Search for Ultra High-Energy Neutrinos with AMANDA-II
aa r X i v : . [ a s t r o - ph ] N ov Search for Ultra High-Energy Neutrinos with AMANDA-II
IceCube Collaboration: M. Ackermann , J. Adams , J. Ahrens , K. Andeen ,J. Auffenberg , X. Bai , B. Baret , S. W. Barwick , R. Bay , K. Beattie , T. Becka ,J. K. Becker , K.-H. Becker , M. Beimforde , P. Berghaus , D. Berley , E. Bernardini ,D. Bertrand , D. Z. Besson , E. Blaufuss , D. J. Boersma , C. Bohm , J. Bolmont ,S. B¨oser , O. Botner , A. Bouchta , J. Braun , T. Burgess , T. Castermans ,D. Chirkin , B. Christy , J. Clem , D. F. Cowen , , M. V. D’Agostino , A. Davour ,C. T. Day , C. De Clercq , L. Demir¨ors , F. Descamps , P. Desiati ,G. de Vries-Uiterweerd , T. DeYoung , J. C. Diaz-Velez , J. Dreyer , J. P. Dumm ,M. R. Duvoort , W. R. Edwards , R. Ehrlich , J. Eisch , R. W. Ellsworth ,P. A. Evenson , O. Fadiran , A. R. Fazely , K. Filimonov , C. Finley , M. M. Foerster ,B. D. Fox , A. Franckowiak , R. Franke , T. K. Gaisser , J. Gallagher ,R. Ganugapati , H. Geenen , L. Gerhardt , ∗ , A. Goldschmidt , J. A. Goodman ,R. Gozzini , T. Griesel , A. Groß , S. Grullon , R. M. Gunasingha , M. Gurtner ,C. Ha , A. Hallgren , F. Halzen , K. Han , K. Hanson , D. Hardtke , R. Hardtke ,Y. Hasegawa , T. Hauschildt , J. Heise , K. Helbing , M. Hellwig , P. Herquet ,G. C. Hill , J. Hodges , K. D. Hoffman , B. Hommez , K. Hoshina , D. Hubert ,B. Hughey , J.-P. H¨ulß , P. O. Hulth , K. Hultqvist , S. Hundertmark , M. Inaba ,A. Ishihara , J. Jacobsen , G. S. Japaridze , H. Johansson , J. M. Joseph ,K.-H. Kampert , A. Kappes ,a , T. Karg , A. Karle , H. Kawai , J. L. Kelley ,J. Kiryluk , F. Kislat , N. Kitamura , S. R. Klein , S. Klepser , G. Kohnen ,H. Kolanoski , L. K¨opke , M. Kowalski , T. Kowarik , M. Krasberg , K. Kuehn ,T. Kuwabara , M. Labare , K. Laihem , H. Landsman , R. Lauer , H. Leich ,D. Leier , I. Liubarsky , J. Lundberg , J. L¨unemann , J. Madsen , R. Maruyama ,K. Mase , H. S. Matis , T. McCauley , C. P. McParland , K. Meagher , A. Meli ,T. Messarius , P. M´esz´aros , , H. Miyamoto , T. Montaruli ,b , A. Morey , R. Morse ,S. M. Movit , K. M¨unich , R. Nahnhauer , J. W. Nam , P. Nießen , D. R. Nygren ,A. Olivas , M. Ono , S. Patton , C. P´erez de los Heros , A. Piegsa , D. Pieloth ,A. C. Pohl ,c , R. Porrata , J. Pretz , P. B. Price , G. T. Przybylski , K. Rawlins ,S. Razzaque , , P. Redl , E. Resconi , W. Rhode , M. Ribordy , A. Rizzo ,S. Robbins , W. J. Robbins , P. Roth , F. Rothmaier , C. Rott , C. Roucelle ,D. Rutledge , D. Ryckbosch , H.-G. Sander , S. Sarkar , K. Satalecka ,S. Schlenstedt , T. Schmidt , D. Schneider , O. Schultz , D. Seckel , B. Semburg ,S. H. Seo , Y. Sestayo , S. Seunarine , A. Silvestri , A. J. Smith , C. Song ,G. M. Spiczak , C. Spiering , M. Stamatikos ,d , T. Stanev , T. Stezelberger ,R. G. Stokstad , M. C. Stoufer , S. Stoyanov , E. A. Strahler , T. Straszheim ,K.-H. Sulanke , G. W. Sullivan , T. J. Sumner , Q. Swillens , I. Taboada , 2 –O. Tarasova , A. Tepe , L. Thollander , S. Tilav , M. Tluczykont , P. A. Toale ,D. Tosi , D. Turˇcan , N. van Eijndhoven , J. Vandenbroucke , A. Van Overloop ,V. Viscomi , C. Vogt , B. Voigt , W. Wagner , C. Walck , H. Waldmann ,T. Waldenmaier , M. Walter , Y.-R. Wang , C. Wendt , C. H. Wiebusch ,C. Wiedemann , G. Wikstr¨om , D. R. Williams , R. Wischnewski , H. Wissing ,K. Woschnagg , X. W. Xu , G. Yodh , S. Yoshida , J. D. Zornoza ,e * Corresponding author: [email protected] III Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK99508, USA CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA Dept. of Physics, University of California, Berkeley, CA 94720, USA Institut f¨ur Physik, Humboldt-Universit¨at zu Berlin, D-12489 Berlin, Germany Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Universit´e Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium Dept. of Physics, Chiba University, Chiba 263-8522 Japan Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Dept. of Physics, University of Maryland, College Park, MD 20742, USA Dept. of Physics, Universit¨at Dortmund, D-44221 Dortmund, Germany Dept. of Subatomic and Radiation Physics, University of Gent, B-9000 Gent, Belgium Max-Planck-Institut f¨ur Kernphysik, D-69177 Heidelberg, Germany Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA Laboratory for High Energy Physics, ´Ecole Polytechnique F´ed´erale, CH-1015 Lausanne, Switzerland Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA Blackett Laboratory, Imperial College, London SW7 2BW, UK Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA Dept. of Physics, University of Wisconsin, Madison, WI 53706, USA Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany University of Mons-Hainaut, 7000 Mons, Belgium Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark,DE 19716, USA Dept. of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA
ABSTRACT
A search for diffuse neutrinos with energies in excess of 10 GeV is conductedwith AMANDA-II data recorded between 2000 and 2002. Above 10 GeV, theEarth is essentially opaque to neutrinos. This fact, combined with the limitedoverburden of the AMANDA-II detector (roughly 1.5 km), concentrates theseultra high-energy neutrinos at the horizon. The primary background for thisanalysis is bundles of downgoing, high-energy muons from the interaction of cos-mic rays in the atmosphere. No statistically significant excess above the expectedbackground is seen in the data, and an upper limit is set on the diffuse all-flavorneutrino flux of E Φ < × − GeV cm − s − sr − valid over the energyrange of 2 × GeV to 10 GeV. A number of models which predict neutrinofluxes from active galactic nuclei are excluded at the 90% confidence level.
Subject headings: neutrino telescope, AMANDA, IceCube, diffuse sources, ultrahigh-energy
1. Introduction
AMANDA-II (Antarctic Muon and Neutrino Detector Array), a neutrino telescopeat the geographical South Pole designed to detect Cherenkov light from secondary parti-cles produced in collisions between neutrinos and Antarctic ice, has placed limits on theflux from point-like and diffuse sources of astrophysical neutrinos (Achterberg et al. 2007; Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA Division of High Energy Physics, Uppsala University, S-75121 Uppsala, Sweden Dept. of Physics and Astronomy, Utrecht University/SRON, NL-3584 CC Utrecht, The Netherlands Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany DESY, D-15735 Zeuthen, Germany a on leave of absence from Universit¨at Erlangen-N¨urnberg, Physikalisches Institut, D-91058, Erlangen,Germany b on leave of absence from Universit`a di Bari, Dipartimento di Fisica, I-70126, Bari, Italy c affiliated with School of Pure and Applied Natural Sciences, Kalmar University, S-39182 Kalmar, Sweden d NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA e affiliated with IFIC (CSIC-Universitat de Val`encia), A. C. 22085, 46071 Valencia, Spain GeV, which we define as ultra high-energy (UHE) neutri-nos. These neutrinos are of interest because they could be associated with the potentialacceleration of hadrons by active galactic nuclei (Mannheim 1995; Mannheim et al. 2000;Halzen & Zas 1997; Protheroe 1996; Stecker et al. 1992); they could potentially be producedby exotic phenomena such as the decay of topological defects (Sigl et al. 1998) or possi-bly associated with the Z-burst mechanism (Yoshida et al. 1998); and they are guaranteedby-products of the interactions of high-energy cosmic rays with the cosmic microwave back-ground (Engel et al. 2001).This analysis is sensitive to all three flavors of neutrinos. Leptons and cascades fromUHE electron, muon and tau neutrinos create bright, energetic events (Fig. 1) which canbe identified by AMANDA-II as far as 450 m from the center of the array (Fig. 2). Thesensitivity of this analysis starts at energies roughly coincident with the highest energythreshold of other diffuse analyses conducted with AMANDA-II (Achterberg et al. 2007;Ackermann et al. 2004).At UHE energies, the interaction length of neutrinos in rock is shorter than the diameterof the Earth (Gandhi et al. 1998), so neutrinos from the Northern Hemisphere will interactbefore reaching AMANDA-II. Combined with the limited overburden above the AMANDA-II detector, this concentrates UHE events at the horizon. This contrasts with the majority ofother astrophysical neutrino analyses completed using data from the AMANDA-II detector,which search for neutrinos from the Northern Hemisphere with energies below 10 GeV.The flux of atmospheric neutrinos is negligible at UHE energies, with fewer than 10events in three years expected from the model in Lipari (1993) after intermediate UHE se-lection criteria have been applied. This drops to 0.1 events after application of all selectioncriteria. Similarly, there are fewer than 0.6 events expected in three years at the final se-lection level from prompt neutrinos from the decay of charmed particles produced in theatmosphere (using the “C” model from Zas et al. (1993)). Therefore, the primary back-ground for the UHE analysis is composed of many lower energy processes that mimic higherenergy signal events. Cosmic ray collisions in the upper atmosphere that generate largenumbers of nearly parallel muons (or “muon bundles”) can generate high-energy signatureseven though the individual muons have much lower energy than single leptons or cascadesfrom UHE neutrinos. Signal and background events spread light over roughly equivalentareas in the detector, but UHE neutrino events are distinguishable because they have higherenergy and higher light density than background events. Specialized selection criteria whichuse these properties, as well as differences in reconstruction variables, separate the UHEneutrinos from the background of muon bundles from atmospheric cosmic rays. 6 –Limits have been placed on the all-flavor neutrino flux in the ultra high-energy rangeby other experiments (Fig. 3). Additionally, a previous analysis using an earlier configu-ration of the AMANDA detector called AMANDA-B10, consisting of 302 optical modules(Ackermann et al. 2005), has placed limits on the all-flavor UHE neutrino flux (Fig. 3). Thisanalysis uses 677 optical modules (OMs) of the AMANDA-II detector and gives a combinedresult using data from three years (2000-2002) with a livetime of 456.8 days.A description of the AMANDA-II detector is given in section 2. Sections 3 and 4 discusspossible sources of astrophysical neutrinos and background, and the simulation of both. Theselection criteria used to separate UHE neutrino signals from background are discussed insection 5. A study of systematic uncertainties is presented in section 6, and the results areshown in section 7.
2. The AMANDA-II Detector
The AMANDA-II detector (Ahrens et al. 2004a) consists of 677 OMs stationed between1500 m and 2000 m beneath the surface of the Antarctic ice at the geographic South Pole.The OMs are deployed on nineteen vertical cables (called “strings”) arranged in three roughlyconcentric circles, giving the detector a cylindrical shape with a diameter of approximately200 m.Each OM contains a Hamamatsu 8-inch photomultiplier tube (PMT) coupled with sil-icon gel to a spherical glass pressure housing for continuity of the index of refraction. TheOMs are connected to the surface by cables which supply high voltage and carry the sig-nal from the PMT to data acquisition electronics at the surface. The inner ten strings useelectrical analog signal transmission, while the outer nine strings primarily use optical fibertransmission (Ahrens et al. 2004a).The AMANDA-II detector uses a majority trigger of 24 OMs recording a voltage abovea set threshold (a “hit”) within a time window of 2.5 µ s. An OM records the maximumamplitude, as well as the leading edge time and time over threshold for each hit, with eachOM recording a maximum of eight hits per event. Each photoelectron has approximately a3% chance of producing an afterpulse caused by ionization of residual gas inside the PMT(Hamamatsu 1999). This afterpulse follows several µ s after the generating hit and aids inthe detection of UHE events.AMANDA-II has been collecting data since February 2000. In 2002/2003, waveformdigitizers were installed which record the full pulse shape from each OM (Silvestri 2005).In 2005 deployment began on IceCube (Ahrens et al. 2004b), a 1 km array of digital OMs 7 –which now encompasses the AMANDA-II detector.
3. Astrophysical Neutrino and Background Sources
Astrophysical neutrinos with energies in excess of 10 GeV may be produced by avariety of sources. A number of theories predict neutrino fluxes from active galactic nuclei(AGN) peaking near 10 GeV. In these scenarios, protons are accelerated by the first orderFermi mechanism in shock fronts. In the favored mechanism for neutrino production, theseprotons interact with the ambient photon field either in the cores (Stecker et al. 1992) or jets(Protheroe 1996; Halzen & Zas 1997; Mannheim et al. 2000; Mannheim 1995) of the AGNand produce neutrinos via the process: p + γ → ∆ + → π + [+ n ] → ν µ + µ + → ν µ + e + + ν e + ν µ , (1)resulting in a ν e : ν µ : ν τ flavor ratio of 1:2:0 at the source . The energy spectrum of theneutrinos produced by these interactions generally follows the E − spectrum of the protons.Theoretical bounds can be placed on the flux of these neutrinos based on the observationof cosmic rays if the p- γ reaction takes place in the jet or other optically thin region of theAGN (Bahcall & Waxman 1998; Mannheim et al. 2000).UHE neutrinos are also associated with models created to explain the apparent excessof cosmic rays at the highest energies. One scenario involves the decay of massive objects,such as topological defects created by symmetry breaking in the early universe (Sigl et al.1998). These objects decay close to the Earth into showers of particles, eventually producingneutrinos as well as a fraction of the highest-energy cosmic rays. Z-burst models couldalso produce some of the highest-energy cosmic rays through the interaction of neutrinoswith energies in excess of 10 GeV with relic neutrinos via the Z resonance. Since theseneutrino-neutrino interactions are rare, it is possible to directly search for the UHE neutrinofluxes required by this mechanism (Yoshida et al. 1998; Kalashev et al. 2002a). It should benoted that Z-burst scenarios which predict the highest flux of neutrinos have already beeneliminated by previous experiments (Barwick et al. 2006). Additionally, Z-burst modelspredict fluxes of neutrinos which peak at energies above the sensitivity of this analysis orrequire unrealistic assumptions and are mentioned primarily for completeness.A guaranteed source of UHE neutrinos comes from the interaction of high-energy cosmicrays with the cosmic microwave background (see e.g. Engel et al. (2001) and Kalashev et al. Neutrino flavor oscillation changes the flavor ratio to 1:1:1 at the Earth. See Kashti & Waxman (2005)for a discussion of different flavor ratios. − . spectrum until about 10 GeV, where the flux steepens to E − (H¨orandel 2003). They come only from the Southern Hemisphere because bundles from otherdirections are absorbed by the Earth. According to simulations, there can be as many as20,000 muons in one bundle spread over a rms cross-sectional area as large as 200 m , andthe highest-energy events can deposit energies as large as 2.4 × GeV in the ice aroundthe AMANDA-II detector.
4. Simulation and Experimental Data
UHE neutrinos are simulated using the All Neutrino Interaction Simulation (ANIS)package (Kowalski & Gazizov 2005) to generate and propagate the neutrinos through theEarth. All three flavors of neutrinos are simulated with energies between 10 GeV and10 GeV. The resulting muons and taus are propagated through the rock and ice nearthe detector using the Muon Monte Carlo (MMC) simulation package (Chirkin & Rhode2004). Finally, the detector response is simulated using the AMASIM2 simulation package(Hundertmark 1998).The background muon bundles from cosmic rays are generated using the CORSIKAsimulation program with the QGSJET01 hadronic interaction model (Heck 1999). At earlylevels of this analysis, cosmic ray primaries are generated with composition and spectralindices from Wiebel-Sooth et al. (1999), with energies of the primary particles ranging be-tween 8 × GeV and 10 GeV. At later levels of this analysis, the lower energy primarieshave been removed by the selection criteria, and a new simulated data set is used with en-ergy, spectral shape, and composition optimized to simulate high-energy cosmic rays moreefficiently. In this optimized simulation, the energy threshold is raised to 8 × GeV andonly proton and iron primaries are generated with a spectrum of E − . These primaries arereweighted following the method outlined in Glasstetter et al. (1999). This optimized simu-lation is used for level 2 of the analysis and beyond (see Table 1). For 2001 and 2002, thebackground simulation is further supplemented with the inclusion of a third set of simulateddata with the energy threshold increased to 10 GeV. For all sets of background simulation,the resulting particles are propagated through the ice using MMC, and the detector responseis simulated using AMASIM2.Data used in this analysis were recorded in the time period between February 2000 and 9 –November 2002, with breaks each austral summer for detector maintenance, engineering,and calibration lasting approximately four months. In addition to maintenance downtime,the detector also has a brief period while recording each event in which it cannot recordnew events. Runs with anomalous characteristics (such as excessive trigger rates or largenumbers of OMs not functioning) are discarded and a method which removes non-physicalevents caused by short term detector instabilities is applied (Pohl 2004). These factorscombine to give a deadtime of 17% of the data taking time for 2000, 22% of the data-takingtime for 2001, and 15% of the data taking time for 2002. Additionally, 26 days are excludedfrom 2000 because the UHE filtered events are polluted with high number of events withincomplete hit information, likely due to a minor detector malfunction. Taking these factorsinto account, there are 173.5 days of livetime in 2000, 192.5 days of livetime in 2001, and205.0 days of livetime in 2002. Finally, 20% of the data from each year is set aside forcomparison with simulations and to aid in the determination of selection criteria, leading toa total livetime for the three years of 456.8 days.
5. Analysis
Twenty percent of the data from 2000 to 2002 (randomly selected from throughout thethree years) is used to test the agreement between background simulations and observations.In order to avoid biasing the determination of selection criteria, this 20% is then discarded,and the developed selection criteria are applied to the remaining 80% of the data. A previousUHE analysis was performed on only the 2000 data using different selection criteria thanthose described below (see Gerhardt (2005) and Gerhardt (2007) for a more detailed descrip-tion). For 2001-2002, improved reconstruction techniques such as cascade reconstructions(Ahrens et al. 2003c) were added to the analysis, and the new selection criteria describedbelow were devised in a blind manner. These selection criteria were also applied to the 2000data to derive a combined three year limit. Due to differences in hit selection for reconstruc-tion between 2000 and 2001-2002, the E − signal passing rate at the final selection level forthe year 2000 is approximately 60% of the rate for the years 2001 and 2002.In order to maximize the limit setting potential, the selection criteria are initially de-termined by optimizing the model rejection factor (Hill & Rawlins 2003) given byMRF = ¯ µ N signal , (2)where ¯ µ is 90% confidence level (CL) average event upper limit given by Feldman & Cousins(1998), and N signal is the number of muon neutrinos expected for the signal being tested, inthis case an E − flux. The selection criteria for this analysis are summarized in Table 1 and 10 –described below.This analysis exploits the differences in total energy and light deposition between bun-dles of many low-energy muons and single UHE muons or cascades from UHE neutrinos.UHE neutrinos deposit equal or greater amounts of light in the ice than background muonbundles. In addition to being lower energy, background muon bundles spread their lightover the cross sectional area of the entire muon bundle, rather than just along a single muontrack or into a single cascade. Both signal and background events can have a large numberof hits in the array, but for the same number of hit OMs, the muon bundle has a lower totalnumber of hits, NHITS (recall each OM may have multiple separate hits in one event; seeFig. 4). The number of hits for UHE neutrinos is increased by the tendency of bright signalsto produce afterpulses in the PMT. Background muon bundles also have a higher fraction ofOMs with a single hit (F1H), while a UHE neutrino generates more multiple hits (Fig. 5).The F1H variable is correlated with energy (Fig. 6) and is effective at removing lower energybackground muon bundle events. The level 1 and 2 selection criteria require that NHITS >
140 and F1H < × relative to triggerlevel (level 0 on Tables 2 and 3).At this point the data sample is sufficiently reduced that computationally intensivereconstructions become feasible. Reconstruction algorithms used in this analysis employa maximum likelihood method which takes into account the absorption and scattering oflight in ice. For muons, the reconstruction compares time residuals to those expected from aCherenkov cone for a minimally ionizing muon (Ahrens et al. 2004a), while the cascade recon-struction uses Cherenkov light from an electromagnetic cascade for comparison (Ahrens et al.2003c). Reconstructions which are optimized for spherical (cascade) depositions of light areused to distinguish UHE neutrinos from background muon bundles which happen to have alarge energy deposition, such as a bremsstrahlung or e + e − pair creation, inside the detectorfiducial volume.Before application of the level 3 selection criteria, the data sets are split into “cascade-like” and “muon-like” subsets. This selection is performed using the negative log likelihoodof the cascade reconstruction (L casc , see Fig. 7), where events with a L casc < Background events in the “cascade-like” subset are characterized by either a large lightdeposition in or very near the instrumented volume of AMANDA-II or a path which clips 11 –the top or bottom of the array. In either case, the energy deposition is significantly lessthan the energy deposited by a UHE neutrino, allowing application of selection criteriawhich correlate with energy. One of these is F1H
ELEC (Fig. 8), a variable similar to theF1H variable described above, except that it uses only OMs whose signal is brought to thesurface by electrical cables. The signal spreads as it propagates up the cable, causing hitsclose together in time to be combined. This gives F1H
ELEC a different distribution fromF1H, and both variables are good estimators of energy deposited inside the detector (Fig.6). Additionally, the fraction of OMs with exactly four hits (F4H) is another useful energyindicator. The value of four hits was chosen as a compromise between the number of hitsexpected from OMs with electrical cables and OMs with optical fibers. OMs with opticalfibers typically have more hits than OMs with electrical cables because very little pulsespreading occurs as the signal propagates up the fiber. The level 3 selection criteria uses theoutput of a neural net with F1H
ELEC , F4H, and F1H as input variables (Fig. 9). As selectionlevels 4 and 5, separate applications of the F4H and F1H
ELEC variables remove persistentlower energy background events.The remaining background muon bundles have a different hit distribution than UHEneutrinos. In the background muon bundles, a large light deposition can be washed outby the continuous, dimmer light deposition from hundreds to tens of thousands of muonstracks. In contrast, UHE muons can have one light deposition that is several orders ofmagnitude brighter than the light from the rest of the muon track and looks very similarto bright cascades from UHE electron and tau neutrinos. For all cases, the initial cascadereconstruction is generally concentric with this large energy deposition, so ignoring OMsthat are within 60 m of the initial cascade reconstruction reduces the fraction of OMs thatare triggered with photons from the cascade. For background, the remaining light will bedominated by light depositions from the tracks of the muon bundles and be less likely toreconstruct as a cascade. In contrast, signal events, with their energetic cascades, will stillappear cascade-like and reconstruct with a better likelihood (L ). The final selection criteriafor “cascade-like” events (chosen by optimizing the MRF) requires that these events be wellreconstructed by a cascade reconstruction performed using only OMs with distances greaterthan 60 m and reduces the background expectation to 0 events for this subset.The number of events at each selection level for experiment, background, and signalsimulation for the “cascade-like” subset are shown in Table 2. 12 – Background events in the “muon-like” subset are characterized by more uniform, track-like light deposition and are more easily reconstructed by existing reconstruction algorithmsthan “cascade-like” events. A reconstruction algorithm based on parameterization of timeresiduals from simulated muon bundles is used to reconstruct the zenith angle of the events(Fig. 10). Since most background muon bundles will come from a downgoing direction, whileUHE neutrinos will come primarily from the horizontal direction (Klein & Mann 1999),requiring that the zenith angle > ◦ (where a zenith angle of 90 ◦ is horizontal) reducesthe background by a factor of 30. The remaining background in the “muon-like” subsetare misreconstructed events, since the actual flux close to the horizon is very small. Areconstruction based on the hit pattern of a Cherenkov cone for a minimally ionizing muonis applied to these events (Ahrens et al. 2004a). Selecting only well-reconstructed eventsusing the likelihood of this reconstruction (L muon ) is sufficient to remove all backgroundevents in this subset. The value of this selection criteria was initially chosen to optimizethe MRF for muon neutrinos with an E − spectrum. However, by increasing the selectionvalue slightly beyond the value which gave the minimum MRF, all background events wererejected with only a few percent drop in the sensitivity (Fig. 11). Since the uncertainty inthe cosmic ray spectrum is very large at these energies, the more stringent selection criterionwas applied to correct for the fact that the MRF is optimized without uncertainties.The number of events at each selection level for experiment, background, and signalsimulation for the “muon-like” subset are shown in Table 3.
6. Statistical and Systematic Uncertainties
Because there is no test beam which can be used to determine the absolute sensitivityof the AMANDA-II detector, calculations of sensitivity rely on simulation. The dominantsources of statistical and systematic uncertainty in this calculation are described below.The systematic uncertainties are assumed to have a flat distribution and are summed inquadrature separately for background and signal. The uncertainties have been included intothe final limit using the method described in Tegenfeldt & Conrad (2005).
Due to computational requirements, background simulation statistics are somewhat lim-ited. Ideally, one would scale the statistical uncertainty on zero events based on the simula- 13 –tion event weights in nearby non-zero bins. However, the optimized background simulationsused in this analysis have large variations in event weights approaching this region, makingdetermination of this factor difficult. Nevertheless, the statistical uncertainties near the edgeof the distribution are on the order of the uncertainties for a simulation with a livetime equiv-alent to the data taking period, so no scaling factor is applied to the statistical uncertainty.A statistical uncertainty of 1.29, the 1 σ Feldman-Cousins event upper limit on zero observedevents (Feldman & Cousins 1998), is assumed at the final selection level. Signal simulationhas an average statistical uncertainty of 5% for each neutrino flavor.
The average energy of cosmic ray primaries at the penultimate selection level is 4.4 × GeV, which is considerably above the knee in the all-particle cosmic ray spectrum.Numerous experiments have measured a large spread in the absolute normalization of theflux of cosmic rays at this energy (see Kampert (2007) for a recent review). Estimates ofthe uncertainty in the normalization of the cosmic ray flux range from 20% (H¨orandel 2003)to a factor of two (Particle Data Group 2006). This analysis uses the more conservativeuncertainty of a factor of two.
There is considerable uncertainty in the cosmic ray composition above the knee (Particle Data Group2006). We estimate the systematic uncertainty by considering two cases: proton-dominatedcomposition and iron-dominated composition. The simulated background cosmic ray fluxis approximated by separately treating proton and iron primaries combined in a total spec-trum that becomes effectively iron-dominated above 10 GeV using the method describedin Glasstetter et al. (1999). The iron-dominated spectrum yields a 30% higher backgroundevent rate than the rate from a proton-dominated spectrum at the penultimate selectionlevel. This value of 30% is used as the uncertainty due to the cosmic ray composition.
The properties of the refrozen ice around each OM, the absolute sensitivity of individualOMs, and obscuration of OMs by nearby power cables can effect the detector sensitivity.This analysis uses the value obtained in Ahrens et al. (2003a) where reasonable variations 14 –of these parameters in the simulation were found to cause a 15% variation in the E − signaland background passing rate. As photons travel through the ice they are scattered and absorbed. The absorptionand scattering lengths of the ice around the AMANDA-II detector have been measured veryaccurately using in situ light sources (Ackermann et al. 2006). Uncertainties are introduceddue to the limited precision with which these parameters are included in the simulation.Varying the scattering and absorption lengths in the detector simulation by 10% were foundto cause a difference in number of expected signal events (for an E − spectrum) of 34%(Ackermann et al. 2005), which is used as a conservative estimate of the uncertainty dueto implementation of ice properties. If too large of a deviation in background rate relativeto the experimental rate was observed for a set of ice property parameters, the backgroundrate was normalized to the experimental rate, and the signal rate was scaled accordingly.This was done to ensure that the variation in absorption and scattering lengths covered areasonable range of ice properties. The uncertainty in the standard model neutrino cross section has been quantified re-cently (Anchordoqui et al. 2006) taking into account the experimental uncertainties on theparton distribution functions measured at HERA (Chekanov et al. 2005), as well as theo-retical uncertainties in the effect of heavy quark masses on the parton distribution functionevolution and on the calculation of the structure functions. The corresponding maximumvariation in the number of expected signal events (for an E − spectrum) is 10%, in agreementwith previous estimates (Ackermann et al. 2005).Screening effects are expected to suppress the neutrino-nucleon cross section at energiesin excess of 10 GeV (see e.g. Kutak & Kwieci`nski (2003); Berger et al. (2007)). This hasa negligible effect on the number of signal events expected for an E − spectrum becausethe majority of signal is found below these energies (Fig. 12). Even if the suppression isas extreme as in the Colour Glass Condensate model (Henley & Jalilian-Marian 2005), theevent rate decreases by only 11%. 15 – An examination of the L muon distribution for the “muon-like” subset after level 3 of thisanalysis suggests the background simulation is shifted by one bin relative to the experiment(Fig. 13). Shifting all simulation distributions to the left by one bin leads to better agreementbetween the background simulation and experimental distributions and an increase in 8% inthe number of expected signal events for an E − spectrum. At ultra high-energies, the LPM effect suppresses the bremsstrahlung cross section forelectrons and the pair-production cross section of photons created in a cascade by an electronneutrino (Landau & Pomeranchuk 1953; Migdal 1957). This lengthens the resultant showerproduced by a factor that goes as √ E . Above 10 GeV, the extended shower length becomescomparable to the spacing between OMs on a string (Klein 2004). Additionally, as the LPMeffect suppresses the bremsstrahlung and pair productions cross sections, photonuclear andelectronuclear interactions begin to dominate which lead to the production of muons insidethe electromagnetic cascade. Toy simulations were performed which superimposed a muonwith an energy of 10 GeV onto a cascade with energy of 10 GeV. While the addition ofthe muon shifted the L casc distribution 5% towards higher (more “muon-like”) values, theresulting events still passed all selection criteria indicating that the effects of muons createdinside cascades are negligible.The LPM effect is not included in the simulations of electron neutrinos, but it can beapproximated by excluding all electron neutrinos with energies in excess of 10 GeV. Thisis an overestimation of the uncertainty introduced by the LPM effect, as extended showersmay manifest as several separate showers which are likely to survive all selection criteriaand the addition of low-energy muons is not expected to significantly alter the UHE cascadelight deposition. Neglecting electron neutrinos with energies in excess of 10 GeV reducesthe number of expected signal events by 2% for an E − spectrum. The systematic errors are shown in Table 4. Summing the systematic errors of the signalsimulation in quadrature gives a systematic uncertainty of ±
7. Results
After applying all selection criteria, no background events are expected for 456.8 days.Incorporating the statistical and systematic uncertainties, the background is expected tobe found with a uniform prior probability between 0 and 2.6 events. A possible sensitivitycalculation which incorporates these uncertainties can be generated by assuming a flat priorwith a mean of 1.3 events and a corresponding data expectation of 1 event. This gives a90% CL event upper limit of 3.5 (Tegenfeldt & Conrad 2005) and a sensitivity of 1.8 × − GeV cm − s − sr − , with the central 90% of the E − signal found in the energy range 2 × GeV to 10 GeV. Table 5 shows the expected number of each flavor of UHE neutrinopassing the final selection level for a 10 − × E − flux. The energy spectra of each flavor areshown in Fig. 12.Two events are observed in the data sample at the final selection level (Fig. 13), whilefewer than 2.6 background events are expected which gives a 90% CL average event upperlimit of 5.3. After applying all selection criteria, 20 events are expected for a 10 − × E − all flavor flux (Table 5). The upper limit on the all-flavor neutrino flux (assuming a 1:1:1 ν e : ν µ : ν τ flavor ratio) isE Φ ≤ . × − GeV cm − s − sr − , (3)including systematic uncertainties, with the central 90% of the E − signal found between theenergies of 2 × GeV and 10 GeV.A number of theories which predict fluxes with non-E − spectral shapes (Fig. 3) werealso tested by reweighting the simulated signal. These include the hidden-core AGN modelof Stecker et al. (1992) which has been updated to reflect a better understanding of AGNemission (Stecker 2005), as well as AGN models in which neutrinos are accelerated in op-tically thin regions (Protheroe 1996; Halzen & Zas 1997; Mannheim 1995; Mannheim et al.2000). Including uncertainties, this analysis restricts at a 90% CL the AGN models fromHalzen & Zas (1997) and Mannheim et al. (2000). Also the previously rejected (Ackermann et al.2005) models from Protheroe (1996) and Stecker et al. (1992) are rejected at the 90% CLby this analysis (see Fig. 14 and Table 6). The model by Stecker et al. (1992) builds on acorrelation between X-rays and neutrinos from AGNs. Other models using the same corre-lation give a similar normalization and violate current limits by an order of magnitude as 17 –well. As previously pointed out by Becker et al. (2007), such a correlation can be excluded.While we do not directly exclude the flux from the Stecker (2005) hidden-core AGNmodel, it is possible to set limits on the parameters used in the model. In this model, theflux of neutrinos is normalized to the extragalactic MeV photon flux measured by COMPTELwith the assumption that the flux of photons from Seyfert galaxies is responsible for 10%of this MeV background. If the neutrino flux scales linearly with the photon flux, then themaximum contribution of hidden-core AGNs, such as Seyfert galaxies, to the extragalacticMeV photon flux must be less than 29%.Fluxes of neutrinos from the decay of topological defects (Sigl et al. 1998) and the UHEfluxes required for the Z-bursts mechanism (Yoshida et al. 1998; Kalashev et al. 2002a) peakat too high of an energy to be detected by this analysis. Neutrinos from the interaction ofcosmic rays with cosmic microwave background photons are produced at too low of a fluxfor this analysis to detect (see Table 6).The number of expected events of a given flavor ( ν and ν ) for spectra not tested in thispaper can be calculated using the formula N signal = T Z dE ν d ΩΦ ν ( E ν ) A ν eff ( E ν ) , (4)where T is the total livetime (456.8 days), A ν eff is the angle averaged neutrino effective area(Fig. 15), and Φ ν is the flux at the Earth’s surface.
8. Conclusion
The diffuse neutrino flux limit for a 1:1:1 ν e : ν µ : ν τ flavor ratio set by this analysis ofE Φ ≤ . × − GeV cm − s − sr − , (5)is the most stringent to date above 10 GeV. A number of models for neutrino productionhave been rejected (see Table 6 for a full list). AMANDA-II hardware upgrades which werecompleted in 2003 should lead to an improvement of the sensitivity at ultra high-energies(Silvestri 2005). Additionally, AMANDA-II is now surrounded by the next-generation Ice-Cube detector which is currently under construction. The sensitivity to UHE muon neutrinosfor 1 year is expected to increase by roughly an order of magnitude as the IceCube detectorapproaches its final size of 1 km (Ahrens et al. 2004b).We acknowledge the support from the following agencies: National Science Foundation-Office of Polar Program; National Science Foundation-Physics Division; University of Wis- 18 –consin Alumni Research Foundation; Department of Energy, and National Energy ResearchScientific Computing Center (supported by the Office of Energy Research of the Depart-ment of Energy); the NSF-supported TeraGrid system at the San Diego SupercomputerCenter (SDSC); the National Center for Supercomputing Applications (NCSA); SwedishResearch Council; Swedish Polar Research Secretariat; Knut and Alice Wallenberg Founda-tion, Sweden; German Ministry for Education and Research; Deutsche Forschungsgemein-schaft (DFG), Germany; Fund for Scientific Research (FNRS-FWO); Flanders Institute toencourage scientific and technological research in industry (IWT); Belgian Federal Office forScientific, Technical and Cultural affairs (OSTC); the Netherlands Organisation for Scien-tific Research (NWO); M. Ribordy acknowledges the support of the SNF (Switzerland); A.Kappes and J. D. Zornoza acknowledges the Marie Curie OIF Program; L. Gerhardt ac-knowledges the support of the University of California, Irvine MPC Computational Clusterand Achievement Rewards for College Scientists (ARCS). REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
21 –Table 1: Selection criteria.Level Selection Criteria0 Hit Cleaning and Retriggering1 F1H < > < casc < casc ≥ > >
854 F4H < muon < ELEC < < × +1 . − . × × +3 . − . × × +1 . − . × +63 − +62 − +32 − +2 . Note. — Levels 0 and 1 show combined numbers for both “muon-like” and “cascade-like” subsets.Signal is shown with a low energy threshold of 10 GeV for a neutrino spectrum of dN/dE = 10 − × E − GeV − cm − s − sr − , with an assumed 1:1:1 ν e : ν µ : ν τ flavor ratio. Values at selection level 0 and1 for data and background simulation are extrapolated from the 2000 datasets. The background simulationis shown with systematic and statistical uncertainties described in Section 6. The number of “muon-like”events are shown in Table 3.
23 –Table 3: Number of experimental, simulated background, and simulated signal events in the“muon-like” subset at each selection level for 456.8 days.Level Data BG Simulation Signal Simulation0 2.7 × +1 . − . × × +3 . − . × × +9 . − . × × +2 . − . × +2 . Note. — Levels 0 and 1 show combined numbers for both “muon-like” and “cascade-like” subsets.Signal is shown with a low energy threshold of 10 GeV for a neutrino spectrum of dN/dE = 10 − × E − GeV − cm − s − sr − , with an assumed 1:1:1 ν e : ν µ : ν τ flavor ratio. Values at selection level 0 and1 for data and background simulation are extrapolated from the 2000 datasets. The background simulationis shown with systematic and statistical uncertainties described in Section 6. The number of “cascade-like”events are shown in Table 2.
24 –Table 4: Simulation UncertaintiesSource BG Sim Sig SimCosmic Ray Normalization +100% / -50% -Cosmic Ray Composition -30% -Detector Sensitivity ± ± ± ± ν e +N ν µ +N ν τ )/dE= 10 − × E − GeV − cm − s − sr − .Neutrino Flavor “Cascade-like” “Muon-like” TotalElectron 7.7 0.1 7.8Muon 3.9 3.6 7.5Tau 4.4 0.3 4.7All Flavors 16.0 4.0 20.0 26 –Table 6: Flux models, the number of neutrinos of all flavors expected at the Earth at thefinal selection level, and the MRFs for 456.8 days of livetime.Model ν all MRF ReferenceAGN a a a a a ν norm AGASA b ν mono-energetic 1.2 4.4 (Kalashev et al. 2002b)GZK ν a=2 1.1 4.8 (Kalashev et al. 2002b)GZK ν norm HiRes b a ν a These values have been divided by two to account for neutrino oscillation from a source with an initial 1:2:0 ν e : ν µ : ν τ flux. b Lower energy threshold of 10 GeV applied.Note. — A MRF of less than one indicates that the model is excluded with 90% confidence. ig. 1.— Simulated muon neutrino event with an energy of 3.8 × GeV. The muon passesroughly 70 m outside the instrumented volume of the detector. Colored circles represent hitOMs. The color of the circle indicates the hit time (red is earliest), with multiple colorsindicating multiple hits in that OM. The size of the circle is correlated with the number ofphotons produced. 28 –Fig. 2.— Distance of closest approach to the detector center for muons from UHE muonneutrinos (shown with an E − spectrum) which pass all selection criteria of this analysis. 29 –Fig. 3.— All-flavor UHE neutrino flux limit for 2000-2002 over the range which con-tains the central 90% of the expected signal with an E − spectrum. Also shownare several representative models: St05 from Stecker (2005) multiplied by 3, P96from Protheroe (1996) multiplied by 3/2, Eng01 from Engel et al. (2001), Si98 fromSigl et al. (1998), Yosh98 from Yoshida et al. (1998), Lip93 from Lipari (1993), andthe Waxman-Bahcall upper bound (Bahcall & Waxman 1998) multiplied by 3/2. Exist-ing experimental limits shown are from the RICE (Kravchenko et al. 2006), ANITA-lite(Barwick et al. 2006), and Baikal (Aynutdinov et al. 2006) experiments, the UHE limit fromAMANDA-B10 (Ackermann et al. 2005), the lower-energy diffuse muon limit multiplied by3 (Achterberg et al. 2007) and cascade limit (Ackermann et al. 2004) from AMANDA-II. 30 –Fig. 4.— NHITS distribution for the experiment, background, and E − muon neutrino signalsimulations before level 1 of this analysis. 31 –Fig. 5.— Distribution of F1H (the fraction of OMs with a single hit) for the experiment,background, and E − muon neutrino signal simulations after level 1 of this analysis. Theaverage F1H drops with energy (see Fig. 6). 32 –Fig. 6.— F1H (top) and F1H ELEC (bottom) distributions for various energy decades of muonneutrino signal. These variables serve as rough estimator of energy for the UHE analysis. 33 –Fig. 7.— Distribution of L casc for the experiment, background, and E − electron, muon,and tau neutrino signal simulations after level 2 of this analysis. Events with L casc < casc ≥ ELEC (the fraction of electrical OMs with a single hit) distribution for theexperiment, background, and E − electron, muon, and tau neutrino signal simulations in the“cascade-like” subset after level two of this analysis. 35 –Fig. 9.— Distribution of neural net output for the experiment, background, and E − electron,muon, and tau neutrino signal simulations in the “cascade-like” subset after level two of thisanalysis. Signal events are expected near one, while background events are expected nearzero. 36 –Fig. 10.— Reconstructed zenith angle distribution for the experiment, background, and E − electron, muon, and tau neutrino signal simulations in the “muon-like” subset after level twoof this analysis. Zenith angles of 90 ◦ correspond to horizontal events, and zenith angles of0 ◦ are downgoing events. 37 –Fig. 11.— Model rejection factor for 10 − × E − muon neutrinos in the “muon-like” subsetas a function of cut level for L muon . 38 –Fig. 12.— Energy spectra of electron, muon, and tau neutrino signal events(d(N ν e +N ν µ +N ν τ )/dE = 10 − × E − GeV − cm − s − sr − ) which pass all selection cri-teria. The peak in the electron neutrino spectrum just below 10 GeV is due to the Glashowresonance. 39 –Fig. 13.— L muon distribution for the experiment, background, and 4.5 × − × E − muonneutrino signal simulations (arbitrary normalization) in the “muon-like” subset after levelthree of this analysis. Two experimental events survive the final selection criteria of L muon <7