High Energy Neutrinos from Space

0.82 MB·English

by  Thomas K. Gaisser

PRAMANA (cid:13)c IndianAcademyofSciences
—journalof
physics
High Energy Neutrinos from Space
2 THOMASK.GAISSERa,∗
1 aBartol Research Institute and Department of Physics and Astronomy, University of Delaware,
0 Newark,DE19716,USA
2

n Abstract. Thispaperreviewsthestatusofthesearchforhigh-energyneutrinosfromastrophysical
a sources. Resultsfromlargeneutrinotelescopesinwater(Antares, Baikal)andice(IceCube)are
J
discussedaswellasobservationsfromthesurfacewithAugerandfromhighaltitudewithANITA.

1 CommentsonIceTop,thesurfacecomponentofIceCubearealsoincluded.
3
Keywords. Neutrinos,cosmicrays

]
E
PACSNos. Appropriatepacshere
H
.
h
p
1. Introduction
-
o
r A principal motivation for finding and studying high-energy neutrinos from space is to
t
s understand better the sources of cosmic rays and how they accelerate particles to high
a
energy. Thisreviewisorganizedaroundtwoconnectionsbetweencosmicraysandneu-
[
trinos. In the first place, it is likely that neutrinos will be produced at some level in

1 interactionsofacceleratedparticleswithgasorradiationfieldsinornearthecosmic-ray
v
sources. Examplesarehadronicinteractionsinthematerialnearanexpandingsupernova
1
remnant or photo-pion production in the radiation fields inside the jets of an accreting
5
6 blackhole. Themainapproachinthesecasesistolookforanexcessofneutrinosfroma
6 particulardirectionintheskyabovethebackgroundofatmosphericneutrinos. Potential
. sourcesmaybeselectedforstudyaccordingtothelikelihoodthatproductionofneutrinos
1
0 isexpected. Suchtargetedsearches mayincreasethediscoverypotential comparedtoa
2 surveyofthewholesky.
1 Productionofneutrinosisalsoexpectedbyinteractionsofcosmicraysastheypropa-
:
v gatethroughtheUniverse. Locally, neutrinosareproducedascosmic-raysinteractwith
i gasintheinterstellarmedium[1]. Theexpectedlevel(whichisquitelow)canbecalcu-
X
lateddirectlyfromtheobservedgamma-rayfluxfromthesamesource,whichtracesthe
r
a gasinthediskofthegalaxy. Amoreinterestingquestionisthelevelofneutrinoproduc-
tionbycosmicraysofultra-highenergy(UHECR)astheypropagatethroughthecosmic
microwavebackground(CMB).Protonswithenergiesabove5×1019 eVareabovethe
thresholdforproductionofpionsonCMBphotons[2,3]. Neutrinoswouldbeproduced
whenthepionsdecay. UHEcosmic-raynucleialsoloseenergyduringpropagationinthe
CMB by photo-disintegration [4], but the level of neutrino production from subsequent
decayofspallationneutronsislower[5].
∗[email protected]
1
ThomasK.Gaisser
Figure1. Compilation of the primary cosmic-ray spectrum measured by air shower
experiments[6].
Figure1isacompilationofmeasurementsofthecosmic-rayspectrumathighenergy.
The spectrum steepens between 1015 and 1016 eV total energy per particle. This fea-
ture,calledtheknee,mayreflectthedecreaseintheabilityofgalacticacceleratorssuch
assupernovaremnantstoachievesuchhighenergy. Thespectrumflattensagainaround
3×1018eV=3EeV,afeatureknownastheankle. Itisgenerallyassumedthatparticles
abovethisenergyoriginateinmorepowerfulextragalacticsources. Finally,thesteepen-
ing of the spectrum above 5×1019 eV is usually assumed to be the effect of expected
energylossesduringpropagationthroughtheCMB.Onereasontosearchforcosmogenic
neutrinos associated with propagation through the CMB is to see if this assumption is
correct.
Detector NumberofOMs Enclosedvolume Depth Status
(Megatons) (m.w.e.)
Baikal[7](NT200+) 230 10 1100-1310 Operating
AMANDA[8] 677 15 1350-1850 2000-2009
ANTARES[9] 900 10 2050-2400 Operating
IceCube[10] 5160+324 900 1350-2280 Operating
(IceCubeDeepCore[11]) (480) (15) (1950-2280) Operating
KM3NeT[12] ∼10,000 km3 2300-3300 Designstudy
km3 3000-4000
km3 1400-2400
GVD[15](futureBaikal) ∼2500 km3 800-1300 Designstudy
Table 1. Parameters of existing and proposed neutrino telescopes ice. Of the total
of 5484 OMs in IceCube, 480 are deployed on DeepCore Strings and 324 in IceTop
tanks. The three depths listed for KM3NeT correspond to three possible locations,
NEMO[13],NESTOR[14]andAntares[9]inthatorder.
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2. Detectorsiniceandwater
TheoperatingprincipleofdetectorslikeIceCube,AntaresandBaikallistedinTable1is
thesameasSuper-Kamiokande[16]andSNO[17]: eventsarereconstructedfromtimes
and amplitudes in an array of optical sensors of Cherenkov light from charged particles
movingfasterthanthelocalspeedoflightinthedetector. Thelargedetectorsare,how-
ever,muchlessdenselyinstrumented. ComparedtoSuper-Kwith11,000photomultiplier
tubes(PMTs)in40kilotonsofwater,IceCubehas5160PMTsofhalfthediameterina
gigatonofice. Theneutrinotelescopesareoptimizedforlargetargetvolumewithsparse
instrumentationtoobtainthegreatestsensitivityforrelativelyrareastrophysicalneutrinos
ofhighenergy.
Figure2. Artist’sdrawingoftheIceCubedetector[18].
IceCube is currently the largest neutrino detector in operation [18]. Construction at
the South Pole was completed at the end of 2010, and the detector has been running
sinceMay20,2011withitsfullcomplementof86strings,eachequippedwith60digital
opticalmodules(DOMs)atdepthsbetween1450and2450mintheice. Fig.2showsthe
completed detector, which also includes a surface air shower array of 81 pairs of tanks,
eachinstrumentedwithtwoDOMsandfullyintegratedintothedataacquisitionsystem
(DAQ) of IceCube. The IceCube DOM includes, in addition to the 25 cm PMT [19],
a programmable data acquisition board [20] that records the amplitude as a function of
timeproducedbyphotonshittingthephotocathode.Digitalsignalsaresenttothesurface
where computers build events from physically related signals in the DOMs. Times in
individualDOMsarekeyedtoasingleGPSclockonthesurfacetoanaccuracyof<3ns
acrosstheentirearrayincludingIceTop.
Antares [9] is located in the Mediterranean Sea near Toulon. It is the first neutrino
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ThomasK.Gaisser
detectortooperateintheopenocean,whichrequiresdeployinglinesofopticalmodules
fromashipandcontinuouslymonitoringthepositionsofthesensorsastheyrespondto
currentsinthewater.Antaresopticalmodulesarearrangedingroupsofthreesothatlocal
coincidencecanbeusedtoovercometherelativelyhighbackgroundofbioluminescence.
TheBaikaldetectoralsooperatesinanaturalbodyofwater,butdeploymentoccursfrom
thesolidiceonthesurfaceofthelakeinwinter.
103
cos((cid:101)) = -0.9
cos((cid:101)) = -0.7
2m) 110012 cccooosss((((cid:101)(cid:101)(cid:101)))) === ---000...531 neutrinos/year111000345 CAPsrootnrmoveppnht tyaiostmincaaolls anptehmeuotrriscinp nohese ur(itIcrCi nn4oe0su l ti(mrEininto)bse (rHg oent daal. )2006)
A (effective 100 11002
1
10-1 10-1
10-2
10-2 10-3
101 102 103 104 105 106 107 108 2 3 4 5 6 7 8 9
E(cid:105) (GeV) log10(Etrue[GeV])
Figure3. Left: Effectiveareaofanidealcubickilometerdetector. Right: Response
of IceCube (with 59 strings in 2009-10) to three different spectral shapes for muon
neutrinos[21].
The muon channel is the most favorable in terms of event rate in the TeV range and
above because the target volume is enlarged by the charged current interactions of neu-
trinos outside the detector that produce muons that go through the detector. The most
sensitiveanalysisusestheEarthasashieldagainstthedownwardbackgroundofcosmic-
ray muons by selecting horizontal and upward moving events. For energies in the TeV
rangeandabove,stochasticenergylossesbymuonsbecomeimportant,andthelightpro-
ducedincreasesinproportiontothemuonenergyaccordingtothestandardformula[6]
dE
µ = −a−bE . (1)
dX µ
The event rate in this channel is a convolution of the neutrino flux with the neutrino
crosssection,thedetectorresponseandtherangeofthemuon. AthighenergytheEarth
becomesopaquetoneutrinos, firstforverticallyupwardneutrinos(∼ 30TeV)andthen
formorehorizontalevents(∼PeV).Thustheeffectiveareaforν inthechargedcurrent
µ
channelis
A (θ,E ) = (cid:15)(θ)A(θ)P (E ,E )exp{−σ (E )N X(θ)}, (2)
eff ν ν ν µ ν ν A
whereX(θ)istheslantdepth(g/cm2)alongazenithangleθ > 90◦, N isAvogadro’s
A
number,σ istheneutrinocrosssectionand(cid:15)(θ)areconstructionefficiency.
ν
(cid:90) Eν dσ (E )
P (E ,E ) = N dE∗ ν ν R(E∗,E )
ν ν µ A µ dE∗ µ µ
Eµ µ
istheprobabilitythatamuonproducedwithenergyE∗ reachesthedetectorwithenergy
µ
E sufficient to trigger the detector. The muon range R is calculated from Eq. 1. The
µ
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leftpanelofFig.3showstheν effectiveareaforanidealcubickilometerdetectorwith
µ
a threshold E = 100 GeV. The neutrino rate is a convolution of effective area with
µ
neutrinoflux.
IntheTeVrangeandabovemuonstypicallypassthroughthedetector,soonlyafrac-
tionofthemuonenergycontributestolightinthedetector. Inthissituation,simulations
thatincorporatethephysicsofneutrinointeractions,ofmuonenergylossandoficeprop-
ertiesmustbeusedtorelatethemeasuredlighttotheenergyofthemuoninthedetector
andthencetotheenergyoftheneutrino. Thisisdoneeitherbyconvolvinganassumed
neutrinospectrumwiththesequenceν → µ →observedlight,orbyanunfoldingpro-
µ
cedure. An important feature of the analysis is that the distribution of ν energies that
µ
give rise to a given signal in the detector is different for the steep atmospheric neutrino
spectrum from what it would be for a hard spectrum of astrophysical neutrinos. This
is illustrated in right panel of Fig. 3, which shows the distributions of neutrino energy
thatcorrespondrespectivelytoatmosphericneutrinosfromdecayofpionsandkaons,to
promptatmosphericneutrinosfromcharmdecayandtoastrophysicalneutrinosassumed
tohaveanE−2 differentialenergyspectrum. Theresponsesareintegratedover2π solid
anglefrombelowthehorizonandusethefullsimulationofIC-59forA .
eff
Figure4. SkymapsshowingexposureofAntares(top)andIceCube(bottom)forat-
mosphericν frombelowthelocalhorizon.FigurefromRef.[22].
µ
3. Pointsourcesearch
Thebasicanalysisinneutrinotelescopesistosearchforpointsourcesofextraterrestrial
neutrinosusingthedirectionoftheneutrino-inducedmuonasaproxyforthedirectionof
(cid:112)
theparentneutrino. IntheTeVrange,ther.m.s. anglebetweenν andµis <ψ2 > ≈
√ µ
1.8◦/ E (TeV). ThemedianangularresolutionforAntaresis0.5◦ [23]. ForIceCube,
ν
60%oftheeventsarereconstructedtobetterthan1◦ [24]basedonanalysisofthemoon
shadowincosmic-rayinducedmuons[25].
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Figure5. Left: Sensitivity of Antares and IceCube (IC-40) for point sources of ν
µ
(lines)andlimitsforpre-selectedsources(points)asafunctionofdeclination. Figure
from Ref. [26]. Right: Color scale in angle and energy space for the neutrino point
sourcesearchinIceCube(notincludingDeepCore).
An important difference between IceCube and the Antares location at Northern mid-
latitudesisexposure,asshowninFig.4fromRef.[22].Inparticular,thecentralregionof
theGalaxyisnotvisibleinupwardgoingeventsfromtheSouthPole. Thesensitivityof
AntaresandIceCubeforpointsourcesisshownbythelinesinFig.5. Inthisplotthesen-
sitivityisshownforIceCuberunningwith40stringsinstalledin2008-2009(IC-40). The
individualpointsarelimitsonpreselectedsources,whichincludegalacticobjectsinclud-
ingsupernovaremnantsaswellaspotentialextragalacticsourcessuchasactivegalactic
nuclei(AGN).Thepoint-sourcelistforIC-40includes13galacticsourcesand30extra-
galactic sources. Among the galactic sources targeted are several supernova remnants.
Theextragalacticcandidatesaremostlyactivegalaxies.
For the Northern sky the larger IceCube detector is by far the most sensitive. Upper
limits on specific point sources of neutrinos in the Northern sky from IceCube are cur-
rently less than 10−11 cm−2s−1TeV−1. The sensitivity to point sources is approaching
the level of 10−12 cm−2s−1TeV−1 [27] at which TeV gamma rays are seen from some
blazars(e.g. Mrk401[28]).
IceCube extends the search for point sources to Southern declinations by raising the
energy threshold to reduce the high background of downward atmospheric muons. The
sensitivityandlimitsfromIC-40fromtheSouthernskyareincludedintheleftpanelof
Fig. 5. The right panel of Fig. 5 shows the energy response of IceCube with 59 strings
(IC-59)asafunctionofdeclination. ForupwardneutrinosfromtheNorthernhemisphere
thelimitsapplytoν energiesintheTeVtoPeVenergyrange. Foreventsfromabovein
µ
IceCube(Southernsky)therelevantenergyrangeisapproximatelytwoordersofmagni-
tudehigher(100TeVto100PeV).
Withdatafrom2010andlateritwillbepossibletoextendthesearchforneutrinosin
theSouthernhemispheretolowerenergybyusingtheDeepCoresubarrayofIceCube. In
thefinalconstructionyearsofIceCubeeightspeciallyequippedstringsweredeployedto
provideamoredenselyinstrumentedsub-arrayinthecenterofIceCubecalledDeepCore.
Eachofthesestringshas60DOMs,50ofwhicharebetweendepthsof2100and2450m,
whichisbelowthemaindustlayerattheSouthPole. TheDeepCoresub-arrayisdefined
to include the bottom half of the central string of IceCube as well as the lower DOMS
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HighEnergyNeutrinosfromSpace
onsixsurroundingstandardstrings. TypicalspacingbetweenstringsinDeepCoreis75
mascomparedto125mbetweenstandardstrings. ThespacingbetweenDOMsonthe8
specialstringsis7m. Oneofthemainmotivationsistoprovideaninnerfiducialvolume
surroundedbyatleastthreeringsofstandardIceCubestringsandthirtylayersofDOMs
abovetoprovideavetoagainstatmosphericmuonsandallowforTeVneutrinoastronomy
intheSouthernsky. ThisandothergoalsofDeepCorearedescribedinRef.[11].
4. Flaring,transientandgamma-rayburstsources
Acorrelationinspaceortime(orboth)withasourceobservedelectromagneticallywould
enhancethelikelihoodthattheobservedneutrinosareofastrophysicalorigin.Twostrate-
giesareusedinIceCubetopursuethisoption.Oneistosendalertsforfollow-upbyother
instruments when an apparently significant grouping of neutrinos is seen. The potential
signalcouldbetwoormoreneutrinosfromthesamedirectionwithinashorttimewindow
orasequenceofeventsfromatargetedsourcethatexhibitsflaresintheelectromagnetic
spectrum, for example. Currently alerts are sent from IceCube to ROTSE and the Palo-
marTransientFactoryandSWIFT[29]. ArrangementsforsendingalertstotheNorthern
hemispheregamma-raytelescopesMAGICandVERITASarealsoinpreparation. These
multi-messenger agreements lead to the possibility that a neutrino signal could be asso-
ciatedwithanidentifiedtypeofobject,suchasasupernovaexplosionoraflaringAGN.
LimitsobtainedfromthefollowupwithROTSE[30]aredescribedinRef.[31].
Goingtheotherdirection,IceCubecanfollowuppotentiallyinterestingastrophysical
eventssuchasnearbysupernovae[32]orflaresfromlikelycosmicaccelerators[33]. A
general search for short-term increases in rates of neutrinos from flaring sources is also
done[34]. Themostimportantresultachievedfromacatalogofeventsisthesearchfor
neutrinos associated with gamma-ray bursts (GRB) [35]. Recently data sets from two
yearsofIceCubewhilethedetectorwasstillunderconstruction(IC-40andIC-59)have
beencombinedtoobtainasignificantlimitonmodels[36]inwhichGRBsarethemain
sourceofextragalacticcosmicrays. Intotal215GRBsreportedbytheGRBCoordinated
NetworkbetweenApril5,2008andMay31,2010intheNorthernskywereincludedin
thesearch. Noneutrinowasfoundduringtheintervalsofobservedgamma-rayemission.
To set limits on the model [36], the expected neutrino spectrum was calculated for
each burst based on parameters derived [37] from features in the spectrum of the GRB.
In particular, a break in the observed photon spectrum marks the onset of photo-pion
production by accelerated protons interacting with intense radiation fields in the GRB
jet. The neutrinos come from the decay of charged pions. Given a predicted neutrino
spectrum,theexpectednumberofeventswascalculatedforeachburst.Thenormalization
ofthecalculationisprovidedbytheassumptionsthatafractionoftheacceleratedprotons
escapeandprovidetheultra-highenergycosmicrays. Inthesimplestcase,theUHECR
areinjectedasneutronsfromthesamephoto-productionprocessesinwhichtheneutrinos
are produced [38]. With this normalization, 8 neutrinos are expected in 215 GRBs and
none are observed. Fig. 6 shows the resulting limits along with the original prediction
ofWaxmanandBahcall[36]. Amodel-independentsearchwasalsocarriedout,simply
lookingforneutrinoswithin10◦inanexpandingtimewindowuptoseveralhoursaround
thetimeofeachburst. Again,nocorrelatedneutrinoswerefound.
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]
1(cid:3)10-8
r ICECUBE-40
s
1 Waxman & Bahcall
s(cid:3) IC40 Guetta et al.
2 ICECUBE-59
(cid:3)
m IC59 Guetta et al.
c COMBINED LIMIT
V IC40+59 Guetta et al.
e
G
[10-9
)
(cid:1)
E
(
(cid:1)
(cid:2)
2E(cid:1) 104 105 106 107
E [GeV]
(cid:0)
Figure 6. Limits on neutrinos from GRB with expected spectra calculated from
Ref.[37].FigureisfromRef.[29].
5. All-skysurveywithν
µ
Itisimportantalsotosearchforanexcessofastrophysicalneutrinosfromthewholeskyat
highenergyabovethesteeplyfallingbackgroundofatmosphericneutrinos.TheUniverse
istransparenttoneutrinos,sothefluxofneutrinosfromsourcesuptotheHubbleradius
maybelarge[39]. AspecificestimatebasedonthedensityofAGNs[40]isthattheevent
ratefromthewholeskyshouldbeafactor20largerthanfromasingleAGN.Limitsfrom
AMANDA[8],Antares[9]andIceCube[41]areshowninFig.7. Thecurrentlimitfrom
the40-stringversionofIceCubeisnowbelowtheoriginalWaxman-Bahcallbound[43].
The limit is obtained by fitting the distribution of light in the detector from upward
movingmuonstoparametersthatdescribeanassumedneutrinospectrumconsistingof
• “conventional”atmosphericmuonneutrinosfromdecayofchargedpionsandkaons;
• “prompt” atmospheric neutrinos, mainly from decay of charmed hadrons with a
spectralshapetakenfromRef.[44];and
• anassumedastrophysicalfluxwithahardE−2differentialenergyspectrum.
The atmospheric neutrino flux used in this analysis [41] is a simple power-law extrapo-
lation of the calculation of Ref. [42]. Its normalization is treated as a free parameter in
fittingthedatainRef.[41], whichisshownasaslightlycurvedbandthatextendsfrom
0.33 to 84 TeV in Fig. 7. The other experimental results on the high-energy flux of at-
mosphericν +ν¯ inFig.7arefromAMANDA[45,46]andIceCube-40[47]. Allthe
µ µ
atmosphericneutrinospectrashownhereareaveragedoverangle. Theunfoldinganaly-
sis of Ref. [47] extends to E ≈ 400 TeV. The integral limit on astrophysical neutrinos
ν
shownforIceCube-40inFig.7assumesahard,E−2spectrum.Forthisreason,thebound
appliesatmuchhigherneutrinoenergies(35TeVto7PeV)thantheobservedspectrum
ofatmosphericneutrinos.
AsdiscussedinRef.[48],oneofthedifficultiesofsearchingforanastrophysicalcon-
tributionattheleveloftheWaxman-Bahcalllimitisthattheatmosphericbackgroundin
the relevant energy range above 100 TeV is not well known. Standard calculations of
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HighEnergyNeutrinosfromSpace
1
-r
s
2-1 s10-3 1 12)) AAMMAANNDDAA--IIII nAmtm uonsfoplhdeinrigc (n2m0 0103-8270 0d3) BHaorntdoal ++ NEanubmerogv MRiQnPM ((89
-m10-4 3) AMANDA-II nm 807 d Waxman Bahcall Prompt GRB(10
c
V 4) ANTARES nm 07-09 Blazars Stecker (11
Ge10-5 5 5) IC40 Atmospheric nm Waxman Bahcall 1998 x 1/2 (12
6) IC40 Atmo. nm Unfolding Becker AGN (13
dEn10-6 7) IC40 nm 375.5 d Mannheim AGNs (14
/Nn 14 6 2
d10-7 3 13
2En 4
12
10-8 7
11
10-9 10 9 8
2 3 4 5 6 7 8 9 10
log E [GeV]
n
10
Figure7. Horizontal lines show limits on an E−2 spectrum of astrophysical muon
neutrinosfromAMANDA-II[8],Antares[9]andIceCube[41]. Thelimitsareshown
alongwithmeasurementsofthefluxofatmosphericmuonneutrinosandanti-neutrinos.
TheplotisfromRef.[41]wherefullreferencesaregiven.
conventionalatmosphericneutrinos[42,49]extendonlyto10TeV.Inaddition,thelevel
ofpromptneutrinos,whichareexpectedtobecomeimportantsomewhereabove100TeV
is highly uncertain. The current IceCube limit appears already to rule out the highest
predictionforcharm[50].
6. Implications
The Waxman-Bahcall bound is an upper limit to the intensity of neutrinos which holds
iftheneutrinosareproducedinthesamesourcesthatproducetheextra-galacticcosmic
rays. Forthistooccur,theacceleratedprotonsmustbeabletoescapefromthesources,
eitherdirectlyorasneutronscreatedbyp + γ →∆+ →n + π+. ForGRB,escape(at
leastoftheneutrons)islikelybecauseoftherapidexpansion,asdiscussedinRef.[38].
InthecaseofAGNs,WaxmanandBahcall[43]showthattheexistenceofTeVphotons
from blazars guarantees that the density of electromagnetic radiation is such that EeV
nucleonscanindeedescape, sotheboundappliestoAGNsaswellasGRBs. Ifprotons
aretrappedintheaccelerationregionbytheturbulentmagneticfieldsneededtomakethe
accelerationprocesswork,thentheboundmayberelatedtoanestimateoftheexpected
level of neutrino production. In this scenario, the high energy protons lose energy by
photo-pionproduction,whiletheneutronsescapeanddecaytoprotonstobecomeultra-
highenergycosmicrays(UHECR).Theneutrinosfromthepiondecayarethenrelatedby
kinematicstotheUHECR.AnotherconsequenceisthattheUHECRwouldbeprotons.
This scenario could be realized in jets of GRB and of AGN if acceleration occurs in
internal shocks in the jets. As IceCube limits become increasingly strong, this class of
models is constrained. A generic alternative could be that the UHECR are accelerated
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ThomasK.Gaisser
outsidethejets,forexampleattheterminationshocksofAGNs.Inthiscasethecomposi-
tionoftheextragalacticcosmicrayswoulddependontheambientmedium,andthelevel
of neutrino production would be contingent on the density of the surrounding medium
andcorrespondinglylow.
Figure8. Collectionoflimitsoncosmogenicandultra-highenergyneutrinos.Theplot
isbasedonRef.[53]wherefullreferencesaregiven. Theextracurveincludedhere,
labeledIC-40UHE(preliminary)isfromRef.[54].
7. Cosmogenicneutrinos
Independentofthelevelofneutrinoproductionincosmicsources,therewillbeproduc-
tionofneutrinosfrom
p+γ →∆+ →n+π+ →ν (→p+π0 →γγ)
CMB µ
providedonlythatthereareprotonsabovethethresholdof∼ 5×1019 eV fromsources
distributedthroughouttheUniverse. Photonsareproduceintheneutralpionchannelof
the same process. These photons would undergo cascading and contribute to the back-
groundofdiffusegamma-raysmeasuredbytheFermiSatellite[51],whichleadstoanup-
perlimitonthespectrumofcosmogenicneutrinos.Thislimitisnowatthelevelwhereno
morethanapproximatelyoneeventperyearwouldbeexpectedinthefullIceCube[52].
LimitsfromIC-40[53]andotherdetectorsarecollectedinFig.8.Thelimitsareforthe
sumofthreeflavorsassumingequalcontributionsfromeachflavor. Bothdifferentialand
integrallimitsareshown. DifferentiallimitsareobtainedbyassuminganE−2 spectrum
over a logarithmic bin of energy and calculating the limit for the each bin. The shapes
of the curves then indicate the energy response of each detector. The limits for a full
10