ABSTRACT
Title of dissertation: AN ALL-SKY, THREE-FLAVOR SEARCH
FOR NEUTRINOS FROM GAMMA-RAY BURSTS
WITH THE ICECUBE NEUTRINO OBSERVATORY
Robert E. Hellauer III, Doctor of Philosophy, 2015
Dissertation directed by: Professor Gregory Sullivan
Department of Physics
Ultra high energy cosmic rays (UHECRs), defined by energy greater than 1018
eV, have been observed for decades, but their sources remain unknown. Protons
and heavy ions, which comprise cosmic rays, interact with galactic and intergalactic
magnetic fields and, consequently, do not point back to their sources upon mea-
surement. Neutrinos, which are inevitably produced in photohadronic interactions,
travel unimpeded through the universe and disclose the directions of their sources.
Among the most plausible candidates for the origins of UHECRs is a class of
astrophysical phenomena known as gamma-ray bursts (GRBs). GRBs are the most
violent and energetic events witnessed in the observable universe. The IceCube
Neutrino Observatory, located in the glacial ice 1450 m to 2450 m below the South
Pole surface, is the largest neutrino detector in operation. IceCube detects charged
particles, such as those emitted in high energy neutrino interactions in the ice, by the
Cherenkov light radiated by these particles. The measurement of neutrinos of 100
TeV energy or greater in IceCube correlated with gamma-ray photons from GRBs,
measured by spacecraft detectors, would provide evidence of hadronic interaction
in these powerful phenomena and confirm their role in ultra high energy cosmic ray
production.
This work presents the first IceCube GRB-neutrino coincidence search op-
timized for charged-current interactions of electron and tau neutrinos as well as
neutral-current interactions of all neutrino flavors, which produce nearly spheri-
cal Cherenkov light showers in the ice. These results for three years of data are
combined with the results of previous searches over four years of data optimized
for charged-current muon neutrino interactions, which produce extended Cherenkov
light tracks. Several low significance events correlated with GRBs were detected,
but are consistent with the background expectation from atmospheric muons and
neutrinos. The combined results produce limits that place the strongest constraints
thus far on models of neutrino and UHECR production in GRB fireballs.
AN ALL-SKY, THREE-FLAVOR SEARCH FOR NEUTRINOS
FROM GAMMA-RAY BURSTS WITH THE ICECUBE
NEUTRINO OBSERVATORY
by
Robert Eugene Hellauer III
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2015
Advisory Committee:
Dr. Gregory Sullivan, Chair/Advisor
Dr. Erik Blaufuss
Dr. Kara Hoffman
Dr. Peter Shawhan
Dr. Cole Miller
c© Copyright by
Robert Eugene Hellauer III
2015
Acknowledgments
Throughout my graduate school career I have benefited from and am thankful
for the work, advice, and friendship of many people. I also acknowledge financial
support from the University of Maryland and the National Science Foundation.
Firstly, I would like to thank my advisor Greg Sullivan for giving me the
opportunity to work on a wonderful experiment with wonderful people. Thank you
for always being available to discuss ideas and for all of your advice. Thank you also
for allowing me to go to the South Pole. It will always be one of the best experiences
of my life.
Many thanks to Erik Blaufuss for your help from the start. Your knowledge,
patience, and humor were pivotal in my understanding of everything I strove to do
in my research. Thanks to Kara Hoffman, Cole Miller, and Peter Shawhan for your
guidance in my graduate research and classes. Thank you also for being on my
committee.
Thanks to Peter Redl, Brian Christy, and Kevin Meagher for welcoming me
into the group and helping me understand so much. Thank you Mike Richman for
teaching me how to code, sharing your many insights, and helping generate myriad
neologisms. Thank you Ryan Maunu, Elim Cheung, Josh Wood, and Ming Song
for being awesome office mates and having so many helpful and fun conversations.
Thank you John Felde for your positive, thoughtful, and helpful perspective on
everything.
Thanks to Don La Dieu and Alex Olivas for your guidance and humor. Thank
ii
you Don for your help in solving so many of my computer quandaries. I did my
very best to fill a fraction of your boots on the ice. Thanks to John Kelley and
all of my Antarctic coworkers for creating such a fun, enthusiastic, and productive
atmosphere during my three weeks on the continent. Thank you Ignacio Taboada
for your valuable input from the start of my analysis and Dawn Williams and Ryan
for your very helpful review. Thank you Naomi Russo for coordinating numerous
details of my research life. Thanks to all of my collaborators. I am lucky to have
worked on an amazing detector with fantastic colleagues and friends.
I made a lot of great memories and have a lot of entertaining stories from
studying for undergraduate and graduate school classes with friends. To Joffrey
Peters, Mike Hischak, Jack Hellerstedt, Chris Najmi, Tom Langford, Matt Severson,
Joyce Coppock, and many others, I could not have gotten through it all without
you. To my roommates, your extraordinary swagger made each year so much fun.
Many thanks to Tom Gleason for taking the time to introduce me to the
University of Maryland Physics Department when I was a senior in high school.
Thanks also to Jordan Goodman for speaking with me that evening about a very
interesting neutrino detector being built in the South Pole ice.
Finally, thanks to my family. To my parents and brother Matthew, thank
you for all of your love, support, and encouragement. You mean more to me than
everything else in the universe.
iii
Table of Contents
List of Tables vii
List of Figures viii
1 Introduction: Cosmic Rays and Neutrinos 1
1.1 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gamma-Ray Bursts 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Satellite Gamma-Ray Burst Detectors . . . . . . . . . . . . . . . . . . 9
2.2.1 Fermi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Swift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Konus/Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.4 INTEGRAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.5 MAXI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.6 SuzakuWAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.7 SuperAGILE . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.8 IPN3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 GRBweb and GRB Data Compilation . . . . . . . . . . . . . . . . . . 15
2.4 Fireball Model of Neutrino Production . . . . . . . . . . . . . . . . . 19
2.4.1 Prompt Photon Spectrum . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Internal Shock Fireball Model . . . . . . . . . . . . . . . . . . 22
2.4.3 Normalizing to Observed Gamma-Ray Fluences . . . . . . . . 27
2.4.4 Photospheric and ICMART Fireball Models . . . . . . . . . . 32
2.4.5 Numerical Fireball Neutrino Spectra Predictions . . . . . . . . 35
2.4.6 Cosmic Ray Connection: The Waxman & Bahcall Prediction . 37
2.4.7 Concerning Proton Escape . . . . . . . . . . . . . . . . . . . . 38
3 IceCube: The Detector, Neutrino Detection, and Event Characteristics 42
3.1 The Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.1 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1.1 Digital Optical Modules and the PMT . . . . . . . . 44
3.1.1.2 Waveform Digitization . . . . . . . . . . . . . . . . . 46
3.1.1.3 DOMHubs and the IceCube Laboratory . . . . . . . 48
3.1.1.4 Timing . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.1.5 Data Triggering and Formatting . . . . . . . . . . . 49
3.1.2 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . 50
3.1.3 Pulse Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1.4 Processing and Filtering . . . . . . . . . . . . . . . . . . . . . 51
3.1.5 Data Transmission to the North . . . . . . . . . . . . . . . . . 52
3.2 Particle Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.1 Signal Characteristics . . . . . . . . . . . . . . . . . . . . . . . 52
iv
3.2.2 Background Characteristics . . . . . . . . . . . . . . . . . . . 54
4 Simulation and Reconstruction Techniques 57
4.1 Simulation Methods and Description . . . . . . . . . . . . . . . . . . 57
4.2 Reconstruction Methods . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 Tensor of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 LineFit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.3 CascadeLlh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.4 SPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.5 Analytic Energy Reconstruction - ACER . . . . . . . . . . . . 66
4.2.6 Credo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2.7 Monopod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.8 Cramer-Rao . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5 Event Selection 72
5.1 Level 1: Trigger at South Pole . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Level 2: Cascade Event Filter at South Pole . . . . . . . . . . . . . . 73
5.3 Level 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Final Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.1 Machine Learning: Boosted Decision Tree Forests . . . . . . . 82
5.4.2 BDT Input Signal - Background Discrimination Variables . . . 91
5.4.3 Loose Pre-BDT Cuts after Level 3 . . . . . . . . . . . . . . . 127
5.4.4 BDT Forest Training . . . . . . . . . . . . . . . . . . . . . . . 129
5.4.5 Final Analysis Level . . . . . . . . . . . . . . . . . . . . . . . 131
6 Unbinned Likelihood Method 142
6.1 The Test Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.2 Probability Distribution Functions . . . . . . . . . . . . . . . . . . . 146
6.2.1 Time PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.2.2 Space PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2.3 Energy PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.3 Pseudo-Experiment Methodology . . . . . . . . . . . . . . . . . . . . 157
6.4 Sensitivity and Discovery Potentials . . . . . . . . . . . . . . . . . . . 158
6.5 Per-GRB Optimization Studies . . . . . . . . . . . . . . . . . . . . . 163
6.6 Characteristics of a Discovery . . . . . . . . . . . . . . . . . . . . . . 165
7 Results 166
7.1 Three Year Cascade Coincidence Search Results . . . . . . . . . . . . 166
7.2 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.2.1 Ice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.2.2 Optical Module Sensitivity . . . . . . . . . . . . . . . . . . . . 175
7.2.3 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . 175
7.2.4 Seasonal Rate Variation . . . . . . . . . . . . . . . . . . . . . 176
7.2.5 Total Systematic Error . . . . . . . . . . . . . . . . . . . . . . 177
7.3 GRB Neutrino Production Model Limits . . . . . . . . . . . . . . . . 178
v
7.3.1 Limits Normalized to Cosmic Ray Production in GRBs . . . . 179
7.3.2 Limits on GRB Fireball Models and Parameter Spaces . . . . 180
8 Conclusions and Outlook 184
A Gamma-Ray Burst Catalog 188
Bibliography 209
vi
List of Tables
2.1 GRB Satellite Detector Contributions . . . . . . . . . . . . . . . . . . 10
5.1 Signal and Background Efficiencies . . . . . . . . . . . . . . . . . . . 139
7.1 Most Significant Event and GRB Properties . . . . . . . . . . . . . . 169
7.2 Sources of Systematic Error . . . . . . . . . . . . . . . . . . . . . . . 177
A.1 IC79 GRB Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.2 IC86I GRB Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 195
A.3 IC86II GRB Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 202
vii
List of Figures
1.1 Cosmic Ray Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Localizations of BATSE GRBs . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Hillas Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 IPN Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 GRBweb Summary Table . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 GRBweb Burst Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 GRBweb Light Curve Display . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Analyzed GRB Localizations . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Fermi GBM GRB Light Curves . . . . . . . . . . . . . . . . . . . . . 21
2.9 Fireball Model GRB Neutrino Flux Predictions . . . . . . . . . . . . 40
2.10 Guetta et al. Model Modifications . . . . . . . . . . . . . . . . . . . . 41
3.1 The IceCube Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 The IceCube Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 DOM Main Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 DOM Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 DOMHub . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 DIS Neutrino-Quark Scattering Diagrams . . . . . . . . . . . . . . . . 53
3.7 Charged Current Neutrino Interaction Topologies . . . . . . . . . . . 54
3.8 Neutrino Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.9 Cascade and Track Event Topologies . . . . . . . . . . . . . . . . . . 56
3.10 Muon Energy Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1 Cherenkov Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Angular Resolutions of Reconstructions . . . . . . . . . . . . . . . . . 70
5.1 L2 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 L2 Track-to-Cascade Likelihood Ratio . . . . . . . . . . . . . . . . . . 78
5.3 L2 Cosine of SPE Zenith vs. ACER Energy . . . . . . . . . . . . . . 78
5.4 L2 Fill-Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5 L3 Signal Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.6 BDT Errors and Boost Factors . . . . . . . . . . . . . . . . . . . . . 86
5.7 Overtrained and Well-trained BDT Score Distributions . . . . . . . . 92
5.8 BDT Variable Correlations . . . . . . . . . . . . . . . . . . . . . . . . 93
5.9 track-cscd-llhratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.10 cscdllh-rlogl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.11 lfv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.12 lfv-z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.13 t-lfv-z-sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.14 t-lfv-z-diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.15 spefit-zenith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.16 ratio-before-to-after-vertex . . . . . . . . . . . . . . . . . . . . . . . . 109
viii
5.17 fill-ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.18 evalratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.19 qtot-eval-ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.20 max-qtot-ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.21 e-qtot-ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.22 charge-per-string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.23 Nch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.24 i3scale-inice-credo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.25 i3scale-inice-monopod . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.26 credo-vertexdist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.27 t-cscdvertexdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.28 t-cscdllh-z-diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.29 t-spevertexdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.30 vertexdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.31 track-cscd-llhratio Pre-BDT Cut Example . . . . . . . . . . . . . . . 128
5.32 lfv Pre-BDT Cut Example . . . . . . . . . . . . . . . . . . . . . . . . 128
5.33 Pre-BDT Cuts Sensitivity Improvement . . . . . . . . . . . . . . . . . 129
5.34 IC86I First Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.35 IC86I Last Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.36 BDT Score Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.37 Survival Rates vs. BDT Score . . . . . . . . . . . . . . . . . . . . . . 136
5.38 Neutrino Flavor Signal Efficiencies . . . . . . . . . . . . . . . . . . . . 137
5.39 Signal Efficiencies per BDT Score . . . . . . . . . . . . . . . . . . . . 138
5.40 Signal Efficiency with Respect to L2 . . . . . . . . . . . . . . . . . . 139
5.41 Effective Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.1 Time PDF Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2 Signal Space PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.3 Background Space PDF . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.4 Angular Resolutions of Neutrino Flavors . . . . . . . . . . . . . . . . 150
6.5 Cramer-Rao Pull vs. Energy . . . . . . . . . . . . . . . . . . . . . . . 152
6.6 Corrected Cramer-Rao Pull vs. Energy . . . . . . . . . . . . . . . . . 153
6.7 Energy PDF Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.8 Reconstructed vs. Simulated True Energy . . . . . . . . . . . . . . . 156
6.9 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.10 E−2 Signal Limit Setting and Discovery Potentials . . . . . . . . . . . 160
6.11 Fireball Model Signal Limit Setting and Discovery Potentials . . . . . 161
6.12 Frequentist Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.13 Null Hypothesis Test Statistic Distributions . . . . . . . . . . . . . . 164
6.14 Stacked and Per-Burst Discovery Potentials . . . . . . . . . . . . . . 164
6.15 Discovery Potentials for Single Random Burst . . . . . . . . . . . . . 165
7.1 Three Year Cascade Test Statistic Distribution . . . . . . . . . . . . . 167
7.2 PDFs for Most Significant IC79 Events . . . . . . . . . . . . . . . . . 170
7.3 PDFs for Most Significant IC86I Events . . . . . . . . . . . . . . . . 170
ix
7.4 Time PDF Ratios and GRB Light Curves for Most Significant IC79
Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.5 Time PDF Ratios and GRB Light Curves for Most Significant IC86I
Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.6 Detector Views for Most Significant IC79 Events . . . . . . . . . . . . 172
7.7 Detector Views for Most Significant IC86I Events . . . . . . . . . . . 172
7.8 Seasonal Variation of Data Rate . . . . . . . . . . . . . . . . . . . . . 176
7.9 Best Possible Upper Limits with Systematic Errors . . . . . . . . . . 178
7.10 Exclusion Contours for Cosmic-Ray-Normalized Models . . . . . . . . 180
7.11 Benchmark Fireball Model Limits . . . . . . . . . . . . . . . . . . . . 182
7.12 Exclusion Contours for Gamma-Ray-Normalized Models . . . . . . . 183
x
Chapter 1
Introduction: Cosmic Rays and Neutrinos
1.1 Cosmic Rays
Earth is constantly bombarded by a stream of astrophysical particles histor-
ically known as cosmic rays and discovered by Victor Hess in 1912. The cosmic
particles consist of roughly 90% p, 9% He2+, 1% heavier nuclei, and traces of single
electrons. The observed cosmic ray spectrum follows a power law with several com-
ponents of different indices due to their multiple origins. The tail of the spectrum
is comprised of the highest energy particles ever observed, with energies over 1020
eV [1–3].
As seen in Figure 1.1, the first component of the spectrum up to about 1015
eV (the “knee”) is characterized by the power law dNdE ∼ E−2.7. The origins of
cosmic rays up to the knee are widely agreed to be galactic supernova remnants
(SNRs). Indeed, the Fermi Large Area Telescope recently measured the expected
characteristic pion-decay “bump” feature in the gamma-ray spectra of two SNRs
[4]. This signature is compelling evidence of proton acceleration in these objects.
As accelerated protons encounter interstellar material, proton-proton interactions
produce neutral pions, which quickly decay into gamma-rays.
The second component up to around 1018.6 eV (the “ankle”) steepens to dNdE ∼
E−3. Cosmic rays from the knee to the ankle of the spectrum are thought to be
1
Figure 1.1: Measured cosmic ray energy spectrum [1]
from a mixture of both galactic and extragalactic sources. It can be reasoned that
this softer spectral shape is due to cosmic rays from galactic accelerators reaching
their maximum energy of propagation within the galaxy, as its size is exceeded by
the particle’s gyroradius [5].
The spectrum beyond the ankle hardens again to dNdE ∼ E−2.7. These highest
energy cosmic rays are most likely due to extragalactic accelerators. The spectrum
drops off above 1020.5 eV because this is the energy where protons interact with the
cosmic microwave background through the ∆ resonance. This drop off is known as
the GreisenZatsepinKuzmin (GZK) cutoff [1,6].
The origins of cosmic rays are difficult to identify using these particles alone.
The charged cosmic rays are deflected significantly by galactic and intergalactic
2
magnetic fields throughout nearly the entire spectrum. Source correlation with
cosmic ray trajectory only becomes feasible at energies approaching GZK energies.
1.2 Neutrinos
Where there is high energy light and baryonic matter, neutrinos are inevitably
produced in photohadronic interactions. While the charged cosmic rays are deflected
electromagnetically, neutrinos travel unimpeded through the universe and disclose
their source directions. Furthermore, the cross-section of the neutrino at all energies
is extremely small and, as a result, these neutral leptons can travel billions of light
years without interacting. Neutrinos are true cosmic messengers and they can be
used to learn about otherwise currently unreachable astrophysical phenomena.
Neutrinos were first proposed by Wolfgang Pauli to solve the missing energy
and momentum in the observed decay products of the neutron:
n→ p+ e (1.1)
This so-called beta decay was observed by a radioactive nucleus A transforming into
a slightly lighter nucleus B and emitting an electron. If only an electron and the
lighter nucleus resulted from this decay, then the measured electron energy in the
center of momentum frame should be constant:
Ee =
m2A −m2B +m2e
2mA
· c2 (1.2)
3
However, researchers measured a wide range of electron energies. Therefore, another
neutral particle, dubbed the the neutrino or “little neutral one” by Enrico Fermi,
must be involved.
In 1953, Reines and Cowan proposed an experiment [7] to measure an effect
of this neutrino through the crossed reaction:
ν + p→ n+ e+ (1.3)
Using a stream of nuclear reactor emitted ν¯e they measured the emission of positrons
through their annihilation with electrons and neutrons through their capture in
cadmium dissolved in the scintillator. The delayed pulse pair in the photomultiplier
tubes proved that the neutrino existed and was measurable [8, 9].
Since this pioneering work by Reines and Cowan, many more neutrino experi-
ments have been proposed and conducted in order to explore the various properties
of these subatomic particles. One such property being actively researched and which
gives power to this work is flavor oscillation. Pontecorvo first proposed that a neu-
trino created with a certain lepton flavor (electron, muon, or tau) can convert to
another of the three flavors [10]. This oscillation is possible due to the weak inter-
action eigenstates able to be described as superpositions of the mass eigenstates,
each of which picks up a phase during propagation that develops with distance trav-
eled [11]. Observation of this phenomenon, and thus evidence of neutrino mass, was
first confirmed by the Super-Kamiokande collaboration in 1998 [12].
Neutrino oscillations over cosmic baselines are taken into consideration in this
4
work. The flavor ratio at the IceCube detector will be different form the flavor
ratio generated at some astrophysical source. The expected neutrino flavor ratio
produced in GRBs and explained in the next chapter is (νe : ντ : νµ)GRB ≈ 2 : 1 : 0.
At Earth, this ratio is expected to be 1 : 1 : 1 due to the effect of oscillations
over the extremely long distances to GRBs. An equal flavor ratio is important for
this analysis because the event selection is tuned to shower-like events that can be
produced by any neutrino flavor and, therefore, is sensitive to all neutrino flavors.
The IceCube collaboration has instrumented over one billion tons of ice in
order to have a reasonable probability of observing an extraterrestrial high energy
neutrino flux. This analysis searches for such a flux coincident with the gamma-ray
emission of gamma-ray bursts (GRBs) to show first evidence of their hypothesized
hadronic makeup. To date, no neutrino signal has been detected in searches for
muon neutrinos from GRBs in multiple years of data from AMANDA, the partially-
instrumented IceCube, and the completed IceCube detector [13–17], nor in four years
of data by the ANTARES collaboration [18–20]. High energy νµ charged-current in-
teractions produce high energy muons that manifest as extended Cherenkov light
patterns in the South Pole glacial ice, referred to as “tracks”; and Southern Hemi-
sphere bursts were often excluded from searches for this signal in order to remove
the dominant cosmic-ray-induced muon background.
The absence of charged-current νµ signal from GRBs motivates this search for
nearly spherical Cherenkov light patterns, referred to as “showers” or “cascades”,
produced by all neutrino flavors correlated with GRBs. Charged-current interactions
of electron and tau neutrinos along with neutral current interactions of all neutrino
5
flavors generate electromagnetic and hadronic showers. The asymmetrical timing
distributions of the Cherenkov photons in these showers is elicited to reconstruct the
direction of the primary particle and calculate the likelihood that any were neutrinos
emitted from observed GRBs over the entire sky.
This dissertation is organized as follows. Chapter 2 discusses the neutrino
spectra predicted by the different fireball models on which limits are placed. Chapter
3 describes the IceCube detector and data acquisition system. The simulation and
reconstruction of events in IceCube are detailed in Chapter 4. The event selection
techniques and likelihood analysis are covered in Chapters 5 and 6. Finally, Chapter
7 presents the results of this all-sky, three-flavor search in combination with those
from the Northern Hemisphere νµ searches, and Chapter 8 concludes with an outlook
on the field.
6
Chapter 2
Gamma-Ray Bursts
2.1 Introduction
GRBs are the most concentrated and luminous explosions observed in the
universe and occur isotropically at an average rate of a few per day [21]. A large
dynamic range of burst durations, from milliseconds to thousands of seconds, has
been observed. During their lifespan, they outshine the rest of the gamma-ray sky.
GRBs were discovered in 1967 by the Vela satellites, which were designed by
the US Department of Defense to detect nuclear detonations in violation of the
1963 Nuclear Test Ban Treaty [22]. The Russian IMP-6 satellite then confirmed the
discovery once the Vela data was released in 1973 [23]. Due to the difficulty in re-
solving the source direction of gamma-rays, the satellites could only confirm that the
flashes did not originate from the direction of the Earth. For the next two decades,
myriad theories on GRB origins were proposed [24]. Little experimental progress
was achieved, though, until the Compton Gamma-Ray Observatory (CGRO) was
launched in 1991 [25]. The Burst And Transient Source Experiment (BATSE) on
board CGRO [26] revealed an isotropic distribution of 2704 GRBs as shown in Fig-
ure 2.1. This distribution was the first strong evidence of the cosmological origin of
GRBs.
In 1997 the Beppo-SAX satellite detected GRBs in x-rays for the first time,
7
Figure 2.1: Distribution of GRBs detected by BATSE [27]
yielding much more accurate position measurements than had been previously achieved
[28]. Large ground-based telescopes were then able to carry out follow up studies
on the GRB progenitor distances from Earth, proving their existence on an extra-
galactic scale [29].
The origins of these remarkable phenomena are still unknown; however, pro-
genitor scenarios can be deduced from the light curves and energy output. GRBs
are typically classified into two categories: long (greater than 2 seconds in duration)
and short (less than 2 seconds in duration). Long bursts are thought to be associ-
ated with collapsars [30], while short bursts are thought to be associated with the
mergers of compact objects [31].
Figure 2.2 shows the conditions necessary for UHECR production and where
astrophysical phenomena lie in terms of these conditions. UHECR production ne-
8
cessitates a source to either be of sufficient size to accelerate particles to the given
energies or possess a sufficient magnetic field to confine particles during acceleration.
GRBs appear to be prime candidates to accelerate protons up to 1021 eV.
Figure 2.2: The Hillas Plot. Solid red marks the conditions necessary to accelerate
protons up to 1021 eV. Dotted red is for proton acceleration to 1020 eV. Green is for
iron acceleration to 1020 eV [32].
2.2 Satellite Gamma-Ray Burst Detectors
Spacecraft are in operation with instruments designed to detect and observe
GRBs. The teams operating the instruments and analyzing their data all share
the high priority goal of the high energy astrophysical community to explain the
physical mechanisms behind these powerful transient phenomena. Many of these
instruments build off of the work of the BATSE instrument which operated from
9
1991 to 2000.
Table 2.1 summarizes the angular resolutions, fields of view, energy ranges,
and contributions to this search for each of the satellite GRB detectors described in
this section.
Team Ang. Resolution Field of View Energy Range T1 T2 Direction Spectrum
FermiGBM 1◦ - 15◦ 3pi sr 8 keV - 40 MeV 524 (64.9%) 509 (63.1%) 480 (59.5%) 464 (57.5%)
FermiLAT 0.1◦ - 1◦ 0.8pi sr 20 MeV - 300 GeV – – 13 (1.6%) -
SwiftBAT 1′ - 4′ 0.5pi sr 15 - 150 keV 188 (23.3%) 203 (25.2%) 63 (7.8%) 137 (17.0%)
SwiftXRT ∼ 3.5′′ – 0.2 - 10 keV – – 154 (19.1) –
SwiftUVOT ∼ 0.5′′ – optical (170 - 650 nm) – – 15 (1.9%) –
KonusWind – 4pi sr 10 keV - 10 MeV 45 (5.6%) 60 (7.4%) – 73 (9.0%)
INTEGRAL 1′ - 2′ 0.5pi sr 8 keV - 40 MeV 14 (1.7%) 13 (1.6%) 13 (1.6%) 8 (1.0%)
MAXI 1′ - 2′ 0.5pi sr 8 keV - 40 MeV 7 (0.9%) 7 (0.9%) 12 (1.5%) –
SuzakuWAM – 2pi sr 50 keV - 5 MeV 25 (3.1%) 12 (1.5%) – 3 (0.4%)
SuperAGILE 1′ - 2′ 0.5pi sr 15 - 45 keV 2 (0.2%) 2 (0.2%) 3 (0.4%) 3 (0.4%)
IPN3 .1◦ - 5◦ 4pi sr keV - MeV – – 51 (6.3%) –
Table 2.1: Data for GRB detectors contributing to this analysis and contribution
number and percentage for analysis parameters.
2.2.1 Fermi
The Fermi Gamma-ray Space Telescope launched in 2008 with the goal of
studying the universe at high energies. The spacecraft has two instruments that
detect GRBs at different energy ranges: the Gamma-ray Burst Monitor (GBM) and
the Large Area Telescope (LAT). These instruments detect high energy gamma-rays
through scintillators and pair production measurement. The combined energy range
of the two instruments is the broadest of all GRB detectors in operation.
The FermiGBM [33–36] is the most prodigious detector of GRBs among all
spacecraft GRB-detecting instruments. The instrument is made up of 12 sodium
iodide (NaI) detectors, with energy range 8 keV to 1 MeV, and two bismuth ger-
manate (BGO) detectors, with energy range 200 keV to 40 MeV. The detectors’
10
positions and orientations achieves a ∼ 9.5 sr field of view. Localization of a burst
is determined to an accuracy of 1◦ to 15◦ degrees using the relative event rates of
the detectors with different orientations with respect to the burst. Upon detec-
tion of GRB prompt emission, GBM provides quick notification to Fermi’s main
instrument, LAT.
The FermiLAT [37] is pair production telescope that consists of a 4x4 array of
identical towers of silicon strips, interleaved tungsten converter foils, and a cesium
iodide calorimeter. An anti-coincidence plastic scintillator detector covers the array
and rejects charged particle background. This arrangement achieves a ∼ 2.4 sr field
of view and . 1◦ burst localization accuracy. The detector covers a much higher
energy range compared to GBM and is sensitive to 20 MeV to 300 GeV gamma
rays.
2.2.2 Swift
The Swift satellite [38] launched in 2004 with its primary mission to study
GRBs. The spacecraft has three instruments that detect different wavelengths of
light: the Burst Alert Telescope (BAT) [39], the X-Ray Telescope (XRT) [40], and
the Ultraviolet/Optical Telescope (UVOT) [41]. The BAT instrument continuously
scans the sky using a coded aperture mask overlaid on a gamma sensitive CCD
array that has a 1.4 sr field of view and 15 - 150 keV energy range. The mask
is an arrangement of lead tiles and when gamma rays are detected, the on-board
computer reads out the array charge pattern and then reconstructs the direction
11
based on the coded arrangement with an angular resolution of 1′ to 4′.
When BAT detects a previously unmeasured gamma-ray transient, the Swift
spacecraft slews over 20 to 75 seconds to point XRT and UVOT at the source. XRT
searches for an X-ray point source in the same location as the gamma-ray source,
with an energy range of 0.2 - 10 keV and angular resolution of ∼ 3.5′′. If XRT
observes an x-ray source, UVOT searches for an 170 - 650 nm optical afterglow and
can localize this point source with an angular resolution of ∼ 0.5′′.
2.2.3 Konus/Wind
Konus [42] is the gamma-ray detector on the Wind spacecraft which launched
in 1994. Wind consists of two NaI crystal detectors oriented perpendicular to the
ecliptic with an energy range of 10 keV - 10 MeV. The detector has no localization
capabilities on its own, but is part of the IPN3 network described below. Lastly,
the Wind spacecraft lies at Lagrange point L1, which is about seven light seconds
from Earth; however its timing information is converted to UTC in its published
circulars and before use in this search.
2.2.4 INTEGRAL
INTEGRAL [43] is a gamma-ray detecting satellite launched in 2002. The
spacecraft consists of three coded aperture mask detectors with a total energy range
of 15 keV - 10 MeV. The detectors on board contribute to the IPN3 collective GRB
localizations described below, while the field of view for burst localizations made by
12
this spacecraft only is ∼ 0.5pi.
2.2.5 MAXI
The Monitor of All-sky X-ray Image (MAXI) [44] is an X-ray detector installed
on the International Space Station in 2009. The instrument localizes bursts based
on their X-ray afterglow using two detector types: (1) gas proportional counters
with an energy range of 2 - 30 keV and (2) X-ray charge-couple devices with an
energy range of 0.5 - 12 keV. MAXI also discovers bursts by extrapolating a hard
X-ray spectrum into the gamma-ray spectrum.
2.2.6 SuzakuWAM
The Suzaku satellite Wide-band All-sky Monitor (WAM) [45] launched in 2005.
This instrument detects GRBs with its 20 thick BGO anti-coincidence shields of its
hard X-ray detectors. The BGO detectors have an energy range of 50 keV - 5 MeV.
SuzakuWAM has no localization capabilities on its own, but is part of the IPN3
network described below.
2.2.7 SuperAGILE
The Super spacecraft launched in 2007. Its AGILE instrument [46] consists of
four independent silicon detectors that are equipped with tungsten coded aperture
masks. The instrument measures gamma rays in the range of 10 - 40 keV, and has
a ∼ 0.3pi sr field of view with an angular resolution around 1′.
13
Figure 2.3: IPN detection mechanism, taken from [47]. The crossings of two annuli
calculated from the different GRB-detecting satellite positions are marked by orange
arrows.
2.2.8 IPN3
The Third Interplanetary Network (IPN3) [47] is a collection of gamma-ray
detecting satellites. IPN3 uses the timing information from multiple satellite mea-
surements of the same GRB to triangulate an error box for the burst localization,
as pictured in Figure 2.3. Degeneracy of the annuli crossings can be lifted by Earth
occultation or detections by other satellites. For the years of this GRB search, the
network consisted of the following nine spacecraft: AGILE, Fermi, RHESSI, Suzaku,
and Swift, in low Earth orbit; INTEGRAL, in eccentric Earth orbit with apogee 0.5
light-seconds; Wind, up to 7 light-seconds from Earth; MESSENGER, en route to
and then in orbit around Mercury; and Mars Odyssey, in orbit around Mars.
14
2.3 GRBweb and GRB Data Compilation
All of the spacecraft GRB detectors detailed in section 2.2 publish circulars
on each detected GRB to the Gamma-ray Coordinates Network (GCN) [48]. The
relevant temporal, spatial, and spectral parameters used in this analysis are ex-
tracted autonomously with PHP scripts from these circulars and imported to an
IceCube MySQL database. Much of the Fermi GBM burst data is located only in
their database and so is extracted separately and imported to the same IceCube
database.
The compiled relevant GRB parameters are then presented on a publicly-
available interactive website, GRBweb [49] [50]. This website contains a summary
table, shown in Figure 2.4 which presents the parameters used in this analysis for
each GRB and the satellite detectors from which they came. For multiple burst
measurements by different detectors, the prompt photon emission time (T100) is de-
fined by the most inclusive start and end times (T1 and T2) reported by any satellite.
The most precise localization available is used as well, with all reported error circle
radii scaled to 1σ containment. Thirdly, the hierarchy of spectral parameters used
is ordered by the widest to narrowest energy ranges, given in Table 2.1.
In addition to the summary table, GRBweb has individual GRB pages, de-
tailing the measured parameters from each detector and links to the relevant GCN
circulars. Light curves of normalized photon counts per time from FermiGBM,
SwiftBAT, KonusWind, and INTEGRAL are also presented, if available. An exam-
ple of an individual GRB page and its measured light curves are shown in Figures
15
Figure 2.4: ]
GRBweb summary table of GRB parameters.
2.5 and 2.6. A table of all bursts analyzed in this analysis and their parameters
compiled by GRBweb is in Appendix A.
807 GRBs during IceCube data taken from May 2010 through May 2013 were
analyzed in this neutrino search. The right ascension and declination coordinates
of these bursts are plotted in Figure 2.7 with colors corresponding to the detector
configuration during which they occurred. Searches over each detector configura-
tion were optimized separately with very similar event selections and sensitivities,
detailed in Chapters 5 and 6.
16
Figure 2.5: GRBweb individual burst page example.
Figure 2.6: GRBweb light curve display example.
17
-150° -120° -90° -60° -30° 0° 30° 60° 90° 120° 150°RA
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
Dec
GRBs (RA, Dec) for IC79, IC86I, IC86II Searches
Figure 2.7: Localizations of the 255 IC79, 288 IC86I, and 264 IC86II GRBs in
equatorial coordinates analyzed during these three IceCube detector configuration
seasons of approximately one year each.
18
2.4 Fireball Model of Neutrino Production
The prevailing phenomenology that successfully describes GRB observations
is that of a relativistically expanding fireball of electrons, photons, and protons
[21,51,52]. The two main engines of the GRB fireball model are the central engine,
that converts roughly a solar rest mass of gravitational energy into kinetic energy;
and the internal shocks between the fireball ejecta and the external medium, that
convert kinetic energy into the observed gamma-rays. These engines allow GRBs
to attain the energies necessary to reconcile their measured luminosities and their
vast distances from us. Additionally, GRB emission must be beamed since their
observed isotropic luminosities exceed the energies that would be available in their
theorized progenitor scenarios [21].
As noted in Section 1.2, no neutrino signal has yet been detected in searches
for neutrinos from GRBs. The resulting limits presented in prior IceCube publica-
tions [14–17] and Chapter 7 focus on two genres of GRB neutrino spectral predic-
tions for this fireball scenario: models normalized to the observed UHECR flux [53]
and models normalized to the observed gamma-ray flux for each burst. Cosmic-
ray-normalized models [54–56] assume protons emitted by GRBs are the dominant
sources of the highest energy cosmic rays observed, and with these models limits are
placed on this assumption. Gamma-ray-normalized models [57, 58] assume protons
from GRBs are only a source of cosmic-rays, and with these models limits are placed
on internal fireball parameters.
Three types of gamma-ray-spectrum-normalized fireball models are considered
19
in this analysis, calculated on a burst-by-burst basis, that differ in their neutrino
emission sites. The internal shock model relates the neutrino production radius to
the variability time scale of the gamma-ray light curves [54,57,58]. The photospheric
model places the radius at the photosphere through combinations of processes such
as internal shocks, magnetic reconnection, and neutron-proton collisions [59–61].
The internal collision-induced magnetic reconnection and turbulence (ICMART)
model favors a neutrino production radius ∼ 10 times larger than the standard
internal shock model due to a Poynting-flux-dominated outflow that remains undis-
sipated until internal shocks destroy the ordered magnetic fields [58, 61]. In these
models, the regions where photons are generated through electron synchrotron radi-
ation and where protons are accelerated are taken to be equivalent. This equivalence
is not necessarily true for scenarios other than the internal shock model and multiple
emission zones can exist [62], but one emission zone allows the predicted neutrino
flux to scale linearly with the proton-to-electron energy ratio in the fireball. For all
GRBs, standard flavor mixing from the source over cosmic baselines to the earth is
assumed.
2.4.1 Prompt Photon Spectrum
Gamma-rays from GRBs are observed on a daily basis by a number of detectors
in space, e.g. those in section 2.2. These missions report on the time, location,
fluence, and spectral information of each burst. GRB output is extremely varied.
Light curves plotted using data from the Fermi GBM mission shown in Figure 2.8
20
below illustrate the wide range of emission GRBs exhibit.
Figure 2.8: GRB light curves generated from the Fermi GBM detector data.
The gamma-ray signal observed by satellites in the keV to MeV range is gen-
erated in the outflow of the fireball scenario by synchrotron radiation or inverse
Compton scattering of electrons accelerated in the internal shocks [63] [64]. This
prompt GRB photon spectrum is typically modeled by a single power law, a power
law with an exponential cut-off, a smoothly broken power law, or the Band func-
tion [34]. The Band function has become the standard for fitting GRB spectra, and
was formulated using time-averaged spectra measured by the BATSE spectroscopy
detectors [65]. The spectral parameters α, β, and E0 vary from burst to burst. The
break energy can range from tens of keV to over 1 MeV.
A broken power law approximation (Equation 2.1) based on the Band function
is typically used in neutrino astrophysics to describe the average photon flux of the
21
GRB prompt emission [66].
Fγ(Eγ) =
dN(Eγ)
dEγ
= fγ ×



( γ
MeV
)αγ ( Eγ
MeV
)−αγ
, Eγ < γ
( γ
MeV
)βγ ( Eγ
MeV
)−βγ
, Eγ ≥ γ
(2.1)
2.4.2 Internal Shock Fireball Model
The current standard fireball phenomenology in the literature involves internal
shock waves with varying boost factors [21]. The fireball plasma is initially opaque
to radiation and expands by radiation pressure until it becomes optically thin and
produces the measured gamma-ray emission. From this manifestation of optical
thinness onward, the growing bulk Lorentz factor Γ becomes constant and its value
depends on the baryonic load of the fireball [56].
The existence of internal shocks is supported by observations of the rapid time
structure of GRBs [67]. The variability time scale of the measured light curves on
the order of milliseconds suggests that the internal shocks collide. These collisions
would be due to the varying baryonic loads and thus differing bulk Lorentz factors.
Also, spikes in the burst spectra on the order of seconds are from synchrotron
radiation electrons accelerated in the strong internal magnetic field [68]. Baryons
must also be accelerated with the electrons in the expanding fireball. The resulting
photohadronic interactions would then produce neutrinos.
As noted above, there are two branches of neutrino production models for the
GRB fireball scenario, and the split is due to the assumptions they make about the
22
relationship between GRBs and UHECRs. The first class of model assumes GRBs
are the dominant sources of the highest energy cosmic rays and allows one to draw
conclusions on this hypothesis. The second type of model assumes that GRBs are
only a source of UHECRs without any relation to the observed CR flux and allows
one to draw conclusions on the makeup of GRBs themselves.
In either case, protons must be accelerated along with the electrons. The
mechanism believed to be responsible for accelerating the protons and giving them
their characteristic power law spectrum shown in Figure 1.1 is that of Fermi accel-
eration. This acceleration process transfers “macroscopic kinetic energy of moving
magnetized plasma to individual charged particles, thereby increasing the energy per
particle to many times its original value and achieving the nonthermal energy dis-
tribution characteristic of particle acceleration” [69]. Following the argument from
chapter 11 of [69], upon each encounter with the magnetized plasma, a charged
particle gains an amount of energy proportional to its energy:
∆E = ξE (2.2)
So after n encounters, the particle’s energy is
E = E0(1 + ξ)n (2.3)
23
and the number of encounters needed to reach energy E is
n =
ln( EE0 )
ln(1 + ξ) (2.4)
Next, if the probability of escape from the acceleration region at each encounter is
Pesc, then the probability of a particle remaining after n encounters is (1 − Pesc)n.
Consequently, the number of particles accelerated to energies greater than or equal
to E is proportional to
N(> E) ∝
∞∑
m=n
(1− Pesc)m =
(1− Pesc)n
Pesc
(2.5)
After taking the natural logarithm of both sides and exponentiating, one can write
N(> E) ∝ 1Pesc
( E
E0
) ln(1−Pesc)
ln(1+ξ)
(2.6)
Let
γ = ln((1− Pesc)
−1)
ln(1 + ξ) ≈
Pesc
ξ (2.7)
The above approximation can be made if one assumes Pesc and ξ are small. So now
N(> E) ∝ 1Pesc
( E
E0
)−γ
(2.8)
and it is clear that the Fermi mechanism naturally leads to the power law spectrum
observed for cosmic rays. The shape of the observed high energy cosmic ray spectrum
24
motivates the common choice of an E−2 power law [69]. Further, one can introduce
the characteristic acceleration cycle and escape times. The ratio of Tcycle to Tesc is
equal to Pesc. Thus γ can also be approximated as
γ ≈ 1ξ ×
Tcycle
Tesc
(2.9)
Fermi acceleration can be divided into two types based on the proportionality
of the energy gain of a particle when encountering a shock front to the velocity
of the shock front. Second order Fermi acceleration was the original mechanism
proposed by Fermi for energy gains of charged particles in moving plasma among
turbulent magnetic fields [70]. This type of acceleration is thought to occur in
particles encountering a moving gas cloud. When a charged particle encounters the
cloud, it moves into and out of it and gains an amount of energy proportional to
β2. In first order Fermi acceleration, a planar shock wave moves with a velocity
v through a magnetized plasma. When a charged particle encounters the shock,
it moves back and forth across it and gains an amount of energy proportional to
β = v/c. First order Fermi acceleration is presumed to be the process through which
very high energy protons and electrons are accelerated in the fireball internal shock
model.
After protons have been Fermi accelerated in the expanding fireball, they
interact with gamma-rays radiated by electrons. Charged and neutral pions are
then produced via the delta resonance shown below.
25
p+ γ → ∆+ → n+ pi+
p+ γ → ∆+ → p+ pi0
In the comoving (primed) fireball frame, the threshold for this interaction is given
by
E ′pE ′γ ≥
m2∆ −m2p
4 (2.10)
In the (unprimed) reference frame of an observer on Earth, the minimum proton
energy for photo-pion production is then
Ep ≥
Γ2
(1 + z)2
m2∆ −m2p
4Eγ
(2.11)
High energy gamma rays are produced by the decay of the pi0, while neutrinos are
produced by the decay of the charged pi+ and product µ+.
pi0 → γ + γ
pi+ → µ+ + νµ → e+ + νe + ν¯µ + νµ
The extremely long baselines from GRBs to the Earth cause the source flavor
ratio of
(νµ : νe : ντ )source ≈ (2 : 1 : 0)
26
to oscillate to
(νµ : νe : ντ )earth ≈ (1 : 1 : 1)
2.4.3 Normalizing to Observed Gamma-Ray Fluences
The GRB neutrino spectrum predicted by Guetta et al. [71] is not built on the
assumption that GRBs are the source of UHECRs. Instead, the prediction assumes
that GRBs are a source of UHECRs, and is a per-burst fluence based on measured
and predicted values of GRB parameters. Photopion production from collisions
of accelerated protons and the observed gamma-rays in the fireball internal shock
scenario results in neutrino emission. The neutrino emission therefore is predicted to
occur during the same gamma-ray emission time window and to follow the gamma-
ray spectrum up to the second break energy.
During photopion production, the peak cross section at the ∆ resonance and
the associated photon energy are used to approximate the fraction of energy lost
by protons to pions fpi [54]. The mean fraction of energy lost to the pion at this
resonance is approximately 〈xp→pi〉 ' 0.2 [54]. If this energy is evenly distributed
between the four decay leptons of the charged pion described above, then following
Eq. 2.11 the neutrino energy in the observer frame is
Eν =
1
4〈xp→pi〉Ep ≥
1
4〈xp→pi〉
Γ2
(1 + z)2
m2∆ −m2p
4Eγ
(2.12)
The first break energy ν,1 of the predicted double broken power law neutrino
spectrum is obtained from the ∆ resonance threshold condition in Eq. 2.12. Given
27
the photon spectrum break energy γ and taking the geometric mean of 100 and
1000 as a standard bulk Lorentz factor value, ν,1 can be written as
ν,1 =
1
4〈xp→pi〉
Γ2
(1 + z)2
m2∆ −m2p
4Eγ
= 7× 105GeV 1(1 + z)2
( Γ
102.5
)2(MeV
γ
) (2.13)
The second break energy ν,2, which again results from synchrotron cooling of
the high energy pi+ and µ+ before they decay, is relevant when the synchrotron loss
time approaches the particle lifetime [71].
t′sync =
3m4pic3
4σTm2eEpiU ′B
→ τ ′pi = τ 0pi
E ′pi
mpic2
(2.14)
where U ′B = B
′2
8pi is the energy density of the shocked plasma magnetic field and the
Thompson cross section σT = 6.65 × 10−25cm2. Following the kinematics of [71]
and [72], the fraction of internal energy carried by the magnetic field B is given by
BLint = 4piR2cΓ2U ′B (2.15)
where R ∼ 2Γ2ctvar is the collision radius of two shock fronts in the plasma that
have a difference in velocities of ∆v ∼ c2Γ2 and the variability time of the source
is the previously introduced tvar. Additionally, the internal luminosity is related to
the observed gamma-ray isotropic-equivalent luminosity by
eLint = Lisoγ (2.16)
28
where the fraction of internal energy converted by accelerating electrons is e. For
simplicity, e and B are both taken to be 0.1 [71].
Now, if the ratio t
′
sync
τ ′pi
approaches unity and the energy of the pion is distributed
evenly among the four resultant leptons, then the break energy of the pion decay
product muon neutrinos is
νµ =
√
t′sync
τ ′pi
= 14
√
12pim5pic8eΓ6t2var
σTm2eτ 0piBLiso(1 + z)2
(2.17)
or more usefully
νµ = 108GeV
1
(1 + z)2
√ e
B
( Γ
102.5
)4( tvar
0.01s
)√1052ergs−1
Lisoγ
(2.18)
The muon decay product neutrinos have a lifetime 100 times longer than those from
the charged pion and because t
′
sync
τ ′ ∝ E−2ν as is described above, their break energy
is 10 times smaller
ν¯µ,νe = ν,2 = 107GeV
1
(1 + z)2
√ e
B
( Γ
102.5
)4( tvar
0.01s
)√1052ergs−1
Lisoγ
(2.19)
A further result of the t
′
sync
τ ′ ∝ E−2ν relationship is that the corresponding high energy
spectral index steepens by two powers. The final form of the neutrino spectrum is
29
then
Fν(Eν) =
dN(Eν)
dEν
= fν ×



( ν,1
GeV
)αν ( Eν
GeV
)−αν , Eν < ν,1
( ν,1
GeV
)βν ( Eν
GeV
)−βν , ν,1 ≤ Eν < ν,2
( ν,1
GeV
)βν ( ν,2
GeV
)γν−βν ( Eν
GeV
)−γν , Eν ≥ ν,2
(2.20)
and the spectral indices are related to the gamma-ray indices and each other by
αν = 3− βγ, βnu = 3− αγ, γν = βν + 2 (2.21)
The above neutrino spectrum is then normalized to the observed GRB gamma-
ray fluence [71] [14]. The gamma-ray fluence is assumed to be proportional to the
neutrino fluence. This proportionality is argued to be
∫ ∞
0
dEνEνFν(Eν) =
1
8
1
fe
fpi
∫ 10MeV
1keV
dEγEγFγ(Eγ) (2.22)
The gamma-ray fluence is defined with finite limits because some GRBs are reported
with divergent Fγ if integrated from zero to infinity. The factor of 18 represents that
roughly half of the photohadronic interactions result in pi+ (and thus leptons), and
the energy is taken to be distributed evenly among the four leptons. In truth, as
can be calculated using isospin arguments, the probability that a ∆+ decays into a
pi+ is 1/3, but 1/2 is taken by [71] and [55] for an approximation. fe is the fraction
of fireball energy carried by electrons compared to protons, and is assumed to be
30
0.1 [14].
Finally, fpi estimates the overall fraction of the proton energy going into the
pions [14]. This fraction is calculated from the size of the shock ∆R, the mean
free path of a proton for photohadronic interactions λpγ, and the average fraction
of proton energy transferred to a pion in a single interaction, which is assumed to
be 〈xp→pi〉 = 0.2. Altogether, the expression for fpi is
fpi = 1− (1− 〈xp→pi〉)∆R
′/λpγ (2.23)
which ensures that the transferred energy fraction is ≤ 1. ∆R′/λpγ yields the ex-
pected number of photohadronic interactions given the size of the shock and the
interaction mean free path. λpγ = 1nγσ∆ , where the number density of photons nγ
in the expanding fireball is in turn given by the ratio of the photon energy density
and the photon energy in the comoving frame
nγ =
U ′γ
′γ
'
(Lisoγ tvar/Γ
4piR2∆R′
)/(γ
Γ
)
' L
iso
γ
16pic2tvarΓ4∆R′γ
(2.24)
The number of photohadronic interactions can then be usefully written as
∆R′
λpγ
= Nint =
(
Lisoγ
)(0.01s
tvar
)(102.5
Γ
)4(MeV
γ
)
(2.25)
where ∆R′ is the comoving width of the causally connected region of the jet.
The benefit of the Guetta et al. approach is clearly in its ability to tailor to
measured parameters of individual bursts. However, each prediction still depends
31
on a number of tenuous assumptions on these internal variables, including the bulk
Lorentz factor, the smallest observed variability time of the light curve, the equipar-
tition fractions B and e, photopion production efficiency, the luminosity of bursts
with no measured redshift, and the ratio of energy carried by electrons to that of
protons. Moreover, conclusions on the GRB contribution to UHECRs cannot be
drawn because there is no intrinsic relation to the observed flux in UHECRs using
this normalization method.
Null results from IceCube [14] [73] [16] have brought about revisions of the
above γ-normalized prompt models of GRB neutrino emission. New and revised
models, both analytically calculated and Monte Carlo-based numerically calculated,
of GRB prompt neutrino emission address the assumptions discussed above as well
as implement more complete particle physics. Further, some models invoke scenarios
that force proton acceleration at different radii compared to the usual internal shock
radius. A sample of these predictions using the northern hemisphere GRB samples
of each season are presented below.
2.4.4 Photospheric and ICMART Fireball Models
As is shown in Chapter 7, any model that invokes high energy proton acceler-
ation at the photosphere is already disfavored by the present limits. If deeper limits
are placed on the internal shock model, then it is argued that the neutrino emission
site is at a much larger radius than the internal shock radius or high energy protons
are not at the site where γ-ray photons are produced [58]. Magnetic dissipation
32
models [61] [74] invoke a larger-radius of proton acceleration and gamma-ray pro-
duction. Such models could be the explanation for the unobserved GRB neutrino
flux.
The per-GRB neutrino flux for two different mechanisms of prompt emission
are shown below and provide alternatives to the fireball internal shock model [58].
These models are normalized to the observed gamma-ray spectra of each GRB. The
differences in the models manifest in the radius of gamma-ray prompt emission.
The dissipative photosphere (photospheric) model requires gamma-ray generation
and proton acceleration at the photosphere, where the fireball becomes optically
thin to γγ interactions [59] [75].
The general formalism used by Zhang and Kumar mostly follows that of the
Guetta-based prediction in Section 2.4.3. One difference between the two is the
consideration of the radius of the proton acceleration site R and the bulk Lorentz
factor Γ as the primary parameters instead of tvar and Γ. This paradigm is chosen
to allow one to probe the resulting neutrino production of models with different
emission radii. Another addition to the formalism is the introduction of the ratio of
the photon luminosity to the non-thermal proton luminosity fγ/p. This parameter
acts as a more general electron-to-proton energy ratio fe and allows for gamma-
ray generation and proton acceleration to occur at different locations. If photon
production and proton acceleration are invoked at the same sight, then fγ/p reduces
to fe. The usual scheme for calculating the neutrino flux is followed, with the
observed photon spectrum fit to a broken power law (Equation 2.1) and the neutrino
spectrum assumed to follow a double broken power law (Equation 2.20).
33
The photospheric model proposes that the prompt GRB spectrum is formed
near the Thomson scattering photosphere given by
Rph ' 3.7× 1011cm
1
e
( Lisoγ
1052ergs−1
)( Γ
102.5
)−3
(2.26)
[58] considers it likely that both photons are generated and protons are accelerated
at Rph such that fγ/p can be set to fe. Thus, compared to the Guetta-based predic-
tion, Nint increases by a factor of RIS( 1014cm)/Rph and ν,2 decreases by the same
factor. Compared to other GRB emission models, the photospheric model has the
smallest possible dissipation scale and, as a result, the highest photon density [76].
Altogether, this scenario leads to an enhancement in neutrino production from the
conventional internal shock model.
The internal collision-induced magnetic reconnection and turbulence (ICMART)
model is presented in [58] as a typical large-radius magnetic dissipation model of
GRB neutrino production. This model invokes a highly magnetized outflow, which
remains undissipated up to a distance of RICMART ( 1015cm) > RIS. At this radius,
internal shocks help to destroy the ordered magnetic fields and a strong runaway
magnetic dissipation process occurs. Photon generation and proton acceleration are
again in the same region, so fγ/p = fe. Thus, compared to the Guetta-based pre-
diction, Nint decreases by a factor of RIS/RICMART and ν,2 increases by the same
factor. Altogether, this model leads to a reduction in neutrino production.
34
2.4.5 Numerical Fireball Neutrino Spectra Predictions
The per-GRB gamma-ray-normalized predictions used in the likelihood anal-
ysis and limit calculations are calculated numerically with a wrapper of the Monte-
Carlo generator SOPHIA [77]. This code was written by a colleague in IceCube [76].
The calculation includes the full particle production chain and synchrotron losses of
all intermediate mesons and leptons of the pγ-interaction cascade before their decay
in the fireball, which must be added to the original SOPHIA setup. The author
notes that this is not a new model, “but simply a direct application of the fireball
model” [76].
For these calculations, the reported gamma-ray spectrum of each GRB is
parametrized as a broken power-law approximation of the Band function, follow-
ing the formula in [58, 65, 66]. As described in Section 2.3, GRB parameters from
the GCN circulars and the Fermi GBM database [35,36] are compiled on the GRB-
web database. Average values of γ fluence 10−5 erg cm−2, redshift 2.15 for long
bursts with durations > 2 s and redshift 0.5 for shorter bursts are used if these
parameters are unmeasured, following the same prescription of IceCube’s previous
model limit calculations [15–17].
The neutrino flux predictions depend on several unnmeasured quantities; vari-
ability time scale 0.01 s and isotropic luminosity 1052 erg cm−2 are used for long
bursts and variability time scale 0.001 s and isotropic luminosity 1051 erg cm−2 are
used for short bursts, which are consistent with the literature [57, 58, 78]. If the
redshift is known for a particular burst, the approximate isotropic luminosity from
35
the redshift, photon fluence, and T100 is calculated [57].
The top plot of Figure 2.9 shows neutrino spectra from the three models with
benchmark fireball parameters. These benchmark parameters are bulk Lorentz boost
factor Γ = 300 and proton-to-electron energy ratio, or baryonic loading, fp = 10.
The middle and bottom plots show neutrino spectra from the three models with
larger boost factors, requiring larger proton energy thresholds for pion, and hence
neutrino, production in the observer frame. These spectra are presented as per-
flavor quasi-diffuse fluxes, in which we divide the total fluence from all GRBs in the
sample by the full sky 4pi steradians and one year in seconds, and scale the total
number of bursts to a predicted average 667 observable bursts per year, which has
been used in our previous publications. The actual number of bursts observed by
satellite detectors in each year is less than the prediction because of detector field
of view limitations and obstruction by the sun, moon, and Earth.
The fireball model neutrino spectra calculations in these figures compare with
a numerical model first presented as an improvement to the analytic approximations
outlined above [57]. The changes lead to an overall reduction in the predicted flux,
shown in Figure 2.10 for an example GRB. In this plot, fCγ comes from removing the
assumption that all photons have an energy at the break energy of the photon spec-
trum. The photons are consequently distributed according to the photon spectrum.
f≈ comes from correcting some rounding errors in the Guetta et al. calculation.
fσ results from considering the width of the ∆ resonance and integrating over the
photon spectrum rather than just the resonance peak. CS follows from the inclusion
of the proton energy in the interaction rate of the photons within the energy range
36
of the ∆ resonance. Finally, the addition of kaon and multi-pion production modes
to the photomeson interactions increases the neutrino flux by the amount seen in
the “full pγ” labeled correction to the numerical calculation in the right panel of
Figure 2.10.
2.4.6 Cosmic Ray Connection: The Waxman & Bahcall Prediction
The GRB neutrino flux derived by Waxman and Bahcall assumes GRBs are
the major source of UHECRs (above 1019 eV) [54]. A relativistic expanding fireball
scenario is assumed with protons and electrons Fermi accelerated by interaction with
internal shocks, as described above. The internal shocks arise from fluctuations in
the expanding wind bulk Lorentz factor Γ, which themselves are a result of the
variability of the source [54]. If the time scale of the variability of the source is tvar,
then the internal shocks in the ejecta form at comoving radius R′ ≈ Γ2ctvar. The
kinetic energy converted by the central engine is then reconverted by the shocks
to acceleration of protons and electrons with similar efficiency for both particles.
Similarity in the two efficiencies is necessary if cosmological GRBs are the sources
of UHECRs.
The energy in protons accelerated in the fireball is normalized to the energy
production rate required to produce the observed flux of cosmic rays at energies
1019 - 1020 eV, which in this case is taken to be about 3× 1044 erg Mpc−3 yr−1 [55].
This rate is comparable to the energy production rate of GRBs through gamma rays
using the BATSE energy range [79]. Assuming an E−2p power law for the proton
37
differential energy spectrum generated at the source, and that each product neutrino
carries about 5% of the primary proton energy, an upper limit to the neutrino flux
is obtained [55]
E2νΦν ≤ 4.5× 10−8
GeV
cm2ssr (2.27)
A Γ ≈ 300 is assumed and for typical Eγ = 1MeV , using Eq. 2.11, one gets
characteristic proton energies of ∼ 107 GeV required for pion production. This
required proton energy leads to an expected production of ∼ 105 GeV neutrinos.
This value is taken as the first break in the neutrino spectrum. The second break
energy is reasoned to be ∼ 107 GeV. The suppression beyond this energy is due to
energy loss of the pions and muons before they decay.
2.4.7 Concerning Proton Escape
Because protons are magnetically confined to the expanding fireball and the
maximum proton energy is significantly reduced due to the fireball’s adiabatic cool-
ing [80], the notion of direct proton escape as UHECRs is problematic. However,
secondary neutrons from photopion production escape the fireball unhindered. Cos-
mic ray protons thus could be identified as protons from the β-decayed escaped
neutrinos, and “a smoking-gun test of this scenario is the production of PeV neu-
trinos from the decay of the charged pions inevitably produced along with the neu-
trons” [56].
In [56], Ahlers et al. present an alternative approach to the per-burst photon
fluence normalized spectra. Instead, their approach directly fits the proton spectra
38
from the β decay of escaped fireball neutrons to HiRes I and II data [81] [82]. Their
analysis assumes that UHECRs above the 4 EeV ankle in the measured spectrum
consists of neutrons emitted from pγ interactions in internal shocks of the GRB
fireball model. The diffuse flux of neutrinos produced in association with these
GRB cosmic rays is then calculated. The authors conclude that the predicted diffuse
neutrino flux associated with GRB-produced cosmic rays exceeds the upper bound
on a diffuse flux of cosmic neutrinos obtained by IceCube with the IC40 detector
[83]. As seen in their Figure 3, the results show that predicted prompt neutrino
fluxes from typical “benchmark” fireball environments with the associated proton
spectrum fit to CR data are ruled out by the IC40 diffuse neutrino limits. “Atypical”
fireball environments with different relative synchrotron and dynamical scales have
some allowed parameter space. The predicted spectrum from secondary neutrino
production during CR propagation in the form of GZK neutrinos was also considered
under two assumptions: (1) that the comoving density of GRBs follows the star
formation rate (SFR evolution) and (2) that GRBs do not follow the SFR and may
have been stronger in the past (strong evolution).
39
103 104 105 106 107 108 109
Neutrino energy (GeV)
10−13
10−12
10−11
10−10
10−9
10−8
Per
-Fl
avo
rE
2 Φ ν
(Ge
Vc
m−
2 s−
1 sr
−1
)
Quasi-diffuse Flux Predictions: fp = 10,Γ = 300
Internal Shock Fireball Prediction
Photospheric Fireball Prediction
ICMART Fireball Prediction
103 104 105 106 107 108 109
Neutrino energy (GeV)
10−13
10−12
10−11
10−10
10−9
10−8
Per
-Fl
avo
rE
2 Φ ν
(Ge
Vc
m−
2 s−
1 sr
−1
)
Quasi-diffuse Flux Predictions: fp = 10,Γ = 600
Internal Shock Fireball Prediction
Photospheric Fireball Prediction
ICMART Fireball Prediction
103 104 105 106 107 108 109
Neutrino energy (GeV)
10−13
10−12
10−11
10−10
10−9
10−8
Per
-Fl
avo
rE
2 Φ ν
(Ge
Vc
m−
2 s−
1 sr
−1
)
Quasi-diffuse Flux Predictions: fp = 10,Γ = 900
Internal Shock Fireball Prediction
Photospheric Fireball Prediction
ICMART Fireball Prediction
Figure 2.9: Per-flavor quasi-diffuse all-sky flux predictions for different models of
fireball neutrino production, assuming fp = 10, full flavor mixing at Earth, 667
total GRBs per year and three different Γ values (300, 600, 900). Red, green, and
blue curves are the internal shock, photospheric, and ICMART models, which differ
in the radius at which photohadronic interactions occur. The solid segments indicate
the central 90% energies of neutrinos that could be detected by IceCube.40
Figure 2.10: Left panel: Step-by-step modifications to the Guetta et al.-based pre-
diction. Right panel: Numerical code applied [57]
41
Chapter 3
IceCube: The Detector, Neutrino Detection, and Event
Characteristics
3.1 The Detector
The IceCube detector [84] consists of 5160 digital optical modules (DOMs)
instrumented over 1 km3 of clear glacial ice 1450 m to 2450 m below the surface
at the geographic South Pole and is the largest neutrino detector in operation.
The detector consists of 86 “strings” of copper twisted wire pairs, each with 60
DOMs [85] positioned vertically at 17 m intervals. Adjacent strings are separated
by about 125 m. These sensors detect the Cherenkov radiation of relativistic charged
particles produced in neutrino-nucleon interactions in the ice and bedrock below.
The DeepCore array [86] is made up of a more densely spaced subset of these strings
that are located in the clearest ice at depths below 2100 m and contain higher
quantum efficiency photomultiplier tubes (PMTs). The IceTop array consists of 81
stations located at the top of IceCube strings and detects cosmic ray air showers.
Each IceTop station has two tanks of two downward-facing DOMs. Data from
IceTop DOMs are not used in this analysis.
Sensor deployment began during the 2004-2005 austral summer. Physics data
collection began in 2006 with the nine-string iteration and continued with partial
42
detector configurations through completion of the 86 strings in December 2010.
This work uses data taken from May 2010 through May 2013, with one year using
79 strings and two years using all 86 strings. Model limits presented in Chapter 7
combine the results of this analysis with those of analyses of data extending back
to May 2008, taken with 40 instrumented strings.
Figure 3.1: The IceCube detector
3.1.1 Data Acquisition
The data acquisition (DAQ) software in IceCube analyzes the packet of data,
assembled by each DOM, and checks if any of the configured trigger conditions (Sec-
tion 3.1.1.5) are met. The DAQ was designed “to capture and timestamp with high
accuracy, the complex, widely varying optical signals over the maximum dynamic
range provided by the PMT” [85]. This goal is accomplished over a decentralized
43
system, with the signal digitization done inside each DOM Main Board (MB) and
then sent to the counting house in the IceCube Laboratory (ICL) computers on the
surface. The ICL is shown in Figure 3.2. A diagram of the DOM Main Board, with
components described in the following sections, is shown in Figure 3.3.
Figure 3.2: The IceCube Laboratory (ICL). There is a cylinder on each side
through which all of the twisted copper wire pair “strings” traverse, connecting
the DOMHubs to the detector below.
3.1.1.1 Digital Optical Modules and the PMT
The first element of the IceCube DAQ is the DOM itself. Each DOM contains
a 10 in. diameter R7081-02 photomultiplier tube made by Hamamatsu Photon-
ics [85]. The PMT detects the blue and near-UV Cherenkov photons and the signal
waveforms are then time-stamped, digitized, and sent from the DOM to the ICL.
At the heart of IceCube, in the clearest ice below 2100 m, the DeepCore array con-
sists of 360 more densely spaced DOMs deployed over 8 additional strings. These
44
Figure 3.3: Diagram of the DOM Main Board. The PMT, CPU, digitizers, FPGA,
and clock are shown.
DOMs contain Hamamatsu R7081MOD PMTs, which have a quantum efficiency
that is about 40% higher than that of the otherwise identical R7081-02 at the pho-
ton wavelength 390 nm. DeepCore provides improved acceptance for neutrinos at
energies as low as about 10 GeV [86].
A photon incident on the grounded PMT cathode that overcomes the cathode’s
electron binding energy results in the emission of a photoelectron. The photoelectron
accelerates over the potential differences between the cathode and the first dynode,
knocking off electrons, which in turn knock off more electrons throughout a series of
10 linear focused dynode stages. The PMT achieves a nominal gain in signal of 107
at about 1300 V from cathode to anode [85]. An illustration of the IceCube DOM
can be seen in Figure 3.4.
45
Figure 3.4: Schematic of a DOM
3.1.1.2 Waveform Digitization
The analog signal is presented to the DOM MB signal path where it is split to
a high-bandwidth discriminator path and to a 75 ns delay line [87]. If the measured
current exceeds the discriminator threshold of 0.25 times the single photoelectron
peak, then the field programmable gate array (FPGA) initiates the capture of the
waveform. Waveform capture is accomplished by two digitization systems: the Fast
Analog to Digital Converter (fADC) and the Analog Transient Waveform Digitizer
(ATWD) [88]. The fADC digitizes the PMT signal every clock cycle (25 ns), and
determines whether the signal passes the discriminator threshold. If the 0.25 photo-
electron threshold is surpassed, then the ATWD begins capturing the delayed signal.
The ATWD is a custom designed application specific integrated circuit (ASIC) and
has three separate channels, which receive the input from three separate wide-band
amplifiers [87] The three amplifiers are characterized by progressively lower gains of
x 16, x 2, and x 0.25. In order to increase the dynamic range of the readout, the
46
next lower gain channel is read out if the previous higher-gain channel saturates.
There is also a fourth channel used only for calibration. Furthermore, “to minimize
dead time, the DOM is equipped with two ATWDs such that while one is processing
input signals, the other is available for signal capture” [87]. Each ATWD has an
array of 128 low-capacitance capacitors, which are connected to the signal for 3.3
ns each in sequence and thus hold a time series of the signal in their charge.
The ATWD is only engaged for photon signals that satisfy an imposed local
coincidence constraint. The Hard Local Coincidence (HLC) condition causes ATWD
data to be read out in a DOM only if it receives a local-coincidence-tagged pulse
from one of its neighboring or next-to-neighboring DOMs within 1 µs [87]. This
procedure allows for a high level of background rejection and reduction in data flow.
Once the HLC requirement is met, then these data is read out through the highest,
unsaturated, gain channel by the ATWD. The process of digitizing the waveform
takes 29 µs if all three channels need to be read out [87]. Data from DOMs failing
the local coincidence condition report a short summary of their recorded waveform
for inclusion in data records, and these events are colloquially known as Soft Local
Coincidences (SLC) in IceCube.
The DOM MB can be thought of as its central processor. Upon detection
of one or more photons, the MB digitizes the received PMT signals. The MB
then formats these data into the fundamental IceCube datum, the “hit.” Each hit
compiled by a DOM is made up of a timestamp and waveform information. Such
waveform information contains a coarse measure of charge and several bits defining
the hit origin. [87].
47
3.1.1.3 DOMHubs and the IceCube Laboratory
The second and third elements of the IceCube DAQ are the cable network and
DOMHub. The cable network connects adjacent DOMs to each other and DOMs on
a string to a DOMHub computer in the ICL. There is a hub computer in the ICL for
each string of the detector. Each hub contains a hard disk, power source, and single
board computer, which buffers packets of data sent to them by the DOMs. Each
cable carries power and data signal through the copper twisted-pair wires bundled
together [85].
Data rates reach ∼ 900 kb/s for the DOMs most remote from the ICL [87].
One DOMHub machine controls an entire string of 60 DOMs (or 8 stations of 32
IceTop DOMs) and stores their packets of data sent to it. The machine supplies
power and communicates with its host DOMs using several custom PCI cards, called
DOR (DOM Readout) cards. A picture of an open DOMHub is shown in Figure
3.5.
3.1.1.4 Timing
The fourth element of the IceCube DAQ is the timing calibration process.
This background-running process consists of the Master Clock and the Reciprocal
Active Pulsing Calibration (RAPCal) system. “The Master Clock makes use of the
Global Positioning System (GPS) satellite radio-navigation system, which dissem-
inates precision time from the UTC master clock at the US Naval Observatory to
our GPS receiver in the ICL” [87] [89]. The RAPcal procedure establishes a com-
48
Figure 3.5: An open DOMHub with hard disk, power source, DOR cards, and single
board computer shown.
mon time-base for all DOM hits. This calibration is accomplished by the DOM and
DOMHub sending and receiving precisely-timed RAPCal pulses to each other using
identical hardware [87]. The DOMHub calculates the travel time offset of the pulses
and the clock drift of the 40 MHz oscillator and sends the appropriate correction
instructions. This procedure is performed periodically at a frequency of 1 Hz.
3.1.1.5 Data Triggering and Formatting
The fifth and final element of the IceCube DAQ is the Stringhub program.
Stringhub resides in the DOMHub CPUs and “converts the flow of DOM hits into
physics-ready hits that are suitable at both trigger and event-building stages of the
surface DAQ” [87]. The program transforms the timestamps accompanying all re-
ceived hits into a UTC-based time domain, orders DOM hits from multiple DOMs
49
on a string, and then applies string-wide trigger filters as necessary. Stringhub com-
municates with the multi-string trigger handlers and, upon receiving the specified
hit criteria, sends a list of all matching hits and then flushes the cached information.
All of these data are buffered until the DOM MB receives a request to transfer data
to the ICL.
There are several in-ice trigger conditions checked by the IceCube DAQ. The
trigger used for the base event selection of this analysis is the requirement of 8
local coincidences within 5 µs. Time windows for any other triggers optimized for
different signal types that overlap with this 5 µs window are combined. Finally, the
waveforms of all hits recorded within -4 µs and +6 µs of this global trigger window
are combined into an “event.” The minimum energy to trigger an event in IceCube
is around 10 GeV.
3.1.2 Feature Extraction
The number and arrival times of Cherenkov photons are then extracted by re-
constructing each waveform as a series of pulses. The best fit pulse series amplitudes
and times for each triggered PMT’s waveform are determined from the linear com-
bination that minimizes the fit error [90]. The relative timing resolution of photons
within an event is 1 ns [84].
An improved feature extraction algorithm called wavedeform [91] is used in
IC86II. Wavedeform avoids the problem of adding large positive and negative pulses
together in the fit by using the Lawson-Hanson algorithm which is a non-negative
50
least squares fit. This algorithm also avoids over-fitting by only using the most
error-reducing pulse at each iteration.
3.1.3 Pulse Cleaning
Early and late noise hits that may make some reconstructions less accurate are
cleaned after the pulse series are produced. Two different cleaning algorithms are
employed. The first, called time window cleaning, keeps only the 6µs of data that
contain the most pulses out of the triggered event. The second, called seeded RT
cleaning, removes all hits that had no other hit within 1µs and 150 m. The “seeded”
part refers to the algorithm only using mostly-signal-like HLC events. Then all other
hits (SLC) in the event are included if they satifsy the RT requirements with respect
to the seeded hits.
3.1.4 Processing and Filtering
Various physics filters choose events based on different signal types. The fil-
ters are implemented by the Processing and Filtering (PnF) system, which receives
events from the DAQ. The PnF system performs the various computationally-light
reconstructions required for the online filters using a computer cluster. The server
monitors the the events being dispatched by the DAQ and distributes the events
to the clients, which are then chronologically recombined into larger files. In this
analysis, the cascade filter-passing events are used. This filter is described in Section
5.2 and uses the LineFit and Tensor-of-Inertia reconstructions.
51
3.1.5 Data Transmission to the North
The DAQ Dispatch sends the triggered data to the processing and filtering
system which reconstructs and filters events to send to the north via communications
satellites. All events are written to tape at the pole for data recovery contingency.
These backups are physically sent to Wisconsin each year and stored.
3.2 Particle Detection
IceCube detects neutrinos by their deep inelastic scattering products traveling
through the ice. Charged particles traversing a dielectric medium faster than the
speed at which light can traverse that medium produce Cherenkov radiation. This
light is emitted in a cone about the particle’s trajectory as illustrated in Figure 3.9.
The angle of the wave front is given by
θC = cos−1(
1
βn) (3.1)
where n is the index of refraction of the medium and β = v/c > 1/n. In the deep
South Pole ice, an electron or muon traveling with β ≈ 1 emits 300 to 600 nm
wavelength photons.
3.2.1 Signal Characteristics
The signal in this search is astrophysical electron, tau, and muon neutrinos
interacting in the ice with energies above 1 TeV. The Feynman diagrams for deep
52
inelastic neutrino-quark scattering that constitute these interactions are given in Fig-
ure 3.6. In charged current interactions, a W boson is exchanged and the charged
lepton corresponding to the neutrino flavor is emitted. In neutral current interac-
tions, a Z boson is exchanged and a neutrino of the same flavor is emitted.
Figure 3.6: Charged current and neutral current deep inelastic neutrino-quark scat-
tering.
The three flavors of neutrino all exhibit similar Cherenkov patterns through
Z boson exchange. In this interaction at high energies, only the hadronic shower of
baryons and mesons produced by the recoiling nucleus manifest in the detector. The
three flavors of neutrinos all exhibit different Cherenkov patterns through W boson
exchange. The three different Cherenkov light topologies in IceCube are illustrated
in Figure 3.7.
Electrons lose their energies as they emit high energy bremsstrahlung photons,
which then create an e+ e− pair. This pair, in turn, emits photons, and so on. The
resulting electromagnetic “shower” or “cascade” manifests as a spherical light pat-
tern. Tau neutrino charged current interactions produce a hadronic cascade at the
interaction vertex and a tau. The short tau lifetime usually means that it decays
within the initial cascade. At energies beyond a few PeV, the tau travels a long
53
Figure 3.7: Electron (left), tau (middle), and muon (right) flavored neutrino high
energy charged current interaction topologies in IceCube.
enough distance to show a “double bang” topology. This type of event has yet to
be observed in IceCube data. Muons traversing the detector produce “tracks” of
Cherenkov light as they lose their energies much more slowly than electromagnetic
cascades. The signal for this search is all neutrino interactions that produce cas-
cades, which means all of the above except for charged current νµ and PeV energy
charged current ντ .
Another possible high energy neutrino interaction that can be observed is
the Glashow resonance, which occurs when a ν¯e with energy ≈ M
2
W
2me = 6.3 PeV
resonantly scatters off of an electron to produce a W− [92]. The cross section for
this resonance is much larger than the charged-current cross section at this energy
as shown in Figure 3.8. The Glashow resonance has yet to be observed but the
decay leptons and hadrons would induce PeV-scale cascades in the ice [93] [94].
3.2.2 Background Characteristics
The primary background of this analysis is muons catastrophically losing their
energies through stochastic processes with little apparent Cherenkov track tail.
54
Figure 3.8: Cross sections of neutrino and anti-neutrino charged-current and neutral-
current interactions as a function of neutrino energy. The Glashow resonance is also
plotted. Plot from [95].
These muons are produced by cosmic rays interacting with the atmosphere. Muons
can lose their energies in the ice through ionization, bremsstrahlung, photo-nuclear
interactions, and pair production. The energy and loss profiles of these processes
are shown in Figure 3.10.
Another background of this search is neutrinos also from cosmic ray air show-
ers. This background is nearly irreducible because the signal is neutrinos as well.
Atmospheric neutrinos can be weighted down to some extent in the likelihood anal-
ysis by their lower energies on-average than the expected astrophysical signal.
Muons dominate the data rate at all event selection levels of this search. There-
fore, data events not within two hours of any reported GRB γ emission are used for
the background dataset in this analysis.
55
Figure 3.9: Two-dimensional schematic of cascade and track event topologies in the
detector
Figure 3.10: The different processes for muon energy loss in IceCube. From [96].
56
Chapter 4
Simulation and Reconstruction Techniques
This chapter describes the simulation of particle interactions in and around
the detector as well as the techniques used to describe real and simulated events.
Monte Carlo simulations model the detector response to both neutrino signal and
muon background. These simulated data allow for accurate estimations of signal
sensitivity and better understanding of the actual data. Event reconstructions use
the timing, position, and intensity of Cherenkov light recorded by the DOMs to
better describe the events that generated the light. Many features are calculated
from these reconstruction algorithms and then are used for particle identification.
4.1 Simulation Methods and Description
Monte Carlo simulations of signal neutrinos interacting in the IceCube de-
tector are used for the signal hypothesis in the event selection and optimization
for this search. Although data outside of GRB gamma-ray emission time win-
dows are used for the background, simulated neutrinos and muons generated in
cosmic-ray air showers are useful checks for background characterization and esti-
mating the signal purity of the final data sample. Neutrinos are generated with the
NEUTRINO-GENERATOR program, a port of the ANIS code [97]. NEUTRINO-GENERATOR
is used to distribute neutrinos with a power-law spectrum uniformly over the entire
57
sky and propagate them through the earth and ice. The simulated neutrino-nucleon
interactions take cross sections from CTEQ5 [98]. The Earth’s density profile is
modeled with the Preliminary Reference Earth Model [99]. The propagation code
takes into account absorption, scattering, and neutral-current regeneration.
Each generated neutrino is given an interaction vertex in or near the detector
volume and a probabilistic weight for this interaction. This weight can then be
manipulated further through multiplication by a model energy spectrum, e.g. E−2
for the optimization of this analysis. For the atmospheric neutrino background, the
Honda et al. spectrum [100] is applied. For electromagnetic and hadronic showers
greater than 1 TeV, the longitudinal profile of the Cherenkov light output is taken
into account. Muons from cosmic-ray air showers, using the CORSIKA simulation
package [101], and νµ interactions are traced through the Antarctic ice and bedrock
incorporating continuous and stochastic energy losses [96]. The PMT detection of
Cherenkov light from showers and muon tracks is simulated using ice and dust layer
properties determined in detailed studies and simulations [102] [103]. Finally, the
DOM triggering and signal is simulated from the aforementioned interactions.
4.2 Reconstruction Methods
The reconstruction methods described below identify physical parameters that
can be used to classify events. The neutrino-induced cascades for which this analysis
searches exhibit different values for these physical parameters compared to muon-
induced tracks. Thus, these reconstructed features are used to identify potential
58
astrophysical neutrinos in Chapter 5 in order to then test the hypothesis that GRBs
emit these particles in Chapter 6.
4.2.1 Tensor of Inertia
The tensor of inertia algorithm [104] involves an analytic calculation of a “cen-
ter of mass”, where the mass terms correspond to the number of photoelectrons
(PMT amplitude) a recorded by each DOM at position −→r with respect to the cen-
ter of the detector:
−→R com =
NhitDOMs∑
i=1
(ai) · −→r i (4.1)
The inertia tensor is calculated using the PMT amplitudes and DOM positions
{−→x i = −→r i −
−→R com
}
with respect to the center of mass:
Ij,k =
NhitDOMs∑
i
ai · (δk,j|−→x i|2 − xjixki ) (4.2)
where xli refers to the xˆ, yˆ, or zˆ component of the i’th DOM position.
Furthering the rigid body analogy, the smallest eigenvalue corresponds to ro-
tation about the longest principal axis. This axis provides a reasonable guess for
muon track trajectory. The direction of the primary particle is inferred from the di-
rection in which the average DOM hit time is latest. An electromagnetic or hadronic
cascade yields nearly equal eigenvalues.
59
4.2.2 LineFit
The line-fit algorithm [104] is an analytic calculation that approximates a
charged particle producing Cherenkov light as a planar wavefront traveling with
some constant velocity through the ice. Given the position −→r i and leading pulse
time ti of each hit DOM in an event, the best-fit track and velocity of the particle
are calculated.
This calculation entails minimizing a function of residuals:
min
t0,−→x 0,−→v
NhitDOMs∑
i=1
ρi(t0,−→x 0,−→v )2 (4.3)
where
ρi(t0,−→x 0,−→v ) = |−→x i −−→x 0 −−→v (ti − t0)| (4.4)
for the reconstructed track passing through a point −→x 0 at time t0 with velocity −→v .
Solving this minimization gives
−→r 0 = 〈−→r i〉 − −→v · 〈ti〉 (4.5)
and
−→v = 〈
−→r i · ti〉 − 〈−→r i〉 · 〈ti〉
〈t2i 〉 − 〈ti〉2
(4.6)
where the angle brackets denote an average over all hit DOMs, e.g.
〈−→r i〉 ≡
1
NhitDOMs
NhitDOMS∑
i=1
−→r i (4.7)
60
This algorithm was improved recently [105] to (1) filter and discard late-
arriving hits that occur over 778ns later than any other hits within a 156 m radius
and (2) perform a Huber fit [106] that penalizes potential outlier hits over 153 m
from the source before performing the above least-squares fit with the outlier hits
removed. The parameters in (1) and (2) were optimized using simulated muons.
These improvements effectively discard hits from scattering in the ice and noise
that degraded the quality of the initial result.
While this fast algorithm is tuned to track-like events, the calculated speed
of the assumed track often provides a good indicator for spherical showers. Low
speeds correspond to spherical events, while near-speed-of-light speeds correspond
to minimally ionizing muon tracks.
4.2.3 CascadeLlh
CascadeLlh is a likelihood-based reconstruction of the time, vertex position,
and energy of a neutrino interacting in the ice, assuming a neutrino-induced cascade
hypothesis. The likelihood problem to solve is as follows: What is the set of cascade
parameters −→a = {a1, a2, ..., am} that maximizes the likelihood function
L({−→x } |−→a ) =
n∏
i=1
p(−→xi ;−→a ) (4.8)
for given sets of observables {−→x } = {−→x1,−→x2, ...,−→xn} of an event? Maximizing L for
the set of hit DOMs of an event lets one solve for the time, vertex position, direction,
and energy (−→a = {t, x, y, z, θ, φ, E}) of the hypothesized cascade-inducing neutrino.
61
No probability distribution functions (PDFs) describing directionality or energy are
used for this reconstruction in this analysis and so the angles θ and φ and the energy
are fixed to the values taken from their seeds, which are described below.
For this reconstruction, the event observable −→xi = {ti, xi, yi, zi} are the time
corresponding to the leading edge of the waveform and the position of the i’th hit
DOM. Specifically, the −→xi for each DOM’s PDF is parametrized in terms of the time
residual :
tres ≡ ti − tdirect = ti −
(
tv +
|−→r i −−→r v|
cice
)
(4.9)
where tv and −→r v are the interaction vertex time and position. tres does peak near
zero for DOMs close to the vertex, but is often positive especially for farther DOMs
since photons often experience scattering in the ice, as discussed in Section 4.1.
tres can also be negative due to PMT jitter [85] and random dark noise hits. The
vertex position is seeded by the center of mass −→R com calculated in Equation 4.1.
The seed vertex time is determined by the following steps: (1) pick one hit DOM
and calculate a trial vertex time
(
thit − |
−→r i−
−→RCOM |
cice
)
; (2) calculate tres for all other
hit DOMs using the trial vertex; (3) repeat steps (1) and (2) for all hit DOMs; and
(4) choose the seed vertex time as the earliest trial tv such that there are greater
than 4 “direct hits” in which 0 ≤ tres ≤ 200 ns.
Thus, p(tres,i|−→a ) gives the probability of measuring a single photoelectron
generated in a cascade with parameters −→a at a given DOM i. This probability can
be calculated by using photon hit probability and arrival time distribution look-up
tables. However, as noted in [104], an analytic function can be calculated for this
62
probability much more quickly than using the archived tables and with good results.
This analytic function that parametrizes p(tres,i|−→a ) as a function of the distance d
from the cascade vertex is named the “Pandel function” after the researcher who
derived it in an analysis of laser light signals in the BAIKAL experiment. This
function is expressed as follows:
p(tres|d) ≡
1
N(d)
τ−(d/λ)t(d/λ−1)res
Γ(d/λ) × e
−(tres( 1τ + ciceλa )+ dλa ) (4.10)
where the normalization factor
N(d) = e−d/λa
(
1 + τciceλa
)−d/λ
(4.11)
and the speed of light in ice cice = cvac1.31 and the absorption length λa = 98.0 m.
There are also two empirically determined free parameters used for this likelihood
reconstruction τ = 450.0 ns λ = 47.0 m [107].
Further, p(tres|d) is modified in order to more accurately describe the detector.
First, negative values of tres are accommodated to account for the DOMs’ imperfect
timing resolution with a half Gaussian function in this regime. Mean µ = 0 ns and
σjitter = 15 ns are chosen for this Gaussian because 10 ≤ σjitter ≤ 20 ns yield the best
reconstruction results. The original Pandel function is used for tres >
√
2piσjitter and
a spline interpolation to connect these two domains. Second, a small flat probability
of 10−10 is added to the function to account for noise hits. This modifed Pandel
function is refered to as the UPandel, which as the form:
63
pU(d, tres) =



p1 for tres < 0;
p2 for 0 ≤ tres <
√
2piσjitter;
p3 for
√
2piσjitter ≤ tres.
(4.12)
where the functions p1, p2, p3 are:
p1 = A
1√
2pi σjitter
exp(−t2res/2σ2jitter) , (4.13)
p2 = c0 + c1tres + c2t2res + c3t3res (4.14)
and
p3 = p(tres|a) (4.15)
The parameters A, c0, c1, c2, and c3 are determined by requiring that the
UPandel function is continuous and differentiable at tres = 0 and tres =
√
2piσjitter,
the slope is zero at tres = 0, and the integral over time from tres = −∞ to tres =∞
equals 1. Therefore, the final likelihood to maximize for this reconstruction is:
L({−→x } |−→a ) =
n∏
i=1
pU(−→xi ;−→a ) (4.16)
Using a minimization software package [108], the likelihood function is max-
imized by minimizing − log(L) with respect to the parameters −→a . In order to aid
the minimizer and improve reconstruction performance, this reconstruction is seeded
with a first guess interaction vertex, interaction time, and energy The seed vertex is
the center of mass calculation in Equation 4.1. The seed vertex time is the earliest
64
time such that there are greater than 4 direct hits on DOMs within 100 m of the ver-
tex. A direct hit for this calculation is defined as a DOM hit with a time residual less
than 200 ns For a DOM at location −→r i hit at time ti, this time residual is defined as
the difference between an unscattered-light trial vertex time
(
ti − |
−→r i−
−→RCOM |
cice
)
and
the interaction vertex time.
4.2.4 SPE
The single photoelectron or SPE fit is a maximum likelihood fit based on
a muon track hypothesis [104]. A likelihood function is maximized, expressed by
Equation 4.8, the same way as described for CascadeVertexLlh above. The likelihood
function used for this reconstruction is the modified Pandel function of Equation
4.12 as well. The empirically determined free parameters of the Pandel function take
the values τ = 557.0 ns and λ = 33.3 m. These parameters have different values for
track and cascade hypotheses because The time residual for this reconstruction is
tres = ti − tgeo = ti −
(
t0 +
pˆ · (ri − r0) + d tan θc
cvac
)
(4.17)
The geometry in figure 4.1 illustrates the time residual calculation. In this
reconstruction, an arbitrary vertex position is chosen and a time along the track is
specified by the direction pˆ. This reconstruction is seeded with the results of the line-
fit algorithm. Although this reconstruction is primarily used for track directions, it
is useful in this analysis in its ability to sift out track-like topologies in the muon
background. The SPE reconstruction values after four iterations are used in this
65
Figure 4.1: Schematic of Cherenkov light front interacting with an optical module
(OM) in the ice
analysis.
4.2.5 Analytic Energy Reconstruction - ACER
For a fast analytic dedicated energy reconstruction [109] for cascades, a Pois-
sonian distribution for the total number of detected photons by a DOM from a
point-like source is taken. The likelihood function then for a given energy E, ob-
served number of photoelectrons k, and expectation λ:
L(E) =
NDOMs∏
i=1
λi(E)ki
ki!
e−λi(E) (4.18)
66
An expected number of photoelectrons in a DOM from a shower event is defined
with some reference energy (1 GeV here) as Λ. Λ is an amplitude that corresponds
to the amount of photoelectrons that reach the PMT. The expectation λ can then be
expressed as (E/(1GeV)Λ = E1Λ due to the linear relationship between Cherenkov
light emission and deposited energy..
After first taking the log of L, this likelihood is maximized with respect to
energy:
0 = ∂L(E)∂E =
∂
∂E
NDOMs∑
i=1
(ki log(E1Λi)− (E1Λi)− log(ki!)) (4.19a)
=
NDOMs∑
i=1
( kiΛiE1Λi
− Λi) (4.19b)
=
NDOMs∑
i=1
ki
E1
−
NDOMs∑
i=1
Λi (4.19c)
and therefore
E = 1GeV ×
∑
ki∑Λi
(4.20)
An intuitive energy calculation is left. The total energy deposited by a neutrino-
induced electromagnetic cascade is the number of photoelectrons recorded divided
by the number of photoelectrons expected by a 1 GeV neutrino, times 1 GeV.
The template function, Λ, used to calculate the expected number of photo-
electrons from a reference point source is evaluated with tabulated Monte Carlo
simulation of light propagation through the ice [85, 110, 111]. The energy recon-
struction described in this section was developed for the first cascade analysis in
IceCube designed to detect atmospheric neutrino interactions [112], and so is named
67
AtmCscdEnergyReco, and hereafter referred to as ACER. The primary purpose of
ACER in this analysis is to provide an energy to the following more computationally
intensive cascade-hypothesis reconstruction.
4.2.6 Credo
Once the filtered data is transmitted beyond the South Pole via satellite, more
computationally expensive likelihood-based reconstructions are calculated. The first
of these reconstructions is performed over the complete seven parameter (E, t, x,
y, z, θ, φ) cascade. This reconstruction was developed for prior atmospheric cas-
cade searches is called Credo [113, 114]. The detection of light follows a Poisson
distribution and thus the likelihood function to maximize is
L(k|E, t, x, y, z, θ, φ) =
NDOM∏
i=1
λkii
ki!
e−λi (4.21)
for the observed and expected number of photoelectrons k and λ in each DOM from
a neutrino traveling in direction θ,φ and depositing energy E at time t and vertex
(x, y, z) [109].
Due to the linear relationship between Cherenkov light emission and deposited
energy the energy is still estimated by comparing to a template event of 1 GeV. The
seed is composed of different prior reconstructions: the tensor-of-inertia direction,
CascadeLlh interaction vertex and time, and ACER energy. Given the shower vertex
and orientation, and the same ice model-dependent tables of photon amplitudes
and time delays used with ACER, the negative log-likelihood is minimized using
68
MINUIT [115] and the best-fit particle parameters are extracted.
4.2.7 Monopod
Another likelihood-based algorithm is run with the Credo results used as the
seed. This reconstruction is called Monopod, and is the the single source specializa-
tion of the general Millipede likelihood [109] which considers multiple light sources,
e.g. for stochastic muon losses along a path through the detector. Because the
signal of this search is defined to be neutrino-induced showers, and showers act as
point-like light sources at all energy scales in IceCube [116], only the single source
hypothesis is necessary.
The likelihood function is the same Equation 4.21 above, but spline-fit tables
of photon amplitudes and time delays are used instead of coarse photon tables.
Additionally, unlike the above reconstructions, an explicit noise rate input (450
Hz used for ACER and Credo) is not required as Monopod handles noise on its
own, reading in the hardware calibration from each simulation or data run. The
minimization is iterated five times to achieve ∼ 30◦ angular resolution, which, with
three flavor acceptance, allows for sensitivities comparable to previous νµ track-
optimized GRB neutrino flux searches. Consequently, the five-iteration Monopod
reconstructed direction and energy are used for each event in the likelihood analysis
detailed in Chapter 6.
The angular resolution capabilities for the different reconstruction techniques
described in this chapter are shown in Figure 4.2 for simulated astrophysical νe at
69
0 20 40 60 80 100 120 140
Cumulative Point Spread Function [◦]
0.0
0.2
0.4
0.6
0.8
1.0
Fr
ac
tio
n
Calculated for νe Signal
Monopod5iter median = 29.34◦
Monopod1iter median = 37.62◦
Credo median = 55.08◦
Cscdllh median = 85.32◦
ToI median = 84.6◦
Figure 4.2: Cumulative point spread functions with median angular resolutions
shown for different reconstructions of simulated astrophysical νe at final event se-
lection.
final event selection. This figure shows the cumulative point spread function, where
each y-axis value is the percentage of events that yield less than or equal to the
corresponding angular difference between truth and reconstruction on the x-axis.
Five iterations of Monopod clearly achieves the best directional reconstruction of
the set.
4.2.8 Cramer-Rao
A lower bound on the error in the reconstructed directions is estimated by
the Cramer-Rao relation [117–119] between the covariance of each fit parameter
cov(am, an) and the inverted Fisher information matrix J(−→a ). For the unbinned
likelihood analysis, detailed in Chapter 6, five iterations of the Monopod reconstruc-
70
tion is used for the estimated direction of each event. Thus, the Fisher information
matrix is given by
Jm,n(−→a ) = −
〈∂2 lnL(−→a )
∂am∂an
〉
(4.22)
where L and −→a are the likelihood and fit parameters of the five iterations Monopod
reconstruction and only hit DOMs are considered.
Because the Cramer-Rao bound is used in this analysis for estimating the
error in the direction, the variances of the zenith σθ =
√
(J−1)θθ and azimuth
σθ =
√
(J−1)θθ are taken. Finally, the circularized per-event error is calculated as
follows:
σCR =
1√
2
√
σ2θ + σ2φ sin2(θMonopod5) (4.23)
71
Chapter 5
Event Selection
The signal in this search is one or more high energy neutrino-induced showers
coincident in space and time with one or more GRBs. Before one can analyze the
likelihood that an event is a GRB-emitted neutrino, one must reduce the over 2.5
kHz triggered data that is dominated by cosmic ray air shower muons to a much
smaller 0.2 mHz selection of possible signal. The geometric pattern, timing, and
amount of recorded photons are used to reconstruct the time, location, direction,
and energy of interacting neutrinos and muons, remove background, and realize the
final sample of signal-like events.
Searches for neutrino-induced showers from astrophysical and atmospheric
sources have been conducted previously in IceCube [112, 120–122]. The predom-
inant difference between these and the search presented in this paper is that this
search assumes neutrinos come from known transient sources. The previous shower-
like event selections assume a diffuse signal or constantly emitting sources and, as a
result, require much more stringent background reduction that leads to data rates
nearly a factor of 100 smaller than what is needed in this search. Cascade con-
tainment constraints in the detector were imposed to reach these low backgrounds,
which are achieved in this search by the effective cuts in time and space around each
GRB in the unbinned likelihood analysis presented in the next chapter.
72
5.1 Level 1: Trigger at South Pole
This analysis starts with the SMT8 trigger requirement of 8 local coincidences
of DOM neighbors or next-to-nearest neighbors within 5 µs. As described in Section
3.1.1.5, the time windows of other signal-specific triggers that overlap with this 5
µs are included as well. Finally, the waveforms of all hits recorded within -4 µs and
+6 µs of the global trigger window are combined into an “event.”
Under this triggering system, IceCube assembles events at a rate of over 2.5
kHz. Most of these events are muons produced in air showers from cosmic rays
bombarding the atmosphere. The task of the following event selection stages is to
reduce this dominating background to a sample of events that could be astrophysical
neutrinos. The final sample does not need to achieve near 100% neutrino purity be-
cause further discrimination is achieved through the unbinned likelihood probability
distribution functions, detailed in Chapter 6.
5.2 Level 2: Cascade Event Filter at South Pole
The first class of background to remove is track-like events generated by muons
losing their energy through continuous ionization processes. This background of
muon tracks is relatively easily separated from the shower-like neutrino signal by use
of a filter run online at the computer farm located above the buried detector. During
the 79-string configuration, two analytic reconstructions described in Section 4.2 are
used to select events with spherical DOM hit topology, indicative of electromagnetic
or hadronic neutrino-induced showers. The CascadeLlh reconstruction is used for
73
the slightly more sophisticated 86-string filter. Both filters reduce the data rate to
around 30 Hz, which is still comprised almost entirely of atmospheric muons that
shower through stochastic processes.
The two calculated parameters used for this initial selection in IC79 are the
tensor-of-inertia eigenvalue ratio and line-fit absolute speed. Using the rigid body
analogy, a spherical shower should provide nearly even tensor-of-inertia eigenval-
ues, while an elongated track should have one eigenvalue much smaller than the
other two. Additionally from line-fit, showers typically provide slower best-fit pla-
nar wavefront speeds than the near speed of light fit tracks.
The online cascade filter for the first two years of the 86-string configuration
imposes SPE reconstructed zenith-dependent cuts to allow more events with en-
ergies below 10 TeV. A cut on the reduced log-likelihood value from CascadeLlh
is implemented to remove many of the muons misreconstructed as upgoing. The
down-going region, which has a greater number of events than the up-going region,
requires a harder reduced log-likelihood cut in combination with the same online
79-string filter selection from above.
The cut parameters for the IC79 cascade filter are as follows:
1. evalratio > 0.05
2. linefit-speed < 0.10 m/ns
The cut parameters for the IC86I and IC86II cascade filters are as follows:
1. Up-going (cos (θzen) < 0.20):
74
(a) cscdllh-rlogl < 11.75
2. Down-going (cos (θzen) ≥ 0.20):
(a) cscdllh-rlogl < 9.50
(b) evalratio > 0.10
(c) linefit-speed < 0.12 m/ns
Below are the E−2-weighted νe signal efficiencies with respect to the SMT8
trigger per energy bin for the 79-string (left) and 86-string (right) detector cascade
event filter selections. The Monte-Carlo truth νe energy distributions at trigger and
filter levels are also shown. Both energy distributions peak at about 10 TeV and
the Glashow Resonance, described in Section 3.2.1, at 6.3 PeV is apparent as well.
Figure 5.1: Left axis: IC79 (left) and IC86I (right) Cascade Filter E−2-weighted νe
signal efficiency with respect to the SMT8 trigger per energy bin. Right axis: Monte-
Carlo truth νe energy distributions at trigger-level and filter-level. The IC86II (left)
Cascade Filter selection is equivalent to the IC86I selection.
75
5.3 Level 3
Upon transmission via satellite from the South Pole, the ∼30 Hz filtered data
of spherically shaped events can be further reduced to about 1 Hz using cuts de-
veloped visually from background and signal distributions. The background at this
Level 3 is still dominated by atmospheric muons that lose their energy through
bremsstrahlung, photonuclear interactions, and pair production, but allows for sen-
sible performance with the BDT forest algorithm described in Section 5.4.4. These
stochastic energy loss mechanisms in muons create nearly spherical hit patterns
that are difficult to differentiate with the neutrino-induced shower signal when the
muon track is at the edge or outside of the detector and therefore not observed.
Even though the background muons after the online filter selection are shower-like
in topology, the Cherenkov light hit patterns of the minimally ionizing muon track
are exploited when possible to differentiate from neutrino-produced electromagnetic
or hadronic showers.
The discrimination variables at this level are derived from the more CPU-
intensive reconstructions run offline. The cut values were optimized on IC79 data
by a colleague for the collaboration with the aim of providing a sub-1 Hz shower-like
data sample on which to develop more sophisticated neutrino-level event selections.
This analysis takes advantage of this sample’s separation of stochastic energy-loss
muons from high energy neutrinos for eventual machine-learning input. A differ-
ent Level 3 event selection was developed using IC86I data, but sacrificed signal
efficiency for higher neutrino purity, needed by diffuse astrophysical neutrino flux
76
searches. This stricter selection reduced this search’s sensitivity because high purity
is achieved in this search by using the transient nature of the hypothesized GRB
signal. As a result, the IC79-optimized Level 3 event selection is used on all three
seasons of this search, with slight alterations in IC86I and IC86II.
The further separation of signal from muon track background is achieved
through two levels of cuts using the fast track hypothesis, SPE, and cascade hypoth-
esis, CascadeLlh, analytic likelihood function reconstructions. The first Level 3 cut
is on events for which the logarithm of the ratio of the track likelihood to the cascade
likelihood heavily favors the track hypothesis. Two other background muon features
that are taken advantage of are their down-going directions and typically lower en-
ergies. Consequently, the track likelihood reconstructed zenith is parametrized in
terms of the ACER reconstructed energy, removing low energy down-going events
from the sample. Events imparting at least 10 TeV are kept regardless of their like-
lihood ratios and reconstructed zeniths. This first selection stage of Level 3 reduces
the 30 Hz Level 2 online filter rate to around 5 Hz. The distributions of 79-string
data and simulated astrophysical and atmospheric νe for each selection variable are
shown with the respective cut values in Figures 5.2 and 5.3. The 86-string data and
simulation distributions are similar to those of IC79.
Lastly at this level, signal-like events that exhibit a large fraction of hit DOMs
inside of a sphere centered on the reconstructed vertex with a radius determined by
the mean hit distance are selected. This calculation is referred to as the fill-ratio, and
the radius and fraction filled of the sphere are optimized separately for reconstructed
vertices inside and outside of the instrumented volume. Both volume regions are
77
Figure 5.2: Track-to-cascade likelihood ratio distribution at Level 2 for background
muon-dominated data, atmospheric νe, and astrophysical νe. Level 3 events are kept
to the left of the vertical line.
Figure 5.3: Cosine of SPE zenith versus ACER energy distribution at L2 for back-
ground muon-dominated data (left) and astrophysical νe (right). Level 3 events are
kept below the parametrized line.
78
incorporated in this search. This second stage of cuts yields a combined contained
and uncontained data rate of about .7 Hz. The distributions of 79-string data and
simulated astrophysical and atmospheric νe for both the contained and uncontained
fill-ratio are shown with the respective cut values in Figure 5.4. As with the pre-
vious selection variable distributions above, the 86-string detector distributions are
similar.
Figure 5.4: Fill-ratio distributions at Level 2 for the contained (left) and uncon-
tained (right) branches for background muon-dominated data, atmospheric νe, and
astrophysical νe. Level 3 events are kept to the right of the vertical line.
The cut parameters for the Level 3 event selection are given below. The
track-to-cascade likelihood ratio and uncontained fill-ratio cut values were loosened
slightly for the IC86I and IC86II data compared to IC79 in order to achieve similar
signal rates. The 86-string detector cut values are in parentheses.
1. Stage 1:
(a) track-cscd-llhratio < 5 (6)
(b) cos (SPE.zenith) < θparam ≡ 0.36 + 0.16 log 10(EACER/GeV)
79
2. Stage 2:
(a) fill-ratio, contained events > 0.50
(b) fill-ratio, uncontained events > 0.35 (0.30)
Figure 5.5 shows the IC79, IC86I, IC86II E−2-weighted νe efficiencies per en-
ergy bin for Level 3 and each of its stages, detailed above. The relatively lower
percentage of 86-string signal kept from the Level 2 filter at 10 TeV and lower en-
ergies compared to 79-string signal is attributed to the relatively higher amount
of signal kept at these energies at Level 2. The different data rates in the figures
from those in Table 5.1 are due to the fact that these rates are calculated from one
eight-hour data-taking run for each season, and rates can vary by a few percent.
5.4 Final Event Selection
After the data rate is reduced to below 1 Hz, the final event selection employs
a machine learning algorithm to optimize the signal-background separation over a
many parameter space. At the Level 3 data rate, stochastic muon losses with little
or no tail in and around the detector volume still dominate the data and strongly
resemble neutrinos. The problem of separating these two types of events is ideal for
a supervised machine learning classification algorithm.
Generally, supervised learning involves constructing a statistical model for
predicting an output based on one or more inputs [123]. In this case, the inputs
are muon-dominated data background events and simulated neutrino signal events.
Each event input includes its background / signal classification, which the statistical
80
Figure 5.5: Components of Level 3 νe signal efficiency with respect to the Level 2
Cascade Filter per energy bin for IC79 (top), IC86I (middle), IC86II (bottom). The
magenta line is the total Level 3 efficiency curve.
81
model aims to predict, as well as values for discriminator variables, which the model
uses to predict the classification. In such a problem, the inputs are separated into
training and testing sets. The training set is used to develop the model while the
testing set is used to ensure the model is not overly fit to peculiarities in the training
set [123]. The model is designed to separate the signal and background events in
the multivariate space as much as possible. The model implemented in this analysis
assigns a score that denotes whether a particular event is background muon-like or
signal neutrino-like.
The algorithm used to create this statistical model is a boosted decision tree
forest (BDT) [124], that also has been used in Northern Hemisphere νµ track GRB
coincidence searches in IceCube [16, 17]. The forest takes as input a collection of
signal and background discrimination variables, many of which were influenced by
past neutrino-induced shower searches conducted in IceCube. A separate BDT is
trained with configuration-specific signal simulation and background data for each of
the three year-long detector configurations of this search. The BDT software used for
this work is a Python-based package written by a colleague and is now the standard
tool for machine-learning-based classification in the IceCube collaboration [125].
5.4.1 Machine Learning: Boosted Decision Tree Forests
The BDT machine learning algorithm used in this search for astrophysical
neutrino-induced cascades involves a collection of sequentially trained classifiers, or
a “forest of trees.” The training begins with designated signal events and designated
82
background events. The signal used for this analysis is a flux of simulated νe events
with an E−2-weighted spectrum distributed evenly over the sky. The background is
a collection of events from IceCube data that did not occur within two hours of any
reported GRB γ emission to prevent bias. These off-time data events were chosen
as background because, as shown in Section 5.3, the atmospheric muon rate still
dominates any presence of astrophysical neutrinos at the 1 Hz level.
The algorithm takes as input a collection of signal and background discrimina-
tion variables, described in Section 5.4.2. A tree begins with a root node. The dis-
crimination variable values for signal and background events are each histogrammed
with a user-defined bin size at this node. The cut choice at a variable bin boundary
that best separates the signal and background events into child nodes is determined.
The best separation can be defined different ways using the signal purity of the child
nodes.
For this analysis, the Gini separation criterion is used to judge cut effectiveness
at a tree node. Let the weight of a simulated signal event s, discussed in Section 4.1,
be defined as ws; and let the weight of a background off-time data event b, which is
the background rate at pre-BDT event selection, be defined as wb; and let the sum
of all signal and background event rates at a given node be defined as
∑
s
ws +
∑
b
wb = W (5.1)
83
The Gini separation criterion is defined as
SGini(p) = p · (1− p) (5.2)
where
p =
∑
sws
W , (1− p) =
∑
bwb
W (5.3)
are the signal and background purity of a given node, respectively. Thus, a purely
signal or purely background node has a SGini of 0.
At each node the algorithm chooses the cut on a variable bin boundary that
maximizes the signal-background separation into its child nodes. The separation
gain from the parent node to the child nodes L and R is calculated as follows:
∆S = W · SGini(p)− (WL · SGini(pL) +WR · SGini(pR)) (5.4)
This procedure is repeated for the child nodes, their children, and so on until
one of several user-defined stopping criteria is fulfilled. The stopping criteria defined
for this analysis are a SGini of 0 in a node or a maximum depth of five levels of nodes.
The final classifying nodes in a tree are called “leaves.” If pleaf > 0.5, all events in
that leaf are classified as signal and given a value of 1. If pleaf < 0.5, all events in
that leaf are classified as background and given a value of -1.
The BDT algorithm consists of a forest of trees trained sequentially. After
the growth of one tree ends, the classification performance of that tree is assessed,
and incorrectly classified events are weighted more heavily so in effect “boosting”
84
the subsequent tree’s performance. This analysis uses the AdaBoost, or “adaptive
boosting,” algorithm [124]. The event reweighting is calculated in the following
way. For event i, define the true classification yi that equals +1 for signal and -1 for
background. Similarly, define the tree-scored classification si. Let the identity test
function for each event in a tree be
It(yi, si) =



0, yi = si
1, otherwise
(5.5)
For each tree t, define the tree error as
et =
∑
i
wiIt(yi, si)
W (5.6)
and the boost factor as
αt = β ln
(1− et
et
)
(5.7)
where β is the user-defined boost strength. Finally, the signal and background
events are reweighted for tree t+ 1 with the factor
wi → eαtIt(yi,si)wi (5.8)
The error et and boost αt for each tree in the IC86I BDT are given in Figure 5.6.
The boost factors correspond to the tree weight in the final scoring. Later trees that
attempt to classify the toughest events have less weight than earlier trees.
The sum of all signal and background event weights are normalized to one
85
0 50 100 150 200Tree Number
0.0
0.1
0.2
0.3
0.4
0.5
e t
IC86I BDT Forest Tree Errors
0 50 100 150 200Tree Number
0.0
0.1
0.2
0.3
0.4
0.5
α t
IC86I BDT Forest Tree Boost Factors
Figure 5.6: Per-tree errors (et, left) and boost factors (αt, right) for the IC86I BDT.
before each tree is trained such that
∑
uwi = W = 1. The boosting method
outlined above is cumulative and forces exaggerated signal/background purity of
nodes with previously misclassified events. This boosting consequently assists the
maximization of ∆S for proper classification. The overall score of each event by the
forest, si is an average of the individual tree classifications, (si)t weighted by the
tree-specific boost factors, αt:
si =
∑
t αt(si)t∑
t αt
(5.9)
It is important to keep a set of signal and background events separate from
the training set, but originally from the same distributions, in order to test the
trained BDT model. Upon reaching sufficient signal/background separation, one
may find that the BDT score distributions of the training and testing samples differ
substantially. This difference would be due to overtraining. A model may be trained
so precisely on a dataset, that statistical fluctuations and outlier characteristics in
86
those data are part of the model. As a result, data from the same distribution as
the training set will be classified differently.
This type of overtraining that leads to disparity in the training and testing
data BDT score distributions can be identified by a Kolmogorov-Smirnov (KS) test
[126,127]. The KS test calculates the probability the null hypothesis - that two data
samples are drawn from the same distribution - is rejected. The KS statistic Dn,m
is the maximum of the difference between the cumulative distribution functions of
two data samples 1 and 2 of sizes n and m, respectively:
Dn,m =
∣∣F 1n(s)− F 2m(s)
∣∣ (5.10)
Given Dn,m and the limiting cumulative distribution function L(z) of
√ nm
n+mDn,m,
the null hypothesis is rejected at level z if
Dn,m > L(z)
√
n+m
nm . (5.11)
Training for each BDT of the three detector configurations was tuned until
the KS p-value was above 10% for each sample. The BDT score distributions of the
training (solid lines) and testing (dashed lines) of the signal (blue) and background
(red) data samples are shown below for an overtrained BDT and the final BDT for
IC86I. The KS p-values (z above) are given in the legends of the figures.
In order to reduce overtraining, one may apply the process of pruning to each
tree in the BDT forest. This process is called pruning because it involves removing
87
leaf nodes from a tree. Upon their removal, the respective parent nodes are then
turned into leaves. Pruning is performed for each tree before the boost factor αt is
calculated and the succeeding tree is created.
A simple pruning procedure occurs automatically in the BDT algorithm and so
is used for all three detector configuration BDTs. If a node cut creates two children
signal leaves or two children background leaves, those leaves are removed and the
parent node becomes a leaf. These pruned leaves would offer no further separation
themselves and are expendable.
A slightly more involved pruning procedure is also used in the IC79 BDT
training in order to maximize the KS p-value for both the signal and background
samples. With this procedure, the cost of pruning is calculated at each parent node
of leaf nodes. This pruning cost ρ is defined using ∆S of Equation 5.4:
ρ = ∆Snsubleaves
(5.12)
where nsubleaves refers to the total number of leaves below this split node. This cost
value quantifies the effect on the tree. The larger the separation gain and the greater
number of subleaves, the larger the effect of pruning at that node.
This “cost-complexity” pruning algorithm creates a copy of the tree and prunes
the copy, starting with the lowest ρ value node and continuing until the root node
is reached. The pruning order and the percentage of the entire sequence is recorded
for each pruned node. The percentage of the pruning sequence to be executed for
all trees is specified by the user and is called the “pruning strength” in this text.
88
As seen above, there are several parameters one may tune to optimize BDT
performance: (1) the number of trees N-trees, (2) the maximum depth of each tree
max-depth, (3) the boosting strength β, (4) the number of cuts to test for each
variable at a node N-cuts, (5) and the pruning strength prune-strength. These
parameters are listed below with descriptions and their values used in this work.
1. N-trees = 200 for each of the three seasons’ BDTs
More trees in the forest allow for more cumulative boosting and more clas-
sification trials of events. There are diminishing returns when increasing the
size of the forest, however, due to the most signal-like background events con-
tinuing to be difficult to classify while exploring the parameter space. Search
sensitivity remained nearly constant beyond 200 trees.
2. max-depth = 5 for each of the three seasons’ BDTs
The maximum depth controls the number of node levels in each tree. A too
large tree depth can lead to overtraining, while a too small tree depth will not
allow sufficient signal/background separation.
3. β = 0.2 for each of the three seasons’ BDTs
The boosting factor β controls the weight of misclassified events, as shown
in Equation 5.7. A too large β can lead to overtraining and reduces the
discriminating power of the forest as misclassified events will dominate the
node purity in most of the trees. Search sensitivity remained nearly constant
up to β = 0.5; overtraining arose beyond this value.
4. N-cuts = 20 for each of the three seasons’ BDTs
89
This parameter determines the number of bins for each variable histogram
constructed at each node. The optimal number of bins depends on the sig-
nal and background event statistics. Each bin must contain a representative
amount of events for the histogram to convey meaningful signal/background
separation.
5. prune-strength = 10% for the IC79 BDT; prune-strength = 0% for the
IC86I and IC86II BDTs
As described above, the pruning strength is the percentage of the cost-complexity
pruning sequence to be executed for all trees in the BDT.
For each node in each tree in the BDT algorithm, every variable is his-
togrammed with an equal number of bins and a single variable cut value is chosen
that yields the best separation between the signal and background hypotheses. Sig-
nal and background data to the left and right of this cut are separated into two
different child nodes. This histogramming and separating continues until five levels
of child nodes are created or if 100% signal or background purity is reached. Events
in each tree are scored +(-)1 if they end up in a signal(background) node. Each
subsequent tree incorporates higher weights, or boosting, for incorrectly categorized
data. Several hundred trees are trained for each season’s BDT. The final BDT
score of each event is a weighted average of its scores in each tree, with the weight
corresponding to the boost factor of each tree.
90
5.4.2 BDT Input Signal - Background Discrimination Variables
The BDT discrimination variables take advantage of topological and energetic
differences between astrophysical neutrino and atmospheric muon spectra. Figure
5.36 shows the distributions of simulation and data with respect to BDT score. The
vertical dashed line corresponds to the optimized final cut described in the next
section. The νµ in these plots is already preselected to be shower-like from Level 2
and Level 3 and has minimal overlap with the Northern Hemisphere track search.
Additionally, the muon background is preselected to be shower-like and with these
variables the BDT is able to effectively discriminate between these events and signal.
Nearly two dozen variables are used in the BDT. While a few of them clearly
dominate in the algorithm, the correlations between the variables are small and all
exhibit effective separation above the 1% level in different areas of the parameter
space. The only strongly correlated variables are the interaction vertex containment
variables, which convey the same idea but are still used by different amounts in the
trees. The correlation matrix for signal (top) and background (bottom) is shown in
Figure 5.8.
The relative importance of each variable in the IC79 BDT is shown below
for different definitions of importance. The values are similar for IC86I and IC86II
with the main difference being less usage of Nch. This energy proxy is used less in
the 86-string BDTs because of the limited high energy statistics in their available
simulated signal datasets relative to IC79.
91
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Hz 
per
 bin
 (Ba
ckg
rou
nd)
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
E−2
ν re
lati
ve 
abu
nda
nce
 (Si
gna
l)
Signal, Training
Signal, Testing(KS p = 1.810e-17)
Background, Training
Background, Testing(KS p = 1.215e-02)
1.0 0.5 0.0 0.5 1.0BDT score
10-1
100
101
102
Sig & Bg Distributions, Overtraining Check
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Hz 
per
 bin
 (Ba
ckg
rou
nd)
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
E−2
ν re
lati
ve 
abu
nda
nce
 (Si
gna
l)
Signal, Training
Signal, Testing(KS p = 6.849e-01)
Background, Training
Background, Testing(KS p = 7.376e-01)
1.0 0.5 0.0 0.5 1.0BDT score
10-1
100
101
102
Sig & Bg Distributions, Overtraining Check
Figure 5.7: Overtrained (top) and well-trained (bottom) BDT score distributions
for signal (blue) and background (red).
92
cha
rge
_pe
r_s
trin
g
cre
do_
ver
tex
dis
t
csc
dllh
_rlo
gl
e_q
tot
_ra
tio
eva
lra
tio
fillr
ati
o
i3s
cal
e_i
nic
e_c
red
o
i3s
cal
e_i
nic
e_m
ono
pod lfv lfv_
z
ma
x_q
tot
_ra
tio nch
qto
t_e
val
_ra
tio
rat
io_
bef
ore
_to
_af
ter
_ve
rte
x
spe
fit_
zen
ith
t_c
scd
llh_
z_d
iff
t_c
scd
ver
tex
dif
f
t_lf
v_z
_di
ff
t_lf
v_z
_su
m
t_s
pev
ert
exd
iff
tra
ck_
csc
d_l
lhr
ati
o
ver
tex
dif
f
charge_per_string
credo_vertexdist
cscdllh_rlogl
e_qtot_ratio
evalratio
fillratio
i3scale_inice_credo
i3scale_inice_monopod
lfv
lfv_z
max_qtot_ratio
nch
qtot_eval_ratio
ratio_before_to_after_vertex
spefit_zenith
t_cscdllh_z_diff
t_cscdvertexdiff
t_lfv_z_diff
t_lfv_z_sum
t_spevertexdiff
track_cscd_llhratio
vertexdiff
1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0
cha
rge
_pe
r_s
trin
g
cre
do_
ver
tex
dis
t
csc
dllh
_rlo
gl
e_q
tot
_ra
tio
eva
lra
tio
fillr
ati
o
i3s
cal
e_i
nic
e_c
red
o
i3s
cal
e_i
nic
e_m
ono
pod lfv lfv_
z
ma
x_q
tot
_ra
tio nch
qto
t_e
val
_ra
tio
rat
io_
bef
ore
_to
_af
ter
_ve
rte
x
spe
fit_
zen
ith
t_c
scd
llh_
z_d
iff
t_c
scd
ver
tex
dif
f
t_lf
v_z
_di
ff
t_lf
v_z
_su
m
t_s
pev
ert
exd
iff
tra
ck_
csc
d_l
lhr
ati
o
ver
tex
dif
f
charge_per_string
credo_vertexdist
cscdllh_rlogl
e_qtot_ratio
evalratio
fillratio
i3scale_inice_credo
i3scale_inice_monopod
lfv
lfv_z
max_qtot_ratio
nch
qtot_eval_ratio
ratio_before_to_after_vertex
spefit_zenith
t_cscdllh_z_diff
t_cscdvertexdiff
t_lfv_z_diff
t_lfv_z_sum
t_spevertexdiff
track_cscd_llhratio
vertexdiff
1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0
Figure 5.8: Variable correlation matrix for signal (top) and background (bottom).
93
The following variable importance list weights by separation per node. This
ranking shows which variables drive the majority of the separation.
1. nch : 0.263219
2. qtot_eval_ratio : 0.206007
3. track_cscd_llhratio : 0.169659
4. cscdllh_rlogl : 0.068819
5. max_qtot_ratio : 0.046522
6. t_lfv_z_diff : 0.037657
7. t_lfv_z_sum : 0.031459
8. t_cscdllh_z_diff : 0.028757
9. lfv_z : 0.021912
10. e_qtot_ratio : 0.018711
11. i3scale_inice_monopod : 0.018262
12. fillratio : 0.017134
13. ratio_before_to_after_vertex : 0.012300
14. spefit_zenith : 0.011471
15. lfv : 0.011163
16. vertexdiff : 0.008894
17. credo_vertexdist : 0.008630
18. i3scale_inice_credo : 0.007794
19. t_spevertexdiff : 0.005102
20. charge_per_string : 0.002859
21. t_cscdvertexdiff : 0.002262
22. evalratio : 0.001406
94
The following variable importance list weights by tree weight. This ranking
shows which variables separate the easiest events in the early trees.
1. ratio_before_to_after_vertex : 0.101122
2. spefit_zenith : 0.085615
3. track_cscd_llhratio : 0.083146
4. qtot_eval_ratio : 0.080421
5. e_qtot_ratio : 0.072368
6. lfv_z : 0.068617
7. max_qtot_ratio : 0.063828
8. i3scale_inice_monopod : 0.053032
9. cscdllh_rlogl : 0.049083
10. t_cscdvertexdiff : 0.048363
11. t_lfv_z_diff : 0.042257
12. fillratio : 0.041723
13. lfv : 0.040528
14. nch : 0.031168
15. t_lfv_z_sum : 0.028530
16. credo_vertexdist : 0.025968
17. t_cscdllh_z_diff : 0.020933
18. t_spevertexdiff : 0.018946
19. vertexdiff : 0.015740
20. charge_per_string : 0.013126
21. i3scale_inice_credo : 0.011495
22. evalratio : 0.003988
95
The following variable importance list based on the number of uses only. This
ranking shows which variables were used in separating the hard events in the later
trees.
1. ratio_before_to_after_vertex : 0.104993
2. track_cscd_llhratio : 0.102712
3. max_qtot_ratio : 0.082781
4. qtot_eval_ratio : 0.078517
5. i3scale_inice_monopod : 0.068034
6. spefit_zenith : 0.065309
7. e_qtot_ratio : 0.059480
8. t_cscdvertexdiff : 0.051972
9. t_lfv_z_diff : 0.045436
10. nch : 0.044225
11. lfv_z : 0.043940
12. t_lfv_z_sum : 0.042579
13. cscdllh_rlogl : 0.030139
14. t_spevertexdiff : 0.025493
15. lfv : 0.025215
16. t_cscdllh_z_diff : 0.024855
17. vertexdiff : 0.021481
18. fillratio : 0.019964
19. i3scale_inice_credo : 0.019936
20. charge_per_string : 0.019010
21. credo_vertexdist : 0.018340
22. evalratio : 0.005590
96
The BDT variables are separated into three classes below. The first class of
variables Topology Separators separate the spherical-like signal from track-like
background topologies. The second class Energy Separators separates signal from
background using various energy proxies. In general, high energy neutrino showers
impart their energy uniformly over a more contained volume than lower energy at-
mospheric muons. The third class Vertex Location Separators separates signal
from background using the location of the reconstructed event vertex. While no
requirements of containment within the detector are imposed on the desired sig-
nal, interaction location in the detector can further elicit differences in muon and
neutrino-induced showers.
Topology Separators
track-cscd-llhratio One of the most effective BDT variables is the same ratio
of the track likelihood to the cascade likelihood used in Level 3. Even though the
analysis selected on this parameter before the BDT cut, the high energy background
muons that passed in spite of it are successfully distinguished from signal with
the BDT algorithm. Note that high energy neutrino-induced showers can yield
large, track-like values. Both analytic likelihood-based reconstructions, SPE and
CascadeLlh, give large log-likelihood values to events with high numbers of hit
DOMs. Because SPE’s L range peaks at much higher values than CascadeLlh,
high-energy events tend to yield large positive log(Ltrack/Lcscd) values.
97
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Figure 5.9: track-cscd-llhratio. Top: linear (left) and logarithmic (right) Level 3
distributions. Middle: BDT score vs. background (left) and signal (right) distribu-
tions. Bottom: final cut level distributions.
98
cscdllh-rlogl Another powerful separator is the reduced negative log-likelihood
value from CascadeLlh likelihood maximization. Events with more hit DOMs will
have a larger log-likelihood value because it is calculated as the sum of the PDFs
of all hits, taking the logarithm of Equation 4.16. The number of free parameters
in CascadeLlh are the number of hit DOMs (Nch) minus the number of degrees of
freedom in the fit (one temporal, three positional, and two directional). Therefore,
if the log-likelihood is divided by the number of degrees of freedom, events with
different Nch values can be compared. The linear distributions are zoomed in to
better see the neutrino-muon separation.
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Figure 5.10: cscdllh-rlogl. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
100
lfv This variable is the reconstructed speed from the improved LineFit algorithm.
Muon tracks should be reconstructed close to the speed of light. A cascade, on
the other hand, is comprised of light diffusing out from the interaction point, and
therefore should exhibit a relatively slow reconstructed LineFit speed.
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Figure 5.11: lfv. Top: linear (left) and logarithmic (right) Level 3 distributions.
Middle: BDT score vs. background (left) and signal (right) distributions. Bottom:
final cut level distributions.
101
lfv-z Background muons originate from above the detector, while astrophysical
neutrinos should have near-isotropic origins. The (vertical) z-component of the
reconstructed LineFit speed exhibits this directionality difference.
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Figure 5.12: lfv-z. Top: linear (left) and logarithmic (right) Level 3 distributions.
Middle: BDT score vs. background (left) and signal (right) distributions. Bottom:
final cut level distributions.
102
t-lfv-z-sum Each event has a charge-weighted mean time calculated and is split on
this mean time. The LineFit reconstruction is calculated for each half. A cascading
neutrino interaction covers a relatively localized volume in the detector and thus its
two event halves are much closer together than the two halves of a muon event. The
sum of the z-component LineFit speeds of the two halves tends to be near zero for
neutrino signal and negative for down-going muon background. Some muon event
halves can be misreconstructed as upgoing, however, and yield near-zero or positive
t-lf-z-sum values. The difference between the z-component speeds, which is also
included and described below, catches and separates background events where one
half is misreconstructed as up-going.
103
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Figure 5.13: t-lfv-z-sum. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
104
t-lfv-z-diff This variable is the difference between the z-component LineFit speeds
of the two charge-weighted mean time-split halves of an event. The sum of the two
halves’ z-component speeds is described above. This difference catches and separates
background events where one half is misreconstructed as up-going. t-lfv-z-diff and
t-lfv-z-sum show little correlation in Figure 5.8 because they are used by the BDT
for different events, depending on LineFit’s success in reconstructing the direction
of each event half.
105
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Figure 5.14: t-lfv-z-diff. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
106
spefit-zenith The event zenith reconstructed by SPE. Background muons are
mostly reconstructed as down-going whereas signal neutrinos are nearly isotropic in
their reconstructed zenith distributions.
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Figure 5.15: spefit-zenith. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
107
ratio-before-to-after-vertex Ignoring noise hits, a cascade ideally should have
all of their DOM hits take place in time after the interaction vertex. A track event
should have about half of their hits take place before and half after its reconstructed
“vertex,” even with the fact that the background muon tracks are already preselected
to be cascade-like at Level 3. This variable equals the total hit times of the DOMs
hit before the Monopod-reconstructed vertex time divided by the total hit times of
the DOMs hit after the Monopod-reconstructed vertex time. Using the time values
instead of the hit counts brings out more separation from signal for background
events with early hits.
108
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Figure 5.16: ratio-before-to-after-vertex. Top: linear (left) and logarithmic (right)
Level 3 distributions. Middle: BDT score vs. background (left) and signal (right)
distributions. Bottom: final cut level distributions.
109
fill-ratio The fill-ratio is the same as used in the Level 3 selection. Signal-like
events exhibit a large fraction of hit DOMs inside of a sphere centered on the re-
constructed vertex with a radius determined by the mean hit distance. Background
tracks exhibit a less-filled sphere. The BDT is able to use this variable to some
extent even though it was employed at Level 3.
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BDT
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000fillratio
100
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Figure 5.17: fill-ratio. Top: linear (left) and logarithmic (right) Level 3 distributions.
Middle: BDT score vs. background (left) and signal (right) distributions. Bottom:
final cut level distributions.
110
evalratio This variable is the tensor-of-inertia eigenvalue ratio employed at Level
2.
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0.06
Bin
Coun
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0.0500 0.0875 0.1250 0.1625 0.2000 0.2375 0.2750 0.3125 0.3500evalratio
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νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.0500 0.0875 0.1250 0.1625 0.2000 0.2375 0.2750 0.3125 0.3500evalratio
100
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0.05 0.10 0.15 0.20 0.25 0.30 0.35evalratio
−1.0
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BDT
Scor
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Off-time Data Background
10−6
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log 10
(wei
ght)
0.05 0.10 0.15 0.20 0.25 0.30 0.35evalratio
−1.0
−0.5
0.0
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BDT
Scor
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E−2νe Signal
10−8
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ght)
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Bin
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0.0500 0.0875 0.1250 0.1625 0.2000 0.2375 0.2750 0.3125 0.3500evalratio
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.0500 0.0875 0.1250 0.1625 0.2000 0.2375 0.2750 0.3125 0.3500evalratio
100
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Figure 5.18: evalratio. Top: linear (left) and logarithmic (right) Level 3 distribu-
tions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
111
Energy Separators
qtot-eval-ratio Another potent variable is the total amount of Cherenkov light
imparted in the DOMs divided by the tensor-of-inertia derived elongation of an
event. The numerator separates lower energy background atmospheric muons from
higher energy astrophysical signal neutrinos, while the denominator separates elon-
gated background atmospheric muons from spherical neutrino-induced showers. As
shown in Figure 5.19, the ratio of these two observables effectively separates the
lower energy atmospheric neutrino background from the signal as well.
112
0.02
0.04
0.06
0.08
Bin
Coun
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−2.500 −2.062 −1.625 −1.188 −0.750 −0.312 0.125 0.562 1.000qtot-eval-ratio
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νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
−2.500 −2.062 −1.625 −1.188 −0.750 −0.312 0.125 0.562 1.000qtot-eval-ratio
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−2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0qtot-eval-ratio
−1.0
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BDT
Scor
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Off-time Data Background
10−6
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log 10
(wei
ght)
−2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0qtot-eval-ratio
−1.0
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BDT
Scor
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E−2νe Signal
10−8
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(wei
ght)
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Bin
Coun
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−2.500 −2.062 −1.625 −1.188 −0.750 −0.312 0.125 0.562 1.000qtot-eval-ratio
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νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
−2.500 −2.062 −1.625 −1.188 −0.750 −0.312 0.125 0.562 1.000qtot-eval-ratio
100
102
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Figure 5.19: qtot-eval-ratio. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
113
max-qtot-ratio The maximum imparted charge to a DOM to the total imparted
charge in an event removes so-called “balloon events,” in which a muon loses its
energy catastrophically close to a DOM.
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0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000max-qtot-ratio
100
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0.0 0.2 0.4 0.6 0.8 1.0max-qtot-ratio
−1.0
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Scor
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Off-time Data Background
10−6
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(wei
ght)
0.0 0.2 0.4 0.6 0.8 1.0max-qtot-ratio
−1.0
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BDT
Scor
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E−2νe Signal
10−8
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(wei
ght)
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Bin
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000max-qtot-ratio
100
102
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Figure 5.20: max-qtot-ratio. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
114
e-qtot-ratio The logarithm of the ratio of the ACER reconstructed energy divided
by the total imparted charge in an event removes interactions in which the total
charge is much smaller than the reconstructed energy.
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0.25
Bin
Coun
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−2.000 −0.812 0.375 1.562 2.750 3.938 5.125 6.312 7.500e-qtot-ratio
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νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
−2.000 −0.812 0.375 1.562 2.750 3.938 5.125 6.312 7.500e-qtot-ratio
100
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−2 0 2 4 6e-qtot-ratio
−1.0
−0.5
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Scor
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Off-time Data Background
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log 10
(wei
ght)
−2 0 2 4 6e-qtot-ratio
−1.0
−0.5
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BDT
Scor
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E−2νe Signal
10−8
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(wei
ght)
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Bin
Coun
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1
−2.000 −0.812 0.375 1.562 2.750 3.938 5.125 6.312 7.500e-qtot-ratio
0.01.0
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
−2.000 −0.812 0.375 1.562 2.750 3.938 5.125 6.312 7.500e-qtot-ratio
100
102
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Figure 5.21: e-qtot-ratio. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
115
charge-per-string The total charge in an event divided by the number of strings
whose DOMs trigger during an event. Cascades have fewer hit strings than tracks
and, therefore, greater charge per string.
0.05
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0.15
0.20
Bin
Coun
tsSu
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1
0.0300 0.0762 0.1225 0.1687 0.2150 0.2612 0.3075 0.3538 0.4000charge-per-string
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0.0300 0.0762 0.1225 0.1687 0.2150 0.2612 0.3075 0.3538 0.4000charge-per-string
100
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0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40charge-per-string
−1.0
−0.5
0.0
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Scor
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Off-time Data Background
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log 10
(wei
ght)
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40charge-per-string
−1.0
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Scor
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E−2νe Signal
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(wei
ght)
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Bin
Coun
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1
0.0300 0.0762 0.1225 0.1687 0.2150 0.2612 0.3075 0.3538 0.4000charge-per-string
0.01.0
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.0300 0.0762 0.1225 0.1687 0.2150 0.2612 0.3075 0.3538 0.4000charge-per-string
100
102
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Figure 5.22: charge-per-string. Top: linear (left) and logarithmic (right) Level 3
distributions. Middle: BDT score vs. background (left) and signal (right) distribu-
tions. Bottom: final cut level distributions.
116
Nch Nch is the number of channels, or equivalently DOMs, that trigger during
an event. An astrophysical neutrino flux reaches higher energies, and larger Nch
values, than atmospheric muons.
0.1
0.2
0.3
0.4
0.5
Bin
Coun
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0 312 625 938 1250 1562 1875 2188 2500nch
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dataµ atmosphericνe atmosphericνµ atmospheric
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0 312 625 938 1250 1562 1875 2188 2500nch
100
102
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0 500 1000 1500 2000 2500nch
−1.0
−0.5
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BDT
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Off-time Data Background
10−6
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log 10
(wei
ght)
0 500 1000 1500 2000 2500nch
−1.0
−0.5
0.0
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BDT
Scor
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E−2νe Signal
10−8
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(wei
ght)
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Coun
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0 312 625 938 1250 1562 1875 2188 2500nch
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 312 625 938 1250 1562 1875 2188 2500nch
100
Data
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Figure 5.23: Nch. Top: linear (left) and logarithmic (right) Level 3 distributions.
Middle: BDT score vs. background (left) and signal (right) distributions. Bottom:
final cut level distributions.
117
Vertex Location Separators
i3scale-inice-credo The I3Scale calculation is the factor by which the nearest
edge of the detector must scale in order to be at the reconstructed vertex. For
example, a vertex with a value of 1 is at the edge of the detector, a vertex with a
value less than one is contained within the detector volume, and a vertex with a
value greater than one is outside of the detector volume. This specific variable is
the measure of containment using the Credo reconstructed vertex.
118
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0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00i3scale-inice-credo
100
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0.0 0.5 1.0 1.5 2.0i3scale-inice-credo
−1.0
−0.5
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Scor
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Off-time Data Background
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log 10
(wei
ght)
0.0 0.5 1.0 1.5 2.0i3scale-inice-credo
−1.0
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BDT
Scor
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E−2νe Signal
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ght)
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1
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00i3scale-inice-credo
0.01.0
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00i3scale-inice-credo
100
102
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Figure 5.24: i3scale-inice-credo. Top: linear (left) and logarithmic (right) Level 3
distributions. Middle: BDT score vs. background (left) and signal (right) distribu-
tions. Bottom: final cut level distributions.
119
i3scale-inice-monopod This variable is a measure of containment using the
I3Scale calculation, described for i3scale-inice-credo above, on the Monopdo recon-
structed vertex. i3scale-inice-monopod is quite correlated with i3scale-inice-credo,
but both are used by the BDT in varying degrees as depicted in the variable impor-
tance lists at the beginning of this section.
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0.04
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0.08
0.10
Bin
Coun
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1
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0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00i3scale-inice-monopod
100
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0.0 0.5 1.0 1.5 2.0i3scale-inice-monopod
−1.0
−0.5
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Scor
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Off-time Data Background
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(wei
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−1.0
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Scor
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E−2νe Signal
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dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00i3scale-inice-monopod
100
102
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Figure 5.25: i3scale-inice-monopod. Top: linear (left) and logarithmic (right) Level
3 distributions. Middle: BDT score vs. background (left) and signal (right) distri-
butions. Bottom: final cut level distributions.
120
credo-vertexdist Similar to i3scale-inice-credo above, this variable is a measure
of containment and is the distance in meters of the Credo reconstructed vertex from
the center of the detector volume.
0.02
0.04
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0.08
0.10
Bin
Coun
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1
0 188 375 562 750 938 1125 1312 1500credo-vertexdist
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0 188 375 562 750 938 1125 1312 1500credo-vertexdist
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0 200 400 600 800 1000 1200 1400credo-vertexdist
−1.0
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Off-time Data Background
10−6
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log 10
(wei
ght)
0 200 400 600 800 1000 1200 1400credo-vertexdist
−1.0
−0.5
0.0
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BDT
Scor
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E−2νe Signal
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(wei
ght)
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0 188 375 562 750 938 1125 1312 1500credo-vertexdist
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dataµ atmosphericνe atmosphericνµ atmospheric
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0 188 375 562 750 938 1125 1312 1500credo-vertexdist
100
102
Data
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Figure 5.26: credo-vertexdist. Top: linear (left) and logarithmic (right) Level 3
distributions. Middle: BDT score vs. background (left) and signal (right) distribu-
tions. Bottom: final cut level distributions.
121
t-cscdvertexdiff Each event has a charge-weighted mean time calculated and is
split on this mean time. The CascadeLlh reconstruction is performed on both halves
and the distance between their reconstructed vertices is calculated. A cascading
neutrino interaction covers a relatively localized volume in the detector and thus its
two event halves are much closer together than the two halves of a muon event, and
thus signal events are expected to have smaller t-cscdvertexdiff values.
0.050.10
0.150.20
0.250.30
0.350.40
Bin
Coun
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1
0 168 335 502 670 838 1005 1172 1340t-cscdvertexdiff
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νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 168 335 502 670 838 1005 1172 1340t-cscdvertexdiff
100
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0 200 400 600 800 1000 1200t-cscdvertexdiff
−1.0
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Scor
e
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10−6
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log 10
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ght)
0 200 400 600 800 1000 1200t-cscdvertexdiff
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e
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10−8
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ght)
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tsSu
mto
1
0 168 335 502 670 838 1005 1172 1340t-cscdvertexdiff
0.01.0
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o 10−13
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10−7
Hzp
erB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 168 335 502 670 838 1005 1172 1340t-cscdvertexdiff
100
102
Data
/MC
Rati
o
Figure 5.27: t-cscdvertexdiff. Top: linear (left) and logarithmic (right) Level 3 dis-
tributions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
122
t-cscdllh-z-diff Each event has a charge-weighted mean time calculated and is
split on this mean time. The CascadeLlh reconstruction is performed on both halves
and the distance between their reconstructed vertex (vertical axis) z values is cal-
culated. The difference in the z components of the vertices reveals additional sep-
aration between signal and background because of the down-going nature of atmo-
spheric muons.
0.1
0.2
0.3
0.4
Bin
Coun
tsSu
mto
1
−1100 −825 −550 −275 0 275 550 825 1100t-cscdllh-z-diff
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Hzp
erB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
−1100 −825 −550 −275 0 275 550 825 1100t-cscdllh-z-diff
100
102
Data
/MC
Rati
o
−1000 −500 0 500 1000t-cscdllh-z-diff
−1.0
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0.0
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Scor
e
Off-time Data Background
10−6
10−5
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log 10
(wei
ght)
−1000 −500 0 500 1000t-cscdllh-z-diff
−1.0
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Scor
e
E−2νe Signal
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ght)
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tsSu
mto
1
−1100 −825 −550 −275 0 275 550 825 1100t-cscdllh-z-diff
0.01.0
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o 10−13
10−11
10−9
10−7
Hzp
erB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
−1100 −825 −550 −275 0 275 550 825 1100t-cscdllh-z-diff
100
102
Data
/MC
Rati
o
Figure 5.28: t-cscdllh-z-diff. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
123
t-spevertexdiff Like with t-cscdvertexdiff above, the SPE reconstruction is per-
formed on both halves of an event and the distance between their reconstructed
vertices is calculated. In general the distance between the vertices is less in a local-
ized cascade compared to more track-like background, but interestingly high energy
signal events display a large spread in the distribution of this variable. This spread
is likely due to the fact that SPE is built on a track hypothesis and often does not
converge on the true shower interaction vertex.
124
0.05
0.10
0.15
0.20
0.25
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0.35
Bin
Coun
tsSu
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perB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 188 375 562 750 938 1125 1312 1500t-spevertexdiff
100
102
Data
/MC
Rati
o
0 200 400 600 800 1000 1200 1400t-spevertexdiff
−1.0
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Scor
e
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10−6
10−5
10−4
10−3
10−2
log 10
(wei
ght)
0 200 400 600 800 1000 1200 1400t-spevertexdiff
−1.0
−0.5
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1.0
BDT
Scor
e
E−2νe Signal
10−8
10−7
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log 10
(wei
ght)
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Bin
Coun
tsSu
mto
1
0 188 375 562 750 938 1125 1312 1500t-spevertexdiff
0.01.0
2.03.0
3.54.0
Data
/MC
Rati
o 10−13
10−11
10−9
10−7
Hzp
erB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 188 375 562 750 938 1125 1312 1500t-spevertexdiff
100
102
Data
/MC
Rati
o
Figure 5.29: t-spevertexdiff. Top: linear (left) and logarithmic (right) Level 3 distri-
butions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
125
vertexdiff This variable is the difference in vertex positions calculated by the
Credo and CascadeLlh reconstructions. This variable identifies the track-like muon
background by the larger distance between the vertices on which these two recon-
structions converge, compared with the neutrino-induced cascade signal.
0.050.10
0.150.20
0.250.30
0.350.40
Bin
Coun
tsSu
mto
1
0 50 100 150 200 250 300 350 400vertexdiff
0.01.0
2.03.0
4.0
Data
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o 10−13
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10−9Hz
perB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 50 100 150 200 250 300 350 400vertexdiff
100
102
Data
/MC
Rati
o
0 50 100 150 200 250 300 350 400vertexdiff
−1.0
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0.0
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BDT
Scor
e
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10−6
10−5
10−4
10−3
10−2
log 10
(wei
ght)
0 50 100 150 200 250 300 350 400vertexdiff
−1.0
−0.5
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1.0
BDT
Scor
e
E−2νe Signal
10−8
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log 10
(wei
ght)
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Bin
Coun
tsSu
mto
1
0 50 100 150 200 250 300 350 400vertexdiff
0.01.0
2.03.0
4.0
Data
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Rati
o 10−13
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10−9Hzp
erB
in
dataµ atmosphericνe atmosphericνµ atmospheric
νe signal (dNdE × 105)ντ signal (dNdE × 105)νµ signal (dNdE × 105)
0 50 100 150 200 250 300 350 400vertexdiff
100
102
Data
/MC
Rati
o
Figure 5.30: vertexdiff. Top: linear (left) and logarithmic (right) Level 3 distribu-
tions. Middle: BDT score vs. background (left) and signal (right) distributions.
Bottom: final cut level distributions.
126
5.4.3 Loose Pre-BDT Cuts after Level 3
Before training the BDT, deep tail values of some variables were removed.
Because the BDT algorithm uses constant bin widths for each variable histogram at
each tree node, bins with poor statistics at outlier values can diminish the separating
power of the given variable. Removing these few outlying events from the signal and
background datasets allows the BDT to identify the separation where the majority
of events in each distribution lie. A possible improvement of the BDT algorithm
that would circumvent this step would be to allow varying bin widths by imposing
constant total signal and background weights in each bin.
Additionally, and as described above in Section 5.4.2, the track versus cascade
likelihood ratio has a very wide range. High energy signal events can end up in the
track-like region of the range. This variable’s separation power can be strengthened
by removing lower-energy background where there is little signal, and this is done
before the BDT training as well.
These loose pre-BDT training cuts are as follows:
1. lfv ≤ 0.5
2. −1 ≤ t lfv z diff ≤ 1
3. −1 ≤ t lfv z sum ≤ 1
4. ratio before to after vertex ≤ 2
5. ln (Ltrack/Lcscd) ≤ 0.5 OR log (Qtot) > 4
127
Figure 5.31: Background (left) and signal (right) distributions of the total charge
versus track-to-cascade likelihood.
Figure 5.32: Linear (left) and logarithmic (right) distributions of the LineFit speed
at L3 for background off-time data and astrophysical νe, with the loose pre-BDT
cuts as vertical lines.
The removal of this class of events reduces the signal sample by less than 0.3%.
The signal and background distributions of the likelihood ratio versus total charge
imparted to the DOMs and LineFit speed at Level 3 and their cut values are shown
in Figures 5.31 and 5.32.
Two additional pre-BDT cuts are made as well on events that will not con-
tribute to the likelihood analysis. The first of which are those with failed Monopod
reconstructions. This reconstruction fails to converge on about 1% of the highest
128
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
0.135
0.140
0.145
0.150
0.155
0.160
Pe
rF
lav
or
E2
F ν
(G
eV
cm
−2
)
Selection w/out Pre-BDT Cuts
Final Selection
Figure 5.33: Improvement in sensitivity to an E−2-weighted per-flavor neutrino flux
with pre-BDT cuts versus without.
energy simulated neutrinos that interact outside of the detector. The second addi-
tional cut is on the Cramer-Rao estimated directional error, before the energy-based
pull correction that is described in Section 4.2.8. All events that have a Cramer-
Rao σ > pi are removed as none would contribute appreciably to a discovery. These
discarded events account for less than 1% of all neutrino signal and are typically
TeV neutrinos that interaction outside of the detector and so cannot allow very
certain reconstructed directions. The improvement in sensitivity, see Chapter 6 for
its calculation, is shown in Figure 5.33.
5.4.4 BDT Forest Training
Once the data rate has been reduced to around 0.7 Hz from Trigger to Level
3, and outlier misreconstructed events have been removed, a boosted decision tree
129
forest is trained and a final collection of data events that very closely resemble
astrophysical neutrino interactions in IceCube is attained. The training parameters
used are outlined in Section 5.4.1. Simulated E−2-weighted νe events were used as
known signal and atmospheric muon-dominated data events that occur outside of
two hours from any GRB prompt flux were used as known background. A different
BDT was trained on each of the three detector configurations’ data and simulation
due to differences in feature extraction algorithms and event selection at the South
Pole.
Half of the available simulated νe signal was used for training the BDT model
while the other half was used for overtraining testing for each detector configu-
ration. 515391, 131661, and 161555 signal events were used for training in IC79,
IC86I, and IC86II, respectively. 793050, 829870, and 745510 background events
distributed evenly throughout the year were used for training in IC79, IC86I, and
IC86II, respectively. A full-year sample of data was necessary to minimize the effects
of the seasonal variation in atmospheric muon and neutrino interaction rates in the
detector, described in Section 3.2.2.
The first tree and the last tree with variable cut and purity values at each
node for the IC86I forest are shown in Figures 5.34 and 5.35.
Figure 5.36 shows the distributions of IC79 simulation and data with respect
to BDT score. The vertical dashed line corresponds to the optimized final cut
described in the next section. Also, the survival rates of different backgrounds from
data and simulation per cut in BDT score are shown in Figure 5.37. The νµ in
these plots is already preselected through Levels 2 and 3 to be shower-like and has
130
minimal overlap with the Northern Hemisphere track search. The overlap is at the
level of .05% for background data and 2% for signal νµ.
5.4.5 Final Analysis Level
Once each BDT has been sufficiently trained, a final selection on the score is
made. This optimal selection is determined by performing the unbinned likelihood
analysis, described in the next chapter, on different (BDT score > minimum value)
cuts. The chosen selection for each BDT is the minimum score that requires the
least amount of signal to surpass thresholds set by the background-only hypothesis.
For each BDT, the optimal final event selection is those events with a score
> 0.525. The fact that each detector configuration search yielded the same optimal
score cut is not surprising given the very similar event selection levels leading to
the machine learning input as well as the fact that the same variables were used in
all three BDTs. The νe signal efficiency per energy bin with respect to Level 3 for
different possible final cuts on the BDT score are shown for the IC79, IC86I, and
IC86II searches in Figure 5.39. The energy cutoffs in the 86-string plots are only
due to the simulation availability for those configurations. The integrated efficiency
and background data rate are given in the legend for each score. The optimal score
curves are in bold orange.
The νe, ντ , and νµ efficiency per energy bin for charged-current and neutral-
current interactions with respect to Level 3 are shown in Figure 5.38 along with
their energy distributions. Hadronic cascades from deep-inelastic neutral current
131
interactions produce similar spherical Cherenkov light patterns for all neutrino fla-
vors, and therefore exhibit similar efficiency curves. The decrease in high energy
astrophysical ντ charged-current events at the final level compared to Level 3 is
due to the fact that the resulting tau lepton can travel an appreciable in-IceCube
distance before decaying. These type of events yield the so-called “double bang”
topology. The BDT-based selection of this search is less accepting of these types
of tau neutrino events than lower energy ones, where the two cascades are so close
together that they are indistinguishable from a single cascade. The efficiency of
astrophysical νµ charged current events is lower than the other two flavors because,
besides the requirement of a large initial hadronic cascade, the resulting muon must
catastrophically lose its energy with little observable Cherenkov tail in order to pass
the cut. This requirement is reflected in the larger peak νµ energy compared to the
other flavors.
Table 5.1 shows efficiences and data rates at each event selection level. Figure
5.40 presents the signal efficiency of each event selection level relative to the online
Level 2 filter as a function of neutrino energy. The data rate is calculated for one
eight hour detector run during the summer and so is at a higher rate than the
average. As illustrated in this figure and the others like it above, the efficiency
improves dramatically for neutrinos with energies beyond 10 TeV. Many energy-
based variables drive the BDT model for this search so that signal neutrinos can be
lifted out of the generally lower energy atmospheric muon background.
132
Cut on "csc
dllh_rlogl" 
at 7.90x10
^0
1 - p = 0.5
00
Cut on "csc
dllh_rlogl" 
at 7.60x10
^0
p = 0.814
<
Cut on "lfv
_z" at 1.43
x10^-2
1 - p = 0.8
33
>=
Cut on "e_
qtot_ratio"
 at 9.05x10
^-1
p = 0.934
< Cut 
on "lfv_z" a
t -1.14x10
^-2
p = 0.515>=
Cut on "fill
ratio" at 8.
67x10^-1
p = 0.745
< S
ignal leaf p = 0.980>=
Cut on "lfv
_z" at -2.0
7x10^-2
1 - p = 0.5
23
< Signa
l leaf p = 0.907>=
Backgroun
d leaf 1 - p = 0.7
70<
Signal leaf p = 0.670>=
Cut on "lfv
" at 1.41x1
0^-1
1 - p = 0.7
00<
Cut on "fill
ratio" at 7.
00x10^-1
p = 0.729>=
Cut on "e_
qtot_ratio"
 at 1.11x10
^0
1 - p = 0.5
02
< Cut on "qto
t_eval_rati
o" at -3.83
x10^-1
1 - p = 0.8
74>=
Backgroun
d leaf 1 - p = 0.6
41<
Signal leaf p = 0.795>=
Backgroun
d leaf 1 - p = 0.8
93<
Signal leaf p = 0.915>=
Cut on "e_
qtot_ratio"
 at 9.61x10
^-1
p = 0.523<
Signal leaf p = 0.884>=
Backgroun
d leaf 1 - p = 0.6
02<
Signal leaf p = 0.755>=
Cut on "lfv
" at 1.14x1
0^-1
1 - p = 0.9
12<
Cut on "fill
ratio" at 6.
33x10^-1
1 - p = 0.5
52
>=
Cut on "fill
ratio" at 7.
33x10^-1
1 - p = 0.7
29
< B
ackground 
leaf
1 - p = 0.9
54>=
Backgroun
d leaf 1 - p = 0.7
84<
Cut on "spe
fit_zenith"
 at 1.04x10
^0
p = 0.542>=
Backgroun
d leaf 1 - p = 0.6
89<
Signal leaf p = 0.646>=
Cut on "cre
do_vertexd
ist" at 6.04
x10^2
1 - p = 0.6
90<
Cut on "spe
fit_zenith"
 at 1.35x10
^0
p = 0.730
>=
Cut on "t_l
fv_z_sum" 
at -2.96x1
0^-2
1 - p = 0.5
08<
Backgroun
d leaf 1 - p = 0.7
48>=
Backgroun
d leaf 1 - p = 0.7
00<
Signal leaf p = 0.578>=
Cut on "t_c
scdvertexd
iff" at 1.07
x10^2
1 - p = 0.5
65<
Signal leaf p = 0.799>=
Signal leaf p = 0.581
< B
ackground 
leaf
1 - p = 0.7
61>=
Figure 5.34: First tree in the IC86I BDT forest
133
Cut on "tc
sdlhd_drh
ggacst7o" s
t .90x1^-
p=-
5 6 p0xp9
Cut on "c
st7oh84<
oc4htohs<t
4chf4ct4^
" st 901-^-p
=.v
5 6 p0z3p
2
Cut on ">
s^hetoth
cst7o" st 1
0-p^-p=.
-
5 6 p0xpvq6
i7finsg g4
s<
5 6 p0zzz
2 Cut on "4
hetothcst
7o" st 10-S
^-p=.-
5 6 p01S-q6
Bsdlficoun
r g4s< - . 5 6 p01
v1
2 Cut on "d
_drggahcg
ofig" st 10xp
^-p=p
5 6 p0zvpq6
i7finsg g4
s<
5 6 p0zxz
2 Bsdlfico
unr g4s< - . 5 6 p03
99q6
Cut on "e
toth4fsgh
cst7o" st .
-011^-p=
.-
5 6 p0xpv2
Cut on "f4
ct4^r7k" 
st v0Sp^-
p=-
- . 5 6 p01
p-
q6
Cut on "e
toth4fsgh
cst7o" st .
v0x1^-p=
p
5 6 p0xpv2
Cut on "th
_54f4ct4^
r7k" st -03
z^-p=v
5 6 p0193
q6
Bsdlficoun
r g4s< - . 5 6 p0S
1S2
i7finsg g4
s<
5 6 p0xpvq6
i7finsg g4
s<
5 6 p01zm
2 Cut on "4
hetothcst
7o" st -0-p^
-p=p
5 6 p0xpzq6
Bsdlficoun
r g4s< - . 5 6 p0z
vv2
i7finsg g4
s<
5 6 p01-9q6
Cut on "f4
ct4^r7k" 
st -03-^-p
=-
- . 5 6 p03
-12
Cut on "th
d_drggahff
hr7k" st .v0
m1^-p=v
- . 5 6 p0S
1S
q6
Cut on "th
g<fhffh_u
>" st .30pS
^-p=.v
5 6 p0x-3
2
Bsdlficoun
r g4s< - . 5 6 p0z
pxq6
Bsdlficoun
r g4s< - . 5 6 p03
z12
i7finsg g4
s<
5 6 p0xSmq6
Cut on "c
st7oh84<
oc4htohs<t
4chf4ct4^
" st -03v^-p
=.-
5 6 p0xSS2
Bsdlficoun
r g4s< - . 5 6 p0z
19
q6
i7finsg g4
s<
5 6 p013p
2 B
sdlficounr
 g4s<
- . 5 6 p0z
xSq6
Figure 5.35: Last tree in the IC86I BDT forest
134
10−11
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
Hz
pe
rB
in
data
µ atmospheric
νe atmospheric
νµ atmospheric
νe signal (dNdE × 105)
ντ signal (dNdE × 105)
νµ signal (dNdE × 105)
-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00
BDT Score
10−1
100
Da
ta
/M
C
Ra
tio
Figure 5.36: Distribution of data, simulated muon background, simulated at-
mospheric neutrino background, simulated E−2-weighted neutrino signal (where
dN
dE = 10−8GeV
−1cm−2s−1sr−1( EGeV )−2) with respect to BDT score. The vertical
dashed line represents the final analysis cut of > 0.525.
135
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Hz
Data
CORSIKA
NuGen nue CC Honda2006
NuGen nue NC Honda2006
NuGen numu CC Honda2006
NuGen numu NC Honda2006
Total MC
1.0 0.5 0.0 0.5 1.0
BDT cut value
10-1
100
101
102
dat
a/m
c r
ati
o
Rate vs. BDT cut
Figure 5.37: Survival rates of different backgrounds as a function of cut on BDT
score.
136
102 103 104 105 106 107 108 109
Energy (GeV)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Effi
cien
cy
w.r
.t.
Lev
el3
Charged Current Interactions
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
No
rm’
dR
elat
ive
Ab
und
anc
e(ν
En
erg
y)
νe Eff. Final wrt L3
ντ Eff. Final wrt L3
νµ Eff. Final wrt L3
Final Level νe Energy
Final Level ντ Energy
Final Level νµ Energy
102 103 104 105 106 107 108 109
Energy (GeV)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Effi
cien
cy
w.r
.t.
Lev
el3
Neutral Current Interactions
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
No
rm’
dR
elat
ive
Ab
und
anc
e(ν
En
erg
y)
νe Eff. Final wrt L3
ντ Eff. Final wrt L3
νµ Eff. Final wrt L3
Final Level νe Energy
Final Level ντ Energy
Final Level νµ Energy
Figure 5.38: E−2-weighted νe, ντ , and νµ efficiency per energy bin for charged-
current (left) and neutral-current (right) interactions with respect to Level 3. The
normalized energy distributions are also shown.
137
102 103 104 105 106 107 108 109Eν (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Effic
iency
with
resp
ectt
oLe
vel3
Efficiency w.r.t. Level 3Pre-BDT: 99.8% Eff.Pre-BDT (w/ mpod failures): 98.9% Eff.Score > 0.4: 68.9% Eff., 1.09 mHzScore > 0.425: 67.0% Eff., 0.79 mHzScore > 0.45: 64.8% Eff., 0.57 mHzScore > 0.475: 62.7% Eff., 0.39 mHz
Score > 0.5: 60.4% Eff., 0.27 mHzScore > 0.525: 57.9% Eff., 0.18 mHzScore > 0.55: 55.4% Eff., 0.13 mHzScore > 0.575: 52.7% Eff., 0.09 mHzScore > 0.6: 50.0% Eff., 0.06 mHzScore > 0.625: 47.3% Eff., 0.03 mHz
102 103 104 105 106 107 108 109Eν (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Effic
iency
with
resp
ectt
oLe
vel3
Efficiency w.r.t. Level 3Pre-BDT: 99.7% Eff.Pre-BDT (w/ mpod failures): 99.1% Eff.Score > 0.4: 66.1% Eff., 0.88 mHzScore > 0.425: 64.0% Eff., 0.64 mHzScore > 0.45: 61.7% Eff., 0.46 mHzScore > 0.475: 59.3% Eff., 0.34 mHz
Score > 0.5: 56.8% Eff., 0.23 mHzScore > 0.525: 54.2% Eff., 0.15 mHzScore > 0.55: 51.8% Eff., 0.11 mHzScore > 0.575: 49.3% Eff., 0.08 mHzScore > 0.6: 46.9% Eff., 0.05 mHzScore > 0.625: 44.5% Eff., 0.04 mHz
102 103 104 105 106 107 108 109Eν (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Effic
iency
with
resp
ectt
oLe
vel3
Efficiency w.r.t. Level 3Pre-BDT: 99.7% Eff.Pre-BDT (w/ mpod failures): 99.1% Eff.Score > 0.4: 68.4% Eff., 0.70 mHzScore > 0.425: 66.1% Eff., 0.50 mHzScore > 0.45: 63.5% Eff., 0.35 mHzScore > 0.475: 60.9% Eff., 0.24 mHz
Score > 0.5: 58.2% Eff., 0.16 mHzScore > 0.525: 55.5% Eff., 0.11 mHzScore > 0.55: 52.8% Eff., 0.07 mHzScore > 0.575: 50.0% Eff., 0.05 mHzScore > 0.6: 47.1% Eff., 0.04 mHzScore > 0.625: 44.3% Eff., 0.02 mHz
Figure 5.39: E−2-weighted νe signal efficiency per energy bin with respect to Level
3 for different possible final cuts on the BDT score. Top: IC79 selection. Middle:
IC86I selection. Bottom: IC86II selection.
138
Cut Level Signal Efficiency (%) Background Efficiency (%) Data Rate (Hz)
Online Filter – – 30
Level 3 72 2.5 0.77
Final 54 0.02 1.6× 10−4
Table 5.1: Signal and background efficiencies and data rates at different event se-
lection levels averaged over the three search years. Signal is E−2-weighted νe simu-
lation. Background is data outside of 2 hours of GRB prompt γ emission.
102 103 104 105 106 107 108 109
Primary νe Energy (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
Sig
na
lE
ffic
ien
cy
w.
r.t
.O
nli
ne
Fi
lte
r
Level 3
L3 Data 0.82Hz (L2 28.10Hz)
Precut
Precut Data 0.81Hz
Final
Final Data 0.0002Hz
Figure 5.40: E−2-weighted νe signal efficiency relative to the online Level 2 filter as
a function of neutrino energy. IC79 is shown, while IC86I and IC86II curves are
similar.
139
Compared to the final event samples of IceCube’s searches for νµ-induced
tracks from Northern Hemisphere GRBs, the background in this all-sky all-flavor
cascade search requires a cut to a data rate ten times smaller. The disparity be-
tween neutrino-induced showers and muon-induced stochastic energy loss showers
is less apparent than that between neutrino-induced tracks and detector-edge and
coincident muon-induced tracks incorrectly reconstructed as upgoing. In the North-
ern Hemisphere track searches, most of these muons are able to be removed, leaving
only atmospheric neutrinos. The final atmospheric neutrino purity with respect to
muons in this search is significantly less (∼40% to ∼90%) as a result. Nevertheless,
similar sensitivity to the track search is achieved through this search’s acceptance
of νe, ντ , and νµ signal from GRBs over the entire sky. The top plot of Figure
5.41 compares the effective areas for the two different GRB neutrino searches, while
the bottom compares the effective areas for the three cascade search seasons over
different detector configurations. The maximum energy in the bottom plot is at the
limit of available IC86II simulation at the time of this analysis.
140
103 104 105 106 107 108 109
Eν (GeV)
10−3
10−2
10−1
100
101
102
103
104
Eff
ect
ive
Ar
ea
(m
2 )
νe Full Sky Cascades
ντ Full Sky Cascades
νµ Full Sky Cascades
νe + ντ + νµ Full Sky Cascades
νµ Northern Hem. Tracks
103 104 105 106 107
Eν (GeV)
10−3
10−2
10−1
100
101
102
103
104
Eff
ect
ive
Ar
ea
(m
2 )
IC79 νe + ντ + νµ
IC86I νe + ντ + νµ
IC86II νe + ντ + νµ
Figure 5.41: Left: three-flavor effective areas for the full-sky shower-like and North-
ern Hemisphere track-like GRB-coincident event searches with the 79 string detector.
Right: effective areas for IC79, IC86I, and IC86II.
141
Chapter 6
Unbinned Likelihood Method
Once a final sample of events that resemble high energy neutrino-induced
electromagnetic or hadronic showers is selected, the likelihood that these events
are neutrino signal from observed GRBs must be calculated. This calculation in-
volves a likelihood function that incorporates the probabilities that an event is a
signal neutrino from a GRB or a background atmospheric neutrino or muon. These
background-like and signal-like probabilities are determined from individually nor-
malized probability distribution functions (PDFs) in time, space, and energy:
S(−→xi ) = P T imes (ti)× P Spaces (−→ri )× PEnergys (Ei)
B(−→xi ) = P T imeb (ti)× P Spaceb (−→ri )× PEnergyb (Ei)
(6.1)
where S and B are the probabilities that an event i with properties −→x i is signal and
background, respectively.
In order to choose the optimal final cut on BDT score and characterize the
significance of the result, a test statistic is constructed in the form of a maximum
likelihood function. This function incorporates probabilities that observed events are
signal and background as well as provides an estimator for the number of observed
signal events. The likelihood function combines the signal and background PDFs
with the Poisson probability PN of observing N events, given an expected number
142
of signal + background events.
This analysis was developed in a blind manner in order to optimally reduce
bias [128]. As mentioned in Section 5.4.1, events in the muon-dominated data outside
of two hours from any recorded GRB T100 are used to characterize the background.
The BDTs described in Chapter 5 are trained and the likelihood analysis described
in this chapter is developed on these blind data. IceCube data taken within two
hours of GRBs are untouched during the development of this analysis and, after
thorough review by the collaboration, “unblinded” and analyzed. The results of
this unblinding are presented in Chapter 7.
6.1 The Test Statistic
In this analysis, the number of signal events to be measured is unknown ahead
of time. The test statistic derived below provides an estimator for the number of
observed signal events in the form of a maximum likelihood function that depends
on measures of signal and background characteristics.
For a collection of n events, each with properties−→xi , represented by {x1, x2, ..., xn} =
{−→xi} and probability p(x; a), in which a is some unknown parameter, the likelihood
function is a product of probabilities.
L({−→xi} ; a) = p(x1; a)p(x2; a)...p(xn; a) =
n∏
i=1
p(x; a) (6.2)
The first probability function in the likelihood is the probability of observing
n events under the assumption that the expected total number of events is N. This
143
probability is defined by Poisson statistics.
PPoiss(n;N) =
Nne−N
n! (6.3)
The remaining probability functions P(−→xi ) are the probabilities that each event
i has properties −→xi . One can define P in the context of expected signal and back-
ground, where
N = ns + nb (6.4)
Let the probabilities of observing a signal(s) and background(b) event be defined as
ps =
ns
N , pb =
nb
N (6.5)
Let the probabilities of signal and background events having properties −→x be defined
as S(−→x ) and B(−→x ). Thus, P can be defined as
P(−→x ) = psS(−→x ) + pbB(−→x ) (6.6)
So now one may write the likelihood function as
L({−→xi} ;N) =
Nne−N
n!
n∏
i=1
P(x; a) (6.7)
The goal is to maximize L and since the logarithm is a monotonic function, maxi-
144
mizing lnL maximizes L.
lnL({−→xi} ;N) = ln
Nne−N
n! +
n∑
i=1
lnP(−→xi )
= n lnN −N − lnn! +
n∑
i=1
lnP(−→xi )
= −N − lnn! +
n∑
i=1
ln [NP(−→xi )]
= −N − lnn! +
n∑
i=1
ln [nsS(−→x ) + nbB(−→xi )]
(6.8)
Now the aim is to manipulate L({−→xi} ;ns) into a useful form for this particular
analysis. Since N is an expectation, one determines nb from off-source data (〈nb〉)
and one determines ns from maximizing L with respect to it (nˆs). Further, the
above likelihood function is simplified by dividing by its null hypothesis
lnL0({−→xi}) = lnL({−→xi} ;ns = 0) = −〈nb〉 − lnn! +
n∑
i=1
ln [〈nb〉B(−→xi )] (6.9)
Dividing the likelihood function by a single scalar has no effect on its maximum
value.
lnLR({−→xi} ;ns) = ln
L({−→xi} ;ns)
L0({−→xi})
= −ns +
n∑
i=1
ln [nsS(−→xi + 〈nb〉B(−→xi )]−
n∑
i=1
ln [〈nb〉B(−→xi )]
= −ns +
n∑
i=0
ln
[ nsS(−→xi )
〈nb〉B(−→xi )
+ 1
]
(6.10)
145
The estimated number of signal events nˆs maximizes the likelihood function.
∂ lnLR({−→xi} ;ns)
∂ns
∣∣∣∣
ns=nˆs
= 0 (6.11)
Finally, the analysis test statistic is defined as the logarithm of this maximum
value of the likelihood function.
T = lnLR({−→xi} ; nˆs) = −ns +
n∑
i=0
ln
[ nsS(−→xi )
〈nb〉B(−→xi )
+ 1
]
(6.12)
6.2 Probability Distribution Functions
PDFs are calculated in time, space, and energy for signal GRB-emitted neu-
trinos and background atmospheric muons using the GRBs and data for each of the
three data-taking seasons. As described in previous chapters, simulated neutrinos
are used for signal and muon-dominated data are used for background. The PDFs
capture the likelihood that signal neutrinos should be on-time and on-direction with
recorded GRBs and higher energy than background muons. This likelihood then is
evaluated in a single test statistic (Equation 6.12) for events in the final data sample
of each season.
6.2.1 Time PDFs
The signal time PDF is flat during the gamma-ray emission duration (T100
defined in Section 2.3) and has Gaussian tails before T1 and after T2. The width
of these Gaussian tails σt equals the duration of measured gamma-ray emission up
146
to 30 s and down to 2 s to account for possible small shifts in the neutrino emission
time with respect to that of the photons. Events are accepted out to ±4σt for each
GRB time window. The background time PDF is flat throughout the total period
of acceptance for each GRB. Examples of the signal time PDF ratios for short,
medium, and long duration bursts are given in Figure 6.1.
-100 0 100 200 300
t− T1 (s)
0.0
0.5
1.0
1.5
2.0
2.5
Tim
eP
DF
Ra
tio
T100 = 5 s GRB
T100 = 50 s GRB
T100 = 200 s GRB
Figure 6.1: Signal / background time PDF ratios for events during and near example
GRBs with different measured T100 values.
6.2.2 Space PDFs
The signal space PDF is a Kent distribution [129]:
P Spaces (−→ri , κ) =
κ
4pi sinh(κ)e
κ(rˆi·rˆGRB) (6.13)
for which the concentration parameter κ = 1σ2GRB+σ2i is the reciprocal of the un-
certainty in the GRB’s localization and the Cramer-Rao uncertainty in the event’s
reconstructed direction. rˆi is the reconstructed direction of the event and rˆGRB is
147
the most precise GRB localization available.
If the most precise GRB localization is from the FermiGBM detector, then
its systematic error is included as well. FermiGBM models its systematic error as
a sum of 2.6◦ with 72% weight and 10.4◦ with 28% weight Gaussian errors [34].
Both of these systematic error components is added in quadrature to the statistical
error, listed in the Appendix A tables. For FermiGBM-localized bursts, the two
concentration parameters are κ2.6 = 1(2.6◦)2+σ2GRB+σ2i and κ10.4 =
1
(10.4◦)2+σ2GRB+σ2i
.
The signal space PDF then becomes:
P Spaces (−→ri , κ) = 0.72× P Spaces (−→ri , κ2.6) + 0.28× P Spaces (−→ri , κ10.4) (6.14)
The background space PDF is a spline fit to the distribution of reconstructed
cos(θzenith) of all final cut level off-time data events. Because the dominating muon
background physically originates from only positive zenith values, higher background
weight is given to events reconstructed to originate from the Southern Hemisphere.
The negative zenith range of the background space PDF has contributions from
both misreconstructed muons as well as Earth-penetrating atmospheric neutrinos.
Small variance in the background reconstructed azimuth distribution has negligible
impact on this analysis, and so the background space PDF only varies with zenith.
The signal space PDFs are shown in Figure 6.2 for different combined event
direction and GRB localization uncertainties. The background space PDFs at final
event selection for the IC79, IC86I, and IC86II searches are shown in Figure 6.3.
As discussed in Section 4.2.7, five iterations of the Monopod reconstruction
148
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Angular Separation (rad)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Sig
nal
Spa
ce
PD
F
√σ2event + σ2GRB = 15◦√σ2event + σ2GRB = 40◦√σ2event + σ2GRB = 130◦
Figure 6.2: Signal space PDFs for three example events and correlated GRBs.
−1.0 −0.5 0.0 0.5 1.0cos (Reconstructed Zenith)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Backg
round
Space
PDF
Background Space PDF — BDT score > 0.525
Background PDFSpline Fit from DataNorm’d Histogram Values −1.0 −0.5 0.0 0.5 1.0cos (Reconstructed Zenith)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Backg
round
Space
PDF
Background Space PDF — BDT score > 0.525
Background PDFSpline Fit from DataNorm’d Histogram Values −1.0 −0.5 0.0 0.5 1.0cos (Reconstructed Zenith)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Backg
round
Space
PDF
Background Space PDF — BDT score > 0.525
Background PDFSpline Fit from DataNorm’d Histogram Values
Figure 6.3: Background space PDF, calculated from a spline fit to the zenith distri-
bution of data events at final event selection for the IC79 (left), IC86I (center), and
IC86II (right) searches.
achieves the best angular resolution and therefore is used for the signal and back-
ground space PDF calculations. Figure 6.4 shows the cumulative point spread func-
tion of νe, ντ , and νµ signal at the final event selection, at which all interactions
exhibit spherical cascade-like hit patterns. In this plot, each y-axis value is the per-
centage of events that yield less than or equal to the corresponding angular difference
between truth and Monopod reconstruction on the x-axis.
Directional error estimators, including the Cramer-Rao calculation used in this
149
0 20 40 60 80 100 120 140
Cumulative Point Spread Function [◦]
0.0
0.2
0.4
0.6
0.8
1.0
Fra
cti
on
νe median = 29.34◦
ντ median = 26.28◦
νµ median = 35.64◦
Figure 6.4: Cumulative point spread functions with median angular resolutions
shown of simulated astrophysical νe, ντ , and νµ at final event selection.
analysis and described in Section 4.2.8, have been observed to underestimate the
degree of misreconstructed direction on IceCube events. These underestimations
increase with energy and are likely due to imperfections in the modeling of the ice.
To correct σCR, a rescaling is applied as a function of the Monopod energy. This
rescaling is calculated by a spline fit to the ratio of the actual error in reconstructed
direction to the Cramer-Rao estimated error, the “pull,” versus Monopod energy for
E−2-weighted νe signal. This spline fit is applied to the 39th percentile pull value,
which is the 1σ percentile for the 2D normal distribution.
The corrective spline is calculated in this way for each detector configuration
at Level 3, for sufficient statistics. Before the pseudo-search trials and unbinned like-
lihood analysis are performed, the correction for σCR is applied to the data and sim-
ulated νe, ντ , νµ signal events based on each event’s original Cramer-Rao estimation
150
and reconstructed energy. The νe signal log10(σTrue/σCR) vs. log10(Monopod.energy/GeV )
distributions before and after the spline correction for each detector are shown in
Figures 6.5 and 6.6.
151
3 4 5 6 7 8 9
log10(energy/GeV)
3
2
1
0
1
2
3
4
5
log
10
(d
Ψ/
err
or)
IC79 Monopod CR Correction vs. Energy | E−2  νe
5.4
4.8
4.2
3.6
3.0
2.4
1.8
1.2
0.6
log
10
(w
eig
ht
)
3 4 5 6 7 8
log10(energy/GeV)
3
2
1
0
1
2
3
4
5
log
10
(d
Ψ/
err
or)
IC86I Monopod CR Correction vs. Energy | E−2  νe
10.5
9.0
7.5
6.0
4.5
3.0
1.5
log
10
(w
eig
ht
)
3 4 5 6 7
log10(energy/GeV)
3
2
1
0
1
2
3
4
5
log
10
(d
Ψ/
err
or)
IC86II Monopod CR Correction vs. Energy | E−2  νe
6.4
5.6
4.8
4.0
3.2
2.4
1.6
0.8
log
10
(w
eig
ht
)
Figure 6.5: Spline correction (black lines) to Cramer-Rao estimated directional un-
certainty for E−2-weighted νe simulated events at Level 3 event selection, for IC79
(top), IC86I (center), and IC86II (bottom).
152
3 4 5 6 7 8 9
log10(energy/GeV)
3
2
1
0
1
2
3
4
5
log
10
(d
Ψ/
err
or)
IC79 Monopod CR Correction Applied
5.4
4.8
4.2
3.6
3.0
2.4
1.8
1.2
0.6
log
10
(w
eig
ht
)
3 4 5 6 7 8
log10(energy/GeV)
3
2
1
0
1
2
3
4
5
log
10
(d
Ψ/
err
or)
IC86I Monopod CR Correction vs. Energy | E−2  νe
9
8
7
6
5
4
3
2
1
log
10
(w
eig
ht
)
3 4 5 6 7
log10(energy/GeV)
3
2
1
0
1
2
3
4
5
log
10
(d
Ψ/
err
or)
IC86II Monopod CR Correction Applied
7.2
6.4
5.6
4.8
4.0
3.2
2.4
1.6
0.8
log
10
(w
eig
ht
)
Figure 6.6: Applied spline correction (black lines) to Cramer-Rao estimated direc-
tional uncertainty for E−2-weighted νe simulated events at Level 3 event selection,
for IC79 (top), IC86I (center), and IC86II (bottom).
153
6.2.3 Energy PDFs
The signal and background energy PDFs are the reconstructed energy distri-
butions of E−2-weighted νe simulation and off-time data, respectively. A spline is fit
to the ratio of these two PDFs. Few background events in the final sample have re-
constructed energies above 1 PeV, and so a constant ratio of signal and background
energy PDFs is conservatively assumed at energies above 1 PeV. The signal and
background energy PDFs, their spline-fit ratio, and the values that correspond to
the two most significant events in the search are shown for the IC79, IC86I, and
IC86II searches in Figure 6.7.
As with the space PDFs, five-iteration Monopod is used for the reconstructed
energy in the signal and background energy PDFs. The reconstructed energy versus
true energy for simulated νe signal at the Level 3 event selection is plotted in Figure
6.8 for charged-current (left) and neutral-current (right) interactions in and around
the detector volume. The energy resolutions for the three E−2-weighted neutrino
flavors at final event selection for charged-current (left) and neutral-current (right)
interactions are plotted in Figure 6.9. The reconstructed energy for neutral cur-
rent interactions is less than that of the primary neutrino because of the energy
dissipation to outlets without Cherenkov emission.
154
2 3 4 5 6 7 8 9log10 (Reconstructed Energy/GeV)
10−6
10−5
10−4
10−3
10−2
10−1
100
Nor
mal
ized
PD
FV
alue
S/B Energy PDF Ratio — BDT score > 0.525
10−2
10−1
100
101
102
103
Ene
rgy
PD
FR
atio
E−2 νe SignalData as Background
2 3 4 5 6 7 8 9log10 (Reconstructed Energy/GeV)
10−6
10−5
10−4
10−3
10−2
10−1
100
Nor
mal
ized
PD
FV
alue
S/B Energy PDF Ratio — BDT score > 0.525
10−2
10−1
100
101
102
103
Ene
rgy
PD
FR
atio
E−2 νe SignalData as Background
2 3 4 5 6 7 8 9log10 (Reconstructed Energy/GeV)
10−6
10−5
10−4
10−3
10−2
10−1
100
Nor
mal
ized
PD
FV
alue
S/B Energy PDF Ratio — BDT score > 0.525
10−2
10−1
100
101
102
Ene
rgy
PD
FR
atio
E−2 νe SignalData as Background
Figure 6.7: IC79 (top), IC86I (middle), and IC86II (bottom) energy PDF ra-
tios. Left vertical axis: Reconstructed energy distributions of data (dots) and
E−2-weighted νe signal (red line) at final cut level. Right vertical axis: Signal /
background energy PDF distribution (black lines) calculated from a spline fit to the
ratio of the two energy distributions.
155
2 3 4 5 6 7 8 9log10 (True Energy / GeV)
2
3
4
5
6
7
8
9
log1
0(M
ono
pod
5It
er.
Rec
o.E
nerg
y/
GeV
) νe CC Interactions
2 3 4 5 6 7 8 9log10 (True Energy / GeV)
2
3
4
5
6
7
8
9
log1
0(M
ono
pod
5It
er.
Rec
o.E
nerg
y/
GeV
) νe NC Interactions
Figure 6.8: Left: Five iteration Monopod reconstructed energy versus Monte Carlo
truth energy for E−2-weighted νe charged-current (left) and neutral-current (right)
interactions in the ice.
−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0log(Ereco) - log(Etrue)
0
10
20
30
40
50
arbi
trar
yun
its
νe CC interactionsντ CC interactionsνµ CC interactions
−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0log(Ereco) - log(Etrue)
0.0
0.5
1.0
1.5
2.0
arbi
trar
yun
its
νe NC interactionsντ NC interactionsνµ NC interactions
Figure 6.9: Left: Energy resolution per neutrino flavor for charged-current inter-
actions at final selection. Right: Energy resolution per neutrino flavor for neutral-
current interactions at final selection.
156
6.3 Pseudo-Experiment Methodology
To set discovery significance thresholds, first 108 pseudo-search trials are per-
formed using only background data for a range of BDT score cuts. As was defined
in the BDT training, background events are taken from data (which are dominated
by atmospheric muons, even at final selection level) with interaction times outside
of two hours from a GRB T100. Each background sample has its own 〈nb〉cut esti-
mated by multiplying the off-time data rate by the summed search windows about
all GRB times, ∑NGRBsi (T100,i + 8σt,i). Lower 〈nb〉cut values are expected for tighter
BDT score cuts.
In each background-only trial, for each GRB, a pseudo-random number of
observed events is chosen within the T100 ± 4σt search time window about the
gamma-ray emission from a Poisson distribution with expectation determined by
the background data rate and time window. If the number of events is 0, then T
receives no contribution from the search window about that GRB. If the number of
events is greater than 0, then each event is constructed using the following steps:
(1) choose a random time PDF value; (2) choose a random azimuth within 0 to 2pi;
(3) choose a reconstructed energy by sampling from the background distribution;
(4) choose a reconstructed zenith by sampling from the background distribution of
events with similar energy; (5) choose an estimated error in reconstructed direction
by sampling from the background distribution of events with similar energy and
zenith. Finally, with the signal and background PDF values for every event, the
test statistic is calculated for each trial. A distribution like those shown in Figure
157
6.13 is obtained for every cut on BDT score.
6.4 Sensitivity and Discovery Potentials
The optimal final cut on BDT score is chosen by injecting simulated neutrino
signal along with background data and performing 104 pseudo-search trials for a
range of BDT score cuts. Electron, tau, and muon neutrinos are used for signal
injection with equal weight because of the expected 1:1:1 astrophysical flavor ratio
at Earth. The background events are selected for each GRB using the same pre-
scription detailed above in Section 6.3 for the background-only trials. The simulated
signal events within an 11◦ circle about each GRB contribute to the likelihood with
probabilities proportional to their simulated weights. Signal is increasingly weighted
until a certain discovery or limit-setting threshold is reached.
The cuts on BDT score that allow the best possible upper limit, defined as the
lowest signal flux required to surpass the median T value in 90% of the trials, and
the best discovery potential, defined as the lowest signal flux required to surpass the
5σ T value in 50% of the trials, is determined. The final cut was optimized to set the
best possible upper limit while suffering little loss in discovery potential. This final
level of event selection is the loosest one that includes possible borderline interesting
events while also providing strong limit setting and discovery capabilities. The final
cut on BDT score is score > 0.525 for each detector configuration’s BDT.
These discovery and limit-setting potentials per BDT score cut are shown in
Figure 6.10 for a general E−2 spectrum for each of the three search seasons. For
158
the E−2-weighted spectrum, the IC86I and IC86II the neutrino fluence required for
the various discovery thresholds are a few percent larger than what is required for
IC79. These differences are due to the limited high energy statistics in the available
simulated neutrino datasets in IC86I and IC86II. Additionally, the extremely long
GRB111209A during IC86I allows more background in each trial compared to that
of the other two seasons. Removing this burst from the optimization reduces the
required signal fluence for discovery by 4% without changing the optimal final cut.
The discovery and limit-setting potentials per BDT score cut are shown in
Figure 6.11 for the benchmark standard internal shock fireball, the photospheric
fireball, and the ICMART fireball spectra plotted in the top panel of Figure 2.9.
These curves were calculated using the IC79 datasets. The photospheric model
predicts more neutrinos to be detected in IceCube than the standard internal shock
model, and therefore requires a lower multiplying factor to surpass a given test
statistic threshold. The inverse is true for the ICMART model.
The sensitivity and discovery potential for a given selection on BDT score can
be expressed on the so-called Frequentist Plane shown in Figure 6.12. The vertical
axis is the per-flavor neutrino signal fluence injected in order to obtain the horizontal
axis test statistic value x% of the time, where x is given by the color scale.
159
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Per
Fla
vor
E2
F ν
(Ge
Vc
m−
2 )
T > 0 in 90% of Trials
T > 3σ in 50% of Trials
T > 4σ in 50% of Trials
T > 5σ in 50% of Trials
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Per
Fla
vor
E2
F ν
(Ge
Vc
m−
2 )
T > 0 in 90% of Trials
T > 3σ in 50% of Trials
T > 4σ in 50% of Trials
T > 5σ in 50% of Trials
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Per
Fla
vor
E2
F ν
(Ge
Vc
m−
2 )
T > 0 in 90% of Trials
T > 3σ in 50% of Trials
T > 4σ in 50% of Trials
T > 5σ in 50% of Trials
Figure 6.10: Limit setting and discovery potentials per BDT score cut for IC79
(top), IC86I (middle), and IC86II (bottom). Horizontal axis corresponds to a cut
on BDT score greater than the given value. The vertical axis corresponds to the
E−2-weighted spectrum signal weight needed in order to reach the given threshold.
The vertical dashed line represents the final analysis cut of BDT score > 0.525.
160
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
6
8
10
12
14
16
18
20
µf
or
Ben
chm
ark
I.S.
Fir
eba
llM
ode
lF
lux T > 0 in 90% of TrialsT > 3σ in 50% of Trials
T > 4σ in 50% of Trials
T > 5σ in 50% of Trials
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
3
4
5
6
7
8
9
10
11
12
µf
or
Ben
chm
ark
Ph
oto
sph
eric
Fir
eba
llM
ode
lF
lux
T > 0 in 90% of Trials
T > 3σ in 50% of Trials
T > 4σ in 50% of Trials
T > 5σ in 50% of Trials
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
200
250
300
350
400
450
500
550
600
650
µf
or
Ben
chm
ark
ICM
AR
TF
ireb
all
Mo
del
Flu
x
T > 0 in 90% of Trials
T > 3σ in 50% of Trials
T > 4σ in 50% of Trials
T > 5σ in 50% of Trials
Figure 6.11: IC79 season limit setting and discovery potentials per BDT score cut
for internal shock (top), photospheric (middle), and ICMART (bottom) models.
Horizontal axis corresponds to a cut on BDT score greater than the given value.
Vertical axis corresponds to the multiplying factor µ on the benchmark fireball
model neutrino flux shown in Figure 2.9 in order to reach the given threshold. The
vertical dashed line represents the final analysis cut of BDT score > 0.525.161
0 5 10 15 20 25 30 35 40
Test Statistic Value
0.0
0.1
0.2
0.3
0.4
0.5
Pe
r
Fl
av
or
E2
F ν
(G
eV
/c
m
2 )
Frequentist Plane
3 σ
4 σ
5 σ
50% Prob. of Observing Test Statistic Value
90% Prob. of Observing Test Statistic Value
Figure 6.12: Frequentist plane for IC79 signal injection over background at final
event selection level. The color corresponds to the probability of observing the test
statistic value given the signal strength.
162
6.5 Per-GRB Optimization Studies
An alternative implementation of the stacked T unbinned likelihood analysis
discussed above that gives more significance to individual GRBs has been stud-
ied [130]. If a single GRB in a stacked search dominates the neutrino flux, then
calculating the test statistic on a per-burst basis improves the discovery potential
for such a scenario. The only modification needed to Equation 6.12 is that ns,
〈nb〉, and consequently T are calculated for each burst. Then for each trial or fi-
nal measurement, the maximum per-burst test statistic max (Tg) is reported. This
method also gives higher weight to multiple neutrinos coincident with the same
GRB, whereas the stacked T method used in this analysis does not.
The background-only test statistic distributions for the current stacked T
method (left) and the max (Tg) method (right) are shown in Figure 6.13. The me-
dian null hypothesis value using the current method is zero but it is nonzero using
max (Tg) because 〈nb〉 is greatly reduced when only applied to a single GRB’s T100,
which allows many more non-zero test statistic values. In Figure 6.14, the max (Tg)
discovery potential curves are worse than those for the stacked T method for an E−2
fluence distributed by a sample of bursts over the whole sky. The current stacking
analysis combines coincidences across multiple GRBs and thus should do better in
this scenario. In Figure 6.15, the max (Tg) method shows to be more powerful than
the stacked T method for observing a single random injected signal source. Ad-
ditionally, a much looser final cut is allowed by the max (Tg) calculation because
background contamination is relatively minor for a wide range of event selections.
163
This search was only optimized using the stacked T methodology. However, fu-
ture stacked and near-real-time searches will be optimized on the per-burst max (Tg).
The results then will have the abilities to be more sensitive to a single burst neutrino
fluence and to set strong limits while accruing a minor trials factor penalty.
0 2 4 6 8 10 12 14T
100
101
102
103
104
105
106
107
108
Tria
lsp
erB
in
3 σ4 σ5 σ
0 5 10 15 20Test Statistic Value
100
101
102
103
104
105
106
107
Tria
lsp
erB
in
median3 σ4 σ5 σ
Figure 6.13: Test statistic distributions for 108 randomized background-only pseudo-
searches at final cut level for the stacked T (left) and the max (Tg) (right) likelihood
methods. The vertical lines represent test statistic values for the median and 3σ,
4σ, and 5σ discovery.
0.35 0.40 0.45 0.50 0.55 0.60 0.65BDT score cut
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Per
Flav
orE
2 F ν
(Ge
Vc
m−2
)
T > 0 in 90% of TrialsT > 3σ in 50% of TrialsT > 4σ in 50% of TrialsT > 5σ in 50% of Trials
0.35 0.40 0.45 0.50 0.55 0.60 0.65BDT score cut
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Per
Flav
orE
2 F ν
(Ge
Vc
m−2
)
T > 0 in 90% of TrialsT > 3σ in 50% of TrialsT > 4σ in 50% of TrialsT > 5σ in 50% of Trials
Figure 6.14: Discovery potential versus cut on BDT score for an E−2 fluence dis-
tributed over the entire sky. Left: stacked T . Right: max (Tg).
164
0.35 0.40 0.45 0.50 0.55 0.60 0.65BDT score cut
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Per
Flav
orE
2 F ν
(Ge
Vc
m−2
)
T > 3σ in 50% of TrialsT > 4σ in 50% of TrialsT > 5σ in 50% of Trials
0.35 0.40 0.45 0.50 0.55 0.60 0.65BDT score cut
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Per
Flav
orE
2 F ν
(Ge
Vc
m−2
)
T > 3σ in 50% of TrialsT > 4σ in 50% of TrialsT > 5σ in 50% of Trials
Figure 6.15: Discovery potential versus cut on BDT score for an E−2 fluence from
a single random burst. Left: stacked T . Right: max (Tg).
6.6 Characteristics of a Discovery
The benchmark internal shock, photospheric, and ICMART fireball model
spectra plotted in Figure 2.9 are expected to yield 3.3, 5.4, and 0.1 neutrinos, re-
spectively, over the combined three years of all-flavor shower searches and four years
of νµ track searches in IceCube. The all-flavor shower search has an average 〈nb〉 of
10 events per year for the three search years. This expectation is concentrated at
lower energies than the expected signal and is weighted by the time, space, and en-
ergy PDFs accordingly in our unbinned likelihood. The expected background during
just the T100 of each GRB is 3 events per year. An observation of three 1 PeV neu-
trinos correlated with three GRBs, with the same temporal and spacial properties
as IC79 Event 1 and its respective GRB in Table 7.1 and Figure 7.2, would yield a
T value over 12 and a 5σ discovery based on the background-only distribution.
165
Chapter 7
Results
7.1 Three Year Cascade Coincidence Search Results
In the three years of data analyzed, 11 events survived the final selection and
were during GRB T100s compared to an expected 9.0±0.2 background events (about
7 atmospheric muons, 1.5 atmospheric νµ, 0.5 atmospheric νe) estimated from off-
time data rates. More than half of the measured on-time events are not correlated
with any GRB, considering their estimated uncertainties in reconstructed direction.
Five events are found to be correlated in the PDF values with five GRBs: two during
IC79 yielding an individual search season T = 0.009 and P-value of 0.21, and three
during IC86I yielding an individual search season T = 0.223 and P-value of 0.11.
IC86II had a T = 0 and P-value of 1. The estimated number of signal events from
the test statistic maximization is 0.20 for the IC79 result and 0.75 for the IC86I
result. These estimations are reasonable given that none of the GRB-correlated
events are very significant on their own.
Results of multiple detector configurations and signal channels can be com-
bined by adding maximized test statistics for each configuration and channel:
T =
∑
c
{
−(nˆs)c +
Nc∑
i=0
ln
[ (nˆs)cSc(−→xi )
〈nb〉cBc(−→xi )
+ 1
]}
(7.1)
166
where c represents each combination of search channel and detector configuration.
The combined three year cascade search P-value is 0.32, determined from the com-
bined null hypothesis test statistic distribution shown in Figure 7.1. Therefore, the
background is likely to produce such a result one in five times, and this result is not
nearly significant enough for a discovery.
0 2 4 6 8 10 12 14 16
Test Statistic Value
100
101
102
103
104
105
106
107
108
Tr
ia
ls
pe
r
Bi
n
3 Year Null Test Statistic Dist.
3 Yr Result: P=32.4%
3 σ
4 σ
5 σ
Figure 7.1: Three year cascade search combined null hypothesis test statistic distri-
bution with the combined test statistic as the vertical solid line.
The Northern Hemisphere track searches in four years of data [17] resulted in
a single neutrino candidate event correlated with a GRB, and the four year track
result combined with the three year cascade result of this work yields a combined P-
value of 0.55. Considering the atmospheric neutrino purity of each search, discussed
167
in Section 5.4.5, the track event is almost certainly a νµ while some of the cascade
events are likely high energy atmospheric muons. Table 7.1 shows the time, space,
and energy data for these events and GRBs. These most significant cascade events
all had BDT scores near 0.6.
The first IC79 event occurred on the edge of the detector, imparted 11 TeV in
the ice, and was reconstructed to be 0.72σ away from the well localized GRB101213A.
The second IC79 event occurred at a corner of the detector configuration, imparted
34 TeV in the ice, and was reconstructed to be 0.94σ away from the poorly localized
GRB110101B. The large directional uncertainty of the second event is due to the
location of its interaction in the detector, with relatively few DOMs able to record
the Cherenkov light.
The first IC86I event occurred inside of the detector, but only imparted 3.4
TeV in the ice, which is relatively small for the expected signal. This event was
reconstructed to be 2.1σ away from the fairly well-localized GRB110521B. The sec-
ond IC86I event occurred on the edge of the detector, imparted 31 TeV in the ice,
and was reconstructed to be 2.7σ away from the well-localized GRB111212A. The
third IC86I event occurred inside of the detector, imparted 3.8 TeV in the ice, and
was reconstructed to be 2.2σ away from the well-localized GRB120114A.
A view of each of these five most significant events’ Cherenkov patterns can be
seen in Figures 7.6 and 7.7. From this view, it is clear that IC86I Event 3 consists of
two coincident muons 20 µs apart, where one loses around a TeV of energy inside of
the detector. The other events, while possibly neutrinos, are not of high significance
individually, but give a non-zero stacked test statistic collectively.
168
Time Angular Uncertainty Angular Separation Fluence/Energy
GRB101213A T100 = 202 s 0.0005◦ 7.4× 10−6 erg cm−2
IC79 Event 1 T1 + 109 s 32.0◦ 23◦ 11 TeV
GRB110101B T100 = 235 s 16.5◦ 6.6× 10−6 erg cm−2
IC79 Event 2 T1 + 141 s 118◦ 112◦ 34 TeV
GRB110521B T100 = 6.14 s 1.31◦ 3.6× 10−6 erg cm−2
IC86I Event 1 T1 + 0.26 s 16.5◦ 34.6◦ 3.4 TeV
GRB111212A T100 = 68.5 s 0.0004◦ 1.4× 10−6 erg cm−2
IC86I Event 2 T1 + 11.7 s 44.8◦ 120.2◦ 30.6 TeV
GRB120114A T100 = 43.3 s 0.04◦ 2.4× 10−6 erg cm−2
IC86I Event 3 T1 + 57.2 s 7.9◦ 17.7◦ 3.8 TeV
GRB100718Aa T100 = 39 s 10.2◦ 2.5× 10−6 erg cm−2
νµ Track Eventa T1 + 15 s 16◦ 1.3◦ & 10 TeV
Table 7.1: GRB and Event Properties for the 3 Year Cascade and 4 Year Track
Search Coincidences. a Corresponds to the νµ track search coincidence discussed
in [17]
The number of Glashow resonance interactions expected to occur during the
summed three season T100 time window is about 0.02. This expectation was deter-
mined by weighting the νe signal simulation to the best-fit astrophysical neutrino
spectrum with IceCube [121]. The number expected on-time and on-source is much
lower. Nevertheless, a Glashow resonance interaction correlated with a GRB would
be a discovery-level event.
169
0.0 0.5 1.0 1.5 2.0 2.5 3.0Angular Separation (rad)
0.0
0.5
1.0
1.5
2.0
Sign
alS
pac
ePD
F
Event 1, GRB101213Aσevent = 32.0◦ σGRB = 0.0005◦Event 2, GRB110101Bσevent = 117.7◦ σGRB = 16.4900◦
−200 −100 0 100 200 300 4000.0
0.5
1.0
1.5
2.0
2.5
3.0
Tim
ePD
FR
atio
GRB101213AEvent 1, r=1.59GRB110101BEvent 2, r=1.53
Figure 7.2: Signal space PDF and signal/background time PDF ratio for each of
the two most significant IC79 events.
0.0 0.5 1.0 1.5 2.0 2.5 3.0Angular Separation (rad)
0.0
0.5
1.0
1.5
2.0
Sign
alS
pac
ePD
F
Event 1, GRB110521Bσevent = 16.5◦ σGRB = 1.3100◦Event 2, GRB111212Aσevent = 44.8◦ σGRB = 0.0004◦Event 3, GRB120114Aσevent = 7.9◦ σGRB = 0.0383◦
−150 −100 −50 0 50 100 150 2000.0
0.5
1.0
1.5
2.0
2.5
3.0
Tim
ePD
FR
atio
GRB110521BEvent 1, r=2.57GRB111212AEvent 2, r=2.15GRB120114AEvent 3, r=2.14
Figure 7.3: Signal space PDF and signal/background time PDF ratio for each of
the three most significant IC86I events.
170
-100 0 100 200 300Seconds from GRB T1
0.0
0.5
1.0
1.5
2.0
2.5
Tim
ePD
FRa
tio
GRB101213ATime PDF RatioIC79Event 1 Time
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Ligh
tcur
veC
ount
spe
rBin
(Arb
.Sca
le)
GRB101213ABAT LightcurveT100 Bounds
−100 0 100 200 300Seconds from GRB T1
0.0
0.5
1.0
1.5
2.0
2.5
Tim
ePD
FRa
tio
GRB110101BTime PDF RatioIC79Event 2 Time
530
540
550
560
570
580
590
600
610
Ligh
tcur
veC
ount
spe
rBin
(Arb
.Sca
le)
GRB110101BGBM LightcurveT100 Bounds
Figure 7.4: Signal/background time PDF ratio and GRB lightcurve for each of the
two most significant IC79 events and their corresponding GRBs.
-20 -10 0 10 20 30Seconds from GRB T1
0.0
0.5
1.0
1.5
2.0
2.5
Tim
ePD
FRa
tio
GRB110521BTime PDF RatioIC86IEvent 1 Time
450
500
550
600
650
700
750
Ligh
tcur
veC
ount
spe
rBin
(Arb
.Sca
le)
GRB110521BGBM LightcurveT100 Bounds
−100 −50 0 50 100 150Seconds from GRB T1
0.0
0.5
1.0
1.5
2.0
2.5
Tim
ePD
FRa
tio
GRB111212ATime PDF RatioIC86IEvent 2 Time
−0.2
0.0
0.2
0.4
0.6
Ligh
tcur
veC
ount
spe
rBin
(Arb
.Sca
le)
GRB111212ABAT LightcurveT100 Bounds
−100 −50 0 50 100 150Seconds from GRB T1
0.0
0.5
1.0
1.5
2.0
2.5
Tim
ePD
FRa
tio
GRB120114ATime PDF RatioIC86IEvent 3 Time
520
540
560
580
600
620
640
660
Ligh
tcur
veC
ount
spe
rBin
(Arb
.Sca
le)
GRB120114AGBM LightcurveT100 Bounds
Figure 7.5: Signal/background time PDF ratio and GRB lightcurve for each of the
three most significant IC86I events and their corresponding GRBs.
171
Figure 7.6: Detector views for the two most significant IC79 events (Events 1, 2 in
Table 7.1 are left and right, respectively). Red is earlier and blue is later Cherenkov
light. DOM sphere size is amount of Cherenkov light collected.
Figure 7.7: Detector views for the three most significant IC86I events (Events 1, 2,
3 in Table 7.1 are left, middle, and right, respectively). Red is earlier and blue is
later Cherenkov light. DOM sphere size is amount of Cherenkov light collected.
172
7.2 Systematic Errors
There are several sources of uncertainty that can contribute to systematic
error in the model limits set by this analysis. Uncertainties in the South Pole ice,
DOM sensitivity to the Cherenkov light, and > TeV neutrino cross sections must be
considered given the simulation’s dependence on them. Potential systematic error
in the background dataset is small in this analysis because detector data was used;
however, the atmospheric muon interaction rate in IceCube varies throughout the
year and this must be considered. All of these factors are taken into account by
fixing them to their expected extrema, processing the varied datasets through the
analysis event selection, and recalculating the upper limits.
The 90% CL best possible (T > 0) E−2 spectrum upper limit for each dataset
was calculated and compared to the limit of the baseline assumptions dataset. For
the sources of error that result in a worse limit than the baseline, the relative changes
in this flux limit compared to the baseline are added in quadrature. At the time
of this writing, the IC86I detector season had the largest amount of νe simulated
data produced with the systematic variations applied. Additionally, the sensitivity
of this analysis does not vary substantially between the three data-taking seasons
considered. Therefore, the total systematic error for IC86I is used for the combined
limits presented in Sections 7.3.1 and 7.3.2 below.
173
7.2.1 Ice Model
As is described in Section 4.1, the simulation chain ends with the propagation
of Cherenkov light from the shower or muon track and its collection in the PMTs.
These simulated light paths rely on a model of the South Pole ice detailing its
optical properties [103]. The average properties over 10 m-thick vertical increments
are characterized in a table of absorption and effective scattering coefficients [102].
A variance up to 10% is accepted for these coefficients [103]. Simulated νe
signal interactions with absorption and scattering adjusted to 1.1 and 0.93 times
the benchmark is processed through the event selection and the best possible limit
is calculated. More absorption reduces the amount of Cherenkov light collected by
the DOMs during a particle interaction, requiring a larger signal flux for a non-zero
test statistic. Simulated νe signal interactions with absorption coefficients adjusted
to 1.1 times the benchmark values yield a 90% CL best possible upper limit flux
9.5% greater than the benchmark. More scattering allows more photons to hit the
DOMs near a cascade, requiring a smaller signal flux for a non-zero T . Simulated νe
signal interactions with scattering coefficients adjusted to 1.1 times the benchmark
values yield an upper limit flux 2.3% less than the benchmark. Simulated νe signal
interactions with absorption and scattering coefficients adjusted to 0.93 times the
benchmark values yield an upper limit flux 11% less than the benchmark.
More recent studies of the ice discovered anisoptropic scattering properties in
it [131]. This slight azimuthal dependence in the scattering of photons is not a result
of DOM behavior or bubbles in the melted and re-frozen string holes, but rather
174
inherent in the glacier as a whole. While the underlying cause of this preferential
alignment is currently unknown, it can be incorporated macroscopically in the ab-
sorption and scattering tables. νe interactions with and without ice anisotropy are
processed through the same event selection criteria. The anisotropy-included ice
model upper limit is 1.9% greater than that of the no-anisotropy ice model used in
this analysis.
7.2.2 Optical Module Sensitivity
The DOM sensitivity to Cherenkov photons was measured in a freezer lab be-
fore South Pole deployment. From these studies, a variance of ±10% is accepted as
possible [85]. As with the uncertainties in the ice model, simulated νe signal inter-
actions with PMT quantum efficiency adjusted to 1.05 and .9 times the benchmark
is processed through the event selection and the best possible limit is calculated.
Reducing the quantum efficiency reduces the amount of charge recorded for a given
amount of Cherenkov light incident on the PMT, and consequently reduces the num-
ber of events passing the final event selection. The higher efficiency upper limit is
3.9% greater than that of the benchmark; and the lower efficiency upper limit is
2.7% less than that of the benchmark.
7.2.3 Neutrino Interactions
Uncertainties in > TeV neutrino interactions may also contribute to systematic
error in this analysis. Neutrino cross sections from the CTEQ5 model [98] are used
175
in simulations for this work. The uncertainty on the neutrino-nucleon cross sections
is estimated to be ∼ 5% [132]. Larger cross sections would increase the probability
of interaction in and near the detector but also decrease the amount of neutrino
measured originating from the Northern Hemisphere sky. A conservative 5% is
chosen to contribute to the total systematic error on the model upper limits.
7.2.4 Seasonal Rate Variation
Jul 2
010
Aug
2010
Sep
2010
Oct
2010
Nov
2010
Dec
2010
Jan
2011
Feb
2011
Mar
2011
Apr
2011
May
2011
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Ra
te
(H
z)
Figure 7.8: Seasonal variation in IC79 data at Level 3 event selection for this anal-
ysis.
The total event rate in IceCube changes throughout the year. This variation is
due to the changing atmospheric temperature [133]. The warmer sunlit atmosphere
is less dense, and so the charged mesons created in cosmic ray interactions are less
likely to interact and thus decay to high energy muons more often than during the
176
colder winter months.
As seen in Figure 7.8, the background rate at Level 3 selection varies by
about 10%. The changing rate is difficult to observe in the much lower final level
background rate. To quantify this seasonal variation’s effect on the result, the
expected background rate 〈nb〉 is varied by ±10% and the limits are recalculated.
Because the background rate at the final event selection level is very low, there is
no appreciable change in the upper limits compared to those from the mean 〈nb〉
value used in the analysis.
7.2.5 Total Systematic Error
Dataset Description % Change w.r.t. Benchmark Limit
10601 Baseline 0
10067 +10% Absorption +9.5
10068 +10% Scattering −2.3
10069 −7.1% Scattering and Absorption −11.2
10413 Anisotropic Ice Model +1.9
10560 +5% DOM efficiency +3.9
10439 −10% DOM efficiency −2.7
– ±10% data rate 0
– ν interactions ±5
Table 7.2: Systematic error sources and effects assuming an E−2-weighted νe signal.
The percent change of the 90% CL best possible (T > 0) upper limit compared
to that of the benchmark assumptions is shown in Table 7.2.5 for each source of
systematic error. The limits per cut on BDT score for the systematics with positive
percent change with respect to the benchmark limits are plotted in Figure 7.9. These
positive percent changes are added in quadrature and the total 11.6% is applied to
the combined upper limits in Sections 7.3.1 and 7.3.2. While the strength of these
177
0.35 0.40 0.45 0.50 0.55 0.60 0.65
BDT score cut
0.30
0.35
0.40
0.45
0.50
Pe
rF
lav
or
E2
F
(G
eV
/c
m2
)
Best Possible Limits
+10% absorption
+10% DOM efficiency
SPICE-Lea ice model
Baseline
Figure 7.9: Best possible upper limits for the sources of systematic error that degrade
the limit compared to the benchmark assumptions.
systematic effects do vary with spectrum shape, as lower energy events yield less
photoelectrons with more ice absorption and lower DOM efficiency, the variation is
small across the range of spectra considered in the limit calculations of the following
sections. Therefore, the total error calculated above for an E−2 spectrum is applied
to all Γ and break energy spectra limit values.
7.3 GRB Neutrino Production Model Limits
Considering the low significance of these results, 90% CL upper limits are
placed on models normalized to the observed flux of UHECRs as well as models
normalized to the observed gamma-ray fluence of each GRB. These limits are cal-
culated by combining the three-year cascade search results and four-year Northern
178
Hemisphere track search results using the multiple configuration and channel test
statistic given in equation 7.1. The limit calculations use a Feldman-Cousins ap-
proach [134] in which simulated electron, tau, and muon neutrinos are weighted to
a certain spectrum and normalization and injected over background in the pseudo-
searches; the exclusion confidence level (CL) is the fraction of pseudo-search trials
that yield T ≥ Tobserved.
7.3.1 Limits Normalized to Cosmic Ray Production in GRBs
Figure 7.10 shows exclusion contours for per-flavor double broken power law
spectra, at different first break energies b and normalizations 2bφ0, of the following
form:
Φν(E) = φ0 ×



E−1−1b , E < b
E−2, b ≤ E < 10b
E−4(10b)2, 10b ≤ E
(7.2)
The combined limits largely rule out cosmic ray escape via neutron production
[135]. Mechanisms allowing for cosmic ray escape via protons [54] are disfavored as
well. The Waxman-Bahcall [54] model has been updated to account for more recent
measurements of the UHECR flux [53] and typical gamma break energy [136]. These
limits placed on neutrino emission models normalized to the observed UHECR flux
are the strongest constraints thus far on the hypothesis that GRBs are the dominant
sources of this flux.
179
104 105 106 107Neutrino break energy εb (GeV)
10−10
10−9
10−8
10−7
ε2 bΦ
0(ε b
)(G
eV
cm−
2 s−
1 sr
−1 )
90%
68%
Ahlers et al.Waxman-Bahcall
30
40
50
60
70
80
90
100
Exc
lusi
onC
L(%
)
104 105 106 107Eν (GeV)
10−10
10−9
10−8
10−7
E2 νΦ
ν(G
eVc
m−2
s−1 s
r−1 )
90%
Waxman-Bahcall
Figure 7.10: Exclusion contours, calculated from the combined three-year all-sky νe
ντ νµ shower-like event search and four-year Northern Hemisphere νµ track-like event
search results, of a per-flavor double broken power law GRB neutrino spectrum of
a given flux normalization φb at first break energy b. The right panel shows several
of these spectra that are excluded at 90% confidence.
7.3.2 Limits on GRB Fireball Models and Parameter Spaces
The expected number of all-flavor neutrinos from fp = 10, Γ ≈ 300 internal
shock, photospheric, and ICMART model fluxes measured by this three-year anal-
ysis are 1.45, 2.49, and 0.07, respectively. Similarly, the expected number of muon
neutrinos from the three benchmark model fluxes measured by the four-year North-
ern Hemisphere track analysis are 1.88, 2.99, and 0.06, respectively. Background
events are concentrated at much lower energies than these expected neutrinos.
As discussed in Section 2.4.5, the GRB theory community has been very active
in light of the null results from IceCube searches for coincident neutrinos. The pro-
gression of models and limits is illustrated in Figure 7.11. The analytic benchmark
fp = 10, Γ ≈ 300 internal shock fireball model is presented as the grey dashed line
and the IceCube limit from 2011 [16] is in solid grey. The current numerically cal-
culated benchmark internal shock fireball model and present limits from this work
180
combined with previous results is presented in red. This result reaches under this
particular model for the first time. The photospheric model in green is ruled out,
while the ICMART model in blue is beyond the current detector’s reach.
These benchmark parameter models, though, are just one point in the phase
space of unmeasured GRB parameters. Figure 7.12 shows exclusion contours in the
baryonic loading and bulk Lorentz factor parameter space for the internal shock,
photospheric, and ICMART per-burst gamma-ray-normalized fireball models, dis-
cussed in Section 2.4. The benchmark model spectra from the top panel of Figure
2.9 and Figures 6.11 and 7.11 are indicated by the intersection of the vertical and
horizontal dashed lines.
These limits placed on the latest neutrino emission models normalized to the
observed gamma-ray fluence from each GRB constrain parts of the parameter space
relevant for the production of UHECR protons. Models that are still allowed require
increasingly lower neutrino production efficiencies through large bulk Lorentz boost
factors, low baryonic loading, or large dissipation radii.
181
103 104 105 106 107 108 109
Neutrino energy (GeV)
10−12
10−11
10−10
10−9
10−8
Pe
r-
Fl
av
or
E
2 Φ
ν
(G
eV
cm
−
2
s−
1
sr
−
1 )
Benchmark Fireball Models & IceCube Limits
2Yr Tracks Guetta et al. 90% CL
4Yr Tracks + 3Yr Cascades Internal Shock 90% CL
4Yr Tracks + 3Yr Cascades Photospheric 90% CL
4Yr Tracks + 3Yr Cascades ICMART 90% CL
Figure 7.11: Evolution of prompt GRB neutrino flux models and the limits IceCube
has placed on them. These models are characterized by benchmark values of fp = 10
and Γ ≈ 300. The dashed lines are the predictions and the solid lines are the limits.
The limits are given over the central 90% energies of neutrinos that could be detected
by IceCube.
182
100 200 300 400 500 600 700 800 900Γ
3
10
30
100
f p
68%
90% 30
40
50
60
70
80
90
100
Exc
lusi
onC
L(%
)
100 200 300 400 500 600 700 800 900Γ
3
10
30
100
f p
68%
90%
30
40
50
60
70
80
90
100
Exc
lusi
onC
L(%
)
50 100 150 200 250 300 350 400Γ
3
10
30
100
f p
68%
90%
30
40
50
60
70
80
90
100
Exc
lusi
onC
L(%
)
Figure 7.12: Exclusion contours, calculated from the combined three-year all-sky νe
ντ νµ shower-like event search and four-year Northern Hemisphere νµ track-like event
search results, in fp and Γ GRB parameter space, for three different models of fireball
neutrino production. These models differ in the radius at which photohadronic
interactions occur. The vertical and horizontal dashed lines indicate the benchmark
parameters used for the top of Figure 2.9 and Figures 6.11 and 7.11. Top: Internal
Shock. Middle: Photospheric. Bottom: ICMART.
183
Chapter 8
Conclusions and Outlook
Data from one year of the 79-string and two years of the complete 86-string
IceCube detector were analyzed for neutrino signal from 807 GRBs. This search is
the first in IceCube for electromagnetic and hadronic showers induced by electron,
tau, and muon neutrinos emitted by GRBs. Similar sensitivity to the much lower-
background Northern Hemisphere muon neutrino track searches [17] was achieved
because of this analysis’s acceptance of all neutrino flavors from GRBs over both
hemispheres. This wide neutrino net was cast through the effective use of BDT
forests to separate neutrino interaction cascades from most of the atmospheric muon
flux and an unbinned likelihood method to weight down the remaining background
events.
No significant correlations were found and, building upon similar results of the
previous track searches, world-leading limits were placed on cosmic ray and neutrino
production in GRBs. Cosmic ray emission from GRB fireballs through either the
escape and then decay of neutrons or an unspecified method of proton escape are
heavily disfavored by the limits presented in Section 7.3.1. Neutrino production
models normalized to the measured gamma-ray spectra of individual bursts with no
explicit connection to the cosmic ray spectrum have been constrained as well by the
limits presented in Section 7.3.2.
184
Unknown quantities still dominate these model calculations. For instance,
the predicted neutrino flux depends strongly on the bulk Lorentz factor Γ. High
Γ values in GRBs increase the proton energy threshold for pion production in the
observer frame and therefore can explain non-detections even well below the current
upper limits. Generally though, Lorentz factors above 2000 are unlikely [21] due
to the non-thermal gamma-ray spectra and the observed UHECR energies that
must be attained. Multiwavelength observations of GRBs are currently placing
constraints on individual burst Lorentz factors [137,138]. Improved electromagnetic
GRB observations will allow for more precise calculations of per-burst neutrino
emission models and strengthen the conclusions that can be drawn from this work’s
upper limits.
As shown in [78], constraints on parameters involved in fireball neutrino pro-
duction via internal shock collisions can be connected to the requirement that GRBs
are the sources of the observed UHECRs in a self-consistent way, assuming a pure
proton composition. The unexcluded parameter space in Figure 7.12 allows for
protons to efficiently diffuse out of the fireball, assuming a galactic-to-extragalactic
source transition at the ankle of the cosmic ray spectrum. Although the allowed
parameter space of this model is plausible, the multiwavelength studies discussed
above conclude that the average GRB likely exhibits Γ and fp values that lead to a
neutrino flux that would have been observed by this and past analyses.
Although no significant neutrino-GRB correlations were found, Table 7.1 shows
several TeV-energy events occurred during the measured prompt emission of GRBs
and had reconstructed directions within 2σ of the bursts. The allowed fireball mod-
185
els expect a similar or fewer number of neutrinos to be seen in IceCube, but at 100 to
1000 times the energy of these events. If each successive year of searching produces
similar results, the upper limit gains on these models will lessen and eventually a
sufficient lift of signal over background will allow for a significant flux to be mea-
sured. An astrophysical neutrino flux has been measured by IceCube [121,139], but
its sources are currently unknown and very unlikely to be due to GRBs [17, 140].
Furthermore, the cascade events of this astrophysical neutrino signal pass the event
selection of this analysis and would have yielded a much larger test statistic if they
were on time and space with GRBs.
IceCube’s acceptance of possible signal will soon increase further with the ad-
dition of searches for νµ-induced tracks from Southern Hemisphere GRBs with the
complete detector. Improved sensitivity through different signal hypotheses and
multiple messengers can also be attained. For example, correlating GRB gamma-
ray fluence to observed neutrinos through an additional fluence PDF would increase
sensitivity to the hypothesized signal if indeed this correlation exists [141]. Addition-
ally, GRBs are proposed to produce another astrophysical messenger: gravitational
waves. Correlating GRB neutrinos with a measurement by LIGO [142] would pro-
vide a powerful probe of the source parameters, but this dual measurement is only
possible for rare nearby short bursts [141].
A near-real-time per-burst analysis using many of the same techniques de-
scribed in this work will soon allow for rapid observational follow-up of any signif-
icant coincidence. Moreoever, the next-generation IceCube-Gen2 detector will be
significantly more sensitive to transient sources of neutrinos [143,144]. The contin-
186
ued pursuit of all neutrino flavors from observed GRBs over the entire sky will either
reveal a flux that is still lower than our current sensitivity or increasingly disfavor
these phenomena as sources of the highest energy cosmic rays.
187
Appendix A
Gamma-Ray Burst Catalog
This work searches for neutrinos coincident with 807 GRBs over three years
of IceCube data, from June 2010 to May 2013. Each burst is named in the format
GRBYYMMDDL where YY denotes the last two digits of the year, MM the month,
and DD the day. L is a letter, beginning with A, that ensures multiple GRBs
that are recorded on the same day have unique names. Alphabetical order of L
does not always correspond to the chronological order of the burst measurements
because often Fermi GBM does not immediately name its GRBs, instead waiting
until the publication of its catalogs. The energy spectrum parameters reported by
the satellite detector teams and listed in the tables below have the following units:
keV for the gamma-ray energy peak (γ) and energy bounds (Emin, Emax), erg cm−2
for the gamma-ray fluence (Fluenceγ).
Some bursts recorded by satellite detectors are not included in this analysis
because IceCube was not in a state to record reliable data during their measure-
ment. For example, GRB110125A was observed by FermiGBM when IceCube was
in between calibration runs in which the DOM LED flashers are used; GRB120403A
was observed by SwiftBAT when IceCube was down following maintenance of its
power supplies; and GRB130112B was observed by FermiGBM when IceCube was
down during testing of an upgraded DOMHub. Additionally, the first three GRBs
188
of the IC86II Table A.3 were observed in the IC86I season but during test runs of
the IC86II base processing and filtering.
The procedure used for multiple burst measurements by different detectors
is described in Section 2.3. As was done in previous GRB neutrino searches with
IceCube [15–17], average values are used when measurements are unavailable. These
values are described in Section 2.4.5 and marked with *. Average values from
the Fermi GBM First Two Years Catalog [34] are used in the fireball spectrum
calculations for GRBs measured only by the Fermi GBM instrument. These values
are marked with † and are also within the uncertainties of the GBM First Four Years
Catalog [36].
Table A.1: IC79 GRB Parameters
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
100604A 248.30 -73.19 3.64◦ 2.15* 2010-06-04 06:53:34.81 -2.3 11.14 13.44 1.05† 2.25† 205† 8 1000 5.509E-6
100605A 273.43 -67.60 7.67◦ 2.15* 2010-06-05 18:35:10.74 -1.02 7.17 8.19 1.05† 2.25† 205† 8 1000 7.565E-7
100606A 350.63 -66.24 1.08′′ 2.15* 2010-06-06 19:12:41.00 0.3 672.3 672.0 1.05 3.05 945 20 2000 3.9E-5
100608A 30.54 20.45 5.33◦ 2.15* 2010-06-08 09:10:06.34 -7.68 22.53 30.21 1.05† 2.25† 205† 8 1000 1.699E-6
100609A 90.48 42.78 2.53◦ 2.15* 2010-06-09 18:48:11.33 6.14 236.55 230.41 1.05† 2.25† 205† 8 1000 1.742E-5
100612A 63.53 13.74 2.69◦ 0.5* 2010-06-12 13:04:21.66 0 0.58 0.58 1.05† 2.25† 205† 8 1000 2.237E-6
100612B 352.00 -1.83 1.58◦ 2.15* 2010-06-12 17:26:06.13 0.7 9.28 8.58 1.05† 2.25† 205† 8 1000 1.363E-5
100614A 263.50 49.23 1.08′′ 2.15* 2010-06-14 21:38:26.00 -9 282 291.0 1.88 2.88 200* 15 150 2.7E-6
100614B 224.76 40.87 2.99◦ 2.15* 2010-06-14 11:57:23.31 -149.76 22.53 172.29 1.05† 2.25† 205† 8 1000 1.963E-5
100615A 177.21 -19.48 1.08′′ 1.398 2010-06-15 01:59:03.00 0 47.4 47.4 1.24 2.27 85.73 8 1000 8.723E-6
100616A 342.91 3.09 45.74◦ 0.5* 2010-06-16 18:32:32.90 -0.19 0 0.19 1.05† 2.25† 205† 8 1000 2.758E-7
100619A 84.62 -27.00 1.08′′ 2.15* 2010-06-19 00:21:07.00 -2.9 105.7 108.6 1.6 2.36 135.3 8 1000 1.129E-5
100620A 80.10 -51.68 1.46◦ 2.15* 2010-06-20 02:51:29.11 0.19 52.03 51.84 1.05† 2.25† 205† 8 1000 3.716E-6
100621A 315.31 -51.11 1.08′′ 0.542 2010-06-21 03:03:32.00 -6 204 210.0 1.7 2.45 95 20 2000 3.6E-5
100621B 103.83 37.35 2.81◦ 2.15* 2010-06-21 10:51:18.26 -6.66 117.25 123.91 1.05† 2.25† 205† 8 1000 7.671E-6
100621C 160.86 14.72 11.41◦ 0.5* 2010-06-21 12:42:16.43 -0.45 0.58 1.03 1.05† 2.25† 205† 8 1000 1.375E-7
100625A 15.80 -39.09 1.08′′ 0.5* 2010-06-25 18:32:27.80 0 1.3 1.3 0.1 2.6 371 20 2000 0.83E-6
100625B 338.26 20.29 4.45◦ 2.15* 2010-06-25 21:22:45.18 -7.42 21.76 29.18 1.05† 2.25† 205† 8 1000 1.401E-6
100628A 225.94 -31.65 0.02◦ 0.5* 2010-06-28 08:16:40.00 -0.004 0.036 0.04 2.67 4.67 74.1 15 150 2.5E-8
100629A 231.21 27.81 3.32◦ 0.5* 2010-06-29 19:14:03.35 -0.13 0.7 0.83 1.05† 2.25† 205† 8 1000 1.153E-6
100701B 43.11 -2.22 0.09◦ 2.15* 2010-07-01 11:45:19.07 0 26.11 26.11 0.95 2.47 1480 8 1000 2.603E-5
100702A 245.69 -56.55 0.01◦ 0.5* 2010-07-02 01:03:47.00 0.036 0.236 0.2 1.54 2.54 1000* 15 150 1.2E-7
100703A 9.52 -25.71 0.03◦ 0.5* 2010-07-03 17:43:37.40 0 0.07 0.07 1* 2* 1000* 20 200 7E-7
189
Table A.1: IC79 GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
100704A 133.64 -24.20 1.08′′ 2.15* 2010-07-04 03:35:08.00 -62.3 202.3 264.6 0.76 2.53 178.30 10 1000 1.040E-5
100706A 255.16 46.89 12.23◦ 0.5* 2010-07-06 16:38:18.92 -0.13 0 0.13 1.05† 2.25† 205† 8 1000 1.316E-7
100707A 358.02 -8.66 1.12◦ 2.15* 2010-07-07 00:46:38.91 -0.5 102.144 102.644 0.95 2.2 264 20 2000 8.8E-5
100709A 142.53 17.38 4.47◦ 2.15* 2010-07-09 14:27:32.98 -2.56 97.54 100.1 1.05† 2.25† 205† 8 1000 8.076E-6
100713A 255.21 28.39 0.03◦ 2.15* 2010-07-13 14:36:06.00 0 20 20.0 1* 2* 200* 20 200 2E-7
100713B 82.06 13.00 3.74◦ 2.15* 2010-07-13 23:31:34.01 -0.38 7.23 7.61 1.05† 2.25† 205† 8 1000 3.047E-6
100714A 106.37 51.14 3.69◦ 2.15* 2010-07-14 16:07:23.78 -0.51 35.07 35.58 1.05† 2.25† 205† 8 1000 3.251E-6
100714B 307.94 61.30 9.69◦ 2.15* 2010-07-14 16:27:20.08 -3.33 2.3 5.63 1.05† 2.25† 205† 8 1000 1.558E-6
100715A 299.27 -54.71 9.32◦ 2.15* 2010-07-15 11:27:17.64 -1.02 13.82 14.84 1.05† 2.25† 205† 8 1000 2.552E-6
100717A 287.06 -0.66 8.84◦ 2.15* 2010-07-17 08:55:06.21 -0.58 5.38 5.96 1.05† 2.25† 205† 8 1000 4.263E-7
100717B 304.31 19.53 9.19◦ 2.15* 2010-07-17 10:41:47.12 -0.13 2.3 2.43 1.05† 2.25† 205† 8 1000 3.328E-7
100718A 298.47 41.43 10.24◦ 2.15* 2010-07-18 19:06:22.58 -2.82 35.84 38.66 1.05† 2.25† 205† 8 1000 2.535E-6
100718B 121.83 -46.18 5.93◦ 2.15* 2010-07-18 03:50:09.61 -21.62 11.02 32.64 1.05† 2.25† 205† 8 1000 2.747E-6
100719A 112.32 -5.86 0.02◦ 2.15* 2010-07-19 03:30:57.00 -3.9 35.1 39.0 1.69 2.69 200* 15 150 5.3E-7
100719B 304.87 -67.14 15.41◦ 0.5* 2010-07-19 07:28:17.62 -1.54 0.06 1.6 1.05† 2.25† 205† 8 1000 3.868E-7
100719D 113.30 5.40 1.00◦ 2.15* 2010-07-19 23:44:04.13 1.54 23.36 21.82 1.05† 2.25† 205† 8 1000 5.194E-5
100722A 238.77 -15.61 1.07◦ 2.15* 2010-07-22 02:18:37.24 0 7.17 7.17 1.01 2.54 68.1 8 1000 9.5E-9
100722B 31.81 56.23 8.06◦ 0.5* 2010-07-22 06:58:24.72 -1.22 0.06 1.28 1.05† 2.25† 205† 8 1000 1.039E-7
100724A 194.54 -11.10 1.08′′ 1.288 2010-07-24 00:42:19.00 0.1 1.6 1.5 1.92 2.92 1000* 15 150 1.6E-7
100724B 120.04 76.74 1.10◦ 2.15* 2010-07-24 00:42:04.70 -4.1 230.608 234.708 0.84 1.84 467.8 8 1000 2.44E-4
100725A 166.48 -26.67 1.08′′ 2.15* 2010-07-25 07:12:52.00 -4.8 172 176.8 1.23 2.23 200* 15 150 2.0E-6
100725B 290.03 76.96 1.08′′ 2.15* 2010-07-25 11:24:34.00 -4.8 226.1 230.9 1.89 2.89 200* 15 150 6.8E-6
100727A 154.18 -21.39 1.08′′ 2.15* 2010-07-27 05:42:17.00 -82 29.8 111.8 1.71 2.71 200* 8 1000 2.03E-6
100728A 88.76 -15.26 0.72′′ 1.567 2010-07-28 02:18:24.00 -84.3 334 418.3 0.75 3.04 344.3 8 1000 1.291E-4
100728B 163.49 -45.47 0.36′′ 2.106 2010-07-28 10:31:54.97 -2.05 14.2 16.25 0.8 2.2 104 8 1000 2.4E-6
100730A 339.79 -22.23 5.40◦ 2.15* 2010-07-30 11:06:14.97 -1.54 62.34 63.88 1.05† 2.25† 205† 8 1000 6.058E-6
100802A 2.47 47.76 1.08′′ 2.15* 2010-08-02 05:45:36.00 -3.3 531.7 535.0 1.17 3.17 149 10 1000 2.24E-6
100804A 248.97 27.45 1.00◦ 2.15* 2010-08-04 02:29:26.35 0.13 6.72 6.59 1.05† 2.25† 205† 8 1000 1.068E-5
100805A 299.88 52.63 0.36′′ 2.15* 2010-08-05 04:12:42.00 -1.4 17.1 18.5 1.76 2.76 200* 15 150 5.1E-7
100805B 22.80 34.19 7.65◦ 0.5* 2010-08-05 07:12:12.48 -0.1 -0.03 0.07 1.05† 2.25† 205† 8 1000 2.043E-7
100805C 112.72 -35.93 3.75◦ 2.15* 2010-08-05 20:16:29.53 0 58.43 58.43 1.05† 2.25† 205† 8 1000 1.061E-5
100807A 55.30 67.67 1.08′′ 2.15* 2010-08-07 09:13:13.00 -6.1 3.1 9.2 2.32 3.32 200* 15 150 3.4E-7
100810A 124.77 -1.61 5.65◦ 2.15* 2010-08-10 01:10:34.24 -1.86 0.7 2.56 1.05† 2.25† 205† 8 1000 3.937E-7
100811A 345.87 15.86 6.04◦ 0.5* 2010-08-11 02:35:49.36 -0.06 0.32 0.38 1.05† 2.25† 205† 8 1000 2.930E-6
100811B 108.14 62.19 3.57◦ 2.15* 2010-08-11 18:44:09.30 -52.99 25.09 78.08 1.05† 2.25† 205† 8 1000 4.675E-6
100814A 22.47 -18.00 1.08′′ 2.15* 2010-08-14 03:50:08.51 -1.5 238 239.5 0.64 2.02 106.4 10 1000 1.98E-5
100814B 122.82 18.49 2.60◦ 2.15* 2010-08-14 08:25:25.75 -0.77 6.66 7.43 0.62 2.49 81.0 10 1000 4.7E-6
100816A 351.74 26.58 1.08′′ 0.8034 2010-08-16 00:37:50.94 0 11.448 11.448 0.31 2.77 136.70 10 1000 3.84E-6
100816B 102.12 -26.66 1.06◦ 2.15* 2010-08-16 00:12:41.41 -21.76 40.64 62.4 1.05† 2.25† 205† 8 1000 2.530E-5
100819A 279.60 -50.04 3.86◦ 2.15* 2010-08-19 11:56:35.26 -4.86 7.68 12.54 1.05† 2.25† 205† 8 1000 3.322E-6
100820A 258.79 -18.51 2.14◦ 2.15* 2010-08-20 08:56:58.47 -0.77 8.19 8.96 1.05† 2.25† 205† 8 1000 2.993E-6
100823A 20.70 5.83 1.44′′ 2.15* 2010-08-23 17:25:33.00 0 25 25.0 2.19 3.19 200* 15 150 4.1E-7
100825A 253.44 -56.57 6.34◦ 2.15* 2010-08-25 06:53:48.67 -1.28 2.05 3.33 1.05† 2.25† 205† 8 1000 1.378E-6
100826A 279.59 -22.13 1.60◦ 2.15* 2010-08-26 22:58:29.73 0 130.56 130.56 1.31 2.1 606 20 10000 3.0E-4
190
Table A.1: IC79 GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
100827A 193.90 71.89 5.68◦ 0.5* 2010-08-27 10:55:49.33 -0.13 0.45 0.58 1.05† 2.25† 205† 8 1000 1.029E-6
100829A 90.41 30.31 0.27◦ 2.15* 2010-08-29 21:02:07.94 0 10.24 10.24 1.44 9.4 278 20 2000 1.40E-5
100829B 115.45 -3.99 4.66◦ 2.15* 2010-08-29 08:59:07.02 0.26 95.23 94.97 1.05† 2.25† 205† 8 1000 7.290E-6
100831A 161.26 33.65 10.16◦ 2.15* 2010-08-31 15:37:25.94 -23.3 16.9 40.2 1.05† 2.25† 205† 8 1000 2.930E-6
100901A 27.27 22.76 1.44′′ 1.408 2010-09-01 13:34:10.00 -2.4 471.8 474.2 1.52 2.52 200* 15 150 2.1E-6
100902A 48.63 30.98 1.08′′ 2.15* 2010-09-02 19:31:54.00 -49.5 409.6 459.1 1.98 2.98 200* 15 150 3.2E-6
100902B 306.04 42.31 7.20◦ 2.15* 2010-09-02 23:45:19.22 -4.1 18.18 22.28 1.05† 2.25† 205† 8 1000 2.107E-6
100904A 172.91 -16.18 0.02◦ 2.15* 2010-09-04 01:33:43.00 -14.5 23 37.5 1.67 2.67 200* 15 150 1.3E-6
100905A 31.55 14.93 1.08′′ 2.15* 2010-09-05 15:08:14.00 -1.6 2.1 3.7 1.09 2.09 200* 15 150 1.7E-7
100905B 262.65 13.08 4.00◦ 2.15* 2010-09-05 21:46:22.99 -4.61 6.91 11.52 1.05† 2.25† 205† 8 1000 1.854E-6
100906A 28.68 55.63 0.72′′ 1.727 2010-09-06 13:49:27.00 -0.2 142.264 142.464 1.34 1.98 106.0 10 1000 2.64E-5
100907A 177.29 -40.63 6.90◦ 2.15* 2010-09-07 18:01:11.64 -1.54 3.84 5.38 1.05† 2.25† 205† 8 1000 7.333E-7
100909A 73.95 54.65 0.02◦ 2.15* 2010-09-09 09:04:00.00 0 60 60.0 1* 2* 200* 20 200 10E-6
100910A 238.10 -34.62 1.02◦ 2.15* 2010-09-10 19:37:43.96 1.34 15.17 13.83 0.92 2.26 143 10 1000 1.48E-5
100911A 151.32 58.99 11.77◦ 2.15* 2010-09-11 19:35:39.91 -0.77 4.86 5.63 1.05† 2.25† 205† 8 1000 8.679E-7
100915A 315.69 65.67 1.08′′ 2.15* 2010-09-15 01:31:05.00 -36.3 72.2 108.5 1.5 3.5 265.2 15 150 1.5E-6
100915B 85.39 25.09 0.02◦ 2.15* 2010-09-15 05:49:39.62 -5.6 4 9.6 1.35 3.35 83.49 10 1000 4.82E-7
100916A 151.96 -59.38 3.48◦ 2.15* 2010-09-16 18:41:12.49 -0.26 12.54 12.8 1.05† 2.25† 205† 8 1000 1.784E-6
100917A 289.25 -17.12 0.02◦ 2.15* 2010-09-17 05:03:25.00 -2.1 76 78.1 1.67 2.67 200* 15 150 8.6E-7
100918A 308.41 -45.96 1.00◦ 2.15* 2010-09-18 20:42:18.01 18.43 104.45 86.02 1.05† 2.25† 205† 8 1000 8.924E-5
100919A 163.24 6.02 1.81◦ 2.15* 2010-09-19 21:12:16.28 -38.4 11.2 49.6 1.05† 2.25† 205† 8 1000 5.760E-6
100922A 356.98 -25.19 15.03◦ 2.15* 2010-09-22 14:59:43.01 -1.02 3.33 4.35 1.05† 2.25† 205† 8 1000 4.246E-7
100923A 106.12 39.60 5.35◦ 2.15* 2010-09-23 20:15:10.67 -0.77 50.94 51.71 1.05† 2.25† 205† 8 1000 3.917E-6
100924A 0.67 7.00 0.01◦ 2.15* 2010-09-24 03:58:08.00 -15.1 128.9 144.0 1.59 2.59 200* 10 1000 3.33E-6
100925A 254.74 -15.24 0.03◦ 2.15* 2010-09-25 08:05:05.00 0 10 10.0 1* 2* 200* 10* 10000* 1.00E-5*
100926A 222.75 -72.35 3.81◦ 2.15* 2010-09-26 14:17:03.94 -24.06 8.19 32.25 1.05† 2.25† 205† 8 1000 6.973E-6
100926B 43.58 -11.10 12.00◦ 2.15* 2010-09-26 16:39:54.52 -3.07 34.82 37.89 1.05† 2.25† 205† 8 1000 1.374E-6
100928A 223.04 -28.54 0.02◦ 2.15* 2010-09-28 02:19:52.00 0.9 4.4 3.5 1.79 2.79 200* 15 150 3.5E-7
100929A 166.33 62.29 13.39◦ 2.15* 2010-09-29 05:38:52.49 -2.3 5.89 8.19 1.05† 2.25† 205† 8 1000 4.955E-7
100929B 243.62 33.33 23.83◦ 2.15* 2010-09-29 07:33:04.05 -0.51 4.1 4.61 1.05† 2.25† 205† 8 1000 3.249E-7
100929C 183.03 -24.94 7.79◦ 0.5* 2010-09-29 21:59:45.82 -0.13 0.19 0.32 1.05† 2.25† 205† 8 1000 7.614E-7
101002A 323.35 -27.47 16.36◦ 2.15* 2010-10-02 06:41:26.95 -4.35 2.82 7.17 1.05† 2.25† 205† 8 1000 4.396E-7
101003A 175.85 2.49 7.39◦ 2.15* 2010-10-03 05:51:08.01 -1.79 8.19 9.98 1.05† 2.25† 205† 8 1000 2.231E-6
101008A 328.88 37.07 1.08′′ 2.15* 2010-10-08 16:43:15.00 -4 106.6 110.6 1.42 2.42 200* 10 1000 2.016E-6
101010A 47.19 43.56 18.63◦ 2.15* 2010-10-10 04:33:46.83 -11.01 54.02 65.03 1.05† 2.25† 205† 8 1000 1.551E-6
101011A 48.29 -65.98 0.72′′ 2.15* 2010-10-11 16:58:35.00 -0.4 84.2 84.6 0.49 2.49 296.6 8 1000 5.24E-6
101013A 292.08 -49.64 1.60◦ 2.15* 2010-10-13 09:52:42.88 0.58 15.94 15.36 1.05† 2.25† 205† 8 1000 6.410E-6
101014A 26.94 -51.07 1.00◦ 2.15* 2010-10-14 04:11:52.62 1.41 450.82 449.41 1.27 2.07 181.40 10 1000 2.072E-4
101015A 73.16 15.46 5.94◦ 2.15* 2010-10-15 13:24:02.67 -2.05 498.5 500.55 1.05† 2.25† 205† 8 1000 3.737E-5
101016A 133.04 -4.62 2.81◦ 2.15* 2010-10-16 05:50:16.07 -1.54 2.3 3.84 1.05† 2.25† 205† 8 1000 2.444E-6
101017A 291.39 -35.15 1.44′′ 2.15* 2010-10-17 10:32:41.69 0 117 117.0 1.18 3.18 600 20 2000 6.7E-5
101017B 27.47 -26.55 4.92◦ 2.15* 2010-10-17 14:51:29.48 -1.02 46.85 47.87 1.05† 2.25† 205† 8 1000 1.775E-6
101020A 189.61 23.13 0.03◦ 2.15* 2010-10-20 23:40:41.00 -50 159 209.0 2.04 3.04 200* 15 150 2.6E-6
101021A 0.87 -23.71 1.33◦ 2.15* 2010-10-21 00:13:25.36 -51.46 69.31 120.77 1.05† 2.25† 205† 8 1000 2.230E-5
191
Table A.1: IC79 GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
101021B 0.46 47.34 12.81◦ 0.5* 2010-10-21 01:30:31.66 -0.51 1.02 1.53 1.05† 2.25† 205† 8 1000 2.926E-7
101023A 317.96 -65.39 1.08′′ 2.15* 2010-10-23 22:50:12.00 -11 137.3 148.3 1.07 2.5 200 20 2000 6.6E-5
101024A 66.51 -77.27 1.08′′ 2.15* 2010-10-24 11:39:33.60 -7.68 16.77 24.45 1.4 3.4 56.25 10 1000 1.2E-6
101025A 240.19 -8.49 24.35◦ 2.15* 2010-10-25 03:30:18.64 -1.79 12.54 14.33 1.05† 2.25† 205† 8 1000 2.788E-7
101026A 263.70 -0.37 7.57◦ 0.5* 2010-10-26 00:49:16.14 -0.13 0.13 0.26 1.05† 2.25† 205† 8 1000 9.295E-7
101027A 79.02 43.97 11.39◦ 0.5* 2010-10-27 05:30:30.76 -1.28 0.06 1.34 1.05† 2.25† 205† 8 1000 1.438E-7
101030A 166.38 -16.38 1.08′′ 2.15* 2010-10-30 15:56:30.72 -69.63 46.8 116.43 1.82 2.82 200* 15 150 2.0E-6
101031A 184.12 -7.47 15.87◦ 0.5* 2010-10-31 14:59:32.73 -0.06 0.32 0.38 1.05† 2.25† 205† 8 1000 2.217E-7
101101A 13.55 45.75 3.06◦ 2.15* 2010-11-01 17:51:34.02 -2.3 1.02 3.32 1.05† 2.25† 205† 8 1000 6.500E-7
101102A 284.68 -37.03 7.85◦ 2.15* 2010-11-02 20:10:07.43 -1.79 41.73 43.52 1.05† 2.25† 205† 8 1000 1.722E-6
101104A 161.02 -7.08 8.53◦ 0.5* 2010-11-04 19:26:14.05 -0.51 0.77 1.28 1.05† 2.25† 205† 8 1000 8.934E-7
101107A 168.33 22.43 4.09◦ 2.15* 2010-11-07 00:16:25.12 2.3 378.12 375.82 1.05† 2.25† 205† 8 1000 7.258E-6
101112A 292.22 39.36 0.02◦ 2.15* 2010-11-12 22:10:24.00 0 15.448 15.448 0.79 2.02 105.8 8 1000 2.96E-6
101112B 100.10 9.62 5.13◦ 2.15* 2010-11-12 23:36:55.81 -9.47 73.47 82.94 1.05† 2.25† 205† 8 1000 8.572E-6
101113A 29.08 0.21 2.67◦ 2.15* 2010-11-13 11:35:36.40 -0.26 12.03 12.29 1.05† 2.25† 205† 8 1000 3.062E-6
101114A 303.19 14.03 0.02◦ 2.15* 2010-11-14 00:32:50.00 -2.2 6.6 8.8 1.15 3.15 296 10* 10000* 4.7E-6
101116A 32.00 -81.20 7.26◦ 0.5* 2010-11-16 11:32:26.74 -0.13 0.45 0.58 1.05† 2.25† 205† 8 1000 3.044E-7
101117A 57.19 -26.87 1.75◦ 2.15* 2010-11-17 11:54:45.75 -2.05 48.13 50.18 1.05† 2.25† 205† 8 1000 8.241E-6
101117B 173.00 -72.66 0.36′′ 2.15* 2010-11-17 19:13:23.00 -0.1 8.6 8.7 1.5 2.5 200* 15 150 1.1E-6
101119A 226.49 59.61 16.19◦ 0.5* 2010-11-19 16:27:02.66 -0.32 0.32 0.64 1.05† 2.25† 205† 8 1000 1.694E-7
101123A 131.38 5.56 0.34◦ 2.15* 2010-11-23 22:51:34.97 41.47 162.272 120.802 0.75 2.14 476 10 1000 1.283E-4
101126A 84.77 -22.55 1.00◦ 2.15* 2010-11-26 04:44:27.48 0 43.84 43.84 1.05† 2.25† 205† 8 1000 3.101E-5
101127A 290.31 7.89 23.17◦ 2.15* 2010-11-27 02:13:59.07 -3.33 26.11 29.44 1.05† 2.25† 205† 8 1000 6.961E-7
101127B 70.95 -11.32 6.55◦ 2.15* 2010-11-27 02:27:30.90 -5.12 55.55 60.67 1.05† 2.25† 205† 8 1000 3.085E-6
101128A 145.47 -35.20 5.70◦ 2.15* 2010-11-28 07:44:04.24 -2.82 5.38 8.2 1.05† 2.25† 205† 8 1000 8.356E-7
101129A 155.92 -17.64 0.03◦ 2.15* 2010-11-29 15:39:30.76 0 2 2.0 0.4 2.4 1210 20 5000 3.5E-6
101129B 271.54 1.01 8.22◦ 0.5* 2010-11-29 17:25:25.34 -0.06 0.51 0.57 1.05† 2.25† 205† 8 1000 8.079E-7
101130A 61.80 -16.75 0.20◦ 2.15* 2010-11-30 09:39:26.18 0 65.792 65.792 0.6 2.6 190 20 1000 3.1E-6
101130B 274.61 26.62 23.61◦ 2.15* 2010-11-30 01:45:54.35 -2.3 2.56 4.86 1.05† 2.25† 205† 8 1000 2.336E-7
101201A 1.96 -16.20 0.02◦ 2.15* 2010-12-01 10:01:49.74 0 112.64 112.64 1.5 3.5 275.70 10 1000 2.41E-5
101202A 254.02 58.48 6.13◦ 2.15* 2010-12-02 03:41:53.84 0 18.43 18.43 1.05† 2.25† 205† 8 1000 1.408E-6
101204A 167.54 -20.42 1.08′′ 2.15* 2010-12-04 23:53:29.00 0 10 10.0 1.3 2.3 200* 15 150 1.2E-6
101204B 191.91 55.67 10.37◦ 0.5* 2010-12-04 08:14:18.60 -0.06 0.06 0.12 1.05† 2.25† 205† 8 1000 2.817E-7
101205A 322.10 -39.10 11.10◦ 2.15* 2010-12-05 07:24:24.86 -3.84 4.1 7.94 1.05† 2.25† 205† 8 1000 3.905E-7
101206A 164.08 -38.11 3.50◦ 2.15* 2010-12-06 00:52:17.53 0 34.82 34.82 1.05† 2.25† 205† 8 1000 5.841E-6
101207A 175.75 8.72 3.73◦ 2.15* 2010-12-07 12:51:41.31 5.63 67.07 61.44 1.05† 2.25† 205† 8 1000 6.648E-6
101208A 212.40 4.04 11.70◦ 0.5* 2010-12-08 04:52:56.92 -0.19 0 0.19 1.05† 2.25† 205† 8 1000 3.098E-7
101208B 280.94 -59.02 1.41◦ 2.15* 2010-12-08 11:57:01.20 -0.64 1.41 2.05 1.05† 2.25† 205† 8 1000 3.843E-6
101211A 31.84 10.06 11.25◦ 2.15* 2010-12-11 11:37:54.52 -2.82 10.75 13.57 1.05† 2.25† 205† 8 1000 1.634E-6
101213A 241.31 21.90 1.08′′ 0.414 2010-12-13 10:49:19.00 -1 201.1 202.1 1.1 2.35 309.7 10 1000 1.40E-5
101214A 0.69 -28.27 5.56◦ 2.15* 2010-12-14 17:57:03.97 -1.41 0.83 2.24 1.05† 2.25† 205† 8 1000 2.371E-7
101214B 181.13 -31.06 5.73◦ 2.15* 2010-12-14 23:50:00.97 -0.77 10.75 11.52 1.05† 2.25† 205† 8 1000 1.092E-6
101216A 284.27 -20.97 2.12◦ 0.5* 2010-12-16 17:17:52.54 0 1.92 1.92 1.05† 2.25† 205† 8 1000 3.044E-6
101219A 74.59 -2.53 0.01◦ 0.718 2010-12-19 02:31:29.00 0 5.6 5.6 0.22 2.22 490 20 10000 3.6E-6
192
Table A.1: IC79 GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
101219B 12.23 -34.57 1.08′′ 0.5519 2010-12-19 16:27:53.00 10 66.66 56.66 0.33 2.12 70 10 1000 5.5E-6
101220A 241.57 46.14 1.25◦ 2.15* 2010-12-20 13:49:58.13 2.3 74.75 72.45 1.05† 2.25† 205† 8 1000 9.596E-6
101220B 2.70 27.20 1.48◦ 2.15* 2010-12-20 20:43:54.12 -1.02 30.72 31.74 1.05† 2.25† 205† 8 1000 5.288E-6
101223A 250.55 48.22 4.34◦ 2.15* 2010-12-23 20:00:18.10 -41.22 14.85 56.07 1.05† 2.25† 205† 8 1000 2.455E-6
101224A 285.94 45.71 0.02◦ 0.5* 2010-12-24 05:27:13.86 -0.06 1.66 1.72 0.83 2.83 330 10 1000 2.4E-7
101224B 289.14 -55.25 4.82◦ 2.15* 2010-12-24 13:52:58.23 -0.13 44.61 44.74 1.05† 2.25† 205† 8 1000 3.892E-6
101224C 290.16 34.46 8.86◦ 2.15* 2010-12-24 14:43:32.93 -2.56 23.04 25.6 1.05† 2.25† 205† 8 1000 2.606E-6
101224D 325.17 -38.66 8.29◦ 2.15* 2010-12-24 23:57:34.94 -9.73 8.96 18.69 1.05† 2.25† 205† 8 1000 1.355E-6
101225A 0.20 44.60 0.72′′ 0.40 2010-12-25 18:37:45.00 0 963 963.0 1.82 2.82 200* 15 150 3E-6
101225B 60.68 32.77 1.81◦ 2.15* 2010-12-25 09:02:53.50 20.54 101.76 81.22 1.05† 2.25† 205† 8 1000 2.016E-5
101227A 186.79 -83.55 7.16◦ 2.15* 2010-12-27 04:40:28.72 -0.77 94.72 95.49 1.05† 2.25† 205† 8 1000 3.431E-6
101227B 240.50 -24.50 1.62◦ 2.15* 2010-12-27 09:45:06.57 0.77 154.11 153.34 1.05† 2.25† 205† 8 1000 1.375E-5
101227C 150.87 -49.44 2.59◦ 2.15* 2010-12-27 12:51:46.19 -0.13 28.74 28.87 1.05† 2.25† 205† 8 1000 6.441E-6
101231A 191.71 17.64 1.41◦ 2.15* 2010-12-31 01:36:50.61 0 23.62 23.62 1.05† 2.25† 205† 8 1000 1.683E-5
110101A 264.26 36.54 11.17◦ 2.15* 2011-01-01 04:50:20.48 -2.3 1.28 3.58 1.05† 2.25† 205† 8 1000 2.499E-7
110101B 105.50 34.58 16.49◦ 2.15* 2011-01-01 12:08:21.58 -103.43 132.1 235.53 1.05† 2.25† 205† 8 1000 6.629E-6
110102A 245.88 7.61 0.36′′ 2.15* 2011-01-02 18:52:25.00 -49.2 294.9 344.1 1.22 2.3 267 20 5000 5.4E-5
110105A 85.11 -17.12 2.03◦ 2.15* 2011-01-05 21:02:39.60 -7.68 115.71 123.39 1.05† 2.25† 205† 8 1000 2.092E-5
110106A 79.31 64.17 1.08′′ 0.093 2011-01-06 15:25:16.00 -1 3.9 4.9 1.71 2.71 200* 15 150 3.0E-7
110106B 134.15 47.00 1.08′′ 0.618 2011-01-06 21:26:16.08 -16.9 24.5 41.4 1.61 2.61 200* 10 1000 5.90E-6
110108A 11.62 -9.64 2.67◦ 2.15* 2011-01-08 23:26:18.52 -1.02 50.43 51.45 1.05† 2.25† 205† 8 1000 2.511E-6
110112A 329.93 26.46 1.80′′ 0.5* 2011-01-12 04:12:18.00 -0.1 0.5 0.6 2.14 3.14 1000* 15 150 3.0E-8
110112B 10.60 64.41 0.03◦ 2.15* 2011-01-12 22:24:54.00 0 2.34 2.34 0.72 2.72 495 10 1000 3.53E-7
110118A 226.57 -39.55 4.07◦ 2.15* 2011-01-18 20:34:18.79 -6.14 28.42 34.56 1.05† 2.25† 205† 8 1000 2.966E-6
110119A 348.59 5.99 1.08′′ 2.15* 2011-01-19 22:20:58.00 -86.4 217.5 303.9 0.6 1.95 126.3 10 1000 1.36E-5
110120A 61.60 -12.00 0.40◦ 2.15* 2011-01-20 15:59:39.22 -0.7 44.216 44.916 0.6 2.6 680 20 5000 3.1E-5
110123A 246.97 28.03 1.16◦ 2.15* 2011-01-23 19:17:45.04 0.7 18.56 17.86 0.64 1.96 280 10 1000 2.61E-5
110124A 53.83 36.35 9.14◦ 2.15* 2011-01-24 18:49:09.07 -3.33 2.05 5.38 1.05† 2.25† 205† 8 1000 1.589E-7
110130A 111.51 38.25 6.75◦ 2.15* 2011-01-30 05:31:52.58 -0.26 47.1 47.36 1.05† 2.25† 205† 8 1000 2.902E-6
110201A 137.49 88.61 0.01◦ 2.15* 2011-02-01 09:35:08.00 -2.8 13.3 16.1 1.09 2.09 200* 15 150 7.0E-7
110204A 1.82 -17.40 4.03◦ 2.15* 2011-02-04 04:17:11.37 -3.84 24.83 28.67 1.05† 2.25† 205† 8 1000 3.096E-6
110205A 164.63 67.53 1.08′′ 2.22 2011-02-05 02:02:41.00 0 330 330.0 1.52 3.52 222 20 1200 3.66E-5
110205B 359.73 -80.44 9.24◦ 2.15* 2011-02-05 00:39:04.65 -2.82 3.58 6.4 1.05† 2.25† 205† 8 1000 1.953E-7
110206A 92.36 -58.81 0.02◦ 2.15* 2011-02-06 18:08:05.00 0 20 20.0 1* 2* 200* 10* 10000* 1.00E-5*
110206B 333.70 1.61 15.47◦ 2.15* 2011-02-06 04:50:36.06 -6.4 5.89 12.29 1.05† 2.25† 205† 8 1000 7.904E-7
110207A 12.54 -10.79 0.01◦ 2.15* 2011-02-07 11:17:20.29 -1.02 108.3 109.32 1.09 3.09 450 10 1000 4.4E-6
110207B 179.00 -58.43 9.03◦ 2.15* 2011-02-07 23:00:26.41 -0.77 6.91 7.68 1.05† 2.25† 205† 8 1000 3.423E-7
110208A 22.46 -20.59 1.08′′ 2.15* 2011-02-08 21:10:46.00 -1.5 40.7 42.2 2.08 3.08 200* 15 150 2.7E-7
110209A 329.70 -21.93 10.63◦ 2.15* 2011-02-09 03:58:08.30 -3.78 1.86 5.64 1.05† 2.25† 205† 8 1000 6.733E-7
110210A 13.06 7.78 1.08′′ 2.15* 2011-02-10 09:52:41.00 -102.9 153.6 256.5 1.73 2.73 200* 15 150 9.6E-7
110212A 69.03 43.72 0.01◦ 2.15* 2011-02-12 01:09:08.00 -1.8 2.6 4.4 0.78 2.78 44.6 15 150 2.4E-7
110212B 311.33 -74.50 4.33◦ 0.5* 2011-02-12 13:12:33.52 -0.05 0.02 0.07 1.05† 2.25† 205† 8 1000 6.349E-7
110213A 42.96 49.27 1.08′′ 1.46 2011-02-13 05:17:29.00 -31.2 32.8 64.0 1.28 2.4 89 20 2000 1.0E-5
110213B 41.77 0.95 0.30◦ 1.083 2011-02-13 14:31:33.00 0 50 50.0 1.52 3.52 123 20 1400 1.77E-5
193
Table A.1: IC79 GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
110213C 6.28 27.54 10.82◦ 0.5* 2011-02-13 21:00:51.34 -0.13 0.19 0.32 1.05† 2.25† 205† 8 1000 3.273E-8
110220A 185.49 16.58 6.06◦ 2.15* 2011-02-20 18:16:21.63 -1.79 31.23 33.02 1.05† 2.25† 205† 8 1000 2.114E-6
110221A 15.18 66.05 1.24◦ 2.15* 2011-02-21 05:51:19.36 -1.54 11.52 13.06 1.05† 2.25† 205† 8 1000 2.246E-6
110223A 345.85 87.56 1.08′′ 2.15* 2011-02-23 20:56:59.00 0.1 8.1 8.0 1* 2* 200* 15 150 1.6E-7
110223B 150.23 -68.30 1.08′′ 2.15* 2011-02-23 21:25:48.00 -45 20 65.0 1.65 2.65 200* 15 150 6.1E-7
110226A 199.29 35.77 7.07◦ 2.15* 2011-02-26 23:44:31.13 -2.3 11.78 14.08 1.05† 2.25† 205† 8 1000 1.896E-6
110227A 148.72 -54.04 11.93◦ 0.5* 2011-02-27 00:12:28.23 -0.19 1.54 1.73 1.05† 2.25† 205† 8 1000 1.638E-7
110227B 25.24 15.89 7.45◦ 2.15* 2011-02-27 05:30:10.82 -1.02 17.41 18.43 1.05† 2.25† 205† 8 1000 2.398E-6
110227C 232.73 -9.94 4.99◦ 2.15* 2011-02-27 10:04:12.55 -11.26 14.34 25.6 1.05† 2.25† 205† 8 1000 2.421E-6
110228A 10.27 -45.67 2.56◦ 2.15* 2011-02-28 00:15:58.91 -30.72 13.76 44.48 1.05† 2.25† 205† 8 1000 5.144E-6
110228B 245.09 16.41 4.74◦ 2.15* 2011-02-28 18:59:50.39 -3.84 13.31 17.15 1.05† 2.25† 205† 8 1000 9.601E-7
110301A 229.35 29.40 1.00◦ 2.15* 2011-03-01 05:08:43.07 0 5.7 5.7 0.81 2.7 106.80 10 1000 3.65E-5
110302A 122.35 2.91 6.84◦ 2.15* 2011-03-02 01:01:51.73 -11.2 27.14 38.34 1.05† 2.25† 205† 8 1000 3.730E-6
110304A 322.93 33.27 4.23◦ 2.15* 2011-03-04 01:42:33.80 -0.26 19.26 19.52 1.05† 2.25† 205† 8 1000 3.456E-6
110305A 260.88 -15.80 1.08′′ 2.15* 2011-03-05 06:38:01.00 -0.9 12.1 13.0 1.62 2.62 200* 15 150 8.0E-7
110307A 193.12 15.64 7.58◦ 2.15* 2011-03-07 23:19:08.26 -1.79 0.51 2.3 1.05† 2.25† 205† 8 1000 5.750E-7
110311A 117.59 34.29 9.68◦ 2.15* 2011-03-11 19:29:21.42 -1.79 4.61 6.4 1.05† 2.25† 205† 8 1000 1.119E-6
110312A 157.48 -5.26 1.08′′ 2.15* 2011-03-12 17:55:37.00 24.1 64.9 40.8 2.32 3.32 200* 15 150 8.2E-7
110315A 279.19 17.54 0.72′′ 2.15* 2011-03-15 23:57:04.00 -66.8 38.8 105.6 1.77 2.77 200* 15 150 4.1E-6
110316A 46.70 -67.58 17.80◦ 2.15* 2011-03-16 03:19:41.86 -3.01 -0.06 2.95 1.05† 2.25† 205† 8 1000 1.150E-7
110318A 338.29 -15.28 0.01◦ 2.15* 2011-03-18 13:14:19.00 -13 10.6 23.6 0.8 2.74 107.00 10 1000 8.05E-6
110318B 211.68 -51.58 1.08′′ 2.15* 2011-03-18 15:27:09.00 -1.7 3.7 5.4 1.09 2.09 200* 15 150 2.9E-7
110319A 356.50 -66.01 1.08′′ 2.15* 2011-03-19 02:16:41.00 -0.3 31.3 31.6 1.31 3.31 21.9 15 150 1.4E-6
110319B 326.09 -56.77 0.01◦ 2.15* 2011-03-19 19:34:02.00 -3.5 28.67 32.17 1.39 2.39 200* 15 150 1.0E-6
110319C 207.96 -51.58 4.94◦ 2.15* 2011-03-19 15:04:45.46 -2.3 13.04 15.34 1.05† 2.25† 205† 8 1000 1.562E-6
110321A 13.31 -21.81 11.83◦ 2.15* 2011-03-21 08:17:42.48 -4.1 26.62 30.72 1.05† 2.25† 205† 8 1000 1.120E-6
110322A 99.04 -48.90 4.72◦ 2.15* 2011-03-22 13:23:42.81 -4.1 32 36.1 1.05† 2.25† 205† 8 1000 3.560E-6
110328A 251.21 57.58 1.08′′ 2.15* 2011-03-28 12:57:45.00 0 10 10.0 1.72 2.72 200* 15 150 3.0E-6
110328B 117.65 43.10 1.70◦ 2.15* 2011-03-28 12:29:19.19 1.02 142.34 141.32 1.11 1.94 369 10 1000 2.6E-5
110331A 6.66 25.99 4.66◦ 2.15* 2011-03-31 14:29:06.84 -0.06 3.14 3.2 1.05† 2.25† 205† 8 1000 2.641E-7
110401A 268.56 26.87 3.76◦ 2.15* 2011-04-01 22:04:19.63 -0.64 1.73 2.37 0.66 2.36 1194 10 1000 1.51E-6
110402A 197.40 61.25 1.08′′ 2.15* 2011-04-02 00:12:58.00 -1.5 83.5 85.0 1.03 3.03 1395 10* 10000* 1.6E-5
110406A 17.34 35.81 0.17◦ 2.15* 2011-04-06 03:44:06.67 0 9.216 9.216 1.24 2.3 326 20 10000 4.8E-5
110407A 186.03 15.71 1.44′′ 2.15* 2011-04-07 14:06:41.00 -2.9 158.8 161.7 0.73 2.73 57.9 15 150 1.7E-6
110407B 97.41 -11.95 1.00◦ 2.15* 2011-04-07 23:56:57.06 0.83 9.86 9.03 1.05† 2.25† 205† 8 1000 2.643E-5
110410A 30.94 -15.95 3.67◦ 2.15* 2011-04-10 03:10:52.43 -11.01 50.94 61.95 1.05† 2.25† 205† 8 1000 6.412E-6
110410B 337.17 -21.96 17.39◦ 2.15* 2011-04-10 18:31:19.88 -4.74 3.33 8.07 1.05† 2.25† 205† 8 1000 9.522E-7
110411A 291.44 67.71 1.08′′ 2.15* 2011-04-11 19:34:11.00 -11.9 86.3 98.2 1.51 3.51 41.0 15 150 3.3E-6
110411B 210.30 -64.99 6.28◦ 2.15* 2011-04-11 15:05:15.35 -3.84 19.71 23.55 1.05† 2.25† 205† 8 1000 3.584E-6
110412A 133.49 13.49 0.02◦ 2.15* 2011-04-12 07:33:21.00 13.7 40.4 26.7 0.7 2.7 87 10 1000 2.2E-6
110414A 97.87 24.36 1.08′′ 2.15* 2011-04-14 07:42:14.00 -38.4 135.6 174.0 1* 2* 200* 15 150 3.5E-6
110420A 2.16 -37.89 0.36′′ 2.15* 2011-04-20 11:02:24.00 -0.1 16 16.1 1.71 3.71 43 10* 10000* 6.54E-6
110420B 320.05 -41.28 0.02◦ 0.5* 2011-04-20 22:42:11.73 -0.06 0.1 0.16 0.12 2.12 296.8 10 1000 2.65E-7
110421A 277.23 50.80 1.71◦ 2.15* 2011-04-21 18:10:39.92 -2.56 37.89 40.45 1.05† 2.25† 205† 8 1000 1.060E-5
194
Table A.1: IC79 GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
110422B 226.69 43.02 21.52◦ 0.5* 2011-04-22 00:41:48.56 -0.13 0.19 0.32 1.05† 2.25† 205† 8 1000 8.065E-8
110424A 293.31 -11.12 12.35◦ 0.5* 2011-04-24 18:11:36.65 -0.06 0.61 0.67 1.05† 2.25† 205† 8 1000 4.652E-8
110426A 219.93 -8.72 1.28◦ 2.15* 2011-04-26 15:06:26.61 14.59 370.95 356.36 2.28 3.28 200* 10 1000 4.54E-5
110428A 5.30 64.80 0.15◦ 2.15* 2011-04-28 09:18:30.00 -2 12.568 14.568 0.2 2.88 175.60 10 1000 2.27E-5
110428B 128.44 19.94 2.94◦ 2.15* 2011-04-28 08:07:05.24 -53.76 47.87 101.63 1.05† 2.25† 205† 8 1000 1.579E-5
110430A 147.06 67.95 2.53◦ 2.15* 2011-04-30 09:00:13.40 1.02 33.54 32.52 1.05† 2.25† 205† 8 1000 7.067E-6
110503A 132.78 52.21 0.36′′ 1.613 2011-05-03 17:35:45.00 -6.6 16.3 22.9 0.98 2.7 219 20 5000 2.6E-5
110503B 70.51 -10.90 4.29◦ 2.15* 2011-05-03 03:28:26.12 -0.26 7.68 7.94 1.05† 2.25† 205† 8 1000 1.865E-6
110505A 16.81 -32.30 3.09◦ 2.15* 2011-05-05 04:52:56.43 -0.38 3.71 4.09 1.05† 2.25† 205† 8 1000 2.034E-6
110509A 180.81 -34.00 4.60◦ 2.15* 2011-05-09 03:24:38.79 -11.01 57.86 68.87 1.05† 2.25† 205† 8 1000 3.761E-6
110509B 74.65 -26.98 8.30◦ 0.5* 2011-05-09 11:24:15.58 -0.32 0.32 0.64 1.05† 2.25† 205† 8 1000 5.257E-7
110511A 214.10 -45.42 10.62◦ 2.15* 2011-05-11 14:47:12.69 -2.56 3.33 5.89 1.05† 2.25† 205† 8 1000 4.894E-7
Table A.2: IC86I GRB Parameters
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
110517A 296.09 -73.76 8.97◦ 0.5* 2011-05-17 10:52:35.41 -0.06 0.51 0.57 1.05† 2.25† 205† 8 1000 9.890E-8
110517B 190.15 6.29 2.11◦ 2.15* 2011-05-17 13:44:47.60 -0.26 22.78 23.04 1.05† 2.25† 205† 8 1000 8.740E-6
110518A 67.18 -34.20 0.20◦ 2.15* 2011-05-18 20:38:10.77 0 35.072 35.072 1.29 2.3 229 20 10000 6.5E-5
110519A 261.64 -23.43 0.01◦ 2.15* 2011-05-19 02:12:16.00 -4.7 37.8 42.5 2.09 3.09 200* 15 150 4.0E-6
110520A 134.34 56.43 1.08′′ 2.15* 2011-05-20 20:28:48.00 -1.2 16.6 17.8 1.13 2.13 200* 15 150 1.1E-6
110520B 71.01 -85.93 12.41◦ 2.15* 2011-05-20 07:14:26.24 -10.5 1.79 12.29 1.05† 2.25† 205† 8 1000 1.043E-6
110521A 120.13 45.83 1.08′′ 2.15* 2011-05-21 15:51:31.00 0.2 18.8 18.6 0.9 1.9 200* 15 150 4.4E-7
110521B 57.54 -62.34 1.31◦ 2.15* 2011-05-21 11:28:58.88 0 6.14 6.14 1.05† 2.25† 205† 8 1000 3.608E-6
110522A 228.91 55.53 5.56◦ 2.15* 2011-05-22 06:08:17.45 -8.7 19.46 28.16 1.05† 2.25† 205† 8 1000 2.109E-6
110522B 184.46 49.33 6.40◦ 2.15* 2011-05-22 07:06:01.93 -5.12 22.02 27.14 1.05† 2.25† 205† 8 1000 1.057E-6
110522C 180.57 -26.81 12.50◦ 2.15* 2011-05-22 15:11:56.61 -0.26 57.86 58.12 1.05† 2.25† 205† 8 1000 3.044E-6
110523A 219.03 -15.42 4.50◦ 2.15* 2011-05-23 08:15:54.58 -1.28 43.26 44.54 1.05† 2.25† 205† 8 1000 2.227E-6
110526A 102.48 -16.42 5.84◦ 0.5* 2011-05-26 17:09:01.81 -0.13 0.32 0.45 1.05† 2.25† 205† 8 1000 8.457E-7
110528A 44.79 -6.87 2.48◦ 2.15* 2011-05-28 14:58:44.30 -1.02 68.61 69.63 1.05† 2.25† 205† 8 1000 4.595E-6
110529A 118.33 67.91 1.50◦ 2.15* 2011-05-29 00:48:40.25 0 2.5 2.5 0.88 2.05 1161 10 1000 2.32E-6
110529B 172.60 8.79 2.10◦ 2.15* 2011-05-29 06:17:41.01 0.26 46.08 45.82 1.05† 2.25† 205† 8 1000 6.779E-6
110530A 282.07 61.93 0.72′′ 2.15* 2011-05-30 15:31:02.00 -4.5 17.4 21.9 2.06 3.06 200* 15 150 3.3E-7
110531A 190.51 11.85 11.06◦ 2.15* 2011-05-31 10:45:10.56 -4.86 33.79 38.65 1.05† 2.25† 205† 8 1000 2.295E-6
110601A 310.71 11.48 3.00◦ 2.15* 2011-06-01 16:20:16.08 0 52.21 52.21 1.05† 2.25† 205† 8 1000 1.237E-5
110604A 271.00 18.47 0.05◦ 2.15* 2011-06-04 14:49:45.67 0 37.376 37.376 1.1 3.2 166 20 5000 3.1E-5
110605A 14.95 52.46 1.00◦ 2.15* 2011-06-05 04:23:32.30 1.54 84.23 82.69 1.05† 2.25† 205† 8 1000 1.925E-5
110605B 242.09 -3.14 10.13◦ 0.5* 2011-06-05 18:42:49.04 -0.26 1.28 1.54 1.05† 2.25† 205† 8 1000 4.385E-7
110609B 317.63 -38.16 4.71◦ 2.15* 2011-06-09 10:12:06.16 -6.66 26.37 33.03 1.05† 2.25† 205† 8 1000 2.353E-6
110610A 308.18 74.83 1.08′′ 2.15* 2011-06-10 15:22:06.00 -53 24 77.0 0.93 2.23 170.0 10 1000 8.70E-6
110613A 336.86 -3.47 2.79◦ 2.15* 2011-06-13 15:08:46.30 -0.26 39.94 40.2 1.05† 2.25† 205† 8 1000 3.256E-6
110616A 274.45 -34.02 11.96◦ 2.15* 2011-06-16 15:33:25.23 -4.61 7.94 12.55 1.05† 2.25† 205† 8 1000 1.295E-6
110618A 176.81 -71.69 0.50◦ 2.15* 2011-06-18 08:47:36.38 -3.07 246.632 249.702 1.4 3.4 569 20 5000 1.1E-4
195
Table A.2: IC86I GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
110618B 147.05 -7.48 2.10◦ 2.15* 2011-06-18 18:14:16.31 -0.51 89.09 89.6 1.05† 2.25† 205† 8 1000 9.781E-6
110622A 133.96 19.46 1.79◦ 2.15* 2011-06-22 03:47:19.10 6.08 76.48 70.4 1.05† 2.25† 205† 8 1000 5.427E-5
110624A 65.02 -15.95 17.34◦ 2.15* 2011-06-24 21:44:25.56 -1.28 2.24 3.52 1.05† 2.25† 205† 8 1000 2.781E-7
110625A 286.75 6.75 0.01◦ 2.15* 2011-06-25 21:08:22.00 -1 146.3 147.3 1.05 2.7 190 20 10000 6.1E-5
110625B 315.33 -39.44 4.60◦ 2.15* 2011-06-25 13:53:24.57 -0.51 35.07 35.58 1.05† 2.25† 205† 8 1000 3.523E-6
110626A 131.91 5.56 7.66◦ 2.15* 2011-06-26 10:44:54.21 -0.77 5.63 6.4 1.05† 2.25† 205† 8 1000 1.163E-6
110629A 69.37 25.01 4.82◦ 2.15* 2011-06-29 04:09:58.20 0 61.7 61.7 1.05† 2.25† 205† 8 1000 2.428E-6
110702A 5.62 -37.66 4.75◦ 2.15* 2011-07-02 04:29:28.92 -10.75 23.62 34.37 1.05† 2.25† 205† 8 1000 7.988E-6
110703A 155.39 -29.30 3.76◦ 2.15* 2011-07-03 13:22:15.58 -4.22 2.5 6.72 1.05† 2.25† 205† 8 1000 9.739E-7
110705B 122.96 28.80 3.08◦ 2.15* 2011-07-05 08:43:43.42 0.26 19.46 19.2 1.05† 2.25† 205† 8 1000 8.943E-6
110706A 100.08 6.14 8.03◦ 2.15* 2011-07-06 04:51:04.03 -1.54 10.5 12.04 1.05† 2.25† 205† 8 1000 3.269E-6
110706B 94.15 -50.77 2.04◦ 2.15* 2011-07-06 11:26:15.76 -2.56 70.66 73.22 1.05† 2.25† 205† 8 1000 6.716E-6
110706C 9.06 31.73 4.11◦ 2.15* 2011-07-06 17:27:56.34 0.13 17.02 16.89 1.05† 2.25† 205† 8 1000 2.341E-6
110706D 347.47 7.11 2.58◦ 2.15* 2011-07-06 23:26:51.41 -14.72 18.5 33.22 1.05† 2.25† 205† 8 1000 6.554E-6
110708A 340.12 53.96 0.02◦ 2.15* 2011-07-08 04:43:22.00 0 50 50.0 1* 2* 200* 20 200 2E-6
110708B 170.38 -50.57 0.16◦ 2.15* 2011-07-08 13:59:46.39 0 47.616 47.616 0.78 2.4 294 20 10000 9.4E-5
110709A 238.89 40.92 1.08′′ 2.15* 2011-07-09 15:24:29.00 -4.3 65.5 69.8 1.03 3.03 356 20 5000 3.7E-5
110709B 164.65 -23.45 0.72′′ 2.15* 2011-07-09 21:32:44.00 -12 850.3 862.3 1 3.0 278 10* 10000* 1.1E-6
110709C 155.38 23.12 1.53◦ 2.15* 2011-07-09 11:06:53.37 0 24.06 24.06 1.05† 2.25† 205† 8 1000 6.909E-6
110709D 156.21 -41.79 10.84◦ 2.15* 2011-07-09 20:40:50.09 -1.79 3.58 5.37 1.05† 2.25† 205† 8 1000 7.974E-7
110710A 229.09 48.40 3.87◦ 2.15* 2011-07-10 22:53:50.60 -4.86 17.86 22.72 1.05† 2.25† 205† 8 1000 9.317E-6
110715A 237.68 -46.24 1.44′′ 0.82 2011-07-15 13:13:49.00 -3 24.432 27.432 1.23 2.7 120 20 10000 2.3E-5
110716A 329.68 -76.98 3.86◦ 2.15* 2011-07-16 00:25:19.97 -3.07 4.1 7.17 1.05† 2.25† 205† 8 1000 1.355E-6
110717A 308.47 -7.85 7.45◦ 0.5* 2011-07-17 04:19:50.66 -0.02 0.1 0.12 1.05† 2.25† 205† 8 1000 2.512E-7
110717B 312.84 -14.84 1.20◦ 2.15* 2011-07-17 07:39:55.86 5.38 95.75 90.37 1.05† 2.25† 205† 8 1000 4.245E-5
110719A 24.58 34.59 1.44′′ 2.15* 2011-07-19 06:09:11.00 -2 42.9 44.9 1.63 2.63 200* 15 150 1.8E-6
110720A 198.65 -44.29 2.60◦ 2.15* 2011-07-20 04:14:32.38 -0.13 11.07 11.2 1.05† 2.25† 205† 8 1000 5.628E-6
110721A 333.40 -39.00 0.75◦ 2.15* 2011-07-21 04:47:43.76 0 29.624 29.624 0.94 1.77 372.50 10 1000 3.52E-5
110722A 215.06 5.00 1.99◦ 2.15* 2011-07-22 16:39:16.68 -0.51 72.96 73.47 1.05† 2.25† 205† 8 1000 2.114E-5
110722B 8.28 62.74 4.66◦ 2.15* 2011-07-22 17:01:45.91 -4.61 9.73 14.34 1.05† 2.25† 205† 8 1000 1.799E-6
110725A 270.14 -25.20 9.06◦ 2.15* 2011-07-25 05:39:42.06 -1.02 19.2 20.22 1.05† 2.25† 205† 8 1000 1.309E-6
110726A 286.72 56.07 0.36′′ 1.036 2011-07-26 01:30:40.00 -0.9 5 5.9 0.64 2.64 46.5 15 150 2.2E-7
110726B 317.71 2.47 3.82◦ 2.15* 2011-07-26 05:03:59.49 -3.84 26.11 29.95 1.05† 2.25† 205† 8 1000 4.361E-6
110729A 353.39 4.97 1.36◦ 2.15* 2011-07-29 03:25:05.93 2.08 410.66 408.58 1.05† 2.25† 205† 8 1000 4.640E-5
110730A 263.08 -22.78 4.28◦ 2.15* 2011-07-30 00:11:54.74 -7.94 20.48 28.42 1.05† 2.25† 205† 8 1000 1.257E-6
110730B 335.10 -2.89 3.80◦ 2.15* 2011-07-30 15:50:43.76 -8.7 25.15 33.85 1.05† 2.25† 205† 8 1000 7.969E-6
110731A 280.50 -28.54 0.36′′ 2.83 2011-07-31 11:09:30.00 -1.5 80.3 81.8 0.8 2.98 304 10 1000 2.218E-5
110801A 89.44 80.96 0.36′′ 1.858 2011-08-01 19:49:42.00 -24.2 385 409.2 1.84 3.84 140 15 150 7.3E-6
110801B 248.27 -57.06 7.30◦ 0.5* 2011-08-01 08:01:43.09 -0.13 0.26 0.39 1.05† 2.25† 205† 8 1000 3.537E-7
110802A 44.45 32.59 0.12◦ 0.5* 2011-08-02 15:19:16.19 0 0.6 0.6 0.63 2.63 3451 20 10000 1.3E-5
110803A 300.42 -11.44 7.49◦ 2.15* 2011-08-03 18:47:25.43 -156.68 30.21 186.89 1.05† 2.25† 205† 8 1000 2.951E-6
110806A 112.04 2.38 2.42◦ 2.15* 2011-08-06 22:25:31.12 0.26 28.67 28.41 1.05† 2.25† 205† 8 1000 7.190E-6
110807A 278.70 -8.76 0.03◦ 2.15* 2011-08-07 19:57:46.00 0 10 10.0 1* 2* 200* 10* 10000* 1.00E-5*
110808A 57.27 -44.20 1.80′′ 2.15* 2011-08-08 06:18:54.00 -7.4 40.6 48.0 2.32 3.32 200* 15 150 3.3E-7
196
Table A.2: IC86I GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
110808B 266.18 -37.74 0.07◦ 0.5* 2011-08-08 15:44:55.24 0 0.5 0.5 1.07 2.5 4238 20 10000 1.6E-5
110809A 172.17 -13.93 1.84◦ 2.15* 2011-08-09 11:03:34.00 -4.35 8.19 12.54 1.05† 2.25† 205† 8 1000 3.905E-6
110812A 358.41 72.21 0.03◦ 2.15* 2011-08-12 00:20:08.00 0 30 30.0 1* 2* 200* 10* 10000* 1.00E-5*
110812B 77.76 1.71 2.49◦ 2.15* 2011-08-12 21:35:08.61 -2.3 8.96 11.26 1.05† 2.25† 205† 8 1000 1.174E-6
110813A 61.24 34.56 1.00◦ 2.15* 2011-08-13 05:40:50.93 -1.79 20.99 22.78 1.05† 2.25† 205† 8 1000 4.768E-6
110815A 85.30 32.44 0.11◦ 2.15* 2011-08-15 09:40:55.97 0 19.2 19.2 0.85 2.5 251 20 10000 5.0E-5
110817A 336.04 -45.84 1.54◦ 2.15* 2011-08-17 04:35:12.12 0 5.95 5.95 1.05† 2.25† 205† 8 1000 1.195E-5
110818A 317.34 -63.98 0.72′′ 2.15* 2011-08-18 20:37:49.00 -14.2 117.4 131.6 1.33 3.33 256.3 10 1000 8.2E-6
110819A 139.49 -76.64 3.19◦ 2.15* 2011-08-19 15:57:54.97 -0.51 15.87 16.38 1.05† 2.25† 205† 8 1000 3.036E-6
110820A 343.19 70.30 1.44′′ 2.15* 2011-08-20 17:38:27.00 -7.07 264.9 271.97 1.92 2.92 200* 15 150 8.2E-7
110820B 157.58 -54.60 0.50◦ 2.15* 2011-08-20 21:27:48.05 0 191.488 191.488 1.22 2.1 481 20 10000 2.5E-4
110820C 90.51 21.63 3.96◦ 2.15* 2011-08-20 11:25:44.35 -4.1 7.17 11.27 1.05† 2.25† 205† 8 1000 7.981E-7
110824A 152.05 1.32 1.68◦ 2.15* 2011-08-24 00:13:09.94 0 76.61 76.61 1.05† 2.25† 205† 8 1000 1.485E-5
110825A 44.90 15.40 0.34◦ 2.15* 2011-08-25 02:27:03.00 -3 61.11 64.11 1.23 2.04 233.6 10 1000 5.45E-5
110825B 251.31 -80.28 5.18◦ 2.15* 2011-08-25 06:22:11.44 -16.38 34.69 51.07 1.05† 2.25† 205† 8 1000 2.179E-6
110827A 164.06 53.82 0.02◦ 2.15* 2011-08-27 00:01:52.00 -2.9 6.3 9.2 1.24 2.24 200* 15 150 1.8E-7
110828A 110.58 -23.81 1.04◦ 2.15* 2011-08-28 13:48:14.72 -1.12 43.55 44.67 1.05† 2.25† 205† 8 1000 2.721E-6
110831A 352.35 33.66 5.86◦ 2.15* 2011-08-31 06:45:26.61 -20.22 78.66 98.88 1.05† 2.25† 205† 8 1000 4.421E-6
110901A 141.28 -15.79 3.37◦ 2.15* 2011-09-01 05:31:44.06 -7.68 14.85 22.53 1.05† 2.25† 205† 8 1000 1.506E-6
110903A 197.06 58.98 0.02◦ 2.15* 2011-09-03 02:39:33.12 0 422 422.0 0.69 2.7 295 20 10000 4.2E-5
110903B 164.21 42.08 1.18◦ 2.15* 2011-09-03 00:13:06.29 -1.02 27.65 28.67 1.05† 2.25† 205† 8 1000 1.521E-5
110904A 359.69 35.90 2.63◦ 2.15* 2011-09-04 02:58:15.96 -0.13 83.78 83.91 1.05† 2.25† 205† 8 1000 1.110E-5
110904B 190.40 -28.85 6.11◦ 2.15* 2011-09-04 03:54:36.02 -1.28 50.18 51.46 1.05† 2.25† 205† 8 1000 3.464E-6
110904C 323.74 23.94 1.68◦ 2.15* 2011-09-04 12:44:19.33 -2.56 17.92 20.48 1.05† 2.25† 205† 8 1000 3.812E-6
110905A 278.96 -19.27 0.03◦ 2.15* 2011-09-05 05:48:40.00 590 963 373.0 1.53 2.53 200* 15 150 7.8E-7
110906A 296.89 -26.21 0.04◦ 2.15* 2011-09-06 12:25:13.00 0 94 94.0 1* 2* 200* 10* 10000* 1.00E-5*
110906B 26.32 17.65 4.03◦ 2.15* 2011-09-06 07:15:13.42 -5.38 18.56 23.94 1.05† 2.25† 205† 8 1000 3.796E-6
110909A 347.34 -24.22 1.98◦ 2.15* 2011-09-09 02:46:58.19 -12.29 8.45 20.74 1.05† 2.25† 205† 8 1000 4.920E-5
110911A 258.58 -66.98 50.00◦ 2.15* 2011-09-11 01:41:41.57 -4.61 4.35 8.96 1.05† 2.25† 205† 8 1000 5.938E-7
110915A 310.82 -0.72 2.16′′ 2.15* 2011-09-15 13:20:44.00 -2.74 92.1 94.84 0.94 2.94 183 15 150 1.35E-5
110915B 77.55 1.93 0.04◦ 2.15* 2011-09-15 18:24:19.00 0 18 18.0 1* 2* 200* 10* 10000* 1.00E-5*
110916A 4.11 40.36 21.86◦ 0.5* 2011-09-16 00:23:01.65 -1.41 0.38 1.79 1.05† 2.25† 205† 8 1000 4.226E-7
110918A 32.58 -27.28 0.06◦ 0.982 2011-09-18 21:27:02.86 0 69.376 69.376 1.2 2 150 20 10000 7.5E-4
110919A 279.97 66.43 1.00◦ 2.15* 2011-09-19 15:12:15.78 10.5 45.57 35.07 1.05† 2.25† 205† 8 1000 2.683E-5
110920A 87.57 38.76 5.00◦ 2.15* 2011-09-20 08:07:16.41 -0.51 9.22 9.73 1.05† 2.25† 205† 8 1000 2.687E-6
110920B 209.82 -27.56 1.00◦ 2.15* 2011-09-20 13:05:43.81 5.12 165.89 160.77 1.05† 2.25† 205† 8 1000 1.723E-4
110921A 294.10 36.33 1.08′′ 2.15* 2011-09-21 13:51:20.00 -31.55 16.45 48.0 1.39 3.39 139 10 1000 4.2E-6
110921B 6.09 -5.83 7.31◦ 2.15* 2011-09-21 10:38:48.20 -68.61 80.9 149.51 1.05† 2.25† 205† 8 1000 5.897E-6
110921C 17.97 -27.75 1.00◦ 2.15* 2011-09-21 21:52:45.09 0.9 18.56 17.66 1.05† 2.25† 205† 8 1000 3.631E-5
110923A 323.40 -10.89 3.69◦ 2.15* 2011-09-23 20:01:58.13 0 46.4 46.4 1.05† 2.25† 205† 8 1000 4.092E-6
110924A 234.75 -66.31 0.03◦ 2.15* 2011-09-24 09:03:20.00 0 10 10.0 1* 2* 200* 10* 10000* 1.00E-5*
110926A 69.44 10.43 3.27◦ 2.15* 2011-09-26 02:33:36.64 -0.77 74.5 75.27 1.05† 2.25† 205† 8 1000 1.198E-5
110928A 257.73 36.54 1.44′′ 2.15* 2011-09-28 01:51:31.00 -0.53 27.88 28.41 1.09 2.09 200* 15 150 6.9E-7
110928B 153.40 34.29 1.42◦ 2.15* 2011-09-28 04:19:51.41 -119.3 28.93 148.23 1.05† 2.25† 205† 8 1000 1.415E-5
197
Table A.2: IC86I GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
110929A 288.19 -62.21 4.03◦ 2.15* 2011-09-29 04:28:53.58 -0.51 4.61 5.12 1.05† 2.25† 205† 8 1000 2.197E-6
110930A 187.31 -53.66 5.05◦ 2.15* 2011-09-30 13:32:31.19 -6.91 30.98 37.89 1.05† 2.25† 205† 8 1000 6.232E-6
111001A 340.01 -15.33 15.11◦ 0.5* 2011-10-01 19:17:58.58 -0.26 0.13 0.39 1.05† 2.25† 205† 8 1000 1.901E-7
111003A 276.76 -62.32 1.11◦ 2.15* 2011-10-03 11:10:00.23 0.51 17.15 16.64 0.94 2.94 231.5 10 1000 1.83E-5
111005A 223.31 -19.72 0.02◦ 2.15* 2011-10-05 08:05:14.00 -5.23 23.06 28.29 2.03 3.03 200* 15 150 6.2E-7
111005B 340.30 75.80 5.28◦ 2.15* 2011-10-05 09:33:03.38 -11.26 19.46 30.72 1.05† 2.25† 205† 8 1000 2.055E-6
111008A 60.45 -32.71 1.08′′ 5.0 2011-10-08 22:12:58.00 -2.64 68.8 71.44 1.36 3.36 149 20 2000 9.0E-6
111008B 220.75 -5.67 4.34◦ 2.15* 2011-10-08 23:49:01.29 -4.1 38.4 42.5 1.05† 2.25† 205† 8 1000 3.034E-6
111009A 183.04 -56.82 1.08◦ 2.15* 2011-10-09 06:45:40.17 -0.26 20.48 20.74 1.05† 2.25† 205† 8 1000 1.203E-5
111010A 87.09 43.98 3.18◦ 2.15* 2011-10-10 05:40:34.56 -3.58 78.85 82.43 1.05† 2.25† 205† 8 1000 1.101E-5
111010B 183.54 -31.70 7.08◦ 2.15* 2011-10-10 15:50:21.80 -1.02 7.68 8.7 1.05† 2.25† 205† 8 1000 8.706E-7
111010C 69.80 41.88 1.67◦ 2.15* 2011-10-10 17:00:35.29 1.54 54.53 52.99 1.05† 2.25† 205† 8 1000 1.256E-5
111010D 77.02 -14.96 7.68◦ 2.15* 2011-10-10 21:34:13.68 -14.66 3.9 18.56 1.05† 2.25† 205† 8 1000 9.588E-7
111011A 37.96 -12.53 6.77◦ 0.5* 2011-10-11 02:15:09.90 -0.06 1.41 1.47 1.05† 2.25† 205† 8 1000 4.205E-7
111012A 154.01 68.09 2.08◦ 2.15* 2011-10-12 10:56:37.44 1.02 21.76 20.74 1.05† 2.25† 205† 8 1000 1.645E-5
111012B 97.22 67.05 1.71◦ 2.15* 2011-10-12 19:27:39.10 -0.51 7.42 7.93 1.05† 2.25† 205† 8 1000 3.294E-6
111015A 220.65 -58.41 1.96◦ 2.15* 2011-10-15 10:15:12.98 -0.64 92.1 92.74 1.05† 2.25† 205† 8 1000 2.420E-5
111016A 153.83 27.46 1.08′′ 2.15* 2011-10-16 18:37:04.00 35.41 614.48 579.07 1.95 2.95 200* 15 150 4.0E-6
111016B 290.50 -4.58 0.18◦ 2.15* 2011-10-16 22:41:40.72 0 145.408 145.408 0.78 2.78 378 20 5000 1.37E-4
111017A 8.10 -7.01 1.00◦ 2.15* 2011-10-17 15:45:23.72 0.26 11.33 11.07 0.91 2.7 692.5 10 1000 2.26E-5
111018A 271.49 -3.91 1.08′′ 2.15* 2011-10-18 17:26:24.00 -4.08 37.3 41.38 2.18 3.18 200* 15 150 4.0E-7
111018B 106.08 66.14 7.15◦ 2.15* 2011-10-18 14:16:48.87 -0.77 7.42 8.19 1.05† 2.25† 205† 8 1000 1.112E-6
111018C 124.18 81.29 7.46◦ 2.15* 2011-10-18 18:50:14.71 -6.4 23.3 29.7 1.05† 2.25† 205† 8 1000 1.763E-6
111020A 287.05 -38.01 1.08′′ 0.5* 2011-10-20 06:33:49.00 -0.04 0.39 0.43 1.37 2.37 1000* 15 150 6.5E-8
111022A 275.87 -23.67 0.01◦ 2.15* 2011-10-22 16:07:04.00 -17.69 18.57 36.26 1.01 3.01 64.7 15 150 2.0E-6
111022B 108.97 49.68 1.08′′ 2.15* 2011-10-22 17:13:04.00 -47.84 53.8 101.64 1.59 2.59 200* 15 150 9.0E-7
111022C 104.50 -33.11 9.32◦ 0.5* 2011-10-22 20:29:23.70 -0.13 0.06 0.19 1.05† 2.25† 205† 8 1000 1.260E-7
111024A 222.18 25.84 0.15◦ 0.5* 2011-10-24 07:21:27.00 0 0 0.0 1* 2* 1000* 10* 10000* 1.00E-5*
111024B 162.74 -44.94 2.57◦ 2.15* 2011-10-24 17:19:02.88 -6.14 62.46 68.6 1.05† 2.25† 205† 8 1000 1.578E-5
111024C 91.23 -1.75 13.15◦ 0.5* 2011-10-24 21:30:02.24 -0.26 1.54 1.8 1.05† 2.25† 205† 8 1000 2.320E-7
111025A 325.62 -35.52 2.73◦ 2.15* 2011-10-25 01:52:45.74 -0.51 51.2 51.71 1.05† 2.25† 205† 8 1000 2.981E-6
111026A 244.26 -47.44 0.02◦ 2.15* 2011-10-26 06:47:29.00 -0.09 4.07 4.16 1.69 2.69 200* 15 150 1.7E-7
111029A 44.78 57.11 1.44′′ 2.15* 2011-10-29 09:44:40.00 19.6 28.92 9.32 0.77 2.77 36.2 15 150 3.9E-7
111103A 327.11 -10.53 0.01◦ 2.15* 2011-11-03 10:35:13.00 -0.42 12.14 12.56 0.43 2.43 152.2 10 1000 3.20E-6
111103B 265.69 1.61 1.08′′ 2.15* 2011-11-03 10:59:03.00 -6.55 250.78 257.33 0.97 2.97 372 20 5000 2.0E-5
111103C 201.58 -43.16 10.99◦ 0.5* 2011-11-03 22:45:05.72 -0.06 0.26 0.32 1.05† 2.25† 205† 8 1000 2.818E-7
111105A 153.48 7.28 14.24◦ 2.15* 2011-11-05 10:57:36.08 -9.98 33.54 43.52 1.05† 2.25† 205† 8 1000 1.681E-6
111107A 129.48 -66.52 1.08′′ 2.893 2011-11-07 00:50:25.48 -1.54 31.83 33.37 1.38 3.38 108 10 1000 1.392E-6
111107B 315.46 -38.53 3.53◦ 2.15* 2011-11-07 01:49:46.02 0.19 77.38 77.19 1.05† 2.25† 205† 8 1000 1.041E-5
111109A 118.20 -41.58 1.44′′ 2.15* 2011-11-09 02:57:46.00 -5.6 8.4 14.0 1.86 2.86 200* 15 150 2.4E-7
111109B 133.73 -33.35 7.38◦ 2.15* 2011-11-09 10:52:32.25 -2.56 2.3 4.86 1.05† 2.25† 205† 8 1000 3.049E-7
111109C 129.98 44.65 1.50◦ 2.15* 2011-11-09 20:57:16.66 -4.61 5.06 9.67 1.05† 2.25† 205† 8 1000 6.692E-6
111112A 223.72 28.81 3.83◦ 0.5* 2011-11-12 21:47:48.16 -0.06 0.13 0.19 1.05† 2.25† 205† 8 1000 7.667E-7
111113A 225.39 2.19 0.10◦ 0.5* 2011-11-13 05:10:13.62 0 0.16 0.16 0.53 2.53 1480 20 10000 7.7E-6
198
Table A.2: IC86I GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
111113B 4.32 -7.52 3.96◦ 2.15* 2011-11-13 09:50:11.76 -1.02 14.34 15.36 1.05† 2.25† 205† 8 1000 3.103E-6
111114A 268.08 -20.01 5.72◦ 2.15* 2011-11-14 05:35:45.35 -1.54 20.48 22.02 1.05† 2.25† 205† 8 1000 1.112E-6
111117A 12.70 23.02 0.02◦ 0.5* 2011-11-17 12:13:41.00 -0.016 1.45 1.466 0.69 2.69 370 10 1000 6.7E-7
111117B 27.16 -16.11 6.22◦ 2.15* 2011-11-17 12:38:00.76 -1.28 22.53 23.81 1.05† 2.25† 205† 8 1000 1.423E-6
111120A 344.60 -37.34 5.17◦ 2.15* 2011-11-20 13:20:24.05 -21.25 77.38 98.63 1.05† 2.25† 205† 8 1000 6.728E-6
111121A 154.76 -46.67 1.08′′ 2.15* 2011-11-21 16:26:24.00 -0.34 141.08 141.42 0.44 3 1780 20 10000 2.3E-5
111123A 154.85 -20.64 1.08′′ 3.1516 2011-11-23 18:13:21.00 -8.7 481.3 490.0 1.68 2.68 200* 15 150 7.3E-6
111124A 94.06 4.63 9.42◦ 2.15* 2011-11-24 07:24:10.09 -0.77 8.19 8.96 1.05† 2.25† 205† 8 1000 6.263E-7
111126A 276.06 51.46 0.03◦ 0.5* 2011-11-26 18:57:42.00 0 0.8 0.8 1.1 2.1 1000* 15 150 7E-8
111127A 103.70 3.50 2.09◦ 2.15* 2011-11-27 19:27:01.70 -0.77 18.24 19.01 1.05† 2.25† 205† 8 1000 8.643E-6
111129A 307.43 -52.71 1.08′′ 2.15* 2011-11-29 16:18:14.00 -6.29 2.88 9.17 2.56 3.56 200* 15 150 1.8E-7
111201A 190.49 32.99 0.02◦ 2.15* 2011-12-01 14:22:45.26 -1.79 15.1 16.89 1.6 2.6 200* 15 150 10E-7
111203A 53.22 33.47 3.23◦ 2.15* 2011-12-03 01:17:04.03 -44.54 11.01 55.55 1.05† 2.25† 205† 8 1000 4.647E-6
111203B 242.83 -22.15 13.30◦ 2.15* 2011-12-03 14:36:45.38 -2.82 19.2 22.02 1.05† 2.25† 205† 8 1000 6.948E-7
111204A 336.63 -31.38 1.44′′ 2.15* 2011-12-04 13:37:28.00 33 81 48.0 1.83 2.83 200* 15 150 4.7E-7
111205A 134.49 -31.97 0.10◦ 2.15* 2011-12-05 13:10:50.30 0 80.384 80.384 0.82 2.82 998 20 10000 1.7E-4
111207A 92.92 -39.00 0.03◦ 2.15* 2011-12-07 14:16:59.00 -1 3 4.0 1* 2* 200* 10* 10000* 1.00E-5*
111207B 164.88 -17.94 9.98◦ 0.5* 2011-12-07 12:17:16.20 -0.9 -0.13 0.77 1.05† 2.25† 205† 8 1000 2.621E-7
111208A 290.21 40.67 0.02◦ 2.15* 2011-12-08 08:28:10.79 -4.1 36.86 40.96 1.5 2.5 200* 15 150 10E-7
111209A 14.34 -46.80 0.72′′ 0.677 2011-12-09 07:12:08.00 -1900 4400 6300.0 1.31 3.31 310 10* 10000* 4.86E-4
111210A 191.48 -7.17 1.44′′ 2.15* 2011-12-10 14:37:03.00 -2.33 0.36 2.69 1.3 2.3 200* 15 150 1.6E-7
111211A 153.09 11.18 0.03◦ 0.478 2011-12-11 22:17:33.00 0 25 25.0 2.77 3.77 200* 20 5000 9.2E-6
111212A 310.43 -68.61 1.08′′ 2.15* 2011-12-12 09:23:07.00 -5.77 62.74 68.51 1.67 2.67 200* 15 150 1.4E-6
111215A 349.56 32.49 0.72′′ 2.15* 2011-12-15 14:04:08.00 -116.4 960.1 1076.5 1.7 2.7 200* 15 150 4.5E-6
111215B 222.40 16.44 0.08◦ 2.15* 2011-12-15 20:28:02.72 0 77.5 77.5 1.03 2.3 413 20 10000 5.3E-5
111216A 185.99 5.83 1.37◦ 2.15* 2011-12-16 09:20:31.51 2.3 86.08 83.78 1.05† 2.25† 205† 8 1000 4.168E-5
111220A 267.60 -56.05 1.39◦ 2.15* 2011-12-20 11:40:26.24 -6.14 32.9 39.04 1.05† 2.25† 205† 8 1000 5.356E-5
111221A 10.16 -29.77 1.92◦ 2.15* 2011-12-21 17:43:30.81 -0.51 26.62 27.13 1.05† 2.25† 205† 8 1000 3.059E-6
111222A 179.22 69.07 0.36′′ 0.5* 2011-12-22 14:51:55.02 -0.06 0.26 0.32 0.35 2.35 762 20 3000 7.2E-6
111225A 13.15 51.57 0.36′′ 0.297 2011-12-25 03:50:37.00 -14.28 111.24 125.52 1.7 2.7 200* 15 150 1.3E-6
111226A 21.50 3.87 1.00◦ 2.15* 2011-12-26 19:04:58.28 -6.14 68.61 74.75 1.05† 2.25† 205† 8 1000 1.145E-5
111228A 150.07 18.30 0.72′′ 0.714 2011-12-28 15:44:43.00 -12.82 115.43 128.25 1.9 2.7 34 10 1000 1.8E-5
111228B 330.65 14.47 3.57◦ 2.15* 2011-12-28 10:52:50.52 0.1 3.04 2.94 1.05† 2.25† 205† 8 1000 2.747E-6
111230A 150.19 33.43 2.78◦ 2.15* 2011-12-30 16:23:08.60 -12.8 15.36 28.16 1.05† 2.25† 205† 8 1000 2.896E-6
111230B 242.61 -22.12 2.02◦ 2.15* 2011-12-30 19:39:32.14 -0.64 12.1 12.74 1.05† 2.25† 205† 8 1000 3.512E-6
120101A 185.87 52.91 8.77◦ 0.5* 2012-01-01 08:30:06.91 -0.1 0.03 0.13 1.05† 2.25† 205† 8 1000 1.092E-7
120102B 341.15 -23.16 3.58◦ 2.15* 2012-01-02 09:59:01.27 -10.24 9.98 20.22 1.05† 2.25† 205† 8 1000 2.553E-6
120105A 203.69 40.07 2.80◦ 2.15* 2012-01-05 14:00:35.90 -8.19 14.34 22.53 1.05† 2.25† 205† 8 1000 1.468E-6
120106A 66.11 64.04 0.72′′ 2.15* 2012-01-06 14:16:24.00 -6.24 60.24 66.48 1.53 2.53 200* 15 150 9.7E-7
120107A 246.40 -69.93 0.50◦ 2.15* 2012-01-07 09:12:12.45 0 27 27.0 0.91 2.11 188.90 10 1000 6.81E-6
120109A 251.33 30.80 11.33◦ 2.15* 2012-01-09 19:46:01.94 -2.05 36.61 38.66 1.05† 2.25† 205† 8 1000 1.919E-6
120111A 95.34 5.00 5.38◦ 2.15* 2012-01-11 01:13:27.63 -2.05 74.75 76.8 1.05† 2.25† 205† 8 1000 3.968E-6
120114A 317.90 57.04 0.02◦ 2.15* 2012-01-14 16:20:05.68 -7.94 35.33 43.27 1.4 2.4 200* 15 150 1.00E-5*
120114B 263.23 -75.64 11.05◦ 2.15* 2012-01-14 10:23:39.21 -0.13 2.62 2.75 1.05† 2.25† 205† 8 1000 1.487E-7
199
Table A.2: IC86I GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
120118A 195.40 -61.64 0.03◦ 2.15* 2012-01-18 06:04:44.00 0 60 60.0 1* 2* 200* 20 200 2E-7
120118C 166.57 47.87 7.17◦ 2.15* 2012-01-18 21:32:45.81 -0.51 16.64 17.15 1.05† 2.25† 205† 8 1000 1.616E-6
120119C 65.96 -33.92 4.42◦ 2.15* 2012-01-19 08:29:29.82 -7.94 8.45 16.39 1.05† 2.25† 205† 8 1000 2.610E-6
120120A 134.72 35.47 5.71◦ 2.15* 2012-01-20 10:21:25.41 0 32.26 32.26 1.05† 2.25† 205† 8 1000 1.503E-6
120121A 249.35 -23.96 1.08′′ 2.15* 2012-01-21 09:42:19.00 -11 18.33 29.33 1.23 2.23 200* 15 150 1.1E-6
120121B 235.67 -39.34 7.86◦ 2.15* 2012-01-21 02:25:53.80 -3.33 15.1 18.43 1.05† 2.25† 205† 8 1000 1.955E-6
120121C 208.90 -1.34 1.61◦ 2.15* 2012-01-21 06:00:45.24 -5.63 31.49 37.12 1.05† 2.25† 205† 8 1000 1.154E-5
120129A 30.44 59.28 3.83◦ 2.15* 2012-01-29 13:55:46.24 0.32 5.328 5.008 0.76 2.9 326 20 10000 2.7E-5
120129B 26.52 -8.51 15.04◦ 0.5* 2012-01-29 07:29:14.05 -0.64 0.64 1.28 1.05† 2.25† 205† 8 1000 8.932E-8
120130A 150.04 -17.45 3.69◦ 2.15* 2012-01-30 16:47:10.88 -0.64 27.14 27.78 1.05† 2.25† 205† 8 1000 6.612E-6
120130B 64.96 9.48 5.55◦ 2.15* 2012-01-30 21:44:54.33 -1.28 2.3 3.58 1.05† 2.25† 205† 8 1000 5.248E-7
120130C 323.30 58.56 1.00◦ 2.15* 2012-01-30 22:30:34.47 -5.12 33.79 38.91 1.05† 2.25† 205† 8 1000 1.041E-5
120202A 203.51 22.77 0.03◦ 2.15* 2012-02-02 21:40:17.00 0 100 100.0 1* 2* 200* 20 200 7E-7
120205A 243.42 25.90 23.83◦ 0.5* 2012-02-05 06:51:05.31 -0.58 0 0.58 1.05† 2.25† 205† 8 1000 1.109E-7
120206A 73.45 58.41 2.25◦ 2.15* 2012-02-06 22:46:16.69 -0.26 9.22 9.48 1.05† 2.25† 205† 8 1000 5.876E-6
120210A 54.65 -58.52 5.51◦ 0.5* 2012-02-10 15:35:43.28 -0.06 1.28 1.34 1.05† 2.25† 205† 8 1000 6.445E-7
120211A 87.75 -24.77 1.08′′ 2.15* 2012-02-11 11:58:28.00 -2.34 64.1 66.44 1.5 2.5 200* 15 150 8.1E-7
120212A 43.10 -18.02 1.08′′ 2.15* 2012-02-12 09:11:23.50 -2.05 7.17 9.22 1.83 2.83 200* 10 1000 1.407E-7
120212B 303.40 -48.10 7.47◦ 0.5* 2012-02-12 08:27:47.59 -0.83 0.03 0.86 1.05† 2.25† 205† 8 1000 5.087E-8
120213A 301.01 65.41 1.44′′ 2.15* 2012-02-13 00:27:19.00 -6.31 74.46 80.77 2.37 3.37 200* 15 150 1.9E-6
120213B 183.49 5.76 4.20◦ 2.15* 2012-02-13 14:32:44.61 -3.07 10.75 13.82 1.05† 2.25† 205† 8 1000 2.678E-6
120217A 122.44 36.77 3.23◦ 2.15* 2012-02-17 19:23:50.57 -0.51 5.38 5.89 1.05† 2.25† 205† 8 1000 1.746E-6
120217B 298.73 32.70 1.50◦ 2.15* 2012-02-17 21:41:57.77 -0.22 2.4 2.62 1.05† 2.25† 205† 8 1000 4.858E-6
120218A 319.76 -25.46 0.02◦ 2.15* 2012-02-18 00:49:22.00 -20.6 8.9 29.5 1.75 2.75 200* 15 150 5.3E-6
120219A 129.79 51.03 1.08′′ 2.15* 2012-02-19 14:30:08.00 -7.83 90.06 97.89 0.6 2.6 51.6 15 150 5.4E-7
120219B 274.85 -31.11 10.94◦ 2.15* 2012-02-19 13:31:23.11 -1.15 6.98 8.13 1.05† 2.25† 205† 8 1000 5.578E-7
120220A 206.13 -57.36 7.39◦ 2.15* 2012-02-20 05:02:21.60 -5.38 15.87 21.25 1.05† 2.25† 205† 8 1000 1.237E-6
120222A 299.55 26.49 2.76◦ 0.5* 2012-02-22 00:29:36.13 -0.06 1.02 1.08 1.05† 2.25† 205† 8 1000 1.728E-6
120222B 340.00 -36.41 5.70◦ 2.15* 2012-02-22 02:51:54.09 -5.12 24.32 29.44 1.05† 2.25† 205† 8 1000 2.451E-6
120223A 219.61 -7.46 2.74◦ 2.15* 2012-02-23 22:23:48.94 -0.51 13.82 14.33 1.05† 2.25† 205† 8 1000 3.879E-6
120224A 40.94 -17.76 1.08′′ 2.15* 2012-02-24 04:39:56.00 -1.08 8.26 9.34 2.25 3.25 200* 15 150 2.4E-7
120224B 118.42 41.34 4.60◦ 2.15* 2012-02-24 06:46:28.52 1.79 62.72 60.93 1.05† 2.25† 205† 8 1000 9.123E-6
120224C 331.06 10.18 3.59◦ 2.15* 2012-02-24 21:33:07.39 0.26 29.44 29.18 1.05† 2.25† 205† 8 1000 2.599E-6
120226A 300.05 48.81 0.50◦ 2.15* 2012-02-26 20:54:19.72 0 78.086 78.086 1.01 2.5 279 20 5000 7.5E-5
120226B 87.59 52.35 1.15◦ 2.15* 2012-02-26 10:44:16.39 -3.26 11.33 14.59 1.05† 2.25† 205† 8 1000 5.848E-6
120227A 84.76 8.50 6.33◦ 2.15* 2012-02-27 09:22:45.97 -0.77 18.94 19.71 1.05† 2.25† 205† 8 1000 3.742E-6
120227B 256.73 -88.86 1.21◦ 2.15* 2012-02-27 17:24:41.05 0.26 17.66 17.4 1.05† 2.25† 205† 8 1000 2.195E-5
120302A 122.43 29.64 0.02◦ 2.15* 2012-03-02 01:55:30.00 0 85.15 85.15 1.62 2.62 200* 10 1000 3.84E-6
120302B 24.09 9.71 13.87◦ 0.5* 2012-03-02 17:19:59.08 -0.13 1.47 1.6 1.05† 2.25† 205† 8 1000 1.187E-7
120304A 127.15 -61.12 1.00◦ 2.15* 2012-03-04 01:27:48.72 -0.26 9.73 9.99 1.05† 2.25† 205† 8 1000 5.046E-6
120304B 277.28 -46.22 1.00◦ 2.15* 2012-03-04 05:57:47.78 -0.26 5.12 5.38 1.05† 2.25† 205† 8 1000 1.144E-5
120305A 47.54 28.49 1.08′′ 0.5* 2012-03-05 19:37:30.00 0 0.136 0.136 1 2.0 1000* 15 150 2.0E-7
120308A 219.09 79.69 1.08′′ 2.15* 2012-03-08 06:13:38.00 -24.15 58.2 82.35 1.71 2.71 200* 15 150 1.2E-6
120308B 30.75 55.22 1.19◦ 2.15* 2012-03-08 14:06:05.77 -21.5 4.1 25.6 1.05† 2.25† 205† 8 1000 6.721E-6
200
Table A.2: IC86I GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
120311A 273.09 14.30 1.44′′ 2.15* 2012-03-11 05:33:38.00 -1.38 3.22 4.6 2.3 3.3 200* 15 150 3.0E-7
120311B 258.56 -13.05 1.08′′ 2.15* 2012-03-11 15:08:10.00 -13.88 21.63 35.51 1.96 2.96 200* 15 150 1.0E-6
120312A 251.81 23.88 0.02◦ 2.15* 2012-03-12 16:06:28.00 -1.42 15.87 17.29 1.72 2.72 200* 15 150 5.7E-7
120314A 17.89 -48.73 17.82◦ 0.5* 2012-03-14 09:52:34.67 -1.28 0 1.28 1.05† 2.25† 205† 8 1000 1.642E-7
120316A 57.02 -56.29 0.47◦ 2.15* 2012-03-16 00:11:02.00 0 28.16 28.16 0.92 2.92 539 20 10000 2.3E-5
120319A 69.85 -45.44 3.67◦ 2.15* 2012-03-19 23:35:04.21 -4.61 67.84 72.45 1.05† 2.25† 205† 8 1000 2.420E-6
120320A 212.52 8.70 1.44′′ 2.15* 2012-03-20 11:56:15.00 -0.01 29.86 29.87 0.31 2.31 62.8 15 150 5.9E-7
120323A 340.41 29.72 0.12◦ 2.15* 2012-03-23 12:10:15.97 0 4.38 4.38 0.82 2.01 64.8 10 1000 1.080E-5
120323B 211.10 -45.23 3.79◦ 2.15* 2012-03-23 03:52:49.27 -0.77 3.58 4.35 1.05† 2.25† 205† 8 1000 1.408E-6
120324A 291.08 24.13 1.08′′ 2.15* 2012-03-24 05:59:11.00 -150.5 142.5 293.0 1.02 2.3 445 20 10000 4.5E-5
120326A 273.90 69.26 1.08′′ 1.798 2012-03-26 01:20:29.00 -67.9 22.56 90.46 0.98 2.53 46.45 10 1000 3.539E-6
120327A 246.86 -29.41 1.08′′ 2.81 2012-03-27 02:55:16.00 -15.79 74.58 90.37 1.52 2.52 200* 15 150 3.6E-6
120327B 170.41 23.76 13.00◦ 0.5* 2012-03-27 10:01:49.23 -0.19 0.06 0.25 1.05† 2.25† 205† 8 1000 1.141E-7
120328A 241.61 -39.34 1.08′′ 2.15* 2012-03-28 03:06:19.00 -17.27 20.61 37.88 1.87 2.87 200* 15 150 4.7E-7
120328B 229.04 25.30 1.08◦ 2.15* 2012-03-28 06:26:20.95 3.84 56.176 52.336 0.75 2 177.90 10 1000 7.74E-5
120331A 26.37 -54.84 6.51◦ 2.15* 2012-03-31 01:19:06.64 -2.82 13.57 16.39 1.05† 2.25† 205† 8 1000 6.774E-7
120401A 58.08 -17.64 1.44′′ 2.15* 2012-04-01 05:24:15.00 -92.97 52.72 145.69 1.66 2.66 200* 15 150 9.1E-7
120402B 223.73 -10.40 2.61◦ 2.15* 2012-04-02 16:04:00.76 -2.08 18.14 20.22 1.35 2.44 37.2 10 1000 3.4E-6
120403B 55.28 -89.01 1.44′′ 2.15* 2012-04-03 20:33:56.00 -3 5.3 8.3 1.51 3.51 182 4 10000* 4.6E-7
120410A 159.63 -17.00 8.60◦ 0.5* 2012-04-10 14:02:00.19 -1.02 0.06 1.08 1.05† 2.25† 205† 8 1000 2.907E-7
120411A 38.07 -7.24 8.45◦ 2.15* 2012-04-11 22:12:25.65 0 38.91 38.91 1.05† 2.25† 205† 8 1000 1.464E-6
120412A 29.44 -24.67 13.47◦ 2.15* 2012-04-12 01:18:42.15 -4.1 5.63 9.73 1.05† 2.25† 205† 8 1000 1.246E-6
120412B 38.91 7.06 2.80◦ 2.15* 2012-04-12 22:04:40.56 0 101.19 101.19 1.05† 2.25† 205† 8 1000 7.029E-6
120415A 213.54 16.73 4.36◦ 2.15* 2012-04-15 01:49:57.68 -0.51 12.03 12.54 1.05† 2.25† 205† 8 1000 2.230E-6
120415B 190.69 4.91 6.88◦ 0.5* 2012-04-15 21:23:41.03 -0.26 0.7 0.96 1.05† 2.25† 205† 8 1000 1.305E-7
120415C 150.46 61.27 4.96◦ 2.15* 2012-04-15 22:59:19.13 -4.35 8.19 12.54 1.05† 2.25† 205† 8 1000 2.314E-6
120419A 187.40 -63.02 0.03◦ 2.15* 2012-04-19 12:56:25.00 0 20 20.0 1* 2* 200* 20 200 2E-7
120420A 47.89 -52.19 5.44◦ 2.15* 2012-04-20 05:58:07.26 -0.77 24.83 25.6 1.05† 2.25† 205† 8 1000 2.878E-6
120420B 109.26 10.76 1.11◦ 2.15* 2012-04-20 20:35:13.07 0 254.92 254.92 1.05† 2.25† 205† 8 1000 4.325E-5
120422A 136.91 14.02 1.08′′ 0.28 2012-04-22 07:12:03.00 -0.8 6 6.8 1.19 2.19 200* 15 150 2.3E-7
120426A 111.54 -65.63 0.30◦ 2.15* 2012-04-26 02:09:14.33 0.22 3.1 2.88 0.61 3.2 140 20 10000 1.9E-5
120429A 165.98 -8.76 15.40◦ 0.5* 2012-04-29 00:04:07.26 -0.19 1.47 1.66 1.05† 2.25† 205† 8 1000 2.794E-7
120429B 133.04 -32.23 5.34◦ 2.15* 2012-04-29 11:37:03.74 -1.02 14.34 15.36 1.05† 2.25† 205† 8 1000 2.368E-6
120430A 47.25 18.52 5.75◦ 2.15* 2012-04-30 23:30:43.35 -2.3 12.29 14.59 1.05† 2.25† 205† 8 1000 5.557E-7
120504A 329.94 46.83 4.06◦ 2.15* 2012-05-04 11:13:39.94 -0.51 41.47 41.98 1.05† 2.25† 205† 8 1000 3.363E-6
120506A 172.22 -33.72 9.33◦ 2.15* 2012-05-06 03:05:02.12 -0.77 1.54 2.31 1.05† 2.25† 205† 8 1000 2.872E-7
120510A 44.05 72.89 2.88′′ 2.15* 2012-05-10 08:47:44.00 0 130 130.0 2.05 3.05 200* 20 1200 3.82E-6
120510B 186.93 -55.24 3.75◦ 2.15* 2012-05-10 21:36:26.10 1.79 64.26 62.47 1.05† 2.25† 205† 8 1000 6.014E-6
120511A 226.93 -60.49 2.07◦ 2.15* 2012-05-11 15:18:47.92 -0.13 45.12 45.25 1.05† 2.25† 205† 8 1000 1.140E-5
120512A 325.56 13.64 0.01◦ 2.15* 2012-05-12 02:41:40.00 0 40 40.0 1.03 2.5 470.5 100 1000 9.33E-6
120514A 283.00 -4.26 1.08′′ 2.15* 2012-05-14 01:12:49.00 -8.75 165.55 174.3 2.3 3.3 200* 100 1000 1.62E-6
201
Table A.3: IC86II GRB Parameters
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
120426B 285.49 -13.68 3.83◦ 2.15* 2012-04-26 14:02:22.36 0 30.98 30.98 1.05† 2.25† 205† 8 1000 3.658E-6
120427A 224.94 29.31 0.22◦ 2.15* 2012-04-27 01:17:27.79 0.26 12.448 12.188 0.77 2.9 133 20 10000 7.8E-6
120427B 114.70 50.21 26.65◦ 2.15* 2012-04-27 03:40:37.87 -2.3 20.48 22.78 1.05† 2.25† 205† 8 1000 6.805E-7
120519A 178.37 22.41 0.63◦ 2.15* 2012-05-19 17:18:14.64 -0.5 5.2 5.7 0.5 2.5 740 20 10000 3.7E-6
120520A 45.86 35.28 8.30◦ 2.15* 2012-05-20 22:46:24.66 -4.74 1.02 5.76 1.05† 2.25† 205† 8 1000 4.409E-7
120521A 148.72 -49.42 1.08′′ 0.5* 2012-05-21 05:59:42.00 0.02 0.56 0.54 0.98 1.98 1000* 15 150 7.8E-8
120521B 197.01 -52.76 1.08′′ 2.15* 2012-05-21 09:07:48.00 -1.39 95.14 96.53 0.34 2.34 213 10 1000 3.11E-6
120521C 214.29 42.15 1.08′′ 6.0 2012-05-21 23:22:07.00 -1.03 31.84 32.87 1.73 2.73 200* 15 150 1.1E-6
120522A 166.00 -62.09 0.08◦ 2.15* 2012-05-22 03:11:07.38 0 78.086 78.086 0.88 2.88 381 20 10000 2.5E-5
120522B 56.07 54.85 2.02◦ 2.15* 2012-05-22 08:39:16.84 -11.52 16.64 28.16 1.05† 2.25† 205† 8 1000 9.324E-6
120524A 358.15 -15.61 10.45◦ 0.5* 2012-05-24 03:12:54.68 -0.13 0.58 0.71 1.05† 2.25† 205† 8 1000 2.527E-7
120526A 66.28 -32.23 1.04◦ 2.15* 2012-05-26 07:16:40.77 3.07 46.72 43.65 1.05† 2.25† 205† 8 1000 1.162E-4
120528A 295.13 6.50 5.98◦ 2.15* 2012-05-28 10:36:00.22 -0.77 15.62 16.39 1.05† 2.25† 205† 8 1000 3.792E-6
120528B 77.59 -37.80 0.06◦ 2.15* 2012-05-28 18:11:48.00 0 26 26.0 0.41 2.41 201 10* 10000* 2.9E-6
120528C 12.93 -0.95 0.06◦ 2.15* 2012-05-28 21:21:58.00 0 30 30.0 1* 2* 200* 10* 10000* 1.00E-5*
120530A 175.96 78.83 3.27◦ 2.15* 2012-05-30 02:53:41.86 0 77.06 77.06 1.05† 2.25† 205† 8 1000 7.173E-6
120531A 290.40 1.22 11.03◦ 2.15* 2012-05-31 09:26:38.36 -2.82 22.53 25.35 1.05† 2.25† 205† 8 1000 9.099E-7
120602A 87.92 -39.35 0.04◦ 2.15* 2012-06-02 05:00:00.23 0 70 70.0 0.77 2.8 300 20 10000 3.6E-4
120603A 198.79 4.33 0.64◦ 2.15* 2012-06-03 10:32:09.85 -0.06 5.3 5.36 0.4 2.4 560 20 10000 1.0E-6
120604A 163.87 -7.40 9.34◦ 2.15* 2012-06-04 05:16:31.31 -2.82 7.68 10.5 1.05† 2.25† 205† 8 1000 1.235E-6
120604B 113.58 -2.79 11.91◦ 2.15* 2012-06-04 08:13:40.16 -2.56 9.47 12.03 1.05† 2.25† 205† 8 1000 1.510E-6
120605A 243.61 41.51 2.62◦ 2.15* 2012-06-05 10:52:15.90 -0.64 17.47 18.11 1.05† 2.25† 205† 8 1000 3.253E-6
120608A 229.98 -26.12 2.52◦ 0.5* 2012-06-08 11:43:51.83 -0.19 0.77 0.96 1.05† 2.25† 205† 8 1000 4.834E-7
120608B 313.26 12.64 5.08◦ 2.15* 2012-06-08 18:38:33.04 -14.34 10.5 24.84 1.05† 2.25† 205† 8 1000 3.174E-6
120609A 67.32 13.00 7.54◦ 0.5* 2012-06-09 13:54:35.62 -0.77 1.02 1.79 1.05† 2.25† 205† 8 1000 4.196E-7
120611A 324.68 -44.79 5.28◦ 2.15* 2012-06-11 02:36:00.52 -9.22 40.7 49.92 1.05† 2.25† 205† 8 1000 4.526E-6
120612A 126.72 -17.57 1.08′′ 2.15* 2012-06-12 02:05:19.00 16.9 125.4 108.5 1.36 2.36 200* 15 150 1.3E-6
120612B 211.88 34.56 7.08◦ 2.15* 2012-06-12 16:19:45.55 -10.5 52.74 63.24 1.05† 2.25† 205† 8 1000 2.062E-6
120612C 39.67 -37.91 10.65◦ 0.5* 2012-06-12 16:29:44.56 -0.19 0.06 0.25 1.05† 2.25† 205† 8 1000 7.051E-7
120614A 312.73 65.16 0.12◦ 2.15* 2012-06-14 05:49:10.00 0 45 45.0 1* 2* 200* 10* 10000* 1.00E-5*
120616A 79.69 56.44 8.54◦ 0.5* 2012-06-16 15:06:50.64 -0.05 0 0.05 1.05† 2.25† 205† 8 1000 2.576E-7
120617A 22.31 33.80 0.25◦ 0.5* 2012-06-17 15:02:47.03 0 0.5 0.5 0.95 2.95 180 20 10000 2.1E-6
120618A 77.31 75.85 2.59◦ 2.15* 2012-06-18 03:03:49.88 -0.13 17.47 17.6 1.05† 2.25† 205† 8 1000 5.580E-6
120618B 213.57 -2.11 4.80◦ 2.15* 2012-06-18 22:03:34.31 -20.48 27.14 47.62 1.05† 2.25† 205† 8 1000 3.629E-6
120619A 190.74 -25.02 2.79◦ 0.5* 2012-06-19 21:13:16.91 -0.26 0.7 0.96 1.05† 2.25† 205† 8 1000 4.242E-7
120622A 205.43 -1.71 0.21◦ 2.15* 2012-06-22 03:21:46.00 0 39 39.0 1* 2* 200* 10* 10000* 1.00E-5*
120624A 4.77 7.17 0.44◦ 2.15* 2012-06-24 07:24:22.98 0 3.58 3.58 0.83 3.4 3700 10 1000 6.5E-6
120624B 170.89 8.93 0.01◦ 2.15* 2012-06-24 22:19:30.98 -20 289.952 309.952 0.85 2.36 566 10 1000 1.916E-4
120625A 51.26 51.07 1.17◦ 2.15* 2012-06-25 02:50:46.04 -0.26 7.17 7.43 1.05† 2.25† 205† 8 1000 1.022E-5
120629A 176.16 -0.60 8.88◦ 0.5* 2012-06-29 13:34:11.68 -0.38 0.32 0.7 1.05† 2.25† 205† 8 1000 5.192E-8
120630A 352.30 42.49 0.03◦ 0.5* 2012-06-30 23:17:33.00 -0.1 0.6 0.7 1.04 2.04 1000* 15 150 6.1E-8
120701A 80.34 -58.53 0.01◦ 2.15* 2012-07-01 07:50:41.00 0 15.4 15.4 1.05 2.05 200* 15 150 1.4E-6
120701B 182.73 -45.70 14.79◦ 0.5* 2012-07-01 15:41:48.32 -0.96 0.06 1.02 1.05† 2.25† 205† 8 1000 8.357E-8
120703A 339.36 -29.72 0.72′′ 2.15* 2012-07-03 17:25:22.00 -7.27 32.6 39.87 0.98 2.08 238.5 10 1000 9.154E-6
202
Table A.3: IC86II GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
120703B 69.49 34.74 2.60◦ 2.15* 2012-07-03 10:01:11.69 -0.51 64 64.51 1.05† 2.25† 205† 8 1000 1.108E-5
120703C 210.51 46.26 5.15◦ 2.15* 2012-07-03 11:56:56.87 -2.05 75.52 77.57 1.05† 2.25† 205† 8 1000 2.597E-6
120707A 291.87 -32.77 2.11◦ 2.15* 2012-07-07 19:12:17.43 1.52 66.6 65.08 1.17 2.31 174 10 1000 1.1E-4
120709A 320.23 -51.13 0.50◦ 2.15* 2012-07-09 21:11:40.37 -0.13 27.832 27.962 0.94 2 643 20 10000 1.8E-5
120710A 120.39 -31.14 4.76◦ 2.15* 2012-07-10 02:23:17.05 0 131.84 131.84 1.05† 2.25† 205† 8 1000 5.338E-6
120711A 94.70 -70.90 0.16◦ 3 2012-07-11 02:45:55.81 0 46.336 46.336 0.94 2.4 973 10 1000 1.942E-4
120711B 331.71 60.00 0.03◦ 2.15* 2012-07-11 03:11:02.58 -12.1 51.4 63.5 1.75 2.75 200* 15 150 5.6E-7
120711C 127.88 -31.83 11.03◦ 2.15* 2012-07-11 10:42:54.57 -1.28 86.27 87.55 1.05† 2.25† 205† 8 1000 1.862E-6
120712A 169.59 -20.03 1.08′′ 4.15 2012-07-12 13:42:27.00 -4.57 18.74 23.31 0.6 1.8 124 10 1000 4.43E-6
120713A 161.68 40.66 16.71◦ 2.15* 2012-07-13 05:25:29.14 -3.07 10.75 13.82 1.05† 2.25† 205† 8 1000 1.130E-6
120714A 167.98 -30.63 1.08′′ 2.15* 2012-07-14 07:46:46.00 -0.74 17.78 18.52 1.62 2.62 200* 15 150 8.2E-7
120714B 355.41 -46.20 0.03◦ 0.3984 2012-07-14 21:18:46.57 -23 154 177.0 1.52 2.52 200* 15 150 1.2E-6
120715A 272.15 58.79 3.73◦ 2.15* 2012-07-15 01:35:15.57 -4.86 24.83 29.69 1.05† 2.25† 205† 8 1000 2.195E-6
120716A 313.09 9.56 0.17◦ 2.48 2012-07-16 17:05:03.91 -1.02 234 235.02 0.48 2.19 115 10 1000 1.47E-5
120716B 304.53 59.41 5.09◦ 2.15* 2012-07-16 13:51:02.13 -5.89 19.07 24.96 1.05† 2.25† 205† 8 1000 5.223E-6
120719A 204.29 -43.45 1.37◦ 2.15* 2012-07-19 03:30:00.82 0.77 75.78 75.01 1.05† 2.25† 205† 8 1000 1.355E-5
120722A 230.50 13.25 1.44′′ 0.9586 2012-07-22 12:53:26.00 -0.3 47.5 47.8 1.9 2.9 200* 15 150 1.2E-6
120724A 245.18 3.51 1.08′′ 1.48 2012-07-24 06:39:02.00 -30 100 130.0 0.53 2.53 27.6 15 150 6.8E-7
120727A 163.26 25.09 15.27◦ 0.5* 2012-07-27 08:29:39.08 -0.9 0 0.9 1.05† 2.25† 205† 8 1000 1.091E-7
120727B 37.76 16.36 1.00◦ 2.15* 2012-07-27 16:20:19.53 -0.22 10.27 10.49 1.05† 2.25† 205† 8 1000 9.235E-6
120728A 137.09 -54.44 1.08′′ 2.15* 2012-07-28 22:25:12.74 -1.54 31.23 32.77 1.66 3.66 119.80 10 1000 5.29E-6
120728B 103.77 -45.89 0.47◦ 2.15* 2012-07-28 10:25:34.98 0 250 250.0 1 2.9 95 20 10000 1.20E-4
120729A 13.07 49.94 1.08′′ 0.80 2012-07-29 10:56:14.00 -3.08 101.94 105.02 1.49 2.49 200* 10 1000 5.1E-6
120801A 245.73 -47.37 2.39◦ 2.15* 2012-08-01 22:05:21.19 -7.17 472.07 479.24 1.05† 2.25† 205† 8 1000 3.340E-5
120802A 44.84 13.77 1.80′′ 3.796 2012-08-02 08:00:51.00 -35.68 28.02 63.7 1.21 3.21 57.2 15 150 1.9E-6
120803A 269.53 -6.73 0.03◦ 2.15* 2012-08-03 07:22:16.00 0.4 11.4 11.0 0.86 1.86 200* 15 150 3.0E-7
120803B 314.24 53.30 1.08′′ 2.15* 2012-08-03 11:06:06.00 -2.67 49.16 51.83 0.84 2.84 117.8 15 150 2.5E-6
120804A 233.95 -28.78 1.08′′ 0.5* 2012-08-04 00:54:14.00 -0.16 0.83 0.99 1.34 3.34 135 15 150 1.45E-6
120805A 216.54 5.83 1.80′′ 2.15* 2012-08-05 21:28:09.00 -15.39 32.61 48.0 1.2 2.2 200* 15 150 8.2E-7
120805B 30.13 -21.51 10.11◦ 0.5* 2012-08-05 16:56:21.72 -0.96 0.9 1.86 1.05† 2.25† 205† 8 1000 1.879E-7
120806A 308.99 6.33 4.25◦ 2.15* 2012-08-06 00:10:08.87 -0.26 26.37 26.63 1.05† 2.25† 205† 8 1000 4.902E-6
120807A 241.26 -47.48 1.08′′ 2.15* 2012-08-07 07:09:37.00 -0.24 24.07 24.31 1.81 2.81 200* 15 150 2.9E-7
120811A 257.18 -22.73 0.03◦ 2.15* 2012-08-11 02:35:18.00 -14.16 169.06 183.22 1.95 2.95 200* 15 150 1.1E-6
120811B 43.66 -31.68 0.23◦ 0.5* 2012-08-11 00:20:30.29 -0.13 1.33 1.46 0.14 2.14 1130 20 10000 4.6E-6
120811C 199.68 62.30 1.08′′ 2.671 2012-08-11 15:34:52.00 -9.7 42.9 52.6 1.4 3.4 42.9 15 150 3.0E-6
120814A 26.19 22.45 3.71◦ 0.5* 2012-08-14 04:49:12.58 -0.38 0.51 0.89 1.05† 2.25† 205† 8 1000 3.831E-7
120814B 90.57 33.13 10.68◦ 0.5* 2012-08-14 19:16:06.75 -0.19 0 0.19 1.05† 2.25† 205† 8 1000 1.284E-7
120815A 273.96 -52.13 1.08′′ 2.358 2012-08-15 02:13:58.00 -0.24 11.97 12.21 2.29 3.29 200* 15 150 4.9E-7
120816A 282.14 -6.94 1.08′′ 2.15* 2012-08-16 19:18:34.00 -1.97 6.66 8.63 2.54 3.54 200* 15 150 4.3E-7
120816B 341.15 2.16 2.51◦ 0.5* 2012-08-16 23:58:18.85 0 0.768 0.768 0.61 2.61 2320 20 10000 9.7E-5
120817A 250.69 -38.35 1.08′′ 2.15* 2012-08-17 06:49:42.00 -2.24 30.77 33.01 1.97 2.97 200* 15 150 6.9E-7
120817B 8.31 -26.43 0.05◦ 2.15* 2012-08-17 04:02:29.72 -0.03 4.08 4.11 0.82 2.82 1740 20 10000 4.1E-6
120817C 259.97 -9.07 7.14◦ 2.15* 2012-08-17 01:22:09.78 -6.4 30.46 36.86 1.05† 2.25† 205† 8 1000 1.040E-6
120819A 235.91 -7.31 1.08′′ 2.15* 2012-08-19 13:10:14.00 4.42 82.88 78.46 1.49 2.49 200* 15 150 1.4E-6
203
Table A.3: IC86II GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
120819B 171.54 49.42 7.94◦ 2.15* 2012-08-19 01:08:26.77 -5.63 60.67 66.3 1.05† 2.25† 205† 8 1000 1.334E-6
120820A 186.64 -12.31 4.81◦ 2.15* 2012-08-20 14:02:21.99 -17.41 90.11 107.52 1.05† 2.25† 205† 8 1000 6.981E-6
120821A 255.27 -40.52 0.02◦ 2.15* 2012-08-21 13:23:45.00 0 12 12.0 1* 2* 200* 20 200 3E-7
120822A 181.72 80.56 7.70◦ 0.5* 2012-08-22 15:03:56.40 -1.28 0.26 1.54 1.05† 2.25† 205† 8 1000 1.085E-7
120824A 70.92 17.63 3.00◦ 2.15* 2012-08-24 14:16:00.73 -8.19 103.43 111.62 1.05† 2.25† 205† 8 1000 5.919E-6
120827A 222.74 -71.89 1.67◦ 2.15* 2012-08-27 05:10:25.01 -1.66 3.39 5.05 1.05† 2.25† 205† 8 1000 3.367E-6
120830A 88.42 -28.81 0.86◦ 0.5* 2012-08-30 07:07:03.53 -0.38 0.9 1.28 0.4 2.4 1212.00 10 1000 3.253E-6
120830B 337.87 -80.04 3.46◦ 2.15* 2012-08-30 05:04:52.74 0.45 16.51 16.06 1.05† 2.25† 205† 8 1000 7.515E-6
120831A 144.02 -16.21 8.54◦ 0.5* 2012-08-31 21:37:31.88 -0.26 0.13 0.39 1.05† 2.25† 205† 8 1000 2.515E-7
120905A 355.96 16.99 1.80◦ 2.15* 2012-09-05 15:46:21.17 -7.17 188.42 195.59 1.05† 2.25† 205† 8 1000 1.957E-5
120907A 74.75 -9.31 1.08′′ 2.15* 2012-09-07 00:24:24.51 -1.92 17.76 19.68 0.75 2.75 154.50 6 10000* 7.8E-7
120908A 230.64 -25.79 0.29◦ 2.15* 2012-09-08 22:31:00.02 -4.61 62.34 66.95 1.21 3.21 205.9 10 1000 1.7E-5
120908B 268.67 -35.79 1.50◦ 2.15* 2012-09-08 20:57:30.95 0.58 47.42 46.84 1.05† 2.25† 205† 8 1000 1.270E-5
120909A 275.74 -59.45 0.72′′ 3.93 2012-09-09 01:41:09.00 0 149.17 149.17 1.23 3.23 335 10* 10000* 2.3E-5
120911A 357.98 63.10 1.08′′ 2.15* 2012-09-11 07:08:33.99 -4.48 24.1 28.58 0.36 2.36 64.2 10 1000 2.34E-6
120911B 172.03 -37.51 0.30◦ 2.15* 2012-09-11 06:25:14.00 0 132 132.0 1.01 2.72 1200 10 1000 1.973E-4
120913A 146.40 26.96 0.01◦ 2.15* 2012-09-13 20:18:22.89 -3.07 38.8 41.87 1.25 3.25 26 10 1000 0.38E-8
120913B 213.66 -14.51 0.01◦ 2.15* 2012-09-13 23:55:58.00 -51.7 111.79 163.49 1.19 1.97 163 10 1000 2.9E-5
120914A 267.94 1.82 5.35◦ 2.15* 2012-09-14 03:26:42.11 -1.28 8.96 10.24 1.05† 2.25† 205† 8 1000 7.350E-7
120915A 283.56 -1.11 6.54◦ 2.15* 2012-09-15 11:22:04.22 -2.3 3.58 5.88 1.05† 2.25† 205† 8 1000 3.829E-7
120916A 205.63 36.70 0.50◦ 2.15* 2012-09-16 04:07:46.69 -2 54.19 56.19 0.99 1.9 312.40 10 1000 1.95E-5
120916B 82.04 -19.22 11.13◦ 0.5* 2012-09-16 02:02:15.91 -0.32 1.02 1.34 1.05† 2.25† 205† 8 1000 8.154E-8
120918A 181.04 -32.76 0.01◦ 2.15* 2012-09-18 11:16:10.00 -2.86 23.9 26.76 1 3.0 85.5 15 150 3.7E-6
120919A 214.77 -45.56 0.09◦ 2.15* 2012-09-19 07:24:38.60 0 25.78 25.78 0.76 2.15 162 10 1000 1.679E-5
120919B 302.63 -37.49 0.27◦ 2.15* 2012-09-19 01:14:23.07 2.05 134.56 132.51 0.9 2.3 250 20 10000 3.1E-5
120919C 303.53 -66.16 11.89◦ 2.15* 2012-09-19 19:35:41.80 -3.33 18.69 22.02 1.05† 2.25† 205† 8 1000 1.031E-6
120920A 27.12 -26.12 7.84◦ 2.15* 2012-09-20 00:04:32.73 -2.3 26.88 29.18 1.05† 2.25† 205† 8 1000 1.193E-6
120921A 96.42 -64.77 3.20◦ 2.15* 2012-09-21 21:03:03.77 -0.26 5.38 5.64 1.05† 2.25† 205† 8 1000 2.478E-6
120922A 234.75 -20.18 1.08′′ 3.1 2012-09-22 22:30:28.00 -22.58 215.73 238.31 1.6 2.3 37.7 180 10000* 6.5E-6
120923A 303.80 6.22 1.08′′ 2.15* 2012-09-23 05:16:06.00 -2.93 26.64 29.57 0.29 2.29 44.4 15 150 3.2E-7
120926A 318.39 58.38 1.51◦ 2.15* 2012-09-26 08:02:56.57 -0.64 3.65 4.29 1.05† 2.25† 205† 8 1000 2.478E-6
120926B 59.72 -37.20 3.76◦ 2.15* 2012-09-26 10:13:16.04 -2.3 57.86 60.16 1.05† 2.25† 205† 8 1000 4.383E-6
120926C 24.61 -45.58 21.32◦ 2.15* 2012-09-26 18:04:35.10 -1.54 1.54 3.08 1.05† 2.25† 205† 8 1000 1.878E-7
121001A 276.03 -5.67 1.08′′ 2.15* 2012-10-01 18:23:02.00 -30 143 173.0 1.34 2.34 200* 15 150 1.7E-6
121004A 137.46 -11.02 9.44◦ 0.5* 2012-10-04 05:03:18.19 -0.51 1.02 1.53 1.05† 2.25† 205† 8 1000 3.794E-7
121005A 195.17 -2.09 9.48◦ 2.15* 2012-10-05 00:42:51.89 -31.23 65.54 96.77 1.05† 2.25† 205† 8 1000 3.731E-6
121005B 149.73 25.40 5.39◦ 2.15* 2012-10-05 08:09:12.86 0 141.57 141.57 1.05† 2.25† 205† 8 1000 5.169E-6
121008A 340.97 -3.10 9.00◦ 2.15* 2012-10-08 10:10:50.66 -0.32 3.14 3.46 1.05† 2.25† 205† 8 1000 3.918E-7
121011A 260.21 41.11 1.44′′ 0.58 2012-10-11 11:15:30.26 -10 80.1 90.1 1.09 3.09 1160 10 1000 1.00E-5
121011B 182.81 44.11 1.49◦ 2.15* 2012-10-11 22:32:20.08 0 2.5 2.5 0.45 1.9 670 20 10000 2.8E-6
121012A 33.42 14.58 6.78◦ 0.5* 2012-10-12 17:22:16.39 -0.13 0.32 0.45 0.47 2.47 540 10 1000 1.15E-6
121014A 166.65 -29.11 0.02◦ 2.15* 2012-10-14 20:11:56.00 -12.21 67.79 80.0 1.91 2.91 200* 15 150 1.1E-6
121014B 320.01 -53.43 17.20◦ 0.5* 2012-10-14 15:19:00.58 -0.58 -0.19 0.39 1.05† 2.25† 205† 8 1000 9.619E-8
121017A 288.83 -1.60 1.08′′ 2.15* 2012-10-17 19:23:28.00 -2.72 2.53 5.25 1.74 2.74 200* 15 150 6.6E-7
204
Table A.3: IC86II GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
121019A 43.47 62.14 7.52◦ 2.15* 2012-10-19 05:35:09.23 -2.56 11.78 14.34 1.05† 2.25† 205† 8 1000 5.886E-7
121023A 313.86 -4.38 4.76◦ 0.5* 2012-10-23 07:44:16.95 -0.13 0.38 0.51 1.05† 2.25† 205† 8 1000 7.727E-7
121024A 70.47 -12.29 0.72′′ 2.298 2012-10-24 02:56:12.00 -8.27 75.73 84.0 1.41 2.41 200* 15 150 1.1E-6
121025A 248.38 27.67 2.16′′ 2.15* 2012-10-25 07:46:30.00 0 20 20.0 1* 2* 200* 10* 10000* 1.00E-5*
121027A 63.60 -58.83 1.08′′ 1.773 2012-10-27 07:32:29.00 -9.34 65.33 74.67 1.82 2.82 200* 15 150 2.0E-6
121027B 4.31 -47.54 2.61◦ 2.15* 2012-10-27 00:54:19.37 -65.54 101.38 166.92 1.05† 2.25† 205† 8 1000 7.395E-6
121028A 271.90 -2.29 1.08′′ 2.15* 2012-10-28 05:04:31.00 -0.8 3.8 4.6 1.79 2.79 200* 15 150 3.7E-7
121028B 52.56 -25.07 7.68◦ 2.15* 2012-10-28 06:43:13.09 -1.79 9.22 11.01 1.05† 2.25† 205† 8 1000 9.978E-7
121029A 226.77 -28.20 1.65◦ 2.15* 2012-10-29 08:24:18.00 -2 20 22.0 0.57 2.82 176 10 1000 7.82E-6
121031A 170.77 -3.52 1.08′′ 2.15* 2012-10-31 22:47:15.27 -27.39 293.31 320.7 0.87 2.87 142.3 10 1000 1.99E-5
121102A 270.90 -16.96 0.72′′ 2.15* 2012-11-02 02:27:00.00 0 37.25 37.25 1.88 2.88 200* 15 150 1.9E-6
121102B 258.47 14.09 12.15◦ 2.15* 2012-11-02 01:32:47.94 -1.54 0.51 2.05 1.05† 2.25† 205† 8 1000 5.672E-7
121104A 72.14 14.08 4.05◦ 2.15* 2012-11-04 15:02:15.49 -1.02 58.11 59.13 1.05† 2.25† 205† 8 1000 4.446E-6
121108A 83.19 54.47 1.08′′ 2.15* 2012-11-08 17:47:39.00 -0.15 137.98 138.13 2.28 3.28 200* 15 150 9.6E-7
121109A 6.84 -42.57 10.37◦ 2.15* 2012-11-09 08:06:56.63 -6.91 15.23 22.14 1.05† 2.25† 205† 8 1000 5.336E-6
121112A 78.98 -55.44 15.56◦ 0.5* 2012-11-12 19:20:44.27 -0.13 1.15 1.28 1.05† 2.25† 205† 8 1000 2.232E-7
121113A 313.17 59.82 2.06◦ 2.15* 2012-11-13 13:02:43.53 1.54 97.03 95.49 1.05† 2.25† 205† 8 1000 2.685E-5
121116A 180.88 -74.79 6.98◦ 0.5* 2012-11-16 11:00:24.60 -0.7 0.64 1.34 1.05† 2.25† 205† 8 1000 2.398E-7
121117A 31.61 7.42 0.36′′ 2.15* 2012-11-17 08:50:56.00 0 158.6 158.6 1.16 2.16 200* 15 150 1.4E-6
121117B 279.14 44.93 4.32◦ 2.15* 2012-11-17 00:25:37.73 -270.34 61.44 331.78 1.05† 2.25† 205† 8 1000 1.063E-5
121118A 299.38 65.65 1.14◦ 2.15* 2012-11-18 13:48:54.26 -0.26 33.54 33.8 1.05† 2.25† 205† 8 1000 6.777E-6
121118B 171.70 -3.06 0.74◦ 2.15* 2012-11-18 22:27:06.66 -30 70 100.0 1.18 3.05 599 20 10000 8.5E-5
121119A 311.65 -16.92 8.13◦ 2.15* 2012-11-19 13:53:14.13 -0.26 2.05 2.31 1.05† 2.25† 205† 8 1000 8.815E-7
121122A 35.26 45.14 3.71◦ 2.15* 2012-11-22 21:14:52.55 0.51 20.616 20.106 0.68 3.1 178 10 1000 5.46E-5
121122B 52.67 46.47 12.89◦ 2.15* 2012-11-22 13:31:27.52 -1.28 7.42 8.7 1.05† 2.25† 205† 8 1000 8.146E-7
121122C 355.45 6.34 2.66◦ 2.15* 2012-11-22 20:52:49.03 0 125.44 125.44 1.05† 2.25† 205† 8 1000 9.070E-6
121123A 307.32 -11.86 0.36′′ 2.15* 2012-11-23 10:02:41.00 -6.34 419 425.34 0.25 3 85 10 1000 2.20E-5
121123B 30.52 -18.79 1.61◦ 2.15* 2012-11-23 10:35:55.71 2.3 44.8 42.5 1.05† 2.25† 205† 8 1000 1.423E-5
121124A 87.93 49.55 14.64◦ 0.5* 2012-11-24 14:32:07.30 -0.13 0.13 0.26 1.05† 2.25† 205† 8 1000 5.660E-8
121125A 228.53 55.31 1.08′′ 2.15* 2012-11-25 08:32:27.00 -6.31 77.64 83.95 1.38 3.38 196 10 1000 9.5E-6
121125B 177.53 38.54 5.24◦ 2.15* 2012-11-25 11:14:47.49 -2.3 10.56 12.86 1.05† 2.25† 205† 8 1000 8.568E-7
121127A 176.44 -52.41 0.08◦ 2.15* 2012-11-27 21:55:57.29 0 3.51 3.51 0.55 1.55 200* 100 1000 9.34E-7
121201A 13.47 -42.94 1.08′′ 3.6 2012-12-01 12:25:42.00 -24 71 95.0 1.9 2.9 200* 15 150 7.8E-7
121202A 256.80 23.95 0.72′′ 2.15* 2012-12-02 04:20:05.00 -2.18 20.84 23.02 1.14 3.14 135.4 10 1000 2.0E-6
121205A 238.59 -49.71 11.72◦ 2.15* 2012-12-05 12:10:04.71 -0.38 2.43 2.81 1.05† 2.25† 205† 8 1000 1.335E-7
121209A 326.79 -8.23 1.08′′ 2.15* 2012-12-09 21:59:11.00 -2.16 44.28 46.44 1.43 2.43 200* 15 150 2.9E-6
121210A 202.54 17.77 8.25◦ 2.15* 2012-12-10 01:56:01.53 -1.54 11.26 12.8 1.05† 2.25† 205† 8 1000 2.024E-6
121211B 72.37 8.63 5.23◦ 2.15* 2012-12-11 16:41:02.77 -0.51 8.45 8.96 1.05† 2.25† 205† 8 1000 1.340E-6
121212A 177.79 78.04 1.08′′ 2.15* 2012-12-12 06:56:12.00 0 10 10.0 2.65 3.65 200* 15 150 1.2E-7
121216A 13.88 -85.44 14.15◦ 2.15* 2012-12-16 10:03:16.45 -2.05 7.17 9.22 1.05† 2.25† 205† 8 1000 3.850E-7
121217A 153.71 -62.35 1.08′′ 0.8 2012-12-17 07:17:47.00 -17.7 783.8 801.5 1.2 3.2 264 10 1000 1.11E-5
121217B 153.71 -62.35 1.80′′ 2.15* 2012-12-17 07:30:01.58 -807.42 21.25 828.67 1.05† 2.25† 205† 8 1000 6.767E-6
121220A 31.07 48.28 8.30◦ 2.15* 2012-12-20 07:28:13.24 -1.28 3.84 5.12 1.05† 2.25† 205† 8 1000 4.532E-7
121221A 214.26 33.55 4.22◦ 2.15* 2012-12-21 21:59:29.97 -3.07 35.84 38.91 1.05† 2.25† 205† 8 1000 5.039E-6
205
Table A.3: IC86II GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
121223A 50.11 21.37 2.74◦ 2.15* 2012-12-23 07:11:19.81 0 11.01 11.01 1.05† 2.25† 205† 8 1000 7.017E-6
121225A 264.86 -66.07 0.17◦ 2.15* 2012-12-25 09:50:24.00 0 33 33.0 1* 2* 200* 10* 10000* 1.00E-5*
121225B 308.91 -34.35 1.25◦ 2.15* 2012-12-25 10:01:03.17 -16 70 86.0 1.08 2.14 277.6 10 1000 7.16E-5
121226A 168.62 -30.41 0.02◦ 0.5* 2012-12-26 19:09:43.00 -0.36 0.8 1.16 1.51 2.51 1000* 15 150 1.4E-7
121229A 190.10 -50.59 1.08′′ 2.707 2012-12-29 05:00:21.00 0 64 64.0 2.43 3.43 200* 15 150 4.6E-7
121229B 315.59 -11.94 4.58◦ 2.15* 2012-12-29 12:47:33.36 0 23.04 23.04 1.05† 2.25† 205† 8 1000 3.508E-6
121231A 335.47 -17.78 6.46◦ 2.15* 2012-12-31 10:41:23.25 -5.63 27.14 32.77 1.05† 2.25† 205† 8 1000 2.937E-6
130102A 311.42 49.82 1.08′′ 2.15* 2013-01-02 18:10:53.00 12.51 100.43 87.92 1.39 2.39 200* 15 150 7.2E-7
130102B 309.58 -72.38 0.17◦ 2.15* 2013-01-02 04:41:42.00 0 30 30.0 2.85 3.85 200* 10* 10000* 3.46E-6
130104A 174.09 25.92 2.44◦ 2.15* 2013-01-04 17:18:07.05 -1.79 24.58 26.37 1.05† 2.25† 205† 8 1000 5.668E-6
130106A 66.67 29.74 4.99◦ 2.15* 2013-01-06 19:53:22.07 -2.56 8.7 11.26 1.05† 2.25† 205† 8 1000 1.586E-6
130106B 28.76 63.38 1.87◦ 2.15* 2013-01-06 23:52:25.79 -1.02 69.38 70.4 1.05† 2.25† 205† 8 1000 1.543E-5
130109A 17.45 19.24 3.72◦ 2.15* 2013-01-09 04:56:26.26 -3.58 5.38 8.96 1.05† 2.25† 205† 8 1000 2.535E-6
130112A 236.03 52.19 4.93◦ 2.15* 2013-01-12 06:52:07.52 -29.7 5.63 35.33 1.05† 2.25† 205† 8 1000 2.614E-6
130114A 310.19 -15.32 10.86◦ 2.15* 2013-01-14 00:27:04.55 -2.05 6.66 8.71 1.05† 2.25† 205† 8 1000 1.113E-6
130115A 171.09 22.62 2.78◦ 2.15* 2013-01-15 17:10:39.18 -3.84 9.73 13.57 1.05† 2.25† 205† 8 1000 2.718E-6
130116A 38.24 15.75 29.85◦ 2.15* 2013-01-16 09:58:14.22 -4.1 62.72 66.82 1.05† 2.25† 205† 8 1000 9.271E-7
130117A 341.24 2.81 6.17◦ 2.15* 2013-01-17 02:05:11.42 1.79 80.64 78.85 1.05† 2.25† 205† 8 1000 2.849E-6
130118A 278.30 40.98 6.70◦ 2.15* 2013-01-18 11:33:29.36 -5.63 15.94 21.57 1.05† 2.25† 205† 8 1000 8.278E-7
130121A 211.31 -49.49 1.14◦ 2.15* 2013-01-21 20:01:59.97 1.79 180.48 178.69 1.05† 2.25† 205† 8 1000 4.345E-5
130122A 194.28 59.02 1.08′′ 2.15* 2013-01-22 23:44:09.00 -12.6 67.4 80.0 1.34 2.34 200* 15 150 7.4E-7
130127A 251.05 -17.07 8.46◦ 0.5* 2013-01-27 17:50:23.93 -0.26 0.19 0.45 0.03 2.4 700 10 1000 4.9E-7
130127B 301.21 -57.21 10.01◦ 2.15* 2013-01-27 07:09:53.16 -3.84 15.62 19.46 1.05† 2.25† 205† 8 1000 1.022E-6
130131A 171.13 48.08 1.08′′ 2.15* 2013-01-31 13:56:22.00 -0.95 52.15 53.1 2.12 3.12 200* 15 150 3.1E-7
130131B 173.96 15.04 1.08′′ 2.539 2013-01-31 19:10:08.00 -0.28 4.37 4.65 1.15 2.15 200* 15 150 3.4E-7
130131C 189.63 -14.48 1.00◦ 2.15* 2013-01-31 12:15:13.39 3.58 151.04 147.46 1.05† 2.25† 205† 8 1000 3.920E-5
130204A 105.64 41.92 7.07◦ 0.5* 2013-02-04 11:36:51.70 -0.13 0.06 0.19 1.05† 2.25† 205† 8 1000 2.809E-7
130206A 140.39 -58.19 0.02◦ 2.15* 2013-02-06 19:36:30.45 -2.56 89.03 91.59 1.1 3.1 132.6 10 1000 3.3E-6
130208A 181.60 50.93 4.67◦ 2.15* 2013-02-08 16:24:23.84 -1.02 40.45 41.47 1.05† 2.25† 205† 8 1000 2.255E-6
130209A 33.59 -27.58 1.00◦ 2.15* 2013-02-09 23:03:41.79 0.13 10.05 9.92 1.05† 2.25† 205† 8 1000 5.900E-6
130211A 147.52 -42.33 0.02◦ 2.15* 2013-02-11 03:36:32.00 -1.56 32 33.56 1.81 2.81 200* 15 150 6.4E-7
130213A 99.09 -8.10 10.62◦ 2.15* 2013-02-13 21:43:55.96 -5.63 9.73 15.36 1.05† 2.25† 205† 8 1000 9.874E-7
130214A 325.02 -1.83 12.77◦ 2.15* 2013-02-14 03:17:05.66 -3.33 93.44 96.77 1.05† 2.25† 205† 8 1000 1.585E-6
130214B 56.93 -0.29 1.60◦ 2.15* 2013-02-14 19:12:21.00 -3.58 10.18 13.76 1.05† 2.25† 205† 8 1000 5.983E-6
130215A 43.49 13.39 0.02◦ 0.597 2013-02-15 01:31:25.44 -7 139.11 146.11 1 1.6 155 10 1000 2.02E-5
130215B 3.11 59.38 2.10◦ 2.15* 2013-02-15 15:34:16.19 6.91 65.02 58.11 1.05† 2.25† 205† 8 1000 2.149E-5
130216A 67.90 14.67 0.01◦ 2.15* 2013-02-16 22:15:24.00 -6.16 4.31 10.47 0.7 2.6 152 10 1000 6.231E-6
130216B 58.87 2.04 0.02◦ 2.15* 2013-02-16 18:58:11.69 -6.27 9.02 15.29 1.6 2.2 91 10 1000 4.8E-6
130217A 96.72 6.80 8.19◦ 2.15* 2013-02-17 16:31:19.12 -11.26 3.58 14.84 1.05† 2.25† 205† 8 1000 1.100E-6
130218A 69.31 -69.13 2.28◦ 2.15* 2013-02-18 06:16:25.56 -6.14 30.98 37.12 1.05† 2.25† 205† 8 1000 9.433E-6
130219A 303.73 40.83 1.21◦ 2.15* 2013-02-19 18:35:51.73 -2 116 118.0 1.08 2.28 200* 10 1000 3.18E-5
130219B 169.29 -22.25 2.20◦ 2.15* 2013-02-19 04:44:07.57 5.38 173.38 168.0 1.05† 2.25† 205† 8 1000 3.186E-5
130219C 211.60 12.22 16.68◦ 0.5* 2013-02-19 15:01:13.95 -1.09 0.45 1.54 1.05† 2.25† 205† 8 1000 2.027E-7
130220A 306.20 31.74 1.14◦ 2.15* 2013-02-20 23:08:48.20 0.26 6.66 6.4 1.05† 2.25† 205† 8 1000 7.235E-6
206
Table A.3: IC86II GRB Parameters (continued)
Name RA (◦) Dec (◦) σ z Trigger (UT) T1 (s) T2 (s) T100 (s) αγ βγ γ Emin Emax Fluenceγ
130224A 205.90 59.72 2.62◦ 2.15* 2013-02-24 08:53:02.38 -35.84 35.07 70.91 1.05† 2.25† 205† 8 1000 4.962E-6
130228A 265.83 55.93 0.50◦ 2.15* 2013-02-28 02:40:02.17 -9.86 101.89 111.75 1.05† 2.25† 205† 8 1000 1.241E-5
130228B 240.75 -55.21 1.28◦ 2.15* 2013-02-28 05:05:57.05 0 15.42 15.42 1.05† 2.25† 205† 8 1000 1.748E-5
130304A 98.93 53.57 1.20◦ 2.15* 2013-03-04 09:49:53.10 0.83 68.67 67.84 1.05† 2.25† 205† 8 1000 3.701E-5
130305A 116.77 52.04 0.02◦ 2.15* 2013-03-05 11:39:11.37 1.28 38.096 36.816 0.67 2.4 640 10 1000 5.7E-5
130305B 73.32 -1.56 1.76◦ 2.15* 2013-03-05 12:37:47.72 1.28 119.81 118.53 1.05† 2.25† 205† 8 1000 1.520E-6
130306A 279.48 -11.68 0.02◦ 2.15* 2013-03-06 23:47:25.57 -17.66 370.1 387.76 1.5 3.5 212 20 10000 2.9E-4
130307A 156.00 23.00 0.36◦ 0.5* 2013-03-07 03:01:44.47 -0.06 0.32 0.38 0.78 2.78 1670 10 1000 1.43E-6
130307B 319.52 10.77 4.42◦ 2.15* 2013-03-07 05:42:19.33 -12.29 51.2 63.49 1.05† 2.25† 205† 8 1000 3.972E-6
130310A 141.91 -17.43 0.22◦ 2.15* 2013-03-10 20:09:41.50 4.1 20.1 16.0 1.01 2.27 2100 10 1000 1.4E-5
130313A 236.44 -0.35 0.03◦ 0.5* 2013-03-13 16:08:11.00 -0.02 0.23 0.25 1.37 2.37 1000* 15 150 3.1E-8
130314A 206.21 46.77 1.41◦ 2.15* 2013-03-14 03:31:16.30 1.54 144.39 142.85 1.05† 2.25† 205† 8 1000 1.460E-5
130315A 157.54 -51.79 0.01◦ 2.15* 2013-03-15 12:45:32.00 -3.3 268 271.3 1.81 2.81 200* 15 150 4.9E-6
130318A 200.74 8.12 9.94◦ 2.15* 2013-03-18 10:56:31.18 -2.82 135.17 137.99 1.05† 2.25† 205† 8 1000 3.407E-6
130320A 192.68 -14.47 1.51◦ 2.15* 2013-03-20 07:08:44.82 0 22.784 22.784 0.78 2.78 295 20 10000 2.6E-5
130320B 195.54 -71.26 0.49◦ 2.15* 2013-03-20 13:24:11.73 0 384.768 384.768 1 2 340 20 10000 7.8E-5
130324A 255.43 0.05 6.03◦ 2.15* 2013-03-24 01:00:24.75 -6.27 31.49 37.76 1.05† 2.25† 205† 8 1000 1.904E-6
130325A 122.78 -18.90 0.25◦ 2.15* 2013-03-25 04:51:54.30 0.58 10.448 9.868 0.73 2.18 202.20 10 1000 8.25E-6
130325B 30.44 62.06 16.14◦ 0.5* 2013-03-25 00:07:46.82 -0.06 0.58 0.64 1.05† 2.25† 205† 8 1000 5.656E-8
130327A 92.04 55.72 1.08′′ 2.15* 2013-03-27 01:47:34.00 -4.38 5.62 10.0 2.26 3.26 200* 15 150 2.3E-7
130327B 218.09 -69.51 0.17◦ 2.15* 2013-03-27 08:24:04.75 -1 43.704 44.704 0.56 3.4 334 10 1000 5.176E-5
130331A 164.47 29.64 2.43◦ 2.15* 2013-03-31 13:35:44.87 -0.51 13.31 13.82 1.05† 2.25† 205† 8 1000 9.331E-6
130403A 199.90 -46.68 8.26◦ 2.15* 2013-04-03 20:46:47.41 -7.94 14.85 22.79 1.05† 2.25† 205† 8 1000 1.094E-6
130404A 30.75 1.54 7.24◦ 2.15* 2013-04-04 10:15:40.05 -1.54 1.79 3.33 1.05† 2.25† 205† 8 1000 8.425E-7
130404B 146.58 -42.16 1.08◦ 2.15* 2013-04-04 20:10:04.03 0.32 34.88 34.56 1.05† 2.25† 205† 8 1000 8.355E-6
130404C 28.29 56.49 18.23◦ 0.5* 2013-04-04 21:02:11.03 -0.13 0.83 0.96 1.05† 2.25† 205† 8 1000 2.202E-7
130406A 157.78 -62.05 2.09◦ 2.15* 2013-04-06 06:55:03.46 -0.51 7.42 7.93 1.05† 2.25† 205† 8 1000 2.924E-6
130406B 109.66 -27.86 7.66◦ 2.15* 2013-04-06 08:00:36.77 -5.12 83.71 88.83 1.05† 2.25† 205† 8 1000 3.211E-6
130406C 138.21 42.83 14.84◦ 2.15* 2013-04-06 08:29:36.58 -1.28 1.28 2.56 1.05† 2.25† 205† 8 1000 2.976E-7
130407A 248.10 10.51 0.06◦ 2.15* 2013-04-07 23:37:01.00 0 25 25.0 1* 2* 200* 10* 10000* 1.00E-5*
130407B 53.53 44.17 9.29◦ 2.15* 2013-04-07 19:12:43.06 -5.63 26.37 32.0 1.05† 2.25† 205† 8 1000 1.746E-6
130408A 134.41 -32.36 1.08′′ 3.758 2013-04-08 21:51:38.00 -2 33.5 35.5 0.7 2.3 272 20 10000 1.2E-5
130408B 118.77 66.34 3.93◦ 2.15* 2013-04-08 15:40:22.85 -4.86 4.35 9.21 1.05† 2.25† 205† 8 1000 2.052E-6
130409A 30.52 44.10 2.22◦ 2.15* 2013-04-09 23:01:59.66 0.26 26.37 26.11 1.05† 2.25† 205† 8 1000 7.871E-6
130416A 99.28 24.70 14.34◦ 2.15* 2013-04-16 16:34:07.06 -2.82 0.26 3.08 1.05† 2.25† 205† 8 1000 2.807E-7
130416B 51.21 -18.25 4.86◦ 0.5* 2013-04-16 18:28:53.30 -0.05 0.14 0.19 1.05† 2.25† 205† 8 1000 9.385E-7
130419A 355.28 9.90 0.03◦ 2.15* 2013-04-19 13:30:29.00 40.09 169.51 129.42 1.43 2.43 200* 15 150 7.8E-7
130420A 196.11 59.42 1.08′′ 1.297 2013-04-20 07:28:29.00 -19.7 189.9 209.6 1 3.0 56 10 1000 1.4E-5
130420B 183.13 54.39 1.08′′ 2.15* 2013-04-20 12:56:32.99 -7.17 15 22.17 0.24 2.24 91 10 1000 1.04E-7
130420D 117.06 -69.03 4.01◦ 2.15* 2013-04-20 10:08:09.20 -2.43 24.9 27.33 1.05† 2.25† 205† 8 1000 3.771E-6
130425A 6.21 -70.18 2.50◦ 2.15* 2013-04-25 07:51:16.23 -1.86 77.216 79.076 1.29 2.46 167 20 10000 5.9E-5
130427A 173.14 27.70 2.16′′ 0.34 2013-04-27 07:47:57.00 -51.05 223.5 274.55 0.789 3.06 830 10 1000 1.975E-3
130427B 314.90 -22.55 1.08′′ 2.78 2013-04-27 13:20:41.00 -1.29 32.71 34.0 1.64 2.64 200* 15 150 1.5E-6
130502B 66.65 71.08 0.09◦ 2.15* 2013-05-02 07:51:12.76 0 37 37.0 0.75 2.47 323.00 10 1000 1.21E-4
207
208
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