The ANITA-I Limit on Gamma Ray Burst Neutrinos

DISSERTATION

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

Graduate School of The Ohio State University

By

Kimberly J. Palladino, A.B., M.S.

Graduate Program in Physics

The Ohio State University

2009

Dissertation Committee:

Dr. James J. Beatty, Adviser Dr. John Beacom Dr. Richard J. Furnstahl Dr. Richard E. Hughes Copyright by

Kimberly J. Palladino

c 2009

Abstract

The ANtarctic Impulsive Transient Antenna (ANITA) searches for ultra high en- ergy neutrinos interacting in the Antarctic ice cap. It is a long duration balloon exper- iment composed of an array of broadband dual-polarized horn antennas that had its

first science flight over Antarctica in December 2006 through January 2007. ANITA relies upon the Askaryan effect, in which a particle shower in a dense medium emits coherent Cherenkov radiation at radio wavelengths, for the detection of a neutrino induced shower. Using the null result reported elsewhere of the detection of neutrino candidates by the ANITA-I experiment, we place a limit upon the flux of neutrinos from Gamma Ray Bursts (GRBs). During the ANITA-I flight, 21 GRBs were detected by spacecraft, but none occurred in the primary ANITA field of view while the instru- ment was operating. Using the measured redshifts of the limited number of localized

GRBs that occurred during the flight, we model their neutrino flux using a basic

Waxman-Bahcall model. We are able to place a 90% CL limit on the E−4 prompt neutrino fluence from GRB061222B in the energy range of 107.7 GeV ǫ 109.7 GeV ≤ ν ≤ of ǫ4 Φ 4.65 1018 GeV3 cm−2 at a ratio of 4.81 107 to the predicted model for a ν ν ≤ × × burst time of 42 seconds. With no neutrino detections over the entire ANITA-I flight, lasting over 17 days, we set a limit with a 90% CL on a E−4 flux over the energy range of 107.65 GeV ǫ 1010 GeV of ǫ4Φ 6.5 1010 GeV3 cm−2 s−1 sr−1. ≤ ν ≤ ν ν ≤ ×

ii ACKNOWLEDGMENTS

Many thanks to my advisor, Jim Beatty, and all the members of the ANITA collaboration, as well as NASA’s Columbia Scientific Balloon Facility and the NSF

Antartic Program for their support making our research possible. Additional thanks to Kevin Hurley of Berkeley’s Space Science Lab for his help in determining potential directions of non-localized Gamma Ray Bursts. Finally, my appreciation to Brian

Baughman and Brian Mercurio for their expertise with matplotlib and IceMC

respectively.

iii VITA

1998 ...... Pennsbury Senior High School

2002 ...... A.B. Physics, Princeton University 2003-2004 ...... Physics Graduate Research Assistant, Pennsylvania State University 2004-present ...... Physics Graduate Research Assistant, The Ohio State University 2006 ...... M.S. Physics, The Ohio State University

PUBLICATIONS

Gorham, P. W. et al. New Limits in the Ultra-high Energy Cosmic Neutrino Flux from the ANITA Experiment. Phys. Rev. Lett. 103: 05113, 2009.

Gorham, P. W. et al. The Antarctic Impulsive Transient Antenna Ultra-high Energy Neutrino Detector Design, Performance, and Sensitivity for 2006-2007 Balloon Flight. Astropart. Phys. 32: 10-41, 2009.

Besson, D. Z. et al. In situ radioglaciological measurements near Taylor Dome, Antarctica and implications for ultra-high energy (UHE) neutrino astronomy. As- tropart. Physics. 29: 130-157, 2008.

Gorham, P. W. et al. Observations of the Askaryan effect in ice. Phys. Rev. Lett. 99: 171101, 2007.

Barwick, S. W. et al. Constraints on cosmic neutrino fluxes from the ANITA experiment. Phys. Rev. Lett. 96: 171101, 2006.

iv FIELDS OF STUDY

Major Field: Physics

Experimental Particle Astrophysics, Neutrino Astronomy

v Contents

Page

Abstract...... ii

Acknowledgments...... iii

Vita ...... iv

ListofTables...... x

ListofFigures ...... xi

Chapters:

1. Introduction...... 1

1.1 NeutrinoParticlePhysics ...... 2

1.2 NeutrinoAstronomy ...... 7

2. UltraHighEnergyNeutrinos ...... 18

vi 2.1 GZKNeutrinos...... 18

2.1.1 TheGZKProcess ...... 19

2.1.2 CRSpectrumCutoff ...... 23

2.1.3 GZKNeutrinoFluxModels ...... 27

2.2 Direct Astrophysical Sources: GRBs ...... 36

2.3 ExoticPhysicsSources...... 38

3. TheANITAInstrument ...... 41

3.1 Askaryan Effect and Radio Detection of Particle Showers ...... 41

3.2 TheANITApayload ...... 44

3.2.1 RFSignalChain ...... 45

3.2.2 SignalCapture ...... 48

3.2.3 SupportSystems ...... 49

3.2.4 Computing and Communication ...... 50

3.3 Prototyping and Preparing ANITA ...... 51

3.3.1 ANITA-lite: 2003-2004 Antarctic Flight ...... 51

3.3.2 Engineering Flight: Ft. Sumner, NM, 2005 ...... 53

3.3.3 SLACTestBeam: EndStationA,2006 ...... 54

4. TheFirstANITAFlight ...... 56

4.1 ANITA-IFlightPath...... 56

4.2 ANITA-IRFPerformance ...... 59

4.3 ANITA-ILiveTime...... 60

vii 4.4 Calibration ...... 68

5. ANITAandGRBNeutrinos ...... 71

5.1 GRBsduringtheANITA-IFlight...... 72

5.2 Estimating GRB Neutrino Fluxes for the ANITA-I Flight . . ... 83

5.3 AcceptancesandFluxLimits ...... 91

Bibliography ...... 107

Appendices:

A. IPN Localizations of ANITA-I Flight GRBs ...... 119

A.1 GRB061221...... 119

A.2 GRB061223...... 119

A.3 GRB061224...... 119

A.4 GRB061225...... 120

A.5 GRB061229...... 120

A.6 GRB061230...... 120

A.7 GRB070106...... 120

A.8 GRB070113...... 120

A.9 GRB070115A...... 120

A.10GRB070115B ...... 121

A.11GRB070116A...... 121

viii A.12GRB070116B ...... 121

A.13GRB070116C...... 121

A.14GRB070117...... 121

ix List of Tables

Table Page

5.1 GRBs that occurred during the ANITA-I Flight ...... 81

5.2 ANITAoperationattimesofGRBs ...... 84

5.3 GRBs with Measured Redshifts from the ANITA-I Flight ...... 87

5.4 ANITA-I Flight GRBs Flux Variables Following Razzaque etal ... 91

5.5 ANITA-I Flight GRBs Flux Variables Following Stamatikosetal... 91

x List of Figures

Figure Page

1.1 Standard hierarchy neutrino mass splitting diagram ...... 4

1.2 Standard Solar Model Neutrino Spectrum ...... 10

1.3 NeutrinosfromSN1987A...... 12

2.1 Photo-production Cross Section Energy Dependence ...... 20

2.2 GZKProtonSpectra ...... 22

2.3 Feynman Decay Diagrams for π+ and µ+ ...... 24

2.4 Differential UHECR flux from the Pierre Auger Observatory ..... 25

2.5 ESSGZKModels...... 29

xi 2.6 Three Flavor ESS GZK Model, updated in 2002 ...... 31

2.7 ESSandWBGZKFluxModels...... 32

2.8 ProtheroeandJohnsonGZKModelFlux ...... 33

2.9 Comparisonof3GZKFluxModels ...... 34

2.10 Comparisonof8GZKFluxModels ...... 36

2.11 GRB Photon/Neutrino Spectral Relationships ...... 39

3.1 Photograph of the ANITA-I Instrument ...... 44

3.2 ANITARFChain...... 46

3.3 Photograph of the ANITA Engineering Flight Payload ...... 52

3.4 DiagramofANITAwiththeSLACTestBeam ...... 55

4.1 ANITA-IFlightPath ...... 57

4.2 Ice Depth in ANITA’s view vs. Time ...... 58

xii 4.3 AverageMeasuredRFPowerindBm ...... 59

4.4 AverageRFPowervs.SolarAngle ...... 61

4.5 RF Power ADC counts vs Phi Sector from Sun ...... 62

4.6 GainLossinAnt23H ...... 63

4.7 ANITA-I LiveTime: Absolute and Fractional Scales ...... 65

4.8 CausesofDeadtimeinANITA-I...... 66

4.9 Seconds Missing Data from ANITA-I ...... 66

4.10 Time between events showing CPU “Coffee Breaks” ...... 67

4.11 ANITA-I Gain and Noise Figure Values ...... 69

5.1 ANITA-INeutrinoFluxLimits ...... 73

5.2 ANITA’s Acceptance at 1018.5 eV ...... 74

5.3 7 Swift-detected GRB Locations during ANITA-I ...... 75

xiii 5.4 GRB061221Localization ...... 76

5.5 GRB061223Localization ...... 76

5.6 GRB061224Localization ...... 77

5.7 GRB061225Localization ...... 77

5.8 GRB061229Localization ...... 78

5.9 GRB061230Localization ...... 78

5.10 GRB070106Localization ...... 79

5.11 GRB070113Localization ...... 79

5.12 GRB070115BLocalization ...... 80

5.13 GRB070116BLocalization ...... 80

5.14 GRB070117Localization ...... 82

5.15 Map of ANITA’s Locationatthe Time of each GRB ...... 85

xiv 5.16 NeutrinoFluxModelsfor3GRBs...... 92

5.17 NeutrinoFluenceModelsfor3GRBs ...... 93

5.18 Skymap for a GRB061222B-like Neutrino Flux ...... 95

5.19 Contoured Skymap for a GRB061222B-like Neutrino Flux ...... 96

5.20 Skymap for a GRB070110-like Neutrino Flux...... 97

5.21 Contoured Skymap for a GRB070110-like Neutrino Flux ...... 98

5.22 Skymap for an E−4 NeutrinoFlux...... 100

5.23 Contoured Skymap for an E−4 NeutrinoFlux ...... 101

5.24 GRBFluenceModelsandLimits ...... 102

5.25 GRB Monte Carlo Neutrino Events from GRB061222B by Flavor .. 103

5.26 GRB Monte Carlo Neutrino Events from GRB070103 by Flavor ... 104

5.27 GRBDiffuseFluxModelsandLimits ...... 105

xv Chapter 1

Introduction

In the past century astronomy has expanded to wavelengths both larger and smaller than those of visible light, and at every point a new window was opened onto the universe, bringing new discoveries and new questions. Particle physicists have also studied the charged particles arriving at Earth from space, hoping to learn about their origins and the environments they travel through. The light and charge- less neutrino has been a particularly attractive and elusive astrophysical messenger that can travel cosmological distances without deflections or interactions. Neutrinos are theoretically detectable across a broader energy spectrum and with a greater dis- tance range than photons or hadrons. Neutrinos can inform us about the early days of the universe, the nuclear burning occurring within stars, and the supernovas that end the life of stars. At higher energies, neutrinos may give insight into the most energetic astrophysical accelerators that also produce ultra high energy cosmic rays and gamma rays.

The ANtarctic Impulsive Transient Antenna (ANITA) is an innovative experiment designed to detect the highest energy cosmic neutrinos that arise from the interactions between ultra high energy cosmic rays and background photons. ANITA is a long duration balloon payload that first flew over Antactica in 2006-2007 and searched

1 for impulsive Askaryan signals from neutrino-induced particle cascades in the radio-

transparent Antarctic ice. Here we will discuss the details of the 2006-2007 ANITA

payload and its flight. No neutrino candidates were recorded, and we place limits

here on the neutrino flux from gamma ray bursts, a class of astrophysical objects with

known production of high energy photons. ANITA stands poised at the crossroads

of high energy particle physics and astrophysics, and the reported results can be

understood in the context of the development of neutrino astronomy.

1.1 Neutrino Particle Physics

Neutrinos are one of the fundamental particles described by the Standard Model.

In the early days of nuclear physics, the neutrino was hypothesized by Pauli and

further developed by Fermi in order to sustain the conservation of angular momentum,

energy and momentum in beta decays.

The past eight decades have witnessed a great deal of synthesis in experiment and

theory on the nature of neutrinos. As basic constituents of the Standard Model of

1 ~ Particle Physics, the neutrino is a fermion with a spin angular momentum of 2 and has members of the three lepton generations. These three flavor eigenstates, νe, νµ, ντ , correspond to the three charged leptons, the electron, muon and tau. Neutrinos carry no charge and the current limit on their magnetic moment is 0.74 10−10µ [1]. × B Neutrinos primarily interact via the weak force, mediated by the W ± and Z bosons.

Neutrinos, although low in mass, are not massless, and as their mass and flavor eigenstates are not identical, neutrino flavor oscillations occur. A neutrino of any

flavor can be described as the superposition of the mass eigenstates, and when a neutrino is born as one flavor eigenstate, as it travels through vacuum or matter it

2 may become a neutrino of a different flavor. This was first identified as the solar

neutrino problem, when in the 1960s the detected solar electron-neutrinos did not

match the predicted flux. Multiple experiments, looking to a variety of neutrino

sources including the Sun, cosmic ray interactions in Earth’s atmosphere, nuclear

reactors and particle accelerators, have now brought us to our current understanding

of neutrino oscillations. The most notable of these experiments are SuperKamiokande,

K2K, SNO, MINOS and MiniBooNE [2,3,4,5,6,7,8].

Evidence supports the existence of three mass eigenstates, denoted ν1, ν2, and ν3, and the unitary mixing matrix U, analogous to the CKM matrix [9,10] in the quark sector, is given as

−iδ iα1/2 c12s13 s12c13 s13e e 0 0 U = s c c s s eiδ c c s s s eiδ s c 0 eiα2/2 0 − 12 23 − 12 23 13 12 23 − 12 23 13 23 13    s s c c s eiδ c s s c s eiδ c c 0 01 12 23 − 12 23 13 − 12 23 − 12 23 13 23 13    (1.1) where s sin θ , and c cos θ , δ is the standard CP violating phase and α only ij ≡ ij ij ≡ ij 1,2 exist if neutrinos are Majorana particles, the import of which will be discussed below.

These phases are also CP violating, but do not impact neutrino oscillation. The fraction of any flavor (ν ) contained in a mass eigenstate (ν ) is given by ν ν 2 = α i |h α| ii| U 2. The complete probability for oscillation from one flavor to another is | αi|

P (ν ν ) = δ 4 (U ∗ U U U ∗ ) sin2[1.27∆m2 (L/E)] α → β αβ − ℜ αi βi αj βj ij i>j X +2 (U ∗ U U U ∗ ) sin[2.54∆m2 (L/E)] (1.2) ℑ αi βi αj βj ij i>j X in which the correct factors of c and ~ are included, and ∆m2 m2 m2 in the units ij ≡ i − j eV2, L is the distance traveled in km, and E is the neutrino energy in GeV.

The current status of experimental data gives of the neutrino sector is depicted

in Figure 1.1. The physical situation we encounter has shown that most experiments

3 Figure 1.1: The standard hierarchy of the neutrino squared-mass spectrum, with ν3 at the top and ν1 at the bottom. The fractions of νe are shown in green cross-hatching, while νµ is in the red right-leaning hatching, and ντ is the blue left-leaning hatching. From the Kayser review of Neutrino mass, mixing and flavor changing in [1].

allow us to probe a simpler, quasi-two-neutrino oscillation due to either one mass splitting being much larger than another, and thus for appropriate length and energies,

∆m2L/E = (1), or due to only two mass or flavor eigenstates being relevant. In O these situations, Equation 1.2 reduces to

P (ν ν ) = sin2 2θ sin2[1.27∆m2(L/E)] (1.3) α → β

Current limits on the electron neutrino component of ν3 are placed by short-

2 baseline reactor experiments and s13 . 0.032 [11] (which is why no νe component

is depicted in ν in Figure 1.1) which leads to θ θ and θ⊙ θ . Reactor 3 atm ≃ 23 ≃ 12 2 and solar neutrino data, when fit assuming CP T invariance, give results of ∆m21=

7.59+0.21 10−5 eV2 and tan2 θ =0.47+0.06 [12]. The best fit for atmospheric neutrino −0.21 × 12 −0.05 oscillations from the MINOS collaboration is ∆m2 = (2.43 0.11) 10−3 and maximal 23 ± × mixing, when restricted to the physical region, of sin2(2θ )=1.00 0.05 [13]. 23 ± The study of neutrinos has pushed the Standard Model perhaps more than any

other aspect of particle physics. The existence of neutrino masses, and mixing angles

significantly larger than those of the quark sector are the most provocative results of

4 neutrino experiments, and further, point to greater questions. One of these mysteries

is the absolute neutrino mass scale. From the atmospheric neutrino experiments, we

know that at least one of the neutrino mass eigenstates, with 90% confidence levels,

must have a mass greater than 45 meV. Cosmologists have placed limits upon the

summed mass of the neutrino eigenstates that were in thermal equilibrium in the early

universe (and thus are involved in expansion, nucleosynthesis, large-scale structure

growth and clustering) with 95% C.L. for differing datasets [14] of

m < (0.17 2.0)eV (1.4) i − i X There are similar limits upon the effective mass of the electron-anti-neutrino from tritium beta decay of 2 eV [1]. Beyond the question of mass scale, it is also an open question whether the mass hierarchy shown in Figure 1.1 is the physically existing one. If it were inverted, much analogy with the quark sector would be lost and many grand unified theories would be disfavored.

Another question that remains regards the number of neutrino species and the possible existence of a sterile neutrino. For neutrinos with masses less than half that of the Z boson, the measurement of e+e− ννγ at the LEP provides a value of → 2.92 0.05 for the number of neutrino types [1]. From cosmology the best fit value is ± +0.7 3.3−0.6 for the number of neutrinos, which includes the newest WMAP 5-yr data [15].

Sterile neutrinos, which need not have weak interactions, are not bound by these

limits. Indeed, a sterile neutrino is a dark matter candidate.

Physicists are keen to determine if neutrinos are Majorana particles, and thus

their own antiparticles. In such a case, lepton number, L, would not be conserved.

To include the neutrino mass in the Standard Model, Dirac mass terms must be added

that include a right-handed neutrino current similar to terms for quarks and charged

5 leptons. However, since charge conservation is not a worry with neutrinos, a Majorana

mass term can be added that is constructed from the right-handed neutrino and its

charge conjugate, which mixes neutrinos and anti-neutrinos and doesn’t conserve L.

Experimentalists are looking for neutrinoless double beta decay, a situation where a nucleus gains two protons with the loss of two neutrons and emitting two electrons, and where the anti-neutrino emitted in one beta decay is the neutrino absorbed in the other. Current experiments can probe this situation if the neutrino mass spectrum is in the inverted hierarchy.

A final question in neutrino physics is whether or not there is CP violation in

the neutrino sector. Both in the Dirac and Majorana neutrino situations, CP vio-

lation may occur. Discovery of leptonic CP violation, a difference in neutrino and

anti-neutrino oscillation probabilities, would indicate that this is not a singular char-

acteristic of quarks. CP violation in the neutrino sector is also of great interest to

cosmologists who believe it could contribute to the universe’s baryon asymmetry. The

unequal numbers of positively and negatively charged leptons could then convert to

baryon asymmetry [16,17,18,19].

For more complete reviews of the current status of neutrino physics, the Particle

Data Group Reviews by Vogel and Piepke, Nakamura, and Kayser are invaluable [1].

The historical development of neutrino physics is discussed in reviews [20] and several books, including Griffiths’ Introduction to Elementary Particles [21] and Fukugita and

Yanagida’s Physics of Neutrinos and Applications to Astrophysics [22].

6 1.2 Neutrino Astronomy

In the 1950s, physicists realized that neutrinos would have played a critical role in the early universe and that detectable numbers of them would be created in the

Sun. Furthermore, since neutrinos are produced in most nuclear reactions, they could be used to probe astrophysical processes that are otherwise hidden from observation.

The other common astrophysical messengers, photons and charged particles, have limitations that the weakly interacting neutrinos avoid. Dense, dusty regions can block conventional signals both from within their confines, and from more distant objects. High energy photons traveling cosmological distances are likely to interact with the Cosmic Microwave Background (CMB) or the Infrared Background (IR) before ever being observed on Earth. Charged particles at low and moderate energies travel paths greatly affected by galactic magnetic fields, making it impossible to trace them back to their origins. As we will discuss later, higher energy cosmic rays will also interact with the photons of the CMB if travelling long distances.

The vital contribution of neutrino astronomy to physics was recognized with the awarding of half the 2002 Nobel Prize in Physics to Raymond Davis, Jr. and

Masatoshi Koshiba. Both experimentalists, they pioneered solar and cosmic neutrino detection techniques and their results opened wide the field of neutrino astronomy.

As nuclear theory and astronomy continued apace in the postwar years, physicists realized that they could look for neutrinos not just from ground-based reactors, but also from the Sun. The reaction of 3He(α, γ)7Be that creates 8B was then calculated to be 2 109 cm−2 s−1 in 1958 [23]. The experimental study of solar neutrinos be- × gan in the 1960s with Raymond Davis’ Homestake Solar Neutrino Detector [24] and has continued to the present with such notable experiments as Kamiokande [25] and

7 Super-Kamiokande [2], GALLEX [26], SAGE [27], GNO [28], SNO [5] and Borex- ino [29]. Through the study of solar neutrinos the conundrum of missing electron- neutrinos was first discovered as discussed in Section 1.1 and the facts of neutrino mass and mixing were cemented. Beyond the particle physics successes, the study of neutrinos from the Sun has also verified out knowledge of how, in layman’s terms, the

Sun shines. Neutrinos are created at multiple stages of nuclear burning in the Sun, as seen in Figure 1.2, although most of the energy of the Sun comes from the fusing of four protons to make Helium, 4p 4He +2e+ +2ν . The initial reaction in this → e series gives rise to the pp neutrinos via:

2p 2H + e+ + ν (1.5) → e

This beta decay neutrino spectrum has a mean energy of 265 keV and an endpoint of 420 keV. Most 4He is then created via ≈

2H + p 3He + γ (1.6) → 3He +3 He 4He +2p (1.7) →

However, with a branching fraction of 15% [22], the side pp II chain occurs which − includes neutrino production.

3He +4 He 7Be + γ (1.8) → 7Be + e− 7Li + ν (1.9) → e 7Li + p 2 4He (1.10) →

The electron capture produces two energetic neutrino lines, at 384 keV, and with a higher branching fraction, at 862 keV, which also lies beyond the pp neutrino spec- trum. In the high-density environment of the Sun, there is also the pep reaction chain

8 of

2p + e− 2H + ν (1.11) → e which produces mono-energetic neutrinos at 1.442 MeV. Further reactions have far less of an impact upon the solar energetics, but play a larger role in neutrino produc- tion. The first of these is the pp III chain, which produces the 8B neutrinos. −

7Be + p 8B + γ (1.12) → 8B 8Be∗ + e+ + ν (1.13) → e 8Be∗ 2 4He (1.14) →

Although this has a probability of only 0.02%, 28% of the nuclear energy is carried

away by the neutrinos with a broad spectrum extending to 15 MeV. Another slow

and rare process is the hep reaction

3He + p 4He + e+ + ν (1.15) → e

which also has a broad spectrum that reaches the highest solar neutrino energies of

> 18 MeV.

In the presence of heavier elements, the CNO chain can produce neutrinos with

intermediate energy beta decay spectra, through

13N 13C + e+ + ν (1.16) → e 150 15N + e+ + ν (1.17) → e 17F 17O + e+ + ν (1.18) → e (1.19)

The 8B neutrino flux has been well studied by a number of the previously men-

tioned experiments, most importantly by the SNO [31,32,33,34] and Super-Kamiokande

9 Figure 1.2: The standard solar model neutrino energy spectrum. From the BS05(OP) model of Bahcall, Serenelli and Basu in [30], which is visually indistinguishable from similar models that rely upon different radiative opacities and heavy-element abun- dances.

10 [2] collaborations, which also gave the strong, convincing evidence for neutrino oscil-

lations. The gallium experiments, SAGE, GALLEX and GNO can access neutrinos

with energies down to the pp signal, however, like the Homestake chlorine experiment which had a higher threshold and was sensitive to the 7Be, pep, CNO, and 8B neutri- nos, are integrated time counting experiments which do not allow for real-time energy measurements. Borexino has measured the 862 keV 7Be neutrinos in real-time [35], and the SNO+ experiment hopes to do the same for the pep and CNO neutrinos and proposals for seeing the high flux of pp neutrinos have also been presented [36].

More details of the science of solar neutrinos and the historical development of the field are given in the reviews mentioned at the end of Section 1.1, as well as in numerous reviews written or edited by John Bahcall and Ray Davis [37, 38, 39, 40].

The future prospects for solar neutrino experiments are discussed by Joshua Klein in his Neutrino 2008 Review [41].

As the 2002 Nobel Prize committee recognized, the detection of neutrinos from

SN1987A was a watershed even in neutrino astronomy. In back-to-back papers in

Physics Review Letters, the Kamiokande [42] and IMB [43] collaborations reported a total of 20 neutrino events, when one may have been expected as background, associated with this supernova event, and this analysis was followed up by the Baksan experiment [44] which contributed another 5 events to the detection. At 7:35 UTC on

February 23, 1987 this neutrino burst arrived at Earth and lasted nearly 13 seconds, having originated in the Large Magellenic Cloud, approximately 50 kpc away. These detected events are shown in Figure 1.3.

The life of a star with a mass greater than 8 solar masses comes to an end with a Type II supernova. Such stars burn to higher elements, and create a iron core.

11 Figure 1.3: The burst of neutrinos from SN1987A from the Kamiokande, IMB and Baksan neutrino detectors, as compiled for the 20th anniversary of the detection [45].

12 This core is maintained by electron-degeneracy pressure, but once it reaches the

Chandrasekhar limit of 1.4 solar masses the core collapses, with photo-nuclear dis- integration and electron capture occurring in the resultant hot, dense environment.

The inner core eventually becomes supported by neutron degeneracy pressure, and the in-falling material bounces off this surface creating an outward moving shock- wave. Although many questions remain about the supernova process, neutrinos play an important role in the initial energy release in the core collapse, the convective heating involved in the in-fall, and the eventual thermal cooling. Nearly all of a star’s binding energy, upwards of 1053 ergs is released in neutrinos, about 1% of which is released in the initial collapse [46, 47]. As the SN1987A observations confirmed, the neutrinos have energies of tens of MeVs, and the cooling burst lasts about 10 s.

With the successful detection of one supernova, the neutrino astronomy commu- nity began to act in coordination to be prepared for the study of any future local supernovae. The Supernova Early Warning System (SNEWS), linking the large, ac- tive neutrino detectors, ensures that a supernova in the Milky Way would be detected in neutrinos and may be able to point optical telescopes to such a supernova in time to see the rise in the photon spectrum [48]. A supernova is expected in a spiral galaxy of the Milky Way’s size and age roughly every few decades [49].

There exists a chance of detecting supernova neutrinos from close neighbor galax- ies, the Magellanic clouds, M31 and M33 [47], but there will also be a diffuse back- ground of relic neutrinos from extragalactic supernovae. Multiple neutrino exper- iments have placed limits upon this flux, including SuperKamiokande and SNO

[50, 51, 52], and the SuperKamiokande 90% confidence level limit for electron anti-

−2 −1 neutrinos with Eν > 19.3 MeV of 1.2 cm s is only a few factors of 2 from the

13 theoretical models [53, 54, 55]. The neutrino flux predictions require inputs from as-

trophysics regarding the Type II supernova rate, and from the collapse particle physics

predicting the neutrino output of a supernova. Observational astronomy, through its

constraints on the star formation rate and initial mass function, constrains the core

collapse supernova rate, and thus the largest source of uncertainty in the flux spec-

trum is in the neutrino emission from a single supernova [53,56]. Future detectors of

the megaton scale could allow measurements of the diffuse supernova neutrino energy

spectrum [57,58], which will help resolve the mechanics of core collapse.

Another diffuse source of astrophysical neutrinos are the relic cosmic neutrinos, that, analogously to the photons of the cosmic microwave background, stopped in- teracting with other particles as the universe cooled and expanded following the Big

Bang. In the earliest moments of the universe, temperatures were so high that all particles were in thermal equilibrium. Neutrinos were produced and destroyed by such reactions as νν¯ e+e−. These reactions decoupled from equilibrium at tem- ↔ peratures of a few MeV, and so the neutrinos underwent a ‘freeze-out’, travelling as free particles except for relatively rare neutrino-nucleon interactions. At the present time, these neutrinos would have a temperature of 1.9 K, or 1.7 10−4 eV, and ∼ × a density per species of 112 cm−3 [22]. The measurement of the cosmic neutrino background would confirm our knowledge of the early universe and probe the last scattering surface which is thicker than that of photons, and complicated by neu- trino oscillations [59]. The detection of the very low energy background neutrinos is difficult and proposals focus on interactions with radioactive nuclei through electron capture, β+ and β− decay [60,61,62,63]. Other suggested methods include coherent

14 elastic scattering on a target [64, 65, 66, 67], or modulations to the ultra high energy

neutrino spectrum via interactions at the Z resonance [68,69,70,71].

Neutrino astronomy is such a broad field that what has been described thus far

may be considered tangential to the primary goal of resolving individual sources

in the neutrino sky. A number of astrophysical objects have long been predicted

to be neutrino point sources. If hadronic acceleration is occurring in locations with

dense material and strong magnetic fields, charged pion and kaon decays will result in

neutrinos. These acceleration sites are also hypothesized to be the origins of very high

energy cosmic rays and gamma rays [72]. Thus, scientists aim to study such objects

as active galactic nuclei, gamma ray bursts, supernova remnants, pulsars and pulsar

wind nebulae with multi-messenger astronomy [73, 74, 75]. When shock acceleration

leads to hadronic interactions that produce pions and kaons which decay to neutrinos,

the resulting neutrino spectrum in the energy range of interest, 100 GeV to 1 PeV, ∼ −2 follows approximately Eν , with the neutrino flavor ratio of νe:νµ:ντ 1 : 2 : 0. Flavor oscillations across astrophysical distances give an expected flavor ratio of 1 : 1 : 1 at

Earth. For a comprehensive review of high energy neutrino astronomy see Learned and Mannheim [76].

High energy neutrinos could also be created by more novel processes, of which the

currently most stimulating would be from the decay or annihilation of dark matter

particles. Dark matter particles may collect in gravitational wells, such as the Sun

or even the Earth, where they may annihilate to produce neutrino pairs directly or,

more likely in most models, they may produce heavy quarks, tau leptons, and gauge

or higgs bosons, all which can produce neutrinos in their decays [77]. If the elastic

scattering cross sections that allow the capture of dark matter and annihilation cross

15 sections are sufficiently large, these processes should be in equilibrium. Neutrino telescopes can provide relevant limits on the spin-dependent elastic scattering cross- section, from the interaction with Hydrogen, whereas a majority of direct dark matter detection experiments only probe spin-independent phase space [78].

Detection of high energy neutrinos is achieved much as it is for solar neutrinos, through instrumenting a large transparent medium where a neutrino may interact and then collecting Cherenkov light from the track of a resultant charged lepton or the light created in a electromagnetic cascade. The predicted fluxes of astrophysical neutrinos is so low that very large detectors, on the order of a cubic kilometer, are required. The detection of high energy astrophysical neutrinos is complicated by the high background flux of atmospheric neutrinos, which are created when a cosmic ray interacts in the Earth’s atmosphere. There has been a long running experiment in

Lake Baikal [79], the completed AMANDA experiment at the South Pole [80,81], and there are three Mediterranean detectors underway: ANTARES [82,83], NESTOR [84] and NEMO [85]. At the South Pole, the IceCube experiment is nearing complete construction [86,87,88]. KM3NET in the Mediterranean is still planning stages [89].

No astrophysical high energy neutrinos have yet been detected, yet a number of limits have been set by AMANDA/IceCube. These include searches for diffuse astrophysical neutrinos [90], point sources [91,92,93], gamma ray bursts [94,95], and dark matter annihilations in the Sun [96].

In the next chapter we will discuss the sources of ultra high energy neutrinos.

These sources may include nearly all those that the high energy neutrino telescopes hope to see, as well as the well-motivated Berezinsky or Greisen-Zatsepin-Kuzmin

(GZK) neutrinos. The excitement in the fields of lower energy neutrino astronomy

16 carries into that of ultra high energy where there is ample opportunity for discoveries as significant as those SN1987A.

17 Chapter 2

Ultra High Energy Neutrinos

Neutrinos are unique astrophysical messengers that are virtually unattenuated at

any energy as they travel cosmic distances, creating the greatest possible window on

the universe. Although the expected fluxes of ultra high energy neutrinos (UHEν),

here referring to & EeV, 1018 eV, are very low because of the falling spectra of

hypothesized emitters, detection is simplified by the lack of a physics background.

The search for UHEν is not merely opportunistic; it is highly motivated by the

quest to discover the well-modeled flux of neutrinos created when ultra high energy

cosmic rays travelling cosmic distances interact with photons of the cosmic microwave

background.

2.1 GZK Neutrinos

Cosmic Rays have been studied since the beginning of the twentieth century.

In 1912, Victor Hess traveled aloft in a hot air balloon with his electro-meter and discovered that the charged particles scientists had been observing came from above, opening the field of cosmic rays. The 1930s were the heyday of cosmic ray physics as the positron and muon were detected and identified.

18 Decades later, a new frontier of physics was opened in 1965 with the discovery of the cosmic microwave background at Bell Labs by Penzias and Wilson [97]. These microwave photons are nearly a perfect blackbody spectrum with a mean temperature of T = 2.725 0.001 K [98] and are the result of the cooling of the universe and γ ± the decoupling of light from matter at the time of recombination when neutral atoms formed. The CMB is isotropic to one part in one hundred thousand, when the known effects of the galactic, solar system’s and Earth’s motion are subtracted. The density of CMB photons is given by: 2ζ(3) n = T 3 411 cm−3 (2.1) γ π2 γ ≃ The energy density of the Planck spectrum is:

13 4 1.32 10 ǫ − ρ (ǫ)= × eV/cm 3 (2.2) γ exp(k T/ǫ) 1 B − which gives a total energy density of ρ = (π2/15)T 4 0.260eV cm−3. The average γ γ ≃ energy of the CMB photons is 5.34 10−4 eV [98] [99]. × 2.1.1 The GZK Process

Soon after the first discovery of the CMB, cosmic ray physicists realized that

there were great implications for their field. In 1966, Kenneth Greisen in the United

States and G.T. Zatsepin and V.A. Kuzmin in the Soviet Union published papers

suggesting a termination of the cosmic ray spectrum [100,101]. The primary channel

for the attenuation of cosmic rays is the photo-pion-production of protons interacting

with the CMB.

p + γ ∆+ p(n)+ π0(π+) (2.3) CMB −→ −→ The threshold energy for this reaction is based upon the rest masses of the products,

the proton and pion. If we have a head on collision, and the velocity of the incident

19 Figure 2.1: The energy dependence of the photo-production cross-section as a function of the photon energy in the rest frame of the nucleon. [99] This interaction gives us the GZK effect in cosmic ray physics, but is well measured in accelerator physics, and the experimental data are from high energy photons incident on a proton target [102].

proton is taken to be the speed of light, the required incident energy for the proton

is given by:

1 2 20 Ep = (mπ +2mpmπ) 10 eV (2.4) 4Eγ ≃ The threshold energy is slightly higher for the neutron and π+ channel due to the higher rest masses of the products. The reaction is allowed at lower energies because of the CMB spectrum’s long tail out to higher energies. Photo-pion-production is well-studied at particle accelerators, where a high energy photon typically collides with a proton at rest. In this case the photon has a threshold energy of 145 MeV.

The cross-section of the photo-pion-production reaction is shown in Figure 2.1.

Once above threshold, the cross-section peaks at the ∆+ resonance, which can be

seen in Figure 2.1 at ǫ′ = 340 MeV. The ∆+ baryon is composed of the uud quarks,

20 3 has a mass of approximately 1232 MeV, and has isospin 2 . The cross-section at the delta-resonance is 0.5 mb, but decreases and has a complicated shape determined by ≈ higher mass resonances and direct pion production, until at √s & 2 GeV it smooths to 0.2 mb where multi-pion production dominates [102]. ≈ When Monte Carlo simulations apply the GZK process to an exponentially falling cosmic ray source spectra, the propagated spectra exhibit the expected GZK cutoff.

Calculations of the GZK cutoff begin with the mean free path λ of the cosmic ray

proton, defined here as in [103], as a function of the proton energy Ep:

∞ smax −1 1 nγ 2 λ (Ep)= 2 dEγ 2 ds(s mp)σpγ (s) (2.5) 8E thr E thr − p ZEγ γ Zs

Here the previously discussed cross section σpγ (s) is a function of the Mandelstam

thr 2 variable s, the square of the total center of mass energy. s = (mp + mπ) is the

max 2 square of the threshold center of mass energy, s = mp +4EpEγ is the square of the maximum energy allowed for the interaction, nγ is the photon number density, and Ethr = (sthr M 2)/(4E ) is the threshold photon energy. The mean free path γ − p p will have units of cm when energies are in eV and the number density is in units of eV−1 cm−3.

To determine the cosmic ray spectrum, the distance at which a particle loses its energy, Lloss, is needed [99]. It is given by:

Ep λpγ(Ep) Lloss = = (2.6) dEp/dx Kinel(Ep)

where Kinel(Ep) is the fraction of the proton’s energy lost in the interaction and may be found in a Monte Carlo simulation [102]. Photo-pion-production dominates at high energies, and above 8 1020 eV the energy loss length is nearly constant at 15 ×

21 Mpc. At low energies, pair production energy loss dominates and the energy loss length is much greater, 1000 Mpc. ∼ The energy spectra of UHECR protons is shown in Figure 2.2. Propagation to only 10 Mpc does not drastically alter the spectrum, but above 40 Mpc the sharp

GZK cutoff may be observed. Other important features of the long distance GZK proton spectra include the total lower normalization due to adiabatic losses and the expansion of the universe and the dip and bump just below the GZK cutoff. The bump is due to the shift of high energy protons to an energy at which the energy loss length is much greater than at higher energies.

Figure 2.2: Example proton cosmic ray spectra at different distances of propagation. The smooth curve is the injected spectrum (E−2exp( E /1021.5)), and the rest, from p − p right to left, are propagations to 10, 20, 40, 100, 200, 400, 800 and 1600 Mpc. They have been weighted by dz/dt, the redshift-dependent injection time [99].

22 Other interactions between cosmic rays and the CMB include: energy loss and the acceleration of photons via inverse Compton scattering of cosmic-ray electrons, elec- tron pair production from high energy (> 1014eV) photon interactions with the CMB, photo-disintegration of nuclei, and pair production from the proton-CMB interaction.

The resultant UHECR spectrum is highly dependent upon the spatial distribution of cosmic ray sources, the initial cosmic ray composition, the spectrum and its cutoff energies, and the energy-dependence of the diffusion of the cosmic rays [104].

Further discussion of the GZK cutoff to the CR spectrum, including the impact on nuclei, the importance of magnetic fields, and the time delays at arrival may be found in references: [99,105,103,104,106,107,108].

Neutrino physicists quickly realized that the GZK mechanism could provide them

with a ‘guaranteed’ high energy neutrino source. In 1969, Berezinsky and Zatsepin

[109]1 discussed the creation of high energy neutrinos from charged pions,via:

π+ µ+ + ν and µ+ e+ + ν + ν (2.7) −→ µ −→ e µ

The Feynman diagrams for these decays are given in Figure 2.3. Lower energy electron anti-neutrinos are also created by the beta decay of neutrons that accompany π+ in

∆+ decay. Negative pions and muons may also be created and decay as part of the

GZK mechanism, but this is highly suppressed at near-threshold energies and plays

a larger role at higher energies where multi-pion production dominates.

2.1.2 CR Spectrum Cutoff

Recent years have seen the construction of detectors large enough to make precise

measurements of the UHECR spectrum, where the flux is on the order of 1 particle

1Although the cosmic ray and neutrino communities have adopted the term GZK neutrino to refer to these UHEνs, they should more appropriately be called BZ neutrinos.

23 d νµ νe

W + µ+ e+

W +

¡ ¡ + u µ νµ

Figure 2.3: The Feynman diagrams for the decays of the positively charged pion, made of a u an d quark, and positively-charged muon.

per km2 per century. The HiRes experiment looked at nitrogen fluorescence created

by cosmic ray air showers [110], while the Pierre Auger Observatory combines this

technique with ground-level water Cherenkov tanks that detect charged particles from

the showers [111]. The HiRes and Auger collaborations have reported seeing the

spectral changes that had been long predicted: the electron pair production dip in

the spectrum at about 1019 eV, which is known as the ankle [112, 113, 114, 115], the

bump in the spectrum at 4 1019 eV from a buildup of particles that lost energy ∼ × to below that of GZK threshold energy, and the steepening of the spectrum above

4 1019 eV [116,117]. × Figure 2.4 shows the Auger UHECR spectrum with 20,000 events. The flux,

J E−γ, is found to have a spectral index γ of 2.69 0.02 (statistical) 0.06 ∝ ± ± (systematic) at energies between 4 1018 eV and 4 1019 eV where it steepens to × × 4.2 0.4 (statistical) 0.06 (systematic) [117]. The hypothesis that a single power ± ± law fits this spectrum is rejected with a 6σ significance [118]. For reviews of these

results on the UHECR spectrum, see Michael Cherry’s Physics Viewpoint [119] and

the recent Annual Review by Beatty and Westerhoff [120].

24 Figure 2.4: Upper Plot: The differential UHECR flux from Auger with statistical uncertainties and the number of events in each bin. Lower Plot: The Auger and HiRes data [116] compared with a flux with spectral index of 2.69. Figure from [117].

25 Most discussion about the GZK cutoff occurs under the assumption that UHECR are protons. At lower energies (. 1014 eV), cosmic ray composition traces that of

the interstellar medium (ISM), strengthening the hypothesis that these cosmic rays

originate in shocks from galactic supernovae accelerating particles in the ISM. Much

study is focused on cosmic ray composition at the knee and ankle [121,122] where it is

believed the transition from galactic to extragalactic cosmic ray sources occurs. For

the highest energy cosmic rays, determining the composition can shed light on the

puzzling questions of where and how particles can be imparted with so much energy.

Since the highest energy cosmic rays are detected through the extended air showers

they initiate, their composition must be determined via indirect methods that rely

upon our models of air shower development [123]. The discussion of UHECR models

focuses upon protons or iron nuclei primaries, but conclusive data is not yet available.

The current data points to a light mixed composition that gets progressively lighter

to energies of 2 1018 eV and then may contain heavier nuclei, with enhanced iron- × richness at the highest measured energy [124].

Calculations have shown, however, that the GZK UHECR spectral feature is not

highly dependent upon composition at the source [125,126], at least such that current

data cannot distinguish between proton dominated and nuclei-rich source cosmic rays

[122]. Heavy nuclei lose energy and decay when they interact with the photons of

the CMB or infrared background starlight through photo-disintegration, creating a

flux of lighter nuclei and protons. The secondary protons undergo the same photo-

pion-production processes discussed above to create GZK neutrinos. However, full

photo-disintegration only occurs for nuclei with energies exceeding 1020.5 eV, and at

lower energies the source composition will play a large role in determining the number

26 of protons available to undergo the GZK process [122]. As we will see in the next

section, although the cosmic ray energy spectrum has little dependence upon the

source composition, the neutrino spectrum is strongly affected and shifts to lower

energies with heavier nuclei primaries.

2.1.3 GZK Neutrino Flux Models

Attempts were made in the early 1970s to calculate the expected neutrino fluxes from the GZK mechanism, but were hindered by a lack of knowledge from the neutrino cross-section at high energies compared to the mass of the W boson. Engel, Seckel and Stanev give a brief historical review of these calculations [127]. Contemporary models have incorporated the advances made in the intervening decades, including using the high energy cosmic rays and gamma-rays events mentioned above.

The simulation of the GZK neutrino flux follows from the calculations of the

interactions between cosmic ray protons and the CMB. Interaction channels other

than the ∆+ resonance must be explored, especially direct pion production at near

threshold energies and multi-pion production at higher energies because of the greater

number of charged pions created in these relatively rare interactions [127]. On average,

a neutrino spectrum is fully evolved if the proton source is more than 200 Mpc distant,

and 40% of the proton energy loss goes into neutrinos. ∼ We will discuss a few of the published GZK neutrino flux models, beginning with that of Engel, Seckel & Stanev [127] (ESS) and extended via ANITA internal col- laboration notes [128]. The ESS flux uses the event generator SOPHIA [102] with uniformly distributed sources, all with the injected proton spectrum of:

dN −2 Ep exp( Ep/Ec) (2.8) dEp ∝ × −

27 21.5 where the cutoff energy Ec = 10 eV. Other cutoff energies were explored, and a

change to 1020.5 would not have a significant effect upon the neutrino flux, but it

would require nearby sources for the UHECR events. The flux of neutrino flavor i is

given by ESS as:

c dEs (E )= (z, Es)Y (Es, E , z) p dz (2.9) Fi νi 4πE L p p νi Es νi Z Z p

s where the proton source energy is Ep, and the function forms and redshift dependen- cies of the neutrino yield function Y and the source function may be found in [127]. L The resultant neutrino fluxes are shown in Figures 2.5, 2.6 and 2.7.

Figure 2.5 shows the ESS electron and muon neutrino fluxes (summing neutrinos and anti-neutrinos) from the GZK mechanism. Plots for two different cosmologies are shown in this update to Figure 4 of ESS, as the original was made for a flat universe with Ωm = 1 instead of the preferred Λ = 0.7, Ωm = 0.3. They are plotted with the

Waxman-Bahcall (WB) bounds for neutrino flux from optically thin sources (appli- cable for AGN jets or GRBs) [129,74] since similar source evolution models, spectra and injection power were used2. Also plotted atop the muon neutrino spectrum is the spectrum presented by Eli Waxman at the International Workshop on Neutri-

−2 nos and Subterranean Science (NeSS 2002). The proton injection spectrum was Ep for 1019 E 1020 eV. The Waxman spectrum is about 10% high than the ESS ≤ p ≤ spectrum at 1019 eV. Where ESS has used a complex Monte Carlo to simulate the appropriate proton propagation and energy loss to each product, Waxman assumes that all proton energy goes to muon neutrinos with 25% efficiency, half of pions are charged, and half of the pion energy goes into muon neutrinos.

2The WB bound was originally mis-plotted in ESS Figure 4.

28 Figure 2.5: Individual looks at the muon and electron neutrino spectra from the GZK mechanism. The upper solid lines are for a flat universe with Λ =0.7 and the lower shows Λ = 0, which impacts the star formation rate. The dotted line on the νµ graph represents the flux presented at NeSS 2002 by Eli Waxman, while the shaded regions represent the Waxman-Bahcall limit of [129]. This follows the methods of [127] with renormalization to a flux presented at NeSS 2002 by Eli Waxman, and received via private communication from Dave Seckel [128].

29 The top graph in Figure 2.5 has a noticeable double peak structure. The first peak is due to the electron anti-neutrinos from the neutron decay. The neutron decay length is approximately the same as the the photo-pion-production length at energies of 4 1020, and lower energy neutrons are more likely to decay than to interact. The × second peak is coincident with the peak in the muon neutrino spectrum, at 3 1017 × eV [127].

The total ESS neutrino flux is shown in Figure 2.6. At the second peak the ratio of muon neutrinos to electron neutrinos is 2 : 1 as expected from pion decay, but over the entire curve it is much closer to 1 : 1 because of the electron anti- neutrino from the neutron decay. The ESS GZK flux model is constantly revised with updated cosmological and UHECR spectrum and composition data, but has not varied significantly since 2001.

Figures 2.7 and 2.8 present the models on energy flux graphs (E2dN/dE). On the left, the same data as Figures 2.5 and 2.6 is presented. In this format, the peak occurs near 5 1018 eV, a decade higher than in the flux graphs. The number of events a × detector will see peaks at an energy somewhere between the maxima of flux or energy

flux, since detection is a product of the flux, the neutrino interaction cross-section which grows slowly at high energies, and the detector efficiency. The WB bound’s labeling regarding evolution refers to the redshift dependence of the assumed sources of the form (1+ z)n.

Another GZK flux model, that of Protheroe & Johnson [103] (PJ), is depicted in

Figures 2.8 and 2.9. The first of these figures places the neutrino flux nicely in the context of all astrophysical fluxes related to the GZK effect. The PJ model uses the event generator SIBYLL [130] to create transfer matrices for each product in the GZK

30 105 104 103 102 10 1 10-1 10-2 10-3 E dN/dE (Gev km^-2 yr^-1 ster^-1) 10-4 10-5 10-6 10-7 1 10 102 103 104 105 106 107 108 109 1010 1011 1012 1013 Energy (GeV)

Figure 2.6: The three flavor GZK neutrino spectrum, in a Λ = .7, Ωtot = 1 universe, −2 21.5 from an injection function of Ep exp( Ep/10 ). This follows the methods of [127] with renormalization to a flux presented− at NeSS 2002 by Eli Waxman, and received via private communication from Dave Seckel [128].ERRATUM: The y-axis units are misquoted; it should be: km−2 yr−1 sr−1.

effect. Their cutoff energy for the proton injection spectrum is 3 1020 eV, though × they also plot the same for a cutoff energy of 3 1021 eV. Their injection source is × given from a calculation by Rachen & Biermann [131] of the power per co-moving volume in cosmic ray protons. The proton spectrum is given by the solid curve and experimental results tracing the CR spectrum circa 1995 are overlaid (the highest energy events are from Fly’s Eye). The gamma ray spectrum from neutral pion decay is shown by the dashed curve, and the four separate neutrino fluxes are shown as dotted curves.

In Figure 2.9 the ESS muon neutrino flux is compared to the PJ and Yoshida &

Teshima [132] (YT) muon neutrino fluxes. This primarily tests the impact of source evolution on the neutrino spectrum. The YT flux depends on a source evolution of

31 Figure 2.7: The same models as in Figure 2.5 plotted on an E2dN/dE chart. The dashed horizontal lines are the Waxman-Bahcall neutrino source limit of [129] and the dashed curve represents the flux presented at NeSS 2002 by Eli Waxman. The solid curves are the muon neutrino fluxes, and the dotted curves are the electron neutrino fluxes [128].

32 Figure 2.8: The GZK fluxes from Protheroe and Johnson [103]. The dotted curves are νµ, νµ, νe, νe from top to bottom. The photon flux is given by the dashed curve. The solid curve is the cosmic ray proton spectrum, and the data points are cosmic ray events from multiple experiments.

33 Figure 2.9: The ESS flux is the lower limit of the shaded area, with a source evolution of n = 3, while the top of the shaded area has n = 4. Flux models of Protheroe & Johnson [103] are shown as crosses and Yoshida & Teshima [132] in this figure from [127].

(1 + z)4 calculated out to z = 4. The PJ flux shown here matches the energy cutoff of ESS, 1021.5 eV. The ESS muon neutrino flux shown at the bottom of Figure 2.5 for Ωm = 1 is the bottom boundary of the shaded area, characterized by a source evolution of (1+z)3, while the top boundary represents a source evolution of (1+z)4.

This upper limit is in good agreement with YT and PJ fluxes for the energy at which the peak flux occurs, although the YT curve has a narrower spectrum. The PJ flux does not have a source evolution of the form (1 + z)n, but rather uses a fudge factor

inherited from the work of Rachen & Biermann.

Other GZK neutrino flux models include those of Aramo et al [133] and Kalashev,

Kuzmin, Semikoz & Sigl [134] (KKSS). Aramo et al use the EGRET gamma-ray

34 data to limit the GZK neutrino flux. As a lower limit they quote a spectrum of

E−2 in accordance with the WB limit of [74]. A maximum flux (MAX) occurs if the extragalactic EGRET data were entirely accounted for by the decay of the π0 of the GZK photo-pion production and an initial proton flux of the form E−1. A median flux (MED) is given by allowing the GZK process to account for 20% of the

EGRET data. On an energy flux graph of E2dN/dE in units of eV cm−2 s−1 sr−1, the maximum flux for the MAX model is 300 at an energy of 1.5 1020 eV, and ∼ ∼ × the maximum flux for the MED model is 85 at an energy of 3 1019 eV. These ∼ ∼ × are decades above the WB peak of 20 at an energy of 1018 eV. ∼ ∼ The KKSS GZK neutrino flux, like that of Aramo et al far exceeds the Waxman-

Bahcall bound because they use a harder injected proton spectrum. They begin with:

φ(E , z)= f(1 + z)mE−αΘ(E E ) (2.10) p c − p where the redshift runs from z z z . They get a maximum flux when these min ≤ ≤ max 23 parameters are tuned to zmax = 2, Ec = 10 eV, m = 3, α = 1 [134]. This plot may be seen against other GZK flux models in the recent RICE preprint [135] where it is nearly excluded. The Yuksel and Kistler [136] flux model is enhanced as it looks to gamma ray bursts as the source of UHECR, and determines that the GRB redshift distribution has a mean of 3. Ahlers et al [137] fit to the UHECR data ∼ a neutrino primary with a neutrino-nucleon cross-section enhanced by four orders of magnitude at the GZK energy, and arrive at a neutrino flux that includes both

GZK neutrinos and neutrinos from optically thin sources. Below all these other GZK neutrino models, Ave et al [138] calculate the GZK neutrino flux if UHECR primaries are iron nuclei and not protons. These models are all shown in Figure 2.10.

35 )] 13 ESS GZK Model −1 WB Limit

sr PJ GZK model −1 KKSS GZK model

yr 12 YK GZK model −2 YT GZK model

Aramo et al GZK model 11 Ave et.al. GZK model Ahlers et.al. GZK model

10 dN/dE, (GeV km 2

9 Log[E

8

7 7 8 9 10 11 12 Log[E,(GeV)]

Figure 2.10: The eight GZK neutrino flux models discussed in this section, [127,128, 103,134,136,132,133,138,137] overlaying the WB bound [129,74].

Detailed discussions of the GZK neutrino flux dependence on source evolution, injected proton spectra, cosmological parameters, source distances and distributions, and maximum proton injection energy are contained in [127,134].

2.2 Direct Astrophysical Sources: GRBs

Although neutrino astronomers have focused upon the flux of high energy neutri- nos due to the GZK effect, there are certainly other possible sources of high energy neutrinos. The most probable of these sources are the sources of the high energy cosmic rays themselves. The most notable hypothesized sources of these cosmic rays are active galactic nuclei (AGN) and gamma ray bursts (GRB) which may have the strong magnetic fields required to accelerate charged particles via the Fermi shock

36 method [99] to energies > 1020 eV. In these regions particle collisions or photo-pion- production may produce neutrinos with very high energies. The Waxman-Bahcall bound [74, 129], created with an injected proton spectrum with energy dependence

−2 EP , provides a strong model for such sources. In this work we are particularly interested in neutrino production in gamma ray bursts. GRBs follow a long tradition of scientific discoveries: they were a new phe- nomena discovered with an instrument that had an entirely different purpose. The

US military Vela satellites were monitoring for signs of nuclear explosions in the late 1960s when they detected gamma rays that did not originate from the Earth or sun. The mystery surrounding these bright, transient flashes persisted until the

1990s saw the deployments of the Compton Gamma-Ray Observatory (CGRO) and

Beppo-SAX, which heralded in the detection of GB afterglows and the determina- tion of source locations and redshifts. Gamma ray bursts are isotropically located at cosmological distances, but are a fairly variable class of objects, characterized by bursts lasting from milliseconds to minutes of non-thermal photons with energies in the range of keV-MeV. Short duration GRBs are currently believed to occur when neutron star/neutron star or neutron star/black hole binary systems collapse. Long duration GRBs, through the association of their afterglows with young star-forming galaxies and core-collapse supernovae, are believed to be highly beamed emissions from the collapse of a high-mass, rapidly rotating star to a black hole. Reviews of the basic properties and theories of GRBs and their photon properties by Peter Meszaros are available [139,140].

GRBs are amongst the top candidates of sources of UHE cosmic rays, and if such

hadronic acceleration is occurring, high energy neutrinos may also be created. GRBs

37 are classically described by a fireball shock model, where relativistic plasma in a

jet collides to produce high energy prompt emission, and subsequent collisions with

interstellar material in external shocks produce the lower energy afterglow. Gamma

rays may be produced through synchrotron radiation and inverse Compton scattering

by high energy electrons. Protons, accelerated alongside electrons in the shocks, will

then produce neutrinos via the pγ interactions we are now familiar with, where the photon may be a hard photon from the initial shock, or a softer afterglow photon.

Waxman and Bahcall have created a canonical GRB neutrino production model that is developed in [141,74,142,143]. In Figure 2.11, the relationship between an observed

GRB gamma ray spectrum and a predicted neutrino flux is explored.

Summaries of GRB neutrino production may be found in [145, 146, 147, 148,

149, 150], and modeled neutrino spectra for individual BATSE bursts are found in [151]. Prospects for GRB neutrino discovery by future experiments are discussed for KM3NeT and ANTARES [152, 153, 154], and JEM-EUSO [155]. Past searches have been done by the AMANDA/IceCube collaboration [156, 157, 158,94,159,95],

RICE [144], and the MAGIC Collaboration [160]. Diffuse GRB neutrino searches are also possible [161,162,163].

2.3 Exotic Physics Sources

More exotic sources that may exceed the WB bound have also been modeled. The

Z-burst model is based upon the creation of a high energy neutrino flux from the decay of Z-bosons which would have been created by interactions of high energy neutrinos with the relic neutrino background (which is analogous to the CMB, or may consist of super-heavy relic neutrinos). The originally incident high energy neutrinos could be

38 (a) −q Ep

−α

(dN/dE) Eγ

log −β Eγ

log (E) Eγ, b

(b) 1−α 1−β Eγ Eγ dN γ τ γ γ (p ) ~ Eγ dE γ (p )] β−1 α−1 [τ E p Ep −1 E p ~ Eγ log log (E) (c) α−1− q ν β−1− q Eν dN (Φ ) p Eν Φ ∼ τ (p γ ) ν dE log p

log (E ν ) Eν,b

Figure 2.11: From [144]: The top plot (a) shows the broken power law photon spec- trum with an index of -α below the break energy ǫγb and -β above. The proton spectrum follows a simple power law fit. The middle plot (b) shows the optical depth for the delta resonance interaction and the interplay between proton and photon spec- 2 2 tral indices as the threshold condition of ǫpǫγ =0.2Γ GeV is met. The bottom plot (c) shows the neutrino spectrum, which follows the proton spectrum with the inclu- sion of the optical depth. At higher energies there is another break in the neutrino spectrum at the synchrotron break energy, which steepens the spectral index by 2.

39 produced in cascades from proton interactions in high redshift sources. Discussions of Z-burst models and possible astrophysical sources, as well as flux models may be found in [164,134,165,166].

Decays of super-heavy particles with little contribution to the UHECR spectrum could also exceed the WB limit and produce a flux of particularly high energy neu- trinos. These particles may be cold dark matter that decays or annihilates, or topo- logical defects in the form of monopoles or strings created at symmetry-breaking phase transitions. Discussions of these models and their flux models may be found in [167,134,168].

40 Chapter 3

The ANITA Instrument

As remarked in Chapter 2, although the flux of ultra high energy neutrinos is low, the strong evidence for their guaranteed existence and the mysteries they may shed light upon with their discovery provide ample impetus to develop experiments to detect such neutrinos. It is not feasible to instrument a large enough volume, hundreds of cubic kilometers, with the same techniques used to detect neutrinos at lower energies, and thus other methods must be pursued.

3.1 Askaryan Effect and Radio Detection of Particle Showers

Logistically and economically, the Askaryan effect allows the detection of high energy neutrinos. Particle showers had been studied by physicists for decades when

Gurgen Askaryan postulated that electromagnetic showers in matter can emit coher- ent Cherenkov radiation in radio frequencies [169, 170]. As the shower propagates in a dense medium a net negative charge excess of nearly 20% develops due to the the annihilation of the the shower positrons, and the forward Compton scattering of electrons of the medium [171].

The charged shower moves as a compact pancake, a few centimeters wide and less than a centimeter thick at a velocity faster than the speed of light in the medium.

41 This shower will emit Cherenkov radiation with a frequency dependence of dP vdv, ∝ and is coherent for wavelengths much greater than the length scale of the shower.

Thus the radiated power is proportional to the square of the shower energy. An

Askaryan signal is linearly polarized, has a duration of only about a nanosecond in

dense materials, and has its peak strength at the Cherenkov angle. The Askaryan

effect has been experimentally verified at SLAC in sand [172], rock salt [173] and,

as will be discussed below, in ice [198]. Anther medium for which the Askaryan

effect is predicted is the lunar regolith, and has been used, like ice, to search for the

interactions of high energy neutrinos [174,175].

The details of radio emission from high energy showers in media have been more

explicitly laid out in the past two decades by a number of investigators using Monte

Carlo techniques [176, 177, 178, 179, 180, 181, 182, 183]. An electromagnetic shower

in a medium develops as photons and electrons lose energy interacting with nuclear

fields through pair-production and bremsstrahlung. For particles with large ener-

gies, screening effects must be taken into account as interaction lengths grow; this

reaches the greatest extreme in the Landau-Pomeranchuk-Migdal (LPM) effect which

originates in the bulk material allowing destructive interference and suppresses the

cross-sections of interest [184,185,186,187]. The density of a material determines the

energy at which this effect is important, and in ice is E 2 PeV. The charge LPM ∼ asymmetry of the electromagnetic shower then occurs as shower photons Compton scatter off atomic electrons in the material, which then join the shower. Bhabha and Møller scattering, where a shower positron (electron) scatters off an atomic electron, which is subsequently incorporated in the shower also contribute to the negative excess, as does positron annihilation. The total excess charge, defined as

42 ∆q = [N(e−) N(e+)]/[N(e−)+ N(e+)], is 0.2 at shower maximum [176]. The − ∼ relativistic electrons then emit Cherenkov radiation, which adds coherently for wave-

lengths greater than the dimensions of the shower, and peaks on the Cherenkov angle.

The electric field amplitude scales with the shower length, and is sharply peaked for

the energetic showers elongated by the LPM effect. The total energy radiated co-

herently in frequencies from νmin to νmax by a shower with Nxs excess electrons is

απh 1 W = 1 N 2 L(ν2 ν2 ) (3.1) tot c − β2n2 xs max − min   where the first term is made of fundamental constants, the track length is L, n is

the index of refraction of the shower medium, and β is the velocity relative to the

−1 speed of light. On the Cherenkov angle, θC = cos(1/nβ) , the electric field E is

parametrized [176,177] as

−7 E0 ν 1 −1 R E(ω,R,θC) =1.1 10 2 V MHz (3.2) | | × 1 TeV ν0 1+0.4(ν/ν0)

R is the observation distance, E is the shower energy and ν 500 MHz. The width 0 0 ≃ about the Cherenkov angle, can be parametrized as a Gaussian [177] to

θ θ 2 E(ω,R,θ)= E(ω,R,θ ) exp ln 2 − C (3.3) C − ∆θ "   # with ∆θ 2.7◦(ν /ν)E−0.003 for showers of energy less than 1018 eV, but due to the ≃ 0 0 LPM effect at higher energies,

ν E 0.3 ∆θ 2.7◦ 0 LPM . (3.4) ≃ ν 0.14E + E  0 LPM  This power will be affected by absorption in the transmission medium, which will determine the upper frequency cutoff.

43 Figure 3.1: The ANITA instrument suspended by the launch vehicle, “The Boss,” just prior to release upon its 2006-2007 flight. Photo courtesy of J. Kowalski.

3.2 The ANITA payload

ANITA is a balloon-borne array of radio antennas that floats over Antarctica seeking radio Cherenkov signals from the ice indicating the interaction of a high energy neutrino. It views nearly 1, 000, 000 cubic kilometers on its month-long flights and is designed to detect the Askaryan radio impulses from showers initiated by neutrinos with energies from 1017.5 to 1021 eV. The ANITA-I payload is pictured in

Antarctica just before its launch in 2006 in Figure 3.1.

44 ANITA exploits many physical and logistical coincidences to see high energy neu- trinos. Antarctica provides the most important components: a vast, deep radio- transparent medium for neutrino interactions, circumpolar winds that occur every

Antarctic summer that allow nearly 30 day balloon campaigns over the continent, and a relatively radio free environment. The long history of ballooning from Mc-

Murdo and the support provided by NASA’s Columbia Scientific Balloon Facility

(CSBF) personnel and the NSF Polar Program allow ANITA to take advantage of these ideal conditions.

Unlike other neutrino detectors such as SuperKamiokande and IceCube, ANITA is

not background limited. There are no known physical sources of background signals

that may be confused with an Askaryan pulse, and other physical restraints limit the

source of the showers creating the Askaryan pulses seen by ANITA to high energy

neutrinos. Confirmation of the lack of radio background in Antarctica was made by

a prototype flight in 2003 [188,171].

3.2.1 RF Signal Chain

ANITA has developed a sophisticated RF system to trigger on and capture the

impulsive signals characteristic of Askaryan pulses. A diagram of the core RF sub-

system, which consists of the receiving antennas, a front-end of filters and low-noise

amplifiers, and triggering and digitizing electronics, is shown in Figure 3.2.

Antennas

The 32 primary ANITA antennas are the first of many important RF subsystems.

They are quad-ridged horns which propagate horizontal and vertical linear polariza-

tions and are sensitive to a frequency range of 200 1200 MHz. For the full ANITA −

45 Figure 3.2: The primary ANITA RF subsystems.

payload, they are cylindrically arranged on three tiers: two upper tiers of 8 antennas each, and one lower tier of 16 antennas. The antennas are placed such that two an- tennas, one from the bottom tier and one from a top tier, share the same azimuthal direction while adjacent antennas have overlapping beams. The antenna separation provides the timing baseline necessary to reconstruct the incident angle of the arriving pulse.

The ANITA antennas have a 9 11 dBi directivity gain over their entire frequency − range, which corresponds to a full-width-half-maximum beam-width of 45◦, and ∼ have a 6 dBi directivity off-axis to provide coincidence between adjacent anten- ∼ nas [188]. The very small phase dispersion allows for sub-nanosecond response to impulsive signals [189]. There are 8 additional vertically polarized antennas placed

46 between the second and third tiers which provide broadband monitoring and are not involved in triggering.

Signal Processing

Situated behind each pair of antennas is the Radio Frequency Conditioning Mod- ule (RFCM) which provides the initial signal processing and amplification for the four voltage signals coming from two antennas. The cable length to the RFCM is 40 in. and less than 30 K of thermal noise is expected to be added to the signal before the

RFCM. The signal first passes through a high-pass and then a low pass filter limiting our bandwidth to .18 1.2 GHz, with very constant power transmitted over the open − bandwidth [190]. After being filtered, the signals pass through a MITEQ low noise amplifier with a gain of 36 dB. Then they pass through a 3 dB attenuator, before the second stage amplifier with a gain of nearly 40 dB.

Signals then travel to the main electronics box along low-loss Heliax cable. Within the electro-magnetic interference (EMI) container, the voltage signals once again pass through the high and low-pass filters to restrict them to the frequency range

.18 1.2 GHz. The signals are then split on separate paths for triggering and digiti- − zation. Along the trigger path, the signal first passes through a 90◦ hybrid combiner which turns the linear horizontal and vertical polarization signals into left- and right- circularly polarized (LCP and RCP) signals. The signals are then split into four frequency bands centered about 270, 435, 650 and 990 MHz with an average frac- tional bandwidth (∆ν/ν) of 44%.

47 3.2.2 Signal Capture

The two paths the signal travels for capture are to the Sampling Unit for RF

(SURF), where digitization occurs, and to the trigger boards, the SURF High Occu-

pancy RF Trigger (SHORT) and Trigger Unit for RF (TURF).

The SURF has been developed by the Instrumentation Development Labora-

tory [191] at the University of Hawaii. The digitization occurs on the IDLAB designed

Large Analog Bandwidth Recorder and Digitizer with Ordered Readout (LABRADOR)

chip. Each SURF and LABRADOR can handle 8 channels, the output of 4 anten-

nas. Analog to digital conversion occurs in every storage cell, and the readout takes

50µs, with only 20µs to digitize and 30µs taken for the data transfer [192]. The ∼ LABRADOR chip has a sampling rate of 3 GSa/s, with 2 mV of noise per chan- ∼ nel [192].

The LABRADOR has a highly linear digitization of the input signal, which goes

as:

y =0.8868x +8.4616 (3.5)

where y is the ADC output code and x is the input voltage in mV. The R2 for this

fit is 0.9974, a significant improvement over former IDLAB digitizing chips [192].

Triggering occurs in three levels: the first in a single antenna (L1), the second amongst 2 adjacent antennas (L2), and the third between upper and lower tier antenna clusters about the same azimuth (L3). For an L1 trigger, 3 of the 8 channels per antenna must be over threshold within 12 ns. Individual channel thresholds adjust to maintain a constant trigger rate in the presence of thermal noise. An L2 trigger requires that two L1 events occur in adjacent antennas within 20ns, and an L3 trigger requires L2 triggers in the upper and lower tiers within 30 ns. The thresholds are set

48 to correspond to a trigger rate of 4 5 Hz on thermal noise. ANITA has a trigger − efficiency of 50% at 5.4σ and is fully efficient near 7σ , where σ is the Gaussian ∼ V V V standard deviation above the thermal noise root-mean square voltage.

For a discussion of trigger rates and trigger thresholds, see [193,202].

3.2.3 Support Systems

ANITA also has subsystems for providing timing and orientation. A Thales ADU5 differential GPS system provides not only timing and location, but also instrument attitude. A Thales G12 GPS unit is also present for basic timing and location data, and the system computer synced to its provided GPS time through Network Transfer

Protocol (NTP). Four sun-sensors, two accelerometers and a magnetometer offer an independent orientation measurement, while two pressure sensors provide altitude information. Testing, EMI shielding, and integration of these subsystems were the responsibility of the author.

ANITA is powered by a photovoltaic (PV) array arranged on eight panels hanging beneath the lower tier of antennas, and pictured in Figure 3.1. Hung vertically, they receive light directly from the sun and in the albedo from the ice. The total power provided by the array is 400 W. An Outback MX-60 charge controller regulates the power to 24 V and balances the power between the PVs and the nine pairs of 12 V lead-acid batteries that can power the entire instrument for 12 hours. The power system also consisted of solid state relays for power control, and DC/DC converters to provide the +1.5, +3.3, +5, +12, -12 and -5 voltages used by the main computer, the triggering and digitization boards, and the remainder of the subsystems.

49 3.2.4 Computing and Communication

The ANITA computer is a conduction-cooled cPCI single board computer, the

SBS CR7, with an Intel Mobile Pentium III processor and operating with Red Hat

Linux 9. Over the cPCI backplane, the CPU collected waveforms from the SURFs and the support system housekeeping data from Acromag digitizing boards. Breakouts from the Rear Transition Module (RTM) provided RS-232 and RS-422 serial lines to the magnetometer, GPS units, and data transmission (additional serial lines were provided with a USB-to-serial converter). Data storage occurred redundantly on solid state IDE laptop drives installed on cPCI blades, an IDE spinning hard drive in its own pressure vessel, and 61 8 GB USB thumb drives on OSU designed hubs, totaling nearly 1.5 TB. The ANITA flight software, which was an OSU institutional responsibility, was designed around autonomous daemons which acquire the data, process it, determine what data is to be telemetered, and control the operation of the other processes.

Communication with the ANITA payload occurs through the CSBF Support In- strument Package (SIP). Three serial cable links relay the ANITA data to the SIP computers which communicate to the ground with line-of-sight radio transmissions when near McMurdo, and via the TDRSS and IRIDIUM satellite systems throughout the flight. When in sight of a TDRSS satellite, 6 kbps is down-linked continuously allowing for only a small amount of the total data written to disk on the payload to be transmitted, and ten minutes of every hour are scheduled to allow commands to be up-linked to the payload. The SIP is powered by the set of solar panels atop the ANITA gondola, as pictured in Figure 3.1. The SIP has two independent and redundant computers and its own temperature, pressure and GPS sensors and a suite

50 of configurable components offered to the science instrument as a Science Stack. The

Science Stack includes analog-to-digital converters and open-collector outputs which are used for turning ANITA and a limited number of powered subsystems on and off. The SIP handles ballast (lead pellets in a ballast-hopper located in the center of the payload) release during the flight, and the final termination of the flight and the separation from the balloon. The SIP is placed in a copper EMI-protective box to eliminate it as a source of radio noise for ANITA to trigger on.

3.3 Prototyping and Preparing ANITA

It took a number of years for ANITA to move from a concept to a full long-duration balloon (LDB) payload. In the interim, a number of design considerations, both hardware and software, were evaluated under test circumstances with prototypes.

3.3.1 ANITA-lite: 2003-2004 Antarctic Flight

The novel detection concept of ANITA as a radio interferometer looking down upon the Antarctic Ice for a pulse from a neutrino-induced shower required that the ambient RF noise levels in the skies above Antarctica. With a limited budget and timescale, the ANITA-lite instrument was developed to be flown piggy-backed onto the TIGER payload [194, 195]. Integration of the ANITA-lite instrument occurred during the summer of 2003 at the Palestine, TX headquarters of the then National

Scientific Balloon Facility, now the Columbia Scientific Balloon Facility (CSBF).

A pressure vessel was used to house the instrument electronics to allow the use of commercially available computers and digitizers, which did not have the costs or lead times of space-hardened components capable of operating in vacuum. Two dual- polarized antennas were flown with a combined field of view of 45◦ in azimuth. For

51 Figure 3.3: The ANITA instrument with mock antennas prior to the engineering flight from Ft. Sumner, NM in the summer of 2005.

triggering, the signals were mixed to left- and right-circular polarization, but there

was no frequency band separation for this prototype.

TIGER and ANITA-lite flew for 18.4 days around Antarctica, having launched on 12/18/03 from near McMurdo Station. The ANITA-lite analysis found trigger events caused by payload noise including the CSBF communications antennas, and the TIGER photo-multiplier tubes. Antarctica proved to be sufficiently radio quiet, and an upper limit upon the ultra high energy neutrino flux was determined by this

ANITA prototype with a 90% CL on a E−2 flux over the energy range of 1018.5 eV

ǫ 1023.5 eV of ǫ2 Φ 1.6 10−6 GeV cm−2 s−1 sr−1 [196, 197, 188]. It became ≤ ν ≤ ν ν ≤ × clear that minimizing payload RF noise would be necessary for a successful full ANITA

flight.

52 3.3.2 Engineering Flight: Ft. Sumner, NM, 2005

Following the ANITA-lite flight, the design of the full ANITA payload progressed.

The superstructure required enough structural integrity to withstand the buffeting of the tropopause, the parachute deployment, and the crash to Earth. As ANITA was not going to fly a pressure vessel, it was also necessary to thermal vacuum test both the commercially acquired and in-house developed electronics. A short engineering and mechanical (EM) flight from the CSBF facility in Ft. Sumner, NM preceded by an instrument integration at UC Irvine where a high-bay large enough to house the completed ANITA gondola would allow the full testing of the frame and operations at altitude, as well as testing the communications interface with CSBF and the instru- ment electro-magnetic interference (EMI) shielding. The payload, just prior to the

EM flight launch is pictured in Figure 3.3. For this engineering flight, only two full antennas were flown, and they were positioned to have the same azimuthal direction, being in the same phi sector, while being in separate vertical tiers to approximate a true ANITA trigger; filling the rest of the payload were dummy-antennas.

Numerous practical lessons were learned from this engineering campaign. Many of these were procedural and related to the construction of the ANITA gondola and the launch and testing schedules. However, some changes in the ANITA design were motivated by lessons learned in Ft. Sumner. Originally, ANITA was designed to have a single plane of solar panels which would remain trained on the sun through the use of a rotator attached between the gondola and the cables to the balloon.

In the EM flight, it became clear that the rotator motor created so much RF noise that it could not be included in the Antarctic payload. Omnidirectional solar panels and a charge controller capable of handling differing power supplies from panels on

53 opposite sides of the payload were incorporated into the final ANITA design. The

filter pins that power and slow serial signals enter the EMI shielded box on and that

filter off high frequency noise were found to interfere with adjacent serial line signals and were removed for those signal lines. The data storage plans for ANITA were also found to be wanting both in capacity and accessibility in the event that the entire payload could not be recovered. This drove the expansion of data storage drives for the ANITA-I flight to include the aforementioned array of USB thumb drives placed both within and without the EMI enclosure, solid state laptop hard drives installed in the cPCI computer, and a spinning hard drive encased in its own small pressure vessel.

3.3.3 SLAC Test Beam: End Station A, 2006

In the subsequent summer, prior to the ANITA 2006-2007 flight, instrument inte- gration again occurred at UC Irvine. Then, ANITA was shipped up to the Stanford

Linear Accelerator Center (SLAC) where it was installed on a crane in End Station

A. Over the course of a week of beam time, SLAC experiment T486 was performed to confirm the Askaryan effect in ice. A diagram of the experiment is shown in Figure

3.4.

The full ANITA payload, with its complete complement of antennas, was hung from the primary End Station A crane, and was able to be moved laterally and vertically about the rear of the facility. A 7.5 ton ice target constructed of large ice blocks primarily intended to be made into ice sculptures was placed, refrigerated and insulated, at the end of the electron beam. To avoid the Askaryan signal reaching the ice surface at an angle of total internal reflection, the upper surface of the ice

54 Figure 3.4: A diagram of the T486 experiment at SLAC when ANITA was suspended in End Station A above a 7.5 ton ice target [198].

was carved to a slope of 8◦ and ferrite sheets were placed beneath the ice to prevent reflections from the floor. The ice was illuminated with bundles of 108 to 109 electrons

of 28.5 GeV, giving total shower energies of 3 1019 eV. At the shower maximum ∼ × there are 2 1010 electron/positron pairs, and the initial negative charge provided ∼ × only 15% of the total charge excess capable of producing the Askaryan signal. ∼ T486 confirmed the predicted Askaryan characteristics of a coherent signal in the

ANITA frequency range of .2 to 1.2 GHz proportional to E2 with the peak strength

along the Cherenkov cone [198].

At the conclusion of the beam test, CSBF personnel travelled to SLAC to certify

that ANITA was indeed ready for its first Antarctic campaign.

55 Chapter 4

The First ANITA Flight

ANITA launched on Dec 15, 2006 from Williams Field, Antarctica and flew for 35 days before terminating on January 19, 2007. The instrument came to ground 360 km away from the South Pole at 84.58◦ S, 22.28◦ W and was subsequently recovered in full.

4.1 ANITA-I Flight Path

Antarctic long-duration balloon (LDB) campaigns operate because in the austral summer a circumpolar vortex sets up in the upper stratosphere, centered on the geographic South Pole and circulating cyclonically. A balloon launched from Williams

Field, McMurdo, Antarctica will take from 10 to 13 days to traverse a circular path at nearly constant latitude around the continent before returning to a location easily accessible for recovery. With multiple orbits, flights of upwards of 30 days are possible.

The ANITA-I flight path, shown in Figure 4.1, is an anomaly in the LDB program because of the off-pole centering of the south polar vortex over West Antarctica.

Although ANITA did not fly over East Antarctica where much of the deep, cold ice of Antarctica resides, Figure 4.2 shows that ANITA passed over ice of average depth greater than 1 km; the average ice depth within ANITA’s horizon was 1.2 km. ∼ 56 Figure 4.1: The ANITA ’06-’07 flightpath, beginning at McMurdo travelling counter- clockwise for 3.5 orbits and terminating 360 km from the South Pole. The path data is taken from the Columbia Scientific Balloon Facility’s Support Instrument Package GPS data. An example horizon of 600 km at float is indicated in dotted lines.

57 4000

3500

3000 Ice Depth (m)

2500

2000

1500

1000

500

0 12-12 12-19 12-26 01-02 01-09 01-16 Time

Figure 4.2: Ice Depth vs. Time for the 4 ANITA orbits; the average ice depth of 1761 m is shown as a dotted line. The depth data is taken from the BEDMAP project [200]. The pale and darker grey lines above the depth plot indicate the times for which McMurdo and the Amundsen-Scott Station were respectively within 680 km of ANITA. After 01/05 ANITA operated with a reduced duty cycle.

At float, ANITA was 36 km aloft, with an average distance to the horizon of ∼ 680 km, thus instrumenting 1.5x106 km3 of ice for radio attenuation lengths on ∼ the order of 1 km [199]. The path and large horizon distance caused ANITA to spend substantial amounts of time in view of bases with high RF noise, including

McMurdo, Admundsen-Scott South Pole Station, and the West Antarctic Ice Sheet

(WAIS). The ANITA noise-riding trigger thresholds were thus higher than anticipated whilst in sight of populated bases because of the anthropogenic signals.

58 Figure 4.3: The measured power over the full ANITA bandwidth vs. date in flight taken from the RF Power monitor values and averaged over the entire payload. The pale and darker grey lines above the depth plot indicate the times for which McMurdo and the Amundsen-Scott Station were respectively within 680 km of ANITA.

4.2 ANITA-I RF Performance

The ANITA RF system, performed well during the first three weeks of the flight.

As ANITA Triggers on the RF Power, with each of the 256 individual frequency bands varying their thresholds with the instantaneous radio noise via a proportional- integral-differential (PID) servo loop, the instrument’s sensitivity is determined by the measured power. The measured power is given by:

Pmeas = kB(Tant + Tsys) (4.1)

where kB is Boltzmann’s constant, Tant is the effective antenna temperature sampling the ice and sky temperature in the antenna field of view, and Tsys is the noise added by the RF System including the filters, amplifiers, cables and the remainder of the signal chain. When not within view of an inhabited base, the effective antenna temperature

59 was T 180 K, which corresponds well with the beam average of the ice, T ant ∼ ∼ 240 K, and the sky, T 10 20 K (see Figure 4.3). The diurnal modulation of ∼ − the antenna temperature is due to the elevation change in the locations of the Sun

and Galactic Center, which is responsible for a 50 K oscillation, as seen in Figure ∼ 4.4. The azimuthal difference in the RF power due to the sun and Galactic Center is

shown in Figure 4.5.

In the latter part of the flight, ANITA operated with a reduced duty cycle due

to an intermittent fault which necessitated a number of reboots of the system. The

first loss of the system, on 1/04/07, also coincided with a significant loss of gain in

one channel, the horizontal polarization of Antenna 23 (see Figure 4.6). This was the

only problem seen in the RF system during the flight, and a minor one as the primary

neutrino hunting analysis focuses on the vertical polarization data.

4.3 ANITA-I LiveTime

One of the first quantities necessary for determining ANITA’s sensitivity to neu-

trinos is the operational livetime. During the ANITA-I flight the TURF calculated

the deadtime fraction on a per second basis and this value was recorded in each

event header file. However, for seconds without events in occurring in them there is

no measure of whether the instrument was operating or not. Other seconds have a

recorded deadtime, but may not reflect true operational times if RF triggering or the

RFCMs were off. The TURF firmware keeps track of time using the once per second

pulses (PPS) of the ADU5 GPS unit, which is counted as the ppsNum. Deadtime is

reported as a fraction of a second, and for every event with the subsequent ppsNum

value that fraction is merely repeated, thus we use only the first event for the same

60 Figure 4.4: Taken from a quiet portion of the flight, from 12/26/06 to 1/3/07, the effective antenna temperature is plotted against the solar elevation angle. When the sun is lower in the sky it is more directly in the ANITA antennas’ view and raises the antenna temperature. The points extending above the main distribution correspond to times ANITA was over open water and thus had a higher temperature in its view.

61 Figure 4.5: The RF Power in uncalibrated ADC counts vs the azimuthal distance from the sun in units of phi sectors, or 22.5◦. The Sun is here always centered at 0. This data is for the period in which ANITA is within 600 km of the South Pole, and the excess extending to 850 ADC counts is due to the South Pole Station. The excess in the center bin is due to both the Sun and Galactic Center. [201]

62 Figure 4.6: The average payload RF Power in ADC counts, and that for the horizontal channel of antenna 23 vs. time, at the first major loss of the instrument. ANT 23H never recovered full gain.

63 ppsNum, and then perform a simple inversion of the fraction to get the live time. We require that RFCMs and SHORTS are powered on, that no antennas are masked off, and that the digitizing clock cycle count (c3poNum) is within limits. No restrictions are placed on band masking, which can be accounted for in the Monte Carlos. Figure

4.7 shows the ANITA liveTime increasing over the course of the flight to its total value of 1491013.9351 seconds (or 17 days, 6 hours, 10 minutes, 13 seconds) which is

50% of the total flight, and 60% of the time with housekeeping on.

Such a low livetime fraction was due both to a measured deadtime that included times when all event buffers were full, and when the flight CPU disappeared entirely for seconds at a time on what have been nicknamed its “coffee breaks”. Figure 4.8 shows the relative impacts of these two causes of deadtime, while Figure 4.9 shows, in hour-long bins, the number of seconds with no data during the ANITA-I flight.

When the time between subsequent events is plotted, the CPU “coffee breaks” are readily apparent, as exemplified by the time between consecutive events for the eight minutes from 06:13 to 06:18 UTC on December 19, 2006, shown in Figure 4.10.

Lab tests had indicated that at periods of high trigger rates there would be excessive time between events as all four event buffers would fill before the appropriate daemon could read the events and write them to permanent storage. However, such conditions were not linked to periods of high trigger rates during the flight, and were not seen in the lab prior to, or following, the flight. The most accepted hypothesis explaining the ANITA-I coffee breaks is that the traffic over the cPCI backplane for the reading of events and writing them to multiple storage disks exceeded what the CPU could handle.

64 Figure 4.7: On top:The growth in liveTime with flightTime. Our payload problems late in flight are evident. Below:Profiles of liveTime with time now taking into account as many ‘0’ liveTimes as possible. Green points are for the counted liveTimes, red for those not counted. The increased spread of red points throughout the flight is due to the bad digitizer clock cycles.

65 Figure 4.8: In orange is the fraction of seconds that we have events occurring during and thus for which a measured deadTime value is available. In goldenrod is the fraction of liveTime, which is taken as the inverse of the measured deadTime. The total livetime fraction, as in Figure 4.7 is shown in green, and is is the product of the other two values.

Figure 4.9: The number of seconds per hour missing through the duration of the flight. After 01/04/07, ANITA suffered long periods of not being on at all. The highest rates of missing seconds occurred when ANITA was in view of McMurdo or the South Pole Station. The cause of the improvement in liveTime (fewer seconds with no events) that occurred on 12/31/06 and 01/02-01/03/07 has not been determined.

66 Figure 4.10: The time between subsequent events plotted against the time o the event for a short period on December 19, 2006. Highlighted with red stars are times between housekeeping events between 1 and 2 seconds long, and in blue stars time between housekeeping events of more than 2 seconds.

67 4.4 Calibration

ANITA-I was calibrated both on the ground in the laboratory before the flight, and in the air during the flight. The ANITA pulse response and the frequency dispersion was measured with the input of sharp pulses to the antennas in an anechoic chamber at the University of Hawaii, while the response of the remainder of the system was determined in McMurdo with the pulses recorded in ANITA waveform data, and, taken just before the SURFs, with an oscilloscope. With the entire payload assembled in Antarctica, the gain and group time delays from the RFCM input to the SURF input were measured using a network analyzer, and duplicate gain and noise figure measurements were made with a noise figure meter with a noise diode on the input.

These measurements for the 72 primary ANITA channels, as well as those for the bi-cone and disc-cone monitoring antennas are shown in Figure 4.11. Timing studies of the digitization were made with the input of sine and square waves with varying periods.

Instrument calibration was performed during the flight using ground and payload based transmitting antennas. Upon launch and during the first return to McMurdo, pulses were sent from surface horn antennas identical to those in flight and from dipole antennas lowered into boreholes, at both Williams Field in McMurdo and a

field camp at Taylor Dome. Analysis of these pulses shows that ANITA has a timing resolution of 40 ps between vertical channels recorded on the same SURF and 60 ps between horizontal channels on different SURFS, which corresponds to a pointing resolution in elevation and azimuth of (∆θ, ∆φ)=(0.2◦, 0.8◦). Throughout the flight, the four deck-mounted bi-cone antennas pulsed periodically, allowing a system check through the entire flight and a diagnostic to search for sync-slips, when some or all

68 Figure 4.11: The gain and noise figure values as a function of frequency, measured for each channel with a noise figure meter in McMurdo.

69 of the event header information including the trigger time do not match the recorded

waveforms.

A full account of the ANITA-I flight and instrument calibration is provided in

[202].

70 Chapter 5

ANITA and GRB Neutrinos

The search for neutrino events from the 2006-2007 Antarctic campaign relies upon

a simple concept: the pulse-phase interferometry reconstruction of an impulsive, ver-

tically polarized signal originating from an isolated locale on the ice. With a well-

calibrated instrument, angular precision in the pointing to the continent is 0.2◦ in elevation and 0.8◦ in azimuth [202]. A blinding strategy was employed in which re- construction was calibrated upon precisely timed pulses sent to the payload from

Williams Field and Taylor Dome, and then cuts were optimized on a 10% sample of the entire data set. The primary analysis of the ANITA-I data has discovered no neutrino candidate events and has set a upper limit with 90% CLona E−2 spectrum

in the energy range of 1018.5 eV ǫ 1023.5 eV of ǫ2 Φ 2 10−7 GeV cm−2 s−1 ≤ ν ≤ ν ν ≤ × sr−1 [203]. The model independent limits are shown in Figure 5.1. The cuts necessary in such an analysis are, in order: requiring a hardware trigger, requiring the event to reconstruct as a plane wave travelling from below the horizon, requiring broadband, impulsive events with signal bandwidth exceeding 100 MHz, requiring the events be isolated from other events and known human camps, and finally the signal must be

71 dominantly vertically polarized. All of these cuts would also be necessary in a ded-

icated GRBν search, and we depend upon this previous search for sensitivity and efficiency estimates.

Monte Carlos, with the ANITA-I flight path and trigger thresholds as inputs,

produce skymaps of ANITA’s acceptance, showing that the primary sensitivity is

a band about the equator. Such a pattern is necessitated by the geometry of an

Earth skimming neutrino that interacts, producing a shower with a Cherenkov cone

of radiation that refracts as it exits the ice and can be detected by the ANITA payload.

The ANITA field of view (f.o.v.) does show a slight energy dependence. Lower energy

neutrinos, on average, come from a slightly more positive latitude than those of the

highest energy neutrinos due to the Earth’s opacity. The Ohio State Monte Carlo

acceptance for mono-energetic neutrinos of 1018.5 eV is shown in Figure 5.2.

5.1 GRBs during the ANITA-I Flight

During the ANITA-I flight, the Swift satellite was the primary GRB detecting experiment in operation, although other satellites were also in operation. The Swift

Gamma Ray Burst Explorer [210] was launched November 20, 2004, with its three onboard instruments: the Burst Alert Telescope [211], the X-ray Telescope [212] and the Ultraviolet/Optical Telescope [213]. Swift detects 100 GRBs a year, and is ∼ able to measure GRB fluxes in multiple wavelengths and determine GRB positions in a matter of minutes with arc-second accuracy. Unfortunately, the Swift Burst

Alert Telescope (BAT) f.o.v. is only 1.4 sr, and thus does not provide full sky cov- erage. A number of other spacecraft comprise the InterPlanetary Network (IPN), including KONUS on the Wind satellite, INTEGRAL, RHESSI, SUZAKU, and the

72 Figure 5.1: The ANITA-I neutrino flux limits from [203]. The other experimental limits shown are from [188,204,135,205,206,207], while the GZK neutrino models are composed from [127,103,134,165,133,138,208].

73 Figure 5.2: A Monte Carlo simulation of the ANITA sky sensitivity produced with mono-energetic 1018.5 eV neutrinos with flavor ratios of 1 : 1 : 1. The total sensitivity in this case is 3 10−4 km2 sr yr. [209] ×

Mars Odyssey, which uses the timing relationships between detections on multiple

instruments to localize GRBs. Both Swift and the IPN relate GRB detections to the

Gamma-ray burst Coordinates Network (GCN) to aid in follow-up observations by

ground- and space-based observatories in other wavelengths.

There were 21 possible GRBs detected by gamma ray observing spacecraft during

the ANITA-I flight, occurring from 12/15/2006 to 01/19/2007. The initial detection

information for these bursts is shown in Table 5.1, where the first column contains

the GRB name3, the next two columns have the date and time of the GRB detection

in UTC, the fourth column lists the detecting instrument(s), and the final column

lists the position of the GRB. Details of the detected GRBs were found through the

3This is a six digit value made from the date of the burst: first the last two numbers from the year, then the two digit month, and finally the two digit day. If multiple GRBs occur on the same date, the first has an ‘a’ appended, the second a ‘b’ and so forth.

74 Figure 5.3: The locations of the seven GRBs detected by Swift during the ANITA-I flight in equatorial J2000 coordinates of right ascension and declination.

GCN Reports at the GRBlog [214,215], and the IPN Masterlist [216]. The Swift de- tected GRBs all have equatorial coordinates, as provided in their catalog [217] which are plotted in Figure 5.3, while for the other GRBS detected by satellites of the IPN, private communication with Kevin Hurley [218] was required for localization informa- tion. None of the non-Swift detected GRBs were precisely located, and determining the error boxes for the remainder of the GRBs was done by Kevin Hurley, taking into account the satellite locations and acceptances, and Earth occultation. The IPN allowed regions for the 14 GRBs not localized by Swift are listed in Appendix A and those with localizations are shown in Figures 5.4 to 5.14.

With just a cursory glance at the GRB locations and the ANITA f.o.v. for neu- trinos at 1018.5 eV, shown in Figure 5.2, it is clear that none of the precisely located

75 Figure 5.4: GRB061221 localization is between annuli, one of which is only a tenth of a degree wide.

Figure 5.5: GRB061223 is localized to two large error boxes in the northern hemi- sphere created by the intersection of a KONUS ecliptic band, in cyan, and the IPN annulus shown in red.

76 Figure 5.6: GRB061224 is localized to a small lens shaped region that is the intersec- tion of a KONUS ecliptic band and an IPN annulus.

Figure 5.7: GRB061225 is localized only to a ecliptic band in the southern hemisphere.

77 Figure 5.8: GRB061229 is localized to two error boxes at the intersection of 2 annuli and an ecliptic band.

Figure 5.9: GRB061230 is localized to a thin error box in the southern sky along the intersection of two annuli, one of which, in magenta, is only a twentieth of a degree wide.

78 Figure 5.10: GRB070106 is only localized to an equatorial ecliptic band.

Figure 5.11: GRB070113 occurred within the intersection of two nearly coincident annuli.

79 Figure 5.12: GRB070115B occurred just below the equator, within the intersection of an ecliptic band and an annulus.

Figure 5.13: GRB0701116B occurred within the intersection of the KONUS ecliptic band, in cyan, and the two red annuli. It lay within the nominal ANITA f.o.v. from -10◦ to +10◦ in equatorial latitude.

80 Table 5.1: GRBs that occurred during the ANITA-I Flight

GRB Date UTC Time Detector Localization 061217 12/17/06 03:40:08.217 Swift RA 160.403◦ Dec -21.152◦ 061218 12/18/06 04:05:05.815 Swift RA 149.260◦ Dec -35.217◦ KONUS/Mars Odyssey/ outside Swift f.o.v./ 061221 12/21/06 09:56:47.445 INTEGRAL/SUZAKU south of -35◦ 061222A 12/22/06 03:28:52.110 Swift RA 358.254◦ Dec 46.524◦ 061222B 12/22/06 04:11:02.350 Swift RA 105.353◦ Dec -25.866◦ 061223 12/23/06 19:35:09.998 KONUS/Swift possibly in ANITA f.o.v. 061224 12/24/06 15:16:11.983 KONUS/SUZAKU outside ANITA f.o.v. 061225 12/25/06 22:48:22.00 KONUS rate ecliptic band -66.1◦ to -41.1◦ 061229 12/29/06 22:25:47.529 KONUS/RHESSI possibly in ANITA f.o.v. KONUS/Mars Odyssey/ 061230 12/30/06 23:09:31.233 outside ANITA f.o.v. INTEGRAL/RHESSI 070103 01/03/07 20:46:39.412 Swift RA 352.581◦ Dec 26.823◦ 070106 01/06/07 11:52:16.729 KONUS ecliptic band -3.8◦ to +16.3◦ 070107 01/07/07 12:05:18.316 Swift RA 159.422◦ Dec -53.202◦ 070110 01/10/07 07:22:41.574 Swift RA 0.934◦ Dec -52.978◦ KONUS/SUZAKU/ 070113 01/13/07 11:56:28.623 in ANITA f.o.v. INTEGRAL 070115A 01/15/07 13:23:34.00 Swift no localization 070115B 01/15/07 17:37:41.029 KONUS/Swift possibly in ANITA f.o.v. 070116A 01/16/07 12:33:30.00 INTEGRAL unconfirmed and demoted KONUS/INTEGRAL/ 070116B 01/16/07 14:32:13.058 in ANITA f.o.v. Swift/RHESSI rate SUZAKU/Swift/ no localization/ 070116C 01/16/07 15:26:22.00 RHESSI rate probable SGR 070117 01/17/07 15:23:01.823 KONUS ecliptic band +2◦ to +22◦

81 Figure 5.14: GRB070117 is only localized to an equatorial ecliptic band.

GRBs falls in this region. Of the IPN localized GRBs, six have at least a portion

of their error boxes within the ANITA f.o.v.; of these, only two have relatively small

error boxes, two have large error boxes that are portions of large annuli, and two can

only be located within a 20◦ ecliptic band. Some neutrinos from the southern sky can be detected because of reflections occurring at the ice/seawater boundary of the ice shelves.

ANITA did not operate constantly during the its flight, and even when on, its fractional liveTime varied greatly due to onboard computer issues and difficulties keeping up with high event rates when near large populated bases. Table 5.2 contains the ANITA operational information at the times of the GRBs that occurred during the flight. The first column lists the GRB name, followed by the time of the burst in

82 Unix time, which is how events were timestamped on ANITA. The third column gives

ANITA’s location in latitude and longitude, which is found from the closest recorded

CSBF GPS data if ANITA was not operating at the time, no interpolation is applied

as this value is reported every two minutes.(The location of the ANITA payload at

the time of each GRB is plotted over the map of Antarctica in Figure 5.15.) The

final column reports if ANITA was off at the time of the GRB, or gives the liveTime

fraction of the fifteen minute interval of the flight that the GRB fell within, which

is not centered about the GRB time. Unfortunately, the problems ANITA suffered

during the last third of the flight indicate that we have no sensitivity to eight of

the twenty-one GRBs that occurred, including GRB010116B which lay most squarely

in the ANITA f.o.v. and another three of the GRBs with a chance of falling within

ANITA’s sights. At the time of GRB061218 ANITA was temporarily not taking data,

but within a few minutes ANITA was functioning, which explains the 20% liveTime

fraction for that period.

5.2 Estimating GRB Neutrino Fluxes for the ANITA-I Flight

To model the UHEν GRB flux, for the purpose of setting a limit, we must first gather the available gamma ray data. Only the Swift satellite observations were able to provide positions accurate enough for follow up surveys to determine the redshifts of the GRBS, and even then, only for a limited number.

We follow the methods and analysis in the Razzaque et al paper of 2007 [144] in which the RICE collaborations places the only other limits on UHE GRB neutrinos.

Their work assumes a standard, isotropic fireball shock model for gamma ray bursts extended to neutrino production by Waxman and Bahcall, [141,74,142] and this

83 Table 5.2: ANITA operation at times of GRBs ANITA Location LiveTime GRB Unix time Latitude Longitude fraction 061217 1166326808 -87.895523 146.118576 0.68164 061218 1166414705 -82.54 -83.18 not taking data, 0.20773 061221 1166695007 -75.867386 -129.663879 0.62389 061222A 1166758132 -76.988167 -149.937866 0.63142 061222B 1166760662 -77.121315 -150.559097 0.63142 061223 1166902510 -81.382896 -179.860916 0.614235 061224 1166973371 -83.460327 170.800430 0.858048 061225 1167086902 -86.137733 107.254196 0.792278 061229 1167431147 -77.597305 -28.953194 0.667836 061230 1167520171 -77.022858 -56.109573 0.77309 070103 1167857199 -82.108597 -152.606537 0.81197 070106 1168084336 -83.501259 109.528206 0.863378 070107 1168171518 -83.35 69.77 ANITA is off 070110 1168413761 -81.734642 -32.078266 0.869482 070113 1168689388 -83.05 -149.56 ANITA is off 070115A 1168867414 -84.39 124.92 ANITA is off 070115B 1168882661 -84.56 113.92 ANITA is off 070116A 1168950810 -84.98 79.88 ANITA is off 070116B 1168957933 -84.92 75.77 ANITA is off 070116C 1168961182 -84.85 73.44 ANITA is off 070117 1169047381 -85.75 27.26 ANITA is off

84 Figure 5.15: The location of ANITA over the Antarctic continent at the time of each GRB during the flight is shown with a green star and labeled with the GRB name from that time. When in sight of a large base the ANITA thresholds rise, and when over an ice shelve there is a chance of detecting neutrinos from the southern hemisphere via reflections at the ice/seawater interface.

85 analysis follows suit. For GRBs without a measured redshift the Waxman-Bahcall

‘average’ model will be applied.

With a measured gamma ray fluence, GRB duration, and the redshift of a GRB, the isotropic energy and luminosity of a GRB in photons may be calculated, with a limited number of assumptions. The bolometric fluence, denoted by Sγ, is commonly taken over a decade in energy, and the GRB duration, t90, is the time from when

5% to 95% of the total background subtracted signal is observed [219], Table 5.3 lists the Swift BAT value for Sγ measured from 15-150 keV [217], as well as t90, the redshift, and the luminosity distance4 for the one short GRB and two long duration

GRBs from the ANITA-I flight for which a redshift was measured. The redshifts of

GRB061217 and GRB061222B were found by the Magellan telescopes; the former through the oxygen doublet lines and the latter with the LDSS3 instrument using the

Lyman-α line and several metal absorption features [220,221,222], and the redshift for

GRB070110 was determined by the VLT through observation of a dampened Lyman-

α trough and metallic absorption lines [223]. The luminosity distance is calculated with Ned Wright’s Cosmology Calculator [224] with parameters for a a ΛCDM flat

−1 −1 universe with H0 = 70 km s Mpc , Ωm = 0.3 and ΩΛ = 0.7 as in [144]. If more

−1 −1 precise values of H0 = 73 km s Mpc , Ωm = 0.27 and ΩΛ = 0.73 are chosen, dL increases.

Although the fluence of gamma rays we see from GRBs probably come from a jet with opening angle Ω 0.1 rad, we can determine an equivalent isotropic γ energy jet ∼ 4 Luminosity distance (dL) is defined to determine the relationship of flux (F ) to luminosity (L) 2 now as the F = L/4πdL and is related to the proper distance χ = c emission dt/a(t) by dL = (1+ z)χ. Thus, luminosity distances for objects with large redshifts will appear to be larger than the size of the universe. R

86 Table 5.3: GRBs with Measured Redshifts from the ANITA-I Flight

Sγ(15−150 keV) t90 dL GRB (ergs cm−2) (s) z (Gpc) 061217 4.2 10−8 0.21 0.827 5.227 × 061222B 2.2 10−6 42 3.355 29.067 × 070110 1.6 10−6 88.4 2.352 18.9 ×

and luminosity with:

2 Sγ 2 Sγ Eγiso =4πdL and Lγiso =4πdL (5.1) (1 + z) t90

The energy released in gamma rays is merely a fraction, εe, of the total kinetic energy

of the of the kinetic energy of the plasma material in the relativistic shock, as is the

energy of the shock magnetic field, εB. We take these fractions to be similar, at 10%

of the total kinetic energy.

The observed gamma ray spectrum is fit to a simple model, following [144] we use a Band fit [225] which is a broken power-law of

−α dNγ ǫγ for ǫγ < ǫγ,b = −β [0.5ex] (5.2) dǫ ǫ for ǫγ > ǫγ,b γ  γ where α 1 and β 2. ∼ ∼ 2 The break energy, ǫγ,b, which is also the peak energy of the ǫγ(dNγ/dǫγ ) spectrum,

can be determined by observation, but as this was not available for the GRBs that

occurred during the ANITA-I flight, following [144], we use the phenomenological

Ghirlanda relationship [226]:

300 E 0.56 ǫ = γiso keV (5.3) γ,b (1 + z) 1053 ergs  

87 Such a fit is not optimal, as has been pointed out by [227], but is used here for

comparison with past searches. Indeed, the Swift collaboration fit the spectra of all

7 detected GRBs during the ANITA-I flight to a simple power law of:

E αP L f(E)= KPL (5.4) 50 50 keV  

PL −2 −1 −1 where K50 is the normalization at 50 keV in units of photons cm s keV and

αPL is the power law index [217]. The fact that the Ghirlanda relationship returns a

photon breaking energy, ǫγ,b, in the Swift energy band is a clear indication that such

a model is insufficient. The calculated photon values for GRB061217, GRB061222B,

GRB070110 are listed in the first columns of Table 5.4.

A GRB neutrino fluence is assumed to exist via the same pγ ∆+ resonance that → gives us the GZKν fluence (p + γ ∆+ n + π+ µ+ + ν e+ + ν + ν + ν ). → → → µ → e µ µ Following Waxman and Bahcall [141, 74, 228], for this interaction to occur, in the observer frame the photon and proton energy must be

2 2 ǫγ ǫp =0.2GeV Γ (5.5)

Using this relation, the break in the proton spectrum is ǫ 1016Γ2 (ǫ )−1 eV p,b ≈ 300 γ,b(MeV) where Γ = 300Γ300 and the break in the neutrino spectrum occurs at roughly 0.05ǫp,b assuming 20% of the initial proton energy is in the pion and the decay products equally split this value. Transforming to units useful in this occasion, the break in the neutrino spectrum is given by:

0.015Γ2 ǫ −1 ǫ = γ,b GeV (5.6) ν,b (1 + z)2 GeV   As in the other calculations we are following, we will take Γ = 300, following [229,230].

88 Another break in the neutrino spectrum occurs at the synchrotron break energy.

The energy density of the magnetic field in the wind rest frame determines the syn-

chrotron loss time, which is inversely proportional to the particle energy [231]. The

magnetic field is given by 2ε L B′ = B γiso (5.7) ε r2Γ2c r e where, as mentioned above we allow the energy fractions to cancel, and r is the radius of the fireball which is given by r 2Γ2ct , in which t is the variability ≃ var var time scale which may range from milliseconds to seconds, and here we take to be

0.01 s. Converting to useful units again, the magnetic field becomes

(1/2) −3 −1 ′ Lγiso Γ tvar B =7.99 105 G (5.8) × 1052 erg/s 300 0.01 s       Such a magnetic field leads to a break energy of

− 1011Γ B′ 1 ǫ = GeV (5.9) ν,sb 4(1 + z) G   We are now able to put together our neutrino flux spectrum. We assume that the

proton luminosity is comparable to the gamma ray luminosity, distributed equally

per decade in energy according to the power-law dN /dǫ ǫ−2 to a cutoff energy p p ∝ p over 1020 eV. The neutrino flux is then β−1 (ǫν/ǫν,b) for ǫν < ǫν,b 2 1 fπ Sγ α−1 ǫνΦν = (ǫν/ǫν,b) for ǫν,sb ǫν ǫν,b (5.10) 2 4 t90 ×  α−1 −2 ≥ ≥  (ǫν,sb/ǫν,b) (ǫν /ǫν,sb) for ǫν > ǫν,sb The prefactor takes includes equal likelihoods for the ∆+ π+, π0, which remains for → consistency with past works although as [144] points out that iso-spin considerations

determine the production ratio of π+ : π0 to be 1 : 2. It also includes equipartition

of the pion energy to the four leptonic decay products. Thus, this flux is for each

of the source neutrino flavors, νmu, νµ, and νe. fπ is the fraction of energy that the

89 proton loses to pions. For an optical depth on the order of unity, fπ =0.2 which we

shall adopt as a constant for our calculations as more complete Monte Carlo studies

of this variable shows to be reasonable [232]. The prefactor then becomes:

− f S t 1 1.56 10−6 π γ 90 GeV cm−2s−1 (5.11) A ≡ × 0.2 −6 2 10 s   10 ergs/cm    The flux prefactor and neutrino break energies for the three GRBs with measured

redshifts are listed in the last three columns of Table 5.4. Although we would generally

expect approximately two decades in energy difference between the spectral breaks,

with average Γ, fπ values, and no experimentally determined break to the photon

spectrum, this model does not have such a feature for these GRBs.

A very similar model is used by Stamatikos et al [157,158,148], but with different

relationships for the neutrinos spectral break energies and the prefactor. The same

average fπ = 0.2, Γ = 300, tvar = 0.01 s, εe = εb = 0.1, and the photon flux properties already calculated are used in this model also. The first neutrino break spectral energy is then given by:

7 105 Γ 2 ǫ −1 ǫ = × γ,b GeV (5.12) ν,b2 (1 + z)2 102.5 1 MeV     and the second, synchrotron, break energy is:

1 8 4 − 2 10 √εe Γ tvar Lγiso ǫν,sb2 = GeV (5.13) (1 + z) √ε 102.5 0.01 s 1052 ergs/s b       Finally, the prefactor in the flux equation 5.10 is given in this model as:

Sγ fπ −2 −1 2 = GeV cm s (5.14) A 8εet90 ln10 which is an approximation to the solution of the integral found in [95,233]. The values for this second model for our three GRBs with measured redshifts are in Table 5.5.

90 Table 5.4: ANITA-I Flight GRBs Flux Variables Following Razzaque et al

Eγiso Lγiso ǫγ,b ǫν,b ǫν,sb GRB (1050 ergs) (1052 ergs/s) (keV) (GeV cmA−2s−1) (106 GeV) (107 GeV) 061217 0.0075 6.537 2.92 3.12 10-6 138.5 2.00 × 061222B 5.15 53.4 47.5 8.17 10-7 1.498 0.2949 × 070110 2.04 7.736 36.75 2.82 10-7 3.27 1.01 ×

Table 5.5: ANITA-I Flight GRBs Flux Variables Following Stamatikos et al

2 ǫν,b2 ǫν,sb2 GRB (GeV cmA −2s−1) (106 GeV) (107 GeV) 061217 1.36 10-5 64.6 17.34 × 061222B 3.55 10-8 0.70 2.55 × 070110 1.22 10-6 1.53 8.69 ×

The two different flux models for the three GRBs that occurred during the ANITA-

I flight for which a redshift was measured are shown in Figure 5.16, while the fluence models are depicted in Figure 5.17. It is clear that there is great variety in GRB neu- trino flux models, both between particular GRBs and between different calculations for spectral break energies, even when many of the inputs to the models are shared.

5.3 Acceptances and Flux Limits

For the diffuse and GRB-particular flux models, the spectrum is always falling as

−4 7.7 ǫν in the UHE ranges that ANITA can probe (> 10 GeV), and so such a spectrum

was input to the primary ANITA Monte Carlo, IceMC5, which is elsewhere referred

to as the UCL or UCLA Monte Carlo. A number of studies were performed, and the

5These studies were performed with the version with CVS tag Connolly Development 051809

91 −2 ) 10 −1 s −2 10−3

10−4

10−5 dN/dE (Gev cm 2 E 10−6

10−7 GRB061217 Razzaque GRB061217 Stamatikos GRB061222B Razzaque 10−8 GRB061222B Stamatikos GRB070110 Razzaque GRB070110 Stamatikos −9 RICE GRBs 10 AMANDA/IceCube GRBs WB average GRB 10−10 105 106 107 108 109 1010 Energy (GeV)

Figure 5.16: Two similar flux models following Waxman and Bahcall [141, 74] with differing spectral break energies and normalizations as listed in Tables 5.4 and 5.5. Also pictured are the flux models for other individual GRBs from [144,157,158,95] and an ‘average’ WB GRB, where the diffuse flux model has been adjusted by 4π × seconds in a day/30 s, where 30 s is taken to be the duration of an average GRB.

92 −1 ) 10 −2

10−2

10−3

10−4 dF/dE (Gev cm 2 E 10−5

10−6 GRB061217 Razzaque GRB061217 Stamatikos −7 GRB061222B Razzaque 10 GRB061222B Stamatikos GRB070110 Razzaque −8 10 GRB070110 Stamatikos RICE GRBs 10−9 AMANDA/IceCube GRBs WB average GRB 10−10 105 106 107 108 109 1010 Energy (GeV)

Figure 5.17: Two similar fluence models following Waxman and Bahcall [141,74] with differing spectral break energies and normalizations as listed in Tables 5.4 and 5.5. Also pictured are the fluence models for other individual GRBs from [144,157,158,95] and an ‘average’ WB GRB, where the diffuse flux model has been adjusted by 4π × seconds in a day.

93 GRBs from the ANITA flight were modeled as point sources and such a flux was also

modeled as diffuse and isotropic.

The simulated fluxes from GRB061222B and GRB070110 were used as isotropic

flux inputs with the payload stationary at its location at the time of the GRB. 8 109 × events were simulated for each location, and the resultant sky plots are shown in

Figures 5.18 and 5.20 and the respective contour plots in Figures 5.19 and 5.21. At

the time of GRB061222B, the ANITA payload was above the edge of the Ross Ice

Shelf, which explains the increased sensitivity to the southern sky through reflections,

and the gap in the equatorial band since there was little ice to the north of the payload

to allow full coverage. Although the ANITA payload was near the edge of the Filchner

Ice Shelf at the time of GRB070110, it was not close enough to gain any sensitivity

to the southern sky.

The 7 Swift-detected GRBs, as well as IPN detected GRBs 061224 and 061230 which were fairly well localized to the southern sky at a time when ANITA was over an ice shelf, were all simulated as point sources. However, the Monte Carlo only had detections from GRB061222B and GRB070103, rendering them the only

GRBs for which a limit can be set. Based upon the Monte Carlo detection of a weighted 2.34085 10−10 events, a 90% CL limit on the E−4 prompt GRBν fluence × from GRB061222B in the energy range of 107.7 GeV ǫ 109.7 GeV of ǫ4Φ ≤ ν ≤ ν ν ≤ 4.647 1018 GeV3 cm−2 at a ratio of 4.81 107 from the predicted Stamatikos flux × × model. The upper limits on the flux from GRB061222B are shown in Figure 5.24, and at nearly two orders of magnitude lower, the theoretical upper limit that could be placed on the neutrino flux from a source like GRB061222B if it occurred in ANITA’s primary field of view, which was modeled at an RA of 0◦ and Dec of -9◦ for the

94 Figure 5.18: Monte Carlo simulation of the number of neutrino events ANITA would see from a GRB with the properties of GRB061222B occurring in any one bin (here there are 360 x bins and 180 y bins in this Hammer-Aitoff equal-area projection), created from an isotropic E−4 flux with flavor ratios of 1:1:1 with the ANITA payload located at -77.121315◦, -150.559097◦ at the edge of the Ross Ice Shelf. The true location of GRB061222B is indicated with a cyan star.

95 Figure 5.19: Filled contours in even logarithmic levels with 30 bins in x and 30 y bins in the Hammer-Aitoff equal-area projection for an isotropic flux like that of GRB0601222B as shown in Figure 5.18.

96 Figure 5.20: Monte Carlo simulation of the number of neutrino events ANITA would see from a GRB with the properties of GRB070110 occurring in any one bin (here there are 360 x bins and 180 y bins in this Hammer-Aitoff equal-area projection), created from an isotropic E−4 flux with flavor ratios of 1:1:1 with the ANITA payload located at -81.734642◦, -32.078266◦, over the continent, but near the Filchner Ice Shelf. The true location of GRB070110 is indicated with a cyan star.

97 Figure 5.21: Filled contours in even logarithmic levels with 30 bins in x and 30 y bins in the Hammer-Aitoff equal-area projection for an isotropic flux like that of GRB070110 as shown in Figure 5.20.

98 payload located at -77.121315◦, -150.559097◦. GRB070103, which had a duration of

t90 = 18.6 s, occurred in the northern sky. A poor upper limit can be set on its

fluence based upon the Monte Carlo detection of a weighted 1.13 10−11 events, a × 90% CL limit on the E−4 prompt GRBν fluence in the energy range of 107.7 GeV

ǫ 108.7 GeV of ǫ4 Φ 4.40 1022 GeV3 cm−2 at a ratio of 2.03 1011 from ≤ ν ≤ ν ν ≤ × × the ‘average’ WB flux model for a single GRB. Also plotted in Figure 5.24 are the

flux models and limits for GRB050603 [144], which was the lowest limit placed in the

RICE study, GRB080319 [95], the naked-eye GRB, and the summed limit placed by

IceCube upon 41 GRBs [233].

For consistency with the literature, we have displayed all limits for the one flavor

GRB neutrino flux, as the AMANDA/IceCube primary analysis looks for muon neu-

trinos via charged-current interactions. ANITA has sensitivity to all three neutrino

flavors, but as Figure 5.25 indicates from the IceMC results, we would expect most

events to come from electron neutrinos. At the ANITA lower energy threshold the

number of events drops to zero because of the smaller cross-section of these low energy

events and the limited ice a down-going neutrino in the ice shelf encounters. Figure

5.26 shows that only low energy neutrinos can possibly make it through the Earth

from the northern sky to be detected by ANITA. The energy range that the fluence

limit for GRB070103 applies to is restricted to below 108.7 GeV since no Monte Carlo events were detected above that energy.

An isotropic E−4 flux is also simulated for the entire ANITA flight. Normalized

with the WB average GRB flux, the point and filled contoured sky-plots for the entire

ANITA flight are shown in Figures 5.22 and 5.23. We set a limit with a 90% CL on

a E−4 flux during the entire ANITA-I flight over the energy range of 107.65 GeV

99 Figure 5.22: Monte Carlo simulation of the number of neutrino events ANITA would see from a GRB with the properties of an average WB GRB occurring in any one bin (here there are 360 x bins and 180 y bins in this Hammer-Aitoff equal-area projection), created from an isotropic E−4 flux with flavor ratios of 1:1:1 with the ANITA payload travelling upon its 2006-2007 flight path with a livetime of 1491013.9 seconds.

ǫ 1010 GeV of ǫ4Φ 6.5 1010 GeV3 cm−2 s−1 sr−1. The diffuse flux WB ≤ ν ≤ ν ν ≤ × model and the ANITA-I and AMANDA limits are shown in Figure 5.27. As a lower

bound we expect 1 GRB per day, and in the ANITA-I live time of 17 days, with

sensitivity to one tenth of the sky, we may expect 1.7 GRBs in the ANITA f.o.v.

during the flight, which easily could escape detection by the GRB instruments.

The ANITA-I flight and the search for ultra high energy neutrinos has comple-

mented the rest of the field of neutrino astronomy and exploited the adventitious

conditions of ballooning in Antarctica, where the ice cap provides a radio-transparent

100 Figure 5.23: Filled contours with logarithmically spaced levels with a binning of 72 x bins and 36 y bins for an isotropic flux of a WB average GRB model as shown in Figure 5.20.

101 8 ) 10 GRB061222B Stamatikos −2 GRB061222B Upper Limit 6 FOV Upper Limit 10 GRB070103 Upper Limit WB average GRB 4 GRB050603 10 RICE Upper Limit on GRB050603 GRB080319 2 IceCube Upper Limit on GRB080319 10 41 GRBs for IceCube dF/dE (Gev cm

2 IceCube Upper Limit on 41 GRBs E 1

10−2

10−4

10−6

10−8

10−10 105 106 107 108 109 1010 Energy (GeV)

Figure 5.24: The ANITA-I upper limit on the fluence from GRB061222B is shown as a dashed green line, while the dotted green line is the limit that could have been set if the GRB had occurred in the ANITA f.o.v. (at RA 0◦, Dec -9◦) where there is maximal sensitivity. The red dashed line is the ANITA-I upper limit on an E−4 flux from GRB070103.The flux models and limits for GRB050603 [144], which was the lowest limit placed in the RICE study, GRB080319 [95], the naked-eye GRB, and the summed limit placed by IceCube upon 41 GRBs [233] are also plotted.

102 ×10−9 0.4 (E)

10 ν e 0.35 νµ ν dN/d log 0.3 τ

0.25

0.2

0.15

0.1

0.05

0 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 log (E / GeV) 10

Figure 5.25: The Monte Carlo detected events from the point source GRB061222B input, distinguished by flavor. The total number of events detected in the Monte Carlo was 2.34085 10−10. ×

103 ×10−12 (E)

10 ν 45 e ν 40 µ ν dN/d log τ 35

30

25

20

15

10

5

0 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 log (E / GeV) 10

Figure 5.26: The Monte Carlo detected events from the point source GRB070103 input, distinguished by flavor. The total number of events detected in the Monte Carlo was 1.13 10−11. ×

104 −4 ) 10 −1 WB diffuse flux sr −1 −5 ANITA−I E−4 Limit s 10 −2 ANITA−I E−2 Limit AMANDA E−2 Limit 10−6

10−7 dN/dE (Gev cm 2 −8 E 10

10−9

10−10

10−11 105 106 107 108 109 1010 1011 1012 Energy (GeV)

Figure 5.27: The WB diffuse GRB flux is plotted, along with the ANITA-I E−4 limit from this work, the ANITA-I E−2 limit from [203] and the AMANDA E−2 limit from [90].

105 target for the interaction of UHEνs where there is less anthropogenic noise than else- where on the planet. The field of neutrino astronomy hopes to soon make a discovery to propel itself forward, and neutrinos from gamma ray bursts are an attractive and soon reachable target. Even at ultra high energies where models predict a falling spectrum of E−4, ANITA-I has set a limit on the diffuse flux and the fluence from two individual GRBs. The orders of magnitude uncertainty in the GRB neutrino flux models and the variability in individual GRBs motivate a careful search for neutrinos coincident with any detected gamma ray burst. During the ANITA-I flight, no GRB was detected in the primary ANITA field of view. Nonetheless, ANITA improved upon RICE’s single GRB neutrino fluence limit by more than an order of magnitude.

Future flights may offer more serendipitous events, and more GRB events can now be detected since the Fermi Gamma-ray Space telescope is in operation. As limits upon diffuse and point neutrino sources improve, even without an identified astrophysical neutrino, we shall begin to learn about the most energetic acceleration mechanisms in the universe.

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118 Appendix A

IPN Localizations of ANITA-I Flight GRBs

The InterPlanetary Network collects the GRB detection information from mul- tiple spacecraft. Using the timing precisions and locations of each spacecraft, GRB locations can be determined through the intersections of multiple allowed regions. The KONUS error boxes include an ecliptic latitude band determined by compar- ing rates in the detectors pointed to the North and South Ecliptic Pole. The North Ecliptic Pole is located in celestial coordinates at RA 270◦ and Dec 66.5◦. Ecliptic latitude is denoted β and ecliptic longitude is λ while the right ascenscion may be denoted RA or by α and the declination by Dec or δ.

A.1 GRB061221

GRB061221 lies within an error box centered at RA 291.643866◦ and Dec - 51.765105◦ with its corners at 279.127143◦ and -61.134547circ, 297.034835◦ and - 39.600338◦, 278.804299◦ and -61.137365◦, and finally 296.873345◦ and -39.742784◦.It was actually viewed by four satelites and its position is overdetermined and true error ellipses could be calculated, but they were not provided by Kevin Hurley.

A.2 GRB061223

GRB061223 has two possible error boxes in the Northern Hemisphere sky: the first is determined by RA 249.599◦ and Dec 23.549◦, 233.892◦ and 27.469◦, 221.251◦ and 10.441◦, and 233.31◦ and 6.719◦ and the second box has corners at RA 329.651◦ and Dec 14.493◦, 315.551◦ and 30.737◦, 317.670◦ and 10.073◦ and 299.877◦ and 25.673◦.

A.3 GRB061224

GRB061224 lies in a small lens shaped region between the ecliptic latitude -43◦ and the circle centered at α = 97.372063◦δ = 18.106238◦ and a radius of 41.335022◦.

119 A.4 GRB061225

GRB061225 as only observed by KONUS, and is thus only restricted to an ecliptic latitude band from -66.1◦ to -41.1◦.

A.5 GRB061229

GRB061229 is restricted to lie in the intersection of an ecliptic latitude band and two annuli, the first is centered at α = 98.370899◦, δ = 18.172404◦ with an inner radius of 43.165911◦ and an outer radius of 47.118401◦, the second annulus is centered at α = 99.814757◦δ = 22.958030◦ with an inner radius of 41.055197◦ and an outer radius of 49.581793◦, and the band in ecliptic latitude from -3.5◦ to +16.5◦.

A.6 GRB061230

GRB061230 is another GRb detected by four satellites; it lies in the error box centered at RA 135.666441◦ and Dec -26.940220◦ with its corners at 132.160517◦ and -31.060750circ, 139.334993◦ and -22.030791◦, 131.995669◦ and -31.153652◦, and finally 139.167905◦ and -22.175621◦.

A.7 GRB070106

GRB070106 can only be localized to the ecliptic latitude band from from -3.8◦ to +16.2◦.

A.8 GRB070113

GRB070113 has a large error box within the ANITA fov which is defined by the intersection of two annuli: the first is centered at α = 102.298607◦δ = 18.588181◦ with inner and outer radii of 26.150247◦ and 31.823229◦, the second is centered at α = 102.744223◦δ = 23.093665◦ with inner and outer radii of 28.129152◦ and 33.297402◦.

A.9 GRB070115A

GRB070115A was not able to be localized as it was only detected by Swift, but was outside its fov.

120 A.10 GRB070115B

GRB070115B has error boxes at the intersection of the annulus centered at α = 103.117362◦, δ = 18.703553◦ with an inner radius of 33.582674◦ and an outer radius of 42.83148◦ and the KONUS ecliptic latitude band is -39.6◦ to -19.6◦.

A.11 GRB070116A

GRB07116A was only seen by one spacecraft and is probably a particle-induced event.

A.12 GRB070116B

GRB070116B has only one error box and it lies almost entirely in the ANITA fov. This box is defined by the intersection of two grazing annuli, the first centered at α = 104.259406◦δ = 23.483965◦ with inner and outer radii of 54.805881◦ and 57.888583◦, the second annulus is centered at α = 103.501777◦δ = 18.767381◦ with inner and outer radii of 56.939249◦ and 60.051369◦ and the ecliptic latitude band from -2.7◦ to -22.7◦, yet it cannot be in the area occulted by the Earth, which is an area with radius 66◦ centered at α = 64.4◦δ = 16.4◦.

A.13 GRB070116C

GRB070116C is an unusual event. It cannot be localized becauase the observing spacecraft were all in a low Earth orbit, but the event was very short with a soft spectrum suggesting a soft gamma repeater (SGR) burst.

A.14 GRB070117

GRB070117 can only be localized to the ecliptic latitude band from from +2◦ to +22◦.

121