An Outer Gap Model of High-Energy Emission from Ro

arXiv:astro-ph/9401034v118Jan1994AnOuterGapModelofHigh-EnergyEmissionfromRotation-PoweredPulsarsJamesChiang1andRogerW.Romani2DepartmentofPhysics,StanfordUniversity,StanfordCA94305-4060Received;acceptedABSTRACTWedescribearefinedcalculationofhighenergyemissionfromrotation-poweredpulsarsbasedontheOuterGapmodelofCheng,Ho&Ruderman(1986a,b).Inthiscalculation,vacuumgapsforminregionsnearthespeed-of-lightcylinderofthepulsarmagnetospherealongtheboundarybetweentheclosedandopenfieldlinezones.Wehaveimproveduponpreviouseffortstomodelthespectrafromthesepulsars(e.g.Cheng,etal.1986b;Ho1989)byfollowingthevariationinparticleproductionandradiationpropertieswithpositionintheoutergap.Curvature,synchrotronandinverse-Comptonscatteringfluxesvarysignificantlyoverthegapandtheirinteractionsviaphoton-photonpairproductionbuilduptheradiatingchargepopulationsatvaryingrates.Wehavealsoincorporatedanapproximatetreatmentofthetransportofparticleandphotonfluxesbetweengapemissionzones.Theseeffects,alongwithimprovedcomputationsoftheparticleandphotondistributions,provideveryimportantmodificationsofthemodelgamma-rayflux.Inparticular,weattempttomakespecificpredictionsofpulseprofileshapesandspectralvariationsasafunctionofpulsephaseandsuggestfurtherextensionstothemodelwhichmayprovideaccuratecomputationsoftheobservedhighenergyemissions.Subjectheadings:gamma-rays:emission—pulsars:gammarays1PresentAddress:CITA,60St.GeorgeSt.,Toronto,Canada,M5S1A12AlfredP.SloanFoundationFellow–2–1.IntroductionSincethediscoveryofradiopulsationsfromrotatingneutronstars(Hewishetal.1968),manytheorieshavebeenproposedtoexplaintheoriginoftheseemissions.Earlymodelsinvoketheaccelerationofelectronsandpositronstoextremelyhighenergiessuchthattheradiationemittedbytheseparticlesresultsinanelectromagneticcascadeofe±pairsandphotons.Thisavalancheofchargesyieldstheobservedcoherentradioflux(Sturrock1971;Ruderman&Sutherland1975).Unfortunately,attemptsatunderstandingthephysicsofthepulsarmagnetospherebylookingonlyattheradioobservationshavemetwithlimitedsuccess.Amorefruitfulapproachwouldbetousethehigherenergyobservations,bothintermsofphotonenergyandintermsofthetotalavailableenergytobeextractedfromthepulsar,tocharacterizethemagnetosphere(Arons1992).ThepolarcapmodelsofHarding,Tademaru,&Esposito(1978),Daugherty&Harding(1982),theslotgapmodelofAronsandhiscollaborators(Scharlemann,Arons,&Fawley1978;Arons1983)andtheoutergapmodelofCheng,etal.(1986a,b;hereafterCHRa,b)andHo(1989)haveallbeenattemptstousethehighenergyobservationstorevealnatureofthepulsarmagnetosphere.GiventherecentdataobtainedbytheinstrumentsaboardtheComptonGamma-RayObservatoryandtheidentificationofadditionalgamma-raypulsars,bringingthetotaltosix—Crab,Vela,Geminga(Bertschetal.1992),PSRB1706−44(Thompsonetal.1992),PSRB1055−52(Fierroetal.1993)andPSRB1509−58(Wilsonetal.1992)—itisnowappropriateforfurthereffortstobemadetowardsunderstandingtheseobjects.Inthispaper,wepresentourownattemptsatmodelingthehighenergyemissionfromyoung,rotation-poweredpulsarsinthecontextofamodifiedoutergapmodel.Insection2,wesummarizetheresultsofapreviouspaper(Chiang&Romani1992;hereafterPaperI),inwhichageometricalcalculationoftheemissionfromtheoutergapregionswasperformedandwhichwasshowntoreproducequalitativelythelightcurvesofallthegamma-raypulsars.Insection3,wereviewthedetailsoftheoutergapspectralcalculationdescribedinCHRa,bandrestatedlaterbyHo(1989);andinsection4,wemotivateandoutlineourrefinementstotheCHRcalculation.Theyconsistofdividingtheoutergapregionintosmallersub-zonesinordertoaccountforthevariationinmagneticfieldandphotonandparticledensitiesasafunctionofpositioninthemagnetosphere.Wehavealsoincludedatreatmentofthetransportofparticlesandphotonsfromoneregionofthemagnetospheretoanother.Wefindthatthistransportcruciallyeffectstheemissionprocessesintheoutergap.Inaddition,weperformmoredetailedradiationandpaircreationcalculations.Insection5,wepresentsomepreliminaryresultsofourmulti-zonespectralcalculations;andinsection6,wediscusslimitationsofthemodelandwaysinwhichitcanbefurtherimproved.–3–2.ASimpleModelfortheOuterGapLightCurvesInPaperI,wepresentedourbasicgeometricalmodelofemissionfromtheoutergapregionsofapulsarmagnetosphere.AdoptingtheassumptionsofCHRa,wedefinedtheoutergaptoliealongtheboundaryoftheclosedfieldlineregionofamagneticdipolefieldconfiguration,boundedonthesideclosesttotheneutronstarbythenull-chargesurface,onwhichΩ·B=0,andontheoutsidebythevelocity-of-lightcylinder.However,incontrasttoCHRa,weassumedthatgap-typeregionscouldbesupportedalongallfieldlinesontheboundaryoftheclosedregionratherthanjustonthebundleoffieldlineslyingintheplaneoftherotationandmagneticdipoleaxes.Assuminguniformemissivityalongoutergapfieldslineswiththeradiationbeamedinthelocalfielddirection,wethencomputedtheemissionprofileofthepulsarprojectedontothesky.Inthismodel,thefieldgeometryisthatofadipoleintheco-rotatingframe,andwehaveincludedtheeffectsofrelativisticaberrationandtime-of-flightdelaysthroughthemagnetosphere.Figure1showstheresultofourcalculationforanearlyorthogonalrotator.AsinPaperI,thecoordinatesofthisimagearedefinedsothatro