Searching for Ultra-High Energy Neutrinos with Data from a Prototype Station of the Askaryan Radio Array

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Searching for Ultra-high Energy Neutrinos with Data from a Prototype Station of the Askaryan Radio Array

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the

Graduate School of The Ohio State University

Eugene S. Hong,

Graduate Program in Physics

The Ohio State University

2014

Dissertation Committee:

Prof. Amy L. Connolly, Adviser Prof. John F. Beacom Prof. Christopher S. Hill Prof. Brian Winer c Copyright by

Eugene S. Hong

2014 Abstract

The observed GZK cutoff in the cosmic ray spectrum has led to a strongly mo- tivated expectation of an ultra-high energy (UHE) neutrino flux arising from the interactions between the highest energy cosmic rays and cosmic microwave background photons. Aside from these diffuse neutrinos, UHE neutrinos are also expected to be produced in the same astrophysics sources producing the UHE cosmic rays such as

Gamma-Ray Bursts (GRB) and AGNs. Here, we discuss two UHE neutrino searches using data from the Askaryan Radio Array (ARA) prototype Testbed station: one search for a diffuse neutrino flux and another for neutrinos from GRBs. Testbed data from 2011 to 2012 are used for the searches in the thesis. We discuss how we define the analysis cuts, optimize the analysis cut parameters for maximum sensitivity to

UHE neutrinos, estimate the number of background and neutrino events, and set neutrino flux constraints in the UHE region (> 1017 eV). We use an optimistic flux model from Kotera et. al. 2010 as our baseline model and optimize our analysis cuts for this model. The GRB neutrino search follows the same analysis technique as the diffuse neutrino flux search with some modifications. A timing constraint for each

GRB reduces the estimated background dramatically and therefore we can loosen some of our analysis cuts for the GRB neutrino search. We also present detailed descriptions about tools that are used for the searches such as AraSim, a Monte-Carlo simulation that we developed, and RaySolver, a code to carry out ray tracing in ice

ii with a depth-dependent index of refraction model. We present constraints on the neutrino flux from the ARA Testbed for diffuse neutrinos and GRB neutrinos separately. These neutrino flux constraints and analysis techniques from the Testbed will provide a benchmark for the future deep ARA stations’ analyses which are expected to improve neutrino flux constraints by a factor of three or more due to differences in the design of the stations.

iii To my parents

iv ACKNOWLEDGMENTS

I would like to thank my advisor Amy Connolly for helping and supporting me for all the work I have done during my Ph.D. It would be impossible for me to ﬁnish all the projects and researches without her support. It was my pleasure and honor to work as her research group and also as a part of Askaryan Radio Array (ARA) experiment.

I appreciate other group members: Carl Pfendner, Patrick Allison who gave me a wonderful experience to work with, especially for Carl Pfendner who helped me a lot in both research and personal life manners. His thoughtful and patience conversations helped and supported my diﬃcult times.

I thank my committee members: John Beacom, James Beatty, Christopher Hill and Brian Winer. Their sincere advices helped me what I have to think about and decide for my future plans.

I also want to thank my friends Paul Shellin, Kenji Oman and Ranjan Laha who shared many hours with me and gave me an enjoyable life in OSU.

Many thanks to ARA collaborators: David Seckel, David Besson, Ming-Yuan Lu and all others.

Finally I would like to thank my family, my parents and my brother. Without their encouragements and supports, I would not be able to ﬁnish my Ph.D.

And also the one whom made my life changed forever...

v VITA

2006 ...... B.Sc., Korea University, S. Korea

2009 ...... M.S., Korea University, S. Korea

PUBLICATIONS

Improved Performance of the Preampliﬁer-Shaper Design for a High-Density Sensor Readout System, Eugene S. Hong, Eunil Won and Jaehyeok Yoo, Journal of the Korean Physical Society, 54, 760 (2009) [1]

First Constraints on the Ultra-High Energy Neutrino Flux from a Prototype Station of the Askaryan Radio Array, Patrick Allison, et. al. [arXiv:1404.5285] [2]

FIELDS OF STUDY

Major Field: Physics

Studies in Experimental Astroparticle Physics: Ultra-High Energy Neutrinos

vi Contents

Page

Abstract...... ii

Dedication...... iv

Acknowledgments...... v

Vita...... vi

List of Tables...... xi

List of Figures...... xiii

Chapters:

1. Introduction...... 1

1.1 Ultra-High Energy Neutrino Source Candidates...... 4

1.2 Detecting Techniques and Experiments...... 5

vii 2. Motivations for Ultra High Energy Neutrinos...... 8

2.1 GZK eﬀect...... 8

2.1.1 Models for GZK induced neutrino...... 13

2.1.2 Models for GZK induced neutrino with UHECR and EGRB

constraints...... 15

2.2 Gamma-Ray Bursts...... 20

2.3 Other Models (other than GZK, GRB models)...... 22

3. Past and Present Experiments for UHE neutrino...... 26

3.1 Detection Methods: Optical and Radio Cherenkov Radiation.... 26

3.2 Radio Ice Cherenkov Experiment (RICE)...... 30

3.3 Goldstone Lunar Ultra-high energy neutrino Experiment (GLUE). 31

3.4 Antarctic Impulsive Transient Antenna (ANITA)...... 32

3.5 IceCube...... 34

4. Askaryan Radio Array...... 39

4.1 Testbed...... 41

5. Simulation: AraSim...... 47

5.1 Simulation Process...... 47

5.1.1 Selecting Neutrino-ice Interaction Location...... 48

viii 5.1.2 Earth Absorption Eﬀect...... 49

5.1.3 Showers from Neutrino-ice Interaction...... 49

5.1.4 Ray Tracing...... 50

5.1.5 Ice Attenuation Factor...... 53

5.1.6 Antenna Response...... 55

5.1.7 Electronics Response...... 58

5.1.8 Generating Noise Waveforms...... 59

5.1.9 Trigger Analysis...... 61

5.2 Askaryan Radiation in AraSim...... 61

5.2.1 Custom parameterized RF Cherenkov emission model... 62

5.2.2 Parameterized AVZ RF Cherenkov emission model..... 73

5.3 Calibrating AraSim to the Testbed Data...... 77

5.3.1 Calibrating Thermal Noise...... 77

5.3.2 Calibrating the Trigger Threshold...... 82

6. A Search for UHE Neutrinos in the Testbed Station of the Askaryan Radio

Array...... 90

6.1 Introduction...... 90

6.2 Method...... 91

6.2.1 Testbed Local Coordinate...... 92

6.2.2 Analysis Cuts...... 92

6.2.3 Background Estimation...... 118

6.3 Survived Events...... 122

6.4 Livetime Calculation...... 123

ix 6.5 Results...... 125

6.6 Systematic Uncertainties...... 129

6.7 Projections for ARA3 and ARA37...... 134

7. Gamma-Ray Burst Neutrino Search...... 138

7.1 Introduction...... 138

7.2 Previous GRB Neutrino Analyses...... 139

7.3 The ARA Instrument...... 140

7.3.1 TestBed station...... 140

7.4 Analysis Tools...... 141

7.4.1 GRB Neutrino Model: NeuCosmA...... 141

7.4.2 Simulation: AraSim...... 142

7.5 Data Analysis...... 143

7.6 Results...... 149

7.7 Conclusions...... 151

8. Conclusions...... 153

Bibliography...... 156

x List of Tables

Table Page

2.1 Best ﬁt parameters for HiRes UHECR data and Fermi-LAT EGRB

data from [3]. The ﬁt results are shown with the data points in Fig. 2.5. 17

4.1 Types and positions of antennas as deployed in the ARA Testbed. See

the text for the description of antenna types...... 42

5.1 The tuned time oﬀset between channels by comparing Testbed cali-

bration pulser waveforms and simulated calibration pulser waveforms.

Oﬀset values are obtained with respect to Channel 0...... 83

5.2 The trigger threshold obtained from the minimum χ2 between the sim-

ulation and the Testbed data. The unit of trigger threshold is RMS of

tunnel diode output from thermal noise waveform...... 84

xi 6.1 This table summarizes the number of events passing each cut in the

Interferometric Map Analysis, in Phase 2 (2011-2012, excluding Feb.-

June 2012). We list how many events survive after each cut in sequence

and how many events each cut rejects as a last cut. After the Event

Quality and Reconstruction Quality Cuts are applied, VPol and HPol

and considered as two separate channels for the purpose of tabulation,

independent of one another...... 126

6.2 Summary of systematic uncertainties on the neutrino eﬃciency at 1018 eV.

...... 134

6.3 Factors that bring the Testbed sensitivity to ARA37 sensitivity for

18 Eν = 10 eV using AraSim...... 134

xii List of Figures

Figure Page

1.1 Cosmic ray ﬂux in broad energy range. AGASA [4] didn’t measured

the cutoﬀ at GZK threshold energy. Image from [5]...... 2

1.2 Cosmic ray ﬂux in the UHE region. Auger and HiRes data which

detected the cosmic ray ﬂux cutoﬀ above 1019.5 eV are shown. Image

from [5]...... 3

2.1 Total hadronic cross sections for γd, γp, and γγ interaction. The cross

section for the GZK interaction is the γp cross section in the plot,

which has the peak at √s 1.1 GeV due to the ∆+ resonance. Image ∼ from [5]...... 10

2.2 Probability for π photo-production by a CR as a function of the dis-

tance of the source at ∆+ resonance...... 12

xiii 2.3 Plotting Auger UHECR data against a model for the CR ﬂux at Earth

with n = 3 and α = 2.6. Auger data is shown as stars and the model − is shown as red solid line...... 16

2.4 Intensity of GZK induced neutrino models based on Auger UHECR

data. Waxman-Bahcall constraint is shown as dash-dotted line.... 16

2.5 GZK induced neutrino ﬂux (green solid line : best ﬁt model shown

in Table 2.1, green dashed line : 99% C.L. of best ﬁt) from Emin =

1017.5 eV model shown with UHECR data from HiRes and EGRB data

from Fermi-LAT. Image from [3]...... 18

17.5 2.6 Expected GZK induced neutrino ﬂux from Emin = 10 eV (green

solid line : best ﬁt, green dashed line : 99% C.L., green dotted line :

without Fermi-LAT EGRB data) compared with the constraints from

experiments. Without Fermi-LAT EGRB data, expected neutrino ﬂux

is much larger than with EGRB data (thin dotted green line). Image

from [3]...... 19

2.7 GRB distribution plot in Galactic coordinates from 2000 GRBs de-

tected by BATSE. GRBs are isotropically distributed which indicates

that GRBs are extragalactic source...... 21

3.1 Schematic of electromagnetic cascade due to electron. Image from [6]. 29

xiv 3.2 Basic schematic of Cherenkov radiation. Charged particle moves along

with the blue arrow, and Cherenkov radiation is shown as a red cone. 30

3.3 Basic schematic for detecting the Askaryan eﬀect in the moon. Image

from [7]...... 32

3.4 Basic schematic of detecting Askaryan eﬀect by ANITA...... 33

3.5 Constraints from GLUE, RICE, FORTE, AMANDA, and ANITA-lite

compared with TD, GZK, and Z-bust models for UHE neutrinos. Z-

burst models are ruled out by ANITA-lite. Image from [8]...... 35

3.6 Constraints from RICE, Auger, HiRes, ANITA-I, and ANITA-II. Satu-

rated GZK neutrino models are ruled out by ANITA-I and ANITA-II.

Image from [9]...... 36

3.7 Basic schematic of IceCube. Image from [10]...... 37

3.8 Constraints from IceCube (red curve) and other experiments with 1:1:1

neutrino ﬂavor assumption. Currently, IceCube has the best neutrino

ﬂux limit below 1019 eV. Image from [11]...... 38

xv 4.1 Diagram showing the layout of the proposed ARA37 array, with the

location of the Testbed and the ﬁrst three deployed deep stations high-

lighted in blue and black respectively, and proposed stations for the

next stage of deployment, ARA10, highlighted in orange...... 40

4.2 Diagram showing the layout of a design station and antennas. Each

station on Fig. 4.1 (one circle on the plot) has the layout shown on this

plot. There are four boreholes for receiving antenna clusters where each

borehole has two Vpol antennas and two Hpol antennas. There are two

additional boreholes for calibration transmitting antennas. Each cali-

bration pulser borehole has one Vpol and Hpol transmitter antennas.

There is central station electronics on the surface of the ice, which

includes DAQ and power supply box...... 41

4.3 Schematic of the ARA Testbed station...... 43

4.4 Photos taken from Testbed deployment. Top left: bicone Vpol antenna

under test in South Pole station, top middle: bowtie-slotted-cylinder

(BSC) Hpol antenna, top right: quad-slotted-cylinder (QSC), bottom

left: string descending down a hole, bottom right: x-mark for locating

the Testbed station...... 44

xvi 5.1 Basic schematic of a neutrino event. The cone at the neutrino-ice

interaction location is the Cherenkov cone from coherent radio emission

and the red curve is ray tracing between the antenna and neutrino-ice

interaction location...... 48

5.2 Antarctic ice index of fraction measurements (red crosses) at the South

Pole and its ﬁt result (green curve). The ﬁt function is n(z) = a1 +

a2 (1.0 exp(b1 z)) (exponential ﬁt model) where n(z) is the index × − · of refraction and z is the depth. Data points are digitized from [70]. 51

5.3 Plot showing the regions with ray-trace solutions for an antenna depth

at 25 m (top) and 200 m (bottom). The greater depth allows an

antenna at 200m depth to observe a larger volume of the ice...... 52

5.4 The electric ﬁeld attenuation length as a function of depth from the

ARA Testbed deep pulser data. The depth of the deep pulser was

2 km and the path length was 3.16 km from the deep pulser to ∼ the ARA Testbed. From the single distance measurement, the average

attenuation length over all depths are extrapolated...... 54

xvii 5.5 Signal receiver system’s simple schematic. Right hand part (source and

ZA) are the components from antenna while left hand part (ZR) is the

signal receiver (such as DAQ). When impedance is matched, we can

let reactance X from both ZA and ZR as zero and resistance for both

ZR and ZA as the same value Rr (ZA = ZR = Rr). V on the plot is the

actual measured voltage signal which is V = Z I = V .... 57 R · measured

5.6 Filter’s gain response which is in use for AraSim. The ﬁlter response

consists of a high pass ﬁlter at 150 MHz, a low pass ﬁlter at 800 MHz,

and a notch at 450 MHz to avoid the electronics communication fre-

quency...... 58

5.7 Simple closed circuit with voltage source (thermal noise source) and

antenna (ZA) and load (RL)...... 60

xviii 5.8 Comparison between the full shower simulation (ZHS) and the semi-

analytic model of a 3 1018 eV electromagnetic shower at a viewing ×

angle of θ = θ 0.3◦. The blue solid curve shows the result from ZHS C − full shower simulation, the red dashed curve shows the result from

semi-analytic model, and the yellow solid curve shows the result from

simple 1D model. The top plot shows the vector potential R A in | | the time domain, the middle plot shows the electric ﬁeld R E in the | | time domain, and the bottom plot shows the spectrum in the frequency

domain. All three plots show that the full ZHS simulation and the semi-

analytic method agree well. The disagreement at the high frequencies

seen in the middle and bottom plots are not important for ARA as the

bandwidth of the system only goes up to 1 GHz. Plots from [12]... 63

5.9 Fractional excess of electrons from ZHS in-ice simulation. Horizontal

axis shows the shower depth in ice. The plot shows that fractional

excess of electrons varies from 20% at the beginning of a shower to

30% for larger depths regardless of the energy of the shower. Based on

this plot, constant 25% excess of electrons is chosen...... 68

5.10 Shower proﬁles from AraSim and ZHS simulation for 1 PeV electromag-

netic shower. The black curve is obtained from AraSim using Greisen

function (Eq. 5.13), and the red curve is obtained from [13] Fig. 3 which

is the result from the ZHS simulation...... 71

xix 5.11 Vector potential obtained from AraSim for the same shower shown in

Fig. 5.10. Here, the vector potential is calculated 1 m from the shower.

Viewing angle is θ = θC + 10◦ = 65.8◦...... 71

5.12 Electric ﬁeld in the time domain from AraSim compared to ZHS sim-

ulation for the same shower as shown in Fig. 5.10 and 5.11. The black

curve is obtained from AraSim, and the red curve is obtained from [13]

Fig. 3 which is the result from ZHS simulation. Even though there was

some disagreement in the shower proﬁle (Fig. 5.10), the overall electric

ﬁeld signal power don’t diﬀer by more than 25%...... 72

5.13 Comparison of spectra obtained from the two Cherenkov emission

modes in AraSim. The red curve is obtained from the AVZ RF model

and the black curve is the result from custom parameterized RF Cherenkov

model (Section 5.2.1). Both results have exactly same shower param-

eters (electromagnetic shower with 10 TeV energy and viewing angle

of θ = θ 5◦). The two RF signal emission models show consistent C − results...... 76

xx 5.14 Distribution of voltages at 200 MHz and its best-ﬁt Rayleigh distribu-

tion function. Thermal noise events from Testbed data set (software

triggered events, blue curve) and their best-ﬁt Rayleigh distribution

function (red curve) are shown. The voltage distribution at 200 MHz,

Channel 2 (Vpol antenna) is chosen for the plot and the integral is

normalized to 1 in order of have same normalization for the Rayleigh

distribution function (Eq. 5.29). Good agreement between the distri-

bution and the ﬁt function is shown on the plot...... 79

5.15 Plot of the RMS voltage distribution from generated thermal noise

waveform using the best-ﬁt Rayleigh distribution. The red curve is the

distribution from generated thermal noise waveforms, while the blue

curve is from Testbed data. In the Testbed data set (blue curve), there

is an extended tail feature which the simulated noise doesn’t have. This

tail is coming from non-thermal background events such as CW and

anthropogenic impulsive events. Overall, the dominant thermal noise

part is well match between the data and the simulation...... 80

xxi 5.16 Plot of the distribution of peak voltages from thermal noise waveforms

generated using the best-ﬁt Rayleigh distribution and Testbed data.

The red curve is the distribution from the generated thermal noise

waveforms, while the blue curve is from the Testbed data. The part

of the distribution at low voltages shows agreement between simulated

noise and the data. Like the RMS distribution (Fig. 5.15), the extended

tail feature in the data set is due to non-thermal background events

such as CW and anthropogenic impulsive events...... 81

5.17 One example of ﬁnding the trigger-threshold sensitive variable from

8 borehole channels. The trigger-threshold sensitive variable is the

3rd highest peak square voltage among channels in trigger coincidence

window. In the plots, red box is the trigger coincidence window for

each corresponding channel. In the plots, Channel 0 has the highest

peak V2 among all channels, Channel 1 has the send highest peak V2,

and Channel 5 has the 3rd highest peak V2 which is the trigger sensitive

variable. The distribution of this trigger-threshold sensitive variable is

shown in Fig. 5.18...... 83

5.18 Comparison between the simulated triggered events and Testbed RF

triggered events for Channel 2. The trigger threshold value used for the

simulation set give us the minimum χ2 from the Testbed data. Good

agreement between the simulation and the data is shown...... 85

xxii 6.1 An example of an event waveform with a weird electronics error. The

DC component of the waveform provides the power contribution below

the 150 MHz high-pass-ﬁlter of the system and thus rejected by the

Event Quality Cuts...... 93

6.2 Series of waveforms that show the process to obtain the correlation

function from a pair of antennas. The top two plots are two voltage

waveforms from two antennas that are chosen as a pair to produce

the correlation function. All plots are obtained from same calibra-

tion pulser event. Both plots are from horizontally polarized antennas

Channel 0 and Channel 1, respectively. The bottom left plot is the

cross-correlation waveform from the top two waveforms. The bottom

right plot is the Hilbert-transformed of the bottom left plot...... 95

xxiii 6.3 Examples of correlation maps and the ﬁnal interferometric map from

the calibration pulser event (same event with Fig. 6.2). All maps are

obtained from 30 m source distance assumption in order to reconstruct

the calibration pulser which is located 30 m from the Testbed. The ∼ top two plots and the bottom left plot are the correlation maps from

diﬀerent pair of antennas in same polarization. From the Testbed,

there are total 6 pairs for each polarization. The correlation value

on the map is the projection of the cross-correlation function (bot-

tom right plot of Fig. 6.2) with the corresponding signal travel time

diﬀerence between the antennas. The bottom right plot is the ﬁnal

interferometric map obtained by summing correlation maps from all

pairs with the normalization factor 6 from the number of pairs. The

best reconstruction direction from the map (red peak region around

0◦ zenith and 140◦ azimuthal angle) is the direction of the calibration

pulser as expected...... 96

6.4 Distribution of calibration pulser events’ reconstructed direction. The

top plot is the distribution in zenith angle (θ) diﬀerence between the

true direction and the reconstructed direction, while the bottom is the

distribution plot in azimuthal angle (φ). Zenith angular resolution is

approximately factor of two worse than azimuthal angular resolution

due to the error in depth-dependent index of refraction model.... 98

xxiv 6.5 An example of a interferometric map used for reconstruction. This map

is obtained from VPol channels with a 3000 m distance assumption

from the station. The shadow region due to the ray-tracing in the

depth-dependent index of refraction yielded the empty horizontal band

in the middle of the plot. The shadow region eﬀect is illustrated in

Fig. 5.3. The 85% contour around the peak of this plot is shown in

Fig. 6.6...... 100

6.6 An example of an 85% contour around the peak. This plot of peak

area is obtained from Fig. 6.5. The red colored ﬁlled area is the 85%

contour region around the peak and the integrated solid angle of the

2 region is Apeak = 226.5 deg ...... 100

6.7 The distribution of 85% contour area from 2012 HPol calibration pulser

events (top) and simulated neutrino events from maximal Kotera et al.

ﬂux model. From the calibration pulser events’ plot, we set the max-

imum allowed A at 2σ away from the mean of the distribution, peak ∼ at 50 deg2. The signal plot (bottom) shows that the minimum allowed

2 Apeak at 1 deg has a minimal eﬀect on the neutrino eﬃciency..... 101

6.8 All Geometric Cuts for each reconstruction map...... 102

xxv 6.9 The distribution of gradient value G from 10% Testbed burned sam-

ple with the Event Quality Cuts applied. Our gradient cut value 3.0

is approximately 2.3 σ away from the mean value 1.5. Distribution

of gradient value from the selected background events are shown in

Fig. 6.10...... 106

6.10 The distribution of gradient value G from the Testbed 10% burned

sample with analysis cuts to select events that should be rejected by

gradient cut. The Saturation cut, Delay Diﬀerence cut, and Geometric

Cuts are applied. The gradient cut value of 3.0 is approximately 1 σ

from the mean value...... 107

6.11 Distribution of the Delay Diﬀerence value ∆Tdelay from calibration

pulser events. As expected, most events are clustered at 0 ns delay ∼ which means there is a strong correlation between the time diﬀerence

between waveforms and the best reconstructed direction. The small

number of events distributed at low Vpeak/RMS are caused by thermal

noise events that have leaked into the calibration pulser trigger timing

window. Our Delay Diﬀerence Cut value of 20 ns is shown as a black

vertical dotted line on the plot...... 109

xxvi 6.12 Distribution of the Delay Diﬀerence value ∆Tdelay from the 10% Testbed

burned sample with the Quality Cuts and Geometric Cuts applied.

The distribution shows that most of events have a Vpeak/RMS value

less than 7 and widely spread over Delay Diﬀerence values. Therefore

the dominant portion of events are thermal noise events and Continu-

ous Waveform (CW) events. Our Delay Diﬀerence Cut value of 20 ns

is shown as a black vertical dot line on the plot...... 110

6.13 Distribution of the Delay Diﬀerence value ∆Tdelay from triggered neu-

trino events from AraSim. The simulation is run with a ﬁxed neutrino

energy at 1019 eV. The delay Diﬀerence Cut value of 20 ns is shown as

a black vertical dotted line on the plot, rejecting only a small portion

of triggered neutrino events. The clustered events at high Vpeak/RMS

and low ∆Tdelay are due to the Saturation Cut which restricts the

maximum V /RMS to 30...... 111 peak ∼

6.14 And example of CW Cut baseline and a spectrum of strong CW back-

ground event. The baseline is an average spectrum for a run data

(approximately 30 minutes period of data). The example event has a

strong CW background at 400 MHz, which is a weather balloon com- ∼ munication signal. The spectrum peak at 400 MHz is strong enough

to exceeds the 6.5 dB above the baseline (dashed curve)...... 112

xxvii 6.15 The distribution of 2nd highest Vpeak/RMS and correlation values for

the vertical polarization channel for the left plot from the 10% exam-

ination data set and the right plot from events simulated at 1018 eV.

Both plots show only events that have survived all other cuts. The red

line shows the selected cut parameter and thus all events above this

line survive the cuts and those below are removed. For the data (left

plot), no events fall above the cut line. For the simulated events (right

plot), there is a sizable percentage of events that lie above the cut line

and thus survive. These simulated events extend to a range of higher

correlation and Vpeak/RMS values...... 114

6.16 These plots are zoomed in versions of the plots above (Fig. 6.15). In

the data (top plot), the events are dominated by thermal noise and

thus concentrate around speciﬁc low correlation and Vpeak/RMS values

of 0.135 and 3.7, respectively. The simulated events (bottom plot) are

dominated by the simulated signal and thus do not tend to cluster

around a particular value for the correlation and signal strength.... 115

6.17 The diﬀerential distribution of events that pass the Peak/Correlation

Cut using the optimal slope shown in 6.15. The horizontal axis is a

measure of the vertical oﬀset of the red line in Fig. 6.15, and is the 2nd

highest Vpeak/RMS where the red line intersects the Max Corr Value=0

axis. This distribution is ﬁtted against an exponential function which

is used to extrapolate to the number of events expected to pass the cut.116

xxviii 6.18 Plot showing the Peak/Correlation Cut for each trial slopes. Among all

20 slopes, we choose a slope of -14 which give us a reasonable p-value

from the corresponding toy simulation set (see Fig. 6.19)...... 118

6.19 Distribution of minimum log likelihood from the toy simulation set with

Peak/Correlation Cut slope of -14. The red vertical line is the value

from the Testbed data set. The p-value is the ratio between the total

number in the toy simulation set to the number in the toy simulation

set that has a smaller 2 log(L) value than the one from the Testbed − data. A p-value of 0.235 is close to 1σ for a normal distribution... 119

6.20 Finding the optimal Peak/Correlation Cut value by maximizing N/Sup.

The red vertical line is the optimal Peak/Correlation Cut value (inter-

cept in 2nd highest Vpeak/RMS in Fig. 6.15 and 6.16) which is 8.8.

Peak/Correlation Cut values smaller than the optimal value are too

weak so allow too many background events. Peak/Correlation Cut

values bigger than the optimized value are, on the other hand, too

stringent and reject too many neutrino events...... 120

xxix 6.21 The eﬃciency of each cut in sequence compared with the total number

of triggered events for a simulated data set generated from an optimistic

Kotera et al. 2010 ﬂux model. After the cuts designed to reject thermal

background are applied (beginning with the Delay Diﬀerence Cut), the

nd eﬃciency turns on and plateaus for 2 highest Vpeak/RMS > 6.... 121

6.22 The reconstruction directions of the events that passed both Stage 1

and Stage 2 of the analysis in the 30 m (upper) and 3 km (lower)

maps. Events that passed the unaltered cuts in Stage 1 are shown in

blue and those that passed the Stage 2 cuts are shown in red. The

initial Geometric Cut regions (dashed blue line) were adjusted after

Stage 1 (solid red lines) based on a Gaussian ﬁt to the background

event distribution with a limited set of cuts applied...... 124

6.23 The limits placed compared with the projected ARA37 trigger-level

sensitivity and results from other experiments...... 128

6.24 Channel 0 waveform from a calibration pulser event. The left plot is

from the Testbed data, the middle plot is from AraSim with default

phase model, and the right plot is from AraSim with simplistic 90◦ ± phase model. Even though the amplitude of the waveforms in two

AraSim plots are not calibrated to the Testbed, we can see that the

pulse in the simplistic phase model is too narrow while the pulse in the

default phase model is too broad compared to the Testbed waveform. 131

xxx 6.25 These ﬁgures show the distribution of zenith angles of incident mo-

menta for simulated neutrinos at 1018 eV that pass the trigger in

AraSim for (left plot) Testbed at 30 m and (right plot) a design sta-

tion at a depth of 200 m. Events on the left side of each plot come

from up-going neutrinos with respect to the South Pole, while events

on the right come from down-going neutrinos. The viewable arrival

direction zenith angles are generally limited to less than 120◦ for the

Testbed and less than 150◦ for a design station. This limited range of

observable arrival directions is due to the combination of the limited

viewing region seen in Fig. 5.3 and the requirement that the coherent

signal is emitted near the Cherenkov angle, which is relative to the

arrival direction. When one adds in the screening eﬀect of the Earth

(red lines), almost all events with zenith angles less than 90◦ disappear

as well and thus the observable range of zenith angles is limited by the

geometry of the Testbed by a factor of about 2...... 135

7.1 Muon neutrino ﬂuence of GRB080603A from analytic calculation based

on WB model (IC-FC, back curve) and NeuCosmA model (NFC, red

curve). Detailed calculations in NeuCosmA yield changes in the magni-

tude and the shape of the neutrino ﬂuence. Figure digitized from [14].

...... 142

xxxi 7.2 Distribution of the reconstruction location from the neutrino source

direction from a simulated sample of 1018 eV neutrinos. The neutrino

source direction is at θ = 0◦ and φ = 0◦. The plot is obtained from

events with neutrino source directions pointing zenith angles from 37◦

to 102◦. Two circular empty bins (white bins) in the plot are caused

by the shadowing eﬀect from the ray tracing in ice (Fig. 6.5)..... 144

7.3 Eﬀective volume as a function of neutrino travel direction plot. θ is

the zenith angle of the neutrino travel direction. Field of view range

is deﬁned as the Full Width Half Maximum (FWHM) of the eﬀective

volume which is 0.4 < cos(θ) < 0.05...... 145 −

7.4 The distribution map of 57 selected GRBs in Testbed local coordinates.

The blue band in the map is the ﬁeld-of-view cut range deﬁned in

Fig. 7.3. Note that cos(θ) in this map is the direction of the GRB

while cos(θ) in Fig. 7.3 is the direction of the neutrino...... 146

7.5 The ﬂuences of 57 selected GRBs (black curves) and the ﬂuence from

the summation of all 57 GRBs (red curve). One GRB is brighter than

other GRBs by an order of magnitude above 1016 eV. This dominant

GRB is chosen as representative of the sum of the 57 GRBs...... 147

xxxii 7.6 The limit on the UHE GRB neutrino ﬂuence from 57 GRBs. Total

ﬂuence from 57 GRBs is shown with a red solid curve and the limit

from the ARA Testbed above 1016 eV is shown with a red dashed curve. 150

7.7 The inferred quasi-diﬀuse ﬂux limit from the selected 57 GRBs. The

quasi-diffuse flux limit is obtained from the fluence limit (Fig. 7.6 with

the assumptions that 57 analyzed GRBs can represent the average

GRB over the year and average number of GRBs in a year is 667. This

is the first quasi-diffuse GRB neutrino flux limit for energies above

1016 eV...... 151

xxxiii Chapter 1

Introduction

Neutrinos are exceptional messenger particles due to their unique properties such as their neutral charge and low cross sections. The first property, the neutral charge, makes it possible for neutrinos, once produced at the source, to travel directly towards the Earth without any influence from magnetic fields. Once we reconstruct the direction of the neutrino, we can learn about the distribution of the source which corresponds to the direction of the neutrino. Neutrinos are one of the few particles that can provide direct information about astrophysical phenomena. The second property, the low cross section, comes from the fact that neutrinos can only interact through the weak force. In other words, they don’t interact with other particles with high probability and therefore neutrinos can travel cosmological distances without being

32 2 attenuated. The cross section of neutrinos in matter is approximately 10− cm at 109 GeV [15]. It is also possible for neutrinos to be produced inside of the source and penetrate out of the source (at 109 GeV, the neutrino mean free path in water is 106 m, [5]) and thus provide us the information about the interior of the source. ∼ This direct measurement of the inner activities of a source is only possible through neutrinos. These unique properties of neutrinos have made them a fascinating topic of research in particle astrophysics. Searching for the source of ultra-high energy (UHE,

1 14 24. Cosmic rays relation between Ne and E0 changes. Moreover, because of fluctuations, Ne as a function of E0 is not correctly obtained by inverting Eq. (24.12). At the maximum of shower development, there are approximately 2/3 particles per GeV of primary energy. There are three common types of air shower detectors: shower arrays that study the shower size Ne and the lateral distribution on the ground, Cherenkov detectors that detect the Cherenkov radiation emitted by the charged particles of the shower, and fluorescence detectors that study the nitrogen fluorescenceexcitedbythecharged particles in the shower. The fluorescence light is emitted isotropically so the showers can be observed from the side. Detailed simulations and cross-calibrations between different types of detectors are necessary to establish the primary energy spectrum from air-shower experiments. Figure 24.8 shows the “all-particle” spectrum. The differential energy spectrum has been multiplied by E2.6 in order to display the features of the steep spectrum that are otherwise difficult to discern. The steepening that occurs between 1015 and 1016 eV is known as the knee of the spectrum. The feature around 1018.5 eV is called the ankle of the spectrum.

Knee 104

] Grigorov -1 JACEE sr

-1 MGU 3 s 10 Tien-Shan -2 Tibet07 Ankle

m Akeno 1.6 CASA-MIA 102 HEGRA Fly’s Eye [GeV Kascade Kascade Grande 2011 F(E) AGASA 2.6 10 HiRes 1 E HiRes 2 Telescope Array 2011 Auger 2011 1 1013 1014 1015 1016 1017 1018 1019 1020 E [eV]

FigureFigure 24.8: 1.1:The Cosmic all-particle ray ﬂux in spectrum broad energy as range. a function AGASA of [4]E didn’t(energy-per-nucleus) measured the from aircutoﬀ shower at GZK measurements threshold energy. [79–90,100–104]. Image from [5]. Color version at end of book.

Measurements of flux with small air shower experiments in the knee region differ by 18 as much> as10 a factoreV) cosmic of two, rays indicative(CRs) is one of of thesystematic most interesting uncertai researchnties topics in interpretation which can of the data. (Forbe achieveda review by see neutrino Ref. 78.) experiment. In establishing Cosmic rays the in spectru the UHEmshowninFig.24.8,e region have been ob- fforts served by multiple experiments, shown in Fig. 1.1,[16], [17], [18]. However, the source February 16, 2012 14:07 of these exceptionally high energy particles is unknown. UHE neutrinos are expected to be produced along with ultra high energy cosmic rays (UHECRs) at the source and therefore we expect to learn about the geometrical location and the internal physics of the sources by detecting UHE neutrinos. Another reason which motivates us to study this UHE region is that, the center of mass of a neutrino interaction in our detectors is higher than that of the most energetic human-made particle collisions

2 16 24. Cosmic rays

103

Δ E/E=20% ] -1 sr

-1 2 s 10 -2 m 1.6 HiRes 1

[GeV HiRes 2 10

F(E) Telescope Array 2011 2.6

E Auger 2011

1 1018 1019 1020 E [eV]

FigureFigure 24.9: 1.2:Expanded Cosmic ray flux view in the of UHE the region. highest Auger energy and HiRes portion data of which the detected cosmic-ray spectrumthe cosmic from ray data flux of cutoff HiRes above 1&2 10 [101],19.5 eV are the shown. Telescope Image Array from [5]. [103], and the Auger Observatory [104]. The HiRes stereo spectrum [112] is consistent with the HiRes 1&2 monocular results. The differential cosmic ray flux is multiplied by E2.6.The red arrow indicates the change in the plotted data for a systematic shift in the energy scale of 20%. background [97,98]. Photo-dissociation of heavy nuclei in the mixed composition model [99] would have a similar effect. UHECR experiments have detected events of energy above 1020 eV [89,100–102]. The AGASA experiment [100] did not observe the expected GZK feature. The HiRes fluorescence experiment [101,112] has detected evidence of the GZK supression, and the3 Auger observatory [102–104] has presented spectra showing this supression based on surface detector measurements calibrated against its fluorescence detector using events detected in hybrid mode, i.e. with both the surface and the fluorescence detectors. Recent observations by the Telescope Array [103] also exhibit this supression. Figure 24.9 gives an expanded view of the high energy end of thespectrum,showing only the more recent data. This figure shows the differential flux multiplied by E2.6. The experiments are consistent in normalization if one takesquotedsystematicerrorsin the energy scales into account. The continued power law type of flux beyond the GZK cutoff previously claimed by the AGASA experiment [100] is notsupportedbytheHiRes, Telescope Array, and Auger data. One half of the energy that UHECR protons lose in photoproduction interactions that

February 16, 2012 14:07 (Large Hadron Collider, 10 TeV) and therefore this study can extend the scope of ∼ particle physics to higher energies [19,20].

1.1 Ultra-High Energy Neutrino Source Candidates

There are many UHE neutrino source candidates such as GZK interactions [21, 22], Gamma-Ray Bursts (GRBs) and Active Galactic nuclei (AGNs). In the 1960’s, Greisen, Zatsepin and Kuzmin predicted UHECRs, with energies above a threshold of 5 1019 eV, would undergo π photo-production through their interactions with cosmic × microwave background photons (CMB) and this is known as GZK effect [21–23]. Fly’s Eye [16], HiRes [17] and Auger [18], have confirmed the phenomenon of a break in the cosmic ray flux above the GZK threshold energy consistent with the GZK process (Fig. 1.1). Fig. 1.2 shows the measured UHECR flux from the Auger, and HiRes experiments. However, it is still possible that cosmic ray sources themselves have injected UHECRs with a cutoff at the GZK threshold energy [24]. Detection of UHE neutrinos can confirm that the GZK effect is the cause of the cutoff in the UHECR flux above 1019 eV. Further details about the GZK effect will be discussed in the next section. GRBs are one of the point source candidates that are expected to produce neutrinos up to 1019 eV. GRBs were first discovered in late 1960s by the Vela satellite network. When a GRB explodes, it is the brightest γ-ray source in the sky. Though the mechanism of GRBs is not well known, measured properties of GRBs such as energetic (> 1050 ergs) in a short period of time (typically < 1 min) are extreme enough to consider GRBs as a candidate of UHE neutrinos. Currently, the most generally accepted model for GRBs is the fireball shock model [25, 26]. In the fireball model, protons are expected to be accelerated by shock accelerations in internal shocks. This

4 prompt emission process can produce neutrinos by pγ interactions. There is also afterglow emission which caused by the interaction between the expanded shock and external matter such as interstellar medium. The afterglow emission is expected to produce neutrinos from pγ interactions. More explanations about GRBs are presented in Section 2.2. AGNs are another strong candidate of UHE neutrino source. AGNs consist of an accretion disk and relativistic jets in the standard model. When there is a super massive black hole (106 to 1010 times the mass of the Sun) at the centre of the galaxy, surrounding materials dissipate toward the black hole and forms a disk like shape which is called accretion disk. Some accretion disks produces jets which are narrowly collimating toward the opposite directions from close to the disk. Similar to the jets in GRBs, shocks in the jet are expected to produce UHECRs, UHE neutrinos and high energy γ-rays via the shock accelerations. The searches on two types of neutrino source, diﬀuse neutrinos (GZK neutrinos) and point source neutrinos (GRB neutrinos), will be presented separately in diﬀerent chapters in this paper.

1.2 Detecting Techniques and Experiments

There are two major detection techniques for UHE neutrinos, optical and radio electromagnetic Cherenkov radiation techniques. Cherenkov radiation is produced when charged particles move faster than the speed of light in the medium. In order to detect Cherenkov radiation, the medium should be a dielectric which is transparent to electromagnetic waves. The optical Cherenkov technique uses optical light that is radiated from individual charged particles in the cascade. On the other hand, the Radio Cherenkov technique (also called the Askaryan eﬀect) uses the coherent radio signal from the charge asymmetry of entire cascade. Therefore we can say that the

5 visible Cherenkov signal is a microscopic aspect of the cascade, while radio Cherenkov signal is a macroscopic aspect of the cascade. Super Kamiokande [27], Astronomy with a Neutrino Telescope and Abyss environmental RESearch (ANTARES) [28], and IceCube [29] are the experiments which use optical Cherenkov technique. On the other hand, Antarctic Impulse Transient Antenna (ANITA) [8], Antarctic Ross Iceshelf Antenna Neutrino Array (ARIANNA) [30], and Askaryan Radio Array (ARA) [31] use radio Cherenkov technique. More detailed descriptions about the detection techniques are shown in Section 3.1. UHE neutrino experiments are mostly located at extreme places such as Antarc- tica in order to overcome some diﬃculties of detecting the particles. Along with

32 2 9 their low interaction cross section in matter ( 10− cm at 10 GeV, [15]), their ∼ 2 1 low flux on Earth (< 10 km− yr− ) make it difficult to for us to detect them in ∼ ordinary laboratory environments. We need a place which can provide us a detection material with a volume of the order of 100 km3 and relatively background free environment. The large volume of nearly pure ice in Antarctica is an ideal detector for UHE neutrinos because of the long attenuation length of the medium. Attenuation length for radio waves in Antarctic ice is approximately 500 m [32] while the optical light is approximately 50 m [33]. It is difficult to build a human-made detector with such a large volume. It is also possible to trace anthropogenic background sources in Antarctica as they come from relatively few isolated locations. In present models for UHE neutrinos, even with 100 km3 volume of instrumented ice, we can detect approximately 10 events in a year [31]. So, new experiments aim for detector to reach the exposure on the order of 100 km3 yr in order to detect UHE neutrinos robustly. · The ARA is a next-generation radio Cherenkov neutrino detector deployed in the ice at the South Pole. The ARA aims to deploy 37 stations of antennas at 200 m depth spanning 100 km2 of ice. To date, one prototype Testbed station and three full

6 stations have been deployed. In 2010-2011 drilling season, the Testbed station was deployed at a depth of 30 m. Full stations A1 at 100 m depth, and A2 and A3 ∼ at 200 m depth are deployed in 2011-2012 and 2012-2013 season, respectively. More information about the ARA is shown in Chapter4. This dissertation presents the first neutrino flux constraint from the ARA Testbed. The techniques that are used to optimize the sensitivity of ARA Testbed will be used as a basis for analyses of the future ARA deep stations or other radio array experiments in Antarctica. This paper is organized as follows. In Chapter2, we discuss different sources of UHE neutrinos. In Chapter3, past and present experiments designed to detect UHE neutrinos will be discussed. Then in Chapter4, we introduce the Askaryan Radio Array (ARA) and its prototype Testbed station, the instrument which we used to carry out our UHE neutrino searches. In Chapter5, we describe the simulation tools we developed for the neutrino searches. In Chapter6 and7, a diffuse and GRB neutrino searches are presented, respectively. In Chapter8, we discuss our conclusions.

7 Chapter 2

Motivations for Ultra High Energy Neutrinos

UHE neutrinos can originate from the GZK interactions or astrophysical sources such as Gamma-Ray Bursts (GRBs) and Active Galactic Nuclei (AGNs). In this chapter, we discuss the different candidates for sources of UHE neutrinos. The GZK effect, which is expected to be a dominant source of UHE neutrinos, is discussed first with a detailed explanation about the interaction between proton and CMB photon. The GRB as a UHE neutrino source is then discussed. Lastly, other candidate models for UHE neutrinos are shown.

2.1 GZK eﬀect

We discuss the GZK process and associated decay chains. When a UHE proton is injected above the threshold energy of 5 1019 eV for the GZK eﬀect, the following × processes are possible.

p + γ π+ +n (2.1) CMB →

n p + e− +ν ¯ → e π+ µ+ + ν → µ µ+ e+ + ν +ν ¯ → e µ 8 p + γ π0 +p (2.2) CMB → π0 γ + γ →

+ + In the ﬁrst process (Eq. 2.1), we can assume that daughters of the π (e , νµ,ν ¯µ,

+ and νe) get approximately 1/4 of π energy. The threshold energy for π photo-production can be calculated from the Mandel- stam variable s:

2 2 s = (Pp + PCMB)lab = (Pπ+ + Pn)CM (2.3)

= m2 + 2 E E (1 cosθ) = (m + m )2 (1.1GeV)2 (2.4) p · p CMB − π n ∼ m2 + 2 m m E GZK π · π p 5 1019 eV (2.5) ∴ p,thres ∼ 4 E ∼ × · CMB

4 where P is a four momentum of particle x, and E 3 k T 3 10− eV/K 3 K x CMB ∼ · B· ∼ × · ∼ 3 10− eV. It is assumed that initial proton is relativistic and hence E P is used. p ∼ p The threshold energy is calculated when the initial proton and the CMB photon in the lab frame are colliding with opposite momenta (θ = π) and the ﬁnal state particles − (π+ and n) are at rest in the center of momentum frame (CM). As both processes (Eq. 2.1 and Eq. 2.2) have approximately the same invariant mass, their threshold energies are same. Also the total energy of the ﬁnal state particles in the center of momentum frame is √s 1.1 GeV (Eq. 2.4) which is approximately the rest mass of ∼ the ∆+ particle. Therefore the ∆+ resonance is a dominant channel and boosts the cross section of the interaction near the threshold energies (see the Fig. 2.1). For the second π photo-production process (Eq. 2.2), when a π0 is created, it will decay to two photons. These photons will each carry approximately half of the π0 energy. However, these UHE photons are attenuated due to two dominant energy loss processes while they travel to Earth. These energy loss processes are pair production

9 41. Plots of cross sections and related quantities 17

! Λp total Λp elastic 10 2 "

⇓

Σ−p total Cross section (mb)

Plab GeV/c -1 2 3 10 1 10 10 10 Σ –p 5 6 7 8 9 10 20 30 40 √s GeV Λp 2.1 3 4 5 6 7 8 10 20

γd total γp total

-1 10 ⇑

-2 10

γγ total

Cross section (mb) -3 10 ⇓

-4 √sGeV 10 2 1 10 10 γp 0.3 1 10 100 1000 10000 P GeV/c lab 0.1 1 10 100 1000 10000 γd

FigureFigure 41.16: 2.1:Total Total and elastic hadronic cross sections cross for Λp,totalcrosssectionfor sections for γdΣ−p,,andtotalhadroniccrosssectionsforγp, and γγ interaction.γd, γ Thep,andγγ cross collisions as a function of laboratory beam momentum and the total center-of-mass energy. Corresponding computer-readable data ﬁles may be sectionfound at http://pdg.lbl.gov/current/xsect/ for the GZK interaction.(CourtesyoftheCOMPASgroup,IHEP,Protvino,August2005) is the γp cross section in the plot, which has the peak at √s 1.1 GeV due to the ∆+ resonance. Image from [5]. ∼

+ with the CMB and pair production with optical light background (γ +γ e +e−) bgr → followed by inverse Compton scattering (e± + γ γ + e±). The threshold energy bgr → for pair production with the CMB is

2 2 s = (P + P ) = (P + + P ) (2.6) γ CMB lab e e− CM = 2 E E (1 cosθ) = (2 m )2 · γ CMB − · e 2 CMB me 14 ∴ Eγ,thres 3 10 eV (2.7) ∼ ECMB ∼ ×

10 and, with optical light, it is

2 2 s = (P + P ) = (P + + P ) (2.8) γ opt lab e e− CM = 2 E E (1 cosθ) = (2 m )2 · γ opt − · e 2 opt me 11 ∴ Eγ,thres 3 10 eV. (2.9) ∼ Eopt ∼ × where ﬁnal state electrons and positrons are at rest in center of momentum frame. Energy of optical light background is taken to be E = hν 1 eV. opt ∼ CMB When photons have energies above the threshold Eγ,thres in Eq. 2.7, pair production with the CMB is the dominant energy loss process as the number density of target CMB photons is approximately four orders of magnitude larger than the

2 3 2 3 optical light background (n 10 cm− , while n 10− cm− [34]). Once the CMB ∼ opt ∼ CMB energy of a photon drops below Eγ,thres, pair production with optical light becomes its dominant energy loss process. Using the results above, we can estimate that the diffuse gamma ray background flux from the GZK effect will have a pile up just be-

opt low the threshold for further pair production, Eγ,thres. With both the cascade diffuse gamma ray background flux and UHE proton flux discussed above, we can derive a strong constraint on the expected neutrino flux [3]. This is discussed further in Section 2.1.2. We can also calculate the distance over which π photo-production becomes im-

nσL portant for UHECRs. The probability to interact is P = 1 e− where n is number − density of target (here, the CMB), σ is the proton-photon cross section, and L is the total travel distance of proton. From the Fig 2.1[5], at √s 1.1 GeV (at ∼ the threshold energy of the GZK interaction), the cross section σpγ is approximately

28 2 2 3 6 10− cm , and the target number density n is approximately 4 10 cm− . × CMB ×

11 1 Probability

0.5

0 10-2 10-1 1 10 102 Distance [Mpc]

Figure 2.2: Probability for π photo-production by a CR as a function of the distance of the source at ∆+ resonance.

Therefore,

n σpγ L P (L) = (1 e− CMB ) (2.10) − 4 102 6 10 28 L (1 e− × × × − × ). ∼ −

Fig. 2.2 shows the probability as a function of distance (at resonance). Above 20 Mpc, π photo-production becomes important as the probability is bigger than 80%. So, the proton is almost guaranteed to undergo π photo-production when sources of UHE protons are beyond 20 Mpc from Earth. When the energy of the proton increases, the distance at which the π photo-production process becomes important increases since the proton-photon cross section goes oﬀ resonance [5] and the average interaction length of π photo-production process becomes 50 Mpc [35]. ∼

12 + The Bethe-Heitler (BH) pair production process (p + γ p + e + e−) is CMB → another possible interaction between UHE protons and the CMB. Above the GZK threshold energy, compared with the π photo-production process, BH pair production has a smaller cross section as it does not have a resonance. BH pair production has a smaller proton threshold energy (EBH 5 1017 eV) than π photo-production, p,thres ∼ × BH GZK and so it will be a dominant energy loss process between Ep,thres and Ep,thres.

2.1.1 Models for GZK induced neutrino

In this section, we discuss the basic prescription for estimating the ﬂux for neutrinos from GZK interactions, and models based on UHECR and gamma ray constraints. Using minimal assumptions and some basic concepts, we can calculate the ﬂux of cosmic rays, or any particles from the GZK process, by the general equations [36–38],

dN J (E) b = ∞ dE G (E,E ) I(E , t), (2.11) b ≡ dE dA dt dΩ i b i · i Z0

where

1 ∂P (E; E , r) G (E,E ) = ∞ dr b i ρ [1 + z(r)]nΘ(z z ) Θ(z z), (2.12) b i 4π ∂E 0 − min · max − Z0

2 d Np I(Ei, t) = . (2.13) dEi dt

In Eq. 2.12, Pb(E; Ei, r) is the probability of a particle b (b can be either p, νe, or

νµ) being detected on Earth with energy E when a proton was initially injected with energy Ei at a distance r away. I(Ei, t) is the injection spectrum of the source, where proton-only injection is assumed. Nb is the number of b particles detected and A, t, and Ω are area, time, and solid angle respectively. The constant ρ0 is the co-moving number density of the source of particles, z is the redshift, and n is a redshift evolution

13 factor related to the evolution of source densities in redshift. The limits of the integral

in Eq. 2.12 are zmin and zmax. Using calculated probabilities from [39], we can let zmin = 0 and zmax = 2 and calculate the distance at a given redshift with

dz = (1 + z)H(z)dr (2.14)

2 2 3 where H(z) is the Hubble parameter H (z) = H0 [ΩM (1+z) +ΩΛ]. H0 is the Hubble constant at present, 70 km/s/Mpc, and the ratio of matter and critical density of

the universe (in other words, matter density for ﬂat universe) ΩM = 0.3 and ratio of

vacuum energy and critical density of universe ΩΛ = 0.7 [5]. Eq. 2.13 describes the injection spectrum for the source. We adopt a basic power-

law injection spectrum with an upper limit on the energy, Emax,

I(E , t) = I Eα Θ(E E ). (2.15) i 0· i · max − i

The authors of [40, 41] provide the values for the probabilities Pb(E; Ei, r) for

b = p, νe, and νµ at [39]. When the probability was calculated by Fodor et al. [40,41], some methods were used to simplify the calculation. To calculate the probabilities, ﬁrst, they used the SOPHIA Monte Carlo simulation for π photo-production. They assumed that the initially injected particle from the source is a proton and sources were assumed to be isotropically distributed. They also assumed that the Bethe-

+ Heitler pair production process (p + γ p + e + e−) is the dominant energy CMB → loss process other than π photo-production, and used a continuous energy loss approximation for the energy loss process. Also, they neglected synchrotron radiation

9 caused by extragalactic magnetic ﬁelds, assuming these ﬁelds are smaller than 10− G.

With these assumptions, they calculated the probability Pb for detecting particle b on Earth using inﬁnitesimal steps in distance (0.1 kpc) from redshift z = 0 to z = 2.

14 So, using these tools, we can only calculate the ﬂux due to sources to a redshift of z = 2. Redshift of z = 2 is approximately 3 Gpc, which can cover near the size of the entire universe ( 10 Gpc). ∼

There are two unknown factors in Eq. 2.12 and 2.15. ρ0 and I0, the co-moving source density and injection spectrum factors. If we assume that the detected UHE- CRs in Auger [18] are entirely protons, we can use the expected proton flux with Eq. 2.11 and estimate the product of ρ I by fitting the flux spectrum. We used a proton 0· 0 flux with parameters n = 3 and α = 2.6, which are typical values as n 3 accounts − ∼ for typical star formation rate (SFR) up to z = 1 [42] and α = 2.6 is the estimated − injection spectrum for UHECRs below the GZK threshold energy [5]. Fig. 2.3 shows the fit result of the Auger UHECR data (stars) compared with a model with n = 3, α = 2.6, z = 0.012, E = 1016 eV, and E = 3 1021 eV. Using the fit − min min max × values from Fig. 2.3, we can calculated the GZK UHE neutrino flux with different models. In Fig. 2.4, we show the estimated GZK UHE neutrino flux from different models. All three models used the same α = 2.6, z = 0.012, E = 1016 eV, and − min min E = 3 1021 eV conditions. WB model is discussed in section 2.3. max ×

2.1.2 Models for GZK induced neutrino with UHECR and

EGRB constraints

In the previous section, Auger cosmic ray data is used to find the normalization factor to estimate the GZK induced neutrino flux. It is possible to use gamma ray data along with cosmic ray data to get more strict estimates for the neutrino flux from GZK interactions. Using Fermi-LATs’ extragalactic gamma ray background (EGRB) data and HiRes’ UHECR data, M. Ahlers et al. calculated constraints on GZK induced neutrino flux models [3]. In order to do this, they first used similar assumptions as in section 2.1.1 to model UHECRs, GZK induced neutrinos, and the

15 ] -26

-1 10 sr -1 10-27 sec -2 -28

cm 10 -1

10-29

Flux [GeV 10-30

10-31

10-32 1010 1011 Energy [GeV]

Figure 2.3: Plotting Auger UHECR data against a model for the CR ﬂux at Earth with n = 3 and α = 2.6. Auger data is shown as stars and the model is shown as red solid line. −

-5 ] 10 -1 n=6, α=-2.6 sr

-1 n=3, α=-2.6 10-6 n=0, α=-2.6 sec -2 WB constraints 10-7

10-8 F [GeV cm 2 E 10-9

10-10

10-11 109 1010 1011 1012 Energy [GeV]

Figure 2.4: Intensity of GZK induced neutrino models based on Auger UHECR data. Waxman-Bahcall constraint is shown as dash-dotted line.

16 17.5 18 18.5 19 Emin 10 eV 10 eV 10 eV 10 eV n 3.50 3.20 4.05 4.60 α -2.49 -2.52 -2.47 -2.50

Table 2.1: Best ﬁt parameters for HiRes UHECR data and Fermi-LAT EGRB data from [3]. The ﬁt results are shown with the data points in Fig. 2.5.

diffuse γ-ray background. They assumed that the UHECRs are only protons. They used a continuous energy loss model for Bethe-Heitler pair production. Unlike in section 2.1.1, they included cascade processes for the diffuse gamma ray background, such as an inverse Compton scattering, e± + γ e± + γ, and pair production, bgr → + γ + γ e + e−. They fitted the simulation result with both Fermi-LAT’s EGRB bgr → data and HiRes’ UHECR data. In Fig. 2.5, the best fit model for the Fermi-LAT

17.5 EGRB and HiRes’s UHECR data from Emin = 10 eV is shown as an example. The maximal cascade line in Fig. 2.5 is obtained through two steps. First, they made models which meet the lower uncertainty bound on the highest energy data point of Fermi-LAT. These models are shown in Table 2.1. Second, they found the maximum value of E2J for the given model. Fig. 2.6 shows the predicted neutrino fluxes and constraints on total diffuse neutrino flux from AMANDA [43, 44], Auger [18], Baikal [45], HiRes [46], ANITA [8], and IceCube [47,48]. The IceCube limit is shown for 5 σ sensitivity after 1 year of observation. It is notable that, without using Fermi-LAT data, they calculated a flux limit approximately an order of magnitude weaker (thin dotted line in Fig. 2.6) than using Fermi-LAT data for fitting the EGRB flux (solid : best fit, dashed : 99% C.L. range in Fig. 2.6). This means, with Fermi-LAT data, they can get a more stringent neutrino flux limit than without by approximately an order of magnitude.

17 6

5 5 10 10 17.5 18 Emin = 10 eV Emin = 10 eV 6 6 10 10 ] ]

1 maximal cascade 1 maximal cascade

sr 7 sr 7 10 10 1 1 s s 2 2

8 8 10 10

9 9 [GeV cm 10 HiRes I&II [GeV cm 10 HiRes I&II J J

2 Fermi LAT 2 Fermi LAT

E p (best ﬁt) E p (best ﬁt) 6 10 10 10 , ¯ (99% C.L.) 10 , ¯ (99% C.L.) (99% C.L.) (99% C.L.)

11 11 10 10 0.1 1 10 102 103 104 105 106 107 108 109 1010 1011 1012 55 5 1010 10 E [GeV] 1718..55 1918 EEminmin == 10 10 eVeV Emin = 10 eV 66 6 1010 10 ] ] ] ] 1 1 1 maximal cascade 1 maximal cascade

sr 7 sr 7 sr 107 sr 107 1 10 1 10 1 1 s s s s 2 2 2 2 88 8 1010 10

9 9 [GeV cm 9 [GeV cm 9

[GeV cm HiRes I&II [GeV cm HiRes I&II 1010 HiRes I&II 10 HiRes I&II J J J J

2 Fermi LAT 2 Fermi LAT

2 Fermi LAT 2 Fermi LAT E E E pp (best(best fit) fit) E p (best fit) 10 1010 10 10 10 ,,¯¯ (99%(99% C.L.) C.L.) 10 , ¯ (99% C.L.) (99%(99% C.L.) C.L.) (99% C.L.) 11 11 101011 1011 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 0.1 1 10 10 10 10 10 10 10 10 10 10 10 10 0.1 1 10 102 103 104 105 106 107 108 109 1010 1011 1012 10 5 10 5 E [GeV] E [GeV] 18.5 19 E [GeV] Emin = 10 eV Emin = 10 eV 6 6 FIG.10 4: Comparison of proton, neutrino and gamma ray fluxes10 for dierent crossover energies. We show the best fit values FigureFigure] 2.5: 4: Comparison GZK induced neutrino of proton, flux (green neutrino solid lineand : best-ray fit fluxes model shown for] di in↵erent crossover energies. We show the best-fit values (solid 1 (solid lines) as well as neutrinomaximal and cascade gamma ray fluxes within1 the 99% C.L. with minimalmaximal and cascade maximal energy density (dashed 17.5 lines)Table 2.1 as, green well dashed as neutrino line : 99% and C.L. of-ray best fluxes fit) from withinEmin = 10the 99%eV model C.L. shown with minimal and maximal energy density (dashed lines). The sr 7 sr 7 lines).10 The gamma ray fluxes at the 99% C.L. are marginally10 consistent with the highest energy bins of the Fermi LAT data. valueswith1 UHECR of the data corresponding from HiRes and model EGRB data parameters from Fermi-LAT. can be Image found from1 in [3 Table.]. 1. The dotted line labeled “maximal cascade” indicates

2 max s Note, that due to the uncertainties of the infrared backgrounds the exact contribution around 100 GeV is uncertain. the approximate limit E Jcas . c !cas /4⇡ log(TeV/GeV), corresponding to a -ray ﬂux in the GeV-TeV range saturating the 2 2

energy 8 density (10). The -ray ﬂuxes are marginally consistent at8 the 99% C.L. with the highest energy measurements by 10 10 Fermi-LAT. The contribution around 100 GeV is somewhat uncertain due to uncertainties in the cosmic infrared background. The marginalization in Eq. ((9)) also determines best and best for the model which are the values of the energy shift 9 9 [GeV cm N [GeV cm and10 normalizationHiRes I&II that render the best description of the10 experimentalHiRes I&II data, i.e. the maximum probability. J J

2 Fermi LAT 2 Fermi LAT

inE Fig.2 for illustration only (hence our results are directlyE comparable to those in Ref.[22]). As described The modelp is(best compatible fit) with the experimental results at givenp goodness(best fit) of the fit (GOF) if 10 10 in Refs.10 [6, 17],, ¯ besides(99% C.L.) the energy scale uncertainty10 there is also, ¯ an(99% (energy-dependent) C.L.) energy resolution (99% C.L.) 18 (99% C.L.) uncertainty which implies thatP~k( bin-to-binn, , best, migrationsbest)⇥ P~k(n, influence, best, thebest reconstruction) Pexp(n, ) of0. the99 flux and spectral (11) 11 N 11 N  shape.10 Since the form of the~k corresponding error matrix10 is not public, this data [6, 17] cannot be analysed 2 3X4 5 6 7 8 9 10⇥ 11 12 2 3 4 ⇤5 6 7 8 9 10 11 12 outside the0.1 Auger 1 10 Collaboration. 10 10 10 10 10 10 10 10 10 10 10 0.1 1 10 10 10 10 10 10 10 10 10 10 10 10 Technically, this is computedE [GeV] by generating a large number Nrep of replica experimentsE [GeV] according to the probability distribution P (n, , , ) and counting the fraction of those which verify P (n, , , ) P (n, ) 0.99 ~k Nbest best ~k N best exp  FIG. 4: Comparison of proton, neutrino and gamma ray fluxes for dierent crossover energies. We show the best fit values Figure4. DiscussionWit 4: Comparison h this method of proton, we determine neutrino the and value-ray of fluxes (n, for) parameters di↵erent crossover that are energies. compatible We show with the the best-fit HiRes values I and (solid HiRes II lines)(solidexperiments as welllines) as as neutrino [5]. well We as andneutrino plot in-ray Fig. and fluxes 1 gamma the within regions ray the fluxes 99% with within C.L. GOF with the 64%, minimal 99% 95% C.L. and and with maximal 99% minimal for energy four and values maximal density of (dashed theenergy minimum lines). density The (dashedenergy. lines). The gamma ray fluxes at the 99% C.L. are marginally consistent with the highest energy bins of the Fermi LAT data. valuesWe of also the show corresponding the corresponding model parameters values can of bewcas found. These in Table. results 1. The are dotted obtained line assuming labeled “maximal an energy cascade” scale indicates uncertainty Note, that due to the2 uncertaintiesmax of the infrared background the exact contribution around 100 GeV is uncertain. the approximateThe cosmogenic limit E neutrinoJcas . c ! fluxescas /4⇡ thatlog(TeV we/GeV), have shown corresponding in Fig. to 4 a are-ray compared flux in the to GeV-TeV present range upper saturating limits the on Es = 25% with a top hat prior for the correspondig energy shifts which are assumed to be uncorrelated for HiRes I energytheand di↵ density HiResuse neutrino II. (10). In TheFig. flux 3-ray we in fluxesexplore Fig. 5. are the As marginally dependence before, consistent the on solid the at greenresults the 99% line on C.L. these shows with assumptions the the neutrino highest by energy using flux measurements (summed a di↵erent over form by for Fermi-LAT. The contribution around 100 GeV is somewhat uncertain due to uncertainties in the cosmic infrared background. flavours)the prior, corresponding assuming the to energy the best shifts fit to of be the correlated proton spectra between and the the two dashed experiments, green line or reducing indicate the the uncertainty range of to The marginalization in Eq. ((9)) also determines best and best for the model which are the values of the energy shift = 15%. As seen in the figure, the main e↵ect,N is associated with the reduction of the energy scale uncertainty neutrinoandEs normalization fluxes within that the render 99% the C.L. best For description all crossover of the energies experimental considered, data, i.e. thethe range maximum of models probability. at the 99% inC.L.which, Fig.2 is consistent for as illustrationexpected, with results existing only into(hence neutrino a worsening our results limits. of are Forthe directly GOF illustration, for comparable models the thinwith to dotted larger thosen line. in This Ref.[22]). shows is directly the As larger described related range to the normalizationThe model is constraint compatible from with Eq. the (10). experimental If one naively results ignores at given the energy goodness scale of uncertainty, the fit (GOF) the if constraint in Eq. (10) inof Refs. neutrino [6, 17], fluxes besides at the the 99% energy C.L. scale corresponding uncertainty to therea fit without is also anthe (energy-dependent) Fermi LAT constraint energy (cf. resolutionthe black uncertainty which implies thatP ( bin-to-binn, , , migrations)⇥ P (n, influence, , the reconstruction) P (n, ) of0. the99 flux and spectral (11) ~k Nbest best ~k Nbest best exp  shape. Since the form of the~ corresponding error matrix is not public, this data [6, 17] cannot be analysed Xk ⇥ 9 ⇤ outside the Auger Collaboration. Technically, this is computed by generating a large number Nrep of replica experiments according to the probability distribution P (n, , , ) and counting the fraction of those which verify P (n, , , ) P (n, ) 0.99 ~k Nbest best ~k N best exp  4. DiscussionWit h this method we determine the value of (n, ) parameters that are compatible with the HiRes I and HiRes II experiments [5]. We plot in Fig. 1 the regions with GOF 64%, 95% and 99% for four values of the minimum energy. We also show the corresponding values of wcas. These results are obtained assuming an energy scale uncertainty The cosmogenic neutrino fluxes that we have shown in Fig. 4 are compared to present upper limits on Es = 25% with a top hat prior for the correspondig energy shifts which are assumed to be uncorrelated for HiRes I theand di↵ HiResuse neutrino II. In Fig. flux 3 we in explore Fig. 5. the As dependence before, the on solid the greenresults line on these shows assumptions the neutrino by using flux (summed a di↵erent over form for flavours)the prior, corresponding assuming the to energy the best shifts fit to of be the correlated proton spectra between and the the two dashed experiments, green line or reducing indicate the the uncertainty range of to neutrinoEs = 15%. fluxes As within seen in the the 99% figure, C.L. the For main all crossover e↵ect, is associated energies considered, with the reduction the range of the of models energy scale at the uncertainty 99% C.L.which, is consistent as expected, with results existing into neutrino a worsening limits. of Forthe GOF illustration, for models the thinwith dotted larger n line. This shows is directly the larger related range to the ofnormalization neutrino fluxes constraint at the 99% from C.L. Eq. (10). corresponding If one naively to ignoresa fit without the energythe Fermi scale uncertainty, LAT constraint the constraint (cf. the in black Eq. (10)

9 7

4 17.5 4 18 10 Emin = 10 eV 10 Emin = 10 eV

HiRes (3 x) HiRes (3 x) ] 5 ] 5 1 10 1 10 sr sr 1 1 RICE (e,µ,⌧ ) RICE (e,µ,⌧ ) s 6 s 6 10 10 2 2 BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) BAIKAL (e,µ,⌧ ) Auger (3 ⌧ )

AMANDA (e,µ,⌧ ) AMANDA (e,µ,⌧ ) 7 AMANDA (3 µ) ANITA (e,µ,⌧ ) 7 AMANDA (3 µ) ANITA (e,µ,⌧ ) 10 10 [GeV cm [GeV cm J J 2 8 IceCube (5, 1yr) 2 8 IceCube (5, 1yr) 10 10 E E 7

9 9 10 10

104 105 106 107 108 109 1010 1011 1012 1013 1014

4 18.5 4 19 E [GeV] 10 4 E = 10 17.5 eV 104 E = 1018 eV 10 Eminmin = 10 eV 10 Emin = 10 eV

HiRes (3 x) HiRes (3 x) ] 5 HiRes (3x) ] 5 HiRes (3 x) ] ] 1 10 5 1 10 5 1 10 1 10 sr sr sr sr 1 1 1 1

RICE (e,µ,⌧ ) RICE (e,µ,⌧ ) s 6 RICE (e,µ,⌧ ) s 6 RICE (e,µ,⌧ ) s 10 6 s 106

2 10 2 10 2 BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) 2 BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) AMANDA (e,µ,⌧ ) AMANDA (e,µ,⌧ ) AMANDA (3 µ) AMANDA (e,µ,⌧ ) ANITA (e,µ,⌧ ) AMANDA (3 µ) AMANDA (e,µ,⌧ ) ANITA (e,µ,⌧ ) 10 77 AMANDA (3 µ) ANITA (e,µ,⌧ ) 10 7 AMANDA (3µ) ANITA (e,µ,⌧ ) 10 10 [GeV cm [GeV cm [GeV cm [GeV cm J J J J 2 8 IceCube (5, 1yr) 2 8 IceCube (5, 1yr) 2 10 8 IceCube (5, 1yr) 2 108 IceCube (5, 1yr) E 10 E 10 E E

99 9 1010 10

4 5 6 7 8 9 10 11 12 13 14 4 5 6 7 8 9 10 11 12 13 14 10 10 10 10 10 10 10 10 10 10 10 104 105 106 107 108 109 1010 101011 101012 101013 101014 E [GeV] E [GeV] 4 18.5 4 19 E [GeV] 10 Emin = 10 eV 10 Emin = 10 eV

FIG. 5: The best fit (solid) and range of cosmogenicHiRes (3 x) neutrino fluxes at the 99% C.L. with (dashed)HiRes and (3 withoutx) (dotted) Figure] 5:5 The predicted best fit (solid) and 99% C.L. range of] cosmogenic5 neutrino fluxes with (dashed) and without (dotted)

1 17.5 1 Figure10 2.6: Expected GZK induced neutrino flux from Emin = 10 eV (green10 solid the the Fermi-LAT Fermi-LAT constraint. data. For The comparison values of we the show corresponding upper limits model on the parameters total diuse can neutrino be found flux in Table. from AMANDA 1. For comparison [34, 35], Lake linesr : best fit, green dashed line : 99% C.L., green dotted line : without Fermi-LATsr Baikal [36], HiRes [37] (minimum of µ and ⌧ channel), RICE [38] and ANITA [39]. The black solid line (with extrapolation [40]) weEGRB1 show data) upper compared limits with on the the constraints total from di↵use experiments. neutrino Without flux fromFermi-LAT1 AMANDA [35, 36], Auger [34], Lake Baikal [37], HiRes [38] RICE (e,µ,⌧ ) RICE (e,µ,⌧ ) showss 6 the sensitivity of IceCube [41] after one year of observation.s 6 We assume an equal distribution between neutrino flavors (minimumEGRB10 data, ofexpected⌫µ and neutrino⌫⌧ channel), flux is much RICE larger than [39] with and EGRB ANITA data (thin [40]. dotted10 The black solid line shows the 5 sensitivity of IceCube after 2 2 2 BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) BAIKAL (e,µ,⌧ ) Auger (3 ⌧ ) N⌫ : N⌫ : N⌫ 1 : 1 : 1 and scale the limits8 if necessary. Integrated limits assuming an E spectrum are shown as solid justgreen 1e line). year Imageµ of observation from⌧ [3]. [42]. The cuto↵ at 10 GeV is artificial so we also show an extrapolation to higher energies as AMANDA (e,µ,⌧ ) AMANDA (e,µ,⌧ ) lines; diAMANDAerential (3 limits ) as dotted lines. (For AugerANITA ( ande,µ,⌧ ) ANITA weAMANDA show (3 both ) limits.) ANITA (e,µ,⌧ ) ablackdashedlinefollowingRef.[41]).Alllimitsareobtainedassuminganequaldistributionbetweenneutrinoflavours:7 µ 7 µ 10 10 2 N⌫e : N⌫µ : N⌫⌧ 1:1:1(andscaledappropriatelywherenecessary).IntegratedlimitsassuminganE spectrum are shown[GeV cm as solid lines⇠ and di↵erential limits as dotted lines (both[GeV cm limits are shown for Auger and ANITA). J J

2 8 IceCube (5, 1yr) 2 8 IceCube (5, 1yr) 10 10 rulesE out models with n & 3 (the precise value dependingE on the assume Emin. However, once the energy scale uncertainty is included, the constraint Eq. (10) plays a very little role on the determination of the GOF of the 9 9 contoursexperiment.10 in the It left does panel however of Fig.imply 1). a maximum It is apparent value of10 that this. indirect bound from GeV-TeV -rays does Nbest reduce the number of possible19 models significantly. We show104 10 in5 the106 right107 panel108 10 of9 Fig.1010 110 the11 10 range12 1013 of10 proton14 104 fluxes105 corresponding106 107 108 10 to9 the1010 99%1011 confidence1012 1013 10 level14 for increasing crossover energies E . As discussed above each fit of the proton spectra is marginalized with respect to At this point it is worth stressingE [GeV]min that the Fermi-LAT spectrum used in thisE analysis[GeV] is not the result of a directthe experimental observation but energy is derived scale uncertainty by a foreground and we show subtraction the shifted scheme. predictions The extra-galactic with best in comparison-ray background to the HiRes data at central value. The corresponding range of gamma ray fluxes and cosmogenic neutrinos (summed over flavor) inferredFIG. 5: by The EGRET best fit [44] (solid) shows and range a significantly of cosmogenic larger neutrino intensity fluxes at and the a 99% harder C.L. withspectral (dashed) index. and withoutA possible (dotted) Figureis shown 5: The in predicted Figs. 4. best As a fit representation (solid) and 99% we C.L. chose range models of cosmogenic with minimal neutrino and fluxes maximal with (dashed) energy and density without at (dotted)the the 99% the Fermi-LAT data. For comparison we show upper limits on the total diuse neutrino flux from AMANDA [34, 35], Lake sourcetheC.L. Fermi-LAT of The the calculation di constraint.↵erences of The thecould valuesgamma be due of ray the to fluxes corresponding the di is↵ illustratederent model di↵use in parameters the galactic Appendix. can emission be The found flux (DGE) in is Table. marginally models 1. For used consistent comparison in the with analysis.weBaikal show upper [36], As HiRes pointed limits [37] on (minimum out the total in [21] diof↵useµ aand re-analysis neutrino⌧ channel), flux of from RICE the AMANDA EGRET [38] and ANITA [35, data 36], [39]. with Auger The an black [34], updated solidLake line Baikal DGE (with [37], model extrapolation HiRes [45] [38] is [40]) theshows Fermi-LAT the sensitivity data of within IceCube the [41] errors. after one year of observation. We assume an equal distribution between neutrino flavors (minimum of ⌫µ and ⌫⌧ channel), RICE [39] and ANITA [40]. The black solid line shows the 5 sensitivity of IceCube after comparable with the intensity observed with8 Fermi-LAT. It is beyond the scope of2 this paper to address justN 1⌫e year: N⌫µ of: observationN⌫⌧ 1 : 1 [42]. : 1 and The scale cuto the↵ at limits 10 ifGeV necessary. is artificial Integrated so we also limits show assuming an extrapolation an E spectrum to higher are energies shown as as solid theseWe systematic have not uncertainties. included in the The analysismaximal the resultse↵ect from of a larger the Auger-ray Collaboration background [6, intensity 26]. As is described indicated in by Ref. the [6, 26] ablackdashedlinefollowingRef.[41]).Alllimitsareobtainedassuminganequaldistributionbetweenneutrinoflavours:besideslines; di theerential energy limits scale as uncertaintydotted lines. there (For Auger is also and an ANITA important, we show and both energy limits.) dependent, energy resolution uncertainty extendedN : N parameter: N 1:1:1(andscaledappropriatelywherenecessary).Integratedlimitsassumingan regions shown in Fig. 1 which are derived without the Fermi-LAT constraintE 2 spectrum together are ⌫whiche ⌫µ implies⌫⌧ that bin-to-bin migrations influence the reconstruction of the flux and spectral shape. No public shown as solid lines⇠ and di↵erential limits as dotted lines (both limits are shown for Auger and ANITA). withinformation the corresponding on the form range of the of correspondingneutrino fluxes bin-to-bin in Fig. 5. migration matrix is given and therefore no analysis of the rules out models with n 3 (the precise value depending on the assume E . However, once the energy scale data can be done outside the& collaboration. min uncertaintyThe overall is range included, of neutrino the constraint fluxes increases Eq. (10) plays along a with very the little crossover role on energythe determination - not only of in the magnitude, GOF of the whichcontoursexperiment. is expected in the It left does already panel however due of Fig.imply to the 1). a reduced maximum It is apparent set value of CR of that data this. used indirect in the bound GOF test, from but GeV-TeV also to significantly-rays does Nbest largerreduceWe neutrino the show number in fluxes. the of right possible Also panel the models of cosmogenic Fig. significantly. 1 the neutrino range of protonflux of fluxes the best-fit corresponding models increasesto the 99% by confidence over a factor level for increasingAt this point crossover it is worth energies stressingEmin. As that discussed the Fermi-LAT above each spectrum fit of the used proton in this spectra analysis is marginalized is not the withresult respect of a to 10 directthe experimental observation but energy is derived scale uncertainty by a foreground and we show subtraction the shifted scheme. predictions The extra-galactic with best in comparison-ray background to the HiRes data at central value. The corresponding range of gamma ray fluxes and cosmogenic neutrinos (summed over flavor) inferred by EGRET [44] shows a significantly larger intensity and a harder spectral index. A possible is shown in Figs. 4. As a representation we chose models with minimal and maximal energy density at the the 99% sourceC.L. of The the calculation di↵erences of thecould gamma be due ray to fluxes the di is↵ illustratederent di↵use in the galactic Appendix. emission The flux (DGE) is marginally models used consistent in the with analysis.the Fermi-LAT As pointed data within out in the [21] errors. a re-analysis of the EGRET data with an updated DGE model [45] is comparable with the intensity observed with Fermi-LAT. It is beyond the scope of this paper to address theseWe systematic have not uncertainties. included in the The analysismaximal the resultse↵ect from of a larger the Auger-ray Collaboration background [6, intensity 26]. As is described indicated in by Ref. the [6, 26] besides the energy scale uncertainty there is also an important, and energy dependent, energy resolution uncertainty extendedwhich implies parameter that regions bin-to-bin shown migrations in Fig. influence 1 which theare derivedreconstructionwithout ofthe the Fermi-LAT flux and spectral constraint shape. together No public withinformation the corresponding on the form range of the of correspondingneutrino fluxes bin-to-bin in Fig. 5. migration matrix is given and therefore no analysis of the dataThe can overall be done range outside of neutrino the collaboration. fluxes increases along with the crossover energy - not only in magnitude, which is expected already due to the reduced set of CR data used in the GOF test, but also to significantly larger neutrino fluxes. Also the cosmogenic neutrino flux of the best-fit models increases by over a factor

10 2.2 Gamma-Ray Bursts

Gamma-Ray Bursts (GRBs) were first discovered in 1967 by Vela satellite network. These military based satellites detected bright γ-ray signals coming from space which was not expected. Multiple satellites with different spectrum responses have confirmed that these strange photon signals peaked in the gamma-ray range [49,50]. GRBs have been monitored by many satellites which are dedicated to study GRBs. Beginng in 1991, the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma Ray Observatory (CGRO) collected GRB data [25]. The GRB distribution map from BATSE shows that GRBs are isotropically distributed (Fig. 2.7). This distribution indicates that GRBs are originated from cosmological distances, in other words, they are located outside of our galaxy [51]. It was an astonishing discovery to notice that GRBs are extragalactic sources as it was difficult to imagine such an energetic astrophysical event, so energetic that we can measure the strong signal from such a far distances ( Gpc). In 2004 NASA’s Swift satellite began to search ∼ GRBs with small sky coverage ( 1/3 of BATSE’s field of view) but much more ∼ precise measurement in spectrum and wavelengths than BATSE. In 2008, the Fermi Gamma-ray Space Telescope (FGST) launched and it is currently collecting GRB events while performing an all-sky survey. Based on the measurements from many GRB telescopes, the understanding about the GRB phenomenon has been expanded and more GRB models that describe the measurements are developed. The Fireball shock model is widely accepted as a standard GRB model where relativistic plasma in a jet collides to produce high energy prompt emission. The Fireball model decouples the inner engine of the source from the mechanism of the gamma-ray emission from the source. It assumed that the unknown inner engine is a compact energy source that can initiate the ultra-relativistic outflow.

20 6.3 Gamma Astronomy 121

γ -ray bursts occur suddenly and unpredictably with a rate of approximately one burst per day. The durations of the γ -ray bursts are very short ranging from fractions of asecondupto100seconds.Thereappeartobetwodis- tinct classes of γ -ray bursts, one with short ( 0.5s),the other with longer durations ( 50 s), indicating≈ the existence of two different populations≈ of γ -ray bursters. Figure 6.48 shows the γ -ray light curve of a typical short burst. Within only one second the γ -ray intensity increases by a factor of nearly 10. The γ -ray bursters appear to be uni- formly distributed over the whole sky. Because of the short burst duration it is very difﬁcult to identify a γ -ray burster with a known object. At the beginning of 1997 researchers succeeded for the ﬁrst time to associate a γ -ray burst with a Fig. 6.48 rapidly fading object in the optical regime. From the spec- Light curve of a typcial γ -ray burst tral analysis of the optical partner one could conclude that the distance of this γ -ray burster was about several billion light-years. The angular distribution of 2000 γ -ray bursters recorded angular distribution until the end of 1997 is shown in Fig. 6.49 in galactic coordinates. From this graph it is obvious that there is no clustering of γ -ray bursters along the galactic plane. Therefore, the most simple assumption is that these exotic objects are at cosmological distances which means that they are extragalactic. Measurements of the intensity distributions of bursts show that weak bursts are relatively rare. This could imply that the weak (i.e., distant)burstsexhibitalowerspa- tial density compared to the strong (near) bursts. Even though violent supernova explosions are considered to be excellent candidates for γ -ray bursts, it is not obvious whether also other astrophysical objects are responsible for this enigmatic phenomenon. The observed spatial spatial distribution

+90

+180 –180 Fig. 6.49 Angular distribution of 2000 γ -ray bursts in galactic coordinates recorded with the BATSE detector (Burst And Transient Source Experiment) on board the CGRO –90 satellite (Compton Gamma Ray 2000 events Observatory) {17}

Figure 2.7: GRB distribution plot in Galactic coordinates from 2000 GRBs detected by BATSE. GRBs are isotropically distributed which indicates that GRBs are extragalactic source.

21 The outflow consist of multiple layers, and when the two layers of outflow collide, it generates an internal shock. The shocks will produce gamma rays by synchrotron radiation and inverse Compton scattering. Protons are also expected to be accelerated during this process by shock acceleration. When there are high energy protons and photons (gamma rays), neutrinos can be produced via p γ interactions (Eq. 2.1 but − replacing γCMB with photons from the jet). This early stage of emission from internal shocks are called prompt emission and the measured gamma ray signals are expected predominantly from this prompt emission. After the prompt emission, there is a second stage of emission from the Fireball model which is called afterglow. When the outflow expanded far enough (> 1018 cm) to interact with external matter such as interstellar medium, the collision between the outflow and the external medium produces shocks. These external shocks will generate photons down to radio frequencies due to the deceleration of the outflow. Waxman and Bahcall (WB) have created an analytic GRB neutrino production model [26] based on the Fireball model. For our GRB analysis, we chose to use a numerical calculation to obtain GRB neutrino fluences instead of the simple analytic (and outdated) WB GRB neutrino fluence model.

2.3 Other Models (other than GZK, GRB models)

There are many models which estimate the UHE neutrino ﬂux without the GZK process or GRBs. In this section, AGNs [52, 53], the Waxman-Bahcall (WB) bound [54], Topological Defects (TDs) [55,56] and Z-burst models [57,58] are introduced as examples of UHE neutrino models or constraints from sources other than the GZK process and GRBs. The emission lines in the nuclei of galaxies were recognized in early 1900s [52]. However the theory of AGNs took decades to be considered as a serious research

22 topic until the discovery of quasars and supermassive black holes (106 to 1010 times the mass of the Sun) in the center of galaxies. In the current standard AGN model, an AGN consists of an accretion disk and relativistic jets. An accretion disk will form when surrounding material is dissipated toward the center of a supermassive black hole. Also two highly relativistic jets are aimed toward opposite directions from close to the disk. When the jet is pointing toward the observer, this specific type of AGN is called blazar [59]. Although the analyses in this paper don’t include an AGN neutrino search, AGNs are expected to be the most luminous and distant object in the universe. Once we figure out reliable AGN neutrino flux models, we can expand our UHE neutrino flux limit to AGNs in future analyses. In 1998, Waxman and Bahcall proposed a highly intuitive model which defines the limit for the UHE neutrino flux. The Waxman-Bahcall bound assumes that the sources are optically thin to π photo-production. This means that, when high energy protons are produced inside the source, they assumed that there is only one interaction to create neutrinos. After this one interaction, protons can travel to Earth as a cosmic rays. Using these assumptions, Waxman and Bahcall could calculate the

2 neutrino intensity (Eν Jν) based on cosmic ray data. They set the injection spectrum

2 of protons from the source as dN /dE E− , which is the typical spectrum for CR CR ∝ CR Fermi acceleration [60]. Fermi acceleration occurs when charged particles get boosted by a magnetic mirror, or shock. AGN jets, for example, have continuous impulsive magnetic shocks, and when charged particles get reﬂected between two shocks, they will boosted to ultra high energies. Using the energy production rate for protons between 1019 1021 eV − in [60], the cosmic ray generation rate is given by

˙ 2 dNCR 44 3 1 ECR 10 erg Mpc− yr− . (2.16) dECR ≈

23 Using Eq. 2.16, we can calculate the present day energy density of muon neutrinos under this model considering of a few other factors. First, we can get the total muon

neutrino energy density (for νµ andν ¯µ summed) by

dN dN˙ E2 νµ 0.25 t E2 CR (2.17) νµ dE ≈ H CR dE νµ max CR

where factor 0.25 is obtained from a factor for the probability of a proton yielding a muon neutrinos and t is a Hubble time factor, t 1010 yr [5] in order to account H H ≈ present-day energy density. There is a factor of 1/2 for the probability that a charged pion is produced (by p + γ π+ + n) instead of a neutral pion (by p + γ π0 + p). → → After the π+ is produced, π+ will eventually decay into four diﬀerent leptons including muon neutrinos, π+ e+ +ν +ν +ν ¯ . And another factor of 1/2 for the probability → e µ µ + of π decaying into νµ andν ¯µ which combination of two 1/2 factors make 0.25 factor shown in Eq. 2.17. Eq. 2.17 is the maximum total muon neutrino energy density as it assumes entire proton energy transferred to π in one π photo-production process. With the maximum total muon neutrino energy density in Eq. 2.17, the maximum expected total neutrino ﬂux (for all νe, νµ andν ¯µ) is

3 c dN E2 Φ E2 νµ (2.18) ν ν ≈ 2 4π · νµ dE max νµ max ˙ 3 c 2 dNCR 0.25 ξZ tH ECR ≈ 2 4π · dECR 8 2 1 1 2 10− ξ GeV cm− s− sr− . ≈ × Z

where the factor 3/2 is the ratio between νµ +ν ¯µ and νe ﬂuxes, and the quantity ξZ is a factor for redshift evolution. In [54], they calculated the redshift evolution factor

ξZ for a quasi-stellar object source (which has rapid redshift evolution) and for non- redshift evolution, and came up with ξ 3 and ξ 0.6 respectively. In Fig. 2.4, Z ∼ Z ∼

24 calculated WB constraints are shown. The upper dash-dotted line is a constraint with rapid redshift evolution (ξ 3) and lower dash-dotted line is a constraint with Z ∼ non-redshift evolution (ξ 0.6). Z ∼ TD models postulate that there was a very massive unknown particle produced in the early universe [55, 56] which decayed into UHECRs that we now observe. From Grand-Uniﬁed Theories (GUTs), the mass of this unknown particle is required to be 1024 eV. So, the spectrum of UHECRs decayed from this unknown massive particle ∼ should extend to the rest mass energy of the particle. The Z-burst model predicts that the relic neutrino background, produced in the early epoch of universe, interacts with UHE neutrinos, resulting in annihilation of both through the ν +ν ¯ Z process [57, 58]. The Z then decays into hadronic → 0 0 secondary particles which include UHE neutrinos. The Z-burst model, however, is ruled out by ANITA experiment (Fig. 3.5).

25 Chapter 3

Past and Present Experiments for UHE neutrino

In this chapter, we discuss experiments in the past and on-going that are searching for UHE neutrinos. Before going through the list of experiments, we ﬁrst deﬁne two detection methods, the optical and radio Cherenkov radiation techniques, and discuss what is complementary between the two methods. The Radio Ice Cherenkov Exper- iment (RICE), Goldstone Lunar Ultra-high energy neutrino Experiment (GLUE), Antarctic Impulsive Transient Antenna (ANITA), Antarctic Ross Iceshelf Antenna Neutrino Array (ARIANNA) and IceCube are introduced.

3.1 Detection Methods: Optical and Radio Cherenkov Ra-

diation

There are two main methods for detecting neutrino signals: optical and radio Cherenkov techniques (radio Cherenkov radiation is induced by what is also called the Askaryan eﬀect [61, 62]). When a UHE neutrino passes through a high density dielectric medium such as ice, either charged current (CC) or neutral current (NC)

26 scattering from nucleon occurs:

+ CC : ν + n l− + p, ν¯ + p l + n (3.1) l → l → NC : ν + N N + ν , ν¯ + N N +ν ¯ (3.2) l → l l → l

where νl can be either νe, νµ, or ντ , and the nucleons N in Eq. 3.2 can be either p or n. In Equation 3.1 and 3.2, while charged current scattering produces an electromagnetic cascade and/or hadronic cascade, neutral current scattering only produces a hadronic cascade from a target nucleon (N in Eq. 3.2). In an νe charged current interaction, the final state electron will produce an electromagnetic cascade (Fig. 3.1), while the target nucleon will produce a hadronic cascade. Charged current scattering from a νµ will produce only a hadronic cascade as the final state µ will penetrate the medium without producing any electromagnetic cascade up to energy approximately 1 TeV [5]. Above a TeV, the dominant energy loss process for µ becomes radiative loss and through radiation, there will be an electromagnetic cascade. So, in the UHE regime, µ will produce an electromagnetic cascade. A τ created through charged current scattering by a ντ can produce electromagnetic and/or hadronic cascades through its decay and/or subsequent interactions. When charged particles produced in an electromagnetic or a hadronic cascade move faster than the speed of light in the medium, they can create Cherenkov radiation. Cherenkov radiation is emitted preferentially at an angle θ with respect to the direction of the charged particle, where the angle depends on the speed of the particle (Fig. 3.2) and the medium. The relation between the angle θ and the speed of the charged particle is cos θ = 1/(n β), where β is the speed as a function of the speed of light (β = v/c), and n is the refraction coefficient of the medium.

27 Experiments that use the optical Cherenkov technique detect the Cherenkov radiation produced as optical light with optical light detectors such as photo-multiplier tubes (PMTs). Optical Cherenkov radiation is emitted from individual charged particles in an electromagnetic or a hadronic cascade. Detecting optical light with a PMT is a very straight forward, well-established technology. The only disadvantage of detecting optical light is that it is very costly to make an extremely large detector (larger than 1 km3) using the optical light detecting technology currently available. Optical light can travel through the medium (e.g. ice) for only 10’s meters due to ∼ the attenuation length of 50 m [33], so a few 10’s of meters is the maximum allow- ∼ able distance between PMTs. Radio Cherenkov detectors overcome this disadvantage of optical Cherenkov detectors. The radio Cherenkov technique uses the coherent radio emission from the charge

+ asymmetry of entire cascade. Pair annihilation (e + e− γ + γ), Compton scatter- → ing (γ + e− e− + γ), and the photoelectric effect (γ + A e− + A0) would induce a → → charge asymmetry of approximately 20% during shower development. This is because positrons in the cascade will annihilate with target electrons in the medium (pair annihilation), and high energy photons will scatter off target electrons in the medium (Compton scattering) which then become part of the shower. The photoelectric effect will remove an electron from an atom in the medium. Hence, an electromagnetic cascade will be negatively charged by processes which increase the number of electrons (Compton scattering and photo electric effect), and a process which decreases the number of positrons (pair annihilation). The negatively charged electromagnetic cascade produces Cherenkov radiation which is coherent in radio frequency. As the Cherenkov radiation is a short impulse in the time domain, the signal will have a wide bandwidth in the frequency domain. The Molièreradius (the radius at the maximum cascade shower) for a cascade in ice is approximately 10 cm and it sets the minimum

28 114 6 Primary Cosmic Rays

The direction of incidence of the photon is derived from the electron and positron momenta where the photon momentum is determined to be p p p .Forhighener- γ e+ e− gies (E m c2)theapproximations= + p E /c and e e+ e+ p "E /c are well satisﬁed. | |= e− e− | The|= detection of electrons and positrons in the crystal calorimeter proceeds via electromagnetic cascades. In these showers the produced electrons initially radiate bremsstrahlung photons which convert into e+e− pairs. In alternating processes of bremsstrahlung and pair production the initial electrons and photons decrease their energy until absorptive processes like photoelectric effect and Compton scattering for photons on the one hand and ionization loss for electrons and positrons on the other hand halt further particle multiplication (Fig. 6.39). The anticoincidence counter in Fig. 6.38 serves the purpose of identifying incident charged particles and rejecting them from the analysis. For energies in excess of 100GeV the photon intensities from cosmic-ray sources are so small that other techniques for their detection must be applied, since sufﬁciently large setups cannot be installed on board of satellites. In this con- text the detection of photons via the atmospheric Cherenkov Fig. 6.38 technique plays a special rôle. Sketch of a satellite experiment for When γ rays enter the atmosphere they produce – like the measurement of γ rays in the already described for the crystal calorimeter – a cascade GeV range of electrons, positrons, and photons which are generally of – e 1 bremsstrahlung low energy. This shower does not only propagate longitu- 2 pair production dinally but it also spreads somewhat laterally in the atmo- 1 3 Compton scattering g – 4 photoelectric effect 13 e sphere (Fig. 6.40). For initial photon energies below 10 eV 2 g ( 10 TeV) the shower particles, however, do not reach – + = e e sea level. Relativistic electrons and positrons of the cas- g cade which follow essentially the direction of the original – 1 e incident photon emit blue light in the atmosphere which is – g e 3 known as Cherenkov light. Charged particles whose veloc-

– 4 ities exceed the speed of light emit this characteristic elec- e 3 2 tromagnetic radiation (see Chap. 4). Since the speed of light 4 in atmospheric air is

cn c/n (6.73) = (n is the index of refraction of air; n 1.000 273 at 20◦C Fig. 6.39 and 1 atm), electrons with velocities = Schematic representation of an electron cascade v c/n (6.74) Figure 3.1: Schematic of electromagnetic cascade due to electron. Image from [6]. Cherenkov radiation ≥ will emit Cherenkov light. This threshold velocity of wavelength where coherence occurs as 10 cm in the ice and the corresponding fre- ∼ quency is 3 GHz. So, we can use frequencies up to 3 GHz as a coherent signal from ∼ the cascade due to the radio Cherenkov radiation in ice. The coherent radio Cherenkov signal will have a stronger amplitude and longer attenuation length compare with the optical Cherenkov signal. Attenuation length for radio waves in ice is approximately 700 m [32] while the optical light is as high as approximately 10 m [33]. Along with the strong amplitude of the signal, long attenuation lengths make it possible to use the radio Cherenkov technique for extremely large detectors at relatively low cost. For the next subsection, we examine some past experiments which used the radio Cherenkov and optical Cherenkov techniques. We will ﬁrst look at experiments that have used the radio Cherenkov technique.

29 Cherenkov cone

✓

Charged particle

Figure 3.2: Basic schematic of Cherenkov radiation. Charged particle moves along with the blue arrow, and Cherenkov radiation is shown as a red cone.

3.2 Radio Ice Cherenkov Experiment (RICE)

RICE was an experiment which sought to detect UHE neutrinos interacting in the ice in Antarctica [63]. It used the radio Cherenkov technique to search for radio frequency signals from neutrinos, and was composed of a 16 channel array of antennas deployed along a string of the AMANDA detector, a predecessor of IceCube. With these antennas, RICE monitored over 15 km3 of ice to search for radio emission from neutrinos. Antennas were deployed within a 200 m 200 m 200 m cube at × × 100 300 m depth. RICE triggered when the signal in four antennas exceeded a − threshold in a 1.2 µs time window, which is the time for a radio signal to cross a 200 m detector length at the speed of light. When the trigger was satisﬁed, signals were saved through the Data Acquisition Module (DAQ) for event reconstruction. In August 2000, RICE was operated with a livetime of 333.3 hrs. Although they did ∼

30 not detect any UHE neutrino candidates, they did set a bound on the neutrino ﬂux (see Fig. 3.5 and 3.6), and demonstrated that the radio Cherenkov is a promising technology for detecting UHE neutrinos. The neutrino ﬂux limit from RICE was the best limit at energies above 1019 eV before ANITA.

3.3 Goldstone Lunar Ultra-high energy neutrino Experiment

(GLUE)

The GLUE experiment also used the radio Cherenkov technique [7]. GLUE, however, used a much larger detection medium, namely the Moon, to search for radio Cherenkov emission. They used the Deep Space Network antennas in Goldstone, CA [64]. In particular, they used the shaped-Cassegrainian 70 m antenna DSS14, and 34 m beam-waveguide antenna DSS13. The two antennas are separated by 22 km, and the DSS14 antenna can receive right and left circular polarization (RCP and LCP) waveforms, while the DSS13 antenna can operate at two different frequencies (high frequency, 300 MHz and low frequency, 150 MHz). With these two antennas, ∼ ∼ they were sensitive to radio emission from UHE neutrinos. RCP and LCP signals detected in coincidence would indicate that the waveform is highly linearly polarized, which is expected for Cherenkov radiation. Also, they selected broadband signals by requiring a coincidence between high frequency and low frequency signals. Despite this well-developed technology, however, with the small effective solid angle and the short livetime (120 hours), GLUE did not detect any UHE neutrino candidate signals and set a limit on the UHE neutrino flux above 1020 eV (Fig. 3.5).

31 2

DSS14 Detectors Comparators LNAs Mixers

back S−LCP 50ns AND front cascade neutrino side side enters HI to earth moon S−RCP

LO 150µ sec gate L−LCP EMI Trigger monitor DSS13 partial Cherenkov cone final HI AND S−RCP LO 50ns AND Figure 3.3: Basic schematic for detecting the Askaryan effect in the moon. Image S−RCP from [7]. FIG. 1: Geometry of lunar neutrino cascade event detection. 1GS/s scope Computer via 1GS/s scope GPIB interface tance for an earth-based detector, at the expense of an increase Trigger 3.4 Antarctic Impulsive Transient Antenna (ANITA) in energy threshold. Our ray tracing shows that similar effects obtain statistically for a more realistic surface as well. ANITA isFor a current our search UHE we neutrino used the experiment shaped-Cassegrainian using the radio Cherenkov 70 m an- tech- FIG. 2: GLUE trigger and data recording system. nique. Ittenna uses a DSS14, NASA long and duration the 34 m balloon beam-waveguide to fly antennas antenna in high DSS13, altitude over separated by 22 km. The S-band (2.2 GHz) right-circular- the Antarctic ice. From approximately 37 km altitude in the sky, ANITA can scan polarization (RCP) signal from DSS13 is filtered to 150 MHz angle of the Moon with respect to the baseline vector, !B.For 1.6 Mkmbandwidth3 of ice. The and basic down-converted schematic for detecting to an intermediate radio Cherenkov frequency by ANITA isour 22 km baseline, we have a maximum delay difference of ∼ (IF) near 300 MHz. The band is subdivided into high and low τmax = 73 µs. Detectable events can occur anywhere on the shown in Fig. 3.4. ± frequency halves with no overlap. The DSS14 dual polariza- Moon’s surface within the antenna beam. This produces a In earlytion 2004, S-band a prototype signals experiment are down-converted called ANITA-lite to the [8 same], flew 300 with MHz a livetimepossible spread of 630 ns in the differential delay of the re- of 10 days.IF, and Using a only combination two antennas, of bandwidths ANITA-lite placed from stronger 40-150 constraints MHz are thanceived pulses at the two antennas. ∼ used for sub-band triggering on impulsive signals. At DSS14, The 2.2 GHz antenna beamwidths between the measured GLUE inan the L-band same energy (1.8 regimeGHz) feed and ruled which out is Z-burst off-pointed models by (Fig.0 3.5.5).pro- ANITA-1first Airy nulls are 0.27 for the 70 m, and 0.56 for the 34 m. ∼ ◦ ◦ ◦ flew for 35duces days (livetime a 40 MHz17 bandwith.3 days) looking monitor for radio of terrestrial waveforms interference in December 2006.We took data in three configurations: pointing at the limb, the signals. ∼ center, and halfway between. The measured source tempera- ANITA-1 includedFig. 2 32 shows antennas the layout which could of the detect trigger. vertical The and signals horizontal from thepolarizedtures varied from 70K at the limb, to 160K at the Moon center, two antennas are converted to unipolar pulses using tunnel- with system temperatures of 30-40K. diode detectors with a 10 ns integration time. A comparator 32 Timing and amplitude calibration are accomplished in sev- then test for pulses above∼ threshold, and a local coincidence eral steps. We internally calibrate the back-end trigger system within 50 ns is formed among the channels at each antenna. using a synthesized IF pulse signal, giving precision of or- The DSS14 coincidence between both circular polarizations der 1 ns. We use a pulse transmitter (single-cycle at 2.2GHz) ensures that the signals are highly linearly polarized, and the aimed at the antennas to calibrate the cross-channel delays of split-channel coincidencesensure that the signal is broadband. each antenna to a precision of 1 ns. The cross-polarization Aglobaltriggerisformedbetweenthelocalcoincidences timing at DSS 14 is also checked since the thermal radiation of the two antennas within a 150 µswindow,whichen- from the limb of the Moon is significantly linearly polarized compasses the possible geometric delay range for the Moon (from differential Fresnel effects [14, 15]), introducing an eas- throughout the year. Although use of a smaller window is ily detectable LCP-to-RCP correlation. possible, a tighter coincidence is applied offline and the out- Dual antenna timing calibration is accomplished by cross- of-time events provide a large background sample. Upon the correlating a 250 µsthermalnoisesampleofabrightquasar, global coincidence, a 250 µsrecord,sampledat1Gsamples/s, typically 3C273, recorded from both antennas at the same is stored. The average trigger rate, due primarily to random time and in the same polarization, using the identical data 3 coincidences of thermal noise fluctuations, is 3 10− Hz. acquisition system used for the pulse detection. This proce- Terrestrial interference triggers are on average a× few percent dure establishes the global 136 µsdelaybetweenthetwo of the total, but we have averaged 95% livetime during the antennas to better than 10 ns.∼ Amplitude calibration is ac- runs to date. ≥ complished by referencing to a known thermal noise source. The precise geometry of the experiment is a crucial discrim- The system temperature during a run fixes the value of the inator for events from the Moon. The relative delay between noise level and therefore the energy threshold. We also check the two antennas is τ = c 1 !B cosθ where θ is the apparent the system linearity using pulse generators to ensure that the − | | Figure 3.4: Basic schematic of detecting Askaryan effect by ANITA.

waveforms, and each antenna had a 200 1200 MHz bandwidth. In the trigger, they − divided the full bandwidth into four different sub-bands, and required coincidences between the four bands to trigger candidate signals, so that triggered signals are broadband. Also as candidate signals are produced inside the ice and ANITA detects the top of the Cherenkov cone (Fig. 3.4), the candidate signals are required to be vertically polarized. However, ANITA-1 also did not detect any candidate neutrino signals during its flight, but set stricter limits on the neutrino flux (Fig. 3.6).

33 ANITA-II [9], which flew in January 2009 for 31 days (livetime 28.5 days), had ∼ an improved sensitivity to UHE neutrinos. Compared to ANITA-1, ANITA-2 reduced the front-end system noise by 20 %, had 8 more antennas for a better angular ∼ resolution and a lower trigger threshold. After data analysis, they detected one [9] candidate neutrino signal during the flight. In their background estimation, however they expected 0.97 0.39 events due to thermal and anthropogenic background events. ± Thus, one candidate signal was consistent with the background estimation, which means we can not say whether the detected signal is a real neutrino signal or not. ANITA-3 is in preparation as a next flight, and it will be launched in the 2014-2015 season.

3.5 IceCube

IceCube [29] is, so far, the largest optical Cherenkov experiment for detecting UHE neutrinos. It is monitoring 1 km3 of ice with photo-multiplier tubes (PMTs) ∼ deployed at a 1450 2450 m depth in the ice (Fig. 3.7). IceCube detects optical − Cherenkov radiation, instead of the radio Cherenkov. They have deployed strings in the ice with inter string spacing of about 125 m on which PMTs are attached about 17 m apart. It took approximately 7 years (from 2005 - 2011) to deploy all 86 strings. Even before deploying all 86 strings, IceCube had gathered an enormous amount of experimental data with its large size. Fig. 3.8 shows the neutrino ﬂux limit from IceCube [11] which is currently the best limit below 1019 eV range. After full 86 strings have been deployed, IceCube started to detect extraterrestrial origin neutrinos. From the three years data set with livetime of 988 days, IceCube detected 37 neutrino candidate events with energies between 30 and 2000 TeV [65]. These IceCube starting neutrinos events are a milestone in astrophysics as they are the ﬁrst detected extraterrestrial neutrino events other than the neutrino events from

34 3

] 100 K [ 90

T S+G Δ 80 Galaxy 70 Sun 60 data 50 40 30 20 10 0 400 500 600 700 800 900 ν [MHz]

FIG. 2: (Color online) Frequency dependence of the excess effective antenna temperature ΔT when pointing to the Sun and the Galactic Center [32]. The top band is a model of the expected ΔT,witha width equal to the systematic uncertainties. The lower two bands give contributions due to galactic and solar emissions, respectively. The antenna frequency response is folded into the model. is the system bandwidth. Calibration of the system gain, timing, and noise temperature was performed by several means. A calibrated noise FIG. 3: (Color online) Limits on various models for neutrino fluxes diode was coupled to the system between the antenna and the Figureat 3.5:EeV toConstraints ZeV energies. from GLUE, The limits RICE, are: FORTE, AMANDA AMANDA, cascades and ANITA-lite [27], compared with TD, GZK, and Z-bust models for UHE neutrinos. Z-burst models are first bandpass filter. Also, during the first day of the flight, RICE [29], the current work, GLUE [30], the FORTE satellite [31], ruledand out projectedby ANITA-lite. sensitivity Image from for the [8]. full ANITA. Models shown are apulsegeneratorandtransmitterantennaatthelaunchsite Topological Defects for two values of the X-particle mass [9], a (Williams field, near McMurdo Station) illuminated the pay- TD model involving mirror matter [14], a range of models for load with pulses synchronized to GPS signals. An onboard GZK cosmogenic neutrinos [4, 21, 22], and several models for Z- GPS signal synchronously triggered the ANITA-lite system. bursts [11, 20]. In the Z-burst models plotted as points, the flux is a These pulses were recorded successfully by the system out to narrow spectral feature in energy, and the error-bars shown indicate several hundred km distance. Timing analysis of these signals the range possible for the central energy and peak flux values. indicates that pulse phase could be estimated to a precision of 35 150 ps for 4σ signal-to-noise ratio. Finally, the response of the antennas≥ to broadband noise from both the Sun and the filtering the data with the expected signal shape and requir- Galactic center and plane was determined by differential mea- ing the filtered data to show better signal-to-noise ratio than surements using data when the payload (which rotated slowly the unfiltered data. Analysis B primarily relied on reject- during the flight) was toward or away from a given source. ing events which show high level of cross-correlation with The results of this analysis are shown in Fig. 2, showing the known payload-induced noise events. This approach very ef- spectral response function with the various contributions from ficiently removes the very common repetitive payload noise astronomical sources. The ambient RF noise levels at balloon events. These constituted about 90% of triggers, with the re- float altitudes were found to be consistent with thermal noise mainder from unknown sources, probably also on the payload. due to the ice at Tef f 250 K and our receiver noise temper- None of these resembled the expected neutrino signals. Anal- ature of 300 500 K,∼ which included contributions from the ysis A determined the signal passing efficiency by tightening cables, LNA,− connectors, filters, and power limiters. Other the cuts until the last background noise event was removed, than our own ground calibration signals, we also detected no and found 53% of the simulated signal still passing the cuts. sources of impulsive noise that could be established to be ex- Analysis B blinded 80% of the data, optimized the cuts with ternal to our own payload. Several types of triggers were in- the other 20% using the model rejection factor technique [24], vestigated for correlations to known Antarctic stations, and no and found 65% signal efficiency. No data events pass either such correlations were found. of the analyses. In both analyses, the systematic uncertainty in passing rates was estimated at 20%. ANITA-lite recorded 113,000 events at an average live- ∼ time of 40% [23]. Of∼ these events, 87,500 are 3-fold- To estimate the effective neutrino aperture and exposure coincident triggers considered for data∼ analysis. The remain- for ANITA-lite, two different and relatively mature simula- der were recorded for system calibration and performance ver- tion codes for the full ANITA instrument were modified to ification. Two independent analyses were performed within account for the ANITA-lite configuration. These simulations collaboration, both searching for narrow Askaryan-like im- account for propagation of neutrinos through earth crust mod- pulses, in which almost all signal power is delivered within els, for the various interaction types and neutrino flavors, for 10 ns about peak voltage, time-coincident in at least two inelasticity, and both hadronic and electromagnetic interac- of four channels. Analysis A primarily relied on matched- tions (including LPM effects [25]). The shower radio emis- arXiv:1011.5004v1 [astro-ph.HE] 23 Nov 2010 confidence. l sgvni al .Tecagsrsl na improve- at an excluded now in are which result evolutio of strong-source changes majority given the The models, the ary on constraints I. the Table in ment in given m representative is constraining els for limits confidence of tion E setal h aea h xetdlmts en longer limit is flux no limit integral we pure CL actual so a 90% the ANITA-II limit on The Now expected curves. the both 1. as show Figure same in the in essentially shown is stronger, akrudo 0 of background valid. truly was demonstratio procedure a blinding su as the event consider that this we that scrutiny fact subsequent The its events. vived pulser actually inserted erro was the 8381355, clerical of Event one events, a surviving to two due the of that one the determined public that After subsequently ways we technique. two tion, analysis of blind one a was employed This analysis analysis. upon the removed be unblinding would events These times signal. random neutrino a undisclosed mimic at events pulser twelve inserting 1 .Gra ta. hsclRve D Review Physical al., et Gorham P. [1] h ii a ae nosrigtoeet asn l cuts all 0 passing events of background two a observing on on based was experiment. ANITA limit the The of flight second the from flux neutrino ν 2 h e euti htAIAI bevdoeeeto a on event one observed ANITA-II that is result net The was procedure analysis blind the in steps first the of One narcn ril 1 erpre ii ntecosmic the on limit a reported we [1] article recent a In F ν ≤ .Matsuno S. .R Binns R. W. 1 .DuVernois M. rau:OsrainlCntanso h lr-ihEner Ultra-high the on Constraints Observational Erratum: . 3 E × − .W Gorham W. P. 10 2 .Ruckman L. pcrmfr10 for spectrum . − 97 7 1 ,B.C.Mercurio e cm GeV ± 6 . ,C.Chen 97 0 1 . ,E.W.Grashorn 2 h e ii,wihi 33-34% is which limit, new The 42. ± H43210. OH ainlTia nv,Tie,Taiwan. Taipei, Univ., Taiwan National 1 0 1 ,D.Saltzberg . − ,P.Allison 42. 2 eak E19716. DE Newark, nv olg odn odn ntdKingdom. United London, London, College Univ. 7 s rmteScn lgto h NT Experiment ANITA the of Flight Second the from ,P.Chen − 18 A90095. CA ahntnUi.i t oi,M 63130. MO Louis, St. in Univ. Washington 1 1 I96822. HI sr 2 1 eV arne S66045. KS Lawrence, 82 ,C.Miki et fPyisadAtooy nv fHwi,Manoa, Hawaii, of Univ. Astronomy, and Physics of Dept. − 3 et fPyisadAtooy nv fClfri o Ange Los California of Univ. Astronomy, and Physics of Dept. 1 ,022004(2010). 1 ≤ .Anupdatedevalua- 2 ,B.M.Baughman 7 ,B.Hill 3 ,J.M.Clem E ,D.Seckel ν 4 et fPyisadAtooy nv fKansas, of Univ. Astronomy, and Physics of Dept. 1 ≤ 2 ,M.Mottram et fPyis hoSaeUi. Columbus, Univ., State Ohio Physics, of Dept. 10 1 9 ,S.Hoover e rplinLbrtr,Psdn,C 91109. CA Pasadena, Laboratory, Propulsion Jet 23 . 5 8 > 8 ,R.Y.Shang Vis eV ,A.Connolly 90% od- 5 et fPyisadAstronomy, and Physics of Dept. n- to a- r- 2 n r 5 ,J.J.Beatty ae Z etiomdl r ue u yAIAIadAIAI.Iaefo [9]. from Image Satu- ANITA-II. ANITA-II. and ANITA-I and by ANITA-I, out HiRes, ruled are Auger, models RICE, neutrino from GZK rated Constraints 3.6: Figure ,J.Nam 3 ,M.Huang 8 et fPyis nv fDelaware, of Univ. Physics, of Dept. ait fmdl.Fl iain r ie nteoiia a original the in given are a citations by Full determined is models. range from of model limit variety neutrino revised a (GZK) and BZ Othe HiRes, The ANITA-I. Auger, candidate. surviving RICE, AMANDA, one the from on are curve blue based The limit, livetime. actual days new 28.5 for limit ANITA-II 1: FIG. 7 ,G.S.Varner 5 7 ,M.Detrixhe ,R.J.Nichol 2 ,K.Belov 7 7 .H Israel H. M. et fPhysics, of Dept. 6 et fPhysics, of Dept. 1 ,A.G.Vieregg 4 5 3 ,D.DeMarco ,K.Palladino ,D.Z.Besson yCsi etioFlux Neutrino Cosmic gy 6 ,A.Javaid 36 les, 2 3 8 ,A.Romero-Wolf 4 ,Y.Wang 8 ,P.F.Dowkontt ,S.Bevan ,K.M.Liewer 71 5 , 9 6 rticle. , , 1 , rlimits sthe is PROBING THE ORIGIN OF COSMIC RAYS WITH ... PHYSICAL REVIEW D 88, 112008 (2013) 100 EeV are expected. These ‘‘cosmogenic’’ neutrinos are The paper is structured as follows: In Secs. II and III, the produced by the Greisen-Zatsepin-Kuzmin (GZK) mecha- IceCube detector and the data samples are described. The nism via interactions of UHECRs with the CMB and improved analysis methods and the associated systematic extragalactic background light (infrared, optical, and ultra- uncertainties are discussed in Secs. IV and V. In Sec. VI, violet) [1–3]. A measurement of cosmogenic (or GZK) results from the analysis are presented. Implications of the neutrinos probes the origin of the UHECRs because the observational results on the UHECR origin are discussed in spectral shapes and flux levels are sensitive to the redshift Sec. VII by testing several cosmogenic neutrino models. dependence of UHECR source distributions and cosmic- The model-independent upper limit of the EHE neutrino ray primary compositions [4,5]. Neutrinos are ideal parti- flux is shown in Sec. VIII. Finally, the results are summa- cles to investigate the origin of UHECRs since neutrinos rized in Sec. IX. propagate to the Earth essentially without deflection and absorption. The main energy range of the cosmogenic II. THE IceCube DETECTOR neutrinos is predicted to be around 100 PeV–10 EeV [6,7]. In this extremely high energy (EHE) region, cosmo- The IceCube detector observes the Cherenkov light from genic production is considered the main source of cosmic the relativistic charged particles produced by high energy neutrinos. neutrino interactions using an array of digital optical A measurement of these EHE neutrinos requires a de- modules (DOMs). Each DOM comprises a 10’’ R7081- tection volume on the order of at least 1 km3 as their fluxes 02 photomultiplier tube (PMT) [21] in a transparent pres- are expected to be very low, yielding approximately one sure sphere along with a high voltage system, a digital event per year in such a volume [8,9]. The IceCube readout board [22], and a LED flasher board for optical Neutrino Observatory [10] at the geographical South Pole calibration in ice. These DOMs are deployed along elec- is the first cubic-kilometer scale neutrino detector. Its large trical cable bundles that carry power and information instrumented volume as well as its omnidirectional neu- between the DOMs and the surface electronics. The cable trino detection capability have increased the sensitivity for assemblies called strings were lowered into holes drilled to EHE cosmogenic neutrinos significantly. Previous EHE a depth of 2450 m with a horizontal spacing of approxi- neutrino searches performed with IceCube [9,11] showed mately 125 m (Fig. 1). The DOMs sit where the glacial ice that IceCube has become the most sensitive neutrino is transparent at depths from 1450 to 2450 m at intervals of detector in the energy range of 1 PeV–10 EeV compared 17 m. PMT waveforms are recorded when the signal in a to experiments using other techniques [12–16]. The sensi- DOM crosses a threshold and the nearest or next-to-nearest tivity of the complete IceCube detector reaches to the DOM observes a photon within 1 s (hard local coinci- modestly high flux cosmogenic models which assume a dence, HLC). An event is triggered if eight DOMs record a pure proton composition of cosmic rays. The flux for a HLC within 5 s. The lower, inner part of the detector heavier composition such as iron is at least 2–3 times called DeepCore [23] is filled with DOMs with a smaller lower, although the decrease depends on the source evolu- vertical and horizontal spacing of 7 and 72 m, respectively. tion [17] and strongly on the maximal injection energy of The DeepCore array is mainly responsible for the enhance- the sources [18]. In order to test the heavier composition ment of the performance below 100 GeV, the threshold model predictions, longer exposure or other detection energy of IceCube. Additional DOMs frozen into tanks techniques such as the radio detection are needed. The EHE neutrino search presented here uses data obtained from May 2010 to May 2012. The analysis is sensitive to all three neutrino flavors. The basic search strategies are similar to previous searches [9,11]. The main improvement comes from the enlargement of the detector and the statistical enhancement of the data as well as improved modeling of optical properties of the deep glacial ice [19] in the Monte Carlo simulations. The improvements allow a refined geometrical reconstruction of background events and thus a better background rejection. Two neutrino-induced PeV-energy particle shower events were discovered by this EHE neutrino analysis as reported in Ref. [20]. In this paper, we describe the details of the analysis. Then, we investigate whether the two observed events are consistent with cosmogenic neutrinos. Afterwards, cosmogenic neutrino models are tested for compatibility with our observation in order to constrain FIG. 1 (color online). A schematic view of the IceCube the UHECR origin. detector.Figure 3.7: Basic schematic of IceCube. Image from [10]

SN 1987A. The energies of detected neutrino events from IceCube are approximately 112008-3 two orders of magnitude lower than ARA’s energy threshold.

37 PROBING THE ORIGIN OF COSMIC RAYS WITH ... PHYSICAL REVIEW D 88, 112008 (2013)

ANITA-II(2010) existence of two events in the ﬁnal sample. The 90% event 10-4 upper limit used in the calculation takes into account the RICE(2012) energy PDFs of each of the observed events using Eq. (3), 10-5 where P is a function of the neutrino energy E and PAO(2012) ντ limit x3 n ]

-1 corresponds to the probability of having n events in the -6 sr 10 interval [log E =GeV 0:5, log E =GeV 0:5]. -1 10 10

s ð ÞÀ 2 ð Þþ

-2 Here, the PDFs for an EÀ spectrum are used since 10-7 IceCube2012 the two observed events are not consistent with a harder spectrum such as from cosmogenic neutrino models. The 10-8 quasidifferential limit takes into account all the systematic ) [GeV cm ) [GeV ν Cosmogenic ν models uncertainties described in Sec. V. The effect of the uncer- (E

φ -9 Engel et al. ν 2 10 tainty due to the angular shift of the cascade events on the Kotera et al. (FRII) E upper limit is negligible above 10 PeV (< 1%) as track Ahlers et al. (max) 10-10 events dominate in this energy range. Below 10 PeV, the Ahlers et al. (best) effect weakens the upper limit by 17% because cascade Yoshida et al. 10-11 events dominate. Other systematic uncertainties are implemented as in previous EHE neutrino searches [9,11]. The 6 8 10 obtained upper limit is the strongest constraint in the EeV log (E /GeV) 10 ν regime so far. In the PeV region, the constraint is weaker due to the detection of the two events. An upper limit for an FIG. 9 (color online). All flavor neutrino flux differential 2 Figure 3.8: Constraints from IceCube (red curve) and other experiments with 1:1:1EÀ spectrum that takes into account the two observed 90% C.L. upper limit evaluated for each energy with a sliding 2 neutrino flavor assumption. Currently, IceCube has the best neutrino flux limit belowevents was also derived and amounts to E e 19 window of one energy decade from the present IceCube EHE þ þ ¼ 10 eV. Image from [11] 2:5 10 8 GeV cm 2 s 1 sr 1 for an energy range of analysis including the IceCube exposure from the previously Â À À À À published result (IC40) [9]. All the systematic errors are in- 1.6 PeV–3.5 EeV (90% event coverage). cluded. Various model predictions (assuming primary protons) are shown for comparison; Engel et al. [7], Kotera et al. [17], IX. SUMMARY Ahlers et al. [33], Yoshida and Teshima [6]. The model- independent differential 90% C.L. upper limits for one energy We analyzed the 2010–2012 data samples collected by decade by other experiments are also shown for Auger (PAO) the 79- and 86-string IceCube detector searching for ex- 38 [62], RICE [63], ANITA [14,15] with appropriate normalization tremely high energy neutrinos with energies exceeding by taking into account the energy bin width and the neutrino 1 PeV. We observed two neutrino-induced cascade events flavor. The upper limit for the flux obtained by Auger is passing the final selection criteria. The energy profiles of multiplied by 3 to convert it to an all flavor neutrino flux limit the two events indicate that these events are cascades with (assuming an equal neutrino flavor ratio). deposited energies of about 1 PeV. The cosmogenic neutrino production is unlikely to be responsible for these search with IceCube, is stable against uncertainties in the events. An upper limit on the neutrino rate in the energy IR/UV backgrounds and the transition model between the region above 100 PeV places constraints on the redshift galactic and extragalactic component of the UHECRs distribution of UHECR sources. For the first time the ob- [4,17,60,61]. We should note, however, that the obtained servational constraints reach the flux region predicted for bound is not valid if the mass composition of UHECRs is some UHECR source class candidates. The obtained upper not dominated by proton primaries. The dominance of limit is significantly stronger compared to our previous proton primaries is widely assumed in the models men- publication [9] because of the enlarged instrumented vol- tioned here while a dominance of heavier nuclei such as ume and the refined Monte Carlo simulations. Future data iron provides at least 2–3 times lower neutrino fluxes. The obtained with the completed detector will further enhance analysis is not sensitive enough to reach these fluxes yet. IceCube’s sensitivity to cosmogenic neutrino models.

VIII. THE MODEL-INDEPENDENT UPPER LIMIT ACKNOWLEDGMENTS The quasidifferential, model-independent 90% C.L. We acknowledge the support from the following agen- upper limit on all flavor neutrino fluxes was e cies: U.S. National Science Foundation - Office of Polar þ þ evaluated for each energy with a sliding window of one Programs, U.S. National Science Foundation - Physics energy decade. It is shown in Fig. 9 using the same method Division, University of Wisconsin Alumni Research as implemented in our previous EHE neutrino searches Foundation, the Grid Laboratory Of Wisconsin (GLOW) [9,11]. An equal flavor ratio of : : 1:1:1 is as- grid infrastructure at the University of Wisconsin - e ¼ sumed here. A difference from the calculation of the limit Madison, the Open Science Grid (OSG) grid infrastructure; shown in our previous publications arises from the U.S. Department of Energy, and National Energy Research

112008-13 Chapter 4

Askaryan Radio Array

The contents of this chapter are largely taken from [2].

The first radio array in ice to search for UHE neutrinos, RICE, was deployed along the strings of the AMANDA detector, an IceCube predecessor, and placed competitive limits on the UHE neutrino flux between 1017 and 1020 eV [66]. Next- generation detectors are under construction aiming to reach the 100’s of km3 target volume of ice. The Askaryan Radio Array (ARA) [31] is one such detector being deployed in the ice at the South Pole and the first physics results from a prototype station of this detector are presented in this paper. ARA aims to deploy 37 stations of antennas at 200 m depth spanning 100 km2 of ice as shown in Fig. 4.1. A schematic of a design station is shown in Fig. 4.2. A design station consists of eight horizontally polarized (HPol) and eight vertically polarized (VPol) antennas at depth and four surface antennas for background rejection and cosmic ray detection via the geomagnetic emission in the atmosphere. The 200 m design depth was chosen because it is below the firn layer, where the index of refraction varies with depth due to the gradual compacting of snow into ice down to 150 m ∼ depth. The trigger and data acquisition are handled by electronics at the surface of the ice at each station.

39 ARA prototype TestBed 2010 Askaryan Radio Array (surface detector in operaon since January 2011) Deployed ARA3 staons (in operaon since January 2013) Staons to complete ARA10 Planned Staons for ARA37 10

9 8 7 South Pole IceCube TestBed South Pole 3 1 Staon

6 2

Skiway 5 4 2 km

Figure 4.1: Diagram showing the layout of the proposed ARA37 array, with the location of the Testbed and the ﬁrst three deployed deep stations highlighted in blue and black respectively, and proposed stations for the next stage of deployment, ARA10, highlighted in orange.

To date, one ARA prototype Testbed station and three full stations have been deployed in the ice. The Testbed station was deployed at a depth of 30 m in the ∼ 2010-2011 drilling season. The ﬁrst full station, A1, was deployed at a depth of 100 m in the 2011-2012 drilling season. The next two stations, A2 and A3, were deployed at the 200 m design depth during the 2012-2013 season. At the time of publication, station A2 and A3 are operational.

40 7#5).%&'8% ĞŶƚƌĂů^ƚĂƟŽŶ ĐŽŵŵƵŶŝĐĂƟŽŶƐ ,$)-(.#'/-0 (#%9:;

6#5'4#$)% ŝŶƐƚƌƵŵĞŶƚĂƟŽŶ

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ĂůŝďƌĂƟŽŶ ŽƩŽŵ,ƉŽů ĂůŝďƌĂƟŽŶ *"#$ &'()''&0 &'()''& &'()''&0 <'()''&% -$20().0 ŽƩŽŵsƉŽů

6)"(4=%>??%@ 102.3&-)%&'()''&0%&.)%'#(%04#5'

Figure 4.2: Diagram showing the layout of a design station and antennas. Each station on Fig. 4.1 (one circle on the plot) has the layout shown on this plot. There are four boreholes for receiving antenna clusters where each borehole has two Vpol antennas and two Hpol antennas. There are two additional boreholes for calibration transmitting antennas. Each calibration pulser borehole has one Vpol and Hpol transmitter antennas. There is central station electronics on the surface of the ice, which includes DAQ and power supply box.

4.1 Testbed

The ARA prototype Testbed station diﬀers from the layout of the design stations for the full array. A more complete description of the design and operation of the Testbed station can be found in [31]. Table 4.1 summarizes the antenna types and deployed positions in the Testbed which are depicted in Fig. 4.3. Here we use the Testbed-centric coordinate system

41 channel x y Type, Pol Depth Hole number (m) (m) (m) 0 BSC, H 20.50 BH 1 -8.42 -4.40 3 Bicone, V 25.50 5 BSC, H 27.51 BH 2 -0.42 -11.13 2 Bicone, V 22.51 7 BSC, H 22.73 BH 3 9.22 -6.15 4 Bicone, V 27.73 1 BSC, H 30.56 BH 5 3.02 10.41 6 Bicone, V 25.56 QS, H 26.41 BH 6 -9.07 3.86 QS, H 30.41 Discone, V 1.21 S1 -2.48 -1.75 Batwing, H 2.21 S2 4.39 -2.41 Batwing (H) 1.19 S3 1.58 3.80 Discone (V) 1.19 S4 Fat Dipole (H) H 17.50 Cal 1 -23.18 17.90 V 22.50 H 34.23 Cal 2 -2.25 -29.81 V 29.23 27.67 13.57 H 1.13 Cal 3 28.69 12.35 V 1.13

Table 4.1: Types and positions of antennas as deployed in the ARA Testbed. See the text for the description of antenna types.

with the origin at the southeast corner of the DAQ box on the surface of ice, +ˆx pointing along the direction of ice ﬂow and thex ˆ yˆ plane tangent to the earth’s − geoid shape at the surface. As with the deep stations, the Testbed antennas deployed in boreholes were designed to be broadband, with a mixture of HPol and VPol, subject to the constraint that they must ﬁt down the 15 cm diameter hole in the ice. For VPol, a wire- ∼ frame hollow-center biconical design was chosen with an annular-shaped feed with the string cable running through the center. These “Bicones” have a bandwidth of

42 Figure 4.3: Schematic of the ARA Testbed station.

150-850 MHz, and four were deployed in boreholes and two near the surface. For HPol, two designs were used in the Testbed, the bowtie-slotted-cylinder (BSC) and the quad-slotted-cylinder (QSC). The BSCs were used in four borehole antennas and a pair of QSC’s in the ﬁfth borehole. Photos for bicone, BSC, and QSC antennas are shown in Fig. 4.4. Larger antennas were deployed at the surface. Two discone antennas (VPol) and two Batwings (HPol) were deployed 1-2 m from the surface. Additionally, two fat dipoles with a bandwidth of 30-300 MHz were deployed within a meter of the surface to assess the feasibility of detecting geosynchotron RF emission from cosmic rays, which has a lower frequency content than the Askaryan emission expected from neutrinos.

43 460 P. Allison et al. / Astroparticle Physics 35 (2012) 457–477

CAL 2 (currently LOW−FREQ 2 active) CAL 3 (inactive) Borehole 3

Borehole 4 (spare) SH2 R=30m Borehole 2

SH1 Borehole 5 SH3 R=10m Borehole 1 power and comms cable 33m

Borehole 6

GRID NORTH to IceCube 4 LEGEND: laboratory LOW_FREQ 1 Deep borehole, bicone+BSC RELATIVE LOCATIONS ARE Surface discone+batwing (SH) APPROXIMATELY CORRECT Deep borehole with quad−slot Hpol

Deep borehole calibration transmitter CAL 1 SCALE: (inactive) Surface calibration transmitter 5 15 Surface low−freq. antenna 0 10 20m Junction Box

Fig. 2. Physical plan view of the ARA testbed system. FIG. 2: ARA testbed downhole antennas: left two images, wire-frame bicone Vpol antennas; right two images, bowtie-slotted-cylinder Hpol antennas.

Elevation angle θ Azimuthal angle φ φ = 0 ο θ = 90 ο +10 +10

0 0

300 MHz +10 +10 500 MHz 700 MHz

Fig. 3. ARA testbed downhole antennas: left two images, wire-frame bicone Vpol antennas; right two images,FIG. bowtie-slotted-cylinder 3: Left: Quad-slot cylinder Hpol antenna antennas. used in one borehole for ARA-testbed. Center: Simulated Gain (dBi) vs. elevation angle ( zero degrees is the vertical direction) for three frequencies for the QSC antenna. Right: Simulated Gain (dBi) in the horizontal plane vs. azimuth, showing the high degree of uniformity of the QSC azimuthal response. quad-slotted-cylinder (QSC) antenna with internal ferrite loading borehole antennas used for the ARA-testbed. VSWR is related to to effectively lower its frequency response. The goal for both sets the complex voltage reflection150 MHz to coefficient 850 MHz. Thisq of goal the was antenna achieved with via the VSWR is related to the complex voltage reflection coefficient of antennas was to cover a frequency range from about 150– the relation Vpol antennas, but the 15 cm diameter borehole constraint r of the antenna via the relation has proved challenging for the Hpol antennas, both of which 850 MHz. This goal was achieved with the Vpol antennas, but the r(n)+1 q m 1 have difficulty getting frequency response below about 200- VSWR(n)=| | 15 cm diameter borehole constraint has proved challenging for VSWR j ð Þþ j 250 MHz in ice. In addition, the BSC antenna, although it r(n) 1 m | | the Hpol antennas, both of which have difficulty getting frequency ð Þ¼ q m 1 was found to have better efficiency than the QSC, suffers from j ð ÞÀ j and the effective power transmission coefficient T (either as a some azimuthal asymmetry in its response, and thus the QSC, response below about 200–250 MHz in ice. In addition, the BSC an- receiver or transmitter from antenna duality) is given by and the effective powerwhich transmission has uniform coefficient azimuthal response,T (either will as be a used recei- for fu- tenna, although it was found to have better efficiency than the QSC, ver or transmitter fromture antenna ARA stations. duality) In is the given current by testbed station, we have T(n)= 1 r(n) 2 suffers from some azimuthal asymmetry in its response, and thus primarily used the BSC antennas because of the ease of their | | Figure 4.4: Photos taken from Testbed deployment.2 manufacture Top left: for bicone the 2011 Vpol season. antenna Figure 2 shows photographs and may be thought of as the effective quantum efficiency of the QSC, which has uniform azimuthal response, will be used for T m 1 q m future ARA stations. In the current testbed station,under we test have in primar- South Pole station,ð Þ¼j topÀ middle:ð Þj bowtie-slotted-cylinderof the wire-frame bicone (BSC) antennas Hpol and the BSCs as they were the antenna vs. frequency n although RF antennas in the VHF antenna, top right: quad-slotted-cylinder (QSC), bottomreadied left: for string deployment. descending Fig 3 shows down a photo of one of the to UHF range never operate in a photon-noise limited regime. ily used the BSC antennas because of the ease of their manufacture and may be thought of asQSC the prototypes effective (only quantum one of theefficiency 4 slots is of evident), the an- along In addition to the coupling efficiency of the antennas, the for the 2011 season. Fig. 3 shows photographsa hole, of the bottom wire-frame right: x-marktenna for locating vs. frequency the Testbedm althoughwith station. simulated RF antennas results for in the the gain VHF patterns to UHF in elevation range and other important parameter for RF performance is the antenna bicone antennas and the BSCs as they were readied for deploy- never operate in a photon-noiseazimuth, illustrating limited the regime. uniformity, Note which that was confirmed initial at directivity gain G, often denoted as just gain, and related to several angles in laboratory measurements. the effective power collection area of the antenna via the fun- ment. Fig. 4 shows a photo of one of the QSC prototypes (only testing of the antennas is done in air to verify the first-order trans- damental relation one of the four slots is evident), along with simulated results for mission characteristics; however,Figures 4 the and actual 5 show design the voltage frequency standing range wave ratio Within 1 m of the antennas, a filter and low noise(VSWR), amplifier along (LNA) with the prepare power transmission the coefficient for Gc2 the gain patterns in elevation and azimuth, illustrating the unifor- of the antennas is only achieved once they are immersed in the sur- A (n)= the primary borehole antennas used for the ARA-testbed. eff 4pn2 mity, which was confirmed at several anglessignal for in transmission laboratory to therounding electronics ice box dielectric at the surface. which varies A notch in filter its radio at 450MHz index of refraction measurements. from n = 1.5 for the typical 25–30 m depths in the ARA testbed, to Figs. 5 and 6 show the voltage standingremoves wave ratio the South (VSWR), Pole communicationsvalues of n = from 1.7–1.8 the atLand the Mobile 180–200 Radio m depthshandheld planned UHF for the full along with the power transmission coefficientsystems. for the A bandpass primary filterarray. sits just after each antenna and blocks power outside of our 150 MHz to 850 MHz band before amplification. The filtered signal in each antenna is then input to a low noise amplifier and transmitted to the surface. At the

44 surface, a second stage 40 dB amplifier boosts the signals before they are triggered ∼ and digitized. After arriving at the electronics box at the surface, the signals are split into a path for the trigger, which determines when a signal is to be stored, and another path to the digitizer, which reads out the waveforms. There are two different trigger modes in the Testbed, an RF trigger and a software trigger. An event passes the RF trigger when the output of a tunnel diode, a few- ns power integrator of the waveforms from each antenna reaching the trigger path, exceeds 5-6 times the mean noise power in three out of the 8 borehole antennas within a 110 ns coincidence window. Due to the differences in responses between channels, each antenna has a different power threshold and thus has different trigger rate between channels. The software trigger causes an event to be recorded every second to monitor the RF environment. Once the station has triggered, the digitization electronics, which are descended from those developed for ANITA [67], process the waveforms and output them to storage. Here, in the digitizer path, the signal undergoes an analog-to-digital con- version using the LAB3 RF digitizer [67], and stored in a buffer (in the Testbed, the buffer was trivially one event deep). The signals from the “shallow” antennas are sampled at 1 GHz, while the signals from the eight borehole antennas were sampled twice, with an time offset of 500 ps for an effective sampling rate of 2 GHz. The digitized waveforms are 250 ns long and are centered within approximately 10 ns of ∼ the time the station triggered. Three calibration pulser VPol and HPol antenna pairs were installed at a distance of 30 m from the center of the Testbed array to provide in situ timing calibration and ∼ other valuable cross checks related to simulations and analysis. An electronic pulser in the electronics box produces a 250 ps broadband impulsive signal at a rate of ∼ 1 Hz. This pulser is connected to one of the three calibration pulser antenna pairs and

45 can transmit from either the VPol or HPol antenna in each pulser borehole. Having multiple calibration pulser locations provides a cross check for the timing calibrations of each channel. Also, the observation, or non-observation, of the constant pulse rate by the station provides an estimate of its livetime. For the Testbed, an event ﬁlter selects one event from every ten events at random to be transmitted to the North by satellite and the remaining data is stored locally and hand-carried during the following summer season. For the other ARA stations, this ﬁlter is now optimized to select events that exhibit a causal trigger sequence and thus are more likely to be events of interest.

46 Chapter 5

Simulation: AraSim

The contents of this chapter are largely taken from [2].

The oﬃcial simulation program for ARA is called AraSim, and is the one we developed and used for the analysis presented in this paper. AraSim is used for multiple other analyses at other institutions, including a neutrino search in deep stations. AraSim draws on ANITA heritage, but much of the program was custom developed for ARA. In this Chapter, we describe each step of the simulation process in AraSim in Section 5.1. In Section 5.2, in-depth description about the radio Cherenkov emission models in AraSim is given. In Section 5.3, we show how we calibrated AraSim using data from the Testbed.

5.1 Simulation Process

AraSim simulates neutrino events in multiple steps. Simulation processes include selecting neutrino interaction location in the ice, modeling neutrino absorption in the Earth, emitting the radio Cherenkov signal, determining the signal’s propagation through the Antarctic ice, and modeling properties of the detector. A schematic plot of a neutrino event is shown in Fig. 5.1. Each individual simulation step is presented in following subsections.

47 ice surface

One of the 200m strings in ARA station Neutrino-ice interaction location in ice

Neutrino : Vpol antenna travel : Hpol antenna direction : ray trace

Figure 5.1: Basic schematic of a neutrino event. The cone at the neutrino-ice interaction location is the Cherenkov cone from coherent radio emission and the red curve is ray tracing between the antenna and neutrino-ice interaction location.

5.1.1 Selecting Neutrino-ice Interaction Location

AraSim generates neutrino events independent of each other, with interaction point locations chosen with a uniform density in the ice. For computational ease, neutrinos are generated within a 3-5 km radius around the center of a single station

17 21 for neutrino energies from Eν = 10 eV-10 eV, with the larger radii used for higher energies. For simulating multiple stations, neutrino interactions are generated up to 3-5 km beyond the outermost stations. For the diﬀuse neutrino search, AraSim randomly distributes the travel directions of the neutrinos over a 4π solid angle. AraSim can also set neutrinos to travel in certain directions for simulating point sources such as GRBs.

48 5.1.2 Earth Absorption Eﬀect

Once the neutrino interaction location and travel direction is chosen, AraSim calculates the probability of the neutrino to reach the interaction location and not be absorbed by the Earth. The probability is calculated by

l /L P = e− i i (5.1) i Ym L = nucleon (5.2) i ρ σ i ·

where Li is the interaction length at the layer of the Earth, li is travel distance at the

27 layer of the Earth, m is the mass of nucleon ( 1.67 10− kg), ρ is the mass nucleon ∼ × i density of the Earth layer i ( 0.917 km/m3 for ice), and σ is the neutrino-nucleon ∼ cross section. The parameters of each Earth layer are obtained from the Crust 2.0 Earth model and the energy-dependent cross sections are from [68]. We weight each event by this factor (P in Eq. 5.1) to account for absorption in the Earth.

5.1.3 Showers from Neutrino-ice Interaction

The primary shower comes from the initial neutrino-ice interaction. The energy for the electromagnetic and hadronic showers from the primary interaction are obtained from the inelasticity distributions from [68]. In addition to the showers from the primary interaction, AraSim considers any secondary interactions from µ or τ leptons that are generated from neutrino-ice charged current interactions. Electro- magnetic and hadronic shower energies for the secondary showers are calculated from interaction probability tables obtained from the MMC particle generation code [69]. AraSim calculates the total energy of the primary showers, hadronic and electromagnetic if there is one, and the energy of the secondary showers and generates the RF

49 signal from the interaction among them that produces the most shower energy as a ﬁrst order estimation. From the energies of the electromagnetic and hadronic showers, we model the radio Cherenkov emission in AraSim. The detailed description about the radio Cherenkov emission models in AraSim is shown in Section 5.2.

5.1.4 Ray Tracing

After AraSim selects a neutrino interaction location in the ice and models the showers in ice, it obtains ray tracing solutions from the neutrino interaction location to each antenna. Ray tracing is not a trivial calculation as the Antarctic ice has a depth dependent index of refraction within 200 m of the surface. ∼ There are two depth-dependent index of refraction models in AraSim. The one which we call the exponential fit model is used as the default index of refraction model if not stated. The exponential fit model is based on Besson et. al. [70, 71] measurements at the South Pole fit to an exponential function (Fig. 5.2). The alternative index of refraction model in AraSim is called the inverse exponential fit function. More detailed information and the systematic error on our result due to choice of index of refraction model is shown in Section 6.6. Based on the depth-dependent index of refraction model, RaySolver, a in-ice ray tracing code [72], derives multiple ray-trace solutions between source and target. For depths within the firn (<150 m), this curvature effect is significant and large regions of the ice beyond 1 km away have no ray-trace solutions to the antennas as can be ∼ seen in Fig. 5.3. RaySolver has a multi-step processes to optimize the computation time. For the first step, it uses an equation, which is driven from Snell’s law, that is not analytically

50 1.8

1.7

1.6 Index of Refraction

1.5

1.4

0 200 400 600 800 Depth [m]

Figure 5.2: Antarctic ice index of fraction measurements (red crosses) at the South Pole and its fit result (green curve). The fit function is n(z) = a1+a2 (1.0 exp(b1 z)) (exponential fit model) where n(z) is the index of refraction and×z is the− depth.· Data points are digitized from [70].

51 0

-0.5 Z Depth (km) -1

-1.5

-2

-2.5 0 0.5 1 1.5 2 2.5 3 3.5 4 XY Distance (km)

-0.5 Z Depth (km) -1

-1.5

-2

-2.5 0 0.5 1 1.5 2 2.5 3 3.5 4 XY Distance (km)

Figure 5.3: Plot showing the regions with ray-trace solutions for an antenna depth at 25 m (top) and 200 m (bottom). The greater depth allows an antenna at 200m depth to observe a larger volume of the ice.

solvable but can be solved numerically (see Appendix):

n2 σ2n2 + A2 σ2n2 A ln − 0 0 − 0 0 + n A A2 σ2n2 ! p − p − 0 0 n2 σ2n2 + A2 σ2n2 p A ln 0 − 0 0 − 0 0 + 2 2 − n0 A A2 σ n ! p −p − 0 0 C A2 σ2n2 p + − 0 0 (x x ) = 0 (5.3) σ n 0 p 0 0 −

52 where A is one of the parameter values from the index of refraction model (n(z) = A+

C z Be · ), n and n0 are the index of refraction at the source and the target respectively, x x is the horizontal distance between the source and the target, and σ = sin θ − 0 0 0 which give us the information about the launch angle θ0 at the source location. From this equation, we ﬁnd an initial launch angle at the source location that makes the left-

4 hand-side of the equation smaller than 10− . This first semi-analytic approach is much faster than the ordinary “trial and error” method as we don’t need to trace the ray step-by-step for multiple trials. If RaySolver couldn’t find the solution with the first semi-analytic method, it uses a “trial and error” technique to find the solution. This second trial of ray-solution calculation insures that we don’t miss any possible ray- solution from the first semi-analytic method. Once RaySolver finds a first solution, it moves on to the next possible solution which is either a U-turned (or highly bent) in- ice trace or a surface reflected trace. It uses only a traditional “trial and error” method to search for a second solution. For the first and second solutions, the minimum distance between the ray and the target should be less than the required accuracy parameter which is 0.2 m. From RaySolver, we obtain the travel distance and time from the shower to each antenna, the polarization of the signal and the receiving angle at each antenna so that we can apply the antenna responses to the signal.

5.1.5 Ice Attenuation Factor

After the travel distance of the ray is obtained from RaySolver, AraSim applies factors to account for ice attenuation to the signal. In AraSim, there are two ice attenuation length models. The default model uses a South Pole temperature pro- ﬁle from [73] folded in with a relationship between ﬁeld attenuation length and ice temperature given in [74] as used in ANITA simulations and described in [75]. The

53 Figure 5.4: The electric ﬁeld attenuation length as a function of depth from the ARA Testbed deep pulser data. The depth of the deep pulser was 2 km and the path length was 3.16 km from the deep pulser to the ARA Testbed.∼ From the single distance measurement, the average attenuation length over all depths are extrapolated.

alternative ice attenuation length model is based on the ARA Testbed measurement from IceCube deep pulser events published in [31]. The alternative model from ARA Testbed deep pulser data was measured with one depth location of the pulser which was 2 km deep. From the data measured from a single distance, we deduced the ice ∼ attenuation length as a function of depth. Fig. 5.4 shows the ice attenuation length versus depth of ice with the mean value shown as a red line, while the error range shown as blue band.

54 The ice attenuation factor applied with no frequency dependence, using the distance along each ray-trace path through the ice and the attenuation factor to the electric ﬁeld is:

Dtravel/Latten FIceAtten = e− (5.4)

where Dtravel is the ray travel distance from RaySolver and Latten is the ice attenuation length.

5.1.6 Antenna Response

When the rays arrive at each antenna, we apply the antenna’s properties to the signal. Antenna models in AraSim are obtained from NEC2 simulation software [76]. In NEC2, we can run an antenna simulation with information about a known antenna shape used in ARA. The vertically polarized antennas (Vpol) and horizontally polarized antennas (Hpol) have different shapes, and therefore different NEC2 simulations are performed. For both, we took a bandwidth from 83 MHz to 1 GHz with 60 steps ∼ in frequency. The angular response was calculated in 5◦ steps in both azimuth and zenith angle. Both gain and phase are obtained at each frequency and angle, for each antenna. For Vpol antennas, NEC2 simulation result is obtained with the geometric information from antenna’s CAD design sheet. For Hpol antennas, however, due to the difficult in modeling slotted antennas in NEC2 we have two different methods to imitate Hpol’s polarization. The first method uses a simple dipole antenna model with a similar length and thickness as the slot of the actual Hpol antenna to reproduce the slot. In order to imitate the slot, we manually swapped the electric field (E-field) and magnetic field (B-field) response from the NEC2 simulation result which makes the antenna have a horizontally polarized response.

55 The second method uses exactly the same gain and phase response as Vpol but again manually changes the polarization by switching the E-field and B-field responses. By default, AraSim uses the second method for the Hpol response as it is found out that the simple dipole response is too optimistic in terms of gain and phase response based on the comparison between the simulated and measured calibration pulser events. A later version of AraSim will include more realistic antenna responses by using measured antenna properties. Once the antenna gain and phase values are obtained from the NEC2 model, the effective height of the antenna is obtained by:

A G = 4π eff λ2 Z h = 2 A r eff eff Z r air Gc2Z = 2 r (5.5) 4πf 2 n2 Z /n s · · air where G is the gain of the antenna at a specific receiving angle and frequency, Aeff is effective area of the antenna, Zr is antenna radiation resistance which is 50 Ω, Zair is resistivity of free space which is 377 Ω, f is frequency and n is the index of refraction of the medium at the antenna. In case of impedances matched between the antenna and the load, the voltage measured by the antenna (see the schematic Fig. 5.5) is V = h E , where E is the E-field strength right in front of the antenna. ant eff · before before

In Fig. 5.5, when impedance matched, ZA and ZR have zero reactance, and the same resistance. When we let the resistance for both ZA and ZR be Rr (ZA = ZR = Rr), the actual signal we measure (the voltage across the load Rr, which is V in Fig. 5.5)

56 I

V ZR ZA

Figure 5.5: Signal receiver system’s simple schematic. Right hand part (source and ZA) are the components from antenna while left hand part (ZR) is the signal receiver (such as DAQ). When impedance is matched, we can let reactance X from both ZA and ZR as zero and resistance for both ZR and ZA as the same value Rr (ZA = ZR = Rr). V on the plot is the actual measured voltage signal which is V = Z I = V . R · measured

57 0 -10 Gain (dB) -20 -30 -40 -50 -60 -70 -80 -90 0 200 400 600 800 1000 Freq (MHz)

Figure 5.6: Filter’s gain response which is in use for AraSim. The filter response consists of a high pass filter at 150 MHz, a low pass filter at 800 MHz, and a notch at 450 MHz to avoid the electronics communication frequency.

is then:

V = I R measured · r V = ant R 2R · r r 1 = E h (5.6) 2 before · eff

where I is the current through the circuit and Vmeasured is the voltage we can actually measure over the load Rr.

5.1.7 Electronics Response

After the antenna, neutrino signals will pass through entire electronics chain such as a low noise amplifier (LNA), filter and fiber optic amplifier module (FOAM). The measured filter gain response which AraSim uses is shown in Fig. 5.6 as an example.

58 The phase response is derived from a Qucs Studio [77] model of ﬁlters with similar characteristics. Other components in the electronics chain (LNA and FOAM) do not have strong phase responses, so we only applied the gain response of them which is simply a multiply of gain to the signal spectrum. Once the received signal is convolved with the detector response, noise is added to the signal.

5.1.8 Generating Noise Waveforms

If any ray trace solution exists for a speciﬁc neutrino event, AraSim generates noise waveforms for each channel. Channel numbers shown in this chapter are introduced in Table 4.1. There are two thermal noise waveform generation models in Arasim, the nominal non-calibrated thermal noise model and calibrated thermal noise model. The nominal noise model is used as a ﬁrst order estimation of the noise in AraSim while an accurately calibrated noise model is applied for all of the data analyses in this paper. A detailed explanation of how the noise model is calibrated can be found in Section 5.3.1. The nominal noise model in AraSim starts with Johnson-Nyquist theory. From [78], one-sided (or single-sided) frequency band mean square noise voltage due to thermal noise from a open circuit is given as:

< V 2 >= 4 k T R BW (5.7) · B · · L · where BW is the bandwidth (only one sided bandwidth, meaning bandwidth in only positive frequencies), RL is the resistance of the load, T is the temperature, and kB is the Boltzmann constant. Now, with the open circuit consisting of a antenna and a load, mean voltage in

Eq. 5.7, we can calculate the measured voltage in our system. In Fig.5.7, ZA is the

59 Figure 5.7: Simple closed circuit with voltage source (thermal noise source) and antenna (ZA) and load (RL).

antenna internal impedance, and RL is the load resistance. In the case when the

impedance is matched, the inductance of ZA is zero (XA = 0), and the resistance of

both antenna and the load are same (RA = RL). Then the measured mean power is:

V 2 R V 2 P = I2 R = · L = (5.8) · L (R + R )2 4 R A L · L < V 2 > < P >= = k T BW. (5.9) 4 R B · · · L

Therefore, in order to get the result in Eq. 5.9, mean power spectral density value inside the bandwidth should be k T in W/Hz. B · Our default temperature value in AraSim is 325 K, found by assuming a 230 K average environmental temperature and a 95 K noise temperature for the low noise amplifier (LNA). From this perfectly flat noise spectrum, AraSim applies the band pass filter response to limit the bandwidth of the system to approximately 150 −

60 850 MHz (shown in Fig. 5.6). From the power spectrum that we produce, we apply a 0 2π random phase to each frequency bin and then obtain the time domain thermal − noise waveform by taking the Fourier Transform. Generated noise waveforms are required to have a long enough time length in order to add all time domain neutrino signals with proper time delay between channels. AraSim typically produce a 6 µs noise waveform to encompass the arrival times for ∼ all ray solutions. The time-domain signal waveform is added to this noise waveform at its arrival time at the antenna from the ray tracing.

5.1.9 Trigger Analysis

Once the noise has been added from the previous step, the signal is split into the trigger and digitization paths. For the trigger path, the time-domain signal is convolved with a model of the tunnel diode power integrator which integrates the input waveform power over 10 ns (Section 4.1). This convolved time-domain ∼ response is then scanned for excursions above the power threshold. For the Testbed simulation, the power thresholds were calibrated against RF triggered events for each antenna as described in Section 5.3.2. When the trigger ﬁnds 3 such excursions among the 8 borehole antennas within a 110 ns window, the event is considered to have triggered. Once the trigger condition is met, waveforms are read out in 256 ns waveforms just like the data, and written into the same format as the data so that the simulated events can be analyzed with identical software.

5.2 Askaryan Radiation in AraSim

The contents of this section are in progress to be published.

61 In this section, two models for generating Askaryan signals in AraSim are described. The default mode in AraSim is one that produces a custom parameterized RF Cherenkov emission for each event. This technique was developed based on an approach suggested by [12,79]. This mode will generate the radiated signal with proper phase information for corresponding frequencies. The second alternative mode is based on the Alvarez-Mu˜niz, V`azquezand Zas (AVZ) model [80]. This second mode is the signal generation mode from icemc, a ANITA simulation software. In this mode,

Askaryan signals are calculated with a simple 90◦ phase assumption which makes an ideal impulsive waveform without dispersion.

5.2.1 Custom parameterized RF Cherenkov emission model

Approach of Alvarez-Mu˜niz,et. al. In Alvarez-Mu˜niz, et. al. [12], the authors suggest to generate Askaryan signals using a semi-analytic method which can maintain outcomes that agree well with results from a full shower simulation without adding too much computational time. The semi-analytic method consists of two separate steps for each event.

1. Generate 1D shower proﬁles from a full shower simulation

2. Use generated shower proﬁles to calculate Askaryan signals using analytic functions

In the first step, one obtains the shower profiles, which describe the charge excess as a function of shower depth. Alvarez-Muñiz, et. al. suggest to generate shower profiles using the ZHAireS shower simulation software which is the ZHS software modified to simulate showers in various media including ice [81]. Shower profiles for electromagnetic and hadronic showers are obtained separately as they have different properties. Obtaining the 1D shower profile for a shower is relatively quick and cheap

62 6

magnetic shower with energy E =100EeVfromtheZHS simulation. The fields are observed in the Fraunhofer region at an angle θ = θC 0.3◦ and they are compared to our results obtained with− Eq. (17) using the longitudinal distribution Q(z!) from the same simulation. The agreement between the vector potential obtained directly in the Monte Carlo simulation and the prediction of Eq. (17) lies within a few percent difference in the region relevant to the pulse (top panel of Fig. 3). The difference between this calculation and the ZHS electric field in the time domain is greater (middle panel of Fig. 3), but as shown in the bottom of Fig. 3 this is due mostly to the incoherent emission of the shower at high frequencies. The Fourier- transformed amplitudes of the time-domain electric field obtained in our approach are based on smooth param- eterizations, while the frequency spectrum obtained directly in the ZHS simulation includes incoherence effects coming from the fine structure of the shower at the individual particle level. Note that when f(r!,z!)=δ(r!)/r!, i.e. if we neglect the lateral distribution of the shower, Eq. (17) reduces to the 1-dimensional model in [29] which fails at describing the features of the radio emission for angles close to the FIG. 3. Results of the ZHS Monte Carlo compared to our cal- Cherenkov angle. To illustrate this, we show in the top Figure 5.8:culation Comparison Eq. (17) between for the the radiation full shower due to simulation a 3 1018 (ZHS)eV elec- and the semi- × panel of Fig. 3 the vector potential obtained in the one di- analytic modeltromagnetic of a 3 shower1018 eV observed electromagnetic at θ = θC shower0.3◦ atin a the viewing far-field angle of θ = − mensional (1D) model in [29], which is a linear rescaling θ 0.3 . Thein ice. blue The solid× method curve is shows applied the to result the chargefrom ZHS excess full longitu- shower simulation, C ◦ of the longitudinal charge excess profile, showing a clear the− red dasheddinal curve profile shows obtained the result from from the semi-analytic same simulation. model, Top and panel: the yellow solid disagreement with the results of the full ZHS simulation curve showsVector the result potential from simple in the 1D time-domain model. The top with plot 10 shows ps time the sam- vector potential pling (corresponding to a sampling frequency of 100 GHz) as as expected. R A in the time domain, the middle plot shows the electric field R E in the time obtained in ZHS simulations. This is compared to the calcula- domain,| | and the bottom plot shows the spectrum in the frequency domain.| | All three tion presented in this work. The longitudinal charge profile is plots show that the full ZHS simulation and the semi-analytic method agree well. shown as the 1D model presented in [29] where the depth and C. Askaryan pulses in the “near-field” The disagreementcharge areat the linearly high rescaled frequencies to give seen the in observer the middle time and and bottom vec- plots are not importanttor for potential. ARA as Middle the bandwidth panel: Electric of the system field in only the time-doma goes up toin 1 GHz. Plots from [12]. comparing our method to ZHS results. Bottom panel: The We can now generalize Eq. (17) for an observer in the electric field amplitude spectrum obtained from the ZHS sim- “near-field” region of the shower. In this case it is more ulation and the Fourier transform amplitudes of the electric natural to work in cylindrical coordinates and place the field obtained from the calculation presented in this work. observer at (r cos φ,rsin φ,z). Without loss of generality Note that the discrepancy between the time-domain electric we can again assume the observer is at φ = 0 giving field of the ZHS simulations and our results are due to the 2 2 2 incoherent radiation at high frequencies. x x! = r + r 2rr cos φ +(z z ) . (18) 63 | − | ! − ! ! − ! In dense media,! the lateral distribution is in the scale of centimeters, which means that for all practical purposes the observer is at any given instant in the far-field region emission from the lateral distribution of the shower, with with respect to the lateral distribution. The idea is to the longitudinal profile of the excess charge. The form solve the vector potential in Eq. (4) using the Fraunhofer factor F is a function that has to be evaluated at the p approximation to account for the lateral distribution at time t at which the observer in the far field sees the por- any given time t!. We expand Eq. (18) to first order in tion of the shower corresponding to the depth z!.That r! giving time is given by t = nR/c + z!/v z!n cos θ/c.We − have made the only assumption that the shape of Fp de- 2 2 x x! = r +(z z ) r! sin θ(z!)cosφ!. (19) pends weakly on the stage of longitudinal evolution of the | − | − ! − shower. At the Cherenkov angle, the far-field observer ! 2 2 where sin θ(z!)=r/ r +(z z!) , but we take into ac- sees the whole longitudinal development of the shower count that the distance in the− denominator of the vector at once i.e. z /v = z n cos θ /c in which case Eq. (17) ! ! ! C potential depends on the time t! or equivalently on the reduces to the vector potential at the Cherenkov angle 2 2 position z! in the shower as r +(z z!) . This is in given by Eq. (14). contrast to the case of the far field calculation− in which In Fig. 3 we show an example of the vector potential the distance in the denominator! of the vector potential and electric field in the time-domain due to an electro- is constant and equal to R. in computational time compared with the full shower simulation that calculates the emitted electric field. The Askaryan signals are calculated in the second step. The vector potential from the shower is obtained from the parameterized Green’s function solutions to Maxwell’s equations. These analytic functions have form factor equations which are fitted to the profiles from the full shower simulation for electromagnetic and hadronic shower separately, for different media. The vector potential equation under a far field assumption with a parameterized

form factor Fp from [12] is:

µ ∞ nR 1 n cos θ A~ (θ, t) = sin θ pˆ dz0Q(z0) F t z0 (5.10) 4πR · · p − c − v − c Z−∞

where µ is the permeability of the medium, R is the distance between the shower and the receiver, pˆ is the unit vector pointing along the direction of vector potential, z0 is

the shower depth in meters, Q(z0) is the shower charge excess as a function of depth (Eq. 5.17), n is the index of refraction of the media, c is speed of light, v is the shower propagation velocity, and θ is the angle between the shower axis and the RF signal

propagation direction (viewing angle). The form factor Fp is a key term in Eq. 5.10

which determines the shape of the radiated signal. The form factor Fp equation at the Cherenkov angle is obtained by ﬁtting to the vector potential at the Cherenkov angle to the ZHS full shower simulation. For the case of an electromagnetic shower

64 in ice, the form factor equation at the Cherenkov angle [12] is:

nR 4π 1 1 14 E F t = 4.5 10− p − c µ LQ sin θ × − × TeV total C t 3 | | exp 0.057 + (1 + 2.87 t )− , if t 0  − | | ≥ (5.11)  t 3.5 exp | | + (1 + 3.05 t )− , if t < 0 − 0.030 | |   where LQtotal is integrated shower charge excess (LQtotal = dz0Q(z0)), θC is the Cherenkov angle, E is the energy of the shower, R is the distanceR between the shower and the observer, and t is the time at the observer frame. The time t is deﬁned that t = 0 is when the observer is at a viewing angle of θC and a distance of R, receives the peak vector potential from the shower. For a hadronic shower in ice, the form factor equation is:

nR 4π 1 1 14 E F t = 3.2 10− p − c µ LQ sin θ × − × TeV total C t 3.21 | | exp 0.043 + (1 + 2.92 t )− , if t 0  − | | ≥ (5.12)  t 2.65 exp | | + (1 + 3.0 t )− , if t < 0. − 0.065 | |   With the far field assumption, the equation for the vector potential becomes Eq. 5.10 with either Eq. 5.11 or 5.12 being substituted for Fp with a proper time offset term accounting for the viewing angle (z0[1/ν n cos θ/c] in Eq. 5.10). − After inserting the form factor equations, the electric field as a function of time is the time derivative of the vector potential. This method uses a 1D approximation of the shower profile but yields consistent results with the full 3D shower simulation (Fig. 5.8,[79]). Fig. 5.8 shows the comparison between ZHS [82] full shower simulation result and the semi-analytic model result. They agree well between each other up to few GHz range which is fine for ARA’s 200 MHz to 850 MHz bandwidth.

65 Customized Approach in AraSim The default mode for generating Askaryan signals in AraSim uses a custom parameterized RF Cherenkov model which is a modified approach from the method suggested by Alvarez-Muñiz, et. al. [79] in order to reduce the computational time even more. Generating a shower profile from a full shower simulation software takes hour while our custom parameterized RF Cherenkov model ∼ takes second to calculate the RF signal. Among the two steps described in the be- ∼ ginning of Section 5.2.1, the first step, the full shower simulation, has been replaced by parameterized shower profile functions. The Greisen function [83] and Gaisser-Hillas function [84] are used to produce electromagnetic and hadronic shower profiles [85], respectively. The next step, calculating Askaryan signals using analytic functions, is the same. AraSim, however, has a custom time binning method to optimize the computational time of the second process, which is described in the next paragraph. This alternative method is a quick and easy way to produce a first order estimation of the shower profiles. Detailed Description of the AraSim Custom Parameterized RF Cherenkov Model Our custom parameterized RF Cherenkov model calculates shower profiles from parameterized functions. For the electromagnetic shower, we chose the Greisen function [83] with proper parameter values for in-ice radiation. The Greisen function used in AraSim gives us the total number of electrons and positrons:

0.31 X 1.5X ln ((3X)/(X+2 ln (E0/Ec))) Ntotal(X) = e − (5.13) ln (E0/Ec) · p

66 where Ntotal is total number of electrons and positrons, Ec is a critical energy, 0.073 GeV

in ice, E0 is the energy of the shower in GeV, and X is shower depth in units of radiation length. Fractional excess of electrons (∆N) is given by:

N(e ) N(e+) ∆N = − 0.25 (5.14) − + N(e−) + N(e ) ∼

and the number of excess electrons (Nexcess) is:

N = N ∆N (5.15) excess total ·

Based on the ZHS in-ice shower simulation (Fig. 5.9), a constant 25% fractional excess of electrons in the shower is chosen. For hadronic showers, a Gaisser-Hillas function [84] is used to obtain shower pro- ﬁles. As for the electromagnetic shower case, parameter values for the Gaisser-Hillas function are chosen for in-ice radiation:

E X λ X Xmax/λ 0 max (Xmax/λ 1) ( X/λ) N (X) = S − e − e − (5.16) total 0 · E · X · X λ · c max max −

2 2 where S0 is 0.11842, λ is 113.03 g/cm , X0 is 39.562 g/cm , Ec is 0.17006 GeV, E0 is the energy of the shower in GeV, and X is shower depth in g/cm2. As for the electromagnetic shower case, we use a constant 25% charge excess over the entire shower. For both electromagnetic and hadronic showers, the charge excess is then:

Q(X) = q N . (5.17) · excess

where q is an electric charge of an electron.

67 Figure 5.9: Fractional excess of electrons from ZHS in-ice simulation. Horizontal axis shows the shower depth in ice. The plot shows that fractional excess of electrons varies from 20% at the beginning of a shower to 30% for larger depths regardless of the energy of the shower. Based on this plot, constant 25% excess of electrons is chosen.

68 We deﬁned a bin size in time for calculating the vector potential in Eq. 5.10 to obtain proper length of the signal with 64 bins. This constant number of bins give us a constant computation time to calculate the signal. In Eq. 5.10, we must integrate

the right-hand-side of the equation over the length of the shower for each time bin ti. The time duration of the signal change as a function of the viewing angle θ [79] and in order to include entire signal waveform in constant 64 bins, we change the size of the time bin as a function of the viewing angle (in Eq. 5.19). While the duration of the signal is minimal when the viewing angle is at the Cherenkov angle, θ = θC , the signal gets stretched in time when the viewing angle is further away from the Cherenkov angle. This is due to the fact that all signals radiated from charged particles in the shower arrive at the receiver at the same time when the receiver is located right at the Cherenkov angle relative to the shower axis. We deﬁne a factor that is a measure of how oﬀ the Cherenkov angle the observer sits:

f 1 n cos θ. (5.18) oﬀcone ≡ − ·

And using this factor, we deﬁne the total duration of the signal:

T = f T A + 2 ns (5.19) total | oﬀcone| · shower · 0

where Tshower is the total travel time of the shower in the medium in ns, and A0 is a constant parameter value which changes the total length of the signal. The A0 value is chosen such that T at θ = θ 10◦ give us a long enough length of time total C ± to include the entire signal (A0 = 1.2). If the receiver is located at the Cherenkov angle relative to the shower axis, then foﬀcone becomes zero and Ttotal will be 2 ns. We calculate the RF Cherenkov signal with 64 time bins for all cases. Therefore, the

69 time domain bin size is:

∆t = Ttotal/64. (5.20)

Our custom parameterized RF Cherenkov emission mode in AraSim shows consistent results with results from the ZHS simulation. Fig. 5.10 shows a shower profile for a 1 PeV electromagnetic shower from AraSim and ZHS simulation. Since it is an electromagnetic shower, AraSim uses a Greisen function (Eq. 5.13) to generate the shower profile. From the shower profile, AraSim calculates the vector potential (Fig. 5.11). From the time derivative of the vector potential (E~ = ∂A~ /∂t), the − electric field is obtained in Fig. 5.12. Again, the plot shows the result from AraSim and the ZHS simulation which agree well with each other. This example shows that our custom parameterized RF Cherenkov emission mode in AraSim generates the RF signal which agree well with ZHS full shower simulation. This custom parameterized RF Cherenkov emission model produces the electric field in the time-domain directly from a custom shower profile. This way, we have improved phase information for each signal compared to the former RF emission model (Section 5.2.2). Limitations of Custom Parameterized RF Emission Model One drawback of the current version of this method is that we cannot account for the Landau-Pomeranchuk- Migdal (LPM) effect [86,87] in the shower as we use the parameterized shower profile functions. The LPM effect becomes significant when the energy of the particle in the shower is larger than the LPM threshold energy (E = 2 1015 eV in ice). Then, the LPM × Bethe-Heitler radiation length and the mean free path for the pair production become comparable. This means there is an interference between a radiated photon and

70 Total N (e- + e+ ), EM, 1e15eV

) 6

+ 10 + e - N (e

105

Total N (e- + e+ ), EM, 1e15eV

) 64

+ 1010 + e - N (e

5 10 0 200 400 600 800 1000 1200 1400 1600 1800 g/cm2

Excess electrons (e- - e+ ), EM, 1e15eV 104 ) + - e - 105 N (e 0 200 400 600 800 1000 1200 1400 1600 1800 g/cm2

104 Excess electrons (e- - e+ ), EM, 1e15eV

Figure 5.10: Shower) proﬁles from AraSim and ZHS simulation for 1 PeV electro- +

magnetic shower.The - e black curve is obtained from AraSim using Greisen function - 105 (Eq. 5.13), and the red103 curve is obtained from [13] Fig. 3 which is the result from the ZHS simulation. N (e

0 2 4 6 8 10 12 14 16 18 20

104 m

Vector potential viewangle 65.8 ×10-12

103 A(t) 0

-10 2 4 6 8 10 12 14 16 18 20 m

-2 Vector potential viewangle 65.8 ×10-12 -3

A(t) 0

-4 -1

0 5 10 15 20 -2 time (ns)

-3 Electric field viewangle 65.8 Figure 5.11: Vector potential obtained from AraSim for the same shower shown in 0.002

Fig. 5.10. Here, theE(t) vector-4 potential is calculated 1 m from the shower. Viewing angle 0.0015 is θ = θC + 10◦ = 65.8◦. 0 5 10 15 20 0.001 time (ns)

0.0005 Electric field71 viewangle 65.8 0 0.002 E(t) -0.0005 0.0015

-0.001 0.001

-0.0015 0.0005 0 5 10 15 20 time (ns) 0

-0.0005 Voltage spectrum viewangle 65.8

-0.001

10-2 -0.0015 0 5 10 15 20 time (ns)

Voltage spectrum viewangle 65.8 V/Hz (factors missing)

10-3 10-2

3 1 10 102 10 freq (MHz) V/Hz (factors missing)

10-3

3 1 10 102 10 freq (MHz) Total N (e- + e+ ), EM, 1e15eV

) 6

+ 10 + e - N (e

105

104

0 200 400 600 800 1000 1200 1400 1600 1800 g/cm2

Excess electrons (e- - e+ ), EM, 1e15eV ) + - e - 105 N (e

104

103

0 2 4 6 8 10 12 14 16 18 20 m

Vector potential viewangle 65.8 ×10-12

A(t) 0

-1

-2

-3

-4

0 5 10 15 20 time (ns)

Electric field viewangle 65.8

0.002 E(t)

0.0015

0.001

0.0005

-0.0005

-0.001

-0.0015 0 5 10 15 20 time (ns)

Voltage spectrum viewangle 65.8 Figure 5.12: Electric field in the time domain from AraSim compared to ZHS simulation for the same shower10-2 as shown in Fig. 5.10 and 5.11. The black curve is obtained from AraSim, and the red curve is obtained from [13] Fig. 3 which is the result from ZHS simulation. Even though there was some disagreement in the shower profile (Fig. 5.10), the overall electric field signal power don’t differ by more than 25%. V/Hz (factors missing)

10-3 a subsequent interaction (or in other words, interference between Bremsstrahlung interaction and pair production). This interference increases the interaction length

3 1 10 102 10 in the shower. freq (MHz) We will revise the method in order to account for the LPM effect in the future. One quick-and-dirty way to account the LPM effects is to simply stretch the shower profile by factor of:

E 0.3 F (E ) = LPM (5.21) 0 0.14 E + E · 0 LPM where ELPM is the LPM eﬀect threshold energy which is 2 PeV for ice, and E0 is the energy of the shower [88]. When we stretch the shower proﬁle by F (E0), we have to conserve the total number of produced particles in the shower (LQtotal = dz0Q(z0)). R

72 Therefore, we have to apply a factor 1/F (E0) to the shower charge excess:

1 Q0(z0) = Q(z0) . (5.22) · F (E0)

Another method which is more sophisticated is to use shower profile, that are generated from a shower simulation that includes the LPM effect. In order to reduce the computation time of the simulation, we can first generate a library of shower profiles for different shower energies using a shower simulation such as ZHAireS. While running the AraSim simulation, we can choose one of the shower profiles from the library for the corresponding shower energy. These improvements will be added to AraSim as a separate simulation mode in near future. For now, we found the amount that the sensitivity changed due to the LPM effect using the old parameterized AVZ model (Section 5.2.2) turned on and off. We accounted the same factor to the sensitivity obtained using our custom parameterized RF Cherenkov emission mode.

5.2.2 Parameterized AVZ RF Cherenkov emission model

The second mode for generating Askaryan signals in AraSim is based on the fully parameterized RF Cherenkov emission model by Alvarez-Muñiz,Vãzquez and Zas (AVZ model) [80]. While the default Cherenkov emission model in AraSim (Sec- tion 5.2.1) produces the electric field with improved phase information, the second

mode calculates the electric ﬁeld with a trivial 90◦ phase in positive frequencies and

90◦ phase in negative frequencies. From the AVZ model, which is a fully param- − eterized model of the frequency spectrum using a 1D approximation of the shower, the electric ﬁeld spectrum at the Cherenkov angle is:

1 7 E0 ν 1 R E~ (ω, R, θ ) 2.53 10− (5.23) | C | ' 2 × × TeV ν 1 + (ν/ν )1.44 0 0

73 where ν0 = 1.15 GHz, E0 is the energy of the shower, and the unit of the equation is V/MHz. The very ﬁrst 1/2 factor is added to the original Eq. 5 in [80]. This is due to the fact that the AVZ model is based on the ZHS model [82] which uses an unconventional Fourier transform equation (Eq. 8 in [82] contains a factor of 2 compared to the conventional Fourier transform equation:

E~ (ω, ~x) = 2 dteiωtE~ (t, ~x) (5.24) Z while Fourier transforms in AraSim follows conventional transform:

E~ (ω, ~x) = dteiωtE~ (t, ~x). (5.25) Z

Also, one point to note is that both [80] and [82] calculate a double-sided electric ﬁeld spectrum, which means even if there is only a spectrum for positive frequencies shown in the plots, there is the same amount of power in the negative frequencies. As the Fourier transform in AraSim assumes a double-sided spectrum, there is no additional factor needed to account double-sided spectrum in Eq. 5.23. In this model, the electric ﬁeld spectrum at a viewing angle away from the Cherenkov angle is obtained by applying a parameterized factor. This factor depends on the width of the Cherenkov cone, which depends on the length of the shower. The longer the length of the shower, the narrower the width of the Cherenkov cone become. The width of the Cherenkov cone for the electromagnetic shower [88] in AraSim is:

ν E 0.3 ∆θ (ν) = 2.7 0 LPM (5.26) em · ν 0.14E + E ν LPM

74 where ν0 = 1.15 GHz, ELPM is the LPM effect threshold energy which is 2 PeV for ice, and Eν is the energy of the electromagnetic shower. Eq. 5.26 above shows that the width of the Cherenkov cone depends on the LPM threshold energy. Since the LPM effect shows up predominantly in electromagnetic showers, AraSim only accounts for this lengthening effect in electromagnetic showers. The width of the Cherenkov cone for hadronic showers is parameterized for different shower energies in [89]. The angular width of the Cherenkov cone is:

ν0 2 ν (2.07 0.33 + 0.075 ), if 0 < 2  − ≤  ν  0 (1.744 0.0121), if 2 < 5  ν − ≤   ν ∆θhad =  0 (4.23 0.785 + 0.0552), if 5 < 7 (5.27)  ν − ≤  ν0 (4.23 0.785 7 + 0.055 72)  ν − × ×    [1.0 + ( 7.0) 0.075], if 7 × − × ≥    where = log10 Eν/TeV. The electric ﬁeld at a viewing angle θ depends on the signal strength at the

Cherenkov angle θC and the width of the Cherenkov cone ∆θ [88, 89]. The equation is:

sin θ θ θ 2 E(θ) = E(θ ) exp − C (5.28) sin θ C · − ∆θ C " em,had #

where the signal strength at the Cherenkov cone, E(θC ), is from Eq. 5.23, and the width of the Cherenkov cone for electromagnetic and hadronic showers are given at Eq. 5.26 and 5.27, respectively. The default custom parameterized RF emission model and the AVZ RF emission model show results comparable with each other. Fig. 5.13 shows an example spectrum

75 Org SP VA 50.8, Pol 0, AntTheta 90, AntPhi 360, TotalP 1.1e-17 V/MHz

10-7

10-8 Spectrum Magnitude (V/MHz)

10-9 1 10 102 103 freq (MHz) Frequency (MHz)

Figure 5.13: Comparison of spectra obtained from the two Cherenkov emission modes in AraSim. The red curve is obtained from the AVZ RF model and the black curve is the result from custom parameterized RF Cherenkov model (Section 5.2.1). Both results have exactly same shower parameters (electromagnetic shower with 10 TeV energy and viewing angle of θ = θC 5◦). The two RF signal emission models show consistent results. −

from the two models with the same shower parameters. Overall the maximum electric field signal difference between the two modes for various shower conditions we tested was 70% where as for most cases the difference was 40%. Considering that the ∼ two models use a significantly different approach, we think the difference between two models is reasonable. For the analysis presented in this paper, we use the first custom parameterized RF Cherenkov model as a default model while we considered the AVZ emission model with a simple model for the detector phase response to estimate a systematic error in Section 6.6.

76 5.3 Calibrating AraSim to the Testbed Data

Calibrating the simulation to data is very important as we are modeling our sensitivity to neutrinos with our simulation. Here we will show how we calibrated thermal noise waveforms and trigger thresholds.

5.3.1 Calibrating Thermal Noise

Thermal noise events dominate the triggered background events from the ARA detector. Therefore, calibrating our thermal noise model to measured data is essential. There are multiple steps for calibrating thermal noise which are going to be explained in following paragraphs. Thermal Sample We first have to select events that are minimally contaminated by anthropogenic noise. The software trigger causes an event to be recorded every second to monitor the RF background. While there is a chance that an event was triggered by both the software trigger and RF triggers, we selected events that are only triggered by the software trigger in order to avoid contamination from anthropogenic backgrounds such as continuous wave (CW) and impulsive signals. Make Waveforms have Consistent Binning As the thermal noise calibration will be done for each frequency bin separately, it is crucial to make each channel and event have the same binning in the frequency domain. From the collected software triggered sample, we make the waveforms in all channels and events have the same number of bins and bin size in time. Due to the limitation in the Testbed DAQ, the number of bins of the waveform varies 10 between events and bin size is not constant. ∼ ± This can be achieved by making time domain waveforms with the same number of bins and the same bin size. We force the waveforms to have the same number of bins by zero-padding them. We made all waveforms have 1024 bins by filling up the first

77 512 bins with the original waveform data and setting the rest of the bins to zero. ∼ After that, we make the zero-padded waveform to have a constant 0.5 ns bin size by interpolating. We use the interpolation function in the ROOT software with the “AKIMA” option, which uses a continuously diﬀerentiable sub-spline interpolation function. Make Frequency Domain Spectrum Using the waveforms that are processed up to the previous step, we produce the frequency domain spectrum from the time domain waveform using a Fast Fourier Transform (FFT). As all channels and events have the same time binning, the frequency domain spectrum will also have the same binning between channels and events. Fit Normalized Plots with Rayleigh Distribution Function We ﬁt the normalized distribution plot with the Rayleigh probability density function:

x x2/(2σ2) f(x; σ) = e− (5.29) freq,ch σ2 where x is the voltage at specific frequency (freq), channel (ch) and σ is the only fit parameter value which is called the scale parameter. We obtained the fit parameter σ for all channels and frequency bins separately. We apply a normalization factor to each plot such that

∞ f(x; σ)freq,chdx = 1. (5.30) Z0 The normalization is done by multiplying by a normalization factor:

1 N = (5.31) n ∆ i i · bin P

78 0.45 Evts 0.4 0.35 0.3 Normalized Events 0.25 0.2 0.15 0.1 0.05 0 -1 0 1 2 3 4 5 6 7 8 Spectrum MagnitudeVoltage/Freq [Volts/Hz]

Figure 5.14: Distribution of voltages at 200 MHz and its best-fit Rayleigh distribution function. Thermal noise events from Testbed data set (software triggered events, blue curve) and their best-fit Rayleigh distribution function (red curve) are shown. The voltage distribution at 200 MHz, Channel 2 (Vpol antenna) is chosen for the plot and the integral is normalized to 1 in order of have same normalization for the Rayleigh distribution function (Eq. 5.29). Good agreement between the distribution and the fit function is shown on the plot.

th where N is the normalization factor, ni is the number of events in i bin, and ∆bin is the bin size of the distribution plot. Fig. 5.14 shows a example of the voltage distribution and its Rayleigh distribution fit result for Channel 2 at 200 MHz (Channel 2 shown in Table 4.1). Generate Thermal Noise Waveforms We use the fit results to generate thermal noise waveforms. A noise waveform for a channel is generated by selecting a voltage for each frequency bin from the fitted Rayleigh probability density function. Each frequency bin has a random phase chosen between 0 and 2π. Figs. 5.15 and 5.16 show the comparison between simulated thermal noise waveforms and the waveforms

79 rms hist ch0 rms hist ch1 rms hist ch2 rms hist ch3 rms hist for TB ch0 rms hist for TB ch1 rms hist for TB ch2 rms hist for TB ch3 5 10 Entries 194139 Entries 194139 Entries 194139 Entries 194139 evts Mean 38 evts Mean 49.52 evts Mean 58.61 evts Mean 43.62 RMS 1.97 RMS 2.279 RMS 2.967 RMS 2.327 4 4 Events 10 104 104 10

3 3 10 3 103 10 10

2 2 10 2 102 10 10

10 10 10 10

1 1 1 1

0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 mV mV mVmV mV rms hist ch4 rms hist ch5 rms hist ch6 rms hist ch7 rms hist for TB ch4 rms hist for TB ch5 rms hist for TB ch6 5 rms hist for TB ch7 5 105 10 10 Entries 194139 EntriesFigure 194139 5.15: Plot of the RMS voltage distribution from generatedEntries 194139 thermal noise Entries 194139 evts Mean 32.8 evts Meanwaveform 47.91 using theevts best-ﬁt Rayleigh distribution. The red curveMean is 40.22 the distributionevts Mean 36.1 RMS 1.888 RMS 7.839 RMS 4.466 RMS 1.904 4 from generated thermal noise waveforms, while the blue curve is from Testbed data. In 10 4 4 104 the Testbed data set10 (blue curve), there is an extended tail feature which the simulated10 noise doesn’t have. This tail is coming from non-thermal background events such as CW and anthropogenic impulsive events. Overall, the dominant thermal noise part 103 3 103 is well match between103 the data and the simulation. 10

2 2 102 10 102 10 from Testbed software-triggered events. Both plots show that the thermal noise part of the distribution (lower voltages) agree well between each other, while the Testbed 10 10 10 10 data has extra non-thermal anthropogenic background events, which make up the

1 1 extended tail on the1 plot. Those non-thermal backgrounds are not reproducible with1

0 20 40 60 80 100 120 0 20 40 60 80 100 the120 ﬁtted Rayleigh distribution0 20 as only40 the pure60 thermal80 noise100 will120 follow the Rayleigh0 20 40 60 80 100 120 mV mV mV mV distribution.

80 peak hist ch0 peak hist ch1 peak hist ch2 peak hist ch3 peak hist for TB ch0 peak hist for TB ch1 peak hist for TB ch2 peak hist for TB ch3 Entries 194139 Entries 194139 Entries 194139 Entries 194139 evts evts evts evts Mean 131.2 Mean 171.8 4 Mean 200.3 Mean 147.8 104 10 4 104 RMS 17.11 RMS 22.42 RMS 24.77 10 RMS 19.11 Events

3 3 10 3 103 10 10

2 2 102 10 10 102

10 10 10 10

1 1 1 1

0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 mV mV mVmV mV peak hist ch4 peak hist ch5 peak hist ch6 peak hist ch7 peak hist for TB ch4 peak histFigure for TB ch5 5.16: Plot of the distribution of peak voltages from thermalpeak hist for TB noise ch6 waveforms peak hist for TB ch7 Entries 194139 Entries 194139 Entries 194139 Entries 194139 evts Mean 121.5 evts Meangenerated 178 using theevts best-ﬁt Rayleigh distribution and TestbedMean data. 145.7 The red curveevts is Mean 130 4 10 the distribution from4 the generated thermal noise waveforms, while the blue curve4 is 104 RMS 17.14 RMS 36.36 10 RMS 23.67 10 RMS 17.29 from the Testbed data. The part of the distribution at low voltages shows agreement between simulated noise and the data. Like the RMS distribution (Fig. 5.15), the

3 extended tail feature in the data set is due to non-thermal background events such 3 10 3 3 10 as CW and anthropogenic10 impulsive events. 10

2 2 2 102 10 10 10

10 10 10 10

81 1 1 1 1

0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 mV mV mV mV 5.3.2 Calibrating the Trigger Threshold

The trigger threshold is directly related to our sensitivity to neutrinos. The best situation to calibrate the trigger level in the simulation would be one where the actual hardware trigger level is well understood which is not the case for the Testbed. Therefore we had to find the variable the most sensitive to the trigger threshold and use it to calibrate the simulation. Our calibration procedure relies on two properties of the trigger in the Testbed. First, a tunnel diode is used in the detector which means the trigger is sensitive to power. Second, the TestBed station requires three or more channels pass the trigger threshold within a 100 ns coincidence window. Combining the first and second conditions, we decided to use the third highest peak square voltage among channels in the trigger coincidence window as the variable sensitive to the trigger threshold (3rd highest V 2). We found the timing of the trigger coincidence window with respect to the stored waveform for each channel separately (red boxes shown in Fig. 5.17). Using calibration pulser events in the data and the simulation, we reproduced calibration pulser events in the simulation and tuned the time difference between the trigger coincidence window and the timing of actual stored waveforms (result shown in Table. 5.1). For this, the unknown trigger threshold level is not crucial as the calibration pulser signal is a strong impulsive signal. Once we set the trigger threshold level high enough to avoid any trigger contamination from the thermal noise, this trigger coincidence window search is good to go. Using the known distribution of trigger coincidence window timings with respect to the waveform, we found the 3rd highest V 2 inside the trigger coincidence window, which is the variable sensitive to the trigger threshold. One example of finding the 3rd highest V 2 from a calibration pulser event data is shown in Fig. 5.17. In order

82 Ch0 Ch1 Ch2 Ch3 mV mV mV mV 1st peak V2

2nd peak V2

Time (ns) Time (ns) Time (ns) Time (ns) Ch4 Ch5 Ch6 Ch7 2

mV mV 3rd peak V mV

Time (ns) Time (ns) Time (ns) Time (ns)

Figure 5.17: One example of ﬁnding the trigger-threshold sensitive variable from 8 borehole channels. The trigger-threshold sensitive variable is the 3rd highest peak square voltage among channels in trigger coincidence window. In the plots, red box is the trigger coincidence window for each corresponding channel. In the plots, Chan- nel 0 has the highest peak V2 among all channels, Channel 1 has the send highest peak V2, and Channel 5 has the 3rd highest peak V2 which is the trigger sensitive variable. The distribution of this trigger-threshold sensitive variable is shown in Fig. 5.18.

Channel Number 0 1 2 3 4 5 6 7 Waveform Time Oﬀset (ns) 0 +50 -10 +20 +30 +20 -10 +10

Table 5.1: The tuned time oﬀset between channels by comparing Testbed calibration pulser waveforms and simulated calibration pulser waveforms. Oﬀset values are obtained with respect to Channel 0.

83 Channel Number 0 1 2 3 4 5 6 7 Trigger Threshold -6.1 -5.4 -5.8 -5.5 -5.1 -5.9 -5.5 -5.9

Table 5.2: The trigger threshold obtained from the minimum χ2 between the simulation and the Testbed data. The unit of trigger threshold is RMS of tunnel diode output from thermal noise waveform.

to calibrate the trigger level for each individual channel, we generated numerous thermal noise simulation sets with diﬀerent trigger threshold levels. For each channel separately, we obtained the distribution of the 3rd highest V 2 from the thermal noise simulations and Testbed data (see Fig. 5.18) with diﬀerent trigger threshold values. The unit of trigger threshold is RMS of tunnel diode output from thermal noise waveform. As tunnel diode is a power integrator, trigger threshold is proportional to the power of the input waveform over 10 ns (Section 4.1). For the Testbed ∼ data, we applied quality cuts and a stringent CW cut to remove CW contamination from the data set. From the distributions, we found the threshold which gave us the minimum χ2 between the simulation and the Testbed data. The trigger threshold values that gave the minimum χ2 between the simulation and the Testbed data are shown in Table. 5.2. After the calibrations on the thermal noise and trigger threshold are done, we generated numerous neutrino simulation sets for our data analysis.

Appendix: First estimation on Ray Tracing

RaySolver in AraSim uses a semi-analytic approach to obtain the ﬁrst estimated launching angle at the source location given the horizontal distance to the source and indices of refraction at the source and target. Here, we provide the derivation of Eq. 5.3 for the exponential index of refraction model. The index of refraction model

84 3rd peak hist ch0 3rd peak hist ch1 3rd peak hist ch2 3rd peak hist ch3 peak ch0 3th file0 peak ch1 3th file0 peak ch2 3th file0 peak ch3 3th file0 Entries 15955 Entries 81457 Entries 53307 Entries 39892 evts evts -1 evts -1 evts -1 10-1 Mean 2.576e+04 10 Mean 2.614e+04 10 Mean 2.791e+04 10 Mean 2.559e+04 RMS 4486 RMS 4673 RMS 4701 RMS 4491

-2 10 -2 10-2 10 10-2 Normalized Events

10-3 10-3 10-3 10-3

10-4 10-4 10-4 10-4

10-5 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000 peak Vsq (mV^2) peak Vsq (mV^2) P ea kpeak Vo lta Vsq g e 2(mV^2) (mV2) peak Vsq (mV^2)

3rd peak hist ch4 3rd peak hist ch5 3rd peak hist ch6 3rd peak hist ch7 peak ch4 3th file0 peak ch5 3th file0 peak ch6 3th file0 peak ch7 3th file0 Entries 6953 EntriesFigure 71594 5.18: Comparison between the simulated triggeredEntries events 53411 and Testbed RF Entries 22207

evts evts -1 evts evts Mean 2.514e+04 10 Meantriggered 2.688e+04 events10 for-1 Channel 2. The trigger threshold valueMean used 2.591e+04 for the simulation-1 Mean 2.563e+04 10-1 10 RMS 4393 RMS set give 4767 us the minimum χ2 from the Testbed data. GoodRMS agreement 4633 between the RMS 4496 simulation and the data is shown.

-2 10 10-2 10-2 10-2

-3 10 10-3 10-3

10-3 10-4 10-4 85 10-4

10-4 10-5 10-5 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000 0 10000 20000 30000 40000 50000 60000 peak Vsq (mV^2) peak Vsq (mV^2) peak Vsq (mV^2) peak Vsq (mV^2) is given as:

C z n(z) = A + Be · (5.32)

where n is index of refraction value, z is the depth, and A, B, and C are ﬁtted parameter values from the South Pole measurements. From the above equation, we can obtain:

dn = BCeC z dz · dn BCeC z = · dz, . (5.33) C z n A + Be ·

Now we take θ to be the launch angle of a signal with respect to the normal to the surface. Taking nr and sin θ for the index of refraction and refracted angle with respect to normal, we can derive using Snell’s law:

n sin θ = nr sin θr n sin θ dn = − r r cos θdθ sin2 θ dn = cot θdθ (5.34) n −

where θ is the direction of the ray with respect to the direction normal to the surface.

86 Using Eq. 5.33 and 5.34 and integrating from the source location to the target location, we obtain:

z BCeCz θ = cot θ A + BeCz − Zz0 Zθ0 C z z θ ln(A + Be · 0 ) = ln(sin θ0) z0 − θ0 C z A + Be · sin θ0 = C z0 A + Be · sin θ A + BeC z0 θ = arcsin sin θ · . (5.35) 0 A + BeC z · where θ0 is the launch angle at the source location with respect to normal to the surface and z0 is the depth at the source. Using Eq. 5.35 and the relation dx/dz = tan θ:

A + BeC z0 dx = tan arcsin sin θ · dz (5.36) 0 A + BeC z · and integrating the equation from the source location to the target location, we obtain:

z C z0 A + Be · x x0 = tan arcsin sin θ0 dz0 − A + BeC z0 Zz0 · z C z0 sin θ0(A + Be · ) = dz0. (5.37) C z 2 z0 sin θ0(A+Be 0 ) Z C z0 · A + Be · 1 C z − A+Be · 0 r

87 In order to make above Eq.5.37 more manageable, we let:

σ sin θ 0 ≡ 0 C z n A + Be · ≡ dn = BCeCzdz dn dz = (5.38) C(n A) − and with these substitutions, Eq. 5.37 becomes:

n σ0n0 dn0 x x0 = 2 − C n0 σ0n0 Z n0(n0 A) 1 − − n0 n C qdn0 (x x0) = . (5.39) 2 2 2 σ0n0 − n (n A) n σ n Z 0 0 − 0 − 0 0 p Now substituting n with m n A, the equation becomes: ≡ −

C (x x0) σ0n0 − m dm = 0 . (5.40) 2 2 2 2 m m m + 2Am + A σ n Z 0 0 0 0 − 0 0 p From Eq. 5.40, we can make the equation more compact with an additional sub-

2 2 2 2 stitution X a + bm0 + cm0 where a = A σ n , b = 2A, and c = 1. With the ≡ − 0 0 replacement, the equation is now:

m C dm0 (x x0) = . (5.41) σ0n0 − m √X Zm0 0

With the condition that a 0 due to the fact that A is the index of refraction ≥ value at the deep ice and σ = sin θ 0, the integration of the right-hand-side of 0 0 ≥

88 the Eq. 5.41 can be solved using [90]:

dx 1 2a + bx + 2√aX = − ln . (5.42) x√X √a x Z !

After the integration from Eq. 5.40, the equation becomes:

C A2 σ2n2 − 0 0 (x x) σ n 0 p 0 0 − (n2 σ2n2)(A2 σ2n2) + An σ2n2 = ln − 0 0 − 0 0 − 0 0 n A p − ! (n2 σ2n2)(A2 σ2n2) + An σ2n2 ln 0 − 0 0 − 0 0 0 − 0 0 . (5.43) − n A p 0 − !

This is Eq. 5.3, and all values are given parameters from the index of refraction model and the source and target locations except the launching angle σ0 which is the single unknown.

89 Chapter 6

A Search for UHE Neutrinos in the Testbed Station of the

Askaryan Radio Array

The contents of this chapter are largely taken from [2].

The Askaryan Radio Array (ARA) is an ultra-high energy (UHE, > 1017 eV) cosmic neutrino detector in phased construction near the South Pole. ARA searches for radio Cherenkov emission from particle cascades induced by neutrino interactions in the ice using radio frequency antennas ( 150-800 MHz) deployed at a design ∼ depth of 200 m in the Antarctic ice. A prototype ARA Testbed station was deployed at 30 m depth in the 2010-2011 season and the first three full ARA stations were ∼ deployed in the 2011-2012 and 2012-2013 seasons. We present the first neutrino search with ARA using data taken in 2011 and 2012 with the ARA Testbed and the resulting constraints on the neutrino flux from 1017-1021 eV.

6.1 Introduction

The Askaryan Radio Array (ARA) aims to measure the ﬂux of ultra-high energy (UHE) neutrinos above 1017 eV. While UHE neutrinos are so far undetected, they are expected both directly from astrophysical sources and as decay products from the

90 GZK process [21, 22], as first pointed out by Berezinsky and Zatsepin [91, 92]. The GZK process describes the interactions between cosmic rays and cosmic microwave and infrared background photons above a 1019.5 eV threshold. ∼ The interaction of a UHE neutrino in dense media induces an electromagnetic shower which in turn creates impulsive radiofrequency (RF) Cherenkov emission via the Askaryan effect [61, 62, 93–96]. In radio transparent media, these RF signals can then be observed by antenna arrays read out with GHz sampling rates. ∼ Currently, the most stringent limits on the neutrino flux above 1019 eV have been placed by the balloon-borne ANITA experiment sensitive to impulsive radio signals from the Antarctic ice sheet [9]. Below 1019 eV, the best constraints on the neutrino flux currently come from the IceCube experiment, a 1 km3 array of photomultiplier tubes in the ice at the South Pole using the optical Cherenkov technique [11]. Ice- Cube has recently reported the first cosmic diffuse neutrino flux, which extends up to 1015 eV. This is two orders of magnitude lower energy than ARA’s energy ∼ threshold [97]. Due to the 1 km radio attenuation lengths in ice [31,98], radio arrays have the ∼ potential to view the 100s of km3 of ice necessary to reach the sensitivity to detect 10 events per year from expected UHE neutrino fluxes. ∼

6.2 Method

Our analysis reconstructs events using an interferometric map technique. For this analysis, we consider RF triggered events from January 8th, 2011 to December 31st, 2012 and use a set of optimized cuts using AraSim calibrated against Testbed data to eliminate background events from our ﬁnal sample. This analysis is performed in two stages. Stage 1 was a complete analysis on a limited data set that had been processed at an early period of data processing. This Stage 1 analysis is carried on

91 data from February-June of 2012 only, optimizing cuts on the 10% set before opening the box on that time period alone. Then, in Stage 2 the analysis is expanded to the remainder of time in the two year period once more processed data became available. In Stage 2, the cuts were re-optimized on the 10% set for the two year period but excluding February-June 2012 which had already been analyzed.

6.2.1 Testbed Local Coordinate

All the correlation and interferometric maps shown in this analysis are based on the Testbed local coordinate system which is defined with the +ˆx along the direction of the ice flow. The x y plane is a tangent to the geoid at the time the Testbed is − deployed andz ˆ is defined asz ˆ =x ˆ yˆ. The origin of the coordinate is the mean of × the antenna positions which is 20 m deep in the ice for the Testbed. The azimuthal ∼ angle at φ = 0◦ is the direction towards +ˆx, and φ = 90◦ is +ˆy direction. The zenith

angle θ = 0◦ the horizontal direction from the origin, while θ = +90◦ and θ = 90◦ − are +ˆz and zˆ direction, respectively. −

6.2.2 Analysis Cuts

Here we begin a description of all of the cuts applied in the Interferometric Map Analysis. In both stages of the analysis, ﬁrst we apply Event Quality Cuts to reject anomalous electronics behavior. Due to the increase in radio backgrounds during the summer season at the South Pole, we only allow events from February 16th to October 22nd in each year to pass our cuts. This period is selected based on the IceCube drilling periods in the 2011 to 2013 seasons. The period from April 6th to May 12th 2012 was characterized by consistent instability in the digitization electronics and thus this period is excluded as well. We remove calibration pulser events with a timing cut of width 80 ms centered around the beginning of the GPS second, which is when the

92 Graph Graph Graph Graph

400 600 400 400 mV 300 300 300 400 200 200 200

100 200 100 100

0 0 0 0 -100 -100 -100 -200 -200 -200 -200 -300 -300 -300 -400 -400 -400 -150 -100 -50 0 50 100 -200 -150 -100 -50 0 50 -150 -100 -50 0 50 100 -150 -100 -50 0 50 Time (ns)

Graph Graph Graph Graph

400 400 Figure 6.1: An example of an event waveform with a weird electronics error. The 400 300 DC component of the waveform300 provides the power contribution below the 150 MHz 300 300 200 high-pass-filter of the system200 and thus rejected by the Event Quality Cuts. 200 200 100 100 100 100 0 0 0 0 -100 -100 -100 -100 calibration pulser signal is expected to arrive. We also remove events with corrupted -200 -200 -200 -200 waveforms, which comprise-300 1% of the entire data set. We also reject an event if, -300 -300 -300 ∼ -400 -400 -400 in two or more channels, the power in frequencies below the high-pass-filter cut-off -150 -100 -50 0 50 100 -200 -150 -100 -50 0 50 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 frequency of 150 MHz is greater than 10% of the waveform’s power. This cut is Graph Graph Graph Graph designed to eliminate specific electronics errors that are otherwise difficult to identify. 400 500 400 400 400 300 Fig. 6.1 is an example waveform300 which is rejected by this cut. The percentage of 300 300 200 200 200 200 simulated neutrino events rejected by this cut is less than 1%. 100 100 100 100 0 0 We attempt a directional reconstruction for each event using the relative timing 0 0 -100 -100 -100 -100 -200 information and maximizing a summed cross-correlation over a set of hypothesized -200 -200 -300 -200 -300 source positions. We perform a cross-correlation on the waveforms from each pair -300 -300 -400 -400

-400 of antennas of the same polarization. This cross-correlation function measures how -100 -50 0 50 100 150 -100 -50 0 50 100 150 -100 -50 0 50 100 150 -100 -50 0 50 100 150 similar the two waveforms are with a given oﬀset in time. For each pair of antennas, Graph Graph weGraph calculate the expected delays betweenGraph the signal arrival times as a function of the 400 400 300 400 300 position of a putative source300 relative to the center of the station. The center of the 300 200 200 200 200 100 100 100 100 93 0 0 0 0 -100 -100 -100 -100 -200 -200 -200 -200 -300 -300 -300 -300 -400 -400 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 -100 -50 0 50 100 150 -100 -50 0 50 100 150 station is located at the mean of the antenna positions 20 m deep in the ice. These ∼ signal arrival times account for the depth-dependent index of refraction in the ﬁrn layer and the abrupt change at the ice-air interface (Section 5.1.4). If there are two ray trace solutions, only the direct one is considered. For a given source position, the cross-correlation value for an antenna pair is given by:

Nbins V V 1,i · 2,i+n C = i=1 (6.1) NbinsP Nbins 2 2 V1,i V2,i+n s i=1 · s i=1 P P th where V1,i is the voltage in the i bin at the ﬁrst antenna in the pair and V2,i+n is the voltage in the (i + n)th bin at the second antenna where n is the number of bins corresponding to the expected time delay between the antennas for a signal from the putative source position. Then, for each source direction, the correlation values for each pair of antennas of the same polarization are weighted by the inverse of the integrated power of the overlap between the waveforms (denominator of Eq. 6.1) and Hilbert-transformed before being summed together to make the summed cross- correlation. The Hilbert-transformation is done in order to interpret the correlation power. Fig. 6.2 shows an example of obtaining the correlation function from a calibration pulser event. The top two plots are the voltage waveforms from two chosen channels to make the correlation function. The cross-correlation waveform from these two waveforms, using the Eq. 6.1, is shown in the bottom left plot of Fig. 6.2. The ﬁnal correlation function, which is the Hilbert-transformation of the bottom left plot of Fig. 6.2, is shown in the bottom right plot of Fig. 6.2.

94 ch0ch0 ch1ch1 ch2ch2 ch3ch3

200 200 400 400 400 400 200 200 150 150 300mV 300 mV 300 300 100 100 100 100 200 200 200 200 50 50 100 100 100 100 0 0 0 0 0 0 0 0 -50 -50 -100 -100 -100-100 -100-100 -100-100 -200 -200 -200-200 -200-200 -150-150 -300 -300 -300-300

-200-200 -400 -400 -400-400 -150 -150 -100 -100 -50 -50 0 0 50 50 100 100 -200-200 -150-150 -100-100 -50 -50 0 0 50 50 100 100 -150-150 -100-100 -50 -50 0 0 50 50 100 100 -150-150 -100-100 -50 -50 0 0 50 50 100 100 Time (ns) Time (ns)

0.3 ch4ch4 0.4 ch5ch5 ch6ch6 ch7ch7 150 150 400 400 250 250 400 400

300 300 200 200 300 300 100 100 200 200 150 150 200 200 50 050 100 100 100 100 100 100 0 0 50 50 0 0 0 0 -100-100 0 0 -100-100 -50 -50 -50 -50 -200-200

Correlation Factor Correlation Factor -100-100 -200-200 -300-300 -100-0.4-100 0 -150-150 -300-300 -200 0 200 -400-400 -200 0 200 -200-200 -150 -150 -100 -100Time-50 -50 Difference0 0 50 50 (ns)100 100 -150-150 -100Time-100 -50 Difference-50 0 0 50 (ns)50 100 100 -150-150 -100-100 -50 -50 0 0 50 50 100 100 -150-150 -100-100 -50 -50 0 0 50 50 100 100

Figure 6.2: Seriesch8 ofch8 waveforms that show the process to obtainch9ch9 the correlation ch10ch10 ch11ch11 800 800 400 400 function150 150 from a pair of antennas. The top two plots are two voltage waveforms from 400 400 600 600 300 two100 antennas100 that are chosen as a pair to produce the correlation function. All plots 300 300 300 400 are obtained50 50 from same calibration pulser event.400 Both plots are from horizontally 200 200 200 200 0 0 200 200 100 100 polarized antennas Channel 0 and Channel 1, respectively. The bottom left plot is 100 100 -50 0 0 -50 0 0 the cross-correlation waveform from the top two waveforms. The bottom right plot 0 0 -100 -100 -100-100 -200-200 is the Hilbert-transformed of the bottom left plot. -100-100 -150 -150 -200-200 -400-400 -200 -200 -300-300 -200-200 -600-600 -100 -100 -50 -50 0 0 50 50 100 100 150 150 -100-100 -50 -50 0 0 50 50 100 100 150 150 -100-100 -50 -50 0 0 50 50 100 100 150 150 -100-100 -50 -50 0 0 50 50 100 100 150 150

ch12ch12 ch13ch13 ch14ch14 ch15ch15

250 250

400 400 400 400 400 400 200 200 150 150 300 300 200 200 200 200 100 100 200 200 95 50 0 0 50 0 0 100 0 0 100

-200 -200 -50 -50 0 -200-200 0 -100-100 -400 -400 -100-100 -400-400 -150-150 -200-200 -600 -600 -200-200 -150 -150 -100 -100 -50 -50 0 0 50 50 100 100 -150-150 -100-100 -50 -50 0 0 50 50 100 100 -100-100 -50 -50 0 0 50 50 100 100 150 150 -100-100 -50 -50 0 0 50 50 100 100 150 150 90 0.4 90 0.35 Theta (deg) 0 Theta (deg) 0 Correlation Value Correlation Value

-90 0 -90 0 -180 0 180 -180 0 180 Phi (deg) Phi (deg)

90 0.22 90 0.35 Theta (deg) Theta (deg) 0 0 Correlation Value Correlation Value

-90 0 -90 0 -180 0 180 -180 0 180 Phi (deg) Phi (deg)

Figure 6.3: Examples of correlation maps and the final interferometric map from the calibration pulser event (same event with Fig. 6.2). All maps are obtained from 30 m source distance assumption in order to reconstruct the calibration pulser which is located 30 m from the Testbed. The top two plots and the bottom left plot are the correlation∼ maps from different pair of antennas in same polarization. From the Testbed, there are total 6 pairs for each polarization. The correlation value on the map is the projection of the cross-correlation function (bottom right plot of Fig. 6.2) with the corresponding signal travel time difference between the antennas. The bottom right plot is the final interferometric map obtained by summing correlation maps from all pairs with the normalization factor 6 from the number of pairs. The best reconstruction direction from the map (red peak region around 0◦ zenith and 140◦ azimuthal angle) is the direction of the calibration pulser as expected.

96 Summed cross-correlations for each polarization for each event are summarized in

maps with 1◦ 1◦ bins in zenith and azimuth for source distances of 3 km and 30 m × only. We use the 30 m map to determine if the event is a calibration pulser signal that has not been properly ﬂagged, and the 3 km map to determine the reconstruction direction of sources hypothesized to be from far away, such as neutrino events. The two top plots and the bottom left plots in Fig. 6.3 are the examples of correlation map from a pair of antennas for a calibration pulser event (same event as in Fig. 6.2). Each

1◦ 1◦ bin value in the correlation map is the correlation function (bottom right plot × of Fig. 6.2) at the expected signal delay difference between antennas for that source direction and distance. The final interferometric map is obtained by summing all correlation maps with the additional normalization factor 6, which is the number of pair of antennas (bottom right plot of Fig. 6.2). We define the reconstruction direction to be the location of the peak in the interferometric map. Based on the calibration

pulser events, our pointing resolution on the RF direction is 1◦ (Fig. 6.4). ∼ Based on the reconstruction map generated by the interferometric reconstruction technique just described, we decide whether the map is of good quality in terms of pointing directionality. When the signal is coming from one specific location and generates a consistent pattern of waveforms across multiple channels, the reconstruction map will point back to the direction of the source location. A set of Reconstruction Quality Cuts ensure that the event can be characterized by a single well-defined pointing direction that does not have an overly broad spot size on the map. Thermal noise events will not exhibit this strong well-defined peak in an interferometric map. The Reconstruction Quality Cuts also require that any strong correlation is not found in only a single 1◦ 1◦ bin on the map with no other comparable sized correlation values × nearby. This would not be consistent with the antenna and electronics responses of the detector.

97 CalibrationCalPul2012HpolCalPul2012Hpol Pulser Events ThetaTheta Distribution DistDist hCalDist_theta hCalDist_theta Entries 1380 EntriesMean 3.5881380 Mean 3.588 RMS 1.325 Events RMS 1.325 102 102

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102 102

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Figure 6.4: Distribution of calibration pulser events’ reconstructed direction. The top plot is the distribution in zenith angle (θ) diﬀerence between the true direction and the reconstructed direction, while the bottom is the distribution plot in azimuthal angle (φ). Zenith angular resolution is approximately factor of two worse than azimuthal angular resolution due to the error in depth-dependent index of refraction model.

98 The Reconstruction Quality Cuts are based on an area surrounding the peak correlation where the correlation remains high, Apeak, and the total area on the map showing high correlations, Atotal. We first find the 85% contour surrounding the point of peak correlation and the area of that contour in square degrees, which we call Apeak. The choice of the 85% level for the contour was somewhat arbitrary. A different choice would have led to a different maximum allowed Apeak. Fig. 6.5 and 6.6 are examples of an interferometric map and its 85% contour area plot, respectively. The total area on the map that shows a correlation higher than 85% of the maximum correlation value is called Atotal.

The ﬁrst Reconstruction Quality Cut condition requires the size of Apeak to be greater than 1 deg2 and less than 50 deg2. The minimum of that range is the area of a single bin on the map, due to individual time bins in the waveforms and in Fig. 6.7

2 bottom plot shows that this Apeak >1 deg cut doesn’t dramatically affect the neutrino efficiency for the maximal Kotera et al. flux model. The 50 deg2 was chosen because in a distribution of Apeak from calibration pulser events shown in the top plot of Fig. 6.7, it was 2σ away from the mean of the distribution at 36.8 deg2. Note ∼ ∼ that the area of the 85% contour around the peak is not the same as the resolution of the reconstruction. Instead, the area of the contour is related to the width of the readout impulse. The second condition for the Reconstruction Quality Cut requires the ratio between Atotal and Apeak to be less than 1.5. This means that only one reconstruction direction dominates the map. Each event is separated into VPol and HPol channels based on which polarizations pass the Reconstruction Quality Cuts. A VPol or HPol channel is required to pass both Reconstruction Quality Cuts in the 3000 m maps. If an event passes both VPol and Hpol Reconstruction Quality Cuts, that event will be analyzed in both VPol and

99 2012.2.28. run13365 event84 V3000m HilbertCorr, peak at theta -39, phi 9

60 0.1 Theta (DEG) 40

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Figure 6.5: An example of a interferometric map used for reconstruction. This map is obtained from VPol channels with a 3000 m distance assumption from the station. The shadow region due to the ray-tracing in the depth-dependent index of refraction yielded the empty horizontal band in the middle of the plot. The shadow region eﬀect is illustrated in Fig. 5.3. The 85% contour around the peak of this plot is shown in Fig. 6.6.

2012.2.28. run13365 event84 V3000m area 226.5, total area 442.1 1 80 0.9 60 0.8 Theta (DEG) 40

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Figure 6.6: An example of an 85% contour around the peak. This plot of peak area is obtained from Fig. 6.5. The red colored ﬁlled area is the 85% contour region around 2 the peak and the integrated solid angle of the region is Apeak = 226.5 deg .

100 CalPul2012Hpol Theta Dist hCalDist_theta Entries 137804 Mean 3.555 104 RMS 1.304

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Trig Nu V3000 PeakArea Dist KoteraTrig Nu Flux V3000 Model PeakArea Triggered DistEvents zoom Apeak 250 hNuDist_PeakArea_V3000 CalPul2012Hpol DeltaDelay 30m Dist hNuDist_PeakArea_V3000_zoom Entries 10000 EntrieshCalDist_DeltaDelay_30m 10000 700 Mean 6.13 35000 MeanEntries 137804 4.538 Events RMS 8.597 RMSMean -0.108 4.06 200 600 RMS 3.003 30000

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Trig Nu H3000 PeakArea Dist Figure 6.7: The distributionCalPul2012HpolTrig Nu of H3000 85% contour DeltaDelayPeakArea area Dist3000m from zoom Dist 2012 HPol calibration pulser 35000 hNuDist_PeakArea_H3000 hCalDist_DeltaDelay_3000mhNuDist_PeakArea_H3000_zoom 900 300 Entriesevents 10000 (top) and simulated neutrino events from maximalEntries Kotera 137804 10000et al. flux model. Mean From 5.416 the calibration30000 pulser events’ plot, we set the maximumMean allowed 3.9054.719 A at 2σ 800 RMS 8.381 RMS 3.76729.67 peak away from the250 mean of the distribution, at 50 deg2. The signal plot (bottom) shows∼ 700 25000 2 that the minimum allowed Apeak at 1 deg has a minimal effect on the neutrino 600 200 efficiency. 20000 500 150 15000 400

100 300 10000 101 200 500050 100 0 0 0-100 -80 -60 -40 -20 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 12 14 16 18 ns20 deg2 deg2

Trig Nu DeltaDelay 30m, FitSigma:4.5 Trig Nu DeltaDelay 30m Dist abs hNuDist_DeltaDelay_30m 300 hNuDist_DeltaDelay_30m_abs 220 Entries 10000 Entries 10000 200 Mean -0.7934 Mean 20.72 RMS 29.48 250 RMS 20.98 180 160 200 140

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Trig Nu DeltaDelay 3000m, FitSigma:3.0 Trig Nu DeltaDelay 3000m Dist abs 300 hNuDist_DeltaDelay_3000m 350 hNuDist_DeltaDelay_3000m_abs Entries 10000 Entries 10000 Mean -1.857 Mean 19.04 250 RMS 28.36 300 RMS 21.09

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Figure 6.8: All Geometric Cuts for each reconstruction map.

HPol channels. For the purpose of tabulating results, the rest of the cuts are applied to VPol and/or HPol channels separately after the Reconstruction Quality Cut. The cuts applied to each polarization are the same and for any event, one or both channels may pass the cuts. A set of Geometric Cuts reject events that reconstruct to locations where background due to anthropogenic noise is expected to be high, either where there is known human activity or where signals reconstruct to the same location repeatedly. See Fig. 6.8 for all Geometric Cuts for each reconstruction map. The reconstructed directions used for this cut are derived using the interferometric reconstruction technique described above. Events that reconstruct to South Pole Station (SPS) are rejected.

This area covers a region from -153◦ to -119◦ in azimuthal angle. Events that reconstruct to within a box in zenith and azimuth centered around the location of a calibration pulser are also rejected. There are two calibration pulsers for the Testbed

102 and therefore two box regions for each of them. The first calibration pulser box includes zenith angles of 23◦ < θ < 15◦ and azimuthal angles of 96◦ < φ < 88◦ − − − − in VPol 30 m map (calibration pulser 1 in Fig. 6.8). The second calibration pulser box is centered at 3◦ zenith angle and 139◦ in azimuthal angle in the HPol 30 m map, and stretches in both zenith and azimuthal angles in 10◦ (calibration pulser 2 in ± Fig. 6.8). Additionally, we reject regions where multiple events reconstruct after the Event Quality Cuts, Reconstruction Quality Cuts, Continuous Wave (CW) Cut, and Delay Difference Cut have been applied (the CW Cut and the Delay Difference Cut are described in following paragraphs). These applied cuts reject known backgrounds (CW backgrounds) and poorly reconstructing events and make us look at the distribution of the direction of the events. Thermal noise events will isotropically distribute over the map while events that are originated from specific locations will cluster toward to source direction. As neutrino events are not expected to originate from the same position repeatedly, we reject events that reconstruct to the repeating source locations. From the distribution maps after the set of cuts, we calculated the expected background events for each repeating location using the Gaussian functional fit in azimuth and zenith angles. We defined the size of the box for the repeating locations so that the total expected background events from the clustering Geometric Cuts are same with the background expectation from the final Peak/Correlation Cut (Section. 6.2.3). Three repeating locations were identified in the Interferometric Map Analysis, two in the VPol 30 m map, and another on the VPol 3 km map (Fig. 6.8). The events reconstructing to either repeating location in the Vpol 30 m map are characterized as “near surface” events as they appear to come from a point near the surface of the ice at θ +40◦ relative to the station center. The two locations in the VPol 30 m ≈

103 map reject the “near surface” events where the best reconstructed location for these type of events can be either of two locations depending on the strength of the signal. The ﬁrst of these two reconstruction locations for “near surface” events is centered at a zenith angle of 40◦ and an azimuth of -140◦. We reject any events whose VPol

30 m reconstruction peak points to within a box that is 10◦ in zenith and 40◦ wide in azimuth and centered on that location. The second of the two reconstruction locations for “near surface” events is centered at a zenith angle of -57◦ and an azimuth of -100◦.

We reject any events whose VPol 30 m reconstruction points within a 30◦ 30◦ box × in zenith and azimuth surrounding that point. One repeating location was identiﬁed in the VPol 3 km map and these events are characterized by an excess of power in a 50 MHz band around 200 MHz, and as ∼ such are labeled “200 MHz” events. This “200 MHz” repeating region from the VPol

3000 m map is centered at a zenith angle of -40◦ and an azimuth of -99◦ with the rejection region being 20◦ wide in azimuth and 34◦ high in zenith. As with the “near surface” events, there is a secondary reconstruction point but it is located within the SPS reconstruction region and thus events that reconstruct there are already rejected. These events from repeating locations are expected to be more effectively rejected by other means after improving the reconstruction method in a future analysis. A Saturation Cut rejects events where the saturation of the amplifier induces dis- tortion of the waveform. When the signal strength is strong enough to saturate the amplifier and change the linearity of the amplification factor, we may have mislead- ing reconstructed information from the event and thus we want to remove it from consideration. As the maximum dynamic range of the amplifiers of the borehole antennas is 1 V, we set the saturation point of the output voltage to 995 mV and ∼ ± ± when two or more channels’ waveforms have maximum voltage values that exceed the saturation point, we reject the event.

104 The Gradient Cut is a pattern recognition cut to reject “200 MHz” background events which have a strong gradient in signal strength across the Testbed in one direction. The Geometric Cut for “200 MHz” was not sufficient to reject this specific type of background event because the Geometric Cuts are effective for sources located at 30 m or > 1 km distance from the Testbed, while only a closer source can give ∼ us such a large gradient in signal strength across the station. We first check whether there is a gradient in signal strength in the direction that matches that of these background events, where one of the two VPol channels facing SPS has the strongest

Vpeak/RMS value for these events while one of other two VPol channels have the weakest signal strength. When the above pattern matches for an event, we calculate the gradient value, G, given by

V V G = | max − min| , (6.2) 2 2 VRMS,max + VRMS,min q where Vmax is the peak voltage of the channel with the highest Vpeak/RMS, Vmin is the peak voltage of the channel with the lowest Vpeak/RMS, and VRMS,max and VRMS,min are the RMS voltages of those same channels respectively. If the gradient value is greater than 3.0 we reject the event. Fig. 6.9 shows the distribution of gradient values from events that pass the Event Quality Cuts, while Fig. 6.10 shows gradient values’ distribution after applying the Event Quality Cuts, the Saturation Cut, the Delay Diﬀerence Cut and the Geometric Cuts. The goal of the Gradient Cut is to reject events in Fig. 6.10 (target background events) and allowing events in Fig. 6.9 (other backgrounds which are not meant to be rejected by the Gradient Cut). A Gradient cut value 3.0 gives us 2.3 σ and 1 σ from the mean value for Fig. 6.9 and 6.10, ∼ ∼ respectively.

105 GradientAllGrad Evts' Value Value Grad from fromValue 164155 164155 1005800evts events Events hAllEvtsGrad Entries 164155 60000Evts Mean 1.501 Events

Events RMS 0.6492 50000

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Figure 6.9: The distribution200MHz of gradient Evts' Grad value ValueG from396evts 10% Testbed burned sample with the Event Quality Cuts applied. Our gradient cut valueh200MHzEvtsGrad 3.0 is approximately 40 Entries 396 2.3 σ away fromEvts the mean value 1.5. Distribution of gradient valueMean from 5.346 the selected RMS 2.006 background events35 are shown in Fig. 6.10.

0 0 1 2 3 4 5 6 7 8 9 10 Grad Value 106 All Evts' Grad Value 1005800evts hAllEvtsGrad Entries 164155 60000Evts Mean 1.501 RMS 0.6492 50000

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GradGradient200MHz Value Evts'Valuefrom Grad Selectedfrom Value 396 396 Events396evts events h200MHzEvtsGrad 40 Entries 396 Evts Mean 5.346 Events RMS 2.006 35

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Figure 6.10: The distribution of gradient value G from the Testbed 10% burned sample with analysis cuts to select events that should be rejected by gradient cut. The Saturation cut, Delay Diﬀerence cut, and Geometric Cuts are applied. The gradient cut value of 3.0 is approximately 1 σ from the mean value.

107 The Delay Diﬀerence Cut ensures that the reconstruction direction derived from all of the borehole antennas of the same polarization is consistent with the delay observed between the signals in the two antennas with the strongest signals. In the case of an impulsive signal like one coming from a neutrino event, we expect this correlation to exist whereas a thermal noise event in general should not exhibit this

behavior in general. We calculate the time delay ∆t1,2,peak between the peak voltages

Vpeak/RMS in the two channels with the highest peak voltages. We also find the time delay that would be expected between those two channels based on the direction of reconstruction, ∆t1,2,reco. We then find the difference between these two values, ∆T = ∆t ∆t . If ∆T > 20 ns, we reject the event. The delay 1,2,peak − 1,2,reco | delay| distribution of ∆T from calibration pulser events, 10% burned sample with the | delay| Quality Cuts and Geometric Cuts applied, and simulated neutrino events are shown in Fig. 6.11, 6.12, and 6.13. Both calibration pulser events and simulated neutrino events (Fig. 6.11 and 6.13) show that most of events are clustered at 0 ns delay. On ∼ the other hand, Fig. 6.12 from the 10% burned sample with the Quality Cuts and

nd Geometric Cuts applied, shows most of events distributed at a 2 highest Vpeak/RMS less than 7 and widely spread over Delay Diﬀerence values. This is because both thermal noise and CW background events don’t have impulsive signals (small 2nd

highest Vpeak/RMS) and correlation between the direction of reconstruction and the peak voltages in the waveforms (large Delay Difference values). An In-Ice Cut rejects events that reconstruct to directions above horizontal as viewed by the Testbed. This cut is made because we are searching for neutrino events that are coming from the ice. A Continuous Waveform (CW) Cut rejects events that are contaminated with narrowband anthropogenic noise. This cut rejects events that show a narrowband peak above an expected noise spectrum. To apply this cut, we need to first find the average

108 iigwno.OrDlyDffrneCtvleo 0n ssona lc vertical black a as shown is ns 20 plot. of the trigger value on pulser Cut calibration line V Difference the best dotted into Delay low the leaked Our at have and that window. distributed events timing waveforms events noise of thermal between by number difference caused small are time The the direction. between at reconstructed clustered correlation are strong events a most ∆T expected, value Difference As Delay the events. of Distribution 6.11: Figure

2nd |Peak/RMS| 25 10 15 20 0 5 0 DeltaDelaysvsPeakVRMS Evts27820 50 100 Calpulser Events Calpulser 150 109 200 Difference in delays (ns) ∼ sdlywihmasteeis there means which delay ns 0 250 delay rmclbainpulser calibration from 300 0 100 200 300 400 500

Events peak / RMS 0n ssona lc etcldtln nteplot. the on line of dot value vertical Cut black Difference a Delay as noise shown Our thermal is are events. ns events (CW) 20 of Waveform portion Continuous dominant and the events distribution Therefore The values. V applied. Difference a Cuts have Delay events Geometric of and most Cuts that Quality shows ∆T the value Difference with Delay sample the burned of Distribution 6.12: Figure

2nd |Peak/RMS| 15 20 25 10 0 5 0 DeltaDelaysvsPeakVRMS Evts824533 50 Events with GeometricCuts Events 100 peak 150 / M au esta n ieysra over spread widely and 7 than less value RMS 110 200 Difference in delays (ns) 250 delay rmte1%Testbed 10% the from 300 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Events • • • • •

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needs$further$tesFng$as$the$simulaFon$is$overly$well$reconstructed$–$using$same$index$of$refracFon$model,$staFon$geometry,$etc.$ ieo h lt eetn nyasalprino rgee etioeet.The events. neutrino triggered of portion at small energy a neutrino only high fixed at rejecting a events plot, with clustered the run on is simulation line The ∆T value Difference AraSim. 10 Delay from the events of trino Distribution 6.13: Figure hc etit h maximum the restricts which $generated$events$at$10^19$ 19 V h ea ieec u au f2 si hw sabakvria dotted vertical black a as shown is ns 20 of value Cut Difference delay The eV.

VPeak/RMS from output waveform 10 15 20 25 30 35 40 0 5 0 Vpeak /RMS$values$will$contribute$to$the$reconstrucFon$direcFon$ 50 eV $ Delta$Delay$Cut$ V peak AraSim 100 /RMS V peak ν /RMS Absolute ValueAbsolute (ns) DifferenceDelays of in Events at 10 at Events n o ∆T low and 150 111 to ∼ 200 30. 19 delay eV r u oteStrto Cut Saturation the to due are 250 delay Vpeak 300 rmtigrdneu- triggered from /RMS$values$$ 0 20 40 60 80 100 120 140

Number of Events (weighted)weight 3$ 3442 Baseline Average 3238 for Example Run 3.56.5 dB above BaselineBaseline 3034 400 MHz Balloon Event 2830 26 2422

Voltage, dB (Arb. Scale) 2218 2014

Voltage, dB (Arb. scale) Voltage, 1810 0 200200 400400 600600 800800 10001000 Frequency (MHz)Frequency (MHz)

Figure 6.14: And example of CW Cut baseline and a spectrum of strong CW background event. The baseline is an average spectrum for a run data (approximately 30 minutes period of data). The example event has a strong CW background at 400 MHz, which is a weather balloon communication signal. The spectrum peak at 400∼ MHz is strong enough to exceeds the 6.5 dB above the baseline (dashed curve).

112 spectrum for each data run to serve as a “baseline” for comparison against individual events. Then for each channel, we compare the individual event’s waveforms against the baseline. A frequency bin is flagged as containing CW if that bin in one channel exceeds 6.5 dB above the baseline, and two other channels also have a bin within 5 MHz of the first that exceeds the threshold. In order to maintain a high efficiency for neutrinos, we require that this excess is narrowband before rejecting the event. Fig. 6.14 shows an example of baseline, a 6.5 dB above the baseline, and a strong CW background event at one of the channels. We define a signal to be narrowband if less than 50% of frequency bins in a 40 MHz band around the peak are above 6.0 dB above the baseline. Before a baseline is determined to be an acceptable representation of the average background for a given run, we examine the characteristics of the run overall to determine if it is contaminated by a large number of CW events. To do this, we calculate the maximum correlation between waveforms of neighboring events. If a significant number of CW events are found, they will be highly correlated with each other. We do not use baselines in which more than 10% of neighboring events are well correlated (contain a correlation between waveforms from any two of the same antennas between events > 0.2). In this case, we use the nearest acceptable baseline from 10 run files (approximately 5 hours) instead. ± ± As a last cut, a Peak/Correlation Cut is applied. Since we expect impulsive events to exhibit a correlation between the Vpeak/RMS values from the waveforms and maximum correlation value from the reconstruction map, we designed a cut using these two values, as in [9]. CW-like events tend have high correlation values but low Vpeak/RMS values. Conversely, thermal noise events may fluctuate to high

Vpeak/RMS values but not correlate well in any particular direction.

113 2 survive. thus and line plot), cut (right V the and events above correlation simulated higher lie of the that range For a events to data of extend line. the events percentage For cut simulated These sizable removed. the are a thus above below and is fall those parameter there events and cut cuts no selected the the plot), survive shows (left line line this red above set The events data all cuts. examination 10 other 10% at all the simulated survived events from have from plot plot left right the the highest for and 2nd channel polarization of vertical distribution the The 6.15: Figure w hnesadntarno utainfo hra os.Frt estconstant set we First, 2 at noise. least thermal cuts at from in fluctuation strength random a signal not the and represents channels value two the that ensure 2 to the order choose in We waveforms ). 6.3 Fig. of plot right peak bottom example, (for Cuts Quality Reconstruction the interferometric a passed The which of value map correlation 6.16). peak Fig. the and as defined 6.15 is value Fig. correlation (see maximum polarization corresponding the for axis horizontal hs edfieacta ieo h lto V of plot the on line a as cut a define we this, hw ntefiue.Eet oae oteuprrgtti iewl astecut. the pass Kotera maximal will line this right upper the to located Events figures. the in shown nd h ekCreainCti ae na2dmninlsatrpo hthsthe has that plot scatter 2-dimensional a on based is Cut Peak/Correlation The ecos h ekCreainCtta ie stebs xetdlmto the on limit expected best the us gives that Cut Peak/Correlation the choose We ihs V highest 2nd Highest V /RMS peak 10 15 20 0 5 0 nd ihs V highest 0.2 peak tal. et / M ntevria xsadtemxmmcreainvleo the on value correlation maximum the and axis vertical the on RMS 0.4 peak pn o-ahdln nFgr ) is epick we First 9). Figure in line dot-dashed (pink [99] model flux 0.6 / RMS Max Corr Value Corr Max 0.8 > 4 . 1 n aiu orlto value correlation maximum and 0 0 500 1000

114 Event 2nd Highest V /RMS peak 15 20 10 18 5 0 peak 0 V nd peak V ohposso nyeet that events only show plots Both eV. / ihs V highest M s aiu orlto as correlation maximum vs. RMS / 0.2 M n orlto ausfor values correlation and RMS 0.4 peak 0.6 / M au rmthe from value RMS Max Corr Value Corr Max peak 0.8 z > / ai au on value -axis M values. RMS 0 . 1 3 After 13. 0 5 10 15

Event (weighted) u au vria ffe)wihgv stebs xetdlmt easm htthere that assume We limit. expected best the us give which offset) (vertical value Cut possible the of one just but result p-value. unique reasonable 1 a with to not choices close was is choice which 0.235 slope at This p-value reasonable distribution. a us Peak/Correlation gives -14 6.19). of (Fig. slope distribution Cut the from p-value the obtain We and ( fit set distribution. nential simulation toy function’s each exponential from value fitted likelihood the the calculated follows events of and number data same Testbed the have the cut which each as For sets simulation value. toy slope 10000 each generated for we function slope, fit exponential dis- its differential and similar events a of obtained tribution We -14. of of distribution slope differential Cut the Peak/Correlation shows from 6.17 events Fig. function events. exponential background an expected obtained different the we 20 for value, tried fit slope We each 6.16). for and and 6.15 6.18 ) Fig. (Fig. in values curve slope (red cut line straight the for slope a strength. signal and correlation the do for thus value and particular signal a simulated around In the cluster by to 6.15). dominated concentrate tend are thus not (Fig. plot) and (right above noise events plots thermal simulated and by the The correlation dominated of low are versions events specific in the around plot), zoomed (left are data plots the These 6.16: Figure fe h lp o h ekCreainCti eie,w n h Peak/Correlation the find we decided, is Cut Peak/Correlation the for slope the After 2nd Highest V /RMS peak 2 4 6 8 0 0.1 0.2 Max Corr Value Corr Max 0.3 V peak 0 50 100 150 200 115 / Event M auso .3 n .,respectively. 3.7, and 0.135 of values RMS 2nd Highest V /RMS peak 4 6 8 2 0 0.1 − log( 2 0.2 Max Corr Value Corr Max L )frteexpo- the for )) σ 0.3 fnormal of 0 1 2 3 4

Event (weighted) Events 102

6 7 8 9 Peak/CorrelationY-intercept Cut Value

Figure 6.17: The differential distribution of events that pass the Peak/Correlation Cut using the optimal slope shown in 6.15. The horizontal axis is a measure of the vertical offset of the red line in Fig. 6.15, and is the 2nd highest Vpeak/RMS where the red line intersects the Max Corr Value=0 axis. This distribution is fitted against an exponential function which is used to extrapolate to the number of events expected to pass the cut.

116 are zero signal event in the Testbed data set due to the low sensitivity to neutrinos compared to other experiments such as ANITA which didn’t detect neutrino events. We use Bayesian statistics to ﬁnd the upper limit on the number of neutrino events with 90% conﬁdential level. In a poisson distribution, the likelihood to detect events is:

n (s + b) (s+b) L(n s) = e− (6.3) | n! where L(n s) is the likelihood to detect n events with s mean signal events expected, | and b is the expected number of background events. Therefore, we let n = b in Eq. 6.3. With 90% conﬁdence level, the upper limit on the number of signal events can be obtained by:

S Sup up L(n s)ds 1 α = p(s n)ds = 0 | (6.4) − | ∞ L(n s)ds Z0 R 0 | R where 1 α is the conﬁdence level (1 α = 0.9 for 90% C.L.), S is the maximum − − up allowed signal events, and p(s n) is the probability to have mean signal events s when | we detected n events from the experiment. From Eq. 6.4, we can obtain Sup for each Peak/Correlation Cut value. The Peak/Correlation Cut value which give us the best limit is determined from:

S = N = f A T F ∆E (6.5) up × eff,i · live · i · X where N is expected neutrino events with a factor f applied to our detector’s sensitivity, Aeff,i is a eﬀective area at energy bin i, Tlive is a livetime of the detector, F is a ﬂux at energy bin i, ∆E is the energy bin size, and f is a constant factor applied to our detector to have Sup expected neutrino events from the detector. The best

117 Evts562, CWdB6.5 BBdB6.0 zoom 8 30 /RMS peak

7 Events 25 2ndPeakRMS 6

Highest V 20 nd 2

5 15

4 10

3 5

2 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Max Corr Value

Figure 6.18: Plot showing the Peak/Correlation Cut for each trial slopes. Among all 20 slopes, we choose a slope of -14 which give us a reasonable p-value from the corresponding toy simulation set (see Fig. 6.19).

limit is achieved when we have maximum 1/f = N/Sup (or minimum f = Sup/N). Fig. 6.20 shows how we found the optimized Peak/Correlation Cut value to be 8.8 where N/Sup is maximum.

6.2.3 Background Estimation

To estimate the background, we use the 10% data set and fit the differential number of events rejected by the Peak/Correlation cut as a function of the vertical offset to an exponential function, shown in Fig. 6.17. We use the fit function Ndiff = a x+b e · where x is the 2nd highest Vpeak/RMS where Max Corr Value=0, Ndiff is the differential number of events rejected by the Peak/Correlation cut when it is vertically

118 Toy logL hist, evts: 10000, data logL: 27.13, P-value: 0.234829

102

10 Toy Simulation Events

0 5 10 15 20 25 30 35 40 -2log(L)

Figure 6.19: Distribution of minimum log likelihood from the toy simulation set with Peak/Correlation Cut slope of -14. The red vertical line is the value from the Testbed data set. The p-value is the ratio between the total number in the toy simulation set to the number in the toy simulation set that has a smaller 2 log(L) value than the one from the Testbed data. A p-value of 0.235 is close to 1σ for− a normal distribution.

119 N vs. Y-intercept, slope-14.0

0.022

0.02

0.018 N (expected nu evts) 0.016

0.014

0.012

0.01

0.008 6 8 10 12 14 Rcut (y-intercept)

BackGround vs. Y-intercept, slope-14.0

104 103 102 10 1 10-1 10-2 10-3 10-4 10-5 BG (expected backgroun evts) 10-6 10-7 10-8 10-9 10-10 10-11 10-12 6 8 10 12 14 Rcut (y-intercept)

S_up vs. Y-intercept, slope-14.0

400

350

300

250

S_up (max allowed signal) 200

150

100

0 6 8 10 12 14 Rcut (y-intercept)

N/S_up vs. Y-intercept, slope-14.0 Finding Optimized Cut Value

up 0.008

N/S 0.007

0.006

0.005

0.004

0.003

0.002

0.001

0 6 8 10 12 14 Peak/CorrelationRcut (y-intercept)Cut Value

Figure 6.20: Finding the optimal Peak/Correlation Cut value by maximizing N/Sup. The red vertical line is the optimal Peak/Correlation Cut value (intercept in 2nd highest Vpeak/RMS in Fig. 6.15 and 6.16) which is 8.8. Peak/Correlation Cut values smaller than the optimal value are too weak so allow too many background events. Peak/Correlation Cut values bigger than the optimized value are, on the other hand, too stringent and reject too many neutrino events.

120 Out-of-band RecoQual Saturation Down Geometric CW Delay Diff Peak/Corr Gradient 1

0.5Trigger from Efficiency

0 0 5 10 15 20 25 2nd Highest V /RMS peak

Figure 6.21: The efficiency of each cut in sequence compared with the total number of triggered events for a simulated data set generated from an optimistic Kotera et al. 2010 flux model. After the cuts designed to reject thermal background are applied (beginning with the Delay Difference Cut), the efficiency turns on and plateaus for nd 2 highest Vpeak/RMS > 6.

offset by dx, and a and b are two fit parameters in the exponential function. From the fit, we obtained a = 4.29 0.26 and b = 31.70 1.67 where the deviation − ± ± of each parameter is the one sigma error from the best fit result. The optimal cut gives us 0.06 estimated background events and 0.02 expected neutrino events from the maximal Kotera et al. flux model in the 90% data set in the Stage 2 analysis. Fig. 6.21 shows the efficiencies of each analysis cut in sequence for triggered events as modeled in AraSim for the Interferometric Map analysis. For this plot, we use the

nd 2 highest Vpeak/RMS on the horizontal axis as in the Peak/Correlation Cut. The

121 analysis efficiency for the maximal Kotera et al. flux model is 40 % for signal ∼ nd strengths between 7 and 20 in 2 highest Vpeak/RMS. The first noticeable cut on the plot is the Saturation Cut which rejects most of events above 20 Vpeak/RMS signal strength. After that, the Geometric Cuts reject 20% of the events mostly ∼ due to the SPS Geometric Cut and are consistent across all signal strengths. The Delay Difference Cut and the Reconstruction Quality Cut reject poorly reconstructing events, bringing the efficiencies to the 40 % for high SNR. The remaining cuts, such ∼ as the Down, CW and Peak/Correlation Cuts, don’t significantly affect the total efficiencies.

6.3 Survived Events

In Stage 1 of the analysis, we had three events survive all cuts from 0.0285 expected background events and 0.00362 expected neutrino events. These three events were all believed to be known types of anthropogenic impulsive events (“200 MHz” and “Near Surface” type events). Among them, one event appears to be a “200 MHz” type event, and we had intended to reject those with the Gradient Cut and so this cut was modified slightly to better match the pattern that it was trying to identify. The original definition of the cut required that the highest Vpeak/RMS value came from a VPol channel before the gradient condition was checked for the event. Through what appears to be an aberrant single-bin fluctuation, this event had its highest Vpeak/RMS in an HPol channel. Since the requirement that the highest Vpeak/RMS value be from a VPol channel is not a necessary condition for the pattern recognition, it was removed from the definition of the cut. The altered cut just checks that the gradient among the VPol channels matches the pattern and using this adjusted definition, the event was then rejected.

122 Remaining two survived events are rejected by alternating the Geometric Cut regions. The Geometric Cut region for “200 MHz” and “Near Surface” type events in Stage 1 analysis was initially defined as a box which contains all those type events from 10% data set. The altered “200 MHz” and “Near Surface” Geometric Cuts were defined by Gaussian fits to the azimuth and zenith distributions of the events with only the Event Quality, Reconstruction Quality Cut, Delay Difference and CW Cuts applied (See Fig. 6.22). The edges of each cut region were defined by the criterion that one would expect a total of 0.04 background events to reconstruct outside the region based on this Gaussian fit with only these four cuts applied. This modification increased the total size of the Geometric Cut area, including the SPS, Calibration Pulser, and Clustering Cuts, by 14%. After these modifications, zero neutrino ∼ candidate events survived from Stage 1 analysis. Using these new Geometric Cut regions, two events survived from Stage 2 analysis. These two events that passed were again leaked anthropogenic impulsive events that were intended to be rejected by the “200 MHz” Geometric Cut (See the bottom plot on Fig. 6.22) and thus were removed by slightly expanding the Geometric Cut region in the 3 km map. The alterations to the Geometric Cut regions increase the total acceptance of the Geometric Cut (which includes the South Pole region) by less than 5%. After these modifications, zero neutrino candidate events survived. In future analyses, we plan to design cuts to reject these type of events by other means, with less reliance on the Geometric Cuts.

6.4 Livetime Calculation

A livetime is obtained for each analysis, deﬁned as the total amount of time covered by the data set where the trigger is available, excluding any periods of time that were rejected by the analysis.

123 Vpol 30 m

Cluster Geom Cut before 1st Analysis 50 Near Surface Cluster Geom Cut st

Theta (DEG) after 1 Analysis

0 Survived Events from 1st Analysis Survived Events from 2nd Analysis -50 Near Surface

-150 -100 -50 0 50 100 150 Phi (DEG) Vpol 3 km

Cluster Geom Cut 50 SPS Geom Cut Theta (DEG) Survived Events 0 from 1st Analysis Survived Events from 2nd Analysis 200 MHz -50

-150 -100 -50 0 50 100 150 Phi (DEG)

Figure 6.22: The reconstruction directions of the events that passed both Stage 1 and Stage 2 of the analysis in the 30 m (upper) and 3 km (lower) maps. Events that passed the unaltered cuts in Stage 1 are shown in blue and those that passed the Stage 2 cuts are shown in red. The initial Geometric Cut regions (dashed blue line) were adjusted after Stage 1 (solid red lines) based on a Gaussian ﬁt to the background event distribution with a limited set of cuts applied.

For each analysis, the trigger deadtime is calculated by accumulating the number of 10 MHz clock cycles Nc during one GPS second when the trigger was not available due to the waveform readout process after the trigger or any other issue that would cause the Testbed to be unable to trigger. This counted number of clock cycles Nc gives us the livetime fraction of that second as 1 N /107. The total livetime of the − c Testbed is obtained by accumulating the livetime fraction from each second over the

124 entire data set while avoiding double counting of the livetime from same GPS second. If any second has a deadtime > 10%, the entire second is rejected. We conservatively reject the events from October 22nd to February 16th for both 2011 and 2012 data set which is the summer season at the South Pole. Additionally, the calibration pulser timing cut reduces the livetime by 8%. This strict timing cut ∼ requirement will be able to be relaxed in future analyses. The CW Cut also requires the identiﬁcation of a good baseline and if this baseline is not found in a nearby time period, that run period is rejected. This requirement reduces the livetime by 15% ∼ but better CW analysis techniques will be able to remove this requirement as well. The overall livetime from the 2011-2012 Testbed data is 224 days.

6.5 Results

No neutrino candidate events were found and the results from this analysis are used to derive constraints on the neutrino flux. The effect of the successive cuts in Stage 2 of the Interferometric Map Analysis is summarized in Table 6.1. After the Event Quality and the Reconstruction Quality Cuts are applied, for this table the events are examined in HPol and VPol channels separately. While a single event can pass the HPol and VPol Reconstruction Quality Cut simultaneously and be considered in both channels, only a small number of events ( 100) did so. ∼ After finding no neutrino candidate events passing all cuts, we set limits on the neutrino flux given the effective volume of the Testbed derived from AraSim and the total livetime of the period examined. The effective volume, Veff , is found for each

125 Total 3.3E8 Cut Number passing (either polarization) Event Qual. 1.6E8 Recon. Qual. 3.3E6 VPol HPol Rejected Rejected In sequence as last cut In sequence as last cut Recon. Qual. 1.8E6 1.4E6 SP Active Period 1.4E6 125 1.1E6 13 Deadtime < 0.9 1.4E6 0 1.1E6 0 Saturation 1.4E6 0 1.1E6 0 Geometric, except SP 1.3E6 7 1.0E6 0 SP Geometric 1.1E6 0 9.0E5 1 Gradient 1.1E6 0 9.0E5 0 Delay Diﬀerence 1.8E5 0 1.5E5 0 CW 1.8E5 0 1.4E5 1 Down 1.7E4 15 1.9E4 1

Vpeak/Corr 0 1.7E4 0 1.9E4

Table 6.1: This table summarizes the number of events passing each cut in the Interferometric Map Analysis, in Phase 2 (2011-2012, excluding Feb.-June 2012). We list how many events survive after each cut in sequence and how many events each cut rejects as a last cut. After the Event Quality and Reconstruction Quality Cuts are applied, VPol and HPol and considered as two separate channels for the purpose of tabulation, independent of one another.

energy bin by simulating a large number ( 106) of events: ∼

N V passed V = cylinder w . (6.6) eﬀ N i i=1 X

Each event is given a weight wi equal to the probability that the neutrino was not ab- Npassed sorbed in the earth, given its direction and position of the interaction. Then wi i=1 is the weighted sum of the number of events that triggered and passed all analysisP

126 cuts, and N is the total number of events thrown. The neutrino interactions are

thrown in a cylindrical volume centered around the detector, denoted Vcylinder. The eﬀective area is then calculated from the eﬀective volume by the following:

Veﬀ Aeﬀ (6.7) ≈ linteraction

where linteraction is the interaction length. The 90% diﬀerential ﬂux limit on the number of events in each decade in energy then be calculated from this equation:

1 2.3 EF (E) = (6.8) 4πAeﬀ T ln(10)

where T is the total livetime of the examined period, the factor of 2.3 is the 90% Poisson conﬁdence level upper limit on number of expected signal events with zero events observed, and the ln(10) is a correction factor for the log-scale binning. Using 2.3 as a number of detected events from the ﬂux F (E) in ∆E bin, we can let:

2.3 = F (E) A 4πT ∆E (6.9) · eff · ∆E = EF (E) A 4πT (6.10) · eff · E = EF (E) A 4πT ∆ ln(E) (6.11) · eff · = EF (E) A 4πT ln(10)∆ log(E). (6.12) · eff ·

We set our limit at 2.3 events in one decade of energy (∆ log(E) = 1) and obtained Eq. 6.8. Fig. 6.23 shows the limit obtained from our Testbed with 224 days of livetime. The projected limits for ARA37 shown in Fig. 6.23 are derived from trigger-level sensitivities only, with 100% analysis eﬃciencies assumed for simplicity.

127 -12

) 10 -1 ANITA II '10 sr

-1 Auger '11 -13 s 10 -2 IceCube '12 (2yrs) IceCude 3yrs HESE 10-14 RICE '11 E F(E) (cm 10-15

10-16

10-17 ARA TestBed 2011-2012 (224 days) 10-18 ARA37 (3yr)

GZK, Kotera '10 10-19 1015 1016 1017 1018 1019 1020 1021 1022 E (eV)

Figure 6.23: The limits placed compared with the projected ARA37 trigger-level sensitivity and results from other experiments.

128 6.6 Systematic Uncertainties

In this section, we will discuss the systematic uncertainties in the Interferometric Map Analysis. We considered systematic uncertainties in both the background estimation and analysis efficiency. While the uncertainty on our background estimation is derived solely from the errors on the best fit line used to extrapolate the background estimate described in Section 6.2.3, for the analysis efficiency we consider the effect of the antenna model, ice index of refraction model, ice attenuation model, and neutrino cross section model. Each systematic error is obtained by changing only one parameter value at a time from the default and estimating the impact on the result from each. The systematic uncertainty on the background estimation is derived from the errors on the best fit exponential function used in the extrapolation described in

a x+b Section 6.2.3. Recall that the best fit to N = e · gave a = 4.29 0.26 and diff − ± b = 31.70 1.67. We moved each fit parameter alone by one standard deviation in ± both the positive and negative directions, and obtained the maximum deviation in the background estimate in each direction. We find the number of background events

+0.52 to be 0.06 0.05 events in the 90% data set in the Stage 2 analysis. − Modeling the expected frequency-dependent phases of the neutrino-induced measured pulses contributes an important systematic error to our analysis efficiencies. We use two different techniques for modeling the phases, and they put upper and lower bounds on our limit and projected sensitivity for ARA37, which are based on our current trigger and given the effects so far included in our simulations. Conserva- tively, our main result in this paper (the red line in Fig. 6.23) uses our default model, while we believe that a more accurate model would give an improved limit.

129 We model the phase of a received pulse from a neutrino interaction using two different methods, the first being the default and the second for comparison. We believe that the “true” phases would give a result that is in between the two. The first, default approach models the frequency-dependent phase of the RF emission, as well as the phase response of antennas, filters and amplifiers as described in Chapter5. The second model for the phase, used for comparison, is quite simplistic, with the phase of the radio emission being +90◦ for positive frequencies and -90◦ for negative frequencies, and the phase response of antennas and electronics being flat. While the second, simple model of the phase response produces a received pulse that is too narrow, we have found by comparing simulated and measured calibration pulser waveforms that our default method simulates pulses that are too broad (see Fig. 6.24). The narrow pulses from the second method result in analysis efficiencies that are too high, and the broader pulses from the default method fail our cuts more often than they should. This excessive broadening of the pulse is believed to be dominated by the antenna response model, and future measurements of the phase response of our antennas are expected to greatly reduce this systematic uncertainty. The second model gives a trigger level sensitivity that is approximately 65% larger than the first model at 1017 eV, 50% larger at 1018 eV and 20% larger at the highest energy simulated, 1021 eV. At low energies, the dispersion of the signal has a more dramatic effect on the trigger efficiency whereas at higher energies the dispersion has less of an effect due to the the strength of the signal. The choice of model for the depth dependence of the index of refraction in the firn, both for event generation and for event reconstruction, provides another source of systematic uncertainty in our analysis efficiency since it determines the path taken through the ice and the arrival direction at the antennas, and also impacts the interferometric maps that are used in analysis. By default, we used the exponential fit

130 TestbedGraph Event AraSim DefaultGraph PhaseGraph Model AraSim SimplisticGraphGraph PhaseGraph Model GraphGraph Graph GraphGraph Graph ×10-3 ×10-3 ×10-3 ×10-3 500 600 mV mV mV 1000 0.06 400 400 0.06600 800 0.06 0.06 400 400 400 300 300 400 0.04 600 300 0.04400 0.04 0.04 500 200 200 200 200 400 200 200 0.02 0.02 0.02200 100 100 0.02 100 200 0 0 0 0 0 00 0 0 0 0 0 0 -100 -100 -0.02 -100 -0.02 -200 -0.02-200 -200 -200 -0.02 -200 -500 -200 -200 -200 -400 -0.04 -0.04 -300 -0.04-400 -400 -300 -0.04 -300 -600 -0.06 -400 -400 -0.06 -400 -400 -400 -0.06-600 -1000 -0.06 -600 -800 -500 -150 -100 -50 0 50 100 -150-200 -100-150 -50-100 0-50 500 10050 100 -150-200 -100-150-150 -100-50-100 -500 -50 500 0 1005050 100 -200 -150 -100-100-150 -50-50-100 00 -50 5050 0 100 50 100 -150 -150-100 -100-50 -500 0 50 50100 100 -150 -100 -50 0 50 100 Time (ns) Time (ns) Time (ns)

Graph GraphGraph GraphGraphGraph GraphGraph Graph GraphGraph Graph ×10-3 ×10-3 ×10-3 ×10-3 0.08 600 0.06 0.04 800 600 Figure 6.24: Channel 0 waveform400 from a calibration pulser event. The left plot is 0.06 300 400 0.03 0.06 400 600 400 0.04 from the Testbed data, the middle300 400 plot is from AraSim with default phase model, and 400 0.02 0.04 0.04 200 400 200 200 200 the right plot is from AraSim with200 simplistic 90◦ phase model.200 Even though the 0.02 0.01 0.02 200 200 100 ± 0.02 amplitude of the waveforms in two AraSim plots are not calibrated to the Testbed, 100 0 0 0 0 0 0 0 0 0 0 -0.01 we can see that the pulse in the simplistic phase model is too narrow while the pulse 0 0 -100 -200 -0.02 -0.02 -200 -200 -0.02 in the default phase model is too broad compared to the Testbed-200 waveform. -200 -200 -200 -0.04 -0.02 -100 -0.03 -400 -400 -300 -400 -0.04 -0.06 -0.04 -400 -0.04 -600 -600 -400 -200 -400 -400 -0.08 -0.05 -150 -100 -50 0 50 100 -150 -150-100 -100-50 -500 050 50100 100 -150 -100-100 -50-50 00 5050 100100 -150 -150-100 -100-50 -500 0 50 50100 100 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 function for the index of refraction as a function of depth: Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph ×10-3 ×10-3 ×10-3 ×10-3 0.1 0.1 1500 0.08 1500 600 300 800 0.04 400 400 0.08 400 0.0132 z 0.06 200 1000 n(z) =600 1.78 0.43 e− · 1000 (6.13) 400 − · 0.06 0.05 200 400 0.04 0.02 200 0.04 200 100 500 500 200 200 0.02 0.02 0 0 0 0 0 0 0 0 0 0 0 0 where n is the index of refraction and z the depth of ice (positive value for deeper loca- -100 -200 -0.02 -200 -0.02 -200 -200 -0.02 -500 -200 -0.04 -400 -500 -0.05 -200 tion). The alternative index of refraction model we tested was-0.04 an inverse exponential -0.06 -400 -400 -400 -400 -0.04 -1000 -600 -300 -0.06 -1000 -0.08 -800 ﬁt function: -100 -50 0 50 100 150 200 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 -0.1 -100 -50 0 50 100 150 200 -1500 -100 -50 0 50 100 150 200 -150 -100-600 -50 0 50 100 -150 -100 -50 0 50 100 -100 -50 0 50 100 150 200 -100 -50 0 50 100 150 -100 -50 0 050.86100 150 -100 -50 0 50 100 150 -100 -50 0 50 100 150 n(z) = 0.92 + . (6.14) 0.0132 z Graph1 + e GraphGraph Graph Graph Graph− · Graph Graph ×10-3 ×10-3 600 0.06 150 0.06 300 Both functions gives an index400 of300 refraction of 1.35 at the surface and 1.78 in deep 400 300 0.04 100 0.04 200 200 200 200 50 200 ice. The exponential model has a more shallow ﬁrn layer0.02 ( 200 m) compared to 0.02 100 100 ∼ 0 0 100 0 0 the0 inverse exponential model ( 2500 m), and thus shows a more dramatic change 0 -200 -50 0 -200∼ -0.02 -100 -100 in index of refraction as a function of depth. The exponential model-100 is chosen as the -0.02 -100 -0.04 -400 -400 -200 -200 -150 -0.04 -200 -0.06 -600 -300 -100 -50 0 50 100 150 200 -100 -50 0 50 100 150 200 -300 -100 -50-200 0 50 100 150 200 -100 -50-300 0 50 100 150 200 -150 -100 -50 0 50 100 -150 -100 -50 0 50 100 -100 -50 0 50 100 150 -100 -50 0 50 100 150

131 default since it fits better with measurements [71], and we use the same model for both event generation and reconstruction in the analysis. This strategy of course assumes perfect knowledge of the index of refraction when carrying out the reconstruction. In order to estimate the systematic error due to imperfect knowledge of the depth-dependence of the ice, we try using each of the two models for event reconstruction and/or reconstruction, giving four combinations including the default combination, and find the largest excursions from the baseline result in either direction. We find the efficiency can increase by 4.9% or decrease by

18 16.4% at Eν = 10 eV compared to the default due to imperfect knowledge of the depth-dependence of the index of refraction in ice. Likewise, we assess the systematic uncertainty due to in-ice field attenuation by comparing our results when two different models are used. The default model uses a South Pole temperature profile from [73] folded in with a relationship between field attenuation length and ice temperature given in [74] as used in ANITA simulations and described in [75]. The alternative ice attenuation length model is based on the ARA Testbed measurement from IceCube deep pulser events published in [31]. By default, our modeling of the effect of ice attenuation is based on ANITA simulations [75], where profiles of ice attenuation vs. depth are considered, and for each event, the ice attenuation length is averaged over depth from the neutrino-ice interaction location to the surface and the result is denoted L . The attenuation h atteni length is assumed to remain a constant L over the entire path of the ray in the h atteni ice, and an ice attenuation factor,

total Dtravel/ Latten FIceAtten,default = e− h i, (6.15)

132 total is then applied to the electric ﬁeld. Here, FIceAtten,default is the ice attenuation factor

and Dtravel is the ray travel distance between the neutrino-ice interaction location and the antenna. The second calculates the total attenuation factor every few 10 m along the path of the ray for each event, and uses the ice attenuation lengths measured by the ARA Testbed [31]. The total ice attenuation factor from this method is then:

N total Di/Latten(zi) FIceAtten,alter = e− (6.16) i=1 Y

total where FIceAtten,alter is the ice attenuation factor applied to the electric ﬁeld strength from the alternative model, N is the total number of ray tracing steps from the

neutrino-ice interaction location to the antenna, Di is the ray travel distance for

the corresponding ray trace step i, and Latten(zi) the ice attenuation length at a

corresponding ray tracing step’s depth zi. Due to the fact that the second technique gives us longer attenuation lengths near the surface, it gives a 10% larger efficiency ∼ 18 at Eν = 10 eV compared to the default model. Finally, we estimate the uncertainty due to our ν N cross section model. The − νN cross section model in our simulation is from Connolly et al. [68] which gives us the central values and upper and lower bounds for the ν N cross section as a − function of ν energy. At E = 1018 eV, the uncertainty in the ν N cross section ν − give us up to 30% variance from the central value (from the upper bound on the ∼ neutral current cross section). A higher cross section will lower the sensitivity due to the increased Earth screening effect. However, there’s also a counter effect from a higher cross section which increases the probability to interact between neutrino and nucleon in the ice, and thus increases the sensitivity. At 1018 eV, the lower bound on the νN cross section gave a 6.2% higher neutrino efficiency while the upper bound ∼

133 Systematic uncertainties at 1018 eV + (%) (%) Index of Refraction 4.9 −16.4 Ice Attenuation Length 10.2 N/A νN Cross Section 6.2 N/A Phase Response 50.9 N/A Total 52.5 16.4

Table 6.2: Summary of systematic uncertainties on the neutrino eﬃciency at 1018 eV.

From the Testbed to ARA37 at 1018 eV AΩeﬀ Accumulative [km2sr] factor Testbed analysis 2.8E-4 1 Testbed trigger 1.5E-3 5 ARA one-station trigger 4.0E-3 14 ARA37 trigger 1.3E-1 464

Table 6.3: Factors that bring the Testbed sensitivity to ARA37 sensitivity for Eν = 1018 eV using AraSim.

on the νN cross section gives a negligible change to the eﬃciency in comparison to the baseline model. Overall, we estimate that we expect 0.06 + 0.52 0.05 background events with − uncertainties of +52.5% and 16.4% on our neutrino eﬃciency. −

6.7 Projections for ARA3 and ARA37

The ARA collaboration aims to build an array of 37 stations to gain enough sensitivity to measure of order 100 UHE neutrinos and exploit the physics and astrophysics information that they carry. In this section we illustrate the factors that bring us from the sensitivity of this Testbed analysis to the expected ARA37 trigger sensitivity

134 18 18 Testbed 30m, Eν=10 eV ARA1 200m, Eν=10 eV 0.05 0.05 without Earth without Earth absorption absorption Events Events 0.04 with Earth 0.04 with Earth absorption absorption

0.03 0.03

0.02 0.02

0.01 0.01

0 0 0 50 100 150 0 50 100 150 Theta (deg) Theta (deg)

Figure 6.25: These ﬁgures show the distribution of zenith angles of incident momenta for simulated neutrinos at 1018 eV that pass the trigger in AraSim for (left plot) Testbed at 30 m and (right plot) a design station at a depth of 200 m. Events on the left side of each plot come from up-going neutrinos with respect to the South Pole, while events on the right come from down-going neutrinos. The viewable arrival direction zenith angles are generally limited to less than 120◦ for the Testbed and less than 150◦ for a design station. This limited range of observable arrival directions is due to the combination of the limited viewing region seen in Fig. 5.3 and the requirement that the coherent signal is emitted near the Cherenkov angle, which is relative to the arrival direction. When one adds in the screening eﬀect of the Earth (red lines), almost all events with zenith angles less than 90◦ disappear as well and thus the observable range of zenith angles is limited by the geometry of the Testbed by a factor of about 2.

in Fig. 6.23. For future detector conﬁgurations we compare sensitivities at the trigger level only. We do not know what our analysis eﬃciencies will be at those stages but expect that they will improve. Table 6.3 lists the factors that bring the Testbed sensitivity in this paper to that

18 expected for an ARA37 array at Eν = 10 eV, where, for many cosmogenic neutrino ﬂux models, we expect to measure the largest number of neutrinos. The factors in Table 6.3 are all derived from the AraSim simulation and we use the eﬀective area ×

solid angle AΩeff as the figure of merit to compare the sensitivity of the detector at different stages. The effective area at the Testbed trigger level is a factor of 5 higher

135 than at the analysis level at 1018 eV. Going from the Testbed trigger level to an ARA deep station, we find a factor of 3.2 improvement in sensitivity. This is both because a shallow station is limited in the angle of incident RF emission that it can observe, and also because neutrinos steep enough to produce observable RF emission are subject to more earth absorption (see Fig. 6.25). From one ARA station to ARA37, the sensitivity scales as the number of stations since at these energies, events tend to be seen by only one station and each station serves as its own independent detector. In addition to the improvements in sensitivity expected from increasing the number of deep stations as listed in Table 6.3, we expect that our livetime, analysis efficiencies, and background rejection will all improve in the next neutrino searches in deep stations. Future improvements to the trigger (from a 3/8 coincidence to one based on pattern recognition, for example) will improve how efficiently we record neutrino signals in the first place. Livetime improvements will come from two factors. The A2 and A3 stations have been running since February 2013 with 95% livetime, without the intermittent ∼ periods of deadtime we encountered with the Testbed. In addition, we expect to be able to remove the cut on the period when the South Pole is active and recover 3 months per year of livetime. We find that the number of events rejected by the cut on the period of South Pole activity (125 VPol, 13 HPol) is manageable and at a level that we can reasonably expect to reject by other means. Also A2 and A3 data will not have as strong anthropogenic backgrounds as Testbed 2011-2012 data set during the summer season at the South Pole since the full IceCube 86 strings have finished deploying. Note that only one event in Table 6.1 was rejected by the SP Geometric Cut and not rejected by any other cut. Another expected improvement from A2 and A3 is the increased field-of-view from SP Geometric Cut. As the Testbed is the closest station to the SP station and

136 IceCube array, the increase distance from SP station and IceCube array to A2 and A3 make the size of the SP Geometric Cut smaller than the Testbed. In case we use the same definition of the SP Geometric Cut, A2 and A3 will have 44% of SP Geometric ∼ Cut region compared with the Testbed. Therefore we expect to have approximately 10% improvement in the analysis efficiency from the new SP Geometric Cut for A2 and A3. We expect analysis efficiencies for deep stations to improve compared to the Testbed due to the better uniformity of deep ice, the increased number of borehole antennas (four to eight), and analysis experience. The deep ice and increased number of antennas bring improved event reconstructions. This leads to improved rejection of backgrounds (which allows for looser analysis cuts) and a higher maximum correlation value for improved separation between signals and noise.

137 Chapter 7

Gamma-Ray Burst Neutrino Search

The contents of this chapter are in progress to be published.

We searched for ultra-high energy (UHE) neutrinos from Gamma-Ray Burst (GRB) with the Askaryan Radio Array (ARA) Testbed station’s 2011-2012 data set. Among 600 GRBs monitored by the Gamma-Ray Coordinate Network (GCN) catalog from ∼ Jan. 2011 to Dec. 2012, 57 GRBs were selected to be analyzed. These GRBs were chosen because they occurred during a period of low anthropogenic background and high stability of the station, and fell within our geometric acceptance. We searched for UHE neutrinos from 57 GRBs and observed 0 events, which is consistent with 0.106 estimated background events. With this result, we set the limits on the UHE GRB neutrino fluence and quasi-diffuse flux from 1016 to 1019 eV. This is the first limit on the UHE GRB neutrino quasi-diffuse flux limit at energies above 1016 eV.

7.1 Introduction

As Gamma-Ray Bursts (GRBs) are among the most energetic events in the universe, GRBs are candidates for the sources of UHECRs and neutrinos [100, 101]. In the standard Fireball shock model, relativistic plasma in the series of jets produce high energy gamma-rays from synchrotron radiation and inverse Compton scattering

138 inside the jet. Neutrinos will be also produced via p γ interactions from gamma-rays − and protons that are accelerated in a jet through the shock acceleration [102]. So far many experiments have searched for neutrinos from GRBs using different techniques [103–105], but most of these experiments are sensitive at energies lower than 1018 eV. In this paper, we present the fluence limit from 57 selected GRBs and the first limit on the UHE GRB neutrino quasi-diffuse flux from 1016 to 1019 eV. GRB neutrino fluences are obtained from Neutrinos from Cosmic Accelerators (Neu- CosmA), a full numerical calculation software package [106] using parameter values from the Gamma-Ray Coordinate Network (GCN) catalog [107].

7.2 Previous GRB Neutrino Analyses

There are multiple UHE or very-high energy (VHE) GRB neutrino searches from IceCube [103], ANTARES [104], and ANITA [105] and they are complementary. Ice- Cube uses the optical Cherenkov technique, located at the South Pole (Southern hemisphere) and searches up-going neutrinos. Recently IceCube reported the most stringent GRB neutrino limit from 1014 to 1016 eV (the VHE region) [103]. An IceCube GRB neutrino search, previously using a Waxman-Bahcall (WB) GRB neutrino flux model [108] has been updated to a new result using a numerical GRB neutrino flux model [103]. ANTARES is an optical Cherenkov experiment similar to IceCube but located in the Mediterranean Sea and therefore uses water as a detection medium. As ANTARES is located at Northern hemisphere, the field of view of Ice- Cube and ANTARES do not overlap significantly. Using the same optical Cherenkov technique, ANTARES is sensitive to a similar region of neutrino energy as IceCube. ANTARES’s GRB neutrino analysis is based on NeuCosmA, a numerical GRB neutrino flux model [106], and its GRB neutrino flux limit is approximately an order of magnitude weaker than the limit from IceCube [109].

139 ANITA is a balloon-born Antarctic experiment that uses the radio Cherenkov technique. At its 37 km altitude, ANITA can monitor an extremely large volume ∼ of Antarctic ice ( 1.6Mkm3 at once [9]). Although ANITA provided the ﬁrst GRB ∼ neutrino limit in the UHE region, there are some limitations. First, the ANITA GRB

4 neutrino analysis was based on a simple model that used an E− spectrum, which is based on the analytic WB GRB neutrino flux model [54]. The GRB neutrino fluence from the WB model shows approximately an order of magnitude difference when compared to numerical calculation models such as NeuCosmA [106]. Secondly, the 30 day livetime of a balloon experiment limits the number of analyzable GRBs to ∼ approximately 30 events as GRBs occur once per day. Compared to the ANITA ∼ analysis, our analysis uses the NeuCosmA package to obtain GRB neutrino fluences and benefits from a 224 day livetime [2].

7.3 The ARA Instrument

The full proposed ARA detector would consist of 37 stations spaced 2 km apart at a depth of 200 m. The ﬁrst three design ARA stations were deployed in the 2011-2012 and 2012-2013 seasons, while an ARA prototype TestBed station, which we use for this GRB neutrino search, was deployed in the 2010-2011 season [2].

7.3.1 TestBed station

The ARA TestBed station is a prototype station of ARA detector. It contains 16 antennas: four bicone vertically polarized (Vpol) antennas, four bowtie-slotted cylinder horizontally polarized (Hpol) antennas, two discone Vpol antennas, two batwing Hpol antennas, two quad-slotted cylinder Hpol antennas and two surface located antennas. Most of the components in the TestBed are similar to the ARA stations.

140 However, the maximum depth of the borehole antennas in the TestBed is approximately 30 m while ARA design stations are at 200 m depth. Each borehole in the TestBed has one Vpol and one Hpol antenna with bandwidth from 150 MHz to 1 GHz. A more detailed description about ARA Testbed can be found in [2,31].

7.4 Analysis Tools

In order to get the expected neutrino spectra and the ARA Testbed eﬃciency for GRB neutrinos, we use NeuCosmA GRB neutrino model and AraSim, the ARA detector simulation software. Highlights for NeuCosmA and AraSim are described in the following sections.

7.4.1 GRB Neutrino Model: NeuCosmA

NeuCosmA is a Monte Carlo GRB neutrino fluence calculation code. It provides detailed calculations for primary pions, kaons and secondary particles production modes using current Standard Model particle physics as shown in [14]. These detailed calculations in NeuCosmA yield a significant difference in the neutrino flux by an order of magnitude compared to the full analytic WB model and add spectral shape content to the neutrino flux (Fig. 7.1). We expect NeuCosmA to deliver more reliable GRB neutrino fluences compared to analytic models.

NeuCosmA uses measured parameter values such as T90, the time in which 90 % of the ﬂuence is emitted, α and β, the ﬁrst and second gamma-ray spectral indexes, and redshift z in order to obtain the neutrino spectrum that is consistent with a measured gamma-ray spectrum. We use parameter values for each GRB taken from the Gamma- Ray Coordinate Network (GCN) catalog. If some of the parameter values are missing for a GRB, default values are used instead. The GCN catalog provides default values

141 -2 ] 10 -2 IC-FC (WB based model)

NFC (NeuComsA model) [GeV cm ν -3 F

2 ν 10 E

10-4

10-5 105 106 107 108 109 Eν [GeV]

Figure 7.1: Muon neutrino ﬂuence of GRB080603A from analytic calculation based on WB model (IC-FC, back curve) and NeuCosmA model (NFC, red curve). De- tailed calculations in NeuCosmA yield changes in the magnitude and the shape of the neutrino ﬂuence. Figure digitized from [14].

for the parameters that are missing or incomplete from the measurements and we used the same default values as inputs into NeuCosmA.

7.4.2 Simulation: AraSim

AraSim is a software package used within the ARA collaboration to simulate neutrino signals as they would be observed by the detector. It simulates the full chain of neutrino events such as the neutrino’s path through the Earth, radio Cherenkov emission, the path and response of the emitted signal in the ice, and the trigger and data acquisition mechanisms of the detector. It uses custom parameterized radio Cherenkov emission model inspired by [12], which generates the signal with proper phase response. In AraSim, neutrino eﬃciencies as a function of source direction are properly accounted through modeling of two main eﬀects, neutrino absorption

142 by the Earth and the path through the ice of the emitted radio Cherenkov signal. With AraSim, we can study the radio Cherenkov emission with respect to the source direction. Fig. 7.2 show the distributions of the reconstructed RF signal source’s direction from various neutrino travel directions from Vpol channels and Hpol channels. For each neutrino event, the reconstructed RF source direction with respect to the neutrino source direction is calculated and plotted on the map (Fig. 7.2). These distribution plots could be used to make a the stringent geometric cut for point sources such as GRBs. However, as the thorough study of the relationship between the reconstructed direction and the source direction has not been carried out, we did not utilized this technique in this GRB neutrino search.

7.5 Data Analysis

We first selected 57 GRBs from a total of 600 GRBs from Jan. 2011 to Dec. ∼ 2012. We used the IceCube GRB catalog, which is a database based on the Gamma- Ray Coordinate Network (GCN), to find GRBs during the time period of interest. From 600 GRBs from Jan. 2011 to Dec. 2012 in the catalog, we rejected ∼ GRBs that failed good-timing cuts which leave us 257 GRBs. The good-timing cuts consist of three cuts which require a low background level and stable data-taking. The first cut is a simple time window cut which rejected GRBs that occurred during the summer season at the South Pole in order to avoid strong anthropogenic backgrounds. For each year, we rejected GRBs that occurred from October 22nd to February 16th. We also require that the data is not contaminated by any strong continuous waveform (CW) source by rejecting any GRBs that occurred within an hour of any run where 10 % or more events are highly correlated with each other. The last timing cut is a livetime cut which requires the detector to be running and stably storing data during the GRB period. The livetime represents the fraction

143 theta (deg) theta (deg) -80 -60 -40 -20 -80 -60 -40 -20 20 40 60 80 20 40 60 80 0 0 -150 -150 -100 -100 -50 -50 H3000 reconwrtsrc H30 reconwrtsrc 0 0 50 50 100 100 150 150 phi (deg) phi (deg) 0 50 100 150 200 250 300 350 400 450 0 20 40 60 80 100 120 140 θ onigznt nlsfo 37 from angles zenith pointing direc- source 10 neutrino of the sample from simulated a location from reconstruction tion the of Distribution 7.2: Figure edo iw nodrt en ag fsniiefil fve o h R Testbed, ARA the for view of field sensitive of range a detector’s Testbed define to the order in In included view. be of should field GRB the that requires which cut tional reject we GRB, a after or before analysis. hour our the from of during GRB livetime % that the 10 when than instance any lower was was there detector If the available. was trigger that second a of 6.5 ). (Fig. ice in tracing ray the from effect shadowing the by caused are plot

0 = Weight Weight rmte27GB htsrie h odtmn us eas ple naddi- an applied also we cuts, good-timing the survived that GRBs 257 the From ◦ and

theta (deg) theta (deg) Theta (deg) Thetatheta (deg) (deg) theta (deg) φ -40 -20 -80 -60 -40 -20 -80 -60 -80 -60 -40 -20 -80 -60 -40 -20 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 0 0 0 0 0 = -150 -150 ◦ -150 -150 h lti bandfo vnswt etiosuc directions source neutrino with events from obtained is plot The . RF Source Distribution from Hpol 3000 m Map m 3000 Hpol Distributionfrom RFSource RF Source Distribution from Vpol 3000 m Map m 3000 Vpol Distributionfrom RFSource -100 -100 -100 -100 RF Source Distribution in Hpol 3000 m Map m 3000 DistributioninHpol RFSource RF Source Distribution in Vpol 3000 m Map m 3000 Vpol Distributionin RFSource ◦ o102 to -50 -50 -50 -50 18 H3000 reconwrtsrc V3000 reconwrtsrc H30 reconwrtsrc V30 reconwrtsrc Vnurns h etiosuc ieto sat is direction source neutrino The neutrinos. eV ◦ w iclrepybn wiebn)i the in bins) (white bins empty circular Two . 0 0 0 0 144 50 50 50 50 100 100 100 100 Phi (deg) Phi (deg) Phi 150 150 150 150 phi (deg) phi (deg) phi (deg) phi (deg) 0 50 100 150 200 250 300 350 400 450 0 20 40 60 80 100 120 140 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 160 180

WeightWeight WeightWeightWeight Weight

theta (deg) theta (deg) -80 -60 -40 -20 -80 -60 -40 -20 20 40 60 80 20 40 60 80 0 0 -150 -150 -100 -100 -50 -50 V3000 reconwrtsrc V30 reconwrtsrc 0 0 50 50 100 100 150 150 phi (deg) phi (deg) 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 160 180

Weight Weight Effective VolumeVeff versusvs. NNU Neutrino’s theta, 17.0eV Zenith Angle sr] 3 10 Veff [km

Field of view

10-1

10-2 -0.8 -0.6 -0.4 -0.2 0 0.2 NeutrinoNNU Direction angle cos(theta) cos(θ)

Figure 7.3: Effective volume as a function of neutrino travel direction plot. θ is the zenith angle of the neutrino travel direction. Field of view range is defined as the Full Width Half Maximum (FWHM) of the effective volume which is 0.4 < cos(θ) < 0.05. − we used simulation set with multiple incident angles of neutrinos at 1017 eV and obtained the effective volume as a function of neutrino direction. In Fig. 7.3, the effective volume versus zenith angle of neutrino direction is shown. The zenith angle range of greatest sensitivity is defined as the Full Width Half Maxi- mum (FWHM) of the effective area (arrow shown in Fig. 7.3). The decrease in effective volume on the right hand side and the left hand side of Fig. 7.3 come from different effects. The Earth absorption effect reduces the effective volume at high cos(θ) (RHS of the plot) while the shadowing effect from the ray tracing in ice (Fig. 5.3) causes the cut-off at low cos(θ) (LHS of the plot). We applied this additional GRB geometric cut to select GRBs that are most likely to be detectable with the ARA Testbed. After applying this field-of-view cut,

145 GRB direction distribution, total 57, InBox 57 1 )] θ 0.8 CosTheta 0.6

0.4

0.2

-0.2 Direction of GRBs [cos( -0.4

-0.6

-0.8

-1 -150 -100 -50 0 50 100 150 PhiPhi (deg) (deg)

GRB direction theta distribution InBox 57

Figure 7.4:4 The distribution map of 57 selected GRBs in Testbed local coordinates. The blue band in the map is the ﬁeld-of-view cut range deﬁned in Fig. 7.3. Note that 3.5 cos(θ) in this map is the direction of the GRB while cos(θ) in Fig. 7.3 is the direction of the neutrino.number of GRBs 3

2.5

57 GRBs1.5 are chosen. Fig. 7.4 shows the distribution map of 57 GRBs in Testbed local coordinates.1 0.5 Fig 7.5 shows the fluences of all 57 selected GRBs with NeuCosmA software. 0 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Among 57 survived GRBs, one GRB was brighter than other GRBs.CosTheta Its fluence was higher than the others by and order of magnitude above 1016 eV. We use this dominant GRB event as representative of the sum of the 57 GRBs and optimized our analysis cuts with a neutrino simulation set that used the fluence from dominant GRB. For this search, we re-optimized the cuts that we used for the diffuse neutrino search [2]. A stringent timing cut surrounding the time of each GRB dramatically reduces the expected background events and thus we can loosen the analysis cuts and increase the sensitivity to GRB neutrinos. Among the set of analysis cuts described in [2], the Delay Difference cut, the Reconstruction Quality cuts, and the

146 GRB fluences, total 57 GRBs ]

-2 1

10-1

-2 F [GeV cm

2 10 E 10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10 -2 0 2 4 6 8 10 12 Nu energy [log (E/GeV)] Neutrino energy [log(E/GeV)]10

Figure 7.5: The ﬂuences of 57 selected GRBs (black curves) and the ﬂuence from the summation of all 57 GRBs (red curve). One GRB is brighter than other GRBs by an order of magnitude above 1016 eV. This dominant GRB is chosen as representative of the sum of the 57 GRBs.

Peak/Correlation cut are re-optimized for this search. Three re-optimized cuts are all based on the quality of the directional reconstruction while the rest of the cuts are designed to reject specific type of backgrounds such as CW and calibration pulser events. A total of four cut parameters from three cuts are changed in 4D space and we obtained a set of cut parameters which give us the best limit on the dominant GRB event from the NeuCosmA model. All three cuts become looser than the diffuse neutrino search [2] and the overall analysis cut efficiency for the dominant GRB fluence increased by factor of 2.4. ∼

147 The expected number of neutrino and background events are obtained from re- optimized cuts. The number of expected neutrino events is calculated for each GRB. For each GRB, the analysis level eﬀective area as a function of energy is obtained from corresponding geometric information of the GRB. The total expected number of neutrino events is:

57 N = d log E EF i(E) Ai (E) ln 10 (7.1) total · · eﬀect · i=1 X Z

i 1 2 where i is a index number of GRB (total 57 GRBs), F (E) is the ﬂuence [GeV− cm− ]

th i of i GRB, and Aeffect(E) is the effective area of the Testbed for the neutrinos from ith GRB direction. The expected number of background events is obtained from an exponential function fit at the final Peak/Correlation cut, which is described in [2]. We use a blinding technique that draws from both the one used for the ARA diffuse neutrino search (Chapter6) and the ANITA GRB neutrino analysis [105]. Our analysis consists of three stages. First, we use a 10 % subset from the full ARA Testbed data set for the preliminary background analysis. We consider a background analysis window to be the hour on either side of each GRB time, minus the closest 5 minutes. The 55 minutes on either side of a GRB (total 110 minutes) is a background analysis window and 5 minutes before and after the GRB is selected as a neutrino signal window. This is the same method used in ANITA GRB analysis [105]. With the events in the background analysis window, we optimize our analysis cuts to give us the best limit. From our optimized cuts, we expect to have 1.166 background events in the 57 GRB background windows and 0.106 background events in the neutrino signal windows from the remaining 90 % data set. Expected number

5 of neutrino events from 57 GRBs is 1.47 10− . ×

148 After the first stage of analysis, we look at the events in the 90 % data set background analysis windows. In this stage of analysis, we make sure our background estimation from the 10 % subset is consistent with what we see in the remaining 90 % of the data. We have one survived event from 90 % data set’s 57 GRB background analysis windows which is consistent with the 1.166 expected events. In the final stage of the analysis, we search for neutrino events in the neutrino signal windows for each GRBs with the 90 % data set. With the same optimized analysis cuts defined in the first analysis stage, we search for events that pass our cuts within the 57 GRB signal windows over a total of 570 minutes.

7.6 Results

There were no events in the 90 % data set signal region which is consistent with 0.106 background events. With a 90% confidence interval from expected background and estimated GRB neutrino events, we placed a limit for the combined fluence from the 57 GRBs. Fig. 7.6 shows the fluence of each GRB, the total fluence from 57 GRBs with NeuCosmA model, and the GRB neutrino fluence limit from 1016 to 1019 eV. In order to compare the limit from other experiments which have different set of GRBs for their analysis, we also provide the inferred quasi-diffuse neutrino flux limit with two assumptions. First, we assume that the 57 analyzed GRBs can represent the average GRB over the year. The second assumption is to let 667 GRBs as an average number of GRBs that are detected by satellites in a year [54, 110]. With these two assumptions, the quasi-diffuse neutrino flux limit is:

1 667 1 E2Φ = E2F (7.2) × 4π N 365 24 60 60 GRB × × ×

149 GRB fluence limit

6 ] 10 -2 105 104

F [GeV cm 3 2 10 E 102 10 1 10-1 10-2 10-3 10-4 10-5 10-6 0 2 4 6 8 10 12 Neutrino energy [log (E/GeV)] 10

Figure 7.6: The limit on the UHE GRB neutrino ﬂuence from 57 GRBs. Total ﬂuence from 57 GRBs is shown with a red solid curve and the limit from the ARA Testbed above 1016 eV is shown with a red dashed curve.

2 2 1 1 where E Φ is the quasi-diﬀuse neutrino ﬂux limit in units of [GeVcm− sr− sec− ],

2 E F is the fluence limit, and NGRB is the number of analyzed GRBs which is 57 for this analysis. Fig. 7.7 shows the quasi-diffuse neutrino flux limit from multiple experiments. Our limit is the first UHE GRB neutrino quasi-diffuse flux limit at energies above 1016 eV. From the future analyses from two ARA deep stations, we expect to have at least a factor of 6 improved sensitivity based on [2]. There is a factor of 3 increment ∼ from the shallow Testbed station to the 200 m deep station and another factor of 2 ∼ for the number of deep stations currently operating. In addition to the improvements from the number of deep stations, we expect to have improved livetime, and analysis efficiencies from the deep stations.

150 GRB quasi-diffuse flux limit ] -1 10-2 sr -1 10-3

sec -4 -2 10 10-5

-6

[GeV cm 10 Φ

2 -7 E 10 10-8 10-9 10-10 10-11 10-12 10-13 0 2 4 6 8 10 12 Neutrino energy [log (E/GeV)] 10

Figure 7.7: The inferred quasi-diffuse flux limit from the selected 57 GRBs. The quasi- diffuse flux limit is obtained from the fluence limit (Fig. 7.6 with the assumptions that 57 analyzed GRBs can represent the average GRB over the year and average number of GRBs in a year is 667. This is the first quasi-diffuse GRB neutrino flux limit for energies above 1016 eV.

7.7 Conclusions

Using ARA Testbed data from January 2011 to December 2012, we have searched UHE GRB neutrinos. Analysis cuts have been re-optimized with reduced background from the coincidence time window for the 57 selected GRBs. The GRB neutrino spectra are based on the NeuCosmA code, an advanced Monte Carlo cosmic neutrino accelerator code. We found zero neutrino candidate events from the analysis which is consistent with the expectation. We present the GRB neutrino fluence limit and the first quasi-diffuse GRB neutrino flux limit for energies above 1016 eV. Future analyses from ARA deep stations are expected to have at least a factor of 6 improvement. This

151 ARA Testbed analysis will serve as a guideline and benchmark for the future ARA deep stations’ analyses.

152 Chapter 8

Conclusions

In this thesis, we described two different searches for UHE neutrinos using ARA Testbed data from 2011 to 2012. With the Testbed data and the simulation set produced by the simulation that we developed, we present diffuse (GZK) and point source (GRB) neutrino searches. In Chapter6 we present a diffuse UHE neutrino search from the Testbed. We use an interferometric map technique for our analyses. From interferometric maps, we apply geometric cuts that reject events that reconstruct to known background sources and clustering directions. We also reject events that have a low quality reconstruction based on the interferometric maps. The overall analysis efficiency for a 1018 eV neutrino was 20%. We found zero neutrino candidate events on an ex- ∼ +0.52 17 pected 0.06 0.05 background events. We set limits on the neutrino flux above 10 eV − given the effective area of the Testbed derived from AraSim and 224 days of livetime examined from the data. A GRB neutrino search from the Testbed is presented in Chapter7. Among 600 GRBs monitored by the GCN catalog from January 2011 to December 2012, ∼ 57 GRBs were selected to be analyzed by a set of cuts that rejects high anthropogenic background periods, unstable station periods, and GRBs located outside of our field-of-view. We only analyze events that occurred during the hour on either side

153 of the time of each GRB. This timing constraint reduced the estimated number of background events and we re-optimized the analysis cuts to get the best limit on the dominant GRB event using the NeuCosmA modeling program. Three analysis cuts that are related to the quality of the directional reconstruction become looser than in the diffuse neutrino search and the overall analysis cut efficiency for the fluence of the dominant GRB increased by a factor of 2.4. There were no neutrino candidate ∼ events passing all cuts on 0.106 estimated background events. We set a limit on the GRB neutrino fluence and the first quasi-diffuse GRB neutrino flux limit for energies above 1016 eV. Although neutrino flux and fluence constraints set by our Testbed analyses are not the best limits in the UHE regime due to the shallowly deployed antennas, analysis techniques from our analyses can provide a benchmark for future deep stations’ neutrino searches which are expected to be improved. For the neutrino search in the two operational deep ARA stations, we expect to have at least a factor of 6 improved sensitivity to UHE neutrinos. This includes a factor of three for due to increased depth, and another factor of two for two operational stations instead of one. Aside from the effect of deep station, we also expect to have improvements in analysis efficiencies due to the increased number of antennas. For each station, the number of antennas that are buried in the ice increases from 8 to 16 by using deep stations instead of the Testbed. With more antennas, we can require more trigger coincidences between antennas which reduces the noise rates and allows us to reduce the trigger threshold. Lower trigger threshold increases the sensitivity of the detector to neutrinos. Also, the quality of the directional reconstruction will be dramatically improved as the total number of pairs of antennas making an interferometric map increase from 6 to 28. This increased number of pairs of antennas will help us to

154 identify the direction of the source more reliably and distinguish between anthropogenic background events and neutrino candidate events. Preliminary research from two deep stations shows consistent result with our ex- pectations that described above. The neutrino sensitivity from two deep stations is improved by factor of 20 from our Testbed analysis. This improvement includes a ∼ factor of 6 from two deep stations as described above and another factor of 3 from the analysis eﬃciency. This preliminary research is currently under preparation to be published in near future. Seven more deep stations are proposed to be deployed in two deployment seasons (Fig. 4.1) and we are looking forward to deploying a full detector with 37 stations. The proposed ARA37 is expected to detect UHE neutrinos robustly [31] and help us to understand UHE astrophysical phenomena.

155 Bibliography

[1] E. Hong et. al., Improved Performance of the Preampliﬁer-Shaper Design for a High-Density Sensor Readout System, Journal of the Korean Physical Society 54 (2009) 760. Cited on page vi.

[2] ARA Collaboration Collaboration, P. Allison et. al., First Constraints on the Ultra-High Energy Neutrino Flux from a Prototype Station of the Askaryan Radio Array, 1404.5285. Cited on pages vi, 39, 47, 90, 140, 141, 146, 147, 148, and 150.

[3] M. Ahlers, L. Anchordoqui, M. Gonzalez-Garcia, F. Halzen and S. Sarkar, GZK Neutrinos after the Fermi-LAT Diﬀuse Photon Flux Measurement, Astropart.Phys. 34 (2010) 106–115 [1005.2620]. Cited on pages xi, xiv, 11, 15, 17, 18, and 19.

[4] M. Takeda, N. Sakaki, K. Honda, M. Chikawa, M. Fukushima et. al., Energy determination in the Akeno Giant Air Shower Array experiment, Astropart.Phys. 19 (2003) 447–462 [astro-ph/0209422]. Cited on pages xiii and2.

[5] Particle Data Group Collaboration, K. Nakamura et. al., Review of particle physics, J.Phys. G37 (2010) 075021. Cited on pages xiii,1,2,3, 10, 11, 12, 14, 15, 24, and 27.

[6] C. Grupen, Astroparticle Physics. Springer, 2005. Cited on pages xiv and 29.

[7] P. W. Gorham, C. Hebert, K. Liewer, C. Naudet, D. Saltzberg et. al., Experimental limit on the cosmic diﬀuse ultrahigh-energy neutrino ﬂux, Phys.Rev.Lett. 93 (2004) 041101 [astro-ph/0310232]. Cited on pages xv, 31, and 32.

[8] ANITA Collaboration Collaboration, S. Barwick et. al., Constraints on cosmic neutrino ﬂuxes from the anita experiment, Phys.Rev.Lett. 96 (2006) 171101 [astro-ph/0512265]. Cited on pages xv,6, 17, 32, and 35.

156 [9] ANITA Collaboration Collaboration, P. Gorham et. al., Erratum: Observational Constraints on the Ultra-high Energy Cosmic Neutrino Flux from the Second Flight of the ANITA Experiment, Phys.Rev. D85 (2012) 049901 [1011.5004]. Cited on pages xv, 34, 36, 91, 113, and 140. [10] F. Halzen and S. R. Klein, IceCube: An Instrument for Neutrino Astronomy, Rev.Sci.Instrum. 81 (2010) 081101 [1007.1247]. Cited on pages xv and 37. [11] IceCube Collaboration Collaboration, M. Aartsen et. al., Probing the origin of cosmic-rays with extremely high energy neutrinos using the IceCube Observatory, Phys.Rev. D88 (2013) 112008 [1310.5477]. Cited on pages xv, 34, 38, and 91. [12] J. Alvarez-Muniz, A. Romero-Wolf and E. Zas, Practical and accurate calculations of Askaryan radiation, Phys.Rev. D84 (2011) 103003 [1106.6283]. Cited on pages xix, 62, 63, 64, 65, and 142. [13] J. Alvarez-Muniz, A. Romero-Wolf and E. Zas, Cherenkov radio pulses from electromagnetic showers in the time-domain, Phys.Rev. D81 (2010) 123009 [1002.3873]. Cited on pages xix, xx, 71, and 72. [14] S. Hummer, P. Baerwald and W. Winter, Neutrino Emission from Gamma-Ray Burst Fireballs, Revised, Phys.Rev.Lett. 108 (2012) 231101 [1112.1076]. Cited on pages xxxi, 141, and 142. [15] R. Gandhi, C. Quigg, M. H. Reno and I. Sarcevic, Ultrahigh-energy neutrino interactions, Astropart.Phys. 5 (1996) 81–110 [hep-ph/9512364]. Cited on pages1 and6. [16] HiRes Collaboration Collaboration, D. Bird et. al., The Cosmic ray energy spectrum observed by the Fly’s Eye, Astrophys.J. 424 (1994) 491–502. Cited on pages2 and4. [17] HiRes Collaboration Collaboration, R. Abbasi et. al., First observation of the Greisen-Zatsepin-Kuzmin suppression, Phys.Rev.Lett. 100 (2008) 101101 [astro-ph/0703099]. Cited on pages2 and4. [18] Pierre Auger Collaboration Collaboration, J. Abraham et. al., Observation of the suppression of the ﬂux of cosmic rays above 4 1019eV, Phys.Rev.Lett. 101 (2008) 061101 [0806.4302]. Cited on pages2,4×, 15, and 17. [19] P. Chen and K. Hoﬀman, Origin and evolution of cosmic accelerators - the unique discovery potential of an UHE neutrino telescope: Astronomy Decadal Survey (2010-2020) Science White Paper, 0902.3288. Cited on page4. [20] A. Olinto, J. Adams, C. Dermer, J. Krizmanic, J. Mitchell et. al., White Paper on Ultra-High Energy Cosmic Rays, 0903.0205. Cited on page4.

157 [21] K. Greisen, End to the cosmic ray spectrum?, Phys.Rev.Lett. 16 (1966) 748–750. Cited on pages4 and 91.

[22] G. Zatsepin and V. Kuzmin, Upper limit of the spectrum of cosmic rays, JETP Lett. 4 (1966) 78–80. Cited on pages4 and 91.

[23] V. Berezinsky and G. Zatsepin, Cosmic rays at ultrahigh-energies (neutrino?), Phys.Lett. B28 (1969) 423–424. Cited on page4.

[24] V. Berezinsky, M. Kachelriess and A. Vilenkin, Ultrahigh-energy cosmic rays without GZK cutoﬀ, Phys.Rev.Lett. 79 (1997) 4302–4305 [astro-ph/9708217]. Cited on page4.

[25] D. Guetta, D. Hooper, J. Alvarez-Muniz, F. Halzen and E. Reuveni, Neutrinos from individual gamma-ray bursts in the BATSE catalog, Astropart.Phys. 20 (2004) 429–455 [astro-ph/0302524]. Cited on pages4 and 20.

[26] E. Waxman and J. N. Bahcall, High-energy neutrinos from cosmological gamma-ray burst ﬁreballs, Phys.Rev.Lett. 78 (1997) 2292–2295 [astro-ph/9701231]. Cited on pages4 and 22.

[27] Super-Kamiokande Collaboration Collaboration, Y. Fukuda et. al., Evidence for oscillation of atmospheric neutrinos, Phys.Rev.Lett. 81 (1998) 1562–1567 [hep-ex/9807003]. Cited on page6.

[28] ANTARES Collaboration Collaboration, A. Margiotta, The ANTARES neutrino telescope, EPJ Web Conf. 52 (2013) 09008. Cited on page6.

[29] IceCube Collaboration Collaboration, J. Ahrens et. al., Icecube - the next generation neutrino telescope at the south pole, Nucl.Phys.Proc.Suppl. 118 (2003) 388–395 [astro-ph/0209556]. Cited on pages6 and 34.

[30] S. Barwick, E. Berg, D. Besson, E. Cheim, T. Duﬃn et. al., Design and Performance of the ARIANNA Hexagonal Radio Array Systems, 1410.7369. Cited on page6.

[31] P. Allison, J. Auﬀenberg, R. Bard, J. Beatty, D. Besson et. al., Design and Initial Performance of the Askaryan Radio Array Prototype EeV Neutrino Detector at the South Pole, Astropart.Phys. 35 (2012) 457–477 [1105.2854]. Cited on pages6, 39, 41, 54, 91, 132, 133, 141, and 155.

[32] S. Barwick, E. Berg, D. Besson, T. Duﬃn, J. Hanson et. al., Radio-frequency Attenuation Length, Basal-Reﬂectivity, Depth, and Polarization Measurements from Moore’s Bay in the Ross Ice-Shelf, 1410.7134. Cited on pages6 and 29.

158 [33] M. Ackermann et. al., Optical properties of deep glacial ice at the South Pole, Journal of Geophysical Research 111 (2006) D13203. Cited on pages6, 28, and 29.

[34] B. C. Lacki, The End of the Rainbow: What Can We Say About the Extragalactic Sub-Megahertz Radio Sky?, Mon.Not.Roy.Astron.Soc. 406 (2010) 863 [1004.2049]. Cited on page 11.

[35] M. Kachelriess, E. Parizot and D. Semikoz, The GZK horizon and constraints on the cosmic ray source spectrum from observations in the GZK regime, JETP Lett. 88 (2009) 553–557 [0711.3635]. Cited on page 12.

[36] R. Engel, D. Seckel and T. Stanev, Neutrinos from propagation of ultrahigh-energy protons, Phys.Rev. D64 (2001) 093010 [astro-ph/0101216]. Cited on page 13.

[37] V. Barger, P. Huber and D. Marfatia, Ultra high energy neutrino-nucleon cross section from cosmic ray experiments and neutrino telescopes, Phys.Lett. B642 (2006) 333–341 [hep-ph/0606311]. Cited on page 13.

[38] Z. Fodor, S. Katz, A. Ringwald and H. Tu, Bounds on the cosmogenic neutrino ﬂux, JCAP 0311 (2003) 015 [hep-ph/0309171]. Cited on page 13.

[39] http://www.desy.de/ uhecr/propagation.html. Cited on page 14. ∼ [40] Z. Fodor and S. Katz, Ultrahigh-energy cosmic rays from compact sources, Phys.Rev. D63 (2001) 023002 [hep-ph/0007158]. Cited on page 14.

[41] Z. Fodor, S. Katz, A. Ringwald and H. Tu, Electroweak instantons as a solution to the ultrahigh-energy cosmic ray puzzle, Phys.Lett. B561 (2003) 191–201 [hep-ph/0303080]. Cited on page 14.

[42] http://www.physics.ohio-state.edu/ connolly/CRnu/z/z.html. Cited on page 15. ∼

[43] IceCube Collaboration Collaboration, A. Achterberg et. al., Multi-year search for a diﬀuse ﬂux of muon neutrinos with AMANDA-II, Phys.Rev. D76 (2007) 042008 [0705.1315]. Cited on page 17.

[44] IceCube Collaboration Collaboration, M. Ackermann et. al., Search for Ultra High-Energy Neutrinos with AMANDA-II, Astrophys.J. 675 (2008) 1014–1024 [0711.3022]. Cited on page 17.

[45] BAIKAL Collaboration Collaboration, V. Aynutdinov et. al., Search for a diﬀuse ﬂux of high-energy extraterrestrial neutrinos with the nt200 neutrino telescope, Astropart.Phys. 25 (2006) 140–150 [astro-ph/0508675]. Cited on page 17.

159 [46] HiRes Collaboration Collaboration, K. Martens, HiRes Estimates and Limits for Neutrino Fluxes at the Highest Energies, 0707.4417. Cited on page 17.

[47] F. Halzen and D. Hooper, AMANDA Observations Constrain the Ultrahigh Energy Neutrino Flux, Phys.Rev.Lett. 97 (2006) 099901 [astro-ph/0605103]. Cited on page 17.

[48] IceCube Collaboration Collaboration, A. Achterberg et. al., First Year Performance of The IceCube Neutrino Telescope, Astropart.Phys. 26 (2006) 155–173 [astro-ph/0604450]. Cited on page 17.

[49] R. W. Klebesadel, I. B. Strong and R. A. Olson, Observations of Gamma-Ray Bursts of Cosmic Origin, Astrophys.J. 182 (1973) L85–L88. Cited on page 20.

[50] F. Halzen and D. Hooper, High-energy neutrino astronomy: The Cosmic ray connection, Rept.Prog.Phys. 65 (2002) 1025–1078 [astro-ph/0204527]. Cited on page 20.

[51] R. White, Some requirements of a colliding comet source of gamma ray bursts, Astrophysics and Space Science 208 (1993), no. 2 301–311. Cited on page 20.

[52] D. Lynden-Bell, Galactic nuclei as collapsed old quasars, Nature 223 (1969) 690. Cited on page 22.

[53] D. Kazanas, K. Fukumura, E. Behar, I. Contopoulos and C. Shrader, Toward a Uniﬁed AGN Structure, 1206.5022. Cited on page 22.

[54] E. Waxman and J. N. Bahcall, High-energy neutrinos from astrophysical sources: An Upper bound, Phys.Rev. D59 (1999) 023002 [hep-ph/9807282]. Cited on pages 22, 24, 140, and 149.

[55] S. Yoshida, H.-y. Dai, C. C. Jui and P. Sommers, Extremely high-energy neutrinos and their detection, Astrophys.J. 479 (1997) 547–559 [astro-ph/9608186]. Cited on pages 22 and 25.

[56] P. Bhattacharjee, C. T. Hill and D. N. Schramm, Grand uniﬁed theories, topological defects and ultrahigh-energy cosmic rays, Phys.Rev.Lett. 69 (1992) 567–570. Cited on pages 22 and 25.

[57] T. J. Weiler, Relic neutrinos, Z bursts, and cosmic rays above 1020 eV, hep-ph/9910316. Cited on pages 22 and 25.

[58] Z. Fodor, S. Katz and A. Ringwald, Determination of absolute neutrino masses from Z bursts, Phys.Rev.Lett. 88 (2002) 171101 [hep-ph/0105064]. Cited on pages 22 and 25.

160 [59] C. M. Urry and P. Padovani, Uniﬁed schemes for radio-loud active galactic nuclei, Publ.Astron.Soc.Pac. 107 (1995) 803 [astro-ph/9506063]. Cited on page 23.

[60] E. Waxman, Cosmological origin for cosmic rays above 1019 eV, Astrophys.J. 452 (1995) L1–L4 [astro-ph/9508037]. Cited on page 23.

[61] G. A. Askaryan JETP 14 (1962) 441. Cited on pages 26 and 91.

[62] G. A. Askaryan JETP 21 (1965) 658. Cited on pages 26 and 91.

[63] I. Kravchenko, C. Cooley, S. Hussain, D. Seckel, P. Wahrlich et. al., Rice limits on the diﬀuse ultrahigh energy neutrino ﬂux, Phys.Rev. D73 (2006) 082002 [astro-ph/0601148]. Cited on page 30.

[64] P. Gorham, K. Liewer and C. Naudet, Initial results from a search for lunar radio emission from interactions of >= 1019 eV neutrinos and cosmic rays, astro-ph/9906504. Cited on page 31.

[65] IceCube Collaboration Collaboration, M. Aartsen et. al., Observation of High-Energy Astrophysical Neutrinos in Three Years of IceCube Data, Phys.Rev.Lett. 113 (2014) 101101 [1405.5303]. Cited on page 34.

[66] I. Kravchenko et. al., Updated Neutrino Flux Limits from the RICE Experiment at the South Pole, 1106.1164. Cited on page 39.

[67] G. S. Varner et. al., The large analog bandwidth recorder and digitizer with ordered readout (LABRADOR) ASIC, Nucl. Instrum. Meth. A583 (2007) 447–460 [physics/0509023]. Cited on page 45.

[68] A. Connolly, R. S. Thorne and D. Waters Phys.Rev. D83 (2011) 113009 [1102.0691]. Cited on pages 49 and 133.

[69] D. Chirkin and W. Rhode, Propagating leptons through matter with Muon Monte Carlo (MMC), 0407075. Cited on page 49.

[70] http://icecube.wisc.edu/ mnewcomb/radio/. Cited on pages xvii, 50, and 51. ∼ [71] I. Kravchenko, D. Besson and J. Meyers, In situ index-of-refraction measurements of the South Polar ﬁrn with the RICE detector, Journal of Glaciology 50 (2004) 522–532. Cited on pages 50 and 132.

[72] Original code from Chris Weaver. Cited on page 50.

[73] P. Price et. al., Temperature proﬁle for glacial ice at the South Pole: Implications for life in a nearby subglacial lake, PNAS 99 (2002) 7844–7847. Cited on pages 53 and 132.

161 [74] F. A. Matsuoda, T. and S. Mae, Eﬀect of temperature on dielectric properties of ice in the range 5-39 GHz, Journal of Applied Physics 80 (1996) 5884. Cited on pages 53 and 132.

[75] F. Wu, Using ANITA-I to Constrain Ultra High Energy Neutrino-Nucleon Cross Section. PhD thesis, University of California, Irvine, 2009. Cited on pages 53 and 132.

[76] http://www.nec2.org/. Cited on page 55.

[77] http://dd6um.darc.de/QucsStudio/qucsstudio.html. Cited on page 59.

[78] IEEE TRANSACTIONS ON EDUCATION 39 (1996), no. 1. Cited on page 59.

[79] J. Alvarez-Muniz, A. Romero-Wolf and E. Zas, Time-domain radio pulses from particle showers, Nucl.Instrum.Meth. A662 (2012) S32–S35. Cited on pages 62, 65, 66, and 69.

[80] J. Alvarez-Muniz, R. Vazquez and E. Zas, Calculation methods for radio pulses from high-energy showers, Phys.Rev. D62 (2000) 063001 [astro-ph/0003315]. Cited on pages 62, 73, and 74.

[81] J. Alvarez-Muniz, J. Carvalho, Washington R. and E. Zas, Monte Carlo simulations of radio pulses in atmospheric showers using ZHAireS, Astropart.Phys. 35 (2012) 325–341 [1107.1189]. Cited on page 62.

[82] E. Zas, F. Halzen and T. Stanev, Electromagnetic pulses from high-energy showers: Implications for neutrino detection, Phys.Rev. D45 (1992) 362–376. Cited on pages 65 and 74.

[83] K. Greisen Prog. Cosmic Ray Phys. 3 (1956). Cited on page 66.

[84] H. A. Gaisser, T.K. Proceedings of the 15th International Cosmic Ray Conference, 13-26 Aug 1977 8 353. Cited on pages 66 and 67.

[85] p. c. Jaime Alvarez-Muniz. Cited on page 66.

[86] L. Landau and I. Pomeranchuk, Electron cascade process at very high-energies, Dokl.Akad.Nauk Ser.Fiz. 92 (1953) 735–738. Cited on page 70.

[87] A. B. Migdal, Bremsstrahlung and pair production in condensed media at high-energies, Phys.Rev. 103 (1956) 1811–1820. Cited on page 70.

[88] J. Alvarez-Muniz and E. Zas, Cherenkov radio pulses from Eev neutrino interactions: The LPM eﬀect, Phys.Lett. B411 (1997) 218–224 [astro-ph/9706064]. Cited on pages 72, 74, and 75.

162 [89] J. Alvarez-Muniz and E. Zas, The LPM effect for EeV hadronic showers in ice: Implications for radio detection of neutrinos, Phys.Lett. B434 (1998) 396–406 [astro-ph/9806098]. Cited on page 75. [90] I. R. I.S. Gradshteyn, Table of Integrals, Series and Products, 5th edition. Academic Press, 1994. Cited on page 89. [91] V. S. Berezinsky and G. T. Zatsepin, Cosmic rays at ultra high energies (neutrino?), Phys. Lett. B28 (1969) 423–424. Cited on page 91. [92] V. S. Berezinsky and G. T. Zatsepin, , Sov. J. Nucl. Phys. 11 (1970) 111. Cited on page 91. [93] P. Gorham et. al., Radio-frequency measurements of coherent transition and Cherenkov radiation: Implications for high-energy neutrino detection, Phys. Rev. E62 (2000) 8590–8605 [hep-ex/0004007]. Cited on page 91. [94] D. Saltzberg et. al., Observation of the Askaryan effect, AIP Conf. Proc. 579 (2001) 225–233. Cited on page 91. [95] P. W. Gorham et. al., Accelerator measurements of the Askaryan effect in rock salt: A roadmap toward Teraton underground neutrino detectors, Phys. Rev. D72 (2005) 023002 [astro-ph/0412128]. Cited on page 91. [96] ANITA Collaboration, P. W. Gorham et. al., Observations of the Askaryan effect in ice, Phys. Rev. Lett. 99 (2007) 171101 [hep-ex/0611008]. Cited on page 91. [97] IceCube Collaboration, M. Aartsen et. al., Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector, Science 342 (2013), no. 6161 1242856 [1311.5238]. Cited on page 91. [98] S. Barwick, D. Besson, P. Gorham and D. Saltzberg, South Polar in situ radio-frequency ice attenuation, J. Glaciol. 51 (2005) 231–238. Cited on page 91. [99] K. Kotera, D. Allard and A. Olinto JCAP 1010 (2010) 013 [1009.1382]. Cited on page 114. [100] P. Meszaros and P. Meszaros, Gamma-ray bursts: Accumulating afterglow implications, progenitor clues, and prospects, Science 291 (2001) 79–84 [astro-ph/0102255]. Cited on page 138. [101] P. Meszaros, Theories of gamma-ray bursts, Ann.Rev.Astron.Astrophys. 40 (2002) 137–169 [astro-ph/0111170]. Cited on page 138. [102] P. Meszaros, Gamma-Ray Bursts, Rept.Prog.Phys. 69 (2006) 2259–2322 [astro-ph/0605208]. Cited on page 139.

163 [103] IceCube Collaboration Collaboration, R. Abbasi et. al., An absence of neutrinos associated with cosmic-ray acceleration in γ-ray bursts, Nature 484 (2012) 351–353 [1204.4219]. Cited on page 139.

[104] ANTARES Collaboration Collaboration, S. Adrian-Martinez et. al., Search for Cosmic Neutrino Point Sources with Four Year Data of the ANTARES Telescope, Astrophys.J. 760 (2012) 53 [1207.3105]. Cited on page 139.

[105] A. Vieregg, K. Palladino, P. Allison, B. Baughman, J. Beatty et. al., The First Limits on the Ultra-high Energy Neutrino Fluence from Gamma-ray Bursts, Astrophys.J. 736 (2011) 50 [1102.3206]. Cited on pages 139 and 148.

[106] S. Hummer, M. Ruger, F. Spanier and W. Winter, Simpliﬁed models for photohadronic interactions in cosmic accelerators, Astrophys.J. 721 (2010) 630–652 [1002.1310]. Cited on pages 139 and 140.

[107] http://grbweb.icecube.wisc.edu. Cited on page 139.

[108] IceCube Collaboration Collaboration, R. Abbasi et. al., Search for muon neutrinos from Gamma-Ray Bursts with the IceCube neutrino telescope, Astrophys.J. 710 (2010) 346–359 [0907.2227]. Cited on page 139.

[109] ANTARES Collaboration Collaboration, S. Adrian-Martinez et. al., Search for muon neutrinos from gamma-ray bursts with the ANTARES neutrino telescope using 2008 to 2011 data, Astron.Astrophys. 559 (2013) A9 [1307.0304]. Cited on page 139.

[110] IceCube Collaboration Collaboration, R. Abbasi et. al., Limits on Neutrino Emission from Gamma-Ray Bursts with the 40 String IceCube Detector, Phys.Rev.Lett. 106 (2011) 141101 [1101.1448]. Cited on page 149.

164