High-energy Emission from Pulsar Magnetospheres

arXiv:astro-ph/0606017v11Jun2006High-energyEmissionfromPulsarMagnetospheresKOUICHIHIROTANI∗ASIAA/NationalTsingHuaUniversity-TIARA,POBox23-141,Taipei,[e-mail]eceived:01May2006Accepted:09May2006AbstractAsynthesisofthepresentknowledgeongamma-rayemissionfromthemagnetosphereofarapidlyrotatingneutronstarispresented,focusingontheelectrodynamicsofparticleaccelerators.Thecombinedcurvature,synchrotron,andinverse-Comptonemissionfromultra-relativisticpositronsandelectrons,whicharecreatedbytwo-photonand/orone-photonpaircreationprocesses,oremittedfromtheneutron-starsurface,provideuswithessentialinformationonthepropertiesoftheaccelerator—electricpotentialdropalongthemagneticfieldlines.Anewacceleratormodel,whichisamixtureoftraditionalinner-gapandoutergapmodels,isalsoproposed,bysolvingthePoissonequationfortheelectrostaticpotentialtogetherwiththeBoltzmannequationsforparticlesandgamma-raysinthetwo-dimensionalconfigurationandtwo-dimensionalmomentumspaces.1PulsarnatureandcharacteristicsWhenastarhasexhausteditsnuclearfuel,theinteriorthermalpressurecannolongersupportitsownweight.Ifthestarisnotverymassive,itcollapsestothepointatwhichelectrondegeneracypressurehaltsgravitationalcollapse,andawhitedwarfisformed.However,beyondthecriticalmass[1],eventheelectrondegeneracypressurebecomesinsufficienttosupportthestar.Inthecollapsingstellarcore,mostoftheelectronsareabsorbedbyprotonsviainverseβdecayandeventuallytheneutrondegeneracypressurehaltsthegravitationalcollapse[2,3,4].Foraprogenitorstartocollapsedirectlytoaneutronstar,itsmassshouldbemorethan10timesgreaterthanourSun.Aneutronstar,whichcanrotatewithaperiodasfastasP∼1ms,isconsideredtobetheonlycandidateforthesourceofremarkablystableradiopulses,ofwhichfastestperiodis1.55ms(PSRJ1939+2134[5]).WhenitwasdeterminedthattheperiodoftheCrabpulsarwasslowlyincreasing[6],theidentificationofpulsarsasrapidlyrotatingneutronstarswasessentiallyconfirmed[7,8].Havingestablishedpulsarsasrotatingneutronstars,thenextthingtodiscussisthepulsarcharacteristicsdeducedfromobservations.Sinceallknownisolatedpulsarsshowgradualspindown,theremustbesomemechanismscausingtheneutronstartolosetheirrotationalenergy.Therotationalenergy-lossrateisgivenby˙E=IΩ˙Ω=−(2π)2I˙P/P3,(1)wheretheneutronstarisrotatingwithangularfrequencyΩ=2π/PandmomentofinertiaI.Fortypicalhigh-energypulsars,P∼0.1s,˙P∼10−13ss−1,I∼1045gcm2;thus,weobtain˙E=−4×1036ergss−1,whichisenoughtoexplaintheobservedγ-rayluminosities,1032.5ergss−1Lγ1035ergss−1.Foranobjectassmallasr∗∼10kminradiustoexperiencesuchalargetorque,itmusthaveastrongcouplingtotheirsurroundings,mostlikelythroughmagneticfieldsintrinsictotheneutronstar.Iftheneutronstarislosingitsrotationalenergyviamagneticdipoleradiation,thespin-downluminosityisgivenbyLdip=kΩ4μ2/c3,(2)∗Postaladdress:TIARA,DepartmentofPhysics,NationalTsingHuaUniversity,101,Sec.2,KuangFuRd.,Hsinchu,Taiwan3001050100150200010203040010020030040005101520CrabVelaB1706-44Geminga0102030400510150100200300010203040010203040500510B1951+32010200246B1055-52Figure1:Lightcurvesofsixγ-raypulsarsabove100MeV(dottedlines,right-handscale)andabove5GeV(darkhistogram,left-handscale).Eachpanelshowsonefullrotationoftheneutronstar.FromThompson(2004).wherek=2sin2αi/3iscommonlyusedforavacuumrotatingmagneticdipolewithinclinationαiwithrespecttotherotationaxis.EquatingLdipwith−˙E,wecaninferthemagneticmoment,μ,ofthestar[9].ForP=0.1s,˙P=10−13ss−1,I=1045gcm2,weobtainμ=2.6×1030Gcm3andthesurfacemagneticfieldstrength,B∗=5.2×1012(r∗/10km)−3G,astheNewtonianvalueatthemagneticpole.Inwhatfollows,weconsiderpossibleemissionmodelsofisolated,rotatingneutronstars,afterbrieflymentioningthehigh-energyobservations.2Gamma-rayobservationsandphysicalprocessesTheEnergeticGammaRayExperimentTelescopeandtheimagingComptonTelescopeaboardtheComptonGammaRayObservatoryhavedetectedpulsedsignalsfromatleastsevenrotation-poweredpulsars(Crabpulsar[10,11];PSRB1509-58[12];Velapulsar[13,11];PSRB1706-44[14];PSRB1951+32[15];Gemingapulsar[16,11];PSRB1055-52[17]).Fourofthem(Crab,Vela,Geminga,andB1951+32)exhibitdouble-peakedlightcurves[18,19,20](fig.1).Sinceinterpretingγ-raysshouldbelessambiguouscomparedwithreprocessed,non-thermalX-rays,theγ-raypulsationsobservedfromtheseobjectsareparticularlyimportantasadirectsignatureofbasicnon-thermalprocessesinpulsarmagnetospheres.Spectralenergydistributions(SEDs)offersthekeytoanunderstandingoftheradiationprocesses.Ref.[17]compiledausefulsetofbroad-bandSEDforthesevenγ-raypulsars.ThemoststrikingfeatureoftheseνFνplotsisthefluxpeakabove0.1GeVwithaturnoveratseveralGeV.Variousmodels[21,22,23,24,25,26]concludethatthesephotonsareemittedbytheelectronsorpositronsacceleratedabove5TeVviacurvatureprocess.Suchultra-relativisticparticlescouldalsocauseinverse-Compton(IC)scatterings.Inparticular,foryoungpulsars,theirstrongthermalX-raysemittedfromthecoolingneutron-starsurface[27,28,29]efficientlyilluminatethegaptobeupscatteredintoseveralTeVenergies.Iftheirmagnetosphericinfrared(0.1–0.01eV)photonfieldisnottoostrong,apulsedICcomponentcouldbeunabsorbedtobedetec