLaunch information, waveforms and trigger information. Also more sophisticated information can be stored like reconstructed particle tracks or the Monte Carlo truth of particle decay chains. Real data is often converted from binary DAQ format (see section 4.5.1) to I3-format for comparison with simulation files which are then identical in structure.

4.6.2

Slow Monopole Generation and Propagation

For the generation and propagation of monopoles two simple modules have been written. They are basically modified versions of standard monopole generation/propagation code, which is optimized for relativistic monopole simulations [65]. The first one is responsible for generation of a monopole at specific point in space with a certain direction, velocity and track length. Figure 4.10 illustrates this process. The monopole starting point is arranged on a circular generation disk. The disk has a certain radius and is placed at a fixed distance either the center of IceCube or DeepCore. This way, it is possible to specifically generate an isotropic flux for DeepCore. The direction of the monopole is determined perpendicular to the surface area, which

45

4 THE ICECUBE NEUTRINO OBSERVATORY

means the alignment of the disk fixes the path the monopole will take. The starting position on the disk and the direction can either be specified for a fixed path or randomized for simulation of an isotropic flux. The path length of the monopole is twice the distance of the disk, which results in a symmetric track. Figure 4.10 illustrates the whole process.

starting point

generating disk

disk radius

monopole track θ Φ detector center

disk distance disk alignment

detector (IceCube/DeepCore)

Figure 4.10: Schematic depiction of monopole generation in the IceTray simulation. The monopole starts at a generation disk and travels perpendicular to that surface. The starting position on the disk and the disk alignment can be held fixed for total control of the path or randomized for the generation of an isotropic flux.

The second module takes the monopole information from the generator as an input and calculates nucleon decay positions along the track using Poissonian statistics. The only parameter that it needs is the mean free path of the nucleon decay. At each position an electromagnetic cascade is put into the particle tree. The exact decay mode is unknown, therefore all electromagnetic depositions are simulated as 940 MeV cascades, which is an optimistic assumption.

46

4.6 Simulation of Monopoles and the Detector Response

4.6.3

General Remarks on Background Simulation

Depending on the method utilized for monopole detection different backgrounds have to be distinguished. For the case of the SLOP filter 5.2, background would arise from multiple cosmic ray muons which arrive closely together in time. Generally, muon simulation is done with two modules called ”UCRGenerator“ and ”MMC” (Muon Montecarlo Code) [61]. UCRGenerator receives CORSIKA [66] files as input, and transforms them into primary cosmic rays in the frame. MMC then handles all energy losses and further fragmentation to secondary particles. In the case of a specialized slow monopole trigger, which is the main part of this thesis, background simulation is more complicated. In addition to muons, which have to be distributed over millisecond timescales, HLC noise hits are the main background. For correct background estimation several modules [67] have been written which are explained in more detail in 6.3.1.

4.6.4

Simulation of Cherenkov Light and Photon Propagation

Since IceCube is a Cherenkov Detector every simulation chain involves the simulation and propagation of Cherenkov light. For this purpose the software package Photonics was used [68]. Photonics does not track photons individually, which is very time inefficient. Instead it has probabilities in lookup tables that a photon at a certain position A arrives at position B. These tables have to be calculated only once and accessing them is fast. Thus, table production needs the effective scattering length and absorption length as input parameters. The tables that have been used in this thesis are based on the AHAv2 ice model which uses flasher measurements from AMANDA-II (see section 4.3.3). In combination to the tables, which are provided as a service called “I3Photonics”, a module named “hitmaker” is used to calculate if a photon actually launches a DOM. It processes all charged particles in the event and calculates hit probabilities from the expected Cherenkov radiation emission profiles [59]. These hits, when registered, are called ”Monte Carlo Hits“. They serve as an input for the detector response simulation.

4.6.5

Simulation of the Detector Response

The first step for the simulation of the detector response is to mimic the internal processes of the PMT. This is done with a module called ”PMT-simulator“. It takes Monte Carlo hits as an input and dumps a waveform. The second step involves digitization of this analog waveform, thus the simulation of the ATWD and FADC chips. This is done with a module called ”DOMSimulator“. One ends up with DOMLaunches from an event containing the digitized waveform, the hit time and the module position. As described in section 4.5.1

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4 THE ICECUBE NEUTRINO OBSERVATORY

this forms the basis for trigger formation. DOMs that are known to be defect are marked as bad DOMs and are usually not simulated in this step. Every detector configuration contains a static list of all DOMs that are permanently switched off. For this work the IC-59 bad DOM list is used, since newer ones are not available yet. Every ”InIce“ trigger has a corresponding IceTray module which takes the DOMLaunches as an input and writes trigger information into the frame. The last step involves a GlobalTrigger module which effectively appends readout windows and looks if throughput triggers overlap. If so, they will get merged into one event. Domlaunches that do not take part in an event can be deleted with a module called ”Pruner“.

48

CHAPTER V Sensitivity of the Full Detector (IC-86 Configuration) This chapter gives an overview of the efficiency of the present standard trigger/filter configuration for subrelativistic monopoles. Effective areas on the level of the slow particle filter are presented for the full IC-86 configuration and the influence of DeepCore is evaluated.

49

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

5.1

Performance with Standard Triggers

Current triggers are suited for muons. Their algorithms (section 4.5.2) are designed for events that have a high hit rate which is a property of relativistic particles. Additionally, if a muon triggers a standard trigger, one can be sure that its whole signature is contained in the event because the muon only needs a few microseconds to traverse IceCube. Both points do not apply for monopoles. A subrelativistic monopole has problems to fire the standard triggers primarily because of its low velocity. To illustrate this for the SMT-3 and SMT-8 triggers (section 4.5.2), two “benchmark tracks” have been simulated using different combinations of λcat and β. As pointed out in 4.4.2, these are the two defining parameters for a subrelativistic monopole. The first track is vertical and moves upwards along string 36, which is the central string in DeepCore. The second is a horizontal track going through the center of DeepCore. Figure 5.1 shows the average HLC rate for different combinations of λcat /β. Using the complete DomLaunch information, it is calculated by HLC rate =

total HLC count tlast HLC − tfirst HLC

(5.1)

Each sample point contains the average of 20 simulated monopoles. Similarity of both tracks suggests that the average HLC rate does not strongly depend on the monopole track. For a faster monopole, more light is deposited within a shorter timescale which increases the rate. Smaller mean free paths increase the HLC rate, too. The plots are useful to estimate at which point in the parameter space a monopole can effectively fulfill the trigger condition continuously. For the SMT-8 trigger this corresponds to 85 µs−1 = 1.65 µs−1 . For 3 the SMT-3 trigger this requires a rate of 2.5 µs−1 = 1.2 µs−1 . Continuous triggering is required to pass the SLOP filter condition (see 5.2). Thus, the behavior of the SMT-8 and SMT-3 in this respect is visible in the SLOP effective area (see section 5.3.2). The strongest condition for continuous triggering is set by the Cluster Trigger (section 4.5.2). 5 hits within 1.5 microseconds result in a required rate of ∼ 3.3 µs−1 . Still, extremely bright monopoles fulfill this condition permanently. For the Cluster Trigger, however, there is the additional geometric “5 hits within 7 nearby DOMs“ condition. This should only allow monopoles which travel along a string to trigger continuously. To show, that even these vertically moving monopoles do not, one can look at the maximally formed event length. Figure 5.2 shows the maximum event length, averaged over 20 monopoles per λcat /β combination, obtained running the cluster trigger only for such a vertical track along a string. To be comparable to the SLOP filter condition (see section 5.2), the event length is defined as event length = tlast HLC − tfirst HLC

(5.2)

using all hits within the respective readout time window. Continuous triggering would lead to long maximum event lengths of several 100 µs.

50

5.1 Performance with Standard Triggers

2D histogram of the average HLC launch rate (vertical track) 102

4.4 1.96 9e-01 average HLC rate [1/µs]

4e-01

101 λcat [cm]

2e-01 8e-02 100

3e-02 2e-02 7e-03

10-1

10-3

β

10-2

3e-03

(a) Average HLC launch rate for a vertical track. Monopoles following this track travel along string 36 (vertically) from bottom to top.

2D histogram of the average HLC launch rate (horizontal track)

4.4

102

1.96 9e-01 average HLC rate [1/µs]

4e-01

101 λcat [cm]

2e-01 8e-02 100

3e-02 2e-02 7e-03

10-1

10-3

β

10-2

3e-03

(b) Average HLC launch rate for a horizontal track. Monopoles following this track travel horizontally through DeepCore.

Figure 5.1: 2-d histograms depicting the average HLC rate for two different tracks in dependence of λcat and β. Color schemes are log-scaled and fixed for comparison.

51

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

vertical track along string 36 - only Cluster Trigger active 102

32 28

101

maximum event length [µs]

24 λcat [cm]

20 16 12

100

8 4 10-1

10-3

β

10-2

0

Figure 5.2: 2d-histogram depicting the maximum event lengths of monopoles following a track vertically along string 36, which is the central string in the detector. Each sample point is an average of 20 monopoles. The z-scale has its maximum at 33 µs which is the SLOP filter condition (see section 5.2).

52

5.1 Performance with Standard Triggers

Event lengths of about 16 µs for the fastest and brightest monopoles indicate the opposite. The reason is the dead time of the ATWD digitizers. As described in section 4.3.2, a DOM can only launch if the FADC and the ATWD are ready at the same time. The dead time for ATWD chips is 29 microseconds. To accommodate this, a second ATWD (ATWD-B) digitizes the analog signal if the first one (ATWD-A) is in its dead interval. The FADC has no dead time. As a consequence, even if a DOM is continuously saturated, the minimal time between DomLaunches is not the 6.4 µs sampling length of the FADC, but switches back and forth between 6.4 µs and 22.6 µs. This ”zig zag“ behavior is visible in figure 5.3, plotting the time differences between all DomLaunches on a single DOM for a single monopole with λcat = 1 cm that passes directly through it. These minimum time differences between successive DomLaunches hinder the continuous fulfillment of the Cluster Trigger condition. In the ”zig-zag“ region the DOM is saturated by the high light output of the monopole. Before and after the saturated region, the time differences get longer because the monopole approaches or leaves the vicinity of the DOM.

Figure 5.3: Plot showing the time difference between successive DomLaunches. A zig-zag structure is visible switching between at least 6.4 and 22.6 microseconds back and forth.

To summarize, a typical subrelativistic monopole with velocity β = 10−3 stays for around 3 milliseconds within the instrumented volume. If it fires one trigger, typically

53

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

an event of length ∼ 20 µs will be formed. Thus, this event contains less than 1 % of the potential monopole signature. Additionally, after triggering the event has to pass the SLOP filter criteria for further analysis or it will be lost (see section 5.2). Long events which pass the SLOP filter or even contain larger fractions the monopole signature require continuous triggering which only happens for monopoles with low mean free path (λcat . 5 cm). For higher mean free path, simple hit rate conditions (SMT-3/SMT-8) do not work because monopoles do not generate a sufficiently high hit rate. The Cluster Trigger behaves even worse because of the additional geometrical condition. In conclusion, it is evident that standard triggers are not suited for subrelativistic monopoles. A more sophisticated and more natural approach for triggering slow monopoles is presented in chapter 6.

5.2

The SLOP-filter

To keep the transferred data volume at a reasonable level, online filter scripts are running at the South Pole which only accept events that look interesting for further analysis (see section 4.5.3). A SLOw Particle (SLOP) filter has recently been installed , which is responsible for filtering possible monopole candidate events [69]. The current implementation looks for the time difference between the last and the first HLC DomLaunch within an event and requires it to be longer than 33 µs. If this is fulfilled, the event is accepted and flagged as a SLOP filtered event. The idea is shortly described: Monopoles typically take up to several milliseconds to move through the detector and have the possibility to trigger continuously which results in unusually long events. Fast relativistic particles can not form such long events by definition. As has been discussed in section 5.1, a monopole will not necessarily have sufficient light output to do so, though. The light output per unit time is directly correlated to the velocity β and the mean free path λcat and thus also to the trigger probability. Extremely bright monopoles will almost certainly produce long events but there is a fast transition where it becomes very unlikely that a trigger fires continuously or that several triggers fire close in time. Background for this filter are muons that arrive within a narrow time frame. Their hit information is merged into one event if they are less than 20 µs apart because of the 10µs throughput extensions (see section 4.5.2). From first test data of IC-79 it can be seen that filtered background events typically consist of three or more such “coincident” muons. One example is depicted in figure 5.4 a). Because of the characteristics of the global trigger (section 4.5.2), long, merged events can contain time windows in which all DomLaunches are cleaned out (see figure 4.9). Since the SLOP-filter searches for long events, many of these contain such DomLaunch

54

5.3 The Effective Area

gaps. Thus, also a potential monopole event will contain these artificial gaps, especially for high λcat when triggers are not fired continuously and the readout windows do not completely overlap. To illustrate these DomLaunch gaps, two SLOP-filtered events are presented in figure 5.4. The first shows a typical background SLOP event from an IC-79 test run. The second was produced by a simulated monopole with λcat = 10 cm. In conclusion, the SLOP filter is an approach which works effectively for monopoles which manage to trigger continuously and produce long events, thus only for the small λcat and high β in the covered parameter space. As shown, filtered events may contain gaps and may represent only a fraction of the monopole signature in the detector. Monopoles which produce triggers from time to time, but do not fulfill the 33 microsecond condition for the event length, will be lost completely.

5.3

The Effective Area

This section covers calculation of the effective area. The importance of this quantity is shortly described and simulation results for different trigger configurations are presented. 5.3.1

Definition and usage

The effective area is a quantity directly related to the count rate of a signal. For further explanation it is useful to establish the definition of a particle flux through a fixed area A first. Φ=

dN 1 · dt A

(5.3)

Φ is the true particle flux that passes through an area A perpendicular to it with a certain rate dN . Every detector has a detection efficiency and will therefore detect a smaller rate dt dNdet. ≤ dN . The area that is associated with the measured count rate dNdtdet. inserted in dt dt equation 5.3 using the true flux Φ is called the effective area Aeff . Aeff ≡

dNdet. 1 · dt Φ

(5.4)

Since Φ is fixed, Aeff is directly proportional to the measured count rate and implicitly contains the detection efficiency. The above illustration holds true for a detector which is flat and all particles enter perpendicular. For IceCube and slow monopoles the situation is different. The incoming monopole flux is assumed to be isotropic (see section 3.4.3) and thus enters from every point on the celestial sphere. Additionally, the efficiency of detection is not the same at the edge compared to the center and may also depend on the incoming direction. It is

55

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

(a) This event was recorded during IC-79 test run 115796. Three InIce triggers have fired. Apparently none of the triggers was an SMT-3, because −4/ + 6µs readout windows were appended. Two hit gaps are visible.

(b) This event stems from a simulated monopole. Its length of about 80µs represents only a small fraction of the residence time of the monopole within the instrumented volume. Two hit gaps are visible. Noise hits are not included.

Figure 5.4: Hit rate distributions of two example events that pass the SLOP-filter. The bin width is 1µs , thus the bin height corresponds to hits per microsecond. Blue areas denote the time windows of InIce triggers. Green windows denote the active readout windows in the event. Red time windows denote ”gaps“ where no hits are 56 present.

5.3 The Effective Area

also dependent on the two crucial parameters λcat and β. Solving equation 5.4 for the count rate, one can then take additional dependencies into account: d2 Ndet. (λcat , β, Ω) = Φ(λcat , β, Ω) · Aeff (λcat , β, Ω) = Φ0 · Aeff dt dΩ

(5.5)

The measured count rate now also depends on the mean free path λcat and velocity β as well as the direction of the incoming monopole. The monopole flux is assumed to be isotropic. It is now called Φ0 to indicate that it is constant in Ω. One should keep in mind that its units are 1/m−2 s−1 sr−1 , thus indicating that this flux is coming from a specific solid angle in the sky. Since the detector rotates with the earth, usually the effective area is calculated in dependence of the zenith angle and averaged over azimuth. For monopoles, where the assumed flux is isotropic, it is sufficient to average over all solid angles. From equation 5.5 it follows Z 4π dNdet. = Φ0 · Aeff (Ω) dΩ = 4π · Φ0 · hAeff i dt 0

(5.6)

were hAeff i is the effective area averaged over all solid angles and is dependent on λcat and β. In Monte Carlo simulation, monopoles are generated on a generating surface, as depicted in figure 4.10. The direction of the surface can be randomized isotropically. This allows to generate an isotropic flux Φtot = Φ0 · 4π. Equation 5.6 can be transposed to the effective area and simplified: 1 dNdet. 1 dNdet. · = · dt Φ · 4π dt Φtot dNdet. Agen. = · dNgen. dt dt Ndet. ⇒ hAeff i = · Agen. Ngen. hAeff i =

(5.7)

Ngen. denotes the total number of generated particles from all directions and Agen. the generating area. Ndet. is distributed according to a binomial distribution. Thus, the total error on the effective area evaluates to q

σAeff =

Ndet. · (1 − Ngen.

Ndet. ) Ngen.

· Agen. .

(5.8)

Systematic errors contribute, too, and are discussed in appendix A. From equation 5.7 it is evident that hAeff i can be determined on trigger level, filter level, or any other stage of analysis by measuring the number of detected signal events Ndet. . The effective area will be evaluated on filter level in the next section.

57

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

5.3.2

Simulation and Results

The parameter space has been sampled with six logarithmically equidistant points in the interval β = [0.001, 0.01] and with 16 logarithmically equidistant points for λcat in the interval [1 cm, 1000 cm] which results in a total of 96 λcat − β combinations. For λcat ≤ 10 cm each sample point contains 3000 isotropic monopoles, all others contain 5000. The disk radius of the generating disk is chosen to be 700 m which is enough to cover most of the detector. It should be noted that these simulations do not contain noise or muons. Both would contribute to the effective area for standard triggers which means the effective area is underestimated. For a comparison of the effective areas, one can calculate an averaged projected area of IceCube or DeepCore. Since both detectors have a cylindrical shape, their instrumental volume can be approximated by a cylinder. For IceCube this cylinder has dimensions r ∼ 550 m, h ≈ 1000 m and for DeepCore it has r ≈ 130 m, h ≈ 350 m. The projected area of a cylinder can be approximated as [70] Aproj. ≈ πr2 · cos(θ) + 2rhsin(θ).

(5.9)

The averaged projected area can then be calculated by integrating over θ: hAproj. i =

1 1 Zπ · Aproj. (θ) dθ = 4 · r · h π 0 π

(5.10)

This yields hAproj. i ≈ 700 · 103 m2 for IceCube and hAproj. i ≈ 60 · 103 m2 for DeepCore. The latter will be used in the next chapter to define a ”trigger efficiency“ (see section 6.6). Figure 5.5 shows the effective area without any DeepCore strings. The 8 DeepCore strings have been ”switched off“ completely and also the SMT-3 trigger is not active. In this configuration, IceCube can only detect monopoles with small λcat and high β, which is already expected from considerations of section 5.1, e.g. when looking at figures 5.1. Figure 5.6 shows the same plot with included DeepCore strings. An increase in sensitivity by a factor of ∼ 10 for λcat is visible. This effect is only due to the higher string spacing in the DeepCore region. No additional triggers are switched on. If one also activates the SMT-3 trigger, the sensitivity is raised again by factor of ∼ 2 − 3 in λcat , as depicted in figure 5.7. Comparing the 3 figures, it is evident that DeepCore has a high impact on the effective area and thus on the sensitivity. This stems mainly from the lower string spacing and additional high-QE DOMs. Inclusion of the SMT-3 trigger has a minor impact. With all standard triggers switched on, the border of the sensitive region (orange/yellow) extends up to around λcat = 20 cm for the lowest simulated velocities of β = 10−3 and up to around λcat = 100 cm for the highest velocities of β = 10−2 . For higher mean free paths,

58

5.3 The Effective Area

Effective Area (SLOP level) - SMT8/Cluster - No DeepCore Strings

1e+06 7e+05

103

102

1000

101

­

®

λcat [cm]

1e4

Aeff. [m2 ]

1e+05 6e+04

100 100

10-3

β

10-2

10

Figure 5.5: Averaged effective area on SLOP filter level without DeepCore strings. Only SMT8 and Cluster Trigger are activated.

59

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

103

Effective Area (SLOP level) - SMT8/Cluster

1e+06 7e+05

102

1000

101

­

®

λcat [cm]

1e4

Aeff. [m2 ]

1e+05 6e+04

100 100

10-3

β

10-2

10

Figure 5.6: Averaged effective area on SLOP filter level. Only SMT-8 and Cluster Trigger are activated.

60

5.3 The Effective Area

103

Effective Area (SLOP level) - SMT3/SMT8/Cluster

1e+06 7e+05

102

1000

101

­

®

λcat [cm]

1e4

Aeff. [m2 ]

1e+05 6e+04

100 100

10-3

β

10-2

10

Figure 5.7: Averaged effective area on SLOP filter level. All standard IC-79 triggers are activated (SMT-3/SMT-8/Cluster).

61

5 SENSITIVITY OF THE FULL DETECTOR (IC-86 CONFIGURATION)

the sensitivity drops off rapidly (blue to white). The disadvantage for low velocities can be compensated by a dedicated slow monopole trigger (see section 6.7).

62

CHAPTER VI Development of a Dedicated Trigger for Slow Magnetic Monopoles This chapter describes the design and development of a dedicated trigger for subrelativistic monopoles, which is the central aim of this thesis. It is in the following referenced to by the name “SlowMPTrigger”.

63

6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

6.1

Motivation and Goal

To summarize the results from chapter 5, standard triggers in combination with the SLOP filter are not sensitive for slow monopoles with mean free paths λcat ∼ 100 cm or higher. Additionally, for the lower mean free paths between 5 cm and 100 cm and especially for slow velocities around β = 10−3 standard triggers do not fire continuously. The monopole event is split up in isolated events that may pass the SLOP condition individually if they are long enough, but do do not cover the whole monopole signal. This is a possible drawback for any later analysis and evaluation of the signal. Thus, a reasonable goal is to develop a trigger that allows to record most of the monopole signature and is sensitive to lower cross sections while retaining high trigger efficiency. It has to be based on simple conditions because it is supposed to work in the online trigger process (see section 4.5.2). It should run as efficient as possible to save computing time.

6.2

Trigger Concept

Slow magnetic monopoles with high mean free paths on the order of λcat ∼ 100 cm or more will most probably fire isolated HLC pairs, if they fire at all (see appendix B). The concept of the SlowMPTrigger is to use isolated HLC pairs as fundamental units. Since the HLC pairs will be located near the true monopole track, they should be geometrically aligned along a line in space. Additionally, the times of their DomLaunches should be correlated, too. In the following, the trigger concept is presented in 4 steps: Step 1 At first, we consider a sample of HLC DomLaunch pairs. Each such pair has a position and a time associated with it. Initially, the idea was to take the geometrical center of gravity of the participating modules and the arithmetic mean of their launch times as those defining properties. It turns out though, it is much more convenient to take the position and time of the first hit within such a pair. This has reasons of compatibility with the Java DAQ system, further explained in chapter 7. The first step of the trigger is to store these pairs with their position and time in a list. This is conceptionally depicted in figure 6.1 a). Step 2 A possible monopole signal may be contaminated by muon HLC pairs. Since the muon moves within a few microseconds through the detector, the resulting muon HLC pairs will be very close in time. This is illustrated as the two orange pairs. To get rid of such muon HLC pairs, the trigger uses a first parameter called t_proximity. All pairs which have another pair in their temporal proximity, closer than the parameter

64

6.2 Trigger Concept

arbitrary y−axis

Schematic of the trigger procedure

HLC−pair time scale arbitrary x−axis

a)

b)

c)

d)

Figure 6.1: Schematic depiction of a sample of HLC pairs. Time and position are arbitrary. a) Two pairs (orange) are close in time and could possibly be due to a relativistic particle. b) The two pairs which are close in time got removed from the sample, because their time difference is smaller than t_proximity. c) All combinations of 3-tuples are formed where the time difference between two pairs is within the boundaries of the interval [t_min, t_max]. d) Second stage cuts on delta_d and rel_v remove two 3-tuples . The three remaining 3-tuples overlap in time. They form a trigger with length from the first to the last pair if min_tuples 100”. The idea here is to test how the trigger handles such very bright events with the parameter t_proximity. These have also been simulated with a rate of 200 Hz. This rate is not physically motivated though,

68

6.3 Simulations

Schematic of mixing muons with another event (noise / monopoles) time

long muon event

random position

pickout event (contains poissonianly distributed muons)

picked timewindow must have same length

target event (event to mix into)

1111 0000 0000 1111 I3MuonBgServiceFactory

Legend: single muons

11111 00000 00000 11111

how long is the desired timewindow?

output event (contains both

signal/noise

MCHitseriesMaps) 1111 0000 0000 1111 0000 1111

Figure 6.3: Schematic depiction of muon mixing. The Service I3MuonBGService picks out a time window at a random position with a length of the target event. It mixes the containing muon MCHitSeriesMap with the MCHitSeriesMap in the target event and puts the resulting MCHitseriesMap back into the frame.

69

6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

Monopole Events (can contain noise)

Modules: "SimpleHitInjector" / "NoiseSimulator"

Events containing pure noise (length 5 ms)

Modules: "UCR−Generator"/"MMC"

Cosmic ray events (mostly muons) sort out Events with a certain property (e.g. hit DeepCore, launch SMT3 etc.)

Module: MuonBgMerger merge muons into one event according to desired rate Service: MuonBgServiceFactory

Service: MuonBgServiceFactory

One event with uniformly distributed muons

pick out desired timewindow and mix MCHitSeries together Monopole Events

Noise events mixed

mixed with muons

with muons

Figure 6.4: Schematic depiction of background generation. Modules are colored blue, events and data are colored green. In addition, also illustrated is the application of the I3Service “MuonBgServiceFactory” to mix muons into signal events. The procedure works similar for both signal and background.

70

6.3 Simulations

since these muons are just thought to used for testing. The third muonic background that has been simulated are very low energetic muons that produce a SMT-2 condition, and will may thus not be removed by t_proximity. There is no measurement of the rate of muons that trigger an SMT-2. These are simulated with 400 Hz, since the SMT-2 is expected to be higher and 400 Hz seems to be a reasonable value. Additionally, pure noise is background, too. This means, 4 different backgrounds are used to study the trigger behavior. For simplification these will be referred to with abbreviations summarized in table 6.1.

Table 6.1: Abbreviations for different simulated backgrounds.

6.3.2

Background

Abbreviation

Noise Noise/200 Hz SMT-3 muons Noise/200 Hz SMT-3 muons (n-channel > 100) Noise/400 Hz muons, low energetic (at least SMT-2)

BG1 BG2 BG3 BG4

Simulation of Signal

Monopoles are generated isotropically as described in section 4.6.2. The considered parameter space extends from 10−2 and 10−3 for β and from 10 cm to 1000 cm for λcat . Each sample point is covered with 2000 monopoles. The generation disk radius is chosen to be 200 m which is appropriate to cover DeepCore. To demonstrate this, 2000 monopoles with β = 10−2 and λcat = 100 m have been generated on a disk with the radius 300 m and 2000 monopoles with the same properties on a disk with the radius 200 m. The SlowMPTrigger has been applied using standard “first stage” parameters (section 6.4.1) and the triggers were counted. The effective area of the monopoles evaluated to ∼ 61000 ± 2570 m2 for the 300 m disk and to ∼ 58900 ± 1380 m2 for the 200 m disk. Therefore, using 200 m indicates a slight underestimation. This is tolerable though, since one can be sure that 2000 monopoles provide enough statistics for high detector coverage, which is also desirable for the following trigger studies. PMT-Noise is mixed into the signal with NoiseGenerator and muons are mixed in at a rate of 200 Hz (SMT-3). This actually compares to BG2 in section 6.3.1 and the process of mixing works the same way as in the case of background simulation, see figure 6.4.

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

6.4 6.4.1

Optimization of the Trigger Parameters “First stage” Parameters

The trigger aims to be sensitive for monopoles which move with a typical velocity of β ∼ 10−3 . The limitations are set by experimental background and DAQ performance. Because the first three parameters are time based, it is useful to know transit times of prominent distances within the detector. An overview of the transit times for different monopole velocities of the four most prominent distances in DeepCore is given in table 6.2. Table 6.2: Transit times for different monopole velocities. Depicted are the four most prominent distances: 7 m (DeepCore DOM spacing), 17 m (IceCube DOM spacing), 75 m (DeepCore string spacing), 125 m (IceCube string spacing).

distance

β = 10−2

β = 10−3

β = 10−4

7m 17 m 75 m 125 m

∼ 2.33 µs ∼ 5.66 µs 25 µs ∼ 41.66 µs

∼ 23.3 µs ∼ 56.6 µs 250 µs ∼ 416.6 µs

∼ 233 µs ∼ 566 µs 2.5 ms ∼ 4.17 ms

To determine the first parameter t_proximity, one has to consider the transit time of a relativistic muon through DeepCore. The largest possible distance between two places in DeepCore is 460 m diagonally through the instrumented volume. The transit time results to ∼ 1.53 µs. Naively, this could be an appropriate value for t_proximity, since the muon will at maximum produce HLC pairs separated by that time. In reality, scattered light and afterpulses may extend the possible muon signal up to ∼ 5 − 20 µs. Looking at table 6.2, it is evident that for β ∼ 10−2 monopoles intra string DOM traversal times are of the same order of magnitude. A compromise between the rejection of muons and acceptance of a β = 10−2 monopole signal is t_proximity = 2.5 µs. Further analysis on real DAQ data reveals that 2.5 µs may even be too conservative since the trigger rate is barely affected by a higher t_proximity (see chapter 7). An obvious choice for t_min is 0. Then all remaining signal HLC pairs are included. Muon HLC pairs have already mostly been removed due to t_proximity. It may be desirable, though, to set this parameter to a fixed value greater than zero in order to enforce a minimum trigger length of 2 · t_min. For example, a value of t_min = 17 µs would ensure that the triggered event would be accepted by the SLOP filter (see section 5.2). Since this is not specifically needed t_min = 0 is used in this thesis. The choice of a value for t_max has implications for the slowest monopoles that may be triggered but also for the background trigger rate. From table 6.2, monopoles with

72

6.4 Optimization of the Trigger Parameters

β ∼ 10−3 still manage to hit two strings by 125 m apart in ∼ 416 µs. Thus, a value of t_max = 500 µs seems to be appropriate to catch such monopoles. A higher value of t_max yields several problems. First, the background rate increases with longer t_max. To give an example, for t_max = 500 µs the trigger rate for noise HLC hits is ∼ 25 Hz while for t_max = 1000 µs it reaches ∼ 56 Hz. Additionally, the event lengths get much longer. This is depicted in figure 6.5 which compares the event lengths for the cases t_max = 500 µs and t_max = 1000 µs, triggering on pure PMT-noise.

0.0020

trigger length distribution for different tmax tmax =500µs tmax =1000µs

normalized count

0.0015

0.0010

0.0005

0.00000

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 trigger length [µs]

Figure 6.5: Trigger lengths for different values of t_max applied on BG1 (noise). t_proximity = 2500 and t_min = 0. No cut on “Second Stage” has been applied. The histograms are normalized to 1.

Event lengths longer than 5 ms are a problem for background simulation, because the background is simulated in 5 ms windows (see section 6.3.1). Thus, t_max must be chosen wisely. For this thesis a t_max = 500 µs is used, which still offers sensitivity for β = 10−4 monopoles as long as they move along strings and produces no problems with the 5 ms

73

6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

time length of the simulated background windows. A value of t_max = 500 µs yields 150 m maximal HLC pair separation for a monopole of β = 10−3 . This means that two pairs further apart than 150 m, for example on two neighboring strings (125 m separation) with a certain height difference, would not take part in triggering. For pure signal this results in a lower rate compared to β = 10−2 monopoles, as can be seen in tables 6.5 and 6.6. It is desired that future trigger studies use a higher value of t_max to be conservative for velocities β = 10−3 and reach larger sensitivity for β < 10−3 .

6.4.2

“Second stage” Parameters

A trigger could already be formed with the “first stage” parameters, taking all overlapping 3-tuples and form a trigger window from the first to the last participating hit. Suitable second stage parameters reduce the background rate substantially though. For the optimization of the parameter choices, the distribution of the individual parameters is plotted for background and for two example monopole signals (β = 10−2 , λcat = 100 cm and β = 10−3 , λcat = 100 cm) for comparison. These example monopoles also contain noise and muons. The simulation is performed as described in section 6.3.

Cut 1 - Geometrical Cut: The first parameter delta_d is chosen to be 100 m. Figure 6.6 shows the distributions for background and for the two example signals. Reduction factors are defined such that, when multiplied with the total number of 3-tuples, the resulting value is the number of 3-tuples that pass the cut. The cut leads to a reduction of 3-tuples for the different cases. This is not to be mistaken with the signal and background trigger rate reduction which is different. Events, in particular signal events, contain several overlapping 3-tuples. A removed 3-tuple does not also necessarily remove a trigger. Depending, how many of 3-tuples within overlapping 3-tuples have a parameter value that fulfills the cut, the true trigger rate reduction can be lower or higher. To illustrate this, figure 6.7 shows the delta_d distributions if only the smallest value of delta_d among overlapping 3-tuples is histogrammed. This is also called “best” 3-tuple, since it has the smallest value of delta_d and resembles a line most closely. Reduction factors now resemble “true“ trigger reduction factors. The true reduction factors are slightly closer to 1 (true trigger reduction is smaller) for β = 10−2 monopoles and slightly smaller (true trigger reduction is higher) for β = 10−3 . As a crosscheck, one can compare these factors with the effective area ratios between level 0 and 1 in table 6.5 and 6.6 or the trigger rate ratios between level 0 and 1 in table 6.4. This comparison is not 100 % valid for effective areas though, since a monopole is detected when at least one trigger is fired. For β = 10−3 monopoles, it

74

6.4 Optimization of the Trigger Parameters

delta_d

distribution with applied cut β =10−2 ,λcat =100 cm β =10−3 ,λcat =100 cm

normalized count [1/m]

10-1 10-2

BG2 Cut: delta_d 100 m

10-3

β =10−2 ,λcat =100 cm - 0.89 β =10−3 ,λcat =100 cm - 0.90

3-tuple reduction factor: BG2 - 0.35

10-4 10-5 10-6 100

0

100

200

300 delta_d

[m]

400

500

600

700

Figure 6.6: delta_d distributions of the two example signals and background (BG2). The cut is applied at delta_d = 100 m and the corresponding reduction factors on the numbers of 3-tuples are given. The histograms are normalized to 1.

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

delta_d

distribution (best) with applied cut β =10−2 ,λcat =100 cm β =10−3 ,λcat =100 cm

normalized count [1/m]

10-1

BG2 Cut: delta_d 100 m

10-2

3-tuple (best) reduction factor: β =10−2 ,λcat =100 cm - 0.96 β =10−3 ,λcat =100 cm - 0.89 BG2 - 0.45

10-3 10-4 10-5 10-6 100

0

100

200

300 delta_d

[m]

400

500

600

700

Figure 6.7: Distributions of the smallest delta_d within overlapping 3-tuples for the two example signals and background (BG2). The cut is applied at delta_d = 100 m and the corresponding reduction factors on the numbers of tuples are given. The histograms are normalized to 1.

76

6.4 Optimization of the Trigger Parameters

happens occasionally that a second one is fired by the same monopole. This explains the slight discrepancy of trigger reduction factor 0.89 compared to hAeff. ilvl 1/hAeff. ilvl 0 = 0.90 for β = 10−3 . Figures D.1, D.2, D.3, D.4,D.5, D.6 in appendix D list shape comparisons of delta_d distributions for all 4 simulated backgrounds and for the two example signals, comparing the behavior for pure signal, signal with noise and signal with noise and muons. Cut 2 - Time Cut: The second parameter rel_v is chosen to be 0.5. Figure 6.8 shows the 3-tuple distribution for both example signals and background (BG2). It should be noted that at this point cut 1 has already been applied. At first sight this cut seems to be much less efficient compared to the delta_d cut.

rel_v

103

distribution with applied cut β =10−2 ,λcat =100 cm β =10−3 ,λcat =100 cm

102

BG2 Cut: rel_v 0.5

normalized count

101

3-tuple reduction factor:

β =10−−23 ,λcat =100 cm - 0.46 β =10 ,λcat =100 cm - 0.44

100

BG2 - 0.28

10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

rel_v

Figure 6.8: rel_v distribution for the two example signals and background (BG2). The cut is applied at rel_v = 0.5 and the corresponding reduction factors on the numbers of 3-tuples are given. The histograms are normalized to 1.

If only the best 3-tuples within overlapping 3-tuples are plotted though, one arrives

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

at figure 6.9. The reduction factors now are on the same order of magnitude as for the delta_d cut. In contrast to the case of delta_d, the reduction factor increases for both simulated velocities. Figures D.7, D.8, D.9, D.10, D.11, D.12 in D list shape comparisons of rel_v distributions for all 4 simulated backgrounds and for the two example signals, comparing the behavior for pure signal, signal with noise and signal with noise and muons.

rel_v

103

distribution (best) with applied cut β =10−2 ,λcat =100 cm β =10−3 ,λcat =100 cm

102

BG2 Cut: rel_v 0.5

normalized count

101

3-tuple −(best) reduction factor: β =10−32 ,λcat =100 cm - 0.79 β =10 ,λcat =100 cm - 0.85 BG2 - 0.35

100 10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

rel_v

Figure 6.9: Distributions of the smallest rel_v within overlapping 3-tuples for the two example signals and background (BG2). The cut is applied at rel_v = 0.5 and the corresponding reduction factors on the numbers of 3-tuples are given. The histograms are normalized to 1.

Cut 3 - Multiplicity Cut: Up to this point, a trigger contains several overlapping 3tuples and ranges from the first to the last HLC pair. If a 3-tuple does not overlap it forms its own trigger. Figure 6.10 shows the number of overlapping 3-tuples (num_tuples) for signal and background. min_tuples is chosen to be 2 so the cut is applied with

78

6.4 Optimization of the Trigger Parameters

num_tuples ≥ 2. It can be seen that this parameter reduces background very effectively. The reduction factor now correspond to the trigger reduction factor, since not single 3tuples are histogrammed but every entry corresponds to a group of overlapping 3-tuples. Figures D.13, D.14 and D.15 in appendix D list shape comparisons of num_tuples distributions for all 4 simulated backgrounds and for the two example signals, comparing the behavior for pure signal, signal with noise and signal with noise and muons.

num_tuples

100

distribution with applied cut β =10−2 ,λcat =100 cm β =10−3 ,λcat =100 cm

BG2 Cut: num_tuples ≥2

normalized count

10-1

trigger reduction factor: β =10−2 ,λcat =100 cm - 0.75 β =10−3 ,λcat =100 cm - 0.87 BG2 - 0.12

10-2

10-3

10-4

0

50

100

150

200

250

num_tuples

Figure 6.10: Distribution of the number of overlapping 3-tuples for background and two example signals.

Table 6.3 summarizes different trigger configurations. These trigger configurations are used to describe the trigger settings. Figure 6.11 summarizes reduction factors of the two example signals and different simulated backgrounds. The trigger efficiency for monopoles is summarized in section 6.6 for the different trigger levels. Estimated background rates are summarized in section 6.5.

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

relative trigger rate for signal and background

trigger rate relative to lvl 0

100

10-1

10-2

BG1 BG2 BG3 BG4

β =10−2 ,λcat =100 cm β =10−3 ,λcat =100 cm 10-3

level 0

level 1

level 2

level 3

Figure 6.11: Trigger reduction factors for different trigger levels normalized on level 0. The behavior is fairly similar for the different backgrounds. The same is true for simulated monopoles, even if their velocity differs by a factor of 10.

80

6.5 IC-86 Background Rates

Table 6.3: Trigger level definitions. Also included are the parameters used in the DAQ testrun (see section 7). Fields marked with a “-” are not constrained.

trigger level

t_proximity

t_min

t_max

delta_d (≤)

0 “DAQ test run” 1 2 3 4 5

2.5 µs 2.5 µs 2.5 µs 2.5 µs 2.5 µs 2.5 µs 2.5 µs

0 µs 0 µs 0 µs 0 µs 0 µs 0 µs 0 µs

500 µs 500 µs 500 µs 500 µs 500 µs 500 µs 500 µs

500 m 100 m 100 m 100 m 100 m 100 m

6.5

rel_v (≤) min_tuples 0.5 0.5 0.5 0.5

2 3 4

IC-86 Background Rates

This section frequently uses the abbreviations already described in table 6.1. The trigger rates at successive trigger levels are listed in table 6.4. Table 6.4: IC-86 background trigger rates (simulated)

trigger level 0 1 2 3 4 5

rate [Hz]

BG1

BG2

25.18 ± 0.50 11.32 ± 0.34 3.78 ± 0.19 0.49 ± 0.07 0.11 ± 0.03 -

28.33 ± 0.53 12.72 ± 0.36 4.45 ± 0.21 0.53 ± 0.07 0.12 ± 0.03 -

BG3

BG4

27.43 ± 0.52 12.80 ± 0.36 4.32 ± 0.21 0.43 ± 0.07 0.08 ± 0.03 -

32.03 ± 0.57 13.67 ± 0.37 4.82 ± 0.22 0.52 ± 0.07 0.21 ± 0.05 -

It is evident that at level 0 BG4 has the highest rate, as is expected from a 400 Hz muon rate in contrast to a 200 Hz rate. In addition, the fact that these muons may produce single HLC pairs contributes, too. The rate of BG3 is almost always smaller than for BG2, which is a confirmation that bright muons are filtered out more effectively than light-faint ones. Naively, one would expect the algorithm to produce the same rate for BG2 and BG3 since t_proximity should remove all HLC pairs from SMT-3 muons. Muons are mixed into noise or signal on MCHitseries level, though, which means they still have to be processed in PMT and DOMSimulator. Because PMTSimulator involves a stochastic process, a muon that initially fulfills the SMT-3 condition on MCHitSeries level, may not fulfill this condition anymore on DomLaunch level. This does not happen for BG3 because n_channel is forced to be greater than 100. At level 3, all rates seem to become fairly equal. At this point, low statistics become apparent and lead to relatively

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

large errors. The 100 seconds of background simulation is not sufficient. Level 5 is not listed because the statistics become too small.

6.6

Effective Areas on Trigger Level

The effective areas for the two signal examples are listed in table 6.5 and 6.6, comparing the cases of pure signal, signal with noise and signal with noise and muons. The effective area increases once noise and muons are included. Looking at pure signal, the first cut on delta_d leaves the sensitivity almost unaffected. Fast monopoles (table 6.5) have a higher effective area than slow monopoles (table 6.6) at this point because the parameter t_max in allows for all possible DOM distances within DeepCore to be used for β = 10−2 monopoles (see section 6.4.1) . The cut on rel_v decreases the effective area more for faster monopoles and the effective areas become similar within the error margin. The third cut leads to a higher effective area for the slow signal. When noise or noise/muons are mixed in, the slow monopoles have a higher effective area from the start since the event duration is much longer and noise induced 3-tuples have a higher chance to participate. Table 6.5: Effective areas (averaged over all solid angles) on different trigger levels for β = 0.01 and λcat = 100 cm. Compared is pure signal, signal/noise and signal/noise/muons. Quantities are rounded to multiples of 10.

trigger level 0 1 2 3

signal

hAeff i [m2 ] signal/noise signal/noise/muons

59190 ± 1400 64470 ± 1400 58060 ± 1400 61950 ± 1400 47060 ± 1360 50010 ± 1370 36380 ± 1270 38450 ± 1290

67610 ± 1400 64840 ± 1400 51400 ± 1380 38330 ± 1290

Table 6.6: Effective areas (averaged over all solid angles) on different trigger levels for β = 0.001 and λcat = 100 cm. Compared is pure signal with signal/noise and signal/noise/muons. Quantities are rounded to multiples of 10.

trigger level 0 1 2 3

signal

hAeff i [m2 ] signal/noise signal/noise/muons

54850 ± 1400 71630 ± 1390 54540 ± 1390 65970 ± 1400 47820 ± 1360 55920 ± 1390 41340 ± 1320 46870 ± 1360

70500 ± 1390 63710 ± 1400 54600 ± 1390 47560 ± 1360

Dividing the effective area by geometrical area of DeepCore (see section 5.3.2), allows to quantify the trigger efficiency. Note, that the values can also be greater than 1 since

82

6.7 Impact on IC-86 SLOP Effective Area

noise is included and the effective DomLaunch radius is increased for lower λcat (see appendix B). Figure 6.12 shows the trigger efficiency in the β, λcat phasespace at different trigger levels. All efficiencies are calculated for the case of signal mixed with noise and muons. To demonstrate that the trigger is independent on different monopole velocities, figure 6.13 shows trigger length distributions for different simulated monopole velocities. To demonstrate the anticipated behavior of the SlowMPTrigger, an event display C.1 in appendix C shows a monopole that triggers the SlowMPTrigger, independent if muons/noise are simulated or not.

6.7

Impact on IC-86 SLOP Effective Area

It is desirable to know the effect of the SlowMPTrigger on the effective area on SLOP filter level (see section 5.3.2). A reasonable parameter choice is trigger level 3, because it reduces the experimental background rate (see section 7) to around 1 Hz while retaining high trigger efficiency. The resulting effective area plot is depicted in figure 6.14. The effective area increases more than an order of magnitude for low velocities compared to figure 5.7. This sensitivity increase for low velocities emphasizes the different functionality of the SlowMPTrigger. Overall, the sensitivity is now fairly constant over β. High effective areas also extend to slower velocities than depicted in the figure, dropping off somewhere between β = 10−3 and β = 10−4 because of the limitations of t_max = 500 µs. Note, that noise and muons are not mixed into these signals. Thus the effective area is underestimated, as has been shown for the two example signals in tables 6.5 and 6.6. Using equations 3.11, 3.13 and table 3.1 one can approximate the theoretically predicted relationship between λcat and β in ice to be λcat =

β2 β2 ≈ · 10−22 cm3 β0 · σ 0 · n σ0

(6.3)

using n ≈ 6 · 1022 for the particle density of hydrogen nuclei. The formula is valid only for β < β0 = 0.175. Oxygen contributes much less since the Rubakov effect is suppressed and can be neglected. A certain parameter range for σ0 between 10−24 cm2 and 10−32 cm2 is suspected from theory (section 3.3). Figure 6.15 is the same as 6.14 but includes the relation between λcat and β for different σ0 . If compared to figure 5.7, it is evident that monopoles for parameters σ0 = 10−30 cm2 and σ0 = 10−31 cm2 become detectable.

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

Trigger Efficiency - SlowMPTrigger level 0

Trigger Efficiency - SlowMPTrigger level 1

2.5

103

Aeff. /(6 ∗ 105 m2 )

®

1e-01

­

®

1e-01

102

­

102

λcat [cm]

1

Aeff. /(6 ∗ 105 m2 )

1

λcat [cm]

2.5

103

101

101 10-3

β

10-2

1e-02

10-3

(a) Level 0

β

10-2

(b) Level 1

Trigger Efficiency - SlowMPTrigger level 2

Trigger Efficiency - SlowMPTrigger level 3

2.5

103

2.5

103

Aeff. /(6 ∗ 105 m2 )

®

1e-01

­

®

1e-01

102

101

­

102

λcat [cm]

1

Aeff. /(6 ∗ 105 m2 )

1

λcat [cm]

1e-02

101 10-3

β

(c) Level 2

10-2

1e-02

10-3

β

10-2

1e-02

(d) Level 3

Figure 6.12: Trigger efficiency for trigger levels 0-3. Noise and muons are included in the signal.

84

6.7 Impact on IC-86 SLOP Effective Area

10-1

normalized count [1/µs]

10-2

trigger length distributions for different monopole velocities β =10−2 ,λcat =100 cm β =10−2.2 ,λcat =100 cm β =10−2.6 ,λcat =100 cm β =10−3 ,λcat =100 cm

10-3

10-4

10-5

0

500

1000 1500 trigger length [µs]

2000

2500

Figure 6.13: Plot showing trigger length distributions for different monopole velocities on trigger level 3. It is evident that the trigger lengths are variable and adapt to the simulated monopole velocity.

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6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

Effective Area (SLOP level) - SMT3/SMT8/Cluster+SlowMPTrig(lvl 3)

1e+06 7e+05

103

102

1000

101

­

®

λcat [cm]

1e4

Aeff. [m2 ]

1e+05 6e+04

100 100

10-3

β

10-2

10

Figure 6.14: Averaged effective area on SLOP filter level. Noise and muons are not simulated. All standard IC-79 triggers are active (SMT3/SMT8/Cluster) and additionally the SlowMPTrigger is run on level 3.

86

6.7 Impact on IC-86 SLOP Effective Area

Effective Area (SLOP level) - SMT3/SMT8/Cluster+SlowMPTrig(lvl 3) −28

cm2

σ_0 =10 σ_0 =10−29 cm2 σ_0 =10−30 cm2 σ_0 =10−31 cm2

102

1e+06 7e+05 1e+05 6e+04

λcat [cm]

1e4 1000

101

Effective Area [m2 ]

103

100 100

10-3

β

10-2

10

Figure 6.15: Averaged effective area on SLOP filter level. Noise and muons are not simulated. All standard IC-79 triggers are active (SMT3/SMT8/Cluster) and additionally the SlowMPTrigger is run on level 3. The Rubakov equation is plotted for several choices of σ0 .

87

6 DEVELOPMENT OF A DEDICATED TRIGGER FOR SLOW MAGNETIC MONOPOLES

88

CHAPTER VII DAQ SlowMPTrigger Testrun To test the trigger algorithm with the real detector, the I3Module “SlowMPTrigger” was ported to a Java version for the DAQ system. Several test runs were conducted on the SPTS (section 4.5.1) to make sure the module works as intended. Several differences between the IceTray system and the DAQ system became apparent during this process. A minor difference was that the time and location of a single HLC pair have to be taken as the true location and time of one participating DOM and not the center of gravity of the two DOMs. This had to be done because predefined tables are used for fast distance calculation of the ∆xab (section 6.2) which only works for true DOM positions. Additionally, the time of a pair can also not be defined as the average because trigger formation requires individual DOM hit times. This new definition of time and location of a HLC pair was adapted to the I3Module. As a second challenge, the I3Module had been written with an algorithm that has direct access to all HLC pairs that are simulated. On the contrary, the DAQ version required to be written with an algorithm that gets single HLC DomLaunches one by one in a time ordered stream (section 4.5.2). The results presented later in this chapter indicate, though, that although the algorithms work differently in this respect, their outcome is very similar and the porting process has been a success. Nonetheless, it may be desirable to rewrite the I3Module to mimic the structure of the DAQ algorithm.

89

7 DAQ SLOWMPTRIGGER TESTRUN

7.1

Results

The 30 minute test run was conducted on August 12, 2010 at 7 p.m. CDT at the SPS (South Pole System) using the “DAQ test run” settings listed in table 6.3. Additionally to the SlowMPTrigger the SMT-8 was activated, too. No compatibility problems occurred and the run was stable. Figure 7.1 shows the number of SMT-8 triggers per SlowMPTriggered event. It is strictly valid only for trigger levels 0-2 but should also be a good approximation for trigger level 3, since trigger lengths are expected to increase only marginally with the requirement min_tuples = 2. In most cases, zero to two SMT8 trigger fall into the window of the SlowMPTrigger. An event display of the longest event (∼ 3.2 ms) that was triggered is illustrated in figure C.3 in appendix C. 80122

100

distribution of the number of SMT-8 trigger per event DAQ test run level

10-1

normalized count

10-2 10-3 10-4 10-5 10-6 10-7 1

0

1

2

3 4 5 6 7 8 no. of SMT-8 trigger per event

9

10 11 12

Figure 7.1: Number of SMT-8 triggers per SlowMpTrigger.

SlowMPTriggered events were collected and transferred north. This results in a trigger rate of about 44.512 Hz. If compared to the expected background rates listed in table 7.1, it is apparent that the experimental rate is about 2.6 times higher than expected for BG2

90

7.2 Investigations on the Data

and about 2.3 times higher than expected for BG4. The increased rate can in principle Table 7.1: IC-79 background trigger rates (simulated)

trigger level

BG1

0 14.40 ± 0.38 “DAQ test run settings” 14.30 ± 0.38 1 5.52 ± 0.23 2 1.87 ± 0.14 3 0.19 ± 0.04

BG2

rate [Hz]

16.78 ± 0.41 16.60 ± 0.41 6.24 ± 0.25 2.21 ± 0.15 0.21 ± 0.05

BG3

BG4

15.76 ± 0.40 15.64 ± 0.40 6.21 ± 0.25 2.08 ± 0.15 0.17 ± 0.04

19.31 ± 0.44 19.02 ± 0.44 7.02 ± 0.26 2.56 ± 0.16 0.21 ± 0.05

be caused by three phenomena: 1. The ported Java version works different than the I3Module IceTray version. 2. Simulation underestimates the background 3. A combination of both. As it turns out, the first point can be ruled out. The collected events were retriggered with the I3Module using the same trigger configuration. If porting had been the problem, the retriggered event rate should also be lower by a factor of around 2. The event count was 80085 after retriggering which corresponds to a rate of about 44.492 Hz. This means in more than 99.9 % of the cases the I3Module also finds a trigger. It could still be that it occasionally finds a trigger but with a shorter event length and thus another n-channel count. To show that this is not the case, figures 7.2 and 7.3 show trigger length and n-channel distributions for the testrun data and the retriggered data. Also depicted are the expected distributions from simulated background. The retriggered distributions overlap almost perfectly with the experimental ones. Thus, point 1 can be excluded and the porting process is verified to be successful. The simulated distribution for the event length looks fairly similar with slight shape differences for trigger lengths greater than one millisecond. On the other hand the simulated n-channel distributions indicate a systematic shift towards lower n-channel. This is further evidence that point 2 is the case. Background is systematically underestimated.

7.2

Investigations on the Data

Since the porting of the trigger was successfull, retriggering with the I3Module with different trigger settings can be used to study the systematic discrepancy between the

91

7 DAQ SLOWMPTRIGGER TESTRUN

normalized count [1/µs]

comparison of trigger length distributions (simulation with old NoiseGen) 10-2 test run test run - retriggered simulation - BG 10-3 simulation - BG4 10-4 10-5 10-6 10-7

0

500

1000

1500 2000 trigger length [µs]

2500

3000

3500

Figure 7.2: Trigger length distributions for experimental data, retriggered data and simulated data.

92

7.2 Investigations on the Data

normalized count

comparison of n-channel distributions (simulation with old NoiseGen) test run test run - retriggered simulation - BG 10-2 simulation - BG4

10-3

10-4 0

100

200 300 400 n-channel (SLC+HLC)

500

600

Figure 7.3: n-channel distributions for experimental data, retriggered data and simulated data.

93

7 DAQ SLOWMPTRIGGER TESTRUN

simulated and experimentally determined rate. Table 7.2 lists trigger rates of experimental data for different trigger levels. An excess of the trigger rate is visible at all trigger levels, if compared to table 7.1. Table 7.2: IC-79 test run trigger rates (retriggered)

trigger level

rate [Hz]

“DAQ test run settings” 44.49 ± 0.16 1 20.97 ± 0.11 2 7.513 ± 0.065 3 1.130 ± 0.025 4 0.3083 ± 0.0131 5 0.1061 ± 0.0077 Two possible contributions to this systematic shift will be briefly investigated in the following: Muons Muons may not get filtered out as expected by the parameter t_proximity. To exclude this, the trigger was run at level 0 settings, with the exception of t_proximity which was set to 20 µs. This eliminates all HLC pairs that have another one 20 µs apart which should prevent muonic signal to be used in trigger formation. The trigger rate drops to 38.36 ± 0.15 Hz which is not enough to explain the discrepancy, though. This indicates that the parameter is working and SMT-3 muons are not the cause for the high rate. Not considered by this test are muons that only touch DeepCore and leave a single HLC pair (see figure C.2 in appendix C) or very low energetic muons. The simulated background BG4, which is intended to simulate such events, is based on an estimation and may not resemble these cases good enough. Noise A bug in NoiseGenerator leads to a constant underestimation of the simulated noise rate per DOM of about 15 %. It turns out that this underestimation had big implications for the trigger rate. Table 7.3 summarizes the trigger rates using the fixed NoiseGenerator. A rate of about 33 − 38 Hz is much closer to the true trigger rate than previous results of about 14 − 19 Hz. The new trigger length and n-channel distributions after the fix are depicted in figures 7.4 and 7.5. In comparison to figure 7.2, the trigger length distributions change marginally. A bigger difference can be seen between the n-channel distributions. The distributions which contain the NoiseGenerator bugfix change in favor of higher n-channel values, thus, the overall shape fits better to the experimental distribution.

94

7.2 Investigations on the Data

normalized count [1/µs]

comparison of trigger length distributions (simulation with fixed NoiseGen) 10-2 test run simulation (fixed NoiseGen) - BG simulation (fixed NoiseGen) - BG4 10-3 10-4 10-5 10-6 10-7

0

500

1000

1500 2000 trigger length [µs]

2500

3000

3500

Figure 7.4: Trigger lengths for experimental data, retriggered data and simulated data. Noise is simulated with the fixed NoiseGenerator.

95

7 DAQ SLOWMPTRIGGER TESTRUN

normalized count

comparison of n-channel distributions (simulation with fixed NoiseGen) test run simulation (fixed NoiseGen) - BG simulation (fixed NoiseGen) - BG4 10-2

10-3

10-4 0

100

200 300 400 n-channel (SLC+HLC)

500

600

Figure 7.5: n-channel distributions for experimental data, retriggered data and simulated data. Noise is simulated with the fixed NoiseGenerator.

96

7.2 Investigations on the Data

Table 7.3: IC-79 background trigger rates (simulated) - with NoiseGenerator fix. Only BG1 and BG4 have been simulated. Fields marked with a “-“ were not simulated.

trigger level

BG1

“DAQ test run settings” 32.55 ± 0.57 1 12.92 ± 0.36 2 4.49 ± 0.21 3 0.39 ± 0.06

rate [Hz] BG2 BG3 -

-

BG4 38.15 ± 0.62 15.64 ± 0.40 5.37 ± 0.23 0.65 ± 0.08

Nontheless, perfect agreement is not yet reached. It is evident that noise alone can not account for the systematic underestimation. Other sources contribute, too (see appendix A). Further investigations are needed, especially for a correct simulation of low energetic muons. In addition to the discrepancy of the trigger rate, a feature in the experimental delta_d distribution of 3-tuples is not understood. Figure 7.6 shows shape comparisons of the delta_d distributions of experimental data and simulated background (BG1) for IC-79. Other backgrounds are expected to have similar shape as BG1 as seen from IC-86 comparisons (see figure D.1 in appendix D). The distribution for experimental delta_d shows several spiky excesses for small values, especially for delta_d = 0, which are not yet understood. Muons can be excluded, since the excess remains visible for retriggered data with t_proximity = 20 µs. The corrected version of NoiseGenerator has no influence on the shape of the simulated distribution.

97

7 DAQ SLOWMPTRIGGER TESTRUN

delta_d

normalized count [1/m]

10-2

distributions - test run retriggered and BG1 (IC-79) test run (retriggered) BG1 (fixed NoiseGen) BG1 (old NoiseGen)

10-3

10-4 100

0

100

200 delta_d

300 [m]

400

500

600

Figure 7.6: delta_d distributions for experimental data (retriggered) and simulated background for IC-79 (BG1). An excess is visible for small delta_d.

98

CHAPTER VIII Conclusion Within this thesis the detection capabailities of subrelativistic monopoles with IceCube have been investigated. The results indicate that the full potential of IceCube has not yet been tapped in this respect. Monopole analysis with the standard detector configuration for IC-79 and IC-86 depends on the SLOP filter. The IC-86 configuration is sensitive to monopoles with mean free paths of the nucleon catalysis up to around λcat = 100 cm for high velocities (β = 10−2 ) and up to around λcat = 20 cm for low velocities (β = 10−3 ) on SLOP filter level. Typically, filtered events only contain a small fraction of the monopole signature. A dedicated trigger for subrelativistic monopoles has been developed, which operates on all DOMs of the DeepCore subdetector. It is sensitive to isolated DomLaunch pairs that have a geometrical and temporal relation to each other, which is the expected signature of a subrelativistic monopole. Integration into the standard trigger configuration yields a rise in sensitivity up to several 100 cm mean free path over the whole velocitiy range on SLOP filter level. A strong improvement is particularly visible for low velocities. The trigger adapts to different monopole velocities and resulting events contain a large fraction of the monopole signature. Muons above a certain energy are succesfully excluded from trigger formation. The trigger is steered by 6 parameters which were chosen to be as simple as possible which is appropriate to work as a low level decision tool at the South Pole. The trigger has been ported to a Java DAQ version and a 30 minute test run has succesfully taken data wich could be analyzed. The resulting trigger rate is about 20 % − 40 % too high in comparison to simulated data. It could be shown, that the discrepancy stems from background simulation, possibly from low energetic muons that have not been simulated accurately or from other unknown systematic effects. Further investigations are needed in this respect. Tests at the South Pole Test System at the University of Wisconsin, Madison, indicate that the algorithm is capable of handling a much higher DomLaunch rate. This suggests the trigger could also be applied to run on the whole IceCube detector instead of DeepCore only. Furthermore, the trigger is generally sensitive to any slowly moving signal within the detector, widening the possibilities of application to other exotic particles like Q-Balls or Nucleorites.

99

8 CONCLUSION

100

APPENDIX A Systematic Effects Systematic effects can occur anywhere in the simulation chain. Effects which appear early may also counterbalance systematics which appear later. At the end, results presented in this thesis depend mostly on these systematics rather than on statistical fluctuations. Since no study of systematics has been done for each step individually, the important steps at which such effects can occur are listed in the following: • Monopole simulation: Nucleon decay signatures from the Rubakov effect are not firmly established. The presented branching ratios for the nucleon decays are estimated to within an order of magnitude (see section 3.3). Currently, nucleon decays are simulated in a simplified manner by inserting 940 MeV positrons at the decay positions with random directions. This mimics the signature of an electromagnetic cascade quite well, but it implies that all decays have a purely electromagnetic part which may be too optimistic. • Cosmic ray simulation: For this thesis muons with different rates and different energies were simulated for testing purposes of the Slow Monopole trigger (see section dΦ ∝ E −α , with α ∼ 2.7) was 6.3.1). The known cosmic ray energy spectrum ( dE not used, also for reasons of simplification. Further investigations are needed here, which is also indicated by the results from the test run (see section 7). • Noise simulation: NoiseGenerator had a bug which could be identified during the last stages of this thesis. It lead to a systematic underestimation of noise and the resulting trigger rate (see section 7). • Ice model and photon propagation: One of the first steps in the simulation chain involves propagation of Cherenkov photons through the ice. Recent studies indicate that the ice properties are not in good agreement with the model used in this thesis (the AHA-2 ice model, see section 4.3.3). Especially in the depth of DeepCore, which is located below the dust layer, the ice properties are not well known. This in turn, is the region where the Slow Monopole trigger is active. • Trigger simulation: Bugs in the trigger simulation can lead to wrong sensitivity estimates. Over the course of this thesis several discrepancies between trigger modules in IceTray and their corresponding DAQ modules have been identified and fixed. To give an example, the Cluster trigger which originally was thought to be highly

101

A SYSTEMATIC EFFECTS

sensitive to magnetic monopoles turned out to be not sensitive after the algorithm of the I3Module was adapted to the correct DAQ structure.

102

APPENDIX B Effective Detection Radius of a Magnetic Monopole When a monopole traverses IceCube, Cherenkov emissions along the track engulf the monopole with a certain effective detection radius. The idea is schematically depicted in figure B.1. A monopole approaches a DOM. As it gets closer, there is a point at which it fires the first DomLaunch. The exact distance varies statistically among different monopoles. The effective radius is defined as the distance at which the first DomLaunch has happened in 50 % of the cases, thus with 50 % probability. Monte Carlo simulations were carried out to determine this quantity. Monopoles covering the parameter space for λcat in the interval [0.1 cm, 1000 cm] and for β in the interval [10−2 , 10−3 ] were simulated along a track approaching horizontally towards a standard DOM and passing directly through it. The entire simulation only considers this single DOM, all others are switched off. Since the propagation speed of photons is much faster than the monopole movement, it is expected that the DomLaunch probability does not depend on the velocity of the monopole. Figure B.2 demonstrates that this is the case. At each sample point in the parameter space the distance at which first DomLaunch occurs is plotted, averaged over 10 monopoles each. As can be seen, it is fairly constant over β, but increases with lower λcat . Because the behavior is independent of β, all entries for a particular λcat can be filled into a histogram. The resulting distribution represents the probability distribution for the distance of the first DomLaunch. An example for λcat = 1 cm is depicted in figure B.3. The median is also plotted, which represents the effective detection radius. Starting from infinity, one could also integrate the probability density up to another value, 0.9, for example. The resulting distance would be smaller but the first DomLaunch should have fired with 90 % probability by then. Figure B.4 shows the behavior for different λcat . A linear fit in log10 (x) is used to describe the dependency of the effective detection radius (= median) on λcat . The resulting parameters are a = −65.08 ± 2.18 and b = 145.69 ± 2.77 assuming an error of half a bin width on each median which is a reasonable guess. Generally, the fitting function has the form deff.

radius

= a(θ) · log10

λcat cm

!

+ b(θ)

(B.1)

which now also includes the angle θ, which is the zenith angle of the monopole direction. The previous examples assume that the monopole comes from θ = 90◦ . In case it comes

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B EFFECTIVE DETECTION RADIUS OF A MAGNETIC MONOPOLE

monopole momentum effective detection radius

monopole DOM

a) Cherenkov photons

b) DomLaunch probability increases

c)

d)

DomLaunch probability decreases

e)

Figure B.1: Schematic of a the effective monopole detection radius. a) The DOM is still out of reach from the Cherenkov photons. b) The DOM is at the effective detection radius. A DomLaunch has happend with 50 % probability at this point. c) The proability for the DOM to launch increases as it gets closer. d) The probability of the DOM to launch decreases as it gets further away. e) The DOM leaves the effective detection radius. Assuming a symmetric situation, the probability that another DomLaunch happens from this moment onwards is 50 %.

104

103

horizontal track through a DOM 225

λcat [cm]

distance at first domlaunch [m]

200

102

175 150

101

125 100

100

75 50 25

10-1

10-3

β

10-2

Figure B.2: Distance at which the first DomLaunch happens. Each sample point is an average of 10 monopoles. The 3 white dots are bad simulation data. At higher values of λcat statistics get too low to take a reasonable mean, because in some occasions the DOM does not fire before the monopole travels by.

probability distribution for first DomLaunch - λcat =1 cm - 160 entries median

0.014

normalized count [1/m]

0.012 0.010 0.008 0.006 0.004 0.002 0.00050

100

150 200 distance at first DomLaunch [m]

250

300

Figure B.3: Example probability distribution for λcat = 1 cm. At a distance of about 80 m all 160 approaching monopoles have at least one DomLaunch. A few have their first DomLaunch already at a distance of around 250 m

105

B EFFECTIVE DETECTION RADIUS OF A MAGNETIC MONOPOLE

500

distance of first DomLaunch in dependence of λcat for a horizontal track median fit fit stats: a = -65.08 ± 2.18 b = 145.69 ± 2.77 2 = 0.31 χndf

400

300 probability density

distance at first DomLaunch [m]

1e-02

200

100 1e-03

0

10-1

100

λcat[cm]

101

102

Figure B.4: Probability distributions for all simulated mean free paths λcat . A linear fit in log10 (λcat ) through the medians of the different distributions demonstrates that the dependency on λcat can be described via equation B.1.

106

vertically from above or below or from any other zenith angle this yields a slightly different “effective radius” because of the non-isotropic photon acceptance of the DOMs. For this study this was not investigated. It should also be remarked that it is strictly only valid for monopoles which pass right through a DOM because the monopoles were simulated that way. Nontheless, it is still useful as an estimate for the effective detection radius for arbitrary paths through the detector.

107

B EFFECTIVE DETECTION RADIUS OF A MAGNETIC MONOPOLE

108

APPENDIX C Event Displays

109

C EVENT DISPLAYS

Figure C.1: Event display of a simulated monopole with λcat = 100 cm and β = 10−3 . Time is color coded (red is early, blue is late). The monopole path is rendered as a line. a) Raw DomLaunch information of pure signal. b) Triggered event with a length of 494 µs for pure signal. c) Triggered event with the same length for signal/noise/muons. A passing muon is rendered as a second line. The trigger formation is not influenced by the muon or by noise in this case.

110

Figure C.2: Event display of a triggered event from the 30 minute test run. Time is color coded (red is early, blue is late). The trigger length is about 1.15 ms. This event is in particular interesting because one HLC pair that takes part in trigger formation stems from a muon that hits the edge of the detector (marked with a white circle). The other pairs are noise hits. Events of this type are a motivation to include background simulation BG4 (section 6.3.1).

111

C EVENT DISPLAYS

Figure C.3: Event display of a triggered event from the 30 minute test run. Time is color coded (red is early, blue is late). The trigger length is about 3.2 ms, which makes it the longest event recorded during the full run. SLC noise hits dominate at such long event lengths. HLC information reveals that a few low energetic muons passed through the detector during readout. The SMT-8 trigger count is eight. Standard events mostly contain zero to two SMT-8 triggers (see figure 7.1).

112

APPENDIX D Parameter Distributions for Different Signal/Background Mixtures This appendix provides supplementary information to chapter 5. It compares the parameter distributions for different backgrounds (table 6.1) and also for signal/background mixtures. Short descriptions are given in the figure captions.

113

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

delta_d

distribution for different backgrounds BG1 BG2 BG3 BG4

normalized count [1/m]

10-1 10-2 10-3 10-4 10-5 10-6 100

0

100

200

300 delta_d

400 [m]

500

600

700

800

Figure D.1: delta_d distributions (all 3-tuples) for different simulated backgrounds (at trigger level 0). The shape looks fairly similar in all cases.

114

delta_d

normalized count [1/m]

10-1 10-2

distribution (best) for different backgrounds BG1 BG2 BG3 BG4

10-3 10-4 10-5 10-6 100

0

100

200

300 delta_d

400 [m]

500

600

700

800

Figure D.2: Distributions of the smallest delta_d within overlapping 3-tuples for different simulated backgrounds (at trigger level 0). The overall shape of the background distributions does not change much in comparison to the case where all 3-tuples are plotted (figure D.1). This is different for signal distributions (see figures D.3 and D.4 for the case of β = 10−2 , figures D.5 and D.6 for the case of β = 10−3 ).

115

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

delta_d

normalized count [1/m]

10-1

distribution for β =10−2 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-2 10-3 10-4 10-5 10-6 100

0

100

200

300 delta_d

[m]

400

500

600

700

Figure D.3: delta_d distributions (all 3-tuples) for monopoles with λcat = 100 cm and β = 10−2 comparing pure signal, signal with noise and signal with noise and muons (at trigger level 0). The distribution for pure signal is slightly sharper for smaller values of delta_d than the other two distributions.

116

delta_d

normalized count [1/m]

10-1

distribution (best) for β =10−2 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-2 10-3 10-4 10-5 10-6 100

0

100

200

300 delta_d

[m]

400

500

600

700

Figure D.4: Distributions of the smallest delta_d within overlapping 3-tuples for pure signal, signal with noise and signal with noise and muons (at trigger level 0). The simulated monopoles have a mean free path λcat = 100 cm and a velocity β = 10−2 . Compared to figure D.3, the difference between the signal and two background distributions becomes slightly smaller.

117

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

delta_d

normalized count [1/m]

10-1

distribution for β =10−3 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-2 10-3 10-4 10-5 10-6 100

0

100

200

300 delta_d

[m]

400

500

600

700

Figure D.5: delta_d distributions (all 3-tuples) for monopoles with λcat = 100 cm and β = 10−3 comparing pure signal, signal with noise and signal with noise and muons (at trigger level 0). The distribution for pure signal is slightly sharper for smaller values of delta_d than the other two distributions. The separation of the distributions is substantially larger than for higher monopole velocities (figure D.3) because for longer traversal times background 3-tuples have a higher chance to contribute.

118

delta_d

normalized count [1/m]

10-1

distribution (best) for β =10−3 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-2 10-3 10-4 10-5 10-6 100

0

100

200 delta_d

300 [m]

400

500

600

Figure D.6: Distributions of the smallest delta_d within overlapping 3-tuples for pure signal, signal with noise and signal with noise and muons (at trigger level 0). The simulated monopoles have a mean free path λcat = 100 cm and a velocity β = 10−3 . The difference between the distributions does not change substantially in comparison to D.5.

119

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

rel_v

101

distribution for different backgrounds BG1 BG2 BG3 BG4

normalized count

100 10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

rel_v

Figure D.7: rel_v distributions for different simulated backgrounds (at trigger level 1). The shape looks fairly similar in all cases.

120

101

rel_v

distribution (best) for different backgrounds BG1 BG2 BG3 BG4

normalized count

100 10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

rel_v

Figure D.8: Distributions of the smallest rel_v (best rel_v) within overlapping 3-tuples for different simulated backgrounds (at trigger level 1). The overall shape of the background distributions does not change much in comparison to the case where all 3-tuples are plotted (figure D.1). This is different for signal distributions (see figures D.9 and D.10 for the case of β = 10−2 , figures D.11 and D.12 for the case of β = 10−3 ).

121

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

rel_v

101

normalized count

100

distribution for β =10−2 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

rel_v

Figure D.9: rel_v distributions (all 3-tuples) for monopoles with λcat = 100 cm and β = 10−2 comparing pure signal, signal with noise and signal with noise and muons (at trigger level 1). The distributions look fairly similar in all cases.

122

101

rel_v

normalized count [1/m]

100

distribution (best) for β =10−2 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5 2.0 [m]

2.5

3.0

3.5

rel_v

Figure D.10: Distributions for the smallest rel_v within overlapping 3-tuples for pure signal, signal with noise and signal with noise and muons (at trigger level 1). The simulated monopoles have a mean free path λcat = 100 cm and a velocity β = 10−2 . Compared to figure D.9, the overall shape of the distributions changes in favor of smaller values.

123

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

rel_v

101

normalized count

100

distribution for β =10−3 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

rel_v

Figure D.11: rel_v distributions (all 3-tuples) for monopoles with λcat = 100 cm and β = 10−3 comparing pure signal, signal with noise and signal with noise and muons (at trigger level 1). The distributions look fairly similar in all cases, although the distribution for pure signal drops off a little earlier. This is a similar behavior to the case of delta_d (figure D.5) and happens because background 3-tuples have a higher chance to contribute for long traversal times. Faster monopoles do not show this separation (figure D.9).

124

101

rel_v

normalized count [1/m]

100

distribution (best) for β =10−3 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

10-1 10-2 10-3 10-4 0.5

0.0

0.5

1.0

1.5 2.0 [m]

2.5

3.0

3.5

rel_v

Figure D.12: Distributions for the smallest rel_v within overlapping 3-tuples for pure signal, signal with noise and signal with noise and muons (at trigger level 1). The simulated monopoles have a mean free path λcat = 100 cm and a velocity β = 10−3 . Compared to figure D.11, the overall shape of the distributions changes in favor of smaller values.

125

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

100

num_tuples

distribution for different backgrounds BG1 BG2 BG3 BG4

normalized count

10-1

10-2

10-3

10-4 0

1

2

3

4

5

6

7

8

num_tuples

Figure D.13: Distributions of the number of overlapping 3-tuples for different backgrounds (at trigger level 2).

126

num_tuples

100

distribution for β =10−2 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

normalized count

10-1

10-2

10-3

10-4

0

50

100

150

200

250

num_tuples

Figure D.14: Distributions of the number of overlapping 3-tuples for monopoles with λcat = 100 cm and β = 10−2 comparing pure signal, signal with noise and signal with noise and muons (at trigger level 2). The shapes of the distributions look fairly similar and extend up to values of around 100 overlapping 3-tuples, which is clearly distinguishable from background (figure D.13).

127

D PARAMETER DISTRIBUTIONS FOR DIFFERENT SIGNAL/BACKGROUND MIXTURES

num_tuples

100

distribution for β =10−3 ,λcat =100 cm Signal Signal/Noise Signal/Noise/Muons

normalized count

10-1

10-2

10-3

10-4

0

50

100

150

200

250

num_tuples

Figure D.15: Distributions of the number of overlapping 3-tuples for monopoles with λcat = 100 cm and β = 10−3 comparing pure signal, signal with noise and signal with noise and muons (at trigger level 2). The shapes of the distributions look fairly similar and extend up to values of a few 100 overlapping 3-tuples, which is clearly distinguishable from background (figure D.13) and also more than for faster monopoles (figure D.14).

128

Acknowledgements First, I want to thank Prof. Dr. Christopher Wiebusch for the possibility to join the IceCube group in Aachen and write about this highly interesting topic. He always had time for questions and discussions in his (very tight) schedule and without his guidance this work could have never been done. Secondly, I like to thank Prof. Dr. Stefan Schael who agreed to review the thesis as a second referee. Many thanks go to Dr. Mohamed Lotfi Benabderrahmane who introduced me to the topic and provided great collaboration throughout the year. Furthermore, I want to thank Alex Olivas and the whole simulation group for many useful discussions and tips. I want to thank Sebastian Böser, Erik Blaufuss, Kael Hanson and especially Dave Glowacki for the success of the trigger test run. Without the introduction from Dave to the SPTS this would not have been possible. The one year within the IceCube Aachen group was great and time went by fast. It was a great time in the “Tanzsaal” with all people that took part. Although the room was crowded, it was always a nice working atmosphere. Especially, I want to thank Markus Vehring for introducing the Rubiks Cube Mania and Jan Blumenthal for his competitive spirit in this regard. Special thanks go to Anne Schukraft and Sebastian Euler who provided useful criticism to the thesis’ chapters and to Marius Wallraff and Thomas Krings who provided the LaTeX template for this work. Finally, I want to express my gratitude to my family who always supported me throughout the year!

I

II

Erklärung Hiermit erkläre ich, dass ich die vorliegende Arbeit selbständig verfasst und keine anderen als die angegebenen Quellen und Hilfsmittel verwendet habe.

Aachen, den 02. Oktober 2010

Declaration I hereby certify that this document has been composed by myself, and describes my own work, unless otherwise acknowledged in the text.

Aachen, October the 2nd , 2010

III

IV

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