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Spectral Gamma-ray Signatures of Cosmological Dark Matter An(2)

时间:2025-05-09   来源:未知    
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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

(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

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