Pulsar shadow as the origin of double notches in r

arXiv:astro-ph/0503411v225Jul2005PulsarshadowastheoriginofdoublenotchesinradiopulseprofilesJ.Dyks1PhysicsDepartment,UniversityofNevadaLasVegas,NV,[e-mail]¸ackowiak,AgnieszkaSlowikowska,B.RudakNicolausCopernicusAstronomicalCenter,Toru´n,[e-mail],[e-mail],[e-mail]artment,UniversityofNevadaLasVegas,NV,[e-mail]odelofeclipsingarotating,spatiallyextendedsourceofdirectionalemissionbyacentralabsorber,andapplyittothepulsarmagnetosphere.Themodelassumestheradiallyextendedinwardradioemissionalongthelocaldirectionofthemagneticfield,andthepulsarastheabsorber.Thegeometryofthemagneticfieldlinesoftherotatingdipoleisfavourableforthedoubleeclipseevents,whichweidentifywiththedoublenotchesobservedinpulseprofilesofnearbypulsars.Forpulsarswithlargedipoleinclinations70◦∼α∼110◦thedoublenotchesarepredictedtooccurwithinanarrowphaserangeof20◦−30◦beforethemainradiopeak.ApplicationofthemodeltoPSRB0950+08establishesitasanearlyorthogonalrotator(α≃75◦,β≃−10◦)withmanypulsecomponentsnaturallyinterpretedintermsoftheinwardradioemissionfromalargerangeofaltitudes.Theinwardcomponentsincludetheintermittentlystrong,leadingcomponentofthemainpulse,whichwouldtraditionallyhavebeeninterpetedasaconalemissionintheoutwarddirection.ThemodelalsoidentifiesthemagneticfieldlinesalongwhichtheradiallyextendedinwardradioemissionoccursinB0950+08.Thesehaveanarrowrangeofthefootprintparameterscloseto∼1.1(closedfieldlineregion,nearthelastopenfieldlines).Wedescribedirectionalcharacteristicsofinwardemissionfromtheradiallyextendedregionandcomparethemwithcharacteristicsofextendedoutwardemission.Ourworkshowsthatpulseprofilesofatleastsomepulsarsmaybeasuperpositionofbothinwardandoutwardemission.Subjectheadings:pulsars:general—pulsars:individual(PSRB0950+08)—polarization—gammarays:theory—radiationmechanisms:nonthermal1OnleavefromNicolausCopernicusAstronomicalCen-ter,Toru´n,Poland1.IntroductionThispaperaddressestwoenigmaticphenomenaobservedinaveragepulseprofilesofradiopulsars:1thedoublenotchesofB0950+08,B1929+10,andJ0437−4715(Navarro&Manchester1996;Rankin&Rathnasree1997;Navarroetal.1997,hereafterNMS97;McLaughlin&Rankin2004,hereafterMR04)aswellassomepuzzlingprofilecompo-nentsobservedinpulseprofiles,especiallyamongnearbyand/orbrightpulsars.Thedoublenotcheshavetheappearanceofab-sorptiondips,oreclipsedips:theylookasslotscarvedinacontinuousemissionpattern,notastheubiqitousminimabetweendifferentemissioncom-ponents(NMS97;MR04).Thephaseatwhichthedoublenotchesoccur,theirdepth,aswellastheirwidthweaklydependontheobservationfrequencyν(NMS97;MR04).Althoughknownforalmosttenyears(Navarro&Manchester1996;Rankin&Rathnasree1997),thedoublenotcheswereinterpretedforthefirsttimeonlyrecentlybyWright(2004).Heassumedthattheyresultfromabsorptionofradiowavesemittedbyaregionwhichisextendedoveraverylargerangeofaltitudes,comparablewiththelightcylinderradiusRlc.Thisradialextentisobvi-ouslymanifestedbythefactthatthenotchesoc-curwithinbroademissionfeaturesextendingoveralargerangeofpulsephase.Asdemonstratedinmanystudiesofhigh-energyemissionfrompulsars,thiseffectistypicalofradiallyextendedemissionregion(eg.Morini1983;Romani&Yadigaroglu1995,hereafterRY95;Dyks&Rudak2003,here-afterDR03).ThepreciousideaofWrightisthatthedoublenotcheffectisproducedbyasingleabsorber,whichprovideshismodelwithelegantsimplicity.However,thelocationoftheabsorber,andthegeometryoftheemittingregionsarefarlessnatural:theyarehardlyidentifiablewithanydiscerniblefeaturesinpulsarmagnetosphere.Inthispaperweshow(Sections2and3)thatthesingleabsorberdoesnothavetobelocatedatsig-nificantfractionofRlctobecapableofproducingthedoublenotcheffect.Thepulsaritselfcandothetrick,andtheshapeoftheemissionregionscanbeidenticaltotheshapeofthedipolarmagneticfieldlines.Thepulsarcanobviouslyplaytheabsorber’sroleonlywhentheradioemissioninthemagneto-sphereisinward,ie.isdirectedroughly“antiradi-ally”,towardstheneutronstar.Thisiswhatweassumeinthispaperatleastfortheradiallyex-tendedemissionregionsresponsiblefortheprofilecomponentswiththenotches.Asweshowintheaccompanyingpaper(Dyksetal.2005),thepecu-liarmodechangingobservedinB1822−09(Fowler&Wright1982;Giletal.1994,seeFig.4therein)canbeinterpretedintermsofemissionthatsome-timesflipsitsdirectionby180◦.Insection3weapplyourtheoryofdoublenotchestoB0950+08.Theinformationwegainfromthemodelofnotchesissubsequentlyusedtointepretenigmaticpulseprofilecomponentsinthisobject(Section5).Perhapsthemostpuzzlingofallcomponentsinpulseprofilesofpulsarsaretheinterpulsessepa-ratedfromthemainpulsesbythephaserangecon-siderablydifferentfrom180◦(eg.Manchester&Lyne1977;Hankins&Fowler1986).Threediffer-entgeometrieshavebeenproposedtoexplainthisphenomenon,butnooneisfreefromproblems.Thetwo-poleinterpretationassumesanearlyor-thogonalrotator(α∼ζ∼90◦,whereαisthedipoleinclination,ζ=α+βistheviewingan-glemeasuredfromtherotationaxis,andβistheimpactangle).Themainradiopulse(MP)andtheinterpulse(IP)aresupposedtobeobservedwhenourlineofsightapproacheseachofthetwopolarcapsandthe