Spectral Gamma-ray Signatures of Cosmological Dark Matter Annihilation

We propose a new signature for weakly interacting massive particle (WIMP) dark matter, a spectral feature in the diffuse extragalactic gamma-ray radiation. This feature, a sudden drop of the gamma-ray intensity at an energy corresponding to the WIMP mass,

SpectralGamma-raySignaturesofCosmologicalDarkMatterAnnihilations

LarsBergstr¨om,JoakimEdsj¨o

DepartmentofPhysics,StockholmUniversity,SCFAB,SE-10691Stockholm,Sweden

PieroUllio

SISSA,viaBeirut4,34014Trieste,Italy

Weproposeanewsignatureforweaklyinteractingmassiveparticle(WIMP)darkmatter,aspectral

featureinthedi useextragalacticgamma-rayradiation.Thisfeature,asuddendropofthegamma-rayintensityatanenergycorrespondingtotheWIMPmass,comesfromtheasymmetricdistortionofthelineduetoWIMPannihilationintotwogamma-rayscausedbythecosmologicalredshift.Unlikeotherproposedsearchesforalinesignal,thismethodisnotverysensitivetotheexactdarkmatterdensitydistributioninhalosandsubhalos.PACSnumbers:95.35.+d;14.80.Ly;98.70.Rz

arXiv:astro-ph/0105048v2 13 Dec 2001

Ithasbeenknownsincelongthatparticledarkmat-terannihilationsmayproduceanobservablegamma-raylineOneoftheprimeparticledarkmattercandi-datesisaWIMP(WeaklyInteractingMassiveParticle),ofwhichthesupersymmetricneutralinoisafavouriteex-ample.WIMPannihilationintoγγandZγwouldgivemonochromaticgammarayswithanenergyequalto(orcloseto)theWIMPmassSincethesegammaraysaremonochromaticandhavehighenergytheywouldcon-stituteaspectacularsignatureofannihilatingdarkmat-ter.

Therehasbeenarapiddevelopmentoftheunderstand-ingofhowstructureformsintheUniverse.Inthecurrentmodelforstructureformation,theΛCDMmodel,mostofthematterisintheformofnon-relativisticcolddarkmatter(CDM),butwithacontributiontotheenergydensityalsofromacosmologicalconstant(Λ).AsshownbydetailedN-bodysimulations(see,e.g.,andref-erencestherein),insuchapicturelargestructuresformbythesuccessivemergingofsmallsubstructures,withsmallerobjectsgenerallybeingdenser.TheN-bodysim-ulationsalsoshowthatthedarkmatterdensitypro leinclustersofgalaxiesandinsinglegalaxiesdevelopsasteepcuspnearthecenter,ρCDM(r)～r αwithαrangingfrom1[9]to1.5Atpresent,itisnotclearwhethertheseN-bodypre-dictionsareinagreementornotwithavailabledata.Onlargescales,thisscenariogivesexcellentagreementwithobservations,see,e.g.,thepredictionoftheLyman-αab-sorptionlinesathighredshiftsOnsmallerscales,oneofthemainpuzzlesishowtoproperlyincludebary-onicmatter.Forinstance,itappearsthatthecontra-dictionbetweenthenumberofsatellitesfoundintheN-bodysimulationofahalowiththesizeoftheMilkyWayandthenumberofthoseobservedmaybeexplainedbyplausiblemechanismswhichmakemostsmallsubhalosdarkItislessclearhowtogetagreementbetweenthemeasuredrotationcurvesofdwarfandlowsurfacebrightnessgalaxiesandthosefoundinΛCDMsimula-tions(seeforarecentreview).

HerewewilltaketheviewthattheΛCDMpictureisbasicallycorrectandthatstructureformshierarchi-cally,withthenumberdensityofhalosofmassMbeingdistributedasdN/dM∝M βwithβ～1.9–2,aspre-dictedbyPress-Schechtertheory[14]andalsoveri edinN-bodysimulations.Furthermore,wewillusethattheconcentrationofhalosgrowswithdecreasingmass.

Previousanalyses(e.g.,[15–20])havefocusedonthedarkmattergamma-raysignalsfromtheGalacticcenterandthehalooftheMilkyWayorisolatednearbygalax-iesandsatellites;inthesecasestheactualdarkmatterdistributionwithinhalosplaysacrucialrolefortheob-servability.Thepresenceofsubstructures,aswellasofcentralcusps,increasesthedetectedrates[15,17–19],butstillitmaybedi culttoresolvesuchindividualsources(see[18]).Wenowshowthattheintegratedsignalofun-resolvedcosmologicaldarkmatterhalosgivesapotentialdetectionmethodwhichismorerobusttochangesofthedetailsofhowthedarkmatterisdistributedlocally.Weconsiderthelightestneutralino,χ,oftheMSSM(theMinimalSupersymmetricStandardModel)asourtemplateparticle.Themassrangeisfromaround50GeVuptoseveralTeV(seeforarecentreview).Westartwiththe(unrealistic)caseofallthedarkmat-terbeingsmoothlydistributedatallredshifts,andthenmodifytheresultsbyintroducingstructure.Thecomov-ingnumberdensityncofneutralinos,afterdecouplingfromchemicalequilibrium(“freeze-out”)atverylargetemperatures(T～mχ/20)isdepletedslightlyduetoself-annihilations,governedbytheBoltzmannequationn˙c= σv (1+z)3n2c,where σv isthethermally-averagedannihilationrate,which,toanexcellentapprox-imationafterfreeze-out,isvelocityindependent,sincetheneutralinosmovenon-relativistically.

EachoftheχparticlesthatdisappearswillgiverisetoNγphotonsontheaverage,withanenergydistributionintherestframeoftheannihilation

dNγ(E)

dE

(E)+bγγδ(mχ E),

(1)

wherethe rsttermgivestheaveragecontinuumgamma1

We propose a new signature for weakly interacting massive particle (WIMP) dark matter, a spectral feature in the diffuse extragalactic gamma-ray radiation. This feature, a sudden drop of the gamma-ray intensity at an energy corresponding to the WIMP mass,

raydistributionperannihilatingχandthesecondtermistheγγlinecontribution,withbγγbeingthebranch-ingratiointoγγ(inthisdiscussion,weneglecttheZγchannel[6]).

Gamma-raysobservedtodaywithanenergyE0corre-spondtoanemittedenergyE=(1+z)E0.Ifwenowtrack,usingtheBoltzmanequation,thenumberofneu-tralinosthathavedisappearedfromredshiftzuntilnow,andfoldintheenergydistributionEq.(1),wecanesti-matethedi useextragalacticgammaray ingtherelationbetweentimeandredshift(see, e.g.,[22])d/dt= H0(1+z)h(z)d/dzwithh(z)=

+z)2

dz

=κ

(1dz

=Ndnγ

c

dnc

dE

dnγ4πzup

(1+z)3e

z/zmax

m2dz

(4)

100

dE

.wherewede nedΓ26= σv /(10 26cm3s 1)andm100themassinunitsof100GeV.Theterme z/zmaxaccountsforabsorptionofgamma-raysalongthelineofsight.theenergiesweareinterestedin,1GeV<<For

itisthestarlightand(poorlyknown)infrared～E0～500

GeV,back-groundradiationwhichisthelimitingfactor.Anopticaldepthoforderunityisreachedforaredshiftwhichcanbeapproximatedbyzmax(E0)～3.3(E0/10GeV) 0.8,whichisasimpli edrepresentationoftheresultsof[23,24].Theexponentialformisagoodapproximationforsmallvaluesofzmaxasinmostofourcases.Theupperlimitofintegrationiszup=mχ/E0 1,sincethemaximumrestframeenergyofaphotoninanannihi-lationeventisE=mχ.Thegammalinecontributionto(4)isparticularlysimple,justpickingouttheinte-grandatz+1=mχ/E0;ithastheverydistinctiveand

potentiallyobservablesignatureofbeingasymmetrically

smearedtolowerenergies(duetotheredshift)andofsuddenlydroppingjustabovemχ.Thecontinuumemis-sionwillproducealessconspicuousfeature,asmooth“bump”belowonetenthoftheneutralinomasswhichmaybemoredi culttodetect.Togiveanexampleoftheresults,weperformedalargescanoftheMSSMpa-rameterspaceobtainedwiththeDarkSUSYpackage[25].

Modelswithlargeγγrates((σv)2γ>～10

29

cm3s 1)ex-istinallthemassrangefrommχ=70GeVtoseveralTeV.Considerahigh-ratemodelwithmχ=86GeV,Γ26～6,bγγ～3·10 3,inthe“concordance”cosmology M=0.3, Λ=0.7,h=0.65(seeRef.[19]forthefullrangeofpredicted uxesintheMSSM).Thecon-tinuousgamma-rayrestframeenergydistributionperannihilatingparticlecomesmainlyfromhadronizationanddecayofπ0sandisconvenientlyparametrizedasdNcont(E)/dE=(0.42/mχ)e 8x/(x1.5+0.00014)wherex=E/mχ.Theresulting uxnear86GeVisaround10 15cm 2s 1sr 1GeV 1,some veordersofmagni-tudebelowthedi useextragalactic uxextrapolatedfromtheEnergeticGamma-RayExperimentTelescope(EGRET)measurements[26].

Wenowincludetheimportante ectsofstructurefor-mation.ConsiderahaloofmassMwhoseradialdensitypro lecanbegenericallydescribedby[20]ρ′DM(r)=

ρDMf(r/a),withρ′

aalengthscale.DMbeingacharacteristicdensityandThesearefoundinN-bodysimula-tionsnottobeindependentparameters,assmallerhalosareassociatedwithhigherdensities.WeassumethatthehaloofmassMaccretedfromasphericalvolumeofradiusRM,determinedbyrequiringthattheaveragecosmologicaldensitytimesthatvolumeisequaltoM,

ρ0·4πR3

3M/3=M(withρ0～1.3·10 6GeV/cm).Theincreaseofaveragesquaredoverdensityperhalo(whichiswhatenterstheannihilationrate)isgivenby:

2≡

ρDM

I2

ρ0

We propose a new signature for weakly interacting massive particle (WIMP) dark matter, a spectral feature in the diffuse extragalactic gamma-ray radiation. This feature, a sudden drop of the gamma-ray intensity at an energy corresponding to the WIMP mass,

aredenser.Again,weresorttothehighest-resolutionN-bodysimulationsavailabletodate.Fittingthecon-centrationparameterofMoore-typehalosby[20]c～100(Mvir/h 1M⊙) 0.084,we ndtoagoodapproxima- 0.22

tion 2～2·105M12,whereM12isthehalomass

12

inunitsof10solarmasses.Thismeansthattheto-tal uxfromahaloofmassMscalesasM0.78.SincethenumberdensityofhalosgoesasM 2,thefractionof uxcomingfromhalosofmassMscalesasM 1.22.Thusthegamma-ray uxwilldominantlycomefromthesmallestCDMhalos.Insimulations,substructurehasbeenfoundonallscales(beinglimitedonlybynumericalresolution).Forverysmalldarkmatterclumps,however,nogaininoverdensityisexpected,sinceoncethematterpowerspectrumentersthek 4regionaconstantdensityispredicted[18].Weconservativelyset105 106M⊙astheminimalscale.

Finally,regardingredshiftdependences,wehaveas-sumedaconstantenhancementfactor 2outtoz～1,andhavearbitrarilyimposedquadraticgrowthintheen-hancementfactorfromz～10tothefullydevelopedepochz=1.(Theobservablefeatureisnotsensitivetothisassumption.)Furthermore,inEq.(4)wemakethereplacement(1+z)3→1[27],re ectingthefactthatthewearenowdealingwithaclumped,ratherthanasmoothdistributionwithdensityscaling～(1+z)3.Wethusarriveatthefollowingexpressionforthe uxincludingstructureformationφγ=

cdE0

=8.3·10 14cm 2s 1sr 1GeV 1×

dNγ(E0(1+z))

h(z)

3

Γ26 2Mh

We propose a new signature for weakly interacting massive particle (WIMP) dark matter, a spectral feature in the diffuse extragalactic gamma-ray radiation. This feature, a sudden drop of the gamma-ray intensity at an energy corresponding to the WIMP mass,

appearwithhighsigni cance,forthelineitisoftheorderof10σfora5-yearexposurewithGLASTassumingthebackgroundextrapolation～E 2.1givenin[26],whichbecomes20σif,inanalogywiththespectralslopeofothercosmicrays,thebackgroundabove10GeVdropslikeE 2.7instead.Evenifhaloshavelesssingulardensitypro les,suchasthecoredisothermalsphere,adetectablesignaturemayappear.Alternatively,fortheMooreandNFWpro les,modelswithsmallergamma-raybranchingratiosand/orhighermassesmaybeprobed.

(f)Therelativelybroadspectralfeaturecausedbytheredshiftedgamma-raylinealleviatesthedemandforveryhighenergyresolutionofthedetectinginstrumentputbytheprevioussuggestionsofsearchingforthelineinthelocalGalacticneighbourhood.We ndthatanenergyresolutionof10–20%isinfactadequate.ForGLAST,thismeansthatthee ectiveareacaninfactbelargerthanwehaveassumed(sinceasmallerrequirementontheenergyresolutionmeansthateventsfromalargerpartofthe eldofviewofthedetectorcanbeused).(g)Ithastoberemindedthatthestrengthofthegamma-raylinecanbemuchlowerthantheexampleswechoseforFig.1,inwhichcaseadetectionwouldbecor-respondinglymoredi cult.However,inmanyofthosecasesthecontinuumsignalmaybelarge.Inparticular,we ndthatmodelscompatiblewiththerecentresultsonthemuong 2[30]accordingtothesuggestedcontri-butionsof“newphysics”(suchassupersymmetry)of[31]allgivehighvaluesforthecontinuumgamma-ray ux.(h)Althoughtheclumpystructureisinthedarkmat-terdistribution,andmaynothaveopticalcounterparts,therateoftheannihilationshouldscalewiththeoverallmatterdistributioninthenearbyUniverse.Thus,oncemassmapsfrom,e.g.,theSloanDigitalSkySurveyareavailable,across-correlationanalysiswiththegamma-raymapsshouldenableafurtherreductionofGalacticgamma-rayforegrounds.

Toconclude,wehavesuggestedanewpossiblesigna-turefordarkmatterdetection,whichemploystheclus-teringpropertiesofColdDarkMatterastheyemergefromN-bodysimulations.TheupcomingGLASTsatel-lite,andpossiblygroundbaseddetectors,mayhaveagoodchanceatdetectingthecharacteristicfeatures,inparticulartheriseandsuddendropingamma-ray uxaroundtheWIMPmassproducedbyannihilationintotwophotons.

ACKNOWLEDGEMENTS

L.B.andJ.E.wishtothanktheSwedishResearchCouncilfor nancialsupport.P.U.wassupportedbytheRTNprojectundergrantHPRN-CT-2000-00152.L.B.wantstothanktheInstituteforAdvancedStudy,Prince-ton,forhospitalitywhilethisworkwascompleted,andD.Spergelforusefuldiscussions.

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