Limits on Diffuse Fluxes of High Energy Extraterrestrial Neutrinos
    with the AMANDA­B10 Detector
    J. Ahrens,
    12
    X. Bai,
    1
    S.W. Barwick,
    6
    R. C. Bay,
    5
    T. Becka,
    12
    K.­H. Becker,
    13
    E. Bernardini,
    2
    D. Bertrand,
    10
    A. Biron,
    2
    S. Boeser,
    2
    O. Botner,
    11
    A. Bouchta,
    11
    O. Bouhali,
    10
    T. Burgess,
    4
    S. Carius,
    3
    T. Castermans,
    16
    D. Chirkin,
    5
    J. Conrad,
    11
    J. Cooley,
    8
    D. F. Cowen,
    7
    A. Davour,
    11
    C. De Clercq,
    15
    T. DeYoung,
    8
    P. Desiati,
    8
    P. Doksus,
    8
    P. Ekstro
    ¨
    m,
    4
    T. Feser,
    12
    T. K. Gaisser,
    1
    R. Ganugapati,
    8
    M. Gaug,
    2
    H. Geenen,
    13
    L. Gerhardt,
    6
    A. Goldschmidt,
    9
    A. Hallgren,
    11
    F. Halzen,
    8
    K. Hanson,
    8
    R. Hardtke,
    8
    T. Hauschildt,
    2
    M. Hellwig,
    12
    P. Herquet,
    16
    G. C. Hill,
    8
    P. O. Hulth,
    4
    B. Hughey,
    8
    K. Hultqvist,
    4
    S. Hundertmark,
    4
    J. Jacobsen,
    9
    A. Karle,
    8
    K. Kuehn,
    6
    J. Kim,
    6
    L. Ko
    ¨
    pke,
    12
    M. Kowalski,
    2
    J. I. Lamoureux,
    9
    H. Leich,
    2
    M. Leuthold,
    2
    P. Lindahl,
    3
    I. Liubarsky,
    18
    J. Madsen,
    14
    K. Mandli,
    8
    P. Marciniewski,
    11
    H. Matis,
    9
    C. P. McParland,
    9
    T. Messarius,
    13
    T. C. Miller,
    1
    Y. Minaeva,
    4
    P. Miocinovic
    ´
    ,
    5
    P. C. Mock,
    6
    R. Morse,
    8
    T. Neunho
    ¨
    ffer,
    12
    P. Niessen,
    15
    D. R. Nygren,
    9
    H. O
    ¨
    gelman,
    8
    P. Olbrechts,
    15
    C. Pe
    ´
    rez de los Heros,
    11
    A. C. Pohl,
    3
    R. Porrata,
    6
    P. B. Price,
    5
    G. T. Przybylski,
    9
    K. Rawlins,
    8
    E. Resconi,
    2
    W. Rhode,
    13
    M. Ribordy,
    2
    S. Richter,
    8
    J. Rodrı
    ´
    guez Martino,
    4
    P. Romenesko,
    8
    D. Ross,
    6
    H.­G. Sander,
    12
    S. Schlenstedt,
    2
    K. Schinarakis,
    13
    T. Schmidt,
    2
    D. Schneider,
    8
    R. Schwarz,
    8
    A. Silvestri,
    6
    M. Solarz,
    5
    M. Stamatikos,
    8
    G. M. Spiczak,
    14
    C. Spiering,
    2
    D. Steele,
    8
    P. Steffen,
    2
    R. G. Stokstad,
    9
    K.­H. Sulanke,
    2
    I. Taboada,
    17
    S. Tilav,
    1
    W. Wagner,
    13
    C. Walck,
    4
    Y.­R. Wang,
    8
    C. H. Wiebusch,
    2
    C. Wiedemann,
    4
    R. Wischnewski,
    2
    H. Wissing,
    2
    K. Woschnagg,
    5
    W. Wu,
    6
    G. Yodh,
    6
    and S. Young
    6
    1
    Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA
    2
    DESY­Zeuthen, D­15735, Zeuthen, Germany
    3
    Department of Technology, University of Kalmar, S­39182, Kalmar, Sweden
    4
    Department of Physics, Stockholm University, SE­106 91 Stockholm, Sweden
    5
    Department of Physics, University of California, Berkeley, California 94720, USA
    6
    Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
    7
    Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
    8
    Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
    9
    Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
    10
    Universite Libre de Bruxelles, Science Faculty CP230, Boulevard du Triomphe, B­1050, Brussels, Belgium
    11
    Division of High Energy Physics, Uppsala University, S­75121, Uppsala, Sweden
    12
    Institute of Physics, University of Mainz, Staudinger Weg 7, D­55099, Mainz, Germany
    13
    Fachbereich 8 Physik, BUGH Wuppertal, D­42097 Wuppertal Germany
    14
    Physics Department, University of Wisconsin, River Falls, Wisconsin 54022, USA
    15
    Vrije Universiteit Brussel, Dienst ELEM, B­1050, Brussels, Belgium
    16
    Universite
    ´
    de Mons­Hainaut, 19 Avenue Maistriau 7000,Mons, Belgium
    17
    Department Fı
    ´
    sica, University Simo
    ´
    n Bolı
    ´
    var, Caracas, Venezuela
    18
    Blackett Laboratory, Imperial College, London SW7 2BW, United Kingdom
    (Received 25 February 2003; published 24 June 2003)
    Data from the AMANDA­B10 detector taken during the austral winter of 1997 have been searched
    for a diffuse flux of high energy extraterrestrial muon neutrinos. This search yielded no excess events
    above those expected from background atmospheric neutrinos, leading to upper limits on the extrater­
    restrial neutrino flux measured at the earth. For an assumed
    E
    ?
    2
    spectrum, a
    90%
    classical confidence
    level upper limit has been placed at a level
    E
    2
    ?
    ?
    E
    ??
    8
    :
    4
    ?
    10
    ?
    7
    cm
    ?
    2
    s
    ?
    1
    sr
    ?
    1
    GeV
    (for a predominant
    neutrino energy range 6–1000 TeV), which is the most restrictive bound placed by any neutrino
    detector. Some specific predicted model spectra are excluded. Interpreting these limits in terms of the
    flux from a cosmological distributions of sources requires the incorporation of neutrino oscillations,
    typically weakening the limits by a factor of 2.
    DOI: 10.1103/PhysRevLett.90.251101 PACS numbers: 95.85.Ry, 95.55.Vj, 96.40.Tv, 98.54.–h
    High energy extraterrestrial neutrinos are believed
    to be produced in energetic accelerated environments
    through proton­proton or proton­photon interactions via
    pion production and decay. Such an accelerator might be
    the core of an active galaxy, powered by a supermassive
    black hole. In their pioneering work, Stecker, Done,
    Salamon, and Sommers [1] calculated the expected dif­
    fuse flux of neutrinos from the sum of all active galaxies
    and found that such a flux could be observable deep
    underground in a large neutrino detector. Further predic­
    tions have followed (for a summary see, for example, the
    review of Learned and Mannheim [2]), and with the
    construction and operation of the first high energy neu­
    trino detectors, the sensitivity has been reached to enable
    such predictions to be tested. Searches have been
    made and limits have been reported by the DUMAND
    PH YSICA L R E VI E W L E T T E RS
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    VOLUME 90, NUMBER 25
    251101­1 0031­9007
    =
    03
    =
    90(25)
    =
    251101(5)$20.00
    2003 The American Physical Society 251101­1
    [3], Frejus [4], Baikal
    ?
    ?
    e
    ?
    [5,6], MACRO [7], and
    AMANDA
    ?
    ?
    e
    ?
    [8] neutrino detectors. In this Letter,
    we describe the search for high energy extraterrestrial
    neutrino­induced muons, using data collected during
    the austral winter of 1997 with the AMANDA­B10 de­
    tector [9,10], located in the antarctic ice cap at the South
    Pole station. This initial data set serves as a test bed for
    the development of analysis and limit­setting techniques
    that will be used to analyze the complete data set in
    the future.
    The AMANDA (Antarctic Muon And Neutrino
    Detector Array) telescope detects high energy muon neu­
    trinos by observing Cherenkov light from muons result­
    ing from neutrino interactions in the ice surrounding, or
    the rock below, the detector. While extraterrestrial neu­
    trinos will produce high energy muons from all arrival
    directions, those coming from
    above
    the detector will be
    very difficult to separate from the overwhelming flux of
    downward­going cosmic­ray induced atmospheric muons.
    The majority of these muons are rejected by accepting
    only upward­going neutrino­induced muons; the earth
    filters out muons produced in the atmosphere on the other
    side of the planet. There is a small remaining flux of
    misreconstructed events which is removed by quality
    cuts that leave only well reconstructed events. After the
    atmospheric muons are removed, there will remain a flux
    of upward­going muons from cosmic­ray induced atmos­
    pheric neutrinos that have penetrated the earth and inter­
    acted near the detector. This relatively well understood
    neutrino flux is a background to the search but has been
    used to verify the performance of the detector [9,10]. The
    separation of the extraterrestrial neutrino­induced muons
    from the atmospheric neutrino­induced muons is based
    on the expected energy spectrum of the detected muons.
    Typically, a model of an extraterrestrial source of neu­
    trinos has a harder spectrum (e.g.,
    ?
    E
    ?
    2
    ) [11] than that of
    the atmospheric neutrinos
    ??
    E
    ?
    3
    :
    7
    ?
    [12,13]. After ac­
    counting for neutrino interaction and muon propagation,
    this energy difference carries over to produce a harder
    muon energy spectrum for the extraterrestrial neutrino­
    induced muons near the detector. The energy of the muon
    is not measured directly, but more energetic muons tend to
    produce more Cherenkov light and thus more hit optical
    modules in the detector; this observable, the channel
    multiplicity (
    N
    ch
    ), is used as the primary separator of
    higher energy extraterrestrial neutrino­induced muon
    events from the background of lower energy atmospheric
    neutrino­induced muons.
    In this analysis, the event selection cuts were designed
    to retain high energy tracklike events [14]. The detector
    simulation has changed from that used in the atmospheric
    neutrino analysis [10]. A new muon propagation code [15]
    was used, which accounts for all relevant stochastic light
    emission from the muons. The depth­dependent optical
    properties of the fiducial ice were determined using at­
    mospheric muons as a calibration source.
    Before the energy sensitive channel multiplicity cut
    was finally applied, 69 events remained in the data
    sample, whereas a full simulation of the detector re­
    sponse to the atmospheric neutrino (Lipari [12]) flux
    (neglecting neutrino oscillations, which would reduce
    the prediction by only a few percent) predicts 85 events
    for the 130 days of live time. The absolute difference in
    the numbers of events is consistent with Poisson fluctua­
    tions, or with the
    ?
    25%
    [13] uncertainty in the atmos­
    pheric neutrino flux, or with uncertainties in the
    simulation efficiencies (
    30%
    –
    40%
    ). The distribution of
    the data and atmospheric simulation are shown in Fig. 1.
    The error bars on the data are
    90%
    unified confidence
    intervals [16] for the fixed but unknown value of the mean
    rate (signal plus background) for each bin. Only one bin
    (
    N
    ch
    ?
    25
    –
    30
    ) has a background prediction inconsistent
    with the confidence interval. More specifically, a gener­
    alized likelihood ratio test of the shape of the atmos­
    pheric neutrino hypothesis as the parent distribution of
    the data yields a chance probability of
    20%
    , which is too
    large to reject the shape of the atmospheric neutrino
    hypothesis. We choose to treat the rate of observed atmos­
    pheric neutrinos as a constraint on the overall detector
    efficiency and then carry through an efficiency uncer­
    tainty from the atmospheric neutrino flux prediction and
    Poisson error on the observed rate. Therefore, to calibrate
    the overall detector sensitivity, we take the 69 events as
    the best­fit estimate of the number of atmospheric neu­
    trinos and rescale all efficiencies by a factor
    69
    =
    85
    .This
    is conservative, since if the first bin discrepancy was
    due, e.g., to a simulation effect, then no renormalization
    would be needed, and the limits would improve slightly.
    We combine the Poisson error on the observed rate of
    Data
    N
    ch
    events
    atmos.
    ν
    µ
    10
    ­5
    E
    ­2
    ν
    µ
    10
    ­1
    1
    10
    20 30 40 50 60 70 80 90 100
    FIG. 1. Channel multiplicity distribution after
    fi
    nal cuts,
    showing the expected excess of events from an
    E
    ?
    2
    spectrum
    at the higher multiplicities.
    PH YSICA L R E VI E W L E T T E RS
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    VOLUME 90, NUMBER 25
    251101­2
    251101­2
    atmospheric neutrinos with the theoretical
    fl
    ux uncer­
    tainty (taken as a uniform probability distribution cen­
    tered about the best­
    fi
    t
    fl
    ux
    ^
    ??
    and extending to
    ?
    0
    :
    25
    ^
    ??
    )
    to compute the correlations between the background and
    ef
    fi
    ciency for later use in the probability distribution
    function used in the con
    fi
    dence interval construction. To
    incorporate these systematic uncertainties in the ef
    fi
    cien­
    cies into the limit calculations, we follow the prescription
    of Cousins and Highland [17], as implemented by Conrad
    et al.
    [18] with the uni
    fi
    ed Feldman­Cousins ordering and
    improved by a more appropriate choice of the likelihood
    ratio test [19]. We also report all limits and sensitivities
    with and without the assumed uncertainty.
    In addition to the data and atmospheric neutrino pre­
    diction, Fig. 1 also shows the prediction for an
    E
    ?
    2
    signal
    fl
    ux at a level
    E
    2
    ?
    ?
    E
    ??
    10
    ?
    5
    cm
    ?
    2
    s
    ?
    1
    sr
    ?
    1
    GeV
    ,a
    fl
    ux
    that would have been readily detected. Setting a limit on a
    fl
    ux
    ?
    ?
    E
    ?
    involves determining an experimental signal
    event upper limit
    ?
    ?
    n
    obs
    ;n
    b
    ?
    , which is a function of the
    number of observed events,
    n
    obs
    , and expected back­
    ground,
    n
    b
    , after the cuts are applied. A simulation chain
    accounting for neutrino absorption, interaction and neu­
    tral current regeneration, muon propagation, and detector
    response gives the number of signal events,
    n
    s
    , expected
    from the source
    fl
    ux
    ?
    ?
    E
    ?
    . The limit on the source
    fl
    ux
    will then be
    ?
    limit
    ?
    E
    ??
    ?
    ?
    E
    ??
    ?
    ?
    n
    obs
    ;n
    b
    ?
    =n
    s
    .The
    choice of
    fi
    nal cut for
    N
    ch
    is optimized before examining
    the data by minimizing the average
    ‘‘
    model rejection
    factor
    ’’
    (MRF)
    ?
    ?
    ?
    ?
    n
    b
    ?
    =n
    s
    [20], where the as yet unknown
    experimental event limit
    ?
    ?
    n
    obs
    ;n
    b
    ?
    is replaced by the
    average
    upper limit
    ?
    ?
    ?
    ?
    n
    b
    ?
    [16]. Over an ensemble of
    hypothetical repetitions of the experiment, this choice
    of cut will lead to the best average limit
    ?
    ??
    limit
    ?
    E
    ?
    .
    When calculating the expected signal from an extra­
    terrestrial source at the earth, it is necessary to take into
    account maximal mixing of neutrinos between
    ?
    ?
    and
    ?
    ?
    during propagation to the earth due to neutrino oscilla­
    tions [21,22]. We would expect to lose half the
    ?
    ?
    signal
    to
    ?
    ?
    ; however, some of these
    ?
    ?
    would regenerate
    ?
    ?
    in
    the earth (
    ?
    ?
    !
    ?
    !
    ?
    ?
    ) lessening the effect [23,24]. In
    what follows, we calculate the signals and model rejec­
    tion factors as if there were no loss of signal during
    passage to the earth (in order to more easily compare to
    previous experiments), but note that the limits and model
    rejection factors would be increased by a factor near but
    less than 2 in the presence of oscillations and
    ?
    ?
    !
    ?
    ?
    regeneration in the earth.
    The integrated channel multiplicity distribution is
    shown in Fig. 2. Also shown is the
    90%
    con
    fi
    dence level
    Feldman­Cousins average upper limit which is a function
    of the expected background. The optimal cut is the one
    where the model rejection factor
    ?
    ?
    ?
    ?
    n
    b
    ?
    =n
    s
    is minimized.
    Figure 2 also shows the average
    fl
    ux upper limit (
    E
    2
    ?
    ?
    MRF
    ) as a function of the choice of multiplicity cut. The
    minimum
    fl
    ux limit occurs at a cut of
    N
    ch
    ?
    54
    , where we
    expect
    n
    b
    ?
    3
    :
    06
    and an average signal event upper limit
    of 4.43 ignoring the uncertainties in the ef
    fi
    ciency
    and background, and 4.93 when the uncertainties
    are included. The
    10
    ?
    5
    E
    ?
    2
    signal
    fl
    ux would produce
    56.7 events. This leads to corresponding expected average
    limits on the source
    fl
    ux of
    E
    2
    ?
    ??
    90%
    ?
    E
    ??
    7
    :
    8
    ?
    10
    ?
    7
    cm
    ?
    2
    s
    ?
    1
    sr
    ?
    1
    GeV
    (excluding uncertainties), and
    8
    :
    7
    ?
    10
    ?
    7
    cm
    ?
    2
    s
    ?
    1
    sr
    ?
    1
    GeV
    (including uncertainties).
    We note that the expected overall
    fl
    ux limit is relatively
    insensitive to the choice of cut, with a broad minimum
    seen in Fig. 2 in the range of multiplicities 50
    –
    70. We
    now apply this optimal multiplicity cut to the data, and
    fi
    nd that three events remain. Ignoring the systematic
    uncertainties gives an event limit of 4.36 and a
    fl
    ux up­
    per limit of
    E
    2
    ?
    90%
    ?
    E
    ??
    7
    :
    7
    ?
    10
    ?
    7
    cm
    ?
    2
    s
    ?
    1
    sr
    ?
    1
    GeV
    .
    Including the systematic uncertainties leads to an event
    limit of 4.75 and our
    fi
    nal
    fl
    ux limit on an
    E
    ?
    2
    spectrum
    of
    E
    2
    ?
    90%
    ?
    E
    ??
    8
    :
    4
    ?
    10
    ?
    7
    cm
    ?
    2
    s
    ?
    1
    sr
    ?
    1
    GeV
    .
    Figure 3 shows the neutrino energy spectrum of the
    simulated events before and after the multiplicity cut of
    54 channels, for both atmospheric neutrinos and neutri­
    nos from an
    E
    ?
    2
    spectrum. The multiplicity cut corre­
    sponds to a sensitive energy range of 6
    –
    1000 TeV
    , which
    contains
    90%
    of the expected
    E
    ?
    2
    signal. The peak
    response energy is just below 100 TeV.
    Just as a limit was placed on an assumed
    E
    ?
    2
    spec­
    trum, limits can be placed on any neutrino
    fl
    ux predic­
    tion, and we consider a sample of predictions that are
    near the limit­setting capability of the detector (
    MRF
    ?
    1
    ). For each case, we optimize the
    fi
    nal
    N
    ch
    cut to mini­
    mize the expected average
    fl
    ux upper limit, then compare
    the expected number of extraterrestrial neutrino events
    after the cuts to the observed event limit; those predic­
    tions that produce expected event numbers greater than
    integrated events
    Data
    atmos.
    ν
    µ
    + atmos.
    µ
    10
    ­5
    E
    ­2
     
    ν
    µ
    ave. event upper limit
    1
    10
    10
    2
    average flux upper limit
    in E
    ­2
    cm
    ­2
    s
    ­1
    sr
    ­1
    GeV
    ­1
    N
    ch
    cut
    Flux
    10
    ­6
    30 40 50 60 70 80 90 100
    FIG. 2. Integrated distributions of event numbers as a func­
    tion of the multiplicity cut (top plot). The minimum in the
    fl
    ux
    average upper limit (bottom) is found by minimizing the ratio
    of the average event upper limit to the expected
    E
    ?
    2
    signal.
    PH YSICA L R E VI E W L E T T E RS
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    251101­3
    251101­3
    the observed event limit are excluded at the stated clas­
    sical con
    fi
    dence level. The results of these calculations are
    shown in Table I and in Fig. 4. For each
    fl
    ux, we again
    report two sensitivities and limits
    —
    one assuming no
    systematic uncertainties and the second including sys­
    tematic uncertainties. We
    fi
    nd that the predictions of
    Szabo and Protheroe (SPH92L [25],
    P96p
    ?
    pp
    [26]) are
    excluded. The quasar core (SSQC) prediction of Stecker
    and Salamon [11] is just excluded (
    MRF
    ?
    0
    :
    98
    ), but the
    blazar jet (SSBJ) prediction is not. The limit of the
    original Stecker, Done, Salamon, and Sommers
    fl
    ux [1]
    (SDSS) is a factor of 2 above the prediction and therefore
    the prediction is not excluded.
    We also place a limit on a model of prompt charm
    induced neutrinos [27] (ZHV92) in the earth
    ’
    s atmosphere
    and
    fi
    nd that the detector sensitivity is about a factor
    of 4 away from excluding the prediction. More recent
    predictions are even further below the sensitivity of the
    detector [28].
    Since most events will originate from neutrinos near
    the peak of the detector sensitivity
    E
    ?
    ?
    10
    5
    GeV
    ,the
    TABLE I. Flux limits calculated for individual models of diffuse neutrino emission. The optimal
    N
    ch
    cut, expected background,
    and signal for each model are shown. The average upper limit [
    ?
    ?
    ?
    ?
    n
    b
    ?
    ] and average model rejection factor [
    ?
    ?
    ?
    ?
    n
    b
    ?
    =n
    s
    ] are shown with
    and without the inclusion of systematic uncertainties. Finally, the experimental limits [observed events
    n
    obs
    , event limit
    ?
    o
    ?
    ?
    ?
    n
    obs
    ;n
    b
    ?
    ] and model rejection factor (
    ?
    o
    =n
    s
    ) are given for both systematic uncertainty assumptions.
    Sensitivities Experimental limits
    No sys. uncer. Sys. uncer. inc. No sys. uncer. Sys. uncer. inc.
    Flux
    N
    ch
    cut
    n
    b
    n
    s
    ?
    ?
    ?
    ?
    n
    b
    ?
    ?
    ?
    ?
    ?
    n
    b
    ?
    n
    s
    ?
    ?
    ?
    ?
    n
    b
    ?
    ?
    ?
    ?
    ?
    n
    b
    ?
    n
    s
    n
    obs
    ?
    o
    ?
    o
    n
    s
    ?
    o
    ?
    o
    n
    s
    10
    ?
    6
    E
    ?
    2
    54 3.06 5.67 4.43 0.781 4.93 0.869 3 4.36 0.769 4.75 0.838
    SDSS [1] 73 0.69 2.42 3.01 1.240 3.38 1.397 2 5.22 2.157 5.61 2.318
    SPH92L [25] 58 2.12 12.66 3.97 0.314 4.33 0.342 3 5.30 0.419 5.69 0.449
    SSQC [11] 71 0.80 5.59 3.11 0.556 3.45 0.617 2 5.11 0.914 5.50 0.984
    SSBJ [11] 57 2.36 4.29 4.13 0.963 4.50 1.049 3 5.06 1.179 5.45 1.270
    P96p
    ?
    pp
    [26] 49 4.83 21.95 5.11 0.233 5.90 0.269 4 3.76 0.171 4.54 0.207
    ZHV Charm D [27] 41 10.9 2.58 6.97 2.702 8.42 3.264 14 10.60 4.109 12.31 4.771
    log
    10
    (E
    ν
    )
    [
    GeV
    ]
    log
    10
    E
    2
    Φ
    ν
    (E)
    [
    cm
    ­2
    s
    ­1
    sr
    ­1
    GeV
    ]
    Atmospheric
    neutrinos
    SS QC pred.
    A­B10 lim.
    Charm D
    A­B10 lim.
    Charm D
    pred.
    MACRO E
    ­2
     
    ν
    µ
    Baikal E
    ­2
     
    ν
    e
    Frejus
    ν
    µ
    (diff. at E
    ν
    =2.6 TeV)
    AMANDA­B10 E
    ­2
     
    ν
    µ
    AMANDA­B10 E
    ­2
     
    ν
    e
    ­7
    ­6.8
    ­6.6
    ­6.4
    ­6.2
    ­6
    ­5.8
    ­5.6
    ­5.4
    ­5.2
    ­5
    3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
    FIG. 4. Summary of experimental
    90%
    classical con
    fi
    dence
    level
    fl
    ux limits from various detectors assuming an
    E
    ?
    2
    spectrum. From top: AMANDA­B10 (
    ?
    e
    ) [8], Frejus [4],
    MACRO [7], Baikal [6], and AMANDA­B10 (
    ?
    ?
    )(this
    work). The background atmospheric neutrinos [12] are indi­
    cated by the hashed region representing the angular depen­
    dence of the
    fl
    ux. Also shown are the predicted
    fl
    uxes (dashed),
    and AMANDA­B10 experimental
    fl
    ux limits (solid) for a
    diffuse neutrino prediction (SSQC [11]
    —
    nearly overlapping
    dotted and dashed curves
    —
    MRF
    ?
    0
    :
    98
    ) and for one predic­
    tion of prompt charm neutrino production in the earth
    ’
    satmo­
    sphere [27]. Since most events will originate from neutrinos
    near the peak of the detector sensitivity (
    E
    ?
    ?
    10
    5
    GeV
    ), the
    limits at that point for different spectral shapes are similar.
    log
    10
    (E
    ν
    )
    [
    GeV
    ]
    events
    10
    ­5
    E
    ­2
     
    ν
    µ
    atmos.
    ν
    µ
    pass initial cuts
    pass
    all
    cuts
    10
    ­1
    1
    10
    234567
    FIG. 3. Energy spectrum of the incident atmospheric (dashed
    lines) and
    E
    ?
    2
    (solid lines) neutrinos for events that pass the
    initial cuts and have channel multiplicity greater than the
    optimum cut of 54 channels.
    PH YSICA L R E VI E W L E T T E RS
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    27 JUNE 2003
    VOLUME 90, NUMBER 25
    251101­4
    251101­4
    limits at that point for the three different spectral shapes
    (
    E
    ?
    2
    , SSQC, and Charm D) are similar, as seen in Fig. 4.
    The limits presented in this Letter, based on the
    fi
    rst
    real­time year of operation of the AMANDA­B10 detec­
    tor, are the strongest placed to date on extraterrestrial
    diffuse neutrino
    fl
    uxes. Since that year, we estimate that
    about 10 times the exposure has been achieved in total
    with AMANDA­B10 (1997
    –
    1999) and the expanded
    AMANDA­II detector (2000
    –
    the present). We anticipate
    this combined data set to have a limit­setting potential
    more than 3 times better than the results presented here.
    We acknowledge the support of the following agencies:
    National Science Foundation
    –
    Of
    fi
    ce of Polar Pro­
    grams, National Science Foundation
    –
    Physics Division,
    University of Wisconsin Alumni Research Foundation,
    Department of Energy, and National Energy Research
    Scienti
    fi
    c Computing Center (supported by the Of
    fi
    ce of
    Energy Research of the Department of Energy), UC
    –
    Irvine AENEAS Supercomputer Facility, U.S.A.;
    Swedish Research Council, Swedish Polar Research
    Secretariat, and Knut and Alice Wallenberg Foundation,
    Sweden; German Ministry for Education and Research,
    Deutsche Forschungsgemeinschaft (DFG), Germany;
    Fund for Scienti
    fi
    c Research (FNRS­FWO), Flanders
    Institute to encourage scienti
    fi
    c and technological re­
    search in industry (IWT), and Belgian Federal Of
    fi
    ce
    for Scienti
    fi
    c, Technical and Cultural affairs (OSTC),
    Belgium. D. F. C. acknowledges the support of the NSF
    CAREER program.
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    251101­5

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