Gamma rays from dark matter annihilation in the Dr

arXiv:astro-ph/0603022v11Mar2006GammaraysfromdarkmatterannihilationintheDracoandobservabilityatARGOXiao-JunBi,1,∗Hong-BoHu,1andXinminZhang21Keylaboratoryofparticleastrophysics,IHEP2TheoreticalPhysicsDivision,IHEPChineseAcademyofSciences,Beijing100049,P.R.ChinaAbstractTheCACTUSexperimentrecentlyobservedagammarayexcessabove50GeVfromthedirectionoftheDracodwarfspheroidalgalaxy.ConsideringthatDracoisdarkmatterdominatedthegammaraysmaybegeneratedthroughdarkmatterannihilationintheDracohalo.IntheframeworkoftheminimalsupersymmetricextensionofthestandardmodelweexploretheparameterspacetoaccountforthegammaraysignalsatCACTUS.Wefindthattheneutralinomassisconstrainedtobeapproximatelyintherangebetween100GeV∼400GeVandasharpcentralcuspyofthedarkhaloprofileinDracoisnecessarytoexplaintheCACTUSresults.WethendiscussfurtherconstraintsonthesupersymmetricparameterspacebyobservationsatthegroundbasedARGOdetector.ItisfoundthattheparameterspacecanbestronglyconstrainedbyARGOifnoexcessfromDracoisobservedabove100GeV.∗Electronicaddress:[e-mail]ofcosmologicaldarkmatterhasbeenestablishedbyvariousastronomicalobservations.However,theevidencescomemainlyfromthegravitationaleffectsofthedarkmattercomponent.Thenatureofdarkmatterremainselusiveandkeepsoneofthemostoutstandingpuzzlesinparticlephysicsandcosmology[1].Theprimordialnucleosynthesisandcosmicmicrowavebackgroundmeasurementsconstrainthebaryoncomponentandmostdarkmattercomponentshouldbenon-baryonic.Thedevelopmentinunderstandingthelargescalestructureformationrequiresthedarkmatterbecold.Fromthetheoreticalconsiderationsthefavoredcandidateforcolddarkmatter(CDM)seemstobetheweaklyinteractingmassiveparticles(WIMPs)[1].TheWIMPscanbedetectedindirectlybyobservingtheannihilationproducts,suchasgammarays,neutrinos,anti-protonsandpositrons.Exploringtheanomalousresultsfromthecosmicrayexperimentsisoneviablewaytoidentifythedarkmatter.Sincetheannihilationrateisproportionaltothesquareofthedarkmatterdensity,theidealsitesfordarkmatterdetectionshouldhavehighdarkmatterdensity.Thegalacticcenterisbelievedtobeapromisingsourceofdarkmatterannihilation[2].However,theexistenceofthecentralsupermassiveblackholeandthesupernovaremnantSgrA∗contaminatesthedarkmattersignalsheavily.Alternativesites,suchasthesubstructuresoftheMilkyWayorthedarkmatterdominateddwarfspheroidalgalaxies(dSph),havebeenstudiedintheRefs[3,4,5,6,7].Recently,theCACTUSgamma-rayexperimentreportedanexcessofgammaraysfromthedirectionofDraco,anearbydSph[8].SinceDracoisdarkmatterdominatedandnoothergammaraysourcesareexpectedtobehosted[9,10]theexcesshasbeenattributedtotheannihilationofdarkmatterintheDracohalo[11,12].Theresultsarestillpreliminaryand,ifconfirmed,willhaveimportantimplicationsonthenatureofdarkmatterandthedensityprofileofDraco.Additionalobservationsofthesignalbyotherexperimentsisthereforeveryimportant.TheGLAST[13],asatellite-basedexperiment,andtheMAGIC[14],aground-basedAtmosphericˇCerenkovTelescope(ACT),havebeenconsideredtochecktheCACTUSresults[11,12].Inthepresentwork,wewilldiscussapossibilityofdetectingorconstrainingthegammaraysobservedbyCACTUSatARGO[15],aground-basedextensiveairshower(EAS)detector.2Inthenextsectionwewillfirstgivethegeneralformulafordarkmatterannihilation.ThenwewilldiscusstheimplicationsofCACTUSresultsonthegammarayspectrumandfluxesinSecIII.ThesensitivityofARGOisgiveninSec.IVandthenumericalresultsarepresentedinSec.V.WeconcludeinSec.VI.II.GAMMARAYSFROMDARKMATTERANNIHILATIONTheannihilationoftwoWIMPscanproducethecontinuousspectrumofgammaraysarisingmainlyinthedecaysoftheneutralpionsproducedinthefragmentationprocessesinitiatedbythetreelevelfinalstates.Thefragmentationanddecayprocessescanbesimu-latedwiththePythiapackage[16].TheannihilationrateinunittimeandunitvolumeisgivenbyR=hσvin2/2=hσviρ22m2(1)whereσandvaretheannihilationcrosssectionandtherelativevelocityofthetwodarkmatterparticlesrespectively,nandρarethenumberandmassdensitiesofdarkmatterandmisitsmass,thefactor2inthedenominatorarisesduetotheidenticalinitialparticles.Wenotethattheannihilationrateisproportionaltothesquareofthedarkmatterdensityandtherefore,ahighdensityregioncangreatlyenhancetheannihilationfluxes.ThegammarayfluxfromtheDracohaloisthereforegivenbyΦγ(E)=φγ(E)hσvi2m2RdVρ24πD2=φγ(E)4πhσvi2m2×1D2ZΔΩdΩZ4πr2drρ2(r)(2)wherethehaloprofileisassumedapproximatelysphericallysymmetricwiththedensityprofileρ(r),D=75.8±0.7±5.4kpcisthedistancetoDraco[17],φγ(E)isthedifferentialfluxatenergyEinasingleannihilationinunitof1gammaGeV−1.ΔΩrepresentstheangularresolutionofthedetector.Thedensityprofileρ(r)ofDracoisconstrainedbyobservations.Arecentanalysisshowsthatbothacoredandacuspyprofile,suchastheNFWprofile[18],areconsistentwiththeobservationaldataandtheresultsofN-bodysimulation[19].The‘astrophysicalfactor’inEq.(2)definedasΦastro=1D2ZΔΩdΩZ4πr2drρ2(r),(3)3whichisdeterminedbytheastrophysicalquantitiessolely,isseverelyconstrainedbyob-servationaldata.ItisfoundthatΦastrovariesbyafactorofapproximatelyonly200,i.e.,Φastro∼=(3.2×10−4∼6.4×10−2)GeV2cm−6kpcsrfollowingRef.[19].TheotherpartinEq.(2)isdete