EnergyCosmicRays”
ArnonDar
TheoryDivision,CERN,CH-1211Geneva23,Switzerland
and
DepartmentofPhysicsandSpaceResearchInstituteTechnion,IsraelInstituteofTechnology,Haifa32000,Israel
Inaletterwiththeabovetitle,publishedsometimeagoinPRL,Waxman[1]madetheinterestingsuggestionthatcosmologicalgammaraybursts(GRBs)arethesourceoftheultrahighenergycosmicrays(UHECR).ThishasalsobeenproposedindependentlybyMilgromandUsov[2]andbyVietri[3].However,hereIshowthattherecentdatafromAGASA[4],whichdoesnotshowthesuppressionintheintensityofcosmicrays(CR)atenergybeyond∼4×1019eVthatwaspredictedbyGreisen,ZatsepinandKuz’min(GZK)forextragalacticcosmicraysduetotheirinteractionwiththecosmicbackgroundphotons[5],rulesoutextragalacticGRBsasthesourceofUHECR.
Forsimplicity,considerfirstauniformdistributionofgalaxies(orsitesofGRBs)inEu-clideanspace,withanumberdensitynperunitvolume.Let∆ECRbethemeanenergyreleaseinCRperGRBandRGtheGRBratepergalaxy.Neglectingscatteringandatten-uationintheintergalacticspace,thecontributionofsuchsourceswithinadistanceDfromEarthtotheobservedCRenergyflux(energyperunitarea,persr,perunittime)is
S≈
nRG∆ECRD
(lifetime)ofCRwithenergiesabove4×1019eV(theGZK“cutoff”energy)duetophoto-productionincollisionswiththecosmologicalbackgroundphotonsyields[6]D<15Mpc(τ<5×108y).TheattenuationofCRprotonsbelowtheGZK“cutoff”energyismainlyduetoe+e−pairproductiononthecosmicbackgroundphotons.Theattenuationlength(time)JustbelowtheGZK“cutoff”energyis[6]D∼1000Mpc(τ∼3×1010y).ItincreaseswithdecreasingenergytotheHubbleradius(Hubbletime)atabout1018.5eV,theenergyoftheCRankle.SinceD(cτ)changesattheGZK“cutoff”energybyafactor≥1000/15∼70,theintensityoftheUHECRfluxbeyondtheGZK“cutoff”issuppressedbythesamefactor.SuchasuppressionwasnotobservedbyAGASA[4].
Moreover,GRBsthatemitisotropicallyandareuniformlydistributedwithinD<20MpccannotproducethemeasuredintensityofUHECRabovetheCRankle:ThemeasuredluminositydensityinthelocalUniverseis[7]n∼1.8h×108L⊙Mpc−3.FromtheobservedrateofcosmologicalGRBs[8],Robs∼103y−1,andfromtherecentlymeasured/estimatedredshiftsofsomeGRBsandhostgalaxiesofGRBs[9],itwasconcludedthat[10]R∗<10−8y−1perL∗∼1010L⊙galaxy.ThekineticenergyreleaseinUHECRperbirth/deathofcompactstellarobjects,whicharetheplausibletriggersofGRBsingalaxies,probably,doesnotexceed[11]∆ECR∼1052erg(Waxman’sassumption,∆ECR=5ǫ×1050ergwhereǫisthemeanenergyofUHECRin1020eVunits,makesthediscrepancyevenlarger).Thus,forh∼0.65,eq.1yieldsanenergyfluxofUHECR,
S∼30
n
10−8y−1
∆ECR
20Mpc
eVm−2s−1sr−1.
(2)
TheCRabovetheanklehaveanapproximatepower-lawspectrum[4]dn/dE≈AE−βwithβ∼2.5.EvenintheveryunlikelysituationwherethebulkoftheGRBenergyiscarriedbyCRwithenergyaboveE0∼1020eV,oneobtainsfromeq.2thatforE∼E0
E
3dn
E0
1−β
∼3×1021eV2m−2s−1sr−1.
(3)
Theobservedvalue[4],E3dn/dE∼4×1024eV2m−2s−1sr−1aroundE∼E0,issmallerbythreeordersofmagnitudethanthatpredictedbyeq.3.Theaboveluminosityproblemcan
2
besolvedbypostulatingthatGRBsemitisotropicallymorethan1055erginUHECR(veryunlikely),orbyjettingtheGRBejecta[11].IftheGRBejectaiscollimatedintoanarrowjet(plasmoid)withabulkmotionLorentzfactorΓ∼103thenitsradiationisbeamedintoasolidangle∆Ω∼π/Γ2.The“isotropic”energyrelease,Eisot≡4π(∆E/∆Ω)=(4π/∆Ω)∆E∼4×106(Γ/103)2∆E,canbemuchlargerthan∆E,thetrueenergyreleaseinGRB.Thus,whilethetotalluminosity,RobsEisot,fromGRBs,isindependentofthebeamingangle,EisotcanbemuchlargerthanthatassumedbyWaxman[1]andVietri[3].However,extragalacticGRBscannotsmeartheGZK“cutoff“unlessthereisa“cosmicconspiracy”,namely,thelargescalelocalmagneticfieldsconspiretotraptheextragalacticUHECRattheGZK“cutoff”energyforatimewhichisapproximatelyequaltotheirattenuationtimeinthebackgroundradiation[12].SuchapossibilityalsoseemsveryremoteinviewofobservationallimitsonextragalacticmagneticfieldsfromlimitsonFaradayrotationofradiowavesfromdistantpowerfulradiosources[13]andfromlimitsonintergalacticsynchrotronemission:TheLarmorradiusof4×1019eVprotonsintypicalextragalacticmagneticfields,(B<10−9G),ismuchlargerthanthetypicalcoherencelength(lc<1Mpc)ofthesefields.Moreover,magnetictrappingiscompletelyruledoutifthearrivaldirectionsofUHECRcoincidewiththedirectionsofcosmologicalGRBs[2]orifthearrivaldirectionsofextragalacticUHECRareclustered[14].Thus,ifextragalacticCRprotonsbelowtheGZK“cutoff”sufferonlysmallrandommagneticdeflectionsthroughintergalacticspaceandreachusfromdistancesasfarasD∼1000Mpcaway,thentheirfluxmustshowthetheGZKsuppressionwhentheirenergyincreasesbeyond∼4×1019eV.
Thesameargumentscanberepeatedforcosmicraynucleiwhichareattenuatedviaphotodissociationbycosmicbackgroundradiations.Theyleadtothesameconclusion,namely,theUHECRwhichareobservednearEarth,mostprobably,arenotproducedbyextragalacticGRBs.However,narrowlycollimatedGalacticGRBs,mostofwhichdonotpointinourdirection,canbethesourceofnonsolarcosmicraynucleiatallenergies[15,16].
3
REFERENCES
[1]E.Waxman,Phys.Rev.Lett.75,386(1995).
[2]M.MilgromandV.V.Usov,Astrophys.J.449,L37(1995);Astropart.Phys.4,365-369(1995).
[3]M.Vietri,Astrophys.J.453,883(1995).
[4]M.Takeda,etal.,Phys.Rev.Lett.81,1163(1998)andreferencestherein.
[5]K.Greisen,Phys.Rev.Lett.16,748-750(1966);G.T.ZatsepinandV.A.Kuz’min,JETPLett.478-80(1966).
[6]S.Lee,Phys.Rev.D55,xxx(1977).
[7]J.Loveday,etal.,Astrophys.J.390,338(1992).
[8]G.J.FishmanandC.A.A.,Meagan,Ann.Rev.Astr.Astrophys.33,415(1995).[9]S.R.Kulkarni,etal.,Nature,393,35(1998);J.S.Bloom,etal.,preprintastro-ph/9808319;S.G.Djorgovski,etal.,preprintastro-ph/9808188;A.S.Fruchter,etal.,preprintsastro-ph/9801169;astro-ph/9807295.
[10]E.WoodsandA.Loeb,preprintastro-ph/9803249,submittedtoAstrophys.J.[11]A.Dar,Astrophys.J.500,L93-L96(1998).
[12]G.Sigl,M.LemoineandP.Biermann,Ultra-highastro-ph/9806283.[13]P.P.Kronberg,Rep.Prog.Phys.57,325(1994).[14]N.Hayashida,etal.,Phys.Rev.Lett.77,1000(1998).[15]A.Dar,Preprintastro-ph/9809193,submittedtoPRL.
[16]A.DarandR.Plaga,Preprint,submittedtoNature,November1998.
4
因篇幅问题不能全部显示，请点此查看更多更全内容