Search for Extraterrestrial Point Sources of Neutrinos with AMANDA­II
    J. Ahrens,
    11
    X. Bai,
    1
    S.W. Barwick,
    10
    T. Becka,
    11
    J. K. Becker,
    2
    E. Bernardini,
    4
    D. Bertrand,
    3
    F. Binon,
    3
    A. Biron,
    4
    D. J. Boersma,
    4
    S. Bo
    ¨
    ser,
    4
    O. Botner,
    17
    A. Bouchta,
    17
    O. Bouhali,
    3
    T. Burgess,
    18
    S. Carius,
    6
    T. Castermans,
    13
    A. Chen,
    15
    D. Chirkin,
    9
    B. Collin,
    8
    J. Conrad,
    17
    J. Cooley,
    15
    D. F. Cowen,
    8
    A. Davour,
    17
    C. De Clercq,
    19
    T. DeYoung,
    12
    P. Desiati,
    15
    J. P. Dewulf,
    3
    P. Ekstro
    ¨
    m,
    18
    T. Feser,
    11
    T. K. Gaisser,
    1
    R. Ganugapati,
    15
    M. Gaug,
    4
    H. Geenen,
    2
    L. Gerhardt,
    10
    A. Goldschmidt,
    7
    A. Groß,
    2
    A. Hallgren,
    17
    F. Halzen,
    15
    K. Hanson,
    15
    R. Hardtke,
    15
    T. Harenberg,
    2
    T. Hauschildt,
    4
    K. Helbing,
    7
    M. Hellwig,
    11
    P. Herquet,
    13
    G. C. Hill,
    15
    D. Hubert,
    19
    B. Hughey,
    15
    P. O. Hulth,
    18
    K. Hultqvist,
    18
    S. Hundertmark,
    18
    J. Jacobsen,
    7
    A. Karle,
    15
    M. Kestel,
    8
    L. Ko
    ¨
    pke,
    11
    M. Kowalski,
    4
    K. Kuehn,
    10
    J. I. Lamoureux,
    7
    H. Leich,
    4
    M. Leuthold,
    4
    P. Lindahl,
    6
    I. Liubarsky,
    5
    J. Madsen,
    16
    K. Mandli,
    15
    P. Marciniewski,
    17
    H. S. Matis,
    7
    C. P. McParland,
    7
    T. Messarius,
    2
    Y. Minaeva,
    18
    P. Mioc
    ˇ
    inovic
    ´
    ,
    9
    R. Morse,
    15
    K. Mu
    ¨
    nich,
    2
    R. Nahnhauer,
    4
    T. Neunho
    ¨
    ffer,
    11
    P. Niessen,
    19
    D. R. Nygren,
    7
    H. O
    ¨
    gelman,
    15
    Ph. Olbrechts,
    19
    C. Pe
    ´
    rez de los Heros,
    17
    A. C. Pohl,
    6
    R. Porrata,
    9
    P. B. Price,
    9
    G.T. Przybylski,
    7
    K. Rawlins,
    15
    E. Resconi,
    4
    W. Rhode,
    2
    M. Ribordy,
    13
    S. Richter,
    15
    J. Rodrı
    ´
    guez Martino,
    18
    H. G. Sander,
    11
    K. Schinarakis,
    2
    S. Schlenstedt,
    4
    T. Schmidt,
    4
    D. Schneider,
    15
    R. Schwarz,
    15
    A. Silvestri,
    10
    M. Solarz,
    9
    G. M. Spiczak,
    16
    C. Spiering,
    4
    M. Stamatikos,
    15
    D. Steele,
    15
    P. Steffen,
    4
    R. G. Stokstad,
    7
    K. H. Sulanke,
    4
    I. Taboada,
    14
    L. Thollander,
    18
    S. Tilav,
    1
    W. Wagner,
    2
    C. Walck,
    18
    Y. R. Wang,
    15
    C. H. Wiebusch,
    2
    C. Wiedemann,
    18
    R. Wischnewski,
    4
    H. Wissing,
    4
    K. Woschnagg,
    9
    and G. Yodh
    10
    1
    Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA
    2
    Fachbereich 8 Physik, BU Wuppertal, D­42097 Wuppertal, Germany
    3
    Universite
    ´
    Libre de Bruxelles, Science Faculty CP230, Boulevard du Triomphe, B­1050 Brussels, Belgium
    4
    DESY­Zeuthen, D­15735, Zeuthen, Germany
    5
    Blackett Laboratory, Imperial College, London SW7 2BW, United Kingdom
    6
    Department of Technology, Kalmar University, S­39182 Kalmar, Sweden
    7
    Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
    8
    Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
    9
    Department of Physics, University of California, Berkeley, California 94720, USA
    10
    Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
    11
    Institute of Physics, University of Mainz, Staudinger Weg 7, D­55099 Mainz, Germany
    12
    Department of Physics, University of Maryland, College Park, Maryland 20742, USA
    13
    University of Mons­Hainaut, 7000 Mons, Belgium
    14
    Departamento de Fı
    ´
    sica, Universidad Simo
    ´
    n Bolı
    ´
    var, Caracas 1080, Venezuela
    15
    Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
    16
    Physics Department, University of Wisconsin, River Falls, Wisconsin 54022, USA
    17
    Division of High Energy Physics, Uppsala University, S­75121 Uppsala, Sweden
    18
    Department of Physics, Stockholm University, SE­10691 Stockholm, Sweden
    19
    Vrije Universiteit Brussel, Dienst ELEM, B­1050 Brussels, Belgium
    (Received 19 September 2003; published 19 February 2004)
    We present the results of a search for point sources of high­energy neutrinos in the northern
    hemisphere using AMANDA­II data collected in the year 2000. Included are flux limits on several
    active­galactic­nuclei blazars, microquasars, magnetars, and other candidate neutrino sources. A search
    for excesses above a random background of cosmic­ray­induced atmospheric neutrinos and misrecon­
    structed downgoing cosmic­ray muons reveals no statistically significant neutrino point sources. We
    show that AMANDA­II has achieved the sensitivity required to probe known TeV
    ?
    ­ray sources such as
    the blazar Markarian 501 in its 1997 flaring state at a level where neutrino and
    ?
    ­ray fluxes are equal.
    DOI: 10.1103/PhysRevLett.92.071102 PACS numbers: 95.85.Ry, 96.40.Tv
    Introduction.—
    The search for sources of high­
    energy extraterrestrial neutrinos is the primary mission
    of the Antarctic Muon and Neutrino Detector Array
    (AMANDA). The mechanism for accelerating cosmic
    rays to energies above the ‘‘knee’’ (
    10
    15
    eV
    ) remains a
    mystery. Cosmic rays are thought to be accelerated in the
    shock fronts of galactic objects such as supernova rem­
    nants, microquasars, and magnetars, and in extragalactic
    sources such as the cores of active galactic nuclei and
    gamma ray bursts [1].
    High energy protons accelerated in these objects will
    collide with the ambient gas and radiation surrounding
    the acceleration region, or with matter or radiation inter­
    vening between the source and the earth. This leads to
    pion production, the charged pions decaying into highly
    energetic muon and electron neutrinos, and the neutral
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    2004 The American Physical Society 071102­1
    pions decaying into the observed
    ?
    rays. Fermi accelera­
    tion of charged particles in magnetic shocks naturally
    leads to power­law spectra,
    E
    ?
    , where
    ?
    is typically close
    to
    ?
    2
    . By the time the neutrinos reach the earth, vacuum
    oscillations will have uniformly populated all three fla­
    vors (unless the neutrinos are unstable [2]). All limits
    quoted in this Letter are on the muon neutrino flux
    arriving at the earth; limits at the source will be approxi­
    mately a factor of 2 higher due to oscillations.
    Neutrino astronomy may provide information comple­
    mentary to the knowledge obtained from high­energy
    photons and charged particles. Accelerated electrons
    and protons can both result in the production of high­
    energy gamma rays, so only neutrinos can distinguish
    between electromagnetic and hadronic processes. Since
    neutrinos propagate directly from their point of origin
    undeflected by magnetic fields, they have the potential to
    reveal ‘‘hidden’’ sources masked by photon absorption.
    Probing the neutrino sky may bring us closer to solving
    the cosmic­ray mystery, or might even reveal something
    completely new and unexpected.
    The AMANDA­II detector.—
    AMANDA­II [3] is a
    Cherenkov detector frozen into the antarctic polar ice
    cap. A high­energy muon neutrino interacting with the
    ice or bedrock in the vicinity of the detector results in a
    high­energy muon propagating up to tens of kilometers.
    The muon track is reconstructed based on detection of
    the Cherenkov light emitted as it propagates through a
    19­string array of 677 photomultiplier tubes. The median
    neutrino pointing resolution is
    2
    ?
    –
    2
    :
    5
    ?
    , depending
    weakly on declination, and is dominated by the resolution
    of the muon track reconstruction. AMANDA­II demon­
    strates a significant improvement over its predecessor in
    acceptance and background rejection, especially near the
    horizon. Results from the first phase of AMANDA, the
    ten­string subdetector AMANDA­B10, have been re­
    ported in [4].
    Atmospheric muons from cosmic rays that penetrate
    to AMANDA depths are the dominant background.
    AMANDA­II views the neutrino sky above the northern
    hemisphere using the earth as an atmospheric muon filter.
    Cosmic rays also produce neutrinos in the earth’s atmo­
    sphere, but with a spectral index of
    ?
    ??
    3
    :
    7
    , softer than
    expected for astrophysical sources. Atmospheric neutri­
    nos are an important source for calibration in AMANDA
    [5], but are also background to a search for extraterres­
    trial point sources. A point source search is conducted by
    looking for excess events above the background, which is
    experimentally measured for a given angular search bin
    by taking the average background rate in the same band
    of declination.
    Data processing and detector simulation.—
    The data
    set comprises
    1
    :
    2
    ?
    10
    9
    triggered events collected over
    238 days between February and November, 2000, with
    197.0 days live time after correcting for
    17
    :
    2%
    detector
    dead time. After application of an iterative series of
    maximum­likelihood reconstruction algorithms, 2.1
    million events reconstructed with declination
    ?>
    0
    ?
    remain in the experimental sample.
    To prevent bias in the selection of cuts, the data are
    ‘‘blinded’’ by randomizing the reconstructed right as­
    cension (RA) angle of each event. The output of a neural
    network (NN) trained on simulated events and using six
    input variables (such as the number of unscattered photon
    hits, track length, likelihood of the muon track recon­
    struction, and topological variables [5]) is used as a
    quality cut. A second cut is placed on the likelihood ratio
    (LR) between the muon track reconstruction and a muon
    reconstruction weighted by an atmospheric muon prior
    [6]. The prior describes the zenith­dependent frequency of
    downgoing muons such that choosing a cut on the LR
    gives downgoing hypotheses a prior weight of up to
    10
    6
    more than the upgoing hypotheses, effectively forcing
    events surviving the cut to be of higher quality. The
    final choice of NN quality cut, likelihood ratio cut, and
    the optimum size for a search bin are determined inde­
    pendently in each
    5
    ?
    band of declination (Dec.) in order
    to optimize the limit setting potential of the experiment
    [7]. The directional information is then restored (data
    ‘‘unblinded’’) for the calculation of the limits and
    significances.
    A full simulation chain [4] including neutrino absorp­
    tion in the earth, neutral current regeneration, muon
    propagation, and detector response is used to simulate
    the point source signal according to an
    E
    ?
    2
    energy spec­
    trum. The limits obtained in this analysis are a function
    of the measured background,
    n
    b
    , as well as the expected
    number of events,
    n
    s
    , from a simulated flux
    ?
    ?
    E
    ?
    :
    ?
    limit
    ?
    E
    ??
    ?
    ?
    E
    ??
    ?
    90
    ?
    n
    obs
    ;n
    b
    ?
    =n
    s
    , where
    n
    obs
    is the
    number of observed events in the given source bin, and
    ?
    90
    is the
    90%
    upper limit on the number of events
    following the unified ordering prescription of Feldman
    and Cousins [8].
    Systematic uncertainties.—
    Atmospheric neutrinos
    were used to determine the absolute normalization of
    the detector simulation. The normalization factor 0.86 is
    consistent with the theoretical uncertainty of
    25%
    on the
    atmospheric neutrino flux [5,9]. The overall systematic
    uncertainty, which includes the theoretical uncertainty of
    the atmospheric neutrino flux and statistical uncertainty
    of the measured background, is incorporated into the
    limits using the Cousins­Highland [10] prescription
    with unified Feldman­Cousins ordering [8,11] but with a
    more appropriate choice of the likelihood ratio test [12].
    Coincident events between the SPASE air shower array
    [13] and AMANDA­II were used to evaluate the system­
    atic error in pointing accuracy. This value was determined
    to be less than
    1
    ?
    , which results in signal loss in a typical
    search bin of only
    5%
    .
    Results.—
    The final sample consists of 699 upwardly
    reconstructed (
    ?>
    0
    ?
    ) events, illustrated in Fig. 1. A
    comparison to the normalized atmospheric neutrino
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    simulation reveals that for declinations
    ?>
    5
    ?
    the
    sample is strongly dominated by atmospheric neutrinos.
    A binned search for excesses in the region
    0
    ?
    <? <
    85
    ?
    has been performed. The search grid contains 301
    rectangular bins with zenith­dependent widths ranging
    from
    6
    ?
    to
    10
    ?
    , based on the aforementioned bin­size
    optimization. The grid is shifted 4 times in declination
    and right ascension to fully cover boundaries between the
    bins of the original configuration. The number of times to
    shift the grid was studied, taking into account statistical
    penalties for the number of shifts by using simulated
    event samples, and set at a level where further shifts do
    not markedly improve the average maximum significance
    obtained on simulated Poisson­fluctuated signals of simi­
    lar magnitude to the background.
    The most significant excess, observed at about
    68
    ?
    Dec
    :;
    21
    :
    1h RA
    , is eight events observed on an ex­
    pected background of 2.1. Simulation reveals a probabil­
    ity of
    51%
    to observe such an excess as a random upward
    fluctuation of the background.
    In addition to the binned search, we place limits on a
    number of extragalactic and galactic candidate sources.
    Circular bins with optimized radii are positioned at each
    candidate position; the number of expected background
    events is given by the number of observed events in the
    declination band scaled down to the search bin area. The
    same method applied to any point in the northern hemi­
    sphere yields neutrino flux upper limits shown in Fig. 2.
    For the region
    ?>
    85
    ?
    , an adjacent region at lower
    declination was used for the background estimation.
    The average flux upper limits for
    E
    ?
    2
    spectra obtained
    in an ensemble of identical experiments in the case of no
    true signal is shown vs declination in Fig. 3. It should be
    pointed out that due to the large number of cells tested a
    single source with a flux at the sensitivity level (
    90%
    average flux upper limit) would normally be interpreted
    as a statistical fluctuation. Therefore a flux a few times
    higher would be needed to make a discovery of a point
    source possible in the binned search.
    In Table I, we present neutrino flux limits for northern
    hemisphere TeV blazars, selected GeV blazars, microqua­
    sars, magnetars, and selected miscellaneous candidates.
    The limits are computed based on an assumed
    E
    ?
    2
    energy
    spectrum. Limits for other spectra can be computed using
    the neutrino effective area shown in Fig. 4: The neutrino
    flux limit for an assumed flux
    d
    ?
    =dE
    /
    E
    ?
    is inversely
    proportional to the energy averaged effective area
    A
    eff
    ?
    ?
    ??
    R
    1
    E
    min
    A
    eff
    ?
    E
    ?
    E
    ?
    dE=
    R
    1
    E
    min
    E
    ?
    dE
    .Effective
    areas at declinations not shown in Fig. 4 can be obtained
    by linear interpolation in
    ?
    ; the systematic shift induced
    by this interpolation is below
    20%
    for spectral indices in
    the range
    ?
    ??
    1
    :
    5
    to
    ?
    2
    :
    5
    . Integrated neutrino flux
    limits are strongly dependent on the spectral index, while
    the differential sensitivities
    d
    ?
    =dE
    remain approxi­
    mately constant at the energy at which most events
    are detected. This energy ranges from about 30 TeV at
    24h 0h
    °
    ­90
    °
    90
    FIG. 1 (color online). Final point source search sample plot­
    ted in equatorial coordinates. The thick band of events at
    ?<
    0
    shows the onset of cosmic muon background contamination.
    FIG. 2 (color). Neutrino flux upper limits (
    90%
    confidence
    level) in equatorial coordinates. Limits (scale on right axis) are
    in units of
    10
    ?
    7
    cm
    ?
    2
    s
    ?
    1
    for an assumed
    E
    ?
    2
    spectrum,
    integrated above
    E
    ?
    ?
    10 GeV
    . Systematic uncertainties are
    not included.
    sin(
    δ
    )
    Φ
    ν
    lim
    (10
    ­7
    cm
    ­2
    s
    ­1
    )
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    ­0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
    FIG. 3 (color online). Average flux upper limits (
    90%
    and
    99%
    confidence) for an
    E
    ?
    2
    signal hypothesis, integrated above
    E
    ?
    ?
    10 GeV
    , are shown vs declination (
    ?
    ), solid lines with
    and dashed lines without the inclusion of systematic uncer­
    tainty (as described in the text). The limits worsen near the
    horizon due to the onset of cosmic ray muon contamination.
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    ?
    ?
    0
    ?
    30
    ?
    to 10 TeV at
    ?>
    30
    ?
    , and the changes at
    these energies are below
    30%
    for
    ?
    ??
    2
    to
    ?
    2
    :
    75
    .The
    integrated muon flux limits for a softer spectrum
    ?
    ?
    ?
    2
    :
    75
    are worse by a factor
    ?
    5
    (
    ?>
    45
    ?
    )to 10 (
    ?
    ?
    0
    ?
    –
    15
    ?
    ) compared to
    ?
    ??
    2
    .
    In [15], expected numbers of neutrino induced muon
    events for galactic microquasars using source parameters
    estimated from radio observations are calculated. For
    microquasars whose jets have not been resolved in the
    radio band, the neutrino emission is estimated from the
    synchrotron luminosity. In the case of the microquasar
    SS433,
    252
    muons
    yr
    ?
    1
    km
    ?
    2
    are predicted. Scaling to
    the AMANDA­II effective area at that declination
    (
    A
    ?
    eff
    ?
    7900 m
    2
    ) and to the live time of this analysis
    yields a prediction of 1.07 events for an assumed
    E
    ?
    2
    spectrum. We observe no events in the search bin for this
    source, and place a
    90%
    upper limit of 1.24 events.
    Because of a random fluctuation, this limit is about 3
    times better than the sensitivity at this declination.
    In Fig. 5, the AMANDA­II neutrino sensitivity is
    compared to the 1997­averaged TeV
    ?
    ­ray flux of the
    blazar Markarian 501 (
    z
    ?
    0
    :
    031
    ), and the intrinsic
    source spectrum (corrected for IR absorption). The figure
    demonstrates AMANDA­II has achieved the sensitivity
    needed to search for neutrino fluxes from TeV
    ?
    ­ray
    sources of similar strength to the intrinsic
    ?
    ­ray flux.
    Conclusions.—
    One year of AMANDA­II data has been
    searched for clusters of neutrino events. No significant
    excesses have been found, and flux limits for 30 candidate
    sources have been calculated. For some candidates, the
    limits are close to neutrino flux predictions. Data col­
    lected in 2001–2002 are being analyzed and should im­
    prove the sensitivity of this analysis approximately by a
    factor 2.3.
    TABLE I.
    90%
    upper limits on candidate sources. The num­
    ber of events observed within the search bin is denoted by
    n
    obs
    ,
    and
    n
    b
    is the number of expected background events deter­
    mined by measuring the background off­source in the same
    declination band. Limits are for an assumed
    E
    ?
    2
    ?
    spectral
    shape, integrated above
    E
    ?
    ?
    10 GeV
    , and presented in units
    of
    10
    ?
    15
    cm
    ?
    2
    s
    ?
    1
    ?
    ?
    ?
    ?
    and
    10
    ?
    8
    cm
    ?
    2
    s
    ?
    1
    ?
    ?
    ?
    ?
    .
    Candidate Dec. [
    ?
    ]RA [h]
    n
    obs
    n
    b
    ?
    lim
    ?
    ?
    lim
    ?
    TeV Blazars
    Markarian 421 38.2 11.07 3 1.50 3.0 3.5
    Markarian 501 39.8 16.90 1 1.57 1.5 1.8
    1ES
    1426
    ?
    428
    42.7 14.48 1 1.62 1.4 1.7
    1ES
    2344
    ?
    514
    51.7 23.78 1 1.23 1.6 2.0
    1ES
    1959
    ?
    650
    65.1 20.00 0 0.93 0.9 1.3
    GeV Blazars
    QSO
    0528
    ?
    134
    13.4 5.52 1 1.09 2.5 2.0
    QSO
    0235
    ?
    164
    16.6 2.62 1 1.49 2.0 1.7
    QSO
    1611
    ?
    343
    34.4 16.24 0 1.29 0.7 0.8
    QSO
    1633
    ?
    382
    38.2 16.59 1 1.50 1.5 1.7
    QSO
    0219
    ?
    428
    42.9 2.38 1 1.63 1.4 1.6
    QSO
    0954
    ?
    556
    55.0 9.87 1 1.66 1.3 1.7
    QSO
    0716
    ?
    714
    71.3 7.36 2 0.74 2.9 4.4
    Microquasars
    SS433 5.0 19.20 0 2.38 1.0 0.7
    GRS
    1915
    ?
    105
    10.9 19.25 1 0.91 2.9 2.2
    GRO
    J0422
    ?
    32
    32.9 4.36 2 1.31 2.9 2.9
    Cygnus X1 35.2 19.97 2 1.34 2.2 2.5
    Cygnus X3 41.0 20.54 3 1.69 3.0 3.5
    XTE
    J1118
    ?
    480
    48.0 11.30 1 0.92 1.7 2.2
    CI Cam 56.0 4.33 0 1.72 0.6 0.8
    LS I
    ?
    61
    303 61.2 2.68 0 0.75 1.0 1.5
    SNR, magnetars, and miscellaneous
    SGR
    1900
    ?
    14
    9.3 19.12 0 0.97 1.4 1.0
    Crab Nebula 22.0 5.58 2 1.76 2.6 2.4
    Cassiopeia A 58.8 23.39 0 1.01 0.9 1.2
    3EG
    J0450
    ?
    1105
    11.4 4.82 2 0.89 4.2 3.2
    M 87 12.4 12.51 0 0.95 1.3 1.0
    Geminga 17.9 6.57 3 1.78 3.7 3.3
    UHE CR Triplet 20.4 1.28 2 1.84 2.4 2.3
    NGC 1275 41.5 3.33 1 1.72 1.4 1.6
    Cygnus OB2 region [14] 41.5 20.54 3 1.72 2.9 3.5
    UHE CR Triplet 56.9 12.32 1 1.48 1.4 1.9
    [GeV]
    ν
    log E
    23 45 67
    ]
    2
    [cm
    ν
    eff
    A
    10
    ­1
    1
    10
    10
    2
    10
    3
    10
    4
    10
    5
    10
    6
    °
    = 0
    δ
    °
    = 25
    δ
    °
    = 50
    δ
    °
    = 75
    δ
    [GeV]
    µ
    log E
    2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
    ]
    2
    [1000 m
    µ
    eff
    A
    0
    5
    10
    15
    20
    25
    30
    35
    40
    45
    50
    °
    = 0
    δ
      
    °
    =25
    δ
      
    °
    =50
    δ
      
    °
    =75
    δ
      
    FIG. 4 (color online). Neutrino and muon effective areas vs
    energy at different declinations (
    ?
    ).
    E
    ?
    is the muon energy at
    the closest approach to the center of the detector. The effect of
    neutrino absorption in the earth is included in the neutrino
    effective areas.
    PH YSICA L R E VI E W L E T T E RS
    week ending
    20 FEBRUARY 2004
    VOLUME92, NUMBER7
    071102­4
    071102­4
    We acknowledge the support of the following agencies:
    National Science Foundation–Office of Polar Programs,
    National Science Foundation–Physics Division, Uni­
    versity of Wisconsin Alumni Research Foundation,
    Department of Energy, and National Energy Research
    Scientific Computing Center (supported by the Office 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 Scientific Research (FNRS­FWO), Flanders
    Institute to encourage scientific and technological re­
    search in industry (IWT), and Belgian Federal Office
    for Scientific, Technical and Cultural affairs (OSTC),
    Belgium; Fundacio
    ´
    n Venezolana de Promocio
    ´
    nal
    Investigador (FVPI), Venezuela; D. F. C. acknowledges
    the support of the NSF CAREER program.
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    ?
    ­ray source; see F. Aharonian
    et al.
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    log(E/TeV)
    E
    2
    dN/dE (TeV cm
    ­2
    s
    ­1
    )
    10
    ­11
    10
    ­10
    10
    ­9
    10
    ­1
    1
    10
    de Jager & Stecker
    HEGRA97 average
    AMANDAII
    AMANDAB10
    α=−2.0
    α=−2.0
    α=−1.8
    E (TeV)
    FIG. 5 (color online). The AMANDA­II
    90%
    average
    fl
    ux
    upper limit (197 days live time) for two assumed spectral
    indices (
    ?
    ) is compared to the average
    ?
    ­ray
    fl
    ux of
    Markarian 501 as observed in 1997 by the HEGRA system
    of air Cherenkov telescopes [16]. These average upper limits
    are based on the assumption that the neutrino spectrum extends
    to beyond 10 PeV. Also shown is the intrinsic source
    fl
    ux after
    correction for IR absorption by de Jager and Stecker [17]. The
    shaded area is bounded by two curves corresponding to differ­
    ent models of galactic luminosity evolution. For comparison,
    the AMANDA­B10 result [4] is also shown.
    PH YSICA L R E VI E W L E T T E RS
    week ending
    20 FEBRUARY 2004
    VOLUME92, NUMBER7
    071102­5
    071102­5

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