198 6ApJ. . .304. .2413 moderately intensesourcewithahardenergyspectrum(Ricker minutes (~700s)werediscoveredbyWhiteetal(1976). et al1973).Itsopticalcounterpartwasidentifiedwithanearly- period ofthisbinarysystem.White,Mason,andSanford(1978, type supergiant(B1.5la),Wray977(Vidal1973;Bradtetal The AstrophysicalJournal,304:241-248,1986May1 made usingspectroscopicandphotometricobservationsof the hereafter WMS)obtainedanorbitalperiodof40.8daysfroma where nisaninteger<20.Orbitalsolutionswithperiods of pulse-timing analysisbasedonAriel5observations.Kelley, © 1986.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. Hammerschlag-Hensberge etal1976;MauderandAmmann optical counterpartWray977(Bordetal1976; all theavailabledata.Variousopticalstudieshavealsobeen orbital periodwhichcouldbeexpressedasPæ456/ndays, Ariel 5data.Theyobtainedseveralacceptablesolutionsfor the pulse-timing analysisbycombiningSAS3datawiththeWMS with eachothernorinagreementtheX-rayperiods. periods suggestedfromtheopticaldataareneitherconsistent 35.0 and32.5daysweresuggestedasthemostcompatible with Rappaport, andPetre(1980,hereafterKRP)alsoperformeda the periodicityinX-rayflaring eventsofGX301-2observed after WWC)havereportedaperiod of41.5daysonthebasis 1977). X-raypulsationsfromGX301-2withaperiodof11.6 with Ariel5.Thisvalueisclose toanothercandidateorbital 1976; vanGenderen1977;Pakull1978).However,theorbital period, 41.4days,inthesolutions derivedfromthepulse- orb 1 The X-raysourceGX301-2/4U1223-62wasdiscoveredasa Many attemptshavebeenmadetodeterminetheorbital More recently,Watson,Warwick,andCorbet(1982,here- NAS/NRCResearchAssociate. events ofthesource.Theorbitalelementsbinarysystem,establishedfromjointtiminganalysis,are viously measuredwithAriel5andSAS3.Thejointtiminganalysisofthesedatasetsyieldsanorbitalperiod presented. OurorbitalsolutionsuggeststhatallthepeaksofX-rayflaresobservedduringpast10yroccur and withTenmain1984April.PulsearrivaltimesmeasuredHakuchowerecombinedthosepre- at theorbitalperiod,butconsistentlyappear~1.4daysbeforetimeofperiastronpassageX-ray of 41.5daysastheonlyacceptablesolution;thisisconsistentwithperiodderivedfromX-rayflaring Subject headings:stars:individual—X-rays:binaries star. Space ScienceDepartmentoftheEuropeanAgency,ResearchandTechnologyCenter,Noordwijk,TheNetherlands © American Astronomical Society • Provided by the NASA Astrophysics Data System X-ray outburstsfromGX301-2wereobservedwithHakuchoontwooccasionsduring1982AprilandMay I. INTRODUCTION ORBITAL ELEMENTSOFTHEBINARYX-RAYPULSARGX301-2 Department ofPhysicsandCenterforSpaceResearch,MassachusettsInstituteTechnology Laboratory forHighEnergyAstrophysics,NASA/GoddardSpaceFlightCenter Department ofAstrophysics,NagoyaUniversity,Japan Institute ofSpaceandAstronauticalScience,Japan Received 1985April8;acceptedOctober23 N. SatoandF.Nagase 1 R. L.Kelley S. Rappaport N. E.White ABSTRACT N. Kawai AND 241 timing analysisofKRP.PriedhorskyandTerrell(1983)have data. ReexaminingtheAriel5/SAS3jointpulsetiming days asthebestestimateofflarerecurrenceperiodbased of theX-rayintensityGX301-2basedonVelasatellite also confirmedthe41.5dayperiodicitybyatimeseriesanalysis observations between1969and1976.Theygive41.52±0.02 (1985) carriedoutatiminganalysisofthesedatainwhich, The detailsoftheseobservationshavebeendescribedby an orbitalperiodof41.46±0.04days. analysis, WhiteandSwank(1984,hereafterWS)haveobtained on boththeAriel5andVelasatelliteX-rayphotometric bility oftheX-rayintensityandpulseprofile.Kawaiet al satellite duringtheperiod1982April6-20andMay16-21. because oftherelativelyshortdurationHakuchodata, consistently supportedbothbythepulsetimingandX-ray 41.524 ±0.006days.Hence,anorbitalperiodof41.5days is period moreaccuratelythanWS,andtheyobtained Hakucho observationenabledthemtodeterminetheorbital baseline betweentheAriel5/SAS3observationsand the orbital parametersfixedatthevaluesgivenbyWS.The long they allowedPtobeafreeparameterbutheldtheremaining Mitani etal(1984),inwhichtheyalsodiscussthetimevaria- intensity andperiastronpassage oftheX-raystaris~1.4days. photometric (i.e.,flares)analyses. GX 301-2/Wray977system,wehavecarriedoutajointfit to ments withanorbitalperiod of41.51days.Thedetailsthe the combinedpulsearrivaltime dataobtainedwithAriel5, find thatthedifferencebetween thetimeofmaximumX-ray SAS 3,andHakucho.Weobtain auniquesetoforbitalele- analysis andthefullorbitalsolutions aredescribedin§II.We orh The X-raypulsarGX301-2wasobservedwiththeHakucho In ordertoestablishdefinitivelytheorbitalelementsof 198 6ApJ. . .304. .2413 lite duringtheinterval1984April21-27.Thelightcurveand measured duringthisintervalwereusedinthepresentanalysis the energyspectrumobservedwithTenmaaredescribedby to furtherconfirmtheorbitalparameters. Makino, Leahy,andKawai(1985).Thepulsearrivaltimes 242 SATOETAL.Vol.304 (2) 109arrivaltimesmeasuredwithSAS3duringtheinterval (4). for dataset(1),KRP(2),andKawaietal(1985)(3) descriptions oftheindividualdatasetsarepresentedbyWMS measured withHakuchoduring1982May16-21.Detailed with Hakuchoduring1982April6-20,and(4)27arrivaltimes an intervalof61daysfrom1977September7toNovember6, data sets:(1)114pulsearrivaltimesmeasuredwithAriel5over interval istooshorttoplayaneffectiveroleinthedetermi- included inthefirststepofanalysissinceobservation found thatthepulsearrivaltimescouldbetrackedcoherently nation oftheorbit. also availablefromobservationsmadewithTenmaduringthe orbital periodfixedateachtrialvalue andoptimizingtheremainingparameters(seetext)areshownforperiods intherange15-70days. throughout eachoftheobservationintervals,butnotover 3 dayinterval1984April24-27.However,thisdatasetisnot gap betweenthedatasets.Accordingly,pulsearrivaltime equation (1)representstheDopplerdelayscausedbyaneccen- derivatives ofthepulseperiodrespectively.Thelasttermin data set.ThequantitiesPandarethefirstsecondtime where PisthepulseperiodatinitialepochTinkth t ofthenthpulseinkihdatasetwasfittedtofunction 1979 January20toFebruary19,(3)39arrivaltimesmeasured k k nk 2 2 GX 301-2wasalsoobservedrecentlywiththeTenmasatel- In thepresentjointanalysis,wehaveusedfollowingfour An additionaldatasetconsistingof13pulsearrivaltimesis Fig. 1.—Reducedxvs.trialorbital period forGX301-2basedonAriel5,SAS3,andHakuchotimingdata.The reducedxvalueswereobtainedbyholdingthe In ouranalysisoftheAriel5,SAS3,andHakuchodatawe © American Astronomical Society • Provided by the NASA Astrophysics Data System =2 II. TIMINGANALYSISOFJOINTDATASETS tk Tk+PniP^P^ nk + asiniF(e,co,t,0),(1) x 2 2 2 2 (a) bothPandarefreeparametersfor/c=1;(b)onlyisa longitude ofperiastronco,timepassaget,and tric orbitwithprojectedsemimajoraxisasin/,eccentricitye, changes intheintrinsicpulseperiodfollowingmanner: mean anomaly6.Theisgivenby0= Hakucho data,althoughtheirmethodsoferrordetermination in pulsearrivaltimesdeterminedbyWMSforAriel5data, free parameterfork=2and3;(c)P0 elements, asini,c,co,t,andPwereassumedtobeconstant 2n(t —T)/P,wherePistheorbitalperiod.All trial valuesbetween15and70daysfittedfortheremaining are eachsomewhatdifferent. KRP forSAS3data,andbyKawaietal.(1985)the discussed later.Inthefollowingfits,wealsoadoptederrors that wasobtained.Inthiscaseall17parameters,includingthe detailed fitsweremadeinthevicinityofeachlocalxminimum steps, thusyieldingaminimumversusorbitalperiod.Next, k =4.ThevalidityofthischoiceP-andP-termswillbe (1M4). during theintervalbetween1977and1982.Thesubscriptkfor clearly seeseverallocalminimaaround32.5,35,38,45,and57 plotted againstorbitalperiodinFigure1.Thesmallestvalueof orbital period,weretakentobefreeparameters. as largethatforanorbitalperiodof41.5days.Theaccept- days (thesevaluescorrespondtothesolutionsderivedbyKRP X (1.16)isobtainedforanorbitalperiodof41.5days.Onecan now berejected,becausethecorrespondingxvaluesaretwice as seenintheirTable1).However,thesealternateperiodscan limits of90%and99%respectively,forthecase273degrees formally acceptablesolution. able valuesofxareformally1.11and1.20forconfidence 16 parameters.Theorbitalperiodwasincrementedin1day of freedom.Hence,theorbitalperiod41.51daysisonly T, P,andPrunsfrom1to4,correspondingdatasets x xorh orb 2 In thefittingprocedure,weincludedtermsrepresenting As afirststep,weheldtheorbitalperiodPfixedatvarious The reducedxvalues(x)obtainedbythisprocedureare orb C/} 1 CM^r • No. 1, 1986 GX 301-2 243 00o ; From our fits to all the orbital parameters (in the vicinity of TABLE 1 ^ Porh = 41.5 days), we obtained a best-fit orbital period of Orbital Elements of the GX 301-2 System and § 41.508 ± 0.007 days (all errors cited are single-parameter 1 a Pulse Period Parameters3 S confidence limits). The best-fit values of the parameters are 2 listed in Table 1. The Doppler delays estimated from the best- Parameter Value fit parameters in Table 1 are compared with the Ariel 5, SAS 3, Orbital Elements and Hakucho pulse arrival times in Figure 2. One might suspect that the choice of the P and P terms Porb (days) 41.508 + 0.007 ax sin i (lt-sec) 371.2 ± 3.3 would afiect the resulting values of the best-fit parameters. To /(M)(Mg) 31.9 ±0.8 examine this question, we performed fits with several com- £? 0.472 ±0.011 binations of P and P for the various data sets and found that œ — 50?1 ± 2?6 the inclusion of such higher order terms did not substantially t(JD) 2,443,906.56 ± 0.16 improve the fits. In most cases, the best-fit orbital parameters Pulse Periods derived with the higher order terms were consistent with those Ariel 5: in Table 1, within the accuracy of the determinations. This P^s) 696.665 ± 0.017 result can be understood in term of the relatively short dura- Pj -2.44 ± 0.19 x 10"7 tion of the Hakucho data sets. Pi (s'1) 7.4 ±0.8 x 10"14 Finally, we used equation (1) to fit jointly the pulse arrival STS 3: times of the four data sets discussed above in addition to a fifth P2(s) 698.376 ± 0.015 7 P2 -0.68 ±0.10 x 10“ data set obtained with Tenma (k = 5). For this fifth data set we Hakucho: assumed that P5 — P5 = 0 (the time span of these data is only P3(s) 697.538 ± 0.041 7 3 days). We find that fits starting with values of Porh around P3 4.66 ±0.64 x 10" 41.5 days yield best-fit parameters and pulse periods which are P4(s) 698.246 ± 0.043 consistent with those derived from the joint fits without the 3 All quoted uncertainties are single-parameter 1 o confidence limits. Tenma data set. All parameters derived from the fits with and without Tenma data are completely self-consistent. A pulse period of 701.14 + 0.03 s was determined for the Tenma data that an orbital period of 41.508 days is the uniquely acceptable set of 1984 April. This value is the largest of the periods thus far solution. This value for the orbital period is consistent with observed for GX 301 -2. that derived by WWC and by Priedhorsky and Terrell (1983) to within the accuracy of those determinations. The present in. DISCUSSION analysis has improved the accuracy of the orbital period and We have found from a joint timing analysis of Ariel 5, SAS 3, has established definitive orbital parameters for the GX 301-2/ and Hakucho data sets of pulse arrival times from GX 301-2 Wray 977 binary system. A schematic orbit corresponding to
600
3420 3440 3460 3480 Julian Day -2,440,000 Fig. 2a Fig. 2.—Doppler delay curves for GX 301-2, from (a) Ariel 5, (b) SAS 3, and (c) Hakucho. Solid curves represent the delays predicted from the orbital parameters in Table 1. The vertical bars are the measured delays after subtracting the delays due to a constant pulse period and changes in the intrinsic period. The dots are the residual differences between the measured delays and the fitted orbit.
© American Astronomical Society • Provided by the NASA Astrophysics Data System 00 O CM j 244SATOETAL.Vol.304 scopic observationsofWray 977.Ourdeterminationofthe Mopt =30±5MbyParkes etal(1980)fromtheirspectro- the best-fitparametersisshowninFigure3foraninclination R =43(Parkesetal.1980)forthecompanionstarWray angle i=90°andanassumedmassM30radius Joss andRappaport1984). eccentric orbit(e=0.47)and thelargestmassfunction 977. Thisbinarysystem,GX301-2/Wray977,hasthemost which theorbitalparameters havebeendetermined(see,e.g., [/(M) =32M]amongthe ~10binaryX-raypulsarsfor 0 optq opt0 0
The massoftheopticalcounterpart hasbeenestimatedtobe Time Delay(sec) Time Delay(sec) © American Astronomical Society • Provided by the NASA Astrophysics Data System 3890 391039303950 5060 5080 5100 5120 I1 1 ^I Julian Day-2,440,000 Julian Day-2,440,000 Fig. 2b Fig. 2c /(M) of30.3M(2aconfidencelimit),which,inturn,yields 0 æ0.2(seeFig.3),thelimit on inclinationangleisestimated mass function,/(M)=31.9+0.8M,yieldsalowerlimit to for theneutronstar(JossandRappaport1984).From lack mass toM>35.Aplausible setofparametersisiä75° the constraintM>33,foranassumedmassof1.4 M to bei<78°.Thisincreases thelowerlimitonprimary of X-rayeclipses,whichwouldoccuraroundorbitalphase and Mæ38,whichtakes intoaccountalltheX-rayand 0 optical constraints. opt0 opt0 0 opt0 Because ofthecorrelation between orbitalelementsand 198 6ApJ. . .304. .2413 No. 1,1986 the structureofneutronstarinGX301-2system. technique forinvestigatingthebehaviorofstellarwind and coverage isunavailable,apoordeterminationoforbital Orbital phasesaremarkedaroundtheperimeteroffigure.ThephaseX-rayflarepeakisindicatedbydoublearrow. parameters willoftenyieldsystematicerrorsinthedetermi- pulse periodsthatcanoccurwhencompleteorbitalphase fact thatboththesesystemsarestellarwind-drivenX-ray with attachedarrowsindicatethechangesinintrinsicperiod have nowestablishedthebinaryorbit,wewereabletorevise more preciselydetermined,detailedstudiesofpulseperiod directly measuredduringtheobservations.Itisclearthat GX in Figure4alongwiththehistoryoflong-termchanges tions. Therevisedpulseperiodvalues(seeTable1)areshown the pulseperiodsandtheirratesofintrinsicchangefordata nation ofpulseperiodsandtheirintrinsicchanges.Sincewe present analysis(Table1). We determinethattheflare sets usedintheanalysisaswellfromotherpreviousobserva- change, suchasthetiming-noisepoweranalysismade by scales ofweekstoyears.Thisbehaviorisquitesimilar that pulse period.Thosevalueswhichareplottedascircleddots based ontheflaredataand obital solutionthenavailable.In the timeofflaremaximumandperiastronpassage, sources. AstheorbitofGX301-2systembecomeseven of VelaX-l(Nagaseetal1984)andmaybeassociatedwith the (KRP), andHakucho(Mitani etal1984),wherephasezero periastron passageasobserved byAriel5(WWC),SAS3 Boynton etal(1984)forVelaX-l,maybecomeapromising 301-2 exhibitsbothspin-upandspin-downepisodeson time refers tothetimeofperiastron passageasdeterminedfromthe Figure 5,weshowtheX-ray lightcurvesnearthetimeof Fig. 3.—SchematicviewoftheGX301-2/Wray977binarysystem,basedonorbitalparametersinTable1withassumedvaluesoïR=43R andi—90°. WWC suggestedthattherewasa1-5daydifferencebetween opt Q © American Astronomical Society • Provided by the NASA Astrophysics Data System GX 301-2 s = we : ephemeris areshowninFigure6.Theunreasonablysmall with aminimumXv°f0-14Theresidualsfromthebest-fit errors withamultiplicativefactorof0.374(asindicatedby the mated errorsinthepublishedflareepochs.Byrescalingall the value ofXvimostlikelycausedbyconservativelyoveresti- following ephemeris: thick errorbarsinFig.6)togiveax?obtain the maximum (PriedhorskyandTerrell1983;WWC;KRP; maximum slightlyprecedesperiastronpassageby~1day.To flare ephemeris: linear functionT=+PN,withanepoch,andflare study thedifferencebetweentimesofflarepeakandperias- the fittoabovedata,wedeterminedfollowingX-ray sured withTenmain1984Aprilisalsoincludedthefit.From period, P,asfreeparameters.Theepochofflarecentermea- tron passage,wefittedallthepublishedepochsofflare Mitani etal1984;RothschildandSoong1983,1985)tothe are givenequalweightandadjusted togiveaXv=1 the assumederrorbars,wecarried outafitwhereallthepoints Finally, asatestofhowsensitive thebest-fitparametersareto FNF0F F T =ID2,443,905.27±0.49, fo T =JD2,443,905.27±0.19, T =JD2,443,905.35±0.21 , P =41.519±0.012days,(2a) fo fo F P =41.519±0.005days.(2b) P =41.514±0.007days. (2c) F F 245 198 6ApJ. . .304. .2413 © American Astronomical Society Áüsudiui pdZ!]DUiJON