P.Kaaret1,E.H.Morgan2,R.Vanderspek2,J.A.Tomsick3
ABSTRACT
Wereportthediscoveryofmillisecondpulsationsfromthelow-massX-raybinaryHETEJ1900.1-2455whichwasdiscoveredbythedetectionofatypeIX-rayburstbytheHighEnergyTransientExplorer2(HETE-2).Theneutronstaremitscoherentpulsationsat377.3Hzandisinan83.3minutecircularorbitwithacompanionwithamassgreaterthan0.016M⊙andlikelylessthan0.07M⊙.Thecompanionstar’sRochelobecouldbefilledbyabrowndwarfwithnoneedforheatingornon-standardevolution.DuringoneintervalwithanunusuallyhighX-rayflux,thesourceproducedquasiperiodicoscillationswithasinglepeakat883Hzandonsubsequentdays,thepulsationsweresuppressed.Weconsiderthedistributionofspinversusorbitalperiodinneutronstarlow-massX-raybinaries.
Subjectheadings:pulsars:individual(HETEJ1900.1-2455)—stars:neutron—X-rays:binaries
1.Introduction
Shortlyafterthediscoveryofradiomillisecondpulsars,itwashypothesizedthattheneutronstarsinlow-massX-raybinaries(LMXBs)wererotat-ingathundredsofrevolutionspersecondandaretheprogenitorsofradiomillisecondpulsars(Al-paretal.1982).ThepresenceofrapidlyrotatingneutronstarsinLMXBswasnotconclusivelyes-tablisheduntilthediscoveryofcoherentmillisec-ondpulsationsfromLMXBs(Wijnands&vanderKlis1998;Chakrabarty&Morgan1998).Thisdiscoveryhasgreatlyadvancedourunderstand-ingofthesesystems.Theunambiguousmeasure-mentofneutronstarspinperiodswasessentialindefinitelyestablishingthatthequasiperiodicoscillationsfoundinthermonuclearX-raybursts(Strohmayeretal.1996)arelinkedtotheneu-tronstarspin.Thehighlyaccuratemeasurementsenabledbythestabilityoftheneutronstarspinhaveenabledthemostaccuratemeasurementsof
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Fig.1.—RXTE/PCAlightcurveofHETEJ1900.1-2455.Eachpointisthefluxinthe2-20keVbandderivedfromspectralfittingtoanindividualRXTEpointing.
withradiusexpansion.AdetectionintheHETE-2SoftX-RayCamera(SXC)(Villasenoretal.2003)localizedthebursttoan80′′accuracy.NoknownX-rayburstsourcewasconsistentwiththeSXCposition.AssumingthattheburstluminosityisequaltotheEddingtonlimitfora1.4M⊙neutron-starburninghelium,Kawai&Suzuki(2005)esti-matethedistanceas5kpc.
Followingdiscoveryofthesource,wetriggeredanRXTETarget-of-Opportunityobservingpro-gramwhichledtomultipleobservationsondatesfrom2005June16toJuly16(MJD53537to53567).ThefirstfewRXTEpointedobserva-tionsledtothedetectionofpulsationsat377.3Hz(Morgan,Kaaret,&Vanderspek2005)andfurtherRXTEobservationsenabledaninitialmeasure-mentoftheorbitalparameters(Kaaret,Morgan,&Vanderspek2005).ApositionwasdeterminedfromRXTEscanningobservations(Markwardtetal.2005)andthenapossibleopticalcounterpartwasidentified(Fox2005).Theopticalcounterpartwasconfirmedwithfurtheropticalobservationswhichshowedthatthesourcewasbrightcomparedwitharchivalplates,blueincolor,andemitsabroadHeiiemissionline(Steeghsetal.2005).AnimprovedX-rayposition,accurateto5′′,and
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Fig.2.—Leahynormalizedpowerspectrumshow-ingdetectionofasinglekHzQPO.ThesolidcurverepresentsthefitofaLorenztianplusaconstanttothedata.ThedashedlinesindicateplusandminusthespinfrequencyandplusandminushalfthespinfrequencyawayfromthekHzQPOcen-troidfrequency.
consistentwiththatoftheopticalcounterpartwasobtainedwiththeSwiftX-RayTelescope(Kong,Homan,&Lewin2005).VLAobservationswereperformed,butnoradiocounterpartwasdetected(Rupen,Mioduszewski,&Dhawan2005).
FortheRXTEobservations,weanalyzeddatafromtheProportionalCounterArray(PCA).Thefirstobservationusedtwosinglebitmodes,SB81sandSB141s,andaneventmode,E16B1s,toprovidehighresolutiontiming.Thesubsequentobservations
usedasingleeventmode,E
64M1s,forhighresolutiontiming.Forallobservations,theStandard-1low-resolution(0.125s)timingmodeandtheStandard-2spectroscopicmodewith16stimeresolutionwereavailable.
AlightcurvederivedfromthePCAStandard-2dataisshowninFig.1.WeusedonlydatafromPCU2becausethisPCUwasonduringalloftheobservationsandfollowedtheanalysispro-ceduresdescribedinKaaretetal.(2002).Aspec-trumwasextractedforeachindividualobserva-tion.Weassigna1%systematicuncertaintyon
2
eachspectralbin(Tomsicketal.1999).Wefitthespectratoamodelconsistingofthesumofapower-lawandablackbodywithinterstellarab-sorption.WefixedtheabsorptioncolumndensitytoNH=1.5×1021cm−2whichistheGalacticHicolumndensityalongthelineofsight.ThesourcehasaGalacticlatitudeofb=−12.87◦andlies1.1kpcoutoftheplaneifatadistanceof5kpc.Therefore,theGalacticHishouldmainlyliebetweenusandthesource.
ThediscoveryX-rayburstoccurredon2005June14(MJD53535).ThefirstRXTEpointingoccurred2dayslaterandshowsthesourceatafluxof6.6×10−10ergcm−2s−1.Thesourcefluxincreasesgraduallyoverthebeginningoftheout-burst,thereisoneobservationwithahighfluxatMJD53559,andsubsequentlythesourcefluxde-cays.Thephotonindexgraduallysoftens,whiletheblackbodytemperaturegraduallyincreases,untilafewdaysafterthepeakfluxwhenthetrendsreverse.Thefirsttwoobservationsmayhavehadsofterandcoolerspectra,buttheuncer-taintiesinthespectralfittingdonotpermitanyfirmconclusionsinthisregard.Wefindtempera-tureshigherthanthosereportedbyCampanaetal.(2005).Wedofindthatadditionofalowertem-peratureblackbodyimprovesthefitinsomecases.ThetruespectrumofHETEJ1900.1-2455mayin-cludetwoblackbodycomponents,ashasbeensug-gestedforothermillisecondpulsars(Gierli´nski&Poutanen2005).
Thespectralmodeldescribedabovewasinad-equateinfittingthehighfluxpointbecausethatspectrumshowsdistinctcurvatureathighener-gies.Atenergiesbelow14keV,thespectrumliesabovethosefromthepreviousorsubsequentday,whileatenergiesabove14keV,thespectrumliesbelow.Tofitthatspectrum,weaddedahighenergyexponentialcutoffandremovedtheblackbodycomponent.TheresultingspectralmodelisthesameasthatcommonlyusedforstandardX-raypulsars,i.e.thosewithspinperiodsof1-1000s(Pravdoetal.1978;White,Swank,&Holt1983).Thephotonindexwas1.88±0.05,thecutoffenergywas6.43±0.15keV,andthefold-ingenergywas5.87±0.20keV.Thecutoffen-ergyissimilartothatfoundfortheX-raypulsarsGS1843+00(Pirainoetal.2000)andSMCX-1(Naik&Paul2004),butthephotonindexissofterthanfoundforthoseorotherstandardaccreting
X-raypulsars.Weattemptedtofitthespectrumwithablackbody,thesumofablackbodyplusapower-law,andthesumoftwoblackbodiesandapower-law,allwithabsorption,butwereunabletoobtaingoodfitswithanyofthesemodels.TheRXTE/ASMlightcurvedoesnotshowunusuallyhighfluxnearthistime.TheaverageratearoundMJD53559iscloseto3c/s,equivalenttoroughly1.2×10−9ergcm−2s−1inthe2-20keVband.Itappearsunlikelythatthehighfluxpointispartofasuperburst.Weexaminedthelightcurveofthisobservationontimescalesof1,8and64s.Thelightcurveshowsnousualvariabilityonthesetimescales,butdoesshowakiloHertzquasi-periodicoscillation(kHzQPO).
WesearchedforhighfrequencyQPOsineachuninterruptedRXTEobservationwindowandincombinationsofthevariousdatasegments.Wecalculatedaveragesof16spowerspectraincludingeventswithenergiesbelow18keVfromallPCUs.AsinglekHzQPOappearsintheobservationbe-ginningMJD53559.447583,seeFig.2.Thedetec-tionhasasignificanceof9.2σ,withnoallowancefortrials.Evenallowingfor6×104trialsforallofthedistinctfrequencyrangesinallthepowerspectragenerated,thedetectionisstillhighlysig-nificant.TheQPOhasacentroidof882.8±1.0Hz,awidthof16.9±2.4Hz,andanrmsamplitudeof0.00787±0.00086.ThereisnoevidenceforQPOsatplusorminusthespinfrequencyoratplusorminushalfthespinfrequencyawayfromthesinglekHzQPO.
WeusedtheStandard-1datawhichhas0.125stimeresolutionandnoenergyinformationtosearchforX-raybursts.Wefoundoneburst-likeeventatMJD53538.76433.However,thiseventappearstobeadetectorbreakdowneventandnotanX-rayburstfromthesource.HETE-2hasreportedonlyoneadditionalX-rayburstontheHETEburstsummarypage1afterthediscoveryburst.TheadditionalburstwasonMJD53558,justbeforethepointinthelightcurvewithahighflux.
WeexaminedtheRXTEAll-SkyMonitor(ASM)lightcurveforHETEJ1900.1-2455.Theonlydetectionisofthecurrentoutburst.There-fore,therecurrencetimeofthetransientislikelylongerthan9years.
Table1
ParametersofHETEJ1900.1-2455
Parameter
Value
Note.—TheseparametersassumethepositionreportedbyFox(2005)ofα=19h00m08s.65andδ=-24◦55′13′′.7(J2000).Thetrailingnumbersinparenthesisindicatesthe1−σuncer-taintyinthefinaldigits.TTindicatesterrestrialtime.
Fig.3.—PulsetimingresidualsforHETEJ1900.1-2455.ThepointsalongthesinusoidalcurverepresentthetimingresidualswithouttheKeplerianorbitcorrection.ThepointscenteredaboutzeroarethethetimingresidualswiththeKeplerianorbitcorrectionincludedandaremulti-pliedby10.3.
Pulsations
Wesearchedforpulsationsusingthe125µstimeresolutiondatabycorrectingtheeventtimestothesolarsystembarycenterandthendividingthedatainto256sintervals,calculatingapowerspectrumforeventsinthe3–8keVband(channels8–32inthe0-255channelrange)foreachinter-val,andincoherentlysummingthepowerspectra
forallintervalswithinagivenpointing.Asig-nalat377.3HzwasdetectedinthefirstpointedRXTEobservationofHETEJ1900.1-2455,butnotatveryhighsignificance.However,signalsnearthatfrequencyweredetectedinthefollow-ingfourRXTEpointingsgivingdefiniteproofoftherealityofthepulsations(Morgan,Kaaret,&Vanderspek2005).
WesearchedtheobservationsbetweenJune17and22forpulsationsnear377.3Hz.Wedividedtheobservationsinto256sintervalsandfoundthepulsefrequencyineachinterval.Thepulsefre-quencieshadaclearsinusoidalmodulation,char-acteristicofmodulationbyorbitalmotion.Wefittedapreliminaryspin/orbitmodeltothefre-quencymeasurementstoenableapulsearrivaltimeanalysisasisstandardinthetiminganal-ysisofpulsars(Manchester&Taylor1977).Inthepreliminarymodel,wefixedtheorbitalec-centricityandpulsefrequencyderivativetozero.Wecorrectedthephotonarrivaltimesusingthepreliminaryspin/orbitmodel,andthencalculatedtheepochofthepulsepeakwithineachinterval.Wethenfittedthepulsearrivaltimesusingalin-earleastsquaresregressiontofindcorrectionstothespinandorbitalparameters.Theprocedurewasiteratedasmoreobservationsbecameavail-ableandeachsetofnewspinandorbitalparame-terswereusedtorecalculatethepulsearrivaltimesforthefulldataset.
Theorbitalandpulsetimingparameterspre-4
0.20
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0.000.00
0.050.100.150.20
Mass (solar masses)
Fig.4.—Mass-radiusrelationforthecompan-ionstarinHETEJ1900.1-2455.Thesolidcurveindicatesthemass-radiusrelationforthecompan-ionasrequiredforaRoche-lobefillingcompanionwiththemeasuredorbitalperiod.Thedashedlinerepresentszero-agemainsequencestarswithsolarmetallicity.Thedottedcurvesrepresentbrowndwarfsofages0.1(top),0.5,1.0,and5.0(bot-tom)Gyr.Theverticaldash-dotlinesrepresentthelowermasslimitandthe95%confidenceup-permasslimit.
sentedinTable1werederivedusingthedatafromallobservationsbeforeMJD53558.Fig.3showstheresidualsofthepulsearrivaltimeswithandwithoutthecorrectionfororbitalmotion.Agoodfitwithχ2/DoF=1.03isobtainedwithoutaspinfrequencyderivativeororbitaleccentricity.Thetimingresidualsaretypicallylessthan500µs.TheupperboundontheeccentricityislistedintheTable.Wewereunabletoconstructaphase-connectedtimingsolutionincludingdatabeyondMJD53558.ObservationsonMJD53559showedthesourcefluxtohavebrighteneddramatically,seeabove,andtheobservedpulsefrequencywasshiftedto377.291596(16)Hz,∆ν/ν∼6×10−7.Insubsequentobservations,pulsationsweresup-pressed.ThermspulseamplitudeinobservationsbeforeMJD53558rangedfrom1.5%to5%,whileforobservationsafterMJD53559,weplaceanup-perlimitonthepulseamplitudeof1%.
5
Fig.5.—SpinversusorbitalperiodforneutronstarX-raybinarieswithspinfrequenciesgreaterthan20Hz–a‘milli-Corbet’diagram.Crossesaremillisecondpulsars,trianglesareburstoscillationsources,diamondsaresourceswithboth.4.
Discussion
Ourdiscoveryofcoherentmillisecondpulsa-tionsfromHETEJ1900.1-2455addsanothertothesixpreviouslyknownX-raymillisecondpul-sars(XMSPs).AsnowappearstypicalforXM-SPs,themassfunctionforthepulsarisverysmall,fx=2.0×10−6M⊙,implyingeitheraverylowmasscompanionoraveryimprobableorbitalin-clination.Theminimumcompanionmass,assum-inganeutronstarmassofMX=1.4M⊙andanorbitalinclinationi=90◦,ism2>0.016M⊙.The95%confidenceupperlimitonthemass,as-sumingauniformaprioridistributionincosiandMX=2.2M⊙,ism2<0.07M⊙.
IfthecompanionstarfillsitsRoche-lobe,thenthedensityofthecompanionstarisfixedbytheorbitalperiod(Frank,King,&Raine1992).Fig.4showsthemass-radiusrelationforthecompanionstar.FollowingBildsten&Chakrabarty(2001),wehaveplottedthemass-radiusrelationsforzero-agesolar-metallicitymainsequencestars(Toutetal.1996)andforbrowndwarfsofvariousagesfrom
Table2
NeutronStarSpinRatesandOrbitalPeriods
Object
SpinRate
OrbitalPeriod
Type
Reference
Note.—Pindicatesmillisecondpulsars,Bindicatesburstoscillationsources.
0.1to5Gyr(Chabrieretal.2000).Thepointsatwhichthestellarmass-radiusrelationsintersectthemass-radiuscurveofthecompanionstarindi-catepossiblestellarcompanionsallowedbytheob-servations.IncontrasttootherXMSPs,therearepossibleRoche-lobefillingcompanionstarswithstandardevolutionaryhistories.Therefore,heat-ingofthecompanionstar,assuggestedforSAXJ1808.4-3658(Bildsten&Chakrabarty2001),isnotrequiredtoexpandthecompanion’sradiusanddrivemasstransferinHETEJ1900.1-2455.Thecompanionstarislikelyabrowndwarf.
OneveryunusualaspectofourobservationsofHETEJ1900.1-2455isthedetectionofadra-maticbrighteningofthesourceonMJD53559,ac-companiedbyashiftinthepulsefrequencywith∆ν/ν∼6×10−7andthenthesuppressionofpul-sationsinsubsequentobservations.Duringtheintervalofhighflux,theX-rayspectrumisex-ponentiallycutoffathighenergies,asisseenforstandardX-raypulsars,wheretheaccretionspotisthoughttobequitecompact.Whatmecha-nismisresponsibleforthesuppressionofpulsa-tionsafterthehighX-rayfluxintervalisanopenquestion.Diamagneticscreeningofthemagneticfield,achangeintheaccretiongeometry,oren-hancedscatteringofthepulsesduetoaccumula-tionofmaterialaroundthepolesarepossibilities.Unfortunately,wedonothavegoodinformationconcerningthetotalfluenceinthehighfluxevent.However,thehighfluxpointcorrespondstoalu-minosityofonly1.5%oftheEddingtonluminosity,assumingthattheEddingtonluminosityisgivenbythebolometricfluxof9×10−8ergcm−2s−1reportedforthediscoveryX-rayburstbyKawai&Suzuki(2005).Cumming,Zweibel,&Bild-sten(2001)statethatdiamagneticscreeningofthemagneticfieldisnotpossibleforaccretionratesbelow2%oftheEddingtonrate,whichmayex-cludethispossibility.
InadditiontotheXMSPs,thespinperiodsofneutronstarsinX-raybinariescanbemeasuredviathedetectionof(quasiperiodic)oscillationsintypeIX-raybursts.Table2presentsthespinfre-quenciesandorbitalperiodsforneutron-starlow-massX-raybinarieswithspinratesgreaterthan20Hzandmeasuredorbitalperiods.Forthemil-lisecondpulsars,theorbitalperiodsaremeasuredviapulsetiming.FortheX-raybursters,theor-bitalperiodsaredeterminedeitherviadetection
6
ofperiodicdipsintheX-rayemissionorbyopticalobservationofellipsoidalmodulationorDoppler-shiftedabsorptionlines.X-raydipsaredetectedonlywhentheinclinationishigh.Thesameinfor-mationispresentedinFig.5;asimilarplotwaspresentedbySwank&Marshall(2004).Indef-erencetothenamecommonlyusedforplotsofspinversusorbitalperiodforstandardX-raypul-sars(Corbet1984,1986),werefertothisplotasa‘milli-Corbet’diagram.
Thereareapparentboundsonthedatapointsatlowspinperiodandatloworbitalperiod.Theoriginoftheapparentlowerboundontheorbitalperiod,andtheclusteringofsourcesnearthislimitof40min,isapuzzle.ThereareLMXBswithshorterorbitalperiods,buttheneutronstarspinfrequencyhasnotbeendefinitivelymeasuredinanyofthosesystems.Thelowerboundonthespinperioddistributionhasbeeninterpretedasevidencethatgravitationalradiationlosseslimitthemaximumaccretiontorquespinningupneu-tronstarsinLMXBs(Chakrabartyetal.2003).Thelongestspinperiod,forEXO0748-676,isafactorof4largerthanthesecondlongest.Theun-usuallyslowspinmaybeduetoanunusuallyhighmagneticfield(Villarreal&Strohmayer2004).Ifweconsidertheneutronstarswithspinratesfasterthan100Hz,thereappearstobealackofpointswithlongspinperiodsandlongorbitalpe-riods.ExcludingEXO0748-676,thelinearcor-relationcoefficientbetweenthelogarithmsofthespinandorbitalperiodsisr=−0.68whichhasachanceprobabilityofoccurrenceof2.5%.Thiscorrelationmayindicatesomecouplingbetweentheneutronspinandorbitalperiod,perhapsindi-rectlyifthemassaccretionratevarieswithorbitalperiod.However,whyEXO0748-676differssosig-nificantlyfromthebehaviorofthemorerapidlyrotatingneutronstarswouldneedtobeunder-stood.Thediscoveryofmoremillisecondpulsars,orthemeasurementoftheorbitalperiodsofad-ditionalX-rayburstoscillationsources,isneededtobetterunderstandtheevolutionofneutronstarspininlow-massX-raybinaries.
WegreatlyappreciatetheeffortsoftheHETE-2teamintheoperationoftheHETE-2satelliteandtheRXTEteam,particularlyEvanSmithandJeanSwankinperformingobservationsandCraigMarkwardtinpromptlycalculatingtheclockcor-rections.PKthanksJeanSwankforusefuldis-cussionsandacknowledgespartialsupportfromaNASAgrantandaUniversityofIowaFac-ultyScholarAward.JATacknowledgespartialsupportfromNASAgrantsNNG04GA49GandNNG04GB19G.REFERENCES
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