High Energy Emission from Rotation-Powered Pulsars

SubmittedtoTHEOPENASTRNOMYJOURNAL,May12,2008HighEnergyEmissionfromRotation-PoweredPulsars:Outer-gapvs.Slot-gapModelsKouichiHirotaniASIAA/NationalTsingHuaUniversity,TIARA,P.O.Box23-141,Taipei,TaiwanPostaladdress:TIARA,DepartmentofPhysics,NationalTsingHuaUniversity,101,Sec.2,KuangFuRd.,Hsinchu,Taiwan300Weexploreparticleacceleratorelectrodynamicsinthemagnetosphereofarapidlyrotatingneutronstar(NS).Weaddresstheimportanceofaself-consistenttreatmentofpairproduction,solvingthePoissonequationdescribingtheaccelerationelectricfield,theBoltzmannequationsforproducedelectronsandpositrons,andtheradiativetransferequationsimultaneously.ItisdemonstratedthattheacceleratorsolutionisobtainedifweonlyspecifytheNSspinperiod,magneticdipolemoment,magneticinclinationanglewithrespecttotherotationaxis,andtheNSsurfacetemperature,andthatthesolutioncorrespondstoaquantitativeextensionofpreviousouter-gapmodels.WeapplytheschemetotheCrabpulsarandshowthatthepredictedpulseprofilesandphase-resolvedspectrumareroughlyconsistentwithobservations.Applyingthesameschemetotheslot-gapmodel,weshowthatthisalternativemodelpredictstoosmallphotonfluxtoreproduceobservations,becausethegaptrans-fieldthicknessissignificantlyrestrictedbyitspair-freecondition.INTRODUCTIONRotation-poweredpulsarsareexcellentlaboratoriesfortestingparticleaccelerationtheories.Themajoradvantageofstudyingpulsarsisthatweknowthattheyarepoweredbyrotationalenergyloss.Itisgenerallyacceptedthattherotatingmagneticfieldworksasaunipolarinductortoexertalargeelectro-motiveforceonthespinningneutronstar(NS)surfaceandthattheresultingpotentialdropintherotatingmagnetosphereleadstotheaccelerationofchargedparticlestoultra-relativisticenergies.Thechallengeisthentoinvestigatewhereandhowtheyconvertthisenergyintoradiationthatweobserve.Thepulsarmagnetospherecanbedividedintotwozones(Fig.1).Theclosedzoneisfilledwithadenseplasmaco-rotatingwiththestar,whereastheopenzoneallowsplasmastoflowalongtheopenfieldlines,escapingtolargedistancesthroughthelightcylinder.Here,thelightcylinderislocatedatdistanceϖLC=c/Ωfromtherotationaxis,whereΩdenotestheNSrotationalangularfrequencyandcthespeedoflight.Thelast-openfieldlines,whichbecomeparalleltotherotationaxisatthelightcylinder,formtheborderoftheopenmagneticfieldlinebundle.Inallthepulsaremissionmodels,particleaccelerationandtheresultingphotonemissionstakeplacewithintheopenzone.Fig.(1).Schematicfigure(sideview)ofthepulsarmagnetosphere.Theslotgapextendsfromthestellarsurfacetothelightcylinderonthelast-openfieldline(intheopenzone)withtrans-fieldthicknessmuchlessthantheoutergap.Theoutergapistraditionallyassumedtobelocatedbetweenthenullchargesurfaceandthelightcylinder.Attemptstomodeltheparticleacceleratorinapulsarmagnetosphereconcentrateontwoscenarios:polar-cap(PC)modelswithemissionaltitudeswithinseveralNSradiiaboveaPCsurface(Hardingetal.1978;Daugherty&Harding1982;Dermer&Sturner1994;Sturneretal.1995),andtheouter-gap(OG)models-2-withaccelerationoccurringnearthelightcylinder(Chengetal.1986a,b;Chiang&Romani1992,1994,Romani&Yadigaroglu1995;Romani1996;Zhang&Cheng1997;Chengetal.2000).Bothmodelspredictthatelectronsand/orpositronsareacceleratedinachargedepletionregion,apotentialdrop,bytheelectricfieldalongthemagneticfieldlinestoradiatehigh-energygamma-raysviathecurvatureandinverse-Comptonprocesses.ItiswidelyacceptedfromphenomenologicalstudiesthatcoherentradiophotonsareemittedfromthePCaccelerator.ItshouldbenotedthatthePCmodelpredictstheso-called‘pencilbeam’emissionwithasmallsolidanglealongthemagneticaxis,becausetheemissiontakesplaceonlyfromtheloweraltitudes(i.e.,neartheNSsurface).Sincetheradiopulsationgenerallyexhibitsasinglesharppeakineachrotationalperiod,wecanreproducesuchpulseprofilesiftheobserver’sviewingangleisclosetothemagneticinclinationangle.However,toexplaintheincoherenthighenergyemissions,whichgenerallyexhibitwidelyseparateddoublepeaks,onehastoinvokeaverysmallmagneticinclinationangleandtheobserver’sviewinganglewithrespecttotherotationaxis.Thus,toexplaintheγ-raypulsationsdetectedfromallthesixbrightestpulsars(forCrab,Nolanetal.1993,Fierroetal.1998;forVela,Kanbachetal.1994;Fierroetal.1998;forGeminga,Mayer-Hasselwanderetal.1994;Fierroetal.1994;forPSRB1706-44,Thompsonetal.1996;forB1509-58,Matzetal.1994;forB1951+32,Ramanamurthyetal.1995,Kuiperetal.1998)intermsofthespin-downluminosity,ahigh-altitudeemission,whichresultsintheso-called‘fanbeam’emissionwithalargesolidangle(~1ster),drewattentionasanalternativepossibility.Thepossibilityofahigh-altitudeextensionofthePCacceleratorwasoriginallyintroducedbyArons&Scharlemann(ApJ1979).Developingthiselectrodynamicalmodel,andincorporatinggeneralrelativisticeffects(MuslimovandTsygan1992,hereafterMT92),Muslimov&Harding(2003,hereafterMH03)begandiscussinghigh-energyemissionfromthepulsarslotgap(SG),anarrowregiononthelast-openfieldlinewherethemagnetic-field-alignedelectricfield,E||,isdecreasingandacceleratingparticlescannotcreatepairs.ThenMuslimov&Harding(2004,hereafterMH04)extendedthislower-altitudesolution(withinafewstellarradii)tohigheraltitudes(neartheligh