On the 110 keV Feature From A0535+26 Direct Eviden

arXiv:astro-ph/9603077v115Mar1996ONTHE110keVFEATUREFROMA0535+26:DirectEvidenceForANear-CriticalMagneticField.RafaelA.Araya.Dept.ofPhysicsandAstronomy,TheJohnsHopkinsUniversity,Homewoodcampus,Baltimore,MD21218.andAliceK.Harding.LaboratoryforHighEnergyAstrophysics,NASAGoddardSpaceFightCenter,Greenbelt,MD20771.Subjectheadings:line:formation—magneticfields—radiativetranfer—stars:neutron—X-rays:starsReceived;accepted–2–ABSTRACTArecenthighresolutionmeasurementofanabsorptionlineatω≃110keVinthephase-averagedspectrumofA0535+26(Groveetal.1994)andtheconspicuousabsenceofapreviouslyreportedharmonicfeatureatω∼50keV(Kendziorraetal.1992,1994)areindicativeofcyclotronscatteringinamagneticfieldofabout1013G.However,controversyhasrisenoverwhetheralowerfieldscenariomayaccountfortheallegedabsenceorweaknessofalowerenergyfundamentalharmonicfeature.Thisworkexploresthesetwoalternativesthroughthegenerationoftheoreticalcyclotronspectra.Forlowerfieldmodels,acylindricalgeometryofthelineformingregionandthestrongangledependenceofthecrosssectionforresonantscatteringconspiretofillinafirstharmonicatω≃57keV.Higherfieldmodels(B≃10.75TG),however,yieldsignificantlybetterfits(X2low/X2high∼71),thusstrengtheningthecaseforanear-criticalfield(Bcrit≃44TG).Phase-resolvedOSSEspectraarenotyetavailablebutwouldgreatlyhelpinresolvingthisissue.–3–1.INTRODUCTIONNotwithstandingthelackofspectralevidenceforfieldsabove∼5TG,near-criticalmagneticfieldsofneutronstarsareinvokedtoexplainsomeveryrapidpulsarspindownratesthroughmagneticdipoleradiation.However,recentspectralobservationsofthetransientX-raypulsarA0535+26bytheOSSEinstrumentonboardtheComptonGammaRayObservatoryhavefurnishedthemostcompellingevidenceyetforthestrongestmagneticfielddirectlyobserved.Groveetal.(1994)reportthedetectionofahighlysignificant(F-testP10−15;Grove,priv.comm.)absorptionlinefeatureatω≃110keVandtheconspicuousabsenceofanobviousharmonicfeatureatalowerenergy.Ifduetocyclotronresonantscatteringatthefundamentalenergy,thisphase-averagedspectrumwouldconfirmtheexistenceofamagneticfieldB≃14Bcritforthisobject.HEXEobservationsofanearlieroutburst(Kendziorraetal.1994)showedafeaturearound100keV(∼4.5σ)aswellasaweak(∼2σ)featureatω≃50keV(theHEXE/TTMinstrumentsonboardMIR,havebetterlowenergyresponsebutcoarserhighenergyresolutionthanOSSE).Cyclotronlinesarequasi-harmonicspectralfeaturesgeneratedbyscatteringofresonantphotonswiththeelectronsofamagnetizedplasma.Theinteractionisresonantbecausetheelectron’smomentumeigenvaluesperpendiculartoB,p⊥/me=n(B/Bcrit),arediscrete.Theresonantphotonenergies,ωn/me=[(1+2n(B/Bcrit)sin2θ)1/2−1]/sin2θ,andthescatteringprofilesdependonthephoton’spropagationanglewithrespecttothefieldθ.Consequently,thelineshapesareheavilyinfluencedbytheplasmageometry.Asevidencedabove,toproperlymodelasourcewithanear-criticalfield,Bcrit=m2c3/e¯h,arelativistictreatmentisrequiredregardlessoftheelectrontemperature.TheoreticalcyclotronspectrahaverecentlybeeninvestigatedbyWang,WassermanandSalpeter(WWS1988),Wangetal.(1989)andbyAlexanderandM´esz´aros(AM1989).OurschemeimprovesonpreviousworkbymakinguseofbothQEDmagnetic–4–scatteringcrosssectionsandrelativisticangleredistributionofphotons.Inaddition,theprocessofphotonspawning(i.e.degradingofphotonstolowerharmonicenergiesthroughelectronexcitationandsubsequentmultipledecay)isconsideredindetailanduptofourharmonicsareincluded.Forlowenoughdensitiesand/orhighmagneticfields(therequirementfortheapplicabilityofoursourcecode),thephoton-electroninteractionsarepredominantandcollisionaltermsmaybeignored.Specifically,theradiativecyclotronde-excitationrateisgivenby(Latal1986)νr=αme[c2/¯h](B/Bcrit)βwithβ∈[2,.5]fortheundercriticalandovercriticalfieldlimitsrespectively.ForB12≃1,thisbecomesνr∼2×1015B212sec−1.Comparingthelatterexpressionwiththatfromthecollisionalrate(Bonazzola,HeyvaertsandPuget1979),νc=5×108(ne/1021cm−3)B−3/212,andconsideringthatthecontinuumopticaldepths,τc∼5.×10−4,inthepresentworkgivelowcolumndensities:nl∼7.5×1020cm−2,theneglectofcollisionsisreadilyjustified.Moreover,thepredominanceofthemagnetizedvacuummotivatesonechiefassumption:theconsiderationofunpolarizedphotonsonly.WWS88reportthataveraged(vacuummode)polarizedspectracloselyresembletheunpolarizedcaseforopticaldepthsofafew.A0535+26isanX-Raybinarytransientpulsarwithapulseperiodof104sec.Theorbitalperiodis111daysandthecompanionoftheneutronstarisa12M⊙Bestar.X-Rayepisodesforthesystemareclassifiedinto:giant,normalandnoburst(Motchetal.1991).Whenanoutburstdoesoccur,itistypicallyassociatedwithperiastronpassage(Hutchings1984).Bothdetectionsofcyclotronlinefeaturesweremadeduringgiantoutbursts.Cyclotronlinefeaturesabove100keVinthespectraofX-raypulsarshavebeendifficulttodetectforseveralreasons.First,highresolutiondetectorswithgoodefficiencyathighenergieshaveonlyrecentlybeguntoobservethesesources.Second,theintrinsicspectraofmanyX-raypulsarsturnoveratenergiesabove∼20keV.Thesefactssuggestthatevenifsuchhighfieldsarecommon,fewmaybediscoveredthroughtheirspectralsignature.ThehardnessofthecontinuumspectrumofA0535+26belowtheturnoveranditsbrightness–5–duringoutburstsmake