Quasi-periodic X-ray brightness fluctuations in an accreting

The relativistic plasma flows onto neutron stars that are accreting material from stellar companions can be used to probe strong-field gravity as well as the physical conditions in the supranuclear-density interiors of neutron stars. Plasma inhomogeneities

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002 lJu 7 1v3217030/hp-ortsa:viXraQuasi-periodicX-raybrightness uctuationsinanaccreting

millisecondpulsar

RudyWijnands1,MichielvanderKlis2,JeroenHoman3,DeeptoChakrabarty4,CraigB.

Markwardt5,EdH.Morgan4

ABSTRACT

Therelativisticplasma owsontoneutronstarsthatareaccretingmaterialfromstellarcompanionscanbeusedtoprobestrong- eldgravityaswellasthephysicalconditionsinthesupranuclear-densityinteriorsofneutronstars.PlasmainhomogeneitiesorbitingafewkilometresabovethestarsareobservableasX-raybrightness uctuationsonthemilliseconddynamicaltimescaleofthe ows1 3.Twofrequenciesinthekilohertzrangedominatethese uctuations:thetwinkilohertzquasi-periodicoscillations(kHzQPOs).Competingmodelsfortheoriginsoftheseoscillations(basedonorbitalmotions)allpredictthattheyshouldberelatedtothestellarspinfrequency4 10,buttestshavebeendi cultbecausethespinswerenotunambiguouslyknown.HerewereportthedetectionofkHzQPOsfromapulsarwhosespinfrequencyisknown.OurmeasurementsestablishaclearlinkbetweenkHzQPOsandstellarspin,butonenotpredictedbyanycurrentmodel.AnewapproachtounderstandingkHzQPOsisnowrequired.WesuggestthataresonancebetweenthespinandgeneralrelativisticorbitalandepicyclicfrequenciescouldprovidetheobservedrelationbetweenQPOsandspin.TwinkHzQPOswithfrequenciesbetween300and1,300Hzoccurinmorethan20accretingneutronstars3.Insevenofthese,duringther-monuclearX-rayburstscausedbytheexplosionofmaterialaccumulatedontheneutron-starsurface,short-livedoscillationsareobservedwithfrequen-ciesνburstintherange270–620Hz,approximatelyconstantbutdi erentineachsource,thatarethoughttobecausedbytheneutron-starspin11.

The relativistic plasma flows onto neutron stars that are accreting material from stellar companions can be used to probe strong-field gravity as well as the physical conditions in the supranuclear-density interiors of neutron stars. Plasma inhomogeneities

factthat νisneitherconstant16,17,norexactlyequal18,19toνspin(butpossiblesolutionsinthebeat-frequencymodelsdoexist20).Thishasmo-tivatedtheproposalofseveralalternativemod-elstoexplainthekHzQPOs7 10,allofwhich,likebeat-frequencymodels,useorbitalmotionasoneoftheobservedfrequencies,butwhichuseanothermechanism–suchasgeneralrelativisticepicyclicmotion,whichisveryfastintheseex-tremegravitational elds–togeneratetheotherfrequency.Noneofthesemodelspredictcommen-surabilitybetweenspinandkHzQPOfrequenciessuchasbeat-frequencymodelsdo.Ithasbeenclearforsometimethatindependentmeasure-mentsoftheneutron-starspinfrequencycouldprovidethede nitivetestofthebeat-frequencyidea.Thediscovery21ofthe rstaccretingmil-lisecondpulsarin1998raisedtheprospectofsuchatest,butuntilnownoaccretingmillisecondpul-sarhasshowntheanticipatedkHzQPOs.

On13October2002,abrightnewoutburstoftherecurrentX-raytransientandaccretingmil-lisecondpulsar,SAXJ1808.4–3658,http://doc.guandang.net-ingtheRossiX-rayTimingExplorersatellite,weobtained～700ksofdatacoveringtheoutburstwithdailyobservationsfrom15Octoberto26November2002.WeperformedaseriesoffastFouriertransformstosearchforkHzQPOs,anddiscoveredseveral.OnekHzQPOwasmonitoredfor12days(Fig.1).Itsfrequencyincreasedfrom570to725Hzbetween15and16October,thengraduallydecreasedtoaminimumof280Hzon21October,suddenlyincreasedagainto400Hzthenextday,andthenresumeditsdecrease,to320Hzon26October.AfterthistheQPOwasnotdetected,presumablyowingtothelimitedstatis-ticsresultingfromthedropincountrate(byafactorofabout4)bythisstageoftheoutburst.On16October,asecondkHzQPOwasdetectedsimultaneouslyatafrequencyof ν=195±6Hzbelowthe rstone(Fig.1,toppanel).Inthere-mainingdata,thissecondQPOwasnotdetectedwithasigni cancegreaterthan2.5σ.Additionalbroadnoisestructuresofmarginalsigni cancearesometimespresentaround350,220and120Hz.Thefrequencies,strengthsandcoherencesofthesetwokHzQPOsinSAXJ1808.4–3658,aswellasthevariationsintheirparametersasafunctionofsourceluminosity,areverysimilartothoseofthetwinkHzQPOsobservedinthoseneutron-starlowmassbinariesforwhichnopulsationsareseenintheirpersistentemission(thenon-pulsingsources3),soweinterpretthisasthesamephe-nomenon.The～195-Hzfrequencydi erencebe-tweenthetwoQPOsisthelowestknown(inothersystems νrangesbetween225and350Hz)3.Itisfarbelowthe401-Hzspinfrequencypredictedinsimplebeat-frequencymodels6,12,yetthereisaclearcommensurability: νisconsistentwithνspin/2.Thisisreminiscentofthosenon-pulsingsourceswhere νisnearνburst/2.Henceourre-sultssupportthespininterpretationoftheburstoscillationsinthosesources,aswellasthesuspi-cionthatνburstisalwaysnearνspin(andnevertwicethat).Moreover,asreportedinacom-panionpaper23,inourobservationswealsode-tectedfourthermonuclearburstsinwhichwedis-coveredburstoscillationsattheneutron-starspinfrequency.Thisdiscoveryfurtherstrengthenstheideathattheburstoscillationsarealwaysatthestellarspinfrequency.

Wenowdemonstratethat,unlesswearewrongaboutthespinfrequencyofthispul-sar,whichseemshighlyunlikely,ourobserva-tionsfalsifycurrentbeat-frequencymodels,yetsoposeaseverechallengetoallothercurrentkHzQPOmodels.Inbeat-frequencymodels5,6,24,thespin-orbitbeatinteractionoccursatafre-quencyνbeat=n(νorbit–νspin),whereνorbitistheorbitalfrequency,andthepositiveintegernisasymmetryfactoraccountingformultiplesymmetricallylocatedspin-orbitinteractionsites(forexample,n=2fortwomagneticpoles).Simplebeat-frequencymodelshaven=1andthetwokHzQPOsatνbeatandνorbit,sothat ν=νorbit–νbeat=νspin.Asnoted,thisisclearlyinconsistentwithourobservations.Ingen-eral,nistheleastcommonmultiple(LCM)ofthenumberofstellarandthenumberoforbitalinteractionsites:n=LCM(nspin,norbit).What-everthevalueofthesenumbers,andevenallowingtheobservedorbitalQPOtobeateitherνorbitornorbitνorbit,thereisnocon gurationpredictingtheobserved ν=νspin/2.

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