19 93MNRAS.261. .113H Mon. Not.R.Astron.Soc.261,113-124(1993) P. A.Harrison,G.LyneandB.Anderson New determinationsofthepropermotions44pulsars Accepted 1992August28.Received28;inoriginalformMay22 tion ofneutronstarstothedetailstheirageing.Theproper to investigateawidevarietyofphenomena,fromtheforma- they havelargespacevelocitiesandtheirstudycanbeused Measurements ofthepropermotionspulsarsindicatethat place andhencetocheckitsassociationwithasupernova itselfcanbeusedtotraceapulsarbackitsbirth- through pulsetiminganalysis(Manchester,Taylor&Van remnant, ashasbeendonerecentlyfortheVelapulsar traditional opticalmethods(Wyckoff&Murray1977; Reichley 1983;Rawley,Taylor&Davis1988),orthrough Bignami &Caraveo1988).However,themostproductive University ofManchester,NuffieldRadioAstronomyLaboratories,JodrellBank,Macclesfield,CheshireSKI19DL 1 INTRODUCTION whether itbebylinkedinterferometer (Anderson,Lyne& dent measureofapulsar’sagewhichcanthenbeusedto (Bailes etal.1989).Itcanalsobeusedtoderiveanindepen- VLBI (Gwinnetal.1986),since propermotionsfromtiming Peckham 1975;Lyne,Anderson &Salter1982;Backer method sofarhasbeenthe useofradiointerferometry, observations aredifficulttomeasure exceptforpulsarswith Sramek 1982;Bailesetal.1990; Fomalontetal.1992),or study theevolutionofneutronstarmagneticfields. low timingnoise. Oftheradiointerferometric studies,byfar 1974; Helfand,Taylor&Manchester1977;Downs It ispossibletomeasurethepropermotionsofpulsars © Royal Astronomical Society • Provided by the NASA Astrophysics Data System 1 ABSTRACT A programmeofobservationstomeasurethepropermotions44pulsarshasbeen proper motionand13upperlimits.Observationswerecarriedoutwithtwointerfero- meters oftheMERLINradiosynthesisinstrumentat408MHz.Bywide-fieldphase carried outatJodrellBankoverafour-yearperiod,yielding31determinationsof number ofepochs.Thechangeinthemeasuredpositionwithepochresults positions ofeachpulsarrelativetoitsreferencesourceshavebeendeterminedfora referencing tomultiplesourceswithintheprimarybeamofinstrument,accurate from thatstudy,i.e.pulsarsformapopulationofhigh-velocityobjects(withrmsspeed Lyne, Anderson&Salter.Thenewmeasurementsdoublethenumberofinterfero- metrically measuredpropermotionsandreinforcethegeneralpicturewhichemerged determination ofthepropermotionpulsar,usingamethodsimilartothat traditionally heldviewsaboutpulsarbirthplaces. movingtowardsthegalacticplane,however,impliesthatthereisasmall population ofpulsarsbornfarfromtheplane,requiringsomemodification decay ontime-scalesofafewmillionyears.Theobservationsmallnumber age determinationsalsosupporttheconclusionthatmagneticfieldsofpulsars Key words:-pulsars:general. - 300kms~)whichseemtobemigratingfromthegalacticplane.Thenewkinetic The measurementswerecarriedoutusingatechnique within theprimarybeamofinterferometer(Peckham the relativepositionofpulsarwithrespecttoitsreference telescope atJodrellBankwith the26-mantennaatDefford possible withabsoluteastrometry. 408 MHzusingwide-fieldphasereferencingtosources similar tothatdescribedbyLAS.Observationsweremadeat MERLIN systemwereusedrather thanone:the76-mLovell ments ontheLASexperiment. First,twobaselinesfromthe 2 THEOBSERVATIONS sources, enablingmuchhigheraccuracythanwouldbe 2.1 Theobservingtechnique the largestisthatofLyneetal,(1982)(hereafterLAS),who of 127and68kmrespectively. Thesecond,shorter,baseline and withthe25-mantennaat Knockin,providingbaselines that study,butincludesthreepulsarsincommonan current surveyof44pulsarsisintendedtobeanextension made propermotionmeasurementsof26pulsars.The allowed theuse ofreferencesourceswhich werefully attempt toimproveuponLyneetal.’smeasurements. 1973). Astrometrycouldthenbeperformedtodetermine There were,however,anumber ofsignificantimprove- 19 93MNRAS.261. .113H 114 P.A.Harrison,G.LyneandB.Anderson increase insensitivity alsoresultedinthenumber ofphase weaker andmoredistantpulsars tobemeasured.This doubling thebandwidthof observations. polarization wererecorded andcorrelated,effectively pendent measureofposition.Secondly, twohandsofcircular resolved onthelongerbaseline, aswellgivinganinde- The consequentincreaseinsensitivity allowedgenerally Table 1.Positionsandpropermotionsof44pulsars.Theassumedpositionsthepulsarsaregiven,togetherwith number ofreferencesources,N,andthepropermotionsinrightascensiondeclination.Notethatju=(da/dt)cos<5. are given,togetherwiththepropermotioningalacticcoordinates,correctedfordifferentialrotationandsolar (see Section3). a(J2000)óNf 0523+11 052556.374111515.403 0458+46 050204.500465404.951 0450+55 045407.600554339.502 0447-12 045008.759-124806.766 0329+54 033259.314543442.731 0320+39 032326.604394453.924 0148-06 015122.628-063500.304 0136+57 013919.876581431.995 0820+02 082309.750015912.694 0655+64 070037.805641811.294 0559-05 060158.974-052749.662 0540+23 054309.600232906.192 0525+21 052852.192220022.803 2306+55 230813.928554735.132 2224+65 222552.270653531.642 2053+36 205531.369363021.033 2044+15 204639.404154032.533 2043-04 204600.138-042125.243 0942-13 094428.923-135441.445 0940+16 094331.046163121.882 0919+06 092213.894063821.655 0906-17 090838.124-173936.553 0818-13 082026.314-135054.862 0751+32 075440.627323157.445 0643+80 065314.679805159.612 0626+24 062905.664241556.783 0611+22 061417.220222958.803 2351+61 235404.681615547.942 2154+40 215701.942401744.922 2148+63 214958.632632943.313 2113+14 211613.774141421.222 2110+27 211304.433275402.644 1839+56 184044.3905653.961 1821+05 182331.014055024.753 1322+83 132145.787832337.982 1946+35 194825.068354011.233 1937+21 193938.585213459.263 1917+00 1950.661002140.194 1911-04 191354.204-044047.592 1905+39 190734.808400206.042 1842+14 184454.885145413.891 1718-02 172057.243-021223.192 1112+50 111538.333503013.884 rda 1953+50 195518.934505954.154 rc © Royal Astronomical Society • Provided by the NASA Astrophysics Data System is thenormalizedcovarianceoftwocomponentspropermotion.Thetotalmotionanditspositionangle 1 -11+5 -30+4 -53+20 -20+19 -23+5 -15+8 -23+2 -13+6 mas yr“ 144+3 -8+3 -9+7 -9+10 -1+32 -3+7 -2+4 -2+30 -4+5 -7+12 -4+5 26+9 30+7 52+6 22+3 23+16 27+11 15+47 22+3 13+29 19+7 17+1 16+6 11+4 19+3 18+8 18+1 14+3 0+20 5+11 9+10 9+16 7+13 5+11 1+35 8+15 Ma 1 -17+2 -30+34 -19+5 -13+1 -30+5 -21+2 -13+6 -51+3 -22+14 -31+7 -14+29 -16+7 -54+3 -40+11 -11+5 mas yr“ 112+3 -2+4 -4+5 -3+18 -4+8 -1+8 -1+3 -3+7 -7+8 -3+3 -1 +10 -5+9 -3+1 45+6 54+5 64+37 13+7 12+8 11 +1 10+4 7+3 7+9 8+5 9+11 2+12 6+2 0+27 3+3 3+4 t¿6 with thepulsar period,sothatthesignalcould becollected general, thelargernumberof referencesourcesalloweda per pulsar,comparedwith1.2 fortheLASexperiment.In reference sources(giveninTable 1)foreachpulsarbeing more accurateestimateofthe proper motion. significantly greater,withanaverage of2.9referencesources In thisexperimentthecorrelator wasgatedsynchronously PpaHi Mtota.1 -0.01 -0.22 -0.14 -0.15 -0.36 -0.25 -0.16 -0.19 -0.10 -0.79 -0.20 -0.33 ^-0.10 -0.28 -0.03 -0.10 -0.41 0.06 0.08 0.62 0.24 0.26 0.47 0.06 0.55 0.25 0.14 0.23 0.43 0.34 0.24 0.48 0.03 0.03 0.41 0.10 0.12 0.48 0.09 0.12 0.27 0.46 0.10 0.11 182+3 masyr“ 48+11 55+6 21 +1 22+5 46+6 22+7 21 +18 30+7 34+5 34+58 37+3 29+8 55+19 56+3 25+15 65+37 32+7 24+8 11+4 59+5 22+14 23+3 59+3 14+45 10+8 16+3 19+3 18+1 17+3 14+10 13+6 11 +18 15+8 3+27 4+3 4+8 8+4 7+17 5+9 2+32 9+16 5+12 5+14 -150+13 -177+83 -110+50 -146+59 -125+4 -157+2 -45+21 -71+29 52.1+0,9 -11 +12 -76+9 -30+33 -77+18 -23+5 -90+100 108+3 127+3 152+10 117+13 157+3 146+13 164+17 132+18 144+53 98+9 45+11 58+20 69+27 93+9 75+5 99+3 54+12 11+26 1 -18+16 -13+5 -24+2 -48+37 -52+3 -11+15 mas yr“ 184+3 -6+5 -9+3 -1+8 -3+8 -5+14 -1+4 40+4 22+1 26+52 40+8 28+6 40+6 22+25 52+19 54+13 34+10 23+9 19+6 21+4 25+3 19+2 14+3 17+1 3+19 3+7 5+9 5+28 2+3 0+7 2+4 2+16 3+6 5+5 1+13 1+10 1+8 1+8 Mi 1 -12+13 -17+26 -20+5 -14+5 -28+8 -10+16 -13+1 -13+13 -16+2 mas yr“ -2+19 -9+25 -7+8 -5+10 -4+5 -4+10 -5+8 -8+14 -5+4 -1+3 24+6 46+29 23+7 34+5 47+3 54+3 30+14 29+9 25+4 19+3 19+3 13+6 0+3 0+1 0+5 9+6 8+10 3+36 6+7 2+27 7+24 5+6 1+8 2+2 1+3 Mb 19 93MNRAS.261. .113H for apulsarwithtypicalpulsedutycycleof4percent.The from thepulsarduringon-pulsetimesandrefer- were subsequentlyaveragedfor1minpriortophase tion ofaccurateoff-linephasecorrectionstothedata,which improvement insignal-to-noiseratiobyafactorofabout5 ence sourcesduringtheoff-pulsetimes.Thisresultsinan have acompletesampleofpulsarsouttocertaindistance, As faraspossibleforstatisticalanalysisitispreferableto referencing. data werecollectedin5-sintegrationstoallowtheapplica- ter thanabout10mJy.Asexplainedabove,aftergatingatthe -averaged fluxdensityofthepulsarat408MHzbegrea- potential candidates.Anadditionalrequirementwasthatthe these criteria,itwasalsonecessarytofindoneormore and inthiscaseallpulsarsnearerthanabout3kpcwere 2.2 Thepulsarsample pulsar. correlator theeffectivefluxdensityofpulsarwouldbe width oftheinterferometer.Beforeastrometricobserva- in theplaneofskythan50-arcminprimarybeam- of itsinterestingevolutionaryhistory,asitisamillisecond about 50mJy,providingsufficientsignal-to-noiseratioina tions started,asurveyofthefieldaroundeachpulsarwas satisfy thefirstofabovecriteria.Itwasobservedbecause This wasperformedusingthefacilityofon-linesystemto suitable referencesourcesthatlaynofurtherfromthepulsar The resultofthisprocedurewasthat,56pulsarsobserved LAS, fig.1),whichisessentiallyacrudemapofthebeam produce asnap-shotfringefrequency/delaydiagram(see carried outinordertodetectpotentialreferencesources. MHz hastheadvantageofprovidinghigherpulsarfluxden- in Table1assuitableformeasurement. required strengthsimplybyvisualexaminationoftheseplots. radio frequencies.Whileahigherfrequencypotentially interferometer’s widerprimarybeam,ascomparedtohigher as potentialcandidates,only12didnothaveatleastone area. Itwaspossibletodetectareferencesourceofthe 1937 +21wasincludedinthesample,althoughitdidnot 1-min integrationtoallowphasereferencing.ThepulsarPSR Bailes etal.(1990)who,usinganobservingfrequencyof1.6 tion anddiminishedionosphericeffects,thenumberofrefer- provides moreaccurateresultsbecauseofincreasedresolu- sities andgreaternumbersofreferencesourceswithinthe suitable phasereferencesource,leavingthe44pulsarslisted ence sourceswithintheprimarybeamisreduced.This was designedtohavemostobservation epochsatthesame aswellbyproper motion.Sincetheexperiment the Sunwillhavetheirapparentpositionsaffectedbyannual pulsars, butwithsubstantiallygreateraccuracythanwaspos- time ofyearinordertominimize systematicerrors,itwasnot GHz, wereabletomeasurethepropermotionsofonlysix possible tosolvefortheannual parallaxasthisrequires is aboutthesize oftheanticipatedmeasurement errors. largest valueofparallaxexpected isonlyabout4mas,which observations spacedthroughout theyear.Furthermore, sible inthisexperiment. dilemma isillustratedbycomparingtheseresultswiththoseof Once apulsarhadbeenselectedfromthecatalogueusing The choiceoftherelativelylowradiofrequency408 It shouldbenotedthatpulsarswhicharerelativelycloseto © Royal Astronomical Society • Provided by the NASA Astrophysics Data System The observationswerecarriedoutbetween1984October for thesubsequentderivationofreferencesource from thetruecentroidposition,dependingonhourangle words, noattemptwasmadetotakeaccountofanyreference the assumedpulsarpositionswerederivedfromdatataken positions. Thepositionsofthereferencesourcesrelativeto these five.TheassumedpulsarpositionsintheJ2000.0ref- and 1988Februaryduringatotaloffiveseparatesessions, of theresidualinterferometerphasedifference.Inother in the1984or1985sessionsbyaleast-squaresminimization out atJodrellBank.Thesepositionswereusedasthebasis of unpublishedsources,mainlytimingobservationscarried catalogue ofManchester&Taylor(1981),andfromavariety erence frameareUstedinTable1andtakenfromthe although mostofthepulsarswereonlyobservedonfour by firstsubtractingthecalculatedinterferometerphase the phasedifferencebetweenpulsarandreferencesource this fashionis10mas,although,ofcourse,theabsolute 2.3 Datareduction mined foreachpulsar-referencesourcepairbymodelling using thephasereferencetechnique,anerrorinabsolute pulsar positionsareknown(typicallyafewarcsec).However, positional accuracyislimitedbythetowhich coverage. Thetypicalerrorinarelativepositionmeasured source structure,whichhastheeffectofcausinganoffset tion atareferenceepoch,andthenbyfittingfortheposition as afunctionofhourangleandepoch.Thiswascarriedout position measurements. position causesonlysecond-ordererrorsintherelative ence sourcestructure,alow-orderpolynomial(fittedatthe dechnation forthepulsar.Inanattempttodealwithrefer- and propermotioncomponentsinrightascension difference fortheassumedpulsar-referencesourcesepara- then thedifferenceininterferometerphasebetweensucces- phase ateachepochbeforethepropermotionfitwas reference )wasremovedfromtheinterferometer proper motionofthepulsar,sincereferencesourcesare attempted. Ifthesourcestructuredoesnotvarywithtime UT1-UTC correctionsandtelescopeaxisoffsetcorrections. must beremovedfromthedata,includingpolarmotion, motion. Inpractice,thereareseveralsystematiceffectsthat phase, gradientsintheintegratedelectroncontentcause ing removesmostoftheeffectsionosphereon due totheinfluenceofionosphere.Whilephasereferenc- assumed tobeextragalacticandhavenointrinsicproper sive epochsataparticularhourangleisonlyfunctionofthe too complextomodelaccuratelywiththesparse phase differenceswhicharedifferentforradiosourcesat measurements ofthetotalelectroncontentthatwereavail- mated thattheeffectofrelativeionosphericrefractioncould slightly separatedpositions.Ionosphericbehaviourproved worst case(Harrison1990). However,withseveral able, andnocorrectionwasappliedtothedata.Itesti- pulsar-reference sourcevectors havingdifferentposition and referencesourceofafew tensofmilliarcsecondsinthe account fordifferentialpositional changesbetweenpulsar increase theobservederrorin thepropermotiondetermina- tion, ratherthan tocauseasystematicoffset. onthesky,average effectoftheionosphereisto An estimateofthepropermotionpulsarwasdeter- The largestsystematicerrorthatremainedinthedatawas Pulsar propermotions115 19 93MNRAS.261. .113H to produceanaveragepropermotionforeachbaseline.For each pulsar-referencesourcepair,andtheresultscombined observations ineachhandofcircularpolarizationandfor Pulsar propermotionsweredeterminedseparatelyfor 3 RESULTS ofeachthereferencesourceswithrespecttoothers identified bytheletterP.Thisexampleshowsthatproper Figure 1.MeasurementsofthepropermotionPSR1112+50 116 P.A.Harrison,G.LyneandB.Anderson pulsars withdeclinationsabove25°,thesetwovalueswere the propermotionactuallylies.Thepulsarvectoris area ontheplotwithinwhichthereisa90percentprobabilitythat and itsassociatedreferencesources.Theerrorellipsesboundthe averaged. Forpulsarsbelowthisdeclination,thefitsmade the propermotionofpulsaritself. are allclusteredabouttheorigin,justifyingtheiruseindetermining © Royal Astronomical Society • Provided by the NASA Astrophysics Data System 0818-13 0611+22 0525+21 0329+54 Table 2.Comparisonofourresultswiththoseotherexperiments. 1937+21 1911-04 1911-04 Pulsar 1 —20±19 mas yr“ —2±4 —4±5 17±1 PSRl112+50 7±13 7±13 9±10 Pa Present —31±7 —13±1 masyr" —5±9 —5±9 —3±3 —3±7 7±9 Mi -1 —0.3+0 2 masyr -50+60 48±9 17±1 Ma <6 0±6 2±28 Previous -1 —0.5+0.3 -12+1 -36+25 masyr 230+140 15+18 <20 8+4 Mi 1 -1 with theLovell-Knockinbaselinewereineffectiveindistin- The componentsofpropermotioninrightascensionand used toobtainthefinalpropermotionvalue. hence thefitsfromLovell-Deffordbaselinealonewere guishing separatelybetweenpropermotioninrightascension by correctingforgalacticrotationandsolarmotion.The and propermotionindeclination(Harrison1990), galactic rotationcorrectionconsistedofremovingaflat together withthepropermotionsingalacticcoordinates intheJ2000.0referenceframearegiven, rotation curveofrotationalvelocity225kms“*,withtheSun after theyhavebeenreducedtotheirlocalstandardofrest tion /=48?8,¿>=26?3(Murray1986). motion oftheSunwasavelocity15.6kms"indirec- at agalactocentricdistanceof8.5kpc.Theassumedpeculiar between referencesourcepairsresultedinsignificantlynon- The benefitofusingmultiplereferencesourcesinincreasing number ofcasesforwhichreferencesourcesdidshowsig- described above,alow-orderpolynomialwasfittedtothe have beenunresolvedonthebaselinesthatwereused,but zero values.Ideally,thephasereferencesourceswouldall be seenbylookingatFig.1,whichshowsaplotoftheerror the confidenceofagivenpropermotiondeterminationcan from thecalculationofaverageforpulsar’sproper with respecttotheotherreferencesources),itwasremoved uneven houranglecoveragefromepochtoepoch. inadequate todescribesourcestructure,coupledwith changes insourcestructureorthefittedpolynomialbeing nificant propermotionspresumablyoccurredbecauseof residual interferometerphaseinanattempttoremovesource within whichthetruepropermotionslieat90percent the pulsaronsamediagram.Theellipsesboundareas ellipses ofthepropermotionsreferencesourcesand motion. Thisprocedureemphasizesthesuperiorityofthis proper motion(bylookingatitsapparent structure effectsfromthefitforpropermotion.Thesmall some ofthesourcesdidshowevidencestructure.As within theerrors. the otherreferencesourcesareclusteredaboutorigin, motions ofthereferencesourcesdeterminedrelativetoall /¿ =22±3masyr,fA,-51+3.Theproper represents thepulsarandshowsapropermotionof confidence level.TheellipsewhosecentreismarkedT’ 3.1 Accuracy a0 The resultsforthe44pulsarsarepresentedinTable1. Timing Timing Timing Interferometry Interferometry Interferometry Interferometry Method In afewcases,determinationsofthepropermotion If aparticularreferencesourcewasseentohavelarge Helfand etal.(1980) Downs &Reichley(1983) Fomalont etal.(1992) LAS LAS LAS Reference Rawley, Taylor & Davis(1988) 19 93MNRAS.261. .113H the formalerrors,anderrorinpulsarpropermotion of this. given inTable1includestheestimatederrorarisingbecause ence sourcepropermotionsweresubstantiallygreaterthan experiment overotherswheretherearefewerreference sources perpulsar.Forasmallnumberofpulsars,therefer- Royal Astronomical Society •Provided by theNASA Astrophysics Data System f f f f 1 r f f f 1 f 1 1 Table 3.Derivedparametersforthepulsarsin1.Thedistancesarederivedfromdispersion plane. ThecharacteristicageriscalculatedintheusualfashionasP/2P. measure usingthegalacticelectrondensitymodelofLyne,Manchester&Taylor(1985).Vis Dashes inthekineticagecolumnsindicatethatpulsarappearstobemovingtowardsgalactic calculated bylettingF=±VJ^2andassumingthatthebirthplaceisanywherewithin|z|<70pc. calculated assumingzeroradialvelocity,andthemaximumminimumkineticages(T=z/Tjare 2224+65 2154+40 2148+63 2113+14 2110+27 2053+36 2044+15 2351+61 2306+55 2043-04 Pulsar 1953+50 1946+35 1937+21 1917+00 1911-04 1905+39 1842+14 1839+56 1821+05 0942-13 0940+16 0919+06 0906-17 0820+02 0818-13 0447-12 0329+54 0320+39 0148-06 0136+57 1718-02 1322+83 1112+50 0751+32 0655+64 0643+80 0540+23 0525+21 0523+11 0458+46 0450+55 0626+24 0611+22 0559-05 c z r k 249 217 225 109 109 104 246 222 236 116 122 154 211 188 212 152 133 189 184 184 193 160 153 145 152 160 129 189 43 46 75 90 64 79 61 85 71 58 37 71 86 35 31 20 1 o +11.6 +14.2 +23.8 +18.9 +33.7 -11.3 -23.4 -14.0 -16.8 +60.4 +28.8 -27.4 +45.4 +36.4 +19.8 +21.2 +12.6 +26.7 +25.2 +26.8 -32.6 -14.3 -65.0 -13.5 -13.2 +5.0 +8.1 +8.9 +6.8 +7.4 -5.6 -0.2 -4.2 -0.3 -6.2 -7.1 +6.2 +3.1 +7.5 +2.4 -1.2 -3.3 -6.9 -4.0 4.584 2.643 5.023 2.107 0.821 3.449 0.944 2.503 5.000 3.041 3.029 2.302 2.358 0.477 1.125 1.413 0.320 0.423 0.749 1.456 1.316 1.071 1.029 1.337 0.518 0.843 0.273 2.000 2.600 0.888 0.967 2.514 1.035 1.482 1.533 3.236 3.281 3.279 2.646 3.183 0.407 1.231 1.211 1.384 kpc D -520 -837 -199 -336 -409 -605 -326 -376 -107 -240 -220 -729 -746 -876 -177 -764 -153 -25 -55 pc 403 648 214 253 381 355 135 765 264 278 204 134 190 533 614 305 323 689 555 176 351 116 z -8 65 53 -1 km s -1 -1 from thereferencesourcepropermotions.Thereareatotal baseline and10±13masyrfortheLovell-Knockinbase- proper motionsis7±7masyrfortheLovell-Defford measured. Theweightedmeanofthemagnitudethese of 99referencesourcesforwhichapropermotioncanbe Ft 489 986 263 212 314 313 301 316 454 126 118 144 121 155 327 247 206 266 248 117 288 107 133 384 131 143 110 100 111 49 The overallaccuracyoftheexperimentcanbejudged 90 89 65 61 48 32 93 85 37 74 26 66 69 7 -1 km s -115 -118 -157 -297 -117 -237 V % -30 -62 -58 -22 -48 -15 -14 -56 -32 -49 -72 -69 235 102 132 345 182 101 287 184 132 -9 -2 -3 48 77 41 85 22 13 75 29 64 19 98 4 3 0 4519.3 234.8 195.6 131.9 My t 24.0 35.8 97.5 36.9 53.0 37.3 87.0 52.1 16.6 15.4 21.3 79.1 67.4 67.7 18.8 10.5 19.1 c 7.1 7.3 9.6 6.0 2.6 3.2 0.9 3.2 4.8 5.5 1.1 1.6 0.5 9.5 9.3 2.3 0.4 5.1 3.8 0.1 0.3 1.5 1.8 Pulsar propermotions117 mm 20.0 r 13.0 68.0 19.0 11.0 My 4.5 0.0 0.3 0.3 2.3 3.3 3.6 0.5 0.0 0.7 0.5 2.1 4.7 1.3 5.2 2.2 0.7 0.0 0.0 0.0 6.4 0.4 1.1 1.0 3.5 3.0 3.5 5.5 3.6 3.3 1.9 1.7 1.0 1000.0 m*x r My 10.2 27.8 11.0 14.4 4.8 2.0 7.8 2.2 8.5 1.5 9.8 1.3 oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo 19 93MNRAS.261. .113H -1 118 P.A.Harrison,G.LyneandB.Anderson between themajorityofreferencesources,andfactthat yr indicatesthatthesame random errorsaredominating the meanerrorintotalpropermotionforpulsarsis7mas line. Thesevaluesareconsistentwithzeropropermotions the results. The smallnumberofpulsars inthissamplewhichhave previous proper motiondeterminationsarelisted inTable2. 3.2 Comparisonwithotherexperiments © Royal Astronomical Society • Provided by the NASA Astrophysics Data System 1 1 f f f f f f Table 4.Derivedparametersforpulsarswithotherpropermotionmeasurements.Onlythemostaccurate proper motionmeasurementisincludedinthistable.Referencekey:1-LAS;2Bailesetal.(1990);3 Fomalont etal.(1992);4-Wyckoff&Murray(1977). Pulsar 0149—16 0450-18 0355+54 0301+19 0628-28 0531+21 0823+26 0809+74 0740-28 0736-40 0833-45 0950+08 0943+10 0834+06 1237+25 1133+16 1556-44 1541+09 1540-06 1508+55 1451-68 1449-64 1426-66 1749-28 1706-16 1642-03 1604-00 1600-49 2021+51 2020+28 2016+28 1857-26 1822-09 1818-04 1804-08 2303+30 2217+47 2045-16 1933+16 1929+10 1919+21 1952+29 1944+17 217 254 237 264 244 148 161 179 220 185 313 252 242 229 225 140 335 314 316 197 332 1 91 47 21 25 20 18 52 56 11 69 68 66 55 10 14 98 98 31 88 0 6 2 1 +31.7 +31.6 -34.1 -33.3 -72.5 -16.8 +86.5 +69.2 +43.7 +43.1 +26.3 +45.8 +36.6 +52.3 +13.7 +26.1 +35.5 -13.5 -26.7 -33.1 +0.8 -5.8 -2.4 -9.2 +2.4 +6.4 -2.8 +4.7 +5.6 -8.5 -4.4 -5.4 +3.5 +1.3 +0.8 -1.0 -2.1 -3.9 +8.4 -4.7 -4.0 -3.5 -7.6 0.559 0.435 2.000 2.000 0.375 0.173 2.000 0.500 1.562 1.555 4.237 1.899 2.110 0.330 0.155 0.130 0.557 0.429 1.252 0.661 0.731 0.450 2.243 0.811 0.160 0.357 0.325 0.507 3.713 1.312 6.000 0.055 1.000 0.199 0.432 1.500 0.384 0.685 1.283 1.300 1.918 1.456 1.300 kpc D -876 -306 -415 -361 -202 -319 -173 -199 -298 -219 -210 -106 -861 -193 -85 -24 -67 pc -17 -90 -26 330 381 197 211 940 394 579 145 190 z 207 361 191 181 124 100 -4 22 91 90 70 20 12 3 1 km s“ v; 734 282 307 253 152 274 124 235 316 192 119 477 645 554 216 341 167 110 210 290 199 180 307 197 162 64 88 35 97 70 35 77 50 56 36 21 63 69 70 39 35 6 9 which the90percenterrorellipsesdonotoverlap,assuming In mostcasestheagreementwithcurrentexperiment is by Fomalontetal.(1992),However, thepropermotionsare measurements forthispulsar. in thesamequadrantand of similarmagnitudeinboth proper motionsinrightascension anddeclinationforthefit satisfactory. TheworstcaseisthatofPSR0818-13,for ment, anditsvery accuratepropermotion agrees wellwith a valueofzerofortheunquoted covariancebetweenthe PSR 0329+54wasincluded asacontrolinthisexperi- 1 km s“ -132 -234 -646 -113 -153 -274 -117 -136 v; -55 -66 -64 -35 -66 -70 -31 -79 -40 -86 -31 177 207 387 203 -4 -4 -8 -6 -4 64 61 22 39 24 59 23 47 53 82 76 21 20 0 7 3363.3 122.2 My 290.4 t 17.0 10.1 42.2 22.8 27.6 c 21.8 17.5 60.6 90.4 12.7 59.2 15.7 0.6 4.9 0.2 2.8 0.0 4.9 3.7 1.5 4.5 0.0 5.0 3.0 4.0 2.3 5.1 1.0 0.2 3.4 0.9 3.1 1.6 2.9 1.5 1.1 2.7 8.6 3.1 2.8 r k ^_min My 0.6 0.0 2.6 0.1 0.3 0.9 0.6 1.2 0.0 1.6 0.3 0.5 0.0 0.8 2.2 0.2 9.3 1.3 0.5 0.0 0.6 0.2 0.0 6.3 0.0 8.8 1.3 0.0 0.5 0.0 1.3 0.0 1.4 0.8 0.7 0.8 3.5 2.1 1.1 m** r My 18.0 40.0 22.0 18.0 70.0 11.0 18.0 30.0 4.5 2.6 0.7 0.9 7.2 2.4 0.9 3.0 3.6 3.7 5.1 3.4 oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo reference 4 3 3 3 2 3 1 2 1 1 1 2 2 2 3 1 1 2 3 1 1 1 3 3 3 3 1 1 3 3 1 1 3 1 1 3 1 1 1 1 1 1 1 19 93MNRAS.261. .113H the pulsarPSR0611+22.Thiswasduetopoorquality nificantly ontheupperlimitofpropermotionobtainedfor that ofLAS.Thecurrentexperimentfailedtoimprovesig- the timingmeasurementofRawleyetal.(1988)wassuperior motion ofthemillisecondpulsarPSR1937+21,forwhich in thisexperiment,aswasourdeterminationoftheproper determination ofPSR1911-04wasalsoonlyanupperlimit of thereferencesourcesinfield.Thepropermotion due tothenarrowpulsewidthandexceptionalrotational The transversespeedofeachpulsarcanbecalculatedusinga stability ofthispulsar. (1985). ThesevaluesaregiveninTable3forthenew electron densitymodelofLyne,Manchester&Taylor distance derivedfromitsdispersionmeasureandthe 4 TRANSVERSEVELOCITIES parameters. Table4liststhesamederivedparametersfor measurements, togetherwithanumberofotherderived and Fomalontetal.(1992). other propermotions,measuredbyLAS,Bailesetal.(1990) listed inTables3and4isshownbythesolidlineupper plot ofFig.2.Theareasthehistogramboundedbya limit hasbeenplacedonthepropermotion,sothatthese dashed lineincludethosepulsarsforwhichonlyanupper Figure 2.(a)Thetransversespeed distributionforthepulsarsin the presentsample,combinedwith thoseofLAS,Bailesetal.(1990) which onlyanupperlimittothevelocity hasbeenmeasured,(b)The transverse speeddistributionof pulsarsdeterminedfromtheir and Fomalontetal.(1992).The dashedlineindicatespulsarsfor scintillation characteristics (Cordes1986). A histogramshowingthetransversespeedsforpulsars © Royal Astronomical Society • Provided by the NASA Astrophysics Data System a) b) _1 2-1 1 1 12/ pulsars mightreallybeinbinssituatedtowardstheleft diagram. verse velocityisnotjustanupperlimit.Forthesepulsarsthe median transversespeedis167kms,themean,(F), (F)i/2 =248kms.Themagnitudesofthree-dimensional it shouldberememberedthatthereareinaddition20upper mates forthesampleasawhole,(F)=177kms~and to halftheirupperlimits,thenweobtain,asthebestesti- these pulsarsareassumedtohavetransversevelocitiesequal limits whichhavenotbeenincludedinthiscalculation.If averages aresubstantiallyhigherthanthoseofLAS,although that themeanandrmsspeedsare217302kms~ measured transversespeedsbyafactorv3/2onaverage,so 217 kms"andthermsspeed,(F),is281s"^These respectively. the interstellarscintillationofsignal(Lyne&Smith1982; of thetransversevelocitieshavebeenmeasuredbystudies different fromthatofthosepulsarsforwhichthemagnitudes space velocitiesofthepulsarsarelikelytobegreaterthan biased towardslowspeeds.Thiseffectiscausedprimarilyby which isunaccountedforinthescintillationspeedestimates the concentrationofscatteringtowardsgalacticplane, sented inFig.2showsthatthescintillationsampleisstrongly Cordes 1986).Comparisonofthetwodistributionspre- Figure 3.Thetransversespeed distributions ofalltheinterfero- metrically measuredpropermotions whenselectedaccordingto(a) age and(b)distance. t t t There arenowatotalof66pulsarsforwhichthetrans- The distributionoftransversespeedsappearstobequite a ) b ) Pulsar propermotions119 19 93MNRAS.261. .113H 120 P-A.Harrison,G.LyneandB.Anderson biased byselectioneffects.Fig.3illustratesthiswell verse speedsisdifficultbecausetheobservedsample underlying pulsarpopulationfromtheobservedtrans- fraction oftheirlifetimesatlowenoughgalactic¿-distanceto pulsars aredividedintotwoclasses,accordingtoeithertheir TRANSVERSE SPEEDANDMAGNETICFIELD teristic ageinFig.3(a),astheyoungerpulsarshaveavelocity borne outbythedistributionsselectedaccordingtocharac- be detectedinpulsarsurveys.Thisinterpretationseemsto pulsars tendedtohavesmallervelocities,whichtheyinter- characteristic ageortheirdistance;theyoungerandmore displaying thetransversespeeddistributionswhen not beenincludedinthesubsequentsectionsofthispaper. preparation). Forthisreason,thescintillationspeedshave Helfand &Tademaru(1977)firstnotedthattherewasa Using thesmallsampleofpropermotionsthenknown, the olderpulsars. number oflow-velocitypulsars.Otherauthors(Cordes i.e. theoverallvelocitydistributionunderestimates than aselectioneffect.Theywentontoarguethat,asthe preted asmeaningthatslowpulsarshadlowerradiolumino- distance-selected plotofFig.3(b)onthesmallerdataset Chugai &Yungel’son(1984)madeasimilarplottothe distant apparentlyhavethegreatervelocities.Tutukov, and isdiscussedinmoredetailbyHarrison&Lyne(in distribution withahigherproportionoffastpulsarsthando objects areselectedagainstbecausetheyspendonlyasmall opposite, sayingthatthelow-,high-velocity nearby pulsarshaveessentiallynoluminosityselection,they available tothematthattime.Theyalsofoundthecloser are indicativeoftheunderlyingvelocitydistributionatbirth, sities, suggestingthatthismightbeatruecorrelationrather 5 THECORRELATIONBETWEEN 1986; Narayan&Ostriker1990)havearguedpreciselythe The determinationofthevelocitydistribution Figure 4.The‘velocity-magnetic fieldcorrelation’. Herethetransversevelocityisplotted asafunctionofsurfacemagnetic fluxdensity. © Royal Astronomical Society • Provided by the NASA Astrophysics Data System 2 V U (0 g g (0 0) S. 0) o o o o o a FomalontetaL(1992) 0 BailesetaL(1990) - LyneetaL(1982) * Currentsample 1 10 Surface magneticflux density (gauss) > ....i 10 11 a * 0 it * .4 fields. However,despitetheincreasingnumberofpointsin to thespeed,Spearmanrankcorrelationcoefficientis plotted. Excludingthepulsarswhichhaveonlyupperlimits tion, withalloftheinterferometricallydeterminedspeeds moment ofpulsars.Thiscorrelationhaspersistedasfurther mechanism dependentonthemagneticmoment(Harrison& tions. data havebeengathered(LAS;Anderson&Lyne1983; correlation betweenthetransversespeedandmagnetic this plot,thereisstillnoobviousseparationintotwopopula- pulsars: onebornwithlowvelocitiesandmagneticfields, tion canbeexplainedintermsoftwodistinctpopulations be empty.Anderson&Lyne(1983)concludedthatselection Cordes 1986).Fig.4showsthecurrentstateofthiscorrela- truly causal,asmaybethecaseina‘rocket’acceleration tion fromconsiderationoftheselectioneffectsalone.They motion studies.Theyfailedtoproducetheobservedcorrela- effects thattheythoughtwouldbeimportantforproper effects wereprobablynotresponsibleforthecorrelation. greater distancesfromthegalacticplaneandwillbeunder- pulsars. Thusold,high-velocitypulsarswilltendtomove is acorrelationbetweenradioluminosityandagewhich 0.23, significantatthe94percentlevel. Tademaru 1975).Whilethepossibihtyofarocketmechan- and theotherbornwithhighvelocitiesmagnetic represented inoursample(seeSection4).Ifmagneticfields causes youngpulsarstobevisiblelargerdistancesthanold that mightinduceacorrelation,themainonebeingthere suggest, alongwithotherauthors(Helfand&Tademaru simulation ofthepulsarpopulation,includingselection & vandenHeuvel(1986),whoperformedaMonteCarlo magnetic fields,hencethetopleft-handcornerofFig.4will are decayingthentheoldpulsarswillgenerallyhavelower 1977; Radhakrishnan1984;Bailes1989),thatthecorrela- A * ** it A*Vtf There is,ofcourse,thepossibihtythatcorrelationis This conclusionwastestedmorethoroughlybyStollman Anderson &Lyne(1983)discussedtheselectioneffects 4 "1\ ir m•” T A 10 12 * VJrO * I■ -1.J .1 10 13 19 93MNRAS.261. .113H Figure 5.AnAitoffprojectionofthepositionsandpropermotionspulsarsinthisexperimentthoseLAS,Bailesetal.(1990) and Fomalont etal.(1992)witherrorsinthepropermotionpositionanglesoflessthan25°.The‘tails’onpulsarsrepresentextrapolated with respecttothegalacticplane(withopeninganglerepresenting theerrorindirection).Thisdoesnottakeintoaccounteffectsof those ofLAS,Bailesetal.(1990)andFomalont(1992).The ‘tails’onthepulsarsrepresentspeedanddirectionofpulsarmotion Figure 6.Arepresentationofthemotionsfromgalacticplane ofallpulsarswithin30°latitudethegalacticplaneinthisexperimentand motion ofthepulsarinlastmillionyears.Thisdoesnottakeintoaccounteffectsunknownradialvelocity,nor thesmall the unknownradialvelocity,norsmallaccelerationduetogalactic gravitationalfield. acceleration duetothegalacticgravitationalfield. extended sampleprovidedby thisexperiment,togetherwith ism hasbeendiscountedby Anderson &Lyne(1983),the metries (Lyne&Manchester 1988), meansthatitshouldbe advances inourunderstanding ofpulsarradiobeamgeo- possible totestthepredictions ofaccelerationmechanisms more thoroughly. © Royal Astronomical Society • Provided by the NASA Astrophysics Data System The propermotionsforthissample andthoseofLAS,Bailes PLANE 6 MIGRATIONFROM THE GALACTIC graphical form in galacticcoordinatesFig. 5,inwhichthe et al.(1990)andFomalont al.(1992)aredisplayedina Pulsar propermotions121 19 93MNRAS.261. .113H 6 1 -1 1 122 P.A.Harrison,G.LyneandB.Anderson tracks thatpulsarshavefollowedinthelast1x10yrare might havemovedinthistime,becausetheunknownradial that thesetracksareonlyapproximationstohowthepulsars proper motionoflessthan25°areplotted.Itshouldbenoted plotted. Onlypulsarswitherrorsinthepositionangleoftheir population havingascaleheightof70pc,andthenmove especially forpulsarsathighgalacticlatitudes. component ofthevelocitycansignificantlyaffectpath, The observedpulsarpopulationhas\z\-300pc,whichLyne the galacticplaneshownbypositionangleofvector. pulsars inFig.5,withthelengthofavectorrepresenting away fromtheplanewithameanvelocityof100kms"and This generalmigrationofpulsarsfromthegalacticplane Ostriker 1970;LAS;Lyneetal.1985). a luminositydecaytime-scaleoffewmillionyears(Gunn& roughly consistentwiththeviewthatpulsarsarebornina exponential scaleheightinzofabout400pc.Thisvalueis et al.(1985)estimaterelatestoapopulationwhichhasan speed ofthepulsar,andanglethatmotionmakesto provides auniquemethodforinvestigationofthepossible with amagnitudeof42kmsabovetheplaneand52 decay ofneutronstarmagneticfieldsfromanobservational motion vectorstobeparallelthegalacticplanebecauseof out, withtheaveragez-velocitydirectedawayfromplane towards thegalacticplane,eventhoughtheyareatalarge the latitudelimitplacedonplot.Thereare,however,a 7 MAGNETICFIELDDECAY seen inFig.6,althoughthereisatendencyfortheproper z-distance, aphenomenonthatwillbediscussedinSection8. small numberofpulsarswhichareapparentlymoving The kineticages for theLASpulsarshavebeenrecalculated fromtheirpropermotion data,asdescribedinSection7. Figure 7.Acomparisonofthekinetic andcharacteristicagesofthosepulsarsforwhichareasonably accuratekineticagecanbedetermined. s "belowtheplane.Thismotionawayfromplanecanbe Fig. 6showsatransformedviewofthelow-latitude The newpropermotionobservationsingeneralbearthis © Royal Astronomical Society • Provided by the NASA Astrophysics Data System o from thegalacticplane,asisevidentlycaseforCrab for thepulsartohavetravelledfromanassumedbirthplace proper motionmeasurementscanbeusedtoobtainanesti- point ofview.Sinceitappearsthatpulsarsaregenerallyborn the pulsar.Thelattermightbeatarelativelylargedistance measured velocity.Themajorsourcesoferrorinthe‘kinetic mate fortheageofpulsarbycalculatingtimetaken close tothegalacticplanefromPopulationIprogenitors, pulsar. of thevelocityanduncertaintyinactualbirthplace age’ thusderivedarisefromtheunknownradialcomponent on thegalacticplanetoitspresentpositionusing few millionyears.Thequalityofthisevidencewascalledinto evidence thatthereissomefielddecayonatime-scaleof observations wereneededtoestablishbetterwhetherornot question byBailes(1989),whosuggestedthatfurther ages t=P/2P,andconcludedthattheirresultsdidshow pulsars. become significantasmorekineticagesarefoundfor on thekineticagecanberelativelylarge,asisshowninTable measurement wasquitelarge.Whileitistruethattheerrors decay wasoccurring,becausetheerroronasingle because ofthehighz-distancesupernovaevent).The which positivekineticageshavebeenmeasured(exceptfor than 40°andagalacticz-distanceofgreater70pc(i.e. PSR 0531+21whichhasananomalouslyhighkineticage ages forpulsarsfromthemeasurementsofLAS,Bailesetal. outside theprogenitorregion).Thez-velocityiscalculated sample isrestrictedtothosehavingagalacticlatitudeofless (1990), Fomalontetal.(1992)andthepresentworkfor 3, anytrendswhichexistinthewholepopulationshould parallel totheplanewaszero),andlimitsonkinetic assuming zeroradialvelocity(LASassumedthatthe c LAS comparedthesekineticageswiththecharacteristic Fig. 7showsthecomparisonofcharacteristicandkinetic 19 93MNRAS.261. .113H This isthebasisofevidencethatmagneticfielddecayin pulsars lieonorbelowthelineofequality(markedr=°o). the kineticage,whichrepresentsagoodestimateof is basedontheratioofcurrentperiodand neutron starsisoccurring.Thecharacteristicageofapulsar be occurringexponentiallywithatime-scaler,thenthe dipole ofconstantstrength. predicted bydipoleradiationfromarotatingmagnetic chronological age,thenthisimpliesthattheperiodderiv- down torque.Ifthederivedcharacteristicageisgreaterthan time-scale andthecharacteristicageas(LAS) ative, andhencespin-downtorque,isnowlessthanthat spin-down rate,whichinturnisrelatedtothecurrentspin- chronological agercanbeexpressedintermsofthedecay for themajorityofpulsars. pulsars wouldtakeifthetorquedecaytime-scalewere10or Fig. 7hasdrawnuponit(asdashedlines)thetwopathsthat interpretation ofkineticandcharacteristicages.However,as on atime-scaleoffewmillionyearsissupportedbythis velocities of±vjjlandarangebirthplaces is discussedinthenextsection,theremaybecomplications 2 Myr.TrackswithintheseUnesseemtobeplausiblepaths measurement, whicheverwasgreatest. âge (r)estimatedbycalculatingthez-velocityforradial While mostpulsarsappeartobemovingawayfromthe D the progenitorlayer.ThesepulsarsarelistedinTable5, motion towardsthegalacticplane(i.e./¿issignificantat galactic plane,thereareeightthathavesignificantapparent along withtheircharacteristicandchronologicalagescalcu- GALACTIC PLANE D 2 olevelandofoppositesigntob)alsohewelloutside to thesimplekineticmodeldescribedabove,and 8 PULSARSMOVINGTOWARDSTHE selection effectsthatshapeFig.7. k b -70