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
…… 此处隐藏:1136字,全部文档内容请下载后查看。喜欢就下载吧 ……