On the instantaneous spectrum of Gamma-Ray Bursts
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arXiv:astro-ph/0405284v1 14 May 2004InternationalJournalofModernPhysicsDcWorldScientificPublishingCompany
ONTHEINSTANTANEOUSSPECTRUMOFGAMMA-RAY
BURSTS
REMORUFFINI,CARLOLUCIANOBIANCOandSHE-SHENGXUE
ICRA—InternationalCenterforRelativisticAstrophysicsandDipartimentodiFisica,Universit`adiRoma“LaSapienza”,PiazzaleAldoMoro5,I-00185Roma,Italy.
PASCALCHARDONNET
ICRA—InternationalCenterforRelativisticAstrophysicsandUniversit´edeSavoie,LAPTH-LAPP,BP110,F74941Annecy-le-VieuxCedex,France.
FEDERICOFRASCHETTI
ICRA—InternationalCenterforRelativisticAstrophysicsandUniversit`adiTrento,ViaSommarive14,I-38050Povo(Trento),Italy.
VAHEGURZADYAN
ICRA—InternationalCenterforRelativisticAstrophysicsandYerevanPhysicsInstitute,AlikhanianBrothersStreet2,375036,Yerevan-36,Armenia.
Received(receiveddate)Revised(reviseddate)
Atheoreticalattempttoidentifythephysicalprocessresponsiblefortheafterglowemis-sionofGamma-RayBursts(GRBs)ispresented,leadingtotheoccurrenceofthermalemissioninthecomovingframeoftheshockwavegivingrisetothebursts.Thedeter-minationoftheluminositiesandspectrainvolvesintegrationoveraninfinitenumberofPlanckianspectra,weightedbyappropriaterelativistictransformations,eachonecorrespondingtoadifferentviewingangleinthepastlightconeoftheobserver.TherelativistictransformationshavebeencomputedusingtheequationsofmotionofGRBswithinourtheory,givingspecialattentiontothedeterminationoftheequitemporalsurfaces.Theonlyfreeparameterofthepresenttheoryisthe“effectiveemittingarea”intheshockwavefront.Aselfconsistentmodelfortheobservedhard-to-softtransitioninGRBsisalsopresented.WhenappliedtoGRB991216aprecisefitχ2≃1.078oftheobservedluminosityinthe2–10keVbandisobtained.Similarly,detailedestimatesoftheobservedluminosityinthe50–300keVandinthe10–50keVbandsareobtained.
Keywords:blackholephysics—gammarays:bursts—gammarays:observations—gammarays:theory—radiationmechanisms:thermal—radiationmechanisms:general
1.Introduction
Gamma-RayBursts(GRBs),followingtheobservationsbytheBATSEinstrument
(Paciesasetal.1),havebeencharacterizedbyafewglobalparameters(seee.g.
Fishman&Meegan2)suchasthefluence,thecharacteristicduration(T90orT50),
12R.Ruffini,C.L.Bianco,P.Chardonnet,F.Fraschetti,V.Gurzadyan,S.-S.Xue
andtheglobalspectraldistributiongivene.g.bytheBandrelation(Bandetal.3).Afterthediscoveryoftheafterglow(Costaetal.4),twoadditionalimportantpa-
rametershavebeenadded:thepower-lawindexesoftheafterglowandthesource
luminosity.
IthasbecomeclearthatavarietyofdifferenterasarepresentintheGRB
dataandthatGRBsquitepossiblyhavethemostextremetime-variationofany
phenomenainnature(seee.g.Ruffinietal.5andreferencestherein).Wepresent
hereanattempttoderivefromfirstprinciplestheinstantaneousGRBluminosityin
selectedenergybandsandtheGRBspectra.WeuseGRB991216astheprototype
(seeRuffinietal.6)sincethissourceoffersasuperbsetofdatabyBATSEinthe50–
300keVband(seeBATSERapidBurstResponse7)andbyR-XTEandChandra
inthe2–10keVband(seePiroetal.8,Corbet&Smith9)tobecomparedtothe
theoreticallypredictedonesinthe2–300keVrange.Wealsogivephysicalreasons
fortheoftenmentionedhard-to-softtransitionobservedinthemajorityofGRBs
(seee.g.Fronteraetal.10,Ghirlandaetal.11,Piran12,Piroetal.13).
2.Themodel
ThecompletedynamicsofGRB991216hasbeencomputed(seeRuffinietal.5).
Theinitialconditionsweadoptedforthissourceatt=10−21s∼0sareaspherical
shellofe+-e−-photonneutralplasmalyingbetweentheradiir0=6.03×106cmand
r1=2.35×108cm:thetemperatureofsuchaplasmais2.2MeV,thetotalenergy
Etot=4.83×1053ergandthetotalnumberofpairsNe+e−=1.99×1058.These
conditionshavebeenderivedfromvacuumpolarizationprocessesoccurringinthe
dyadosphereofanElectroMagneticBlackHole(EMBH)(Ruffini14,Preparataet
al.15).
Theopticallythickelectron-positronplasmaself-propelsitselfoutwardreaching
ultrarelativisticvelocities(Ruffinietal.16),theninteractswiththeremnantofthe
progenitorstarandbyfurtherexpansionbecomesopticallythin(Ruffinietal.17).
Asthetransparencyconditionisreached,theProper-GRB(P-GRB)isemittedwith
anextremelyrelativisticshellofAcceleratedBaryonicMatter(theABMpulse,see
Ruffinietal.18).ItisthisABMpulsewhichgivesorigintotheafterglowthrough
itsinteractionwiththeISM,whoseaveragedensityisassumedtobenism=1
particle/cm3.Insuchacollisionthe“fullyradiativecondition”isimplemented(see
Ruffinietal.5fordetails):theinternalenergy∆Eintwhichresultsisinstantaneously
radiatedaway.
Theequationsofmotioninourmodeldependonlyontwofreeparameters:
thetotalenergyEtot,whichcoincideswiththedyadosphereenergyEdya,andthe
amountMBofbaryonicmatterleftoverfromthegravitationalcollapseofthepro-
genitorstar,whichisdeterminedbythedimensionlessparameterB=MBc2/Edya.
Thesetwoparametershavebeendeterminedbyfitting,withhighaccuracy,the
bolometricintensityandtheslopeoftheafterglow(Ruffinietal.18).Wehavealso