Indirect Search for Dark Matter in M31 with the CELESTE Experiment

0.34 MB·English

by  J. Lavalle

1
M31 (Andromeda)is our nearest neighbourspiral galaxy,and both its high mass and its low distance make it a source of
interest for the indirect search for dark matter through γ-ray detection. The ground based atmospheric Cherenkov telescope
CELESTEobservedM31from2001to2003,inthemostlyunexploredenergyrange50-500GeV.Theseobservationsprovide
anupperlimitonthefluxabove50GeVaround10 10cm 2s 1 intheframeofsupersymmetricdarkmatter,andmoregenerally
− − −
onanygammaemissionfromM31.
Keywords.Gamma-RayObservations–DarkMatter–SpiralGalaxy
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Astronomy&Astrophysicsmanuscriptno.celeste˙M31 February5,2008
(DOI:willbeinsertedbyhandlater)
Indirect Search for Dark Matter in M31 with the CELESTE
Experiment
J.Lavalle1,⋆,H.Manseri2,A.Jacholkowska1,E.Brion3,R.Britto1,P.Bruel2,J.BussonsGordo1,D.Dumora3,E.
Durand3,E.Giraud1,B.Lott3,F.Mu¨nz4,E.Nuss1,F.Piron1,T.Reposeur3,andD.A.Smith3
1 Laboratoire de Physique The´orique et Astroparticules, CNRS-IN2P3 / Universite´ de Montpellier II, 34095 Montpellier,
France
2 LaboratoireLouisLeprince-Ringuet,CNRS-IN2P3/E´colePolytechnique,91128Palaiseau,France
3 Centred’EtudesNucle´airesdeBordeaux-Gradignan,CNRS-IN2P3,33175Bordeaux,France
4 Laboratoired’AstroparticuleetCosmologie,CNRS-IN2P3/Colle`gedeFrance,75231Paris,France
Receivedxx,xx;acceptedxx,xx
Abstract.Ifdarkmatterismadeofneutralinos,annihilationofsuchMajoranaparticlesshouldproducehighenergycosmic
rays,especiallyingalaxyhalohighdensityregionslikegalaxycentres.
1. Introduction
The presence of dark matter in the Universe has been known for decades. Since early measurements in galaxy clusters
(Zwicky, 1937), the mass distribution of the Universe has been studied at different scales with a focus on dynamical effects
bymeansofgalaxystarrotationcurves,large-scalegalaxyclusterdynamics(Ostrikeretal.,1974).Recentdevelopmentsinob-
servationaltechniquesincosmologyhaveresultedinindependentestimatesofthemattercontentoftheUniverseΩ h2,through
m
large-scale structure surveys(Hawkins et al., 2003 ; Lovedayet al., 2002) and measurementsof the cosmic microwave back-
groundradiation(themostrecentbeingtheWMAPmission(Spergeletal.,2003)).Givenstandardcosmology,allsuggestthat
mostofthematterintheUniverseisdark,coldandnon-baryonic.SuchhypotheseshaveledtotheconstructionoftheColdDark
Matter(CDM)paradigm(Blumenthaletal.,1984):darkmatterwouldbemadeofWeaklyInteractingMassiveParticles(WIMPs)
whichareneutral,stableandoriginatingfromtheBigBangera(Lee&Weinberg,1977).
Supersymmetrictheories(SUSY) (see for instanceNilles, 1984) offer an excellentWIMP candidate(Goldberg,1983), the
neutralino,whichisamixtureofthesuperpartnersoftheneutralHiggsbosonsandoftheelectroweakgaugebosons.Wewillnot
discussthecaseofextra-dimensionphenomenologicaltheories,whichalsoprovideinterestingcandidates(Servant&Tait,2003).
Thenatureofdarkmatterispresentlyprobedinbothdirectsearches,bymeansofundergroundexperimentsthatcoulddetect
elastic interactionsofneutralinoswithnuclei,andindirectsearchesusinggroundbasedorsatellite telescopestodetectcosmic
rays (gamma, leptons or hadrons) created by neutralino pair annihilations in galactic or extragalactic media (for review, see
Bergstro¨m2000).
Thesedifferenttypesofsearches,togetherwithcolliderexperiments,arenecessarytoconstraininawiderviewthequantum
natureofdarkmatter,becausetheyalloweitheradditionalorcomplementarysurveysoftheparticlemodelparameterspaces.
SearchingforWIMPannihilationsignatureswithgroundbasedγ-raytelescopesleadstothequestionofthechoiceoftargets.
Agoodcandidatewillhavealargeamountofdarkmatter,andcombineasbigadensityaspossible,assmalladistancefromus
aspossible,andfinally,willtransitathighelevationintheexperimentalsky.TheGalacticcentreisaprimecandidateexceptfor
beingtooclosetothehorizonforCELESTE,whichisinthenorthernhemisphere.Instead,wehavechosenM31andtheDraco
dwarfgalaxyfor oursearches.M31,whichis the nearestgiantspiralgalaxy,is verymassive ( 1012M ),and itsstar rotation
∼ ⊙
curve indicates a large amount of dark matter. Draco, a neighbour dwarf spheroidal galaxy dominated by a dark component
(Kleynaetal.,2001),isalsoaverygoodcandidatebutourattemptstostudyitwerefoiledbybadweather.
Inthispaper,wepresenttheresultofsearchesforγ-rayemissionfromM31withtheCELESTEtelescope.Insection2,we
reviewthepredictionsmadefortheobservations(moredetailsinFalvard2004,hereafterF04),forwhichweconsideredCDMin
theframeofminimalsupergravity(mSUGRA)phenomenology.Theimpactoftheastrophysicalmodellingisbrieflyrevisited,as
Sendoffprintrequeststo:[email protected]
⋆ Presentaddress:CentredePhysiquedesParticulesdeMarseille,CNRS-IN2P3/Universite´Aix-MarseilleII,13288France
J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment 3
wellaspossibleconsequencesofnon-standardcosmologies.Focusingontheexperimentaltechniques,wepresentinsection3the
methodweusetosearchforaγ-raysignal,withexplicitcomparisonstoCrabdata.Intheabsenceofadetection,2σconfidence
levellimitsarecomputedforallstudiedSUSYmodels.
2. Gamma-rayfluxpredictionsforsupersymmetricannihilatingdarkmatterinM31
Undertheassumptionthatneutralinoshaveanisotropicandhomogeneousvelocitydistribution,whichislikelytobethecasein
halocentreswheretheWIMPvelocityisexpectedtobelow,theaveragedγ-rayfluxduetotheirannihilation,integratedabove
anenergythresholdE andwithinthesolidangle∆Ωcanbewrittenas:
th
Φ(E )= 1 Nγ(Eth)<σv> ρ2(s)dsdΩ 1 Nγ(Eth)<σv> Σ(θ) (1)
th 4π 2m2χ0 Z∆Ω(θ)Zl.o.s. ≡ 4π 2m2χ0
We thus decoupleastrophysicsmodellingfrom SUSY contributions.The first part of the right hand term is related to particle
physics, via the thermally averaged product of the cross section σ with the velocity v producing N (E ) photons of energy
γ th
E > E , and the neutralino mass m . The second term refers to the (squared) halo density profile ρ integrated within an
th χ0
experimentalfieldofviewofangularradiusθ alongthelineofsightds. Atthesame time,wedefineΣ(θ) astheastrophysical
factoroftheflux.
As γ-rays result mainly from hadronization of annihilation final states (mainly quarks and gauge bosons), their spectral
shapemainlytakesits origininthedecayofπ0.Ithasbeenshownbyseveralauthors(seeforinstanceBergstro¨metal.,1998,
or Tasitsiomi et al., 2002) that such a spectrum can be fitted or modelled with respect to the neutralino mass. Therefore, the
differentialspectrumaboveathresholdenergyE canbewrittenasfollows:
th
dΦ
(E > E ) Φ(E ) f(E,m ) (2)
dE th ≡ th × χ0
where f(E,mχ0) is the spectral shape derived from the SUSY model and normalized such that E∞th f(E,mχ0)dE = 1, so that
Φ(E )istheintegratedspectrumaboveanenergythresholdE .ThisexpressionwillbeusefulwhRenweinterprettheM31data
th th
collectedbyCELESTE.
2.1.Halomodelling
M31isalate-typeSbspiralgalaxy,whichliesatadistanceofabout675kpc,andisobservablefromtheNorthernhemisphere(RA
=10.68o,DEC=41.27o).AstudybyBraun(1991),basedupontheanalysisofHIdataandamodel-independentreconstruction
ofthevelocityfield,showedthatthestar rotationcurvearisesnaturallybyconsideringtwo opticallytracedmasscomponents:
abulge,withatotalmassof(7.8 0.5) 1010M ,andadiskof(1.22 0.05) 1011M within28kpc.Nevertheless,itseems
thatthestarmass-to-lightratiosus±edint×hispaper⊙,Υ =6.5andΥ ±=6.4(×solaruni⊙tsinblueband),areover-estimated(cf.
bulge disk
F04).
Byloweringthebulgeanddiskcontributions,thatisΥ =3.7andΥ =2.5asindicatedbyF04,weassumedthatadark
bulge disk
halosignificantlyaccountsforthegravitationalpotential.LetusconsiderthefollowingCDMdensityprofile:
r γ rα+aα ǫ
ρ (r)=ρ 0 0 , (3)
CDM 0(cid:18) r (cid:19) rα+aα!
wherer usuallystandsforacoreradiusandaascalelength.AnNavarro-Frenk-Whiteprofile(Navarroetal.,1996),i.e.with
0
γ = 1,α = 1andǫ = 2,fitstherotationcurve,andhasitsparametersentirelydeterminedbythepreviousmass-to-lightratios.
Thefittedvaluesareρ 0.07GeV.cm 3,r 20kpcanda 5kpc.Theresultingcontributiontotheγ-fluxwithinCELESTE’s
0 − 0
∼ ∼ ∼
fieldofview(θ=5mrad 0.3o,correspondingtoa3.5kpcradius)hasbeencalculated:
∼
Σ(θ=5mrad)=3 1019GeV2cm 5. (4)
−
×
Thisresultdependsstronglyonthecentraltailofthedarkhalo,butisratherconservativesincecalculatedwithar 1profile.
−
2.2.ProbingtheSUSYparameterspace
We choose the minimal supergravity framework (mSUGRA) to scan over the SUSY parameter space. In this frame, a SUSY
modelcanbedefinedattheunificationscalewith5parameters:theunifiedscalarmassm ,theunifiedgauginomassm ,the
0 1/2
Higgsvacuumexpectedvalueratio tan(β), the unifiedtrilinear coupling A and the sign ofthe mixingparameterof the Higgs
0
superfieldsµ.WeuseaninterfacebetweenthepubliccodesSuspect(Djouadietal.,2002)andDarkSusy(Gondoloetal.,2004)
to compute SUSY masses, annihilation rates and relic densities for various random models. The constraints on these models
4 J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment
1 )
2 - s 10-8
-m
x (c 10-9
d Flu 10-10 150000 << mmχχ << 161000 GGeeVV
e
at
gr 10-11
e
nt
I -12
10
-13
10
-14
10
-15
10
-16
10
-17
10
2
1 10 10
Energy Threshold (GeV)
Fig.1.Integratedexpectedγ-fluxfromM31asafunctionoftheenergythreshold,fortwoselectionsoflow(100-110GeV)and
high(500-600GeV)neutralinomasses(Ω h2 [0.086,0.14]),showingthemass-dependenceoftheflux,andthecomplemen-
χ0 ∈
taritybetweenEGRETandCELESTE.
comefromstandardacceleratorlimits,andweselectaratherlargerangefortherelicdensity(Ω h2 [0.05,0.14])1,according
χ0 ∈
totheWMAPmeasurementΩ h2 =0.113 0.009(Bennettetal.,2003).
χ0 ±
Combining the resulting γ-spectrum with the astrophysical factor Σ, we calculate the integrated flux as a function of the
thresholdenergy,asshowninFig.1,inwhichwehaveselectedonlytwogroupsofWMAPcompatibleneutralinos(respectively
small and high masses) in order to exhibit the mass-dependence of the expected flux. The SUSY models plotted there are
characterizedbyahighvalueoftanβ(typically>30),forwhichtheproductionofγ-raysismoreefficient(duetohighbranching
ratioinbquarks).Onthesameplot,werepresenttheupperlimitprovidedbytheEGRETcollaboration(Blometal.,1999)and
CELESTE’ssensitivity, 6 10 11ph.cm 2s 1, estimated for50hoursofobservation.Thisfigureillustratesthe mass-and/or-
− − −
∼ ×
energyexperimentalcomplementarities.
2.3.Othercontributions
Althoughthepredictedfluxesarelow( 10 13cm 2s 1 atathresholdof 50GeV), 3ordersofmagnitudesmallerthanfor
− − −
∼ ∼ ∼
theCrabnebula(thereforefarfromCELESTE’ssensitivity),severaleffectscouldenhancethem.
First ofall, darkmattersubstructures,the so-calledclumps,arise naturallyinthe hierarchicalschemeofgalaxyformation,
and simulations of the non-linear regime of collapse allow a semi-theoretical study of their statistics and structure (Moore et
al.,1999).Suchlocaloverdensitiesshouldinduceextraneutralinoannihilations,andtranslatetoanadditionalfactortotheflux.
Although it is rather difficult to estimate how clumpy the galaxies remain today, this enhancement factor was until recently
supposedtobesmallerthan 10(Stoehretal.,2003).Nevertheless,arecentstudybyDiemandetal.(2005)suggeststhatabout
∼
50%ofaMilky-Way-likegalaxymassispossiblyboundtodarkmattersubstructures,whosemassrangespreadsfrom10 6 up
−
to107M .Theauthorsclaimthatabout 1015ofsuchsubstructuresmayhavesurvivedagainstgravitationaldisruption,leading
⊙ ∼
toa boostfactorofovertwoordersofmagnitudecomparedtothe smoothcontribution.M31beingverysimilar toourgalaxy,
thisstatementshouldalsostandforthatsource.
As another possible astrophysical effect, the supermassive black hole at the centre of M31 could raise the central halo
profile up due to adiabatic accretion (Gondolo & Silk, 1999). There are other interesting mechanisms involving baryons to
enhancethedarkmatterdensity.Gnedinetal.(2004)sketchsuchresponsesofhalostocondensationofbaryons,whileBertone
1 Theupper limitisgivenbytheWMAPresultplusthreesigma.Higher valuesfortherelicdensityarenot thatinterestingbecausethey
correspondtolowervaluesoftheannihilationcross-section.
J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment 5
etal.(2005)proposeapossibleenhancementoftheWIMPannihilationrateduetothepresenceofintermediate-massblackholes.
Beside those astrophysical effects, some recent developments in the frame of theoretical cosmology have focused on the
quintessencescheme(Caldwelletal.,1998)tosolvetheso-calledcoincidenceproblem(thefactthatΩ Ω today).Sucha
Λ matter
∼
quintessentialfieldcouldundergoakinationregimeintheearlyuniverse(Salati,2003),sothatitskineticenergydominatesover
itspotential.Inthisregime,theexpansionrateoftheuniverseisenhancedandthethermalhistoryofneutralinosisconsequently
modified: the decoupling of neutralinos can take place more rapidly at earlier times. Therefore, the WMAP constraint leads
to a higherneutralinoannihilationcross-section.Thismeansthatthis phenomenonrehabilitatesSUSY modelsfor whichrelic
densities are too low, when calculated in standard cosmology. Salati (2003) shows that the relic density enhancement can be
parameterizedby:
m
Ω Ω˜ 1000 χ0 √η Ω withη 0.3. (5)
χ0 → χ0 ≃ (cid:18)100GeV(cid:19) 0 χ0 0 ≤
η ρ /ρ ,wherethe0-indexreferstoatemperatureof1MeV,andρ (respectivelyρ )isthequintessence(photon)energy
0 Φ,0 γ,0 Φ γ
≡
density.Theupperlimitonη comesfromBigBangNucleosynthesisstagesthatshouldnotbeperturbedbythekinationregime
0
(Yahiroetal.,2002).
Accordingtothiscosmology,higherannihilationratemodelsarerequired,whichthereforemeansthattheγ-rayproduction
isenhanced.ThiseffectappearsinthefinalresultsshowedinFig.7,forasmallsampleofselectedSUSYmodels.
Finally,weemphasizeanotherinterestingeffectcomingfromAffleck-DinebaryogenesisinSUSY(Fujiietal.,2004),which
yieldsnaturalmatter-antimatterasymmetryintheearlyuniverse.Insuchascenario,meta-stableparticlesresultfromoscillations
in flat directions of the scalar potential, carrying baryon and/or lepton number, namely Q-balls. These Q-balls can have a
lifetimelongenoughtodecayafterthefreeze-outofneutralinos.Thisinducesanon-thermalproductionofneutralinos,andthus
enhancestheirrelicdensity.Thisalsorequires,aspreviously,higherneutralinoannihilationratestonotoverclosetheuniverse.
Therefore,althoughstandard conservativepredictionsare notthat optimistic, all these putative contributionsmay increase
the γ-flux from M31 significantly.This further motivatesobservationsof such a source with CELESTE, keepingin mind that
CDMcouldbesomethingbesidesSUSY.
3. ObservationsofM31withCELESTE
3.1.TheCELESTEexperiment
CELESTE(Pare´ etal. 2002, deNauroisetal. 2002)is anatmosphericCherenkovtelescopedetectingγ-raysabove 50GeV
∼
(theexperimentshutdowninJune2004).Reachingsuchalowenergythresholdrequiredalargelightcollectionarea,achieved
by exploitingthe mirrorsofa solar plant.These mirrorsare used to sample the arrivaltime and photonflux of the Cherenkov
wavefrontgeneratedbyatmosphericshowersinitiatedbycosmicraysatmanypointsinthelightpool.Incontrasttotheimag-
ing technique(Weekes, 1988) the sampling technique uses informationon the shape of the wavefrontfor hadronrejection, as
describedbelow.
TheCELESTEexperimentuses53heliostats(40until2001)oftheThe´misformersolarplant(FrenchPyre´ne´es,42.50oN,
1.97oE, altitude 1650 m). Each heliostat (54 m2) reflects the light onto the secondary optics, located at the top of a 100 me-
ter tower, focussing the light onto a single photomultiplier (PMT) for each heliostat. The PMT signals are sent to the trigger
electronicsandtothedataacquisitionsystemwheretheyaredigitizedby 1GHzflashanalog-to-digitalconverters(FADCs).
∼
The mean altitude of the maximum Cherenkov emission for γ-ray induced showers is around 11 km above the site. The
heliostatsareaimedatthisaltitude inthe directionofthe sourceunderstudyto enhancelightcollection.Theobservationsare
made in the On-Off tracking mode: the observationof the source (On) is followedor preceded by an observationat the same
declinationoffsetinrightascensionby20minutes.Thelatterisusedasareferenceforthecosmic-raybackgroundandthesignal
isgivenbythedifferencebetweenOnandOff,afteranalysiscuts.
M31 is a specialsourceforCELESTE in thatits bluemagnitudeis about4.3,and 5.4if integratedin the 5 mradfield
∼ ±
ofviewofCELESTE(deVaucouleurs,1958).Hence,pointingOn-sourceincreasesthePMTilluminationcomparedtotheOff-
sourcedata.ThesameproblemarisestoalesserdegreeforthestudyoftheblazarMrk421,duetothepresenceofthem =6.16
B
star51UMainthesamefield-of-view.On-offilluminationdifferencesintroducebiasesatthetriggerlevelandintherecorded
datawhichfakeasignalifnothandledproperly.Weremovethesebiasesby“padding”theOff-sourcedatawithextrabackground
lightaspartofthedataanalysis,andbymakingapulseheightcut10%abovethehardwaretriggerthreshold,asdescribedin(de
Nauroisetal.,2002)andupdatedin(Manseri,2004).
In the following, all Monte Carlo simulations are performed at the transit position of sources in the The´mis sky, unless
specified.We haveusedtheatmosphericshowersimulatorCorsika(Hecketal.,1998)forourMonteCarlo studies.Moreover,
stellarphotometrystudiesusingthePMTanodecurrentsprovidedanimproveddescriptionofouropticsinthedetectorsimulation
(Smith&Brion,2004).
6 J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment
s
0.35 vt1400
e
N
1200
0.3
1000
0.25
800
0.2 600
0.15 400
200
0.1
0
0.05
-200
0 -400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ξ ξ
Fig.2.Left:normalizeddistributionsofthediscriminatinganalysisvariableξ forasimulationofγ-rays(solidline)fromM31
following a CDM-like spectrum (m = 500 GeV), with respect to M31 Off-data (2001-03, black markers). Right: number
χ0
distribution of ξ for a E 2-spectrum simulated at the Crab transit (solid line), with respect to the On-Off difference for a data
−
sampleoftheCrabnebula(takenbetween2002and2004,blackmarkerswitherrorbars).
3.2.Hadronrejection
In our energy range, the Cherenkov wavefront from γ-ray induced showers is, on average, more spherical than for showers
initiated by hadrons(that is, by charged cosmic rays, mainly protons). The CELESTE field of view is small comparedto the
angularextentoftheshowers,whichlessensthedifference,butefficienthadronrejectionisstillpossible.
Justabovethetriggerthreshold,theCherenkovsignalformanyheliostatsiscomparabletothefluctuationsofthenightsky
backgroundlight,so we sum allthe signalsinsteadof usingeachindividually.Summingthe signalsimpliescompensatingfor
thepropagationdelays,whichrequiresknowledgeoftheshowercorepositionwhenassumingasphericalCherenkovwavefront.
AsdescribedinManseri2004,thisisdonebyscanningtheplaneat11kmandevaluatingtheratioH/W foreachpositionofthe
scan,whereH andW aretheheightandthewidthofthesummedsignal.ThelargestvalueoftheratioH/W yieldsourmeasure
oftheshowercoreposition.ThesphericityofthewavefrontisestimatedbyhowmuchtheratioH/W decreaseswhenestimated
200m away fromthe shower coreposition.Thisrelative decrease,called ξ, is shownin Fig. 2-leftfor an Off observationand
forasimulationofaγ-rayspectrum.Asexpected,becauseoftheirCherenkovwavefrontsphericity,γ-rayshowershavelowerξ
valuesthanhadronicshowers.
The On-Offdifferenceofthisrelativedecreaseisshownin Fig.2-rightfora sample ofCrab nebuladata, whichwastaken
between2002and2004withthesameexperimentalsetupasforM31.Itexhibitsaclearexcessduetotheγ-rayemissionfrom
theCrabnebula.Requiringξ <0.35leadstoa13.5σexcessandasensitivityof6.5σ/√h.
3.3.Observations,dataselectionandsignalsearches
M31 was observed with CELESTE from 2001 to 2003, and 68 On-Off pairs were collected ( 22 hours of On-source data).
∼
Nevertheless,variationsinatmosphericconditionsareknowntocausesystematicshiftsintheOn-Offdifference,soweapplied
aselectionbasedoncriteriarequiringstabledetectoroperation(characterizedbyPMTanodiccurrentandtriggerratestability).
Thisselectionreducedthedatasetto6.5hoursbecauseofbadweatherconditionsatThe´missince2001.
TheOn-OffdifferenceofξfortheM31dataisshowninFig.3-left.Noevidenceofanexcesscanbefound,andtheOn-Off
differenceis 0.75σwhenrequiringξ<0.35.
−
SUSY annihilating dark matter could produce soft spectra or peaked signals, so we search for a signal in various energy
bands.Our energyreconstructionusesγ-ray simulationswith fixedenergies,and is basedon the correlationbetweenthe total
chargerecordedwiththeFADCsandthetrue(i.e.MonteCarlo)energy,foragivenimpactparameter.(Theshowercoreposition
at11km,obtainedbymaximizingH/W asdescribedabove,givestheimpactparameteronthegroundassumingthatthegamma
ray comes from the source under study.) Figure 4 (left) shows the mean charge per heliostat versus the reconstructed impact
parameter,fordifferentγ-rayenergies.Weusethechargedistributionsateachenergyandimpactparametertobuildtheinverse
function,thatis,thefunctionpredictingtheenergyfromtheobservedchargeandthereconstructedimpactparameterintherange
of[0 120]m.Tocheckthefunction,weinverseitagainandcompareittotheoriginalpoints,alsoshowninFig.4(left).The
−
rightpanelofFig.4showstheenergybiasandresolutioncurvesobtainedfromthisestimationmethod.Theenergyresolutionis
below30%withasmallbiasof 5%,adequatetosearchforanexcessinthedata.
∼
The On-Off difference of the measured energy distribution, after analysis cuts, is shown in Fig. 3-right, in which the 50
GeVbinningcoversatleastonestandarddeviationoftheenergyresolutionfunction.Noexcesshasbeenfound.Allresultsare
J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment 7
s1500 s
evt evt150
N N
100
1000
50
0
500
-50
0 -100
-150
-500 -200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 200 400 600 800 1000
ξ Estimated energy Eγ (GeV)
Fig.3.Left:On-OffdistributionofξforM31data(2001-03,blackmarkerswitherrorbars),withrespecttothesamesimulated
spectrumasFig.2-left(solidline).Right:On-Offdistributionoftheestimatedenergyforalleventswithinanalysiscuts.
el 0.3
h
>/1000
<Q 0.25
800 0.2
0.15
600
0.1
400
0.05
200
0
0 -0.05
0 20 40 60 80 100 120 140 50 100 150 200 250 300 350 400 450 500
Impact parameter (m) True energy (GeV)
Fig.4.Left:Thecrossesarethe meanchargeper heliostat(arbitraryunits)forγ-rayssimulatedwith energiesof50,100,150,
200,300and400GeV (bottom-top),versusthe reconstructedcoreposition(i.e.theimpactparameter).Thesolidcurvesshow
thechargeobtainedfromthefunctionsusedtopredicttheenergy.Right:resolution(soliduppercurve)andbias(lowerdashed
curve)fortheenergyreconstructionmethodwithrespecttothetrueenergy(sameMonte-Carloset-upasinplotatleft).
Analysislevel On-sourceevts Off-sourceevts On-Off Significance(N )
σ
Rawdata 463520 462327 1193 -0.59
Analysiscuts 10615 10740 -125 -0.75
Emeas <100GeV 6101 6167 -66 -0.53
100 Emeas <200GeV 3143 3197 -54 -0.61
≤
200 Emeas <300GeV 870 824 46 1.02
≤
300 Emeas <400GeV 260 269 -9 -0.35
≤
Table1.FinalstatisticsresultingfromM31dataanalysis.Theanalysiscutsarethefollowing:weimposeasoftwaretrigger10%
higherthan thehardwareone,andwe applya cutξ < 0.35(see textfordetails) ;forsignalsearchesinenergybins, we adda
selectiononthereconstructedimpactparameter–<120m–accordingtothevalidityrangeofourenergyreconstructionmethod.
Nosignificantexcessappearsoverthewholesample,norwithindifferentrangesofenergy.
summarizedinTable1,inwhichasearchforanexcesswithinbinsof100GeV,muchlargeratlowenergythantheresolution,is
presented.
3.4.Stabilityandupperlimit
Wehavealsostudiedthestabilityofthisresult,asacheckofpossiblesystematiceffects.WeshowinFig.5howthesignificance
remainsstablewhenvaryingthecutvalueonthemaindiscriminatingvariableξ. Asacomparison,thesameexercisehasbeen
8 J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment
Nσ 15
Crab 2003
10
5
M31 2001-03
0
M31 2001
M31 2002
M31 2003
-5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
cut ξ <x
Fig.5.Significancelevelaccordingtovaryingthecutonξ (afterraisingthethresholdby10%).Thisfigureshowsthestudyof
stabilityoftheanalysisaswellforCrabasforM31data.AsignalevidenceisclearlyseenfortheCrab,whereasthesignificance
levelremainsflatforM31.
done for a Crab dataset (same figure), and the γ-ray signal clearly exhibits a bump in significance up to N 13.5 around
σ
∼
ξ <0.35.
On-Offdifferencemeasurestheintegraloverenergyofthetheoreticalspectrumofequation2convolutedwiththeeffective
area,timestheobservationtime.Asthestatisticscollectediscompatiblewiththeabsenceofasignal,wehaveonlymeasuredthe
backgroundanditsfluctuationsindirectionofM31.Thiscanbetranslatedtoanupperlimitonafluxcomingfromthatsource,
givena normalizedtheoreticalspectralshape f(E). Fora N upperlimit,andgivenan experimentalenergythreshold E ,any
σ th
integratedfluxabovethisenergyshouldbeboundedlike:
δN
Φ(E > E ) N bkgd (incm 2s 1), (6)
th σ − −
≤ Tobs E∞thA(E)f(E)dE
R
whereδN 2 N isthemeasuredbackgroundRMS,T isthetotalexposuretimeand (E)standsfortheenergy-
bkgd Off obs
≃ × A
dependenteffectipvedetectionarea.Thelatterisdeterminedbymeansofsimulations,andisplottedinFig.6-left.Accordingto
equation2,notethatthespectrum f(E)ismass-dependentincaseofneutralinoannihilation,sothatthelimitshoulddependon
themass.Forthesakeofsimplicity,wewillusetheparametrizationgiveninTasitsiomietal.(2002)forthespectralshape,that
is:
6√x 10 5 3x2+6x 1
th
f(E)= − (7)
5mχ0(√xth−1)4 3 − 12 x3/2 !
where x E/m and x E /m . This spectrum dependson the mass, butassumes that γ-rays come only from π0 decay.
≡ χ0 th ≡ th χ0
Therefore, it does not take into account all specificities of SUSY models. Nevertheless, it is sufficient for our purpose. This
parametrizationisillustratedinFig.6-rightfortwomasses,250and500GeV,andcomparedwitha1/E2powerlawspectrum.
The threshold is set to 50 GeV, taken from the effective area shown in Fig. 6 (left). Given this threshold, a flux limit can
becomputedforeachneutralinomass,usingequation6.TheresultispresentedinFig.7,wherethepredictedintegratedfluxes
of γ-raysabove50 GeV are plottedwith respectto neutralinomasses. The averagedlimit in a mass rangeof [50 700]GeV
−
lies around 10 10ph.cm. 2s 1. We emphasize that this is the first experimental result in the energy range 50-500 GeV, and is
− − −
complementarytothoseprovidedbyEGRET(Blometal.,1999)andHEGRA(Aharonianetal.,2003)observationsofM31.
4. Discussionandconclusion
ObservationsofM31withCELESTEprovidea2σupperlimitontheγ-fluxabove50GeV,dependingontheexpectedspectrum.
This limit, around10 10ph.cm 2s 1, is quite far from the SUSY parameter space, but significantly constrainscombinationsof
− − −
different enhancement factors discussed in 2.3 (which are also likely to be excluded by EGRET limits, depending on the
§
neutralino mass), and also any other model of annihilating dark matter besides SUSY. Whereas these observationshave been
motivatedbyindirectsearchesforSUSYCDM,thisresultyieldsageneralastrophysicalresult:thefirstobservationofaspiral
galaxyinthisenergyrange,somehowconstrainingγ-rayemissionfromthisclassofobjects.
AnygammaraydetectionfromagalaxylikeM31wouldbedifficulttointerpretintermsofdarkmatterannihilation.Spiral
galaxiesareknownsitesofnon-thermalprocessesandcosmicrayacceleration,andtherelevantphysicalmechanismsarenotyet
wellunderstood.Inthissense,aDwarfSpheroidalgalaxylikeDracoisaverypromisingsourceforindirectdetection,givenitis
clearlydominatedbythedarkmattercomponent.Unfortunately,wehavetoofewdataonDracotoperformarelevantanalysis.
J.Lavalleetal.:IndirectSearchforDarkMatterinM31withtheCELESTEExperiment 9
2)m
A(4405000000 )f(E,mχ1100--21 Emm-2χχ == 520500 GGeeVV
35000
30000 10-3
25000 10-4
20000 10-5
15000
10-6
10000
5000 10-7
100 200 300 400 500 600 700 800 900 1000 10-8
Eγ (GeV) 60 70 80 90 100 200 300 E4γ0 0(GeV)
Fig.6.Left:effectivedetectionarea–dashedlinefortrigger,fullaftereventselection–asafunctionofthetrueenergy,basedon
simulationsofγ-rayscomingfromthetransitpositionofM31.Right:normalizedspectrabetween50and500GeVforapower
lawofindex-2,andforformulaofequation7withm =500(dashedcurve)and250GeV(dottedcurve).
χ0
However, the upcoming generation of γ-ray instruments will undoubtedly further constrain dark matter models and halo
modelsforvariousastrophysicalsources.Thesesearchesarenotonlycomplementarytofutureparticlephysicsexperiments,but
alsoveryimportanttounderstandhowthequestionofdarkmatterisconnectedtotheparticlecontentoftheUniverse.
Aknowledgements
Funding was provided by the IN2P3 of the French CNRS and by the Grant Agency of the Czech Republic. We gratefully
acknowledgethesupportoftheRegionalCouncilofLanguedoc-Roussillon,andofElectricite´ deFrance.Thetechnicalsupport
byAntoinePe´rez,JacquesMaurandandSte´phaneRivoireatThe´miswasinvaluable.Lastbutnotleast,weappreciativelythank
KarstenJedamzik,GilbertMoultakaandPierreSalatiforveryusefuldiscussionsduringthiswork.
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