Real-Time Supernova Neutrino Burst Monitor at Super-Kamiokande

0.5 MB·

by  K. Abe

Real-Time Supernova Neutrino Burst Monitor at
Super-Kamiokande
K.Abea,ac,Y.Hagaa,Y.Hayatoa,ac,M.Ikedaa,ac,K.Iyogia,J.Kamedaa,ac,Y.Kishimotoa,ac,
M.Miuraa,ac,S.Moriyamaa,ac,M.Nakahataa,ac,Y.Nakanoa,S.Nakayamaa,ac,H.Sekiyaa,ac,
M.Shiozawaa,ac,Y.Suzukia,ac,A.Takedaa,ac,H.Tanakaa,ac,T.Tomuraa,ac,K.Uenoa,
R.A.Wendella,ac,T.Yokozawaa,T.Irvineb,T.Kajitab,ac,I.Kametanib,K.Kaneyukib,ac,1,
K.P.Leeb,T.McLachlanb,Y.Nishimurab,E.Richardb,K.Okumurab,ac,L.Labargac,
6
1 P.Fernandezc,S.Berkmane,H.A.Tanakae,S.Tobayamae,J.Gustafsond,E.Kearnsd,ac,
0 J.L.Raafd,J.L.Stoned,ac,L.R.Sulakd,M. Goldhaberf,1,G.Carminatig,W.R.Kroppg,
2 S.Mineg,P.Weatherlyg,A.Renshawg,M.B.Smyg,ac,H.W.Sobelg,ac,V.Takhistovg,

r K.S.Ganezerh,B.L.Hartfielh,J.Hillh,W.E.Keigh,N.Hongi,J.Y.Kimi,I.T.Limi,T.Akirij,
p
A.Himmelj,K.Scholbergj,ac,C.W.Walterj,ac,T.Wongjiradj,T.Ishizukak,S.Tasakal,
A
J.S.Jangm,J.G.Learnedn,S.Matsunon,S.N.Smithn,T.Hasegawao,T.Ishidao,T.Ishiio,

1 T.Kobayashio,T.Nakadairao,K.Nakamurao,ac,Y.Oyamao,K.Sakashitao,T.Sekiguchio,
1 T.Tsukamotoo,A.T.Suzukip,Y.Takeuchip,ac,C.Bronnerq,S.Hirotaq,K.Huangq,K.Iekiq,
T.Kikawaq,A.Minaminoq,A.Murakamiq,T.Nakayaq,ac,K.Suzukiq,S.Takahashiq,
]
E K.Tateishiq,Y.Fukudar,K.Chois,Y.Itows,G.Mitsukas,P.Mijakowskiah,J.Hignightt,
H J.Imbert,C.K.Jungt,C.Yanagisawat,M.J.Wilkingt,H.Ishinou,∗,A.Kibayashiu,
Y.Koshiou,ac,T.Moriu,M.Sakudau,R.Yamaguchiu,T.Yanou,Y.Kunov,R.Tacikw,ae,
.
h S.B.Kimx,H.Okazaway,Y.Choiz,K.Nishijimaaa,M.Koshibaab,Y.Sudaab,Y.Totsukaab,1,
p
M.Yokoyamaab,ac,K.Martensac,Ll.Martiac,M.R.Vaginsac,g,J.F.Martinad,P.dePerioad,
-
o A.Konakaae,S.Chenaf,Y.Zhangaf,K.Connollyag,R.J.Wilkesag
r
t (TheSuper-KamiokandeCollaboration)
s
a
[ aKamiokaObservatory,InstituteforCosmicRayResearch,UniversityofTokyo,Kamioka,Gifu506-1205,Japan
bResearchCenterforCosmicNeutrinos,InstituteforCosmicRayResearch,UniversityofTokyo,Kashiwa,Chiba

2 277-8582,Japan
v cDepartmentofTheoreticalPhysics,UniversityAutonomaMadrid,28049Madrid,Spain
8 dDepartmentofPhysics,BostonUniversity,Boston,MA02215,USA
7 eDepartmentofPhysicsandAstronomy,UniversityofBritishColumbia,Vancouver,BC,V6T1Z4,Canada
7 fPhysicsDepartment,BrookhavenNationalLaboratory,Upton,NY11973,USA
4 gDepartmentofPhysicsandAstronomy,UniversityofCalifornia,Irvine,Irvine,CA92697-4575,USA
0 hDepartmentofPhysics,CaliforniaStateUniversity,DominguezHills,Carson,CA90747,USA
. iDepartmentofPhysics,ChonnamNationalUniversity,Kwangju500-757,Korea
1 jDepartmentofPhysics,DukeUniversity,DurhamNC27708,USA
0 kJuniorCollege,FukuokaInstituteofTechnology,Fukuoka,Fukuoka811-0295,Japan
6 lDepartmentofPhysics,GifuUniversity,Gifu,Gifu501-1193,Japan
1 mGISTCollege,GwangjuInstituteofScienceandTechnology,Gwangju500-712,Korea
: nDepartmentofPhysicsandAstronomy,UniversityofHawaii,Honolulu,HI96822,USA
v oHighEnergyAcceleratorResearchOrganization(KEK),Tsukuba,Ibaraki305-0801,Japan
Xi pDepartmentofPhysics,KobeUniversity,Kobe,Hyogo657-8501,Japan
qDepartmentofPhysics,KyotoUniversity,Kyoto,Kyoto606-8502,Japan
r rDepartmentofPhysics,MiyagiUniversityofEducation,Sendai,Miyagi980-0845,Japan
a
sSolarTerrestrialEnvironmentLaboratory,NagoyaUniversity,Nagoya,Aichi464-8602,Japan
tDepartmentofPhysicsandAstronomy,StateUniversityofNewYorkatStonyBrook,NY11794-3800,USA
uDepartmentofPhysics,OkayamaUniversity,Okayama,Okayama700-8530,Japan
vDepartmentofPhysics,OsakaUniversity,Toyonaka,Osaka560-0043,Japan
wDepartmentofPhysics,UniversityofRegina,3737WascanaParkway,Regina,SK,S4SOA2,Canada
xDepartmentofPhysics,SeoulNationalUniversity,Seoul151-742,Korea
yDepartmentofInformaticsinSocialWelfare,ShizuokaUniversityofWelfare,Yaizu,Shizuoka,425-8611,Japan
1
zDepartmentofPhysics,SungkyunkwanUniversity,Suwon440-746,Korea
aaDepartmentofPhysics,TokaiUniversity,Hiratsuka,Kanagawa259-1292,Japan
abTheUniversityofTokyo,Bunkyo,Tokyo113-0033,Japan
acKavliInstituteforthePhysicsandMathematicsoftheUniverse(WPI),TheUniversityofTokyoInstitutesfor
AdvancedStudy,UniversityofTokyo,Kashiwa,Chiba277-8583,Japan
adDepartmentofPhysics,UniversityofTorront,60St.,Torront,Ontario,M5S1A7,Canada
aeTRIUMF,4004WesbrookMall,Vancouver,BC,V6T2A3,Canada
afDepartmentofEngineeringPhysics,TsinghuaUniversity,Beijing,100084,China
agDepartmentofPhysics,UniversityofWashington,Seattle,WA98195-1560,USA
ahNationalCentreForNuclearResearch,00-681Warsaw,Poland
Abstract
Wepresentareal-timesupernovaneutrinoburstmonitoratSuper-Kamiokande(SK).Detecting
supernovaexplosionsbyneutrinosinrealtimeiscrucialforgivingaclearpictureoftheexplosion
mechanism. Since the neutrinos are expected to come earlier than light, a fast broadcasting of
thedetectionmaygiveastronomersachancetomakeelectromagneticradiationobservationsof
the explosions right at the onset. The role of the monitor includes a fast announcement of the
neutrinoburstdetectiontotheworldandadeterminationofthesupernovadirection. Wepresent
the online neutrino burst detection system and studies of the direction determination accuracy
basedonsimulationsatSK.
Keywords: Supernova,Neutrinos,Super-Kamiokande
1. Introduction
ThedetectionofneutrinosfromSN1987Aopenedaneweraofneutrinoastronomy[1]. Al-
thoughthenumberofthedetectedneutrinoevents[2]wassmall, significantinformationabout
thesupernova(SN)explosionandneutrinopropertieswasobtained[3]. Thecurrentgeneration
ofdetectorsarewaitingforthenextSNneutrinobursttoaccumulateeventstatisticsmuchlarger
thanthoseofSN1987A.
The SN burst neutrinos arrive at the Earth earlier than the electromagnetic radiation, since
the neutrinos generated at the core of the explosion and emitted from the surface of the neu-
trinospheretravelatnearlythespeedoflight,whiletheshockwavespropagatingtotheoutside
with velocity much slower than the neutrino velocity result in the emission of electromagnetic
radiation[4]. Thedelaymaydependonthestructureoftheenvelopeofthecoreaswellasthe
surrounding stellar environment, and is expected to range between tens of minutes and tens of
hours [5]. Therefore, the detection of the neutrino burst can generate a warning able to allow
theastronomerstoobservetheradiationfromtheonsetoftheexplosion. Suchwarningsystems
havebeendevelopedbyseveralneutrinoobservatories[6][7]aswellasbythesupernovaearly
warningsystem(SNEWS)[8].
∗CorrespondingAuthor,HirokazuIshino,DepartmentofPhysics,OkayamaUniversity,[email protected]
1Deceased.
PreprintsubmittedtoAstroparticlePhysics April13,2016
It is also important to determine the SN direction using the neutrino signal: the direction
information can guide optical instruments toward the SN explosion and enable observation of
the onset of radiation. Among the neutrino detectors operating at present, Super-Kamiokande
(SK) is the only detector able to determine the SN direction using neutrino events. We have
developedaSNdirectiondeterminationmethodbyapplyingamaximumlikelihoodfit.
SK is the world’s largest water Cherenkov detector located 1,000 m underground, inside a
mountain in Kamioka, Gifu, Japan. The detector consists of 50,000 tons of ultra-pure water
andabout13,000photomultipliertubes(PMTs). Basedontheinformationoftheyieldsandthe
arrival timing of Cherenkov photons for individual PMTs as well as the PMT locations, SK is
abletomeasuretheposition,directionandenergyofaneutrinoeventinrealtime. Detailsofthe
SKdetectoranditsperformancearedescribedin[9]. In2008,SKupgradeditsreadoutsystem.
The system has improved the data processing speed significantly, lowering the trigger energy
thresholdanddeadtimefortheSNburstevents[10].
WewilldescribetheSNneutrinoburstmonitoratSK.InSection2, wewilldescribedetails
ofthemonitorsystemanditsperformance. WefirstdescribeSNmodelsusedinthisreportfor
performanceevaluations. AMonte-Carlo(MC)simulationwiththeSNmodelsisutilizedforthe
estimationofthedetectionefficiency. WewillexplaintheselectioncriteriatodiscriminateSN
bursts and the main background in SK: radioactive decays caused by cosmic ray muon spalla-
tion[11]. InSection3,wewilldescribeamethodtoreconstructtheSNdirectionandstudiesof
itsperformance.
2. Realtimesupernovaneutrinoburstmonitor
2.1. Supernovamodels
We first describe the SN models we use in this report. We employ two models for the SN
neutrino burst: the Wilson model [12] and the Nakazato model [13]. For the Nakazato model,
wechoosetwoparametersets: M = 20, t = 200msecandZ = 0.02(NK1), and M = 13,
revive
t = 100 msec and Z = 0.004 (NK2), where M is the progenitor mass in units of the solar
revive
mass,t istheshockrevivaltimeandZisthemetallicity,respectively.Wechoosethefirstone
revive
fortheSN1987Aprogenitormass,whichisabout20timesthesolarmass. Themodelwiththe
latterparametersgivesthesmallestneutrinofluxesintheNakazatomodel. Bothmodelsprovide
timedependencesofneutrinoluminositiesandenergyspectraforν , ν¯ andν , for18seconds
e e x
(20seconds)fortheWilson(NK)model,whereν referstothemuonandtautypesofneutrinos
x
andanti-neutrinos. Theanti-electronneutrinofluencesofthemodelsofWilson,NK1andNK2
are16.0,9.8and9.4,respectively,inunitsof1010/cm2intheenergyrangeof7to50MeVatthe
distanceof10kpcwithoutneutrinooscillation. Wealsotakeintoaccountneutrinooscillations
based on [14]. We assume P = 0 in the parameterization of [14], which implies adiabatic
H
transitionsbetweenelectronandtau(anti-)neutrinosduetosin22θ = 0.095±0.010[15]. In
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this report, we do not take into account collective effects. We use the cross sections [16] for
theinversebetadecays,[17][18]forthechargedcurrentinteractionstooxygen,and[19]forthe
electronelasticscatterings.
Monte-Carlo simulation samples are generated for the three SN models and three neutrino
oscillationhypothesesbymakinguseofthefullSKdetectorMCsimulatorbasedonGeant3in
theSKinnerdetectorvolume(32.5-kton)intheenergyrangeof3to60MeVtakingintoaccount
thetriggerthresholdcurve.Thecalibrationofthedetectoranditssimulationaredescribedin[20].
WeapplytheSKstandardreconstructionprogramtothegeneratedMCeventstoobtainthevertex
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Table1:NumbersofexpectedeventsatSKinthe22.5-ktonfiducialvolumewiththe7MeVtotalenergythresholdfor
aSNburstwithadistanceof10kpc. WeestimatedthesenumbersusingSKMC:wegenerate3,000ensemblesofthe
MCsamples,reconstructedtheeventswiththeSKstandardreconstructiontool,appliedtheselectioncriteria,andthen
calculatedtheaveragenumbers.
Wilson NK1 NK2
noosc. NH IH noosc. NH IH noosc. NH IH
ν¯ +p→e++n 4923 5667 7587 2076 2399 2745 1878 2252 2652
e
ν +e− →ν +e− 74 130 114 43 56 56 39 54 54
e e
ν¯ +e− →ν¯ +e− 25 29 37 10 12 14 9 11 13
e e
ν +e− →ν +e− 41 33 34 17 19 18 17 17 17
x x
ν¯ +e− →ν¯ +e− 34 33 29 14 14 14 13 13 14
x x
ν +16O→e−+X 8 662 479 22 78 74 16 72 68
e
ν¯ +16O→e++X 64 196 531 27 48 70 20 41 64
e
total 5169 6750 8811 2209 2626 2991 1992 2460 2882
position,thedirectionandthetotalenergyofeachevent. IntheSNmonitor,weuseeventswith
total energy greater than 7 MeV in the 22.5-kton fiducial volume, where the fiducial volume
is defined as the volume whose surface is located 2 m inside from the surface of the SK inner
detectorvolume.
WegenerateMCsamplesforthethreeSNmodelsforthethreeneutrinooscillationhypotheses:
nooscillation,normalhierarchy(NH)andinvertedhierarchy(IH).Table 1showstheexpected
numbersofeventsofthethreeSNmodelsatSKinthe22.5-ktonfiducialvolumewiththetotal
energy threshold of 7 MeV, obtained by averaging the 3,000 MC ensembles at the distance of
10 kpc. Figure 1 shows the reconstructed energy distributions at SK for the Wilson and NK1
models with and without neutrino oscillations to display the effect of the neutrino oscillations.
Figure 1 also shows the energy spectrum of the spallation events found in the silent warnings
describedinSec.2.2.
2.2. Themonitorsystem
In this section, we will describe details of the SN neutrino burst monitor system. Figure 2
showsa flowdiagramofthe system. TheSKdatacollected bythedata acquisitionsystemare
senttotheeventbuilder. Attheeventbuilder,theeventdataarepackedandstoredinadatafile
which we call a sub-run file. Each sub-run file contains about one minute of event data. The
sub-runfilesaresenttoboththeofflineprocessandtheSNburstmonitor. Intheofflineprocess,
thedatafilesareconvertedtoanofflinedataformatthatisusedforvariousphysicsanalysesand
detectorcalibrations.TheSNmonitorsystemisrunningonasinglecomputeronwhichacontrol
processoperatingcontinuouslyhandlesalltheprocessesandthedatafiles.
For each sub-run file sent to the SN monitor, two processes are automatically executed by
the control process: a reformat process (the first process) and an event reconstruction process
(the second process). The reformat process converts the online data format to the offline data
format. Using the offline format data, the event reconstruction process reconstructs the vertex
position, directionandenergyforeachevent. Ittakesabouttwominutestofinishthereformat
and event reconstruction for one sub-run file.Events with total energy greater than 7 MeV and
vertex position within the 22.5-kton fiducial volume in SK are selected. We remove cosmic
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raymuonsandtheirsubsequentdecayelectronevents.Afterthereconstructionofeachselected
event,a20-secondtimewindowisopenedbackwardsintimefromtheevent,andthenumberof
selected events in the window (N ) is counted. If there is a sub-run file boundary, the time
cluster
windowextendstotheprevioussub-runfile.
WealsocomputeavariableDthatcharacterizesthevertexdistribution. ThevariableDidenti-
fiesthedimensionofthevertexdistributionandisanintegernumberfrom0to3,corresponding
topoint-,line-,plane-andvolume-likedistributions,respectively. ThevariableDisdetermined
bycomparingχ2valuesobtainedfromthelengthsofthemajorandminoraxesthatcorrespondto
theeigenvaluesofacorrelationmatrixofthevertexdistribution.Thecorrelationmatrixisa3×3
matrixwhoseelementsaredefinedas(cid:104)(x −(cid:104)x(cid:105))(x −(cid:104)x (cid:105))(cid:105),wherei, j=1, 2, 3identifythever-
i i j j
texpositionaxesand(cid:104)x(cid:105)isthemeanvalueofavariablex.Weconstructaχ2 =(cid:80)Ncluster|d(cid:126) −d(cid:126)((cid:126)s)|2,
n=1 n
whered(cid:126) isthen−theventvertexpositionandd(cid:126)((cid:126)s)isapositionclosesttod(cid:126) oneitherapoint,a
n n
lineoraplanewithparameters(cid:126)sthatdeterminethegeometryofthethreecases. Thethreeeigen-
valuesλ (i = 1, 2, 3,andλ ≤ λ ≤ λ )areusedtoconstructtheminimumχ2 valuesthatare
i 1 2 3
(λ +λ +λ )/3,(λ +λ )/2andλ ,computedbyassumingthevertexdistributionispoint-,line-
1 2 3 1 2 1
andplane-like,respectively,withtheconditionof∂χ2/∂(cid:126)s = 0. Thecomparisonoftheχ2 values
todetermineaDvalueistunedusingMCsimulationssothatthecalculatedDvaluereproduces
theinputone. IncaseofarealSNburst,thevertexdistributionshouldbeuniforminSK,andwe
wouldhaveD=3,dependingonthenumberofburstevents,whichisconfirmedbyasimulation.
Incontrast,forthecaseofabackgroundburstmainlyoriginatingfromspallationevents,thever-
texpositionsdistributealongtheparentmuontracks,andwewouldhave D = 2,1or0,where
the spallation events are the radioactivities created by both high-energy cosmic ray muons and
by constituents of the resulting hadronic showers. When the process finds N ≥ 60 events
cluster
and D = 3, it generates a prompt SN burst warning which initiates phone-callings and emails
senttoexpertsintheSKcollaborationwithinafewminutesaftertheSNburstoccurs. Wecall
suchawarninga“golden”warning. Subsequenttoagoldenwarning, theexpertsstartameet-
ing in order to make a world-wide announcement within one hour. The threshold of N is
cluster
determinedsothatwewouldhave100%SNdetectionefficiencyattheLargeMagellanicCloud
(LMC)assumingthethreeSNmodelsdescribedinSection2.1.
The third process in Fig. 2 combines all the sub-run data and determines the SN direction
by a fit. All the SN burst event information is summarized and sent to the experts by e-mail,
whichisalsousedastheinputtothediscussions.Followingthesediscussionstheannouncement
containingtheinformationaboutthenumberofobservedneutrinos,thebursttimeduration,the
universaltimethebursthappensandtheestimateddirectionoftheSNintheequatorialcoordinate
systemisbroadcasttotheATEL[21],GCN[22],IAU-CBAT[23]andSNEWS[8].Theuniversal
timeisdeterminedusing1pps(pulsepersecond)signalsfromtheglobalpositioningsystemand
a local time clock system consisting of a commercial rubidium clock [24]. No golden prompt
warninghasbeensentsofar.
WhentheSNbursthaslessthan60events,thegoldenwarningwillnotbegenerated. Instead
we set another threshold. The threshold for generating the warning is determined so that the
backgrounds are suppressed: we set the threshold of N ≥ 25 and require D = 3. The
cluster
warninggeneratedwiththisconditioniscalledanormalwarning. Thenormalwarningissentto
theexpertsonlybye-mail, withoutphone-calls, andtoSNEWS.Convenersamongtheexperts
check the event cluster found by this warning and make a decision about whether to have a
meetingfortheannouncement.Thenormalwarningthresholdissetsothatwewouldhave100%
SN detection efficiency at the Small Magellanic Cloud (SMC) assuming the three SN models.
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The details of the detection efficiency will be described in Section 2.3. The reason to provide
thenormalwarningistoavoidanyfakewarningscausedbyunexpectedsoftwareandhardware
troubles. Wehavehadnonormalwarningsofar.
Insummary,theSNmonitorreformatsthedataanddeterminesthevertexposition,direction,
and energy of events within a few minutes of the data being collected. It then searches for
burstsofevents-aclusteroccurringwithin20seconds-withenergiesabove7MeVandwhose
verticesfallwithinSK’s22.5-ktonfiducialvolume. Withinanhourofawarningbeingissued,
theexpertsgatherandholdameetingtodeterminetheappropriatepublicannouncementtomake,
ifany,basedonthequalityandnatureofthedetectedburst.
Wealsoprovidealowerthresholdsuchthatwerequiremorethan13eventsin10seconds. We
call a warning generated with this condition a “silent” warning. The conditions were tuned so
thatwewouldhaveafewwarningsperdayfromspallationevents. Thesilentwarningsaresent
toonlyafewexpertsofthemonitorsystemoperationanddetectorcondition,andarenotusedas
thefastalertforaSNburst.
2.3. PerformancestudyoftheSNburstmonitorwithsimulations
Figure 3 shows the minimum χ2 distributions for the three geometrical assumptions and D
distributionsforSNMCandspallationdatatriggeredbythesilentwarnings.Thespallationevent
clusterisidentifiedfromthevertex,energyandtimedistributions,i.e.,thevertexdistributionis
concentratedaroundtheparentmuontrack,theenergiesoftheeventshavethetypicalspallation
energyspectrumupto20MeV,andthetimedistributionisanexponentialdecayconsistentwith
thelifetimesofthespallationproducts. Inthefigure,wegenerateMCsimulationsamplesinthe
rangeof60≤ N ≤100uniformly,andplotthedistributionsforthesamples.Theprobability
cluster
tohave D ≤ 2forSNMCwiththe N rangeis8×10−4. NoSNMCsamplehaving D ≤ 2
cluster
isfoundfor930,000sampleswith100 < N < 1,000. Foranormalwarningcondition,i.e.,
cluster
25 ≤ N < 60,theprobabilitytohaveD ≤ 2is1.3%. ThisdemonstratesthatthevariableD
cluster
candiscriminatebetweentheSN-likeclustersandspallationbackgroundclusters.
Figure4showstheSNdetectionefficiencyasafunctionofadistancetoaSNforthenormal
and golden warnings for the three SN models without neutrino oscillation and with neutrino
oscillationsfornormalandinvertedmasshierarchyhypotheses. Itisfoundthatthesystemhas
100% detection efficiency up to the LMC located at 50 kpc away for all three models for the
golden warning with the three hypotheses. For the SNe at the SMC, about 64 kpc away, the
efficiencydependsonthehypothesesfortheNakazatomodel,andis100%fortheWilsonmodel.
Thenormalwarninghasalmost100%detectionefficiencyforthethreemodels. Theefficiency
is basically determined by the number of inverse beta decay events. The difference between
detection efficiencies among the three hypotheses of the neutrino oscillations is caused by the
difference between the ν¯ energy spectra. The average energy of ν¯ is smaller than that of ν¯
e e x
when those neutrinos are emitted from the neutrinosphere. With neutrino oscillations, ν¯ are
x
convertedtoν¯ andthereforetheaverageenergyofν¯ atSKincreases,resultinginahigherevent
e e
rate of the inverse beta decays. Due to this effect, the detection efficiency of SNe at the SMC
increasesforthecaseofneutrinooscillations.
2.4. OperationoftheSNburstmonitor
WehaveoperatedtheSNburstmonitorsystemforabout20years,sincethebeginningofSK
data-taking in 1996. The SN burst selection criteria and operation scheme have been changed,
updated,andimprovedthroughoutthisperiod. TheSNmonitorsystemschemedescribedinthis
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reportcameintoserviceinAprilof2013.Beforethattime,earlierversionsofthemonitorsystem
hadbeenrunningasoneoftheofflineprocesses.
InFig. 5(a),weshowthesilentwarningratesper24hoursasafunctionoftheelapseddays
fromJan.1st,2010.Theratehastrendsasaconsequenceof–andwhichtrack–variationsofthe
watertransparencyinSK.TheenergyscaleusedintheenergyreconstructionprogramintheSN
monitorprocesshasbeencontinuallyadjustedtocompensateforthesetransparencyfluctuations.
Despitethesefluctuations,thewarningratehasbeenrelativelystableoverthelastsixyears,with
anaveragerateof2.4warningsper24hours.
Theexpectednumberofaccidentalbackgroundeventssatisfyingtheeventselectionis0.121
events per 10 seconds with a root mean square of 0.007 events. We estimate this by counting
thenumberofeventsintheSKfiducialvolumewithatotalenergygreaterthan7MeVforone
day,andscalethisnumbertoarateper10seconds. Figure5(b)showstheestimatedaveraged
backgroundeventrateforarecentperiodof434days. Thebackgroundeventsareconsideredto
bespallationproducts,sincethereshouldbenegligiblecontaminationfromknownradioactivities
otherthanspallationproductsgiventheappliedenergythreshold.
Figure 5 (c) shows the data processing time distribution for the silent warnings found. The
average time to finish the processing is about 170 seconds; fluctuations are caused by the re-
construction process and the condition of the network through which the data sample files are
copied from the SK data acquisition system. The offline SN monitor that had run before April
2013 took about five minutes to finish the reformat and reconstruction processes, as the offline
reconstruction program was tuned for physics analysis andcalibration. We have optimized the
reconstructionprogramfortheonlineSNmonitortoincreasetheprocessingspeedwithoutde-
gradingitsperformance.
Figure5(d)showstheaveragedmonthlydutycycleoftheSNmonitorsystemoverarecent34-
monthperiod;theSNmonitoroperateswithadutycycleofabout97%.Themonitorsearchesfor
SNeventburstsduringnormalSKrunning,butitdoesnotoperateduringSKdetectorcalibration
runs, particularly during those calibration runs employing artificial sources that intentionally
generate event bursts. Most of the 3% loss of the SN monitor duty cycle comes from planned
calibration. NotethatevenwhentheSNmonitorisoff,SKstillhasanon-realtimecapabilityto
detect a SN burst during these calibration runs. This is achieved via dedicated offline analyses
whichremovelikelysourceeventsbasedontheirvertexpositionsandeventtimings.
We use the spallation events found as silent warnings to estimate the false alarm rate by as-
suming constant rate Poisson processes rather than generating simulation samples of the back-
grounds.Wecombinemultiplesilentwarningsrandomlyandformacombinedclustertoestimate
aprobabilityofhavingagolden(normal)warning. Using2,551silentwarnings, wecombined
twoofthemforallcombinationsoftwospallationbursts,toform C = 3,252,525patterns,
2551 2
and estimate the probability for the combined burst to pass the criteria for a golden (normal)
warningtobe0(4.3·10−6). Forthreecombinationswith C patterns,theprobabilityises-
2551 3
timatedtobe4.1·10−5(1.9·10−4)foragolden(normal)warning. Onesilentwarninghappens
every10hours. Theprobabilitytohavetwo(three)spallationclusterscoincidentwithin20sec
is5.6·10−4(3.1·10−7). Thereforetheprobabilitytohaveagolden(normal)warningduetoacci-
dentallycoincidentspallationburstsis3.1·10−7×4.1·10−5 =1.3·10−11(5.6·10−4×4.3·10−6 =
2.4·10−9).Thefalsealarmratesarecalculatedtobeonceper9.0·107yearsforagoldenwarning
andonceper4.7·105yearsforanormalwarning.
The processes in the SN burst monitor are kept under observation by a web-based monitor
runningonadedicatedPC.Anyproblemsaredisplayedonthewebmonitorimmediatelyafter
theyarefound,andtheSKshifttakersarenotifiedbyvisibleandaudioalerts.
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3. DeterminationoftheSNdirection
The determinationof theSN directionis crucialsince thedirection information providedby
neutrinosisusefulforastronomerstoobservetheSNexplosionprocessfromtheonsetviaelec-
tromagnetic waves. At present, SK is the only operating experiment with sufficient detector
mass to determine the neutrino direction from elastic scattering events which preserve the SN
direction. Though the inverse beta decay events also have a correlation with the SN direction,
theelasticscatteringeventsmainlydominatethedirectiondeterminationpower. Astudyofthe
determinationoftheSNdirectionusingneutrinoswasperformedby[25][18]. Here,wepresent
amethodwehavedeveloped. WewillexplainthealgorithmtodeterminetheSNdirection,and
thenwillshowitsperformanceobtainedusingSKMC.
3.1. Algorithm
WedeterminetheSNdirectionbasedonamaximumlikelihoodmethod.Alikelihoodfunction
L fori-theventisdefinedas:
i (cid:88)
L = N p (E,dˆ;dˆ ), (1)
i rk r i i SN
r
where the index r indicates one of the four neutrino interaction channels: inverse beta decay
(ν¯ p),electronelasticscatteringofanti-electronneutrino(ν¯ e),otherelasticscatterings(νe)and
e e
thecharged-currentinteractionsonoxygen(ν16O).Theindexkindicatestheenergybin,running
from 1 to 5 for the energy ranges of 7 < E < 10, 10 < E < 15, 15 < E < 22, 22 < E < 35
and 35 < E < 50, respectively, where E is the measured total electron energy in MeV. N is
rk
thenumberofeventsoftheinteractionrinthek-thenergybin. E isthei-theventtotalelectron
i
energy, which uniquely determines the index k, dˆ is the i-th event direction and dˆ is the SN
i SN
direction we want to determine. The p (E,dˆ;dˆ ) function is a probability density function
r i i SN
(PDF)forinteractionrasafunctionoftheenergyE andaninner-productofdˆ ·dˆ =cosθ .
i i SN SN
ThePDFisdeterminedusingSKMC.Thenumberofν¯ elasticscatteringeventscanbeinferred
e
from the number of inverse beta decay events with the relation N = (cid:80) A N , where
ν¯ee,k m km ν¯ep,m
thematrix A iscalculatedfromaratioofthetotalcrosssectionsofthetwointeractions. We
km
determine PDFs for elastic scatterings with the following procedure. We divide the SN MC
sampleelasticscatteringeventsgeneratedwiththeWilsonmodelintoone-MeVbinsfrom7to
35 MeV. For energies greater than 35 MeV, we combined all events into one bin. Then we fit
the cosθ distribution with the known SN direction in MC using a model function that is the
SN
superpositionoffourexponentialfunctionsandcontainingeightparametersforeachenergybin.
Foragivenenergyvalue,wecomputetheeightparametervaluesbyinterpolatingtheparameter
values of neighboring two energy bins and applying those to the model function to obtain the
PDFvalue. AsimilarprocedureisappliedtothePDFsforinversebetadecaysandinteractions
 
onoxygentodeterminethePDFvalues. WeconstructalikelihoodL=exp(cid:88)Nrk(cid:89)Li,and
k,r i
maximizeitsothat:
∂L ∂L
= =0, (2)
∂Nrk ∂dˆSN
wherefor N wevaryr = ν¯ p, νeandν16O.Forr = ν16O,weassumethecosθ issamefor
rk e SN
neutrino and anti-neutrino interactions. We set N = 0 for r = ν16O with k = 1, 2, 3, as the
rk
expectednumberofchargedcurrentinteractionsonoxygenisnegligibleinthoseenergyranges,
as shown in Fig. 1.The SN direction dˆ contains two parameters: zenith and azimuth angles,
SN
8
thataretranslatedtothedirectionintheequatorialcoordinatesystemwiththetimetheburstis
found. Hence,wevary14parametersofN anddˆ intotal.
rk SN
Whenweperformafitwiththelikelihoodmethod,wefirstdeterminetheinitialvalueofthe
directionbasedonagridsearch: wescanalldˆ tothe4πdirectionswithacoarsegridstepand
SN
count the number of events that satisfy cosθ > 0.8 at each step, and we set the initial value
SN
thatgivesthelargestnumberofevents.
3.2. Performance
Figure 6 demonstrates cosθ distributions of a fit to a MC sample of the Wilson model at
SN
10kpcforthefiveenergybinsandcombinedonewiththesuperpositionsofthefittedlikelihood
functions. Figure 7 shows the corresponding direction distribution on a sky map in the equa-
torial system. The red (blue) points are the reconstructed directions of each elastic scattering
event (inverse beta decay or charged current reaction on oxygen), and the star mark shows the
reconstructed SN direction. The elastic scattering events concentrate around the reconstructed
SNdirection,whilethedistributionofinversebetadecaysandchargedcurrenteventsisalmost
uniformacrosstheentiresky.
Figure 8 shows ∆θ distributions of the three models (Wilson, NK1 and NK2) for 3,000 MC
samples at 10 kpc without neutrino oscillation, where ∆θ is the angle between the input SN
directionandthefitteddirection. ThesolidlinesarefitresultsusingthevonMises-Fisher(MF)
distribution[26]:
κ
f(∆θ;κ)= eκcos∆θsin∆θ, (3)
2sinhκ
whereκdeterminesthesharpnessofthedistributionconcentrationonasphere.
WeestimatetheangularresolutionsoftheSNdirectiondeterminationusinganensemblees-
timation. Inordertocopewithanypossiblecombinationsoftheelasticscatteringsandinverse
betadecays,weemploythefollowingmethod.WegenerateanumberofMCsamplesforvarious
combinationsoffittedyieldsoftheelasticscatteringsandinversebetadecaysintherangesupto
1,500fortheformerand60,000forthelatter. Wedivideeachrangeinto15toobtaina15×15
matrix. Eachmatrixelementcontainsabout3,000MCsamples. Foreachelement,wedetermine
theangleθ thatcovers68.2%,90%and95%oftheMCsamples. Wealsoprovideprobabilities
en
tohavethetrueSNpositionin2,5and10degreeswithrespecttothefitteddirection. Wegen-
eratethematricesfortheWilsonandNK1modelswith(NH)andwithoutneutrinooscillations.
Thedependenceoftheθ onthemodelshasabouta10%variation.Weemploythelargestvalues
en
ofθ andthesmallestvalueoftheprobabilitiesforeachmatrixelementconservatively. When
en
wefindaSNneutrinoburst, weapplythefittothebursteventstoobtaintheSNdirectionand
theyieldsoftheelasticscatteringsandinversebetadecays.Withthefittedyields,weidentifythe
matrixelementandobtaintheangularresolutionsandtheprobabilitiesthataretobeannounced
tothepublic.Forexample,wefindθ =3.1∼3.8◦(4.3∼5.9◦)at68.2%coveragefortheWilson
en
(NK1)modelat10kpc,wheretherangecoversvariousneutrinooscillationscenariosinTable1.
TheNakazatomodelalsoprovidesaSNmodelwithablackholeformationfor M = 30solar
mass [13] . The model predicts that neutrino emission suddenly stops 842 ms after the core
bounce. IftheSNmonitorobserves anabruptcutoff ofthesupernova neutrinoflux, thiscould
bethesignatureofthebirthofablackhole.Basedonthismodel,wegenerateMCsamplesand
apply the fit. We obtain an angular resolution of 2.3 degrees at 10 kpc with 68.2% confidence
level. Therefore this may help the identification of a position of a disappeared massive star as
proposedby [27].
9
In order to understand the behavior of the estimated angular resolution, we make use of the
curvatureofthelikelihoodatitsmaximalposition: wedefineavalueσas:
σ= (cid:118)(cid:117)(cid:117)(cid:117)(cid:117)(cid:116)− 1 , (4)
∂2lnL
∂θ2
SN
where the second derivative is the curvature calculated at the point on the sphere at which the
likelihoodfunctionLbecomesmaximal. Wecalculateσvaluesalongfourplanesthatinclude
the maximal point and have different azimuth angles with respect to the point, and employ the
maximumamongthefourσvalues. Thenweobtaintheresolutionθ (q)thatcoversanareawith
σ
afractionofq=1−poftheMFdistributionwitha pvalue:
(cid:34) (cid:35)
1 (cid:16) (cid:17)
θ (q)=arccos ln 1−q+qe−2κ +1 , (5)
σ κ
andκ=1/σ2.
In Fig. 9 (a) and (c), we show the obtained angular resolution at the 68.2% coverage for the
ensemble estimation of the fit, the likelihood curvature method and the ensemble estimation
usingagridsearchasafunctionofthedistancefortheWilsonandNK1models. Wefindthat
the∆θdistributionsarewellmodeledbytheMFfunctionandthelikelihoodcurvatureestimation
θ (q)(q = 0.682)isconsistentwiththatoftheensembleestimationforthestatisticslargerthan
σ
those of SNe at 10 kpc (7 kpc) for the Wilson (NK1) model. However, θ (q) is found to be
σ
an underestimate for the smaller statistics. The degradation of the angular resolution for the
distant SNe is likely due to failure in giving a proper initial value of the SN direction by the
gridsearch,indicatedbythefactthattheθ valueapproachesthatofthegridsearchforlarger
en
distances (smaller statistics). The small statistics produce a large fluctuation that sometimes
makes a fake peak on the grid direction search. That makes the initial value a wrong direction
andthelikelihoodfitfindsalocalminimumaroundthedirection. Figure9(b)and(d)showthe
ensembleestimationoftheangularresolutionasafunctionoftheSNdistanceforthreeneutrino
oscillationhypotheses. Theangularresolutionswiththetwoneutrinooscillationhypothesesare
smaller than those without neutrino oscillation. This is due to an increase in elastic scattering
eventsasshowninTable1.
WeestimatetheprecisionoftheangularuncertaintyusingEq.(5)undertheassumptionsofthe
(cid:112)
SNmodelsused;theprecisionof∆θ isdeterminedusing∆θ =dθ /dq·∆q=dθ /dq· q/N,
σ σ σ σ
where N = 3,000isthenumberofsamplesintheensemble. Wefind∆θ = 0.09degreeswith
σ
q = 0.682fortheNK1modelwiththeNHneutrinooscillationatadistanceof10kpc,whichis
muchsmallerthantheangularresolutionvariationofvariousneutrinooscillationscenarios.
4. Summary
Wedescribeareal-timemonitorofaSNneutrinoburstatSK.Themonitorisabletoprovide
a fast warning to the world within one hour. The system is operating on a dedicated computer
independentoftheofflineprocesses. TheSNneutrinoburstselectioncriteriaaredeterminedso
that fake event bursts mainly caused by spallation events are rejected. Using MC simulations,
we find that the system has 100% detection efficiency up to the LMA for the three SN models
withthegoldenwarningcriteria.Theexpectedtotalnumberofneutrinoeventswiththeselection
10