Spectral Gamma-ray Signatures of Cosmological Dark Matter An

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