On the instantaneous spectrum of Gamma-Ray Bursts

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arXiv:astro-ph/0405284v1 14 May 2004InternationalJournalofModernPhysicsDc󰀁WorldScientificPublishingCompany

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.WhenappliedtoGRB991216aprecisefit󰀁χ2≃1.078󰀄oftheobservedluminosityinthe2–10keVbandisobtained.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,whoseaveragedensityisassumedtobe󰀈nism󰀉=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