Constraining black hole spins with low-frequency quasi-periodic oscillations in soft states

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by  Alessia Franchini

MNRAS000,1–10(2016) Preprint31January2017 CompiledusingMNRASLATEXstylefilev3.0
Constraining black hole spins with low-frequency quasi-periodic
oscillations in soft states
Alessia Franchini1⋆, Sara Elisa Motta2 and Giuseppe Lodato 1
1DipartimentodiFisica,UniversitàDegliStudidiMilano,ViaCeloria,16,Milano,I-20133,Italy
2UniversityofOxford,DepartmentofPhysics,Astrophysics,DenisWilkinsonBuilding,KebleRoad,OX13RH,Oxford,UK
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ABSTRACT
a
J
Black hole X-ray transients show a variety of state transitions during their outburst
0
3 phases,characterizedbychangesintheirspectralandtimingproperties.Inparticular,power
densityspectra(PDS)showquasiperiodicoscillations(QPOs)thatcanberelatedtotheac-

] cretionregimeofthesource.Welookedfortype-CQPOsinthedisc-dominatedstate(i.e.the
E
highsoftstate)andintheultra-luminousstateintheRXTEarchivaldataof12transientblack
H hole X-ray binaries known to show QPOs during their outbursts. We detected 6 significant
. QPOsinthesoftstate thatcanbeclassified astype-CQPOs. Undertheassumptionthatthe
h
accretiondiscindisc-dominatedstatesextendsdownorclosetotheinnermoststablecircular
p
orbit (ISCO) and that type-C QPOs would arise at the inner edge of the accretion flow, we
-
o use the relativistic precessionmodel(RPM) to place constraintson the blackhole spin. We
r wereabletoplacelowerlimitsonthespinvalueforallthe12sourcesofoursamplewhilewe
t
s couldplacealsoanupperlimitonthespinfor5sources.
a
[ Keywords: accretion,accretiondiscs–binaries:close–blackholephysics–X-rays:stars

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1 INTRODUCTION (see,e.g.,Mottaetal.2012).Whilethehardstatesarecharacterized
7
byhighervariability(30−40%rmsintheLHSand5−20%rmsin
1 Blackhole(BH)low-massX-raybinaries(LMXBs)aredoublesys-
theintermediatestates),thevariabilityintheULSandintheHSS
0 temsharboringastellarmassblackholethataccretesmatterfroma
isverylow(aroundandbelow5%rms,respectively).
. Sun-likecompanionstar.ThevastmajorityofBHLMXBsaretran-
1
0 sientsystems,i.e.theyspendmostoftheirlifeinadim,quiescent Thedifferentstatesaredefinedbasedonthespectralproper-
7 state(LX∼1030–1034erg/s),occasionallyinterruptedbybrightout- tiesofthesourceandontheinspectionofthepowerdensityspec-
1 burstsduringwhichtheyshowlargeincreasesinluminosity(reach- tra(PDS),wherechangesinthefasttimevariabilitycanbeclearly
v: ing occasionally the Eddington limit) and remarkable variations observed. The most remarkable features detected in the PDS are
i in their spectral and fast variability properties (Belloni&Motta narrowpeaksknownasquasi-periodicoscillations(QPOs),whose
X 2016). These changes can be described through the Hardness- centroid frequency are thought to be associated with dynamical
r IntensityDiagram(HID)(Homanetal.2001;Bellonietal.2011), time scales in the accretion flow. The origin of QPOs is still un-
a wherehysteresisloopscanbeidentified(Miyamotoetal.1992)and derdebateandseveralmodelshavebeenproposedtoexplaintheir
differentbranchesofaq-shapedtrackroughlycorrespondtodiffer- existence(seeMotta2016forareview).However,itiscommonly
entspectral/timingstates.MostactiveBHLMXBsshowfivemain acceptedthatmostQPOsoriginateinthevicinityoftheblackhole,
different states:theLow HardState(LHS),dominated byComp- thustheypotentiallycarryinformation onthepropertiesand mo-
tonized emission; the High Soft State (HSS), where the thermal tionofmatterinastronggravitationalfield.
emissionfromanaccretiondiscdominatesthespectrum;theHard
IntermediateState(HIMS)andtheSoftIntermediateState(SIMS), QPOs are usually divided in two groups based on their fre-
wherethespectrumshowsthecontributionsfromboththeaccretion quency: low frequency and high frequency (LFQPOs and HFQ-
discandtheComptonizedemission,butwherethemostdramatic POs, respectively). LFQPOs have frequencies typically varying
changesinthetimingpropertiesareobserved.Afewsourcehave fromafewmHzupto∼ 30Hzandarefurtherdividedintothree
alsoshownananomalousorultra-luminousstate(ULS),whichcan types-type-A,type-Bandtype-C-basedontheirproperties(e.g.
beseenasasoft-intermediateandhard-intermediatestateinwhich peakfrequency,width,energydependenceandphaselags)andon
theluminosityissignificantlyhigherwithrespecttotheotherstates theassociatedbroadbandnoiseinthePDS(shapeandtotalvari-
abilitylevel,Wijnandsetal.1999,Casellaetal.2005,Mottaetal.
2011).AccordingtotheclassificationofHoman&Belloni(2005),
⋆ [email protected] Type-A QPOs are commonly found in the SIMS and are charac-
(cid:13)c 2016TheAuthors
2 Franchini,MottaandLodato
terized by a weak and broad peak around 6−8 Hz. 1 Their ori- able to rigidly precess around the compact object spin axis. Ac-
gin is still under debate. Type-B are usually seen in the SIMS cording to this model type-C QPOs are produced by the Lense-
(whichisdefinedbytheirpresence,Belloni&Motta2016).They Thirringprecessionofaradiallyextendedportionofthehotinner
arecharacterizedbyarelativelystrongandnarrowpeakaround6 accretion flow that produces a modulation of the X-ray flux, dif-
Hz(Mottaetal.2011)andithasbeensuggestedthattheyareas- ferentlyfromtheRPMwhereatestparticleisresponsibleforthe
sociated with relativistic jets during the transition from the hard QPO. Inthe first case, the QPO frequency isa weighted average
tothe soft state(Fenderetal.2009).Type-C QPOsarefound es- ofthefreeprecessionfrequenciesatthevariousradii.However,for
sentially in any spectra/timing state (including the ULS, Motta the disc to precess rigidly, its radial extent must be narrow (tens
2016). They are characterized by a strong (up to 20% rms), nar- ofR )(Lodato&Facchini2013;Franchinietal.2016;Nixonetal.
g
row(ν/∆ν > 3,butoftenmuchlarger)andvariablepeak(itsfre- 2016).Inparticular,intheHSS,wheretheaccretiondiscinnerra-
quencyandstrengthvaryingbyfewordersofmagnitudealongan dius is expected to be close to or coincident with the innermost
outburst;see,e.g.,Mottaetal.2015)superposedonaflat-topnoise stable circular orbit (ISCO, e.g. Dunnetal. 2010), the inner hot
that steepens above a frequency comparable to the centroid fre- (geometrically thick) accretion flow is expected to be extremely
quencyoftheQPO.Type-CQPOsappearatlowfrequencies(from narrow (itsouter radiusdetermined bytheinner thindisctrunca-
afewmHzuptotenthsofHzMottaetal.2011)inthehardstate tionradius).Therefore,itsprecessionfrequencyisreasonablywell
where the disc is thought to be truncated at a large radius (tens describedbythatofatestparticleorbitingattheISCO.Thus,inthe
tohundredsofR ).Theyincreasetheirfrequencyduringthetran- HSSandinparticularclosetotheISCO,theRPMandtherigidpre-
g
sition from the hard to the soft state, reaching their maximum in cessionarepracticallycoincident andtheRPMrepresentsagood
theHSS,wheretheyshowfrequenciesaround30Hz(Mottaetal. approximationoftherigidprecession(Ingram&Motta2014).
2014a,Mottaetal.2014b).HFQPOsarefairlyrareinBHbinaries Themeasurementoftheblackholeparametersisamajoris-
(whiletheyarecommonlyobservedinNSsystems,wheretheyare sueinastrophysics.Whilethemasscanbeestimatedthroughoften
referredtoaskHzQPOs,seevanderKlis2006)andhavebeende- complexdynamicalstudies,thespincanonlybeinferredinanin-
tected only inafew sources (Bellonietal. 2012). HFQPOsseem directway.IntheHSSmeasurementsofthespinscanbeobtained
to appear preferentially in the HSS and in the ULS, even though through X-ray spectroscopy by modelling the thermal disc emis-
observational biases could be at play because of the low number sion in the spectrum (McClintocketal. 2011, 2014; Steineretal.
ofdetectionscurrentlyavailable.Remillard&McClintock(2006), 2010, 2011, 2012). In the hard and intermediate states, the spin
usingadifferentclassification(Table1inMcClintocketal.2009), isinstead measured bymodelling thediscreflectionspectrum, in
showedthatmostHFQPOshavebeendetectedinobservationswith particularbymodellingtheeffectsofthespinontheIron-Kαline
asubstantialpower-lawcontribution. (Miller2007;Reynolds2013).Bothmethodsrelyuponidentifying
There are different models that attempt to describe the ori- theinnerradiusoftheaccretiondiscwiththeISCO.Inaddition,for
thespectralcontinuummethod,onemustalsoknowthemassofthe
ginofQPOsinLMXBs.Therelativisticprecessionmodel(RPM)
blackhole,theinclinationoftheaccretiondisc(generallyassumed
is one of those. This model has been originally proposed by
equal to the inclination of the binary system) with respect to the
Stella&Vietri(1998);Stellaetal.(1999) andwasrecentlyrevis-
lineofsightandthedistancetothebinary.Forthesereasons,such
itedbyMottaetal.(2014a,b);Ingram&Motta(2014),toexplain
methodsareoftenaffectedbylargesystematicerrorsandinafew
threetypesofQPOs:type-CQPOs,thelowerandtheupperHFQ-
POs.IntheRPM,thecentroidfrequencyofthreedifferenttypesof casestheyhavelead toinconsistent values of theblackhole spin
whenusedonthesamesource(Shafeeetal.2006).TheRPM,on
QPOsisassociatedwiththefrequenciesofatestparticleorbitinga
theotherhand,isbasedonlyonmeasurementsthatcanbeinferred
spinningblackhole,aspredictedbythetheoryofGeneralRelativ-
throughverypreciseX-raytimingmeasurements(i.e.theprecision
ity.TheLense-Thirring(LT)frequencyisassociatedwiththetype-
of the measurement of a QPO centroid frequency is only limited
CQPO,theperiastronprecessionfrequencywiththelowerHFQPO
bythetimeresolutionofthedataused,whichisusuallyextremely
andtheorbitalmotioncorrespondstotheupperHFQPO.TheRPM
high).Therefore,theRPMcanbeusedtoestimateBHspinsinde-
predictsthattheexpectedvaluesofthesefrequenciesdependsolely
pendentlyfromothermethods.
onthefundamental parametersoftheBH,i.e.massandspin,and
InthisworkweapplytheRPMtoQPOsdetectedintheHSS,
on the radius at which the particle motion occurs (i.e. where the
i.e.producedcloseorattheISCO,placinglimitsontheblackhole
QPOsareproduced). Basedon thisfact, once atype-C QPO and
spinofanumberofsourcesbymakingreasonableassumptionson
two HFQPOsare observed simultaneously, one can obtain apre-
themass,whenthisisnotknownapriori.
cisemeasurementofthefundamentalparametersoftheblackhole,
spinandmass(Mottaetal.2014a).Aspinmeasurementcanalsobe
obtainedwhenonlytwosimultaneousQPOsoftherelevanttypes
aredetectedandwhenanindependent massmeasurement,forin-
2 OBSERVATIONSANDDATAANALYSIS
stancedetermineddynamically,isavailable(Mottaetal.2014b).If
themass isunknown, theRPMstillallowstoplace limitson the Based on Mottaetal. (2015) we analyzed RXTE/Proportional
massandspinoftheblackhole(seeIngram&Motta2014). Counter Array(PCA)archival observations of12transient BHBs
Ingrametal. (2009) proposed a model based on relativis- showing QPOs. We selected those sources that show a standard
tic precession that requires a geometrically thin accretion disc HSSamongthe14sourcesconsideredbyMottaetal.(2015).We
(Shakura&Sunyaev1973)truncatedatsomeradius(theinnerdisc did also include observations in the ULS for those sources that
truncationradius)filledinwithaninnerhotaccretionflowthatis showed thiskind of stateduring their outbursts. Inthiswork, we
excludedSwiftJ1753.5-0127 sinceithasnotshownaHSSinthe
RXTEera(Solerietal.2013),andXTEJ1720-318, whichdidnot
1 However, we note that more recent works (Bellonietal. 2011; Motta showQPOsduringtheoutburstobservedbyRXTE.Welookedfor
2016;Belloni&Motta2016)placedthistypeofQPOsintheHSS,since QPOsintheHSSandintheULS,wheretheyarethoughttobepro-
theytypicallyappearattotalfractionalrmsbelow5%inBHBs. duced at or closeto theISCO (seeMottaetal. 2012, Mottaetal.
MNRAS000,1–10(2016)
Type-C QPOs insoftstate 3
2015). We analyzed all the observations in the RXTE catalogue where r is the radius (in units of the gravitational radius R =
g
in the HSS and ULS that have not been included in Mottaetal. GM/c2)atwhichthefrequenciesareproduced,aisthedimension-
(2014a,b,2015).ThenweaddedalsotheQPOsfoundintheprevi- lessblackholespinparameter,and Mistheblackholemass.The
ousworks. signs plus and minus refer to prograde and retrograde orbits, re-
WecomputedthePDSusingacustomsoftwareunderIDLin spectively.
the total and hard energy band (∼ 2−37 keV, absolute channels According to the RPM, type-C QPOs are associated with
0-64, and ∼ 6−37 keV, absolute channels 14-64, respectively). the Lense-Thirring precession frequency ν , the lower HFQPO
LT
SinceQPOstypicallyshowahardspectrum(Sobolewska&Z˙ycki totheperiastronprecessionfrequencyν andtheupper HFQPO
per
2006),producingthePDSusingonlyhardphotonsmaximizesthe to the orbital frequency ν . Under the hypothesis that when ob-
φ
chancesofdetectingafaintsignal,whoseintrinsicvariabilitycould servedsimultaneously,thesefrequenciesareproducedatthesame
bedilutedbythenon-variablephotonsfromtheaccretiondisc,that radius r, the equations above - linking the black hole parameters
dominatesinthesoftstatesandemitsmostlybelow6keV.Forsim- (spin and mass) to the QPO centroid frequencies - form a sys-
ilarreasons,wedidnotconsiderthephotonsabovechannel64:the temofthreeequationsinsixvariables:(a,M,r,ν ,ν ,ν ).There-
φ per LT
efficiencyof thePCAdrops dramaticallyabove∼30keV andthe fore, when a type-C QPO and two HFQPOs are detected simul-
variabilitycomingabovethisenergyismostlyPoissonnoise.Inad- taneously, one can solve the RPM system of equations exactly
dition,intheHSStheenergyspectrumistypicallyverysteep,with (Ingram&Motta 2014), obtaining precise values for a, M and r
verylittleornosignalabove∼20keV.Inafewcaseswecouldnot (Mottaetal.2014b,a).
producePDSinthehardbandsincethedatamodesdidnotallowit, Inthisworkweassumethatthehighestfrequencytype-CQPO
thereforeweonlyanalyzedthetotalenergybandPDS(channel0- detected in the HSS or ULS for each source corresponds to the
64ifavailable,otherwisechannels0-249).Weused16s-longinter- Lense-ThirringprecessionfrequencyofatestparticleattheISCO.
valsandaNyquistfrequencyof2048HztoproducethePDS,which TheradiusoftheISCO(r ),aspredictedbythetheoryofGen-
ISCO
werethennormalizedfollowingLeahyetal.(1983)andconverted eralRelativity,isonlyafunctionof theblackholedimensionless
tosquarefractionalrms(Belloni&Hasinger1990).Wemeasured spinparameter(see,e.g.,Stella&Vietri1998).Therefore,substi-
theintegratedfractionalrms(i.e.thermsfromtheentirePDS)in tutingthe expression of r into theequations above, allows us
ISCO
the2-15keVbandandbetween0.1and64Hz.Fromnowon,ifnot toremovethervariablefromtheRPMsystemandthustoobtain
otherwisestated,byrmswerefertotheintegratedfractionalrms. equationsthatonlydependonManda.Thisimpliesthat,ifeither
Then,weinspectedallthePDSselectingonlythosewherewe themassorthespinareknown,onecanobtainanestimateofthe
detectedoneormorenarrowpeaksandfittedthemusingthestan- otherparameterdetectingjustoneQPOandusingtherelatedRPM
dard XSPEC fitting package with a one-to-one energy-frequency equation. While BH spin measurements can be obtained only in-
conversion and a unity response matrix. Following Bellonietal. directlyandareoftenaffectedbylargeuncertainties, BHmasses,
(2002), we fitted the noise components with a number of broad instead, canbeinferredthroughdynamical studies. Theliterature
Lorentzians and the hints of QPOswith narrow Lorentzians 2. A includestodatemassmeasurementsforafewtensofcompactob-
constant component wasadded totake intoaccount thecontribu- jectinbinarysystems,includingseveralstellarmassBHs.Wecan
tionofthePoissonnoise.Weestimatedthestatisticalsignificance thusmake reasonableassumptions onthemassrangespanned by
ofthesepeaksandweexcludedallfeatureswithsingletrialsignif- theBHshostedinthesystemsofoursample.Thismeansthat,even
icancebelow3σ.Thenweconsideredalsothenumberoftrialsin without a dynamically determined BH mass, we are now able to
thecalculationof thesignificanceand wediscarded allthepeaks placelimitsontheblackholespinusingtheRPM.Inprinciple,this
thatresultednotsignificantafterthisanalysis.Werejectedalsothe couldbedonewithanyQPOrelevantfortheRPM(type-CQPO,
peakswithqualityfactor(i.e.theratiobetweencentroidfrequency upper or lower HFQPO).However, type-C QPOsare much more
andFWHMoftheQPOpeak)Q<2.SinceintheHSSbothtype-C commonandeasiertodetectthanHFQPOsandcanbedetectedin
QPOsandHFQPOscanbeseen,weclassifiedtheQPOswefound basicallyallspectral/timingstates(Motta2016),includingtheHSS
followingMottaetal.(2011)andMottaetal.(2012). andULS.
In order to place limits on the spin in those cases where
a dynamical BH mass is not available, we choose a conserva-
3 THERELATIVISTICPRECESSIONMODEL: tive range of masses, based on the mass distribution of BHBs
CONSTRAININGTHESPIN (Casares&Jonker2014):3−20M .Thesmallestdynamicallycon-
⊙
firmedstellarmassblackholeisGROJ1655-40,withM =5.4M
Thefundamentalfrequenciesofaparticleorbitingaspinningblack ⊙
(Beer&Podsiadlowski 2002).Inasimilarway,theupper limitis
holearegivenby(fromlowesttohighestfrequency):
based on the fact that the heaviest dynamically confirmed stellar
mass black hole in a Galactic binary system is the one in GRS
νLT =νφ(cid:20)1−(cid:16)1∓4ar−3/2+3a2r−2(cid:17)1/2(cid:21) (1) J1915+105(Reidetal.2014),withablackholeof12.4M⊙.There
isnoevidenceforheavierstellarmassblackholes(eventhougha
binarywithtwo30M BHshasbeenrecentlydetectedAbbottetal.
⊙
ν =ν 1− 1−6r−1±8ar−3/2−3a2r−2 1/2 (2) 2016),thereforeweassumedaconservativeupperlimitonthemass
per φ(cid:20) (cid:16) (cid:17) (cid:21)
of20M .
⊙
We explore the range between 3 and ∼ 150 Hz for the LT
c3 1
ν =± (3) frequency. The lower limit is chosen based on the observational
φ 2πGMr3/2±a evidencethatallBHBsshowtype-CQPOsreachingatleast3Hz
(Mottaetal. 2015). Even if type-C QPOs are typically observed
2 Type-CQPOssometimesshowsignificantharmoniccontentespeciallyin below∼30Hz,wedecidedtoconservativelyexploreawiderrange
thehardstates.However,asingleLorentzianisalwaysenoughtofittype-C of frequencies. Indeed, it is worth noticing that a type-C QPO
QPOsintheHSS. produced around an almost maximally spinning black hole (e.g.
MNRAS000,1–10(2016)
4 Franchini,MottaandLodato
110
20 20
18 18 140
16 147 16 170
14 14 200
]⊙ 12 138 ]⊙ 12 230 260 290 320 350
M 3 M
M[ 10 129 M[ 10
8 120 8
111
6 93 102 6
4 12 21 30 39 48 57 66 75 84 4
0.0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8
a a
Figure 1. Couples of mass-spin values that give the LT precession fre- Figure2.Couplesofmass-spinvaluesthatgivetheperiastronprecession
quency.ThenumbersarethefrequenciesevaluatedinHz.Eachlineisob- frequency. The exactly sameplot is obtained considering the orbital fre-
tainednumericallysolvingeq.1assumingafrequencyrangefrom3to147 quencyattheISCO.Indeed,attheISCOthereisnoradialoscillationinthe
Hz. frequency,thusνper=νφ.ThenumbersarethefrequenciesevaluatedinHz.
Eachlineisobtainednumericallysolvingeq.2assumingafrequencyrange
from50to350Hz.
a = 0.98 obtained for GRO J1655-40 using spectroscopic meth-
ods) should have a frequency above 100 Hz. Sinceinprinciple a
type-CQPOthesehighcouldbedetected,wechooseawiderrange types of QPOs, which in a rms vs frequency plot are known to
offrequenciestoexplorethispossibilityandinordertoguarantee generallyformdifferent,welldefinedgroups(seee.g.Casellaetal.
anunbiasedanalysis. 2005,Kalamkaretal.2011,Mottaetal.2012).Inparticular,type-
GRSJ1915+105showsHFQPOsaround67Hz(Morganetal. C QPOs are known to correlate well with the rms, forming in a
(1997)) while the other sources show this type of QPOs above frequencyversusrmsplaneacurvedtrackwithrmsdecreasingfor
150 Hz.Therefore, for periastronprecession frequencies (and or- increasing frequency, breaking at νBreak ∼10 Hz. The slope is al-
bitalfrequency,coincidentwiththeperiastronprecessionfrequency ways steeper for the high-frequency half of the correlation track
at the ISCO) we assume a lower limit of 50 Hz and an upper (see,e.g.,Mottaetal.2012forthecaseofGROJ1655-40).HFQ-
limit of 350 Hz since this isthe highest observed HFQPO so far POs,instead,formadifferentgroupofpointsatsignificantlyhigher
(Strohmayer 2001; Bellonietal. 2012). We stress that, according frequenciesandrmscomparabletothatoftype-CQPOsfoundin
to the RPM, it is possible to distinguish type-C QPOs from the thesoftstate(Mottaetal.2016,inprep).
HFQPOassociatedtoeitherorbitalorperiastronmotionsincethere InFig.3,weplottheintegratedfractionalrmsversusthecen-
isnomass-spincombinationthatgivesthesamefrequencyforboth troidfrequencyoftheQPOsforeachsourceofoursample.Wesee
motions. thatformostofthesourcestheQPOcentroidfrequencycorrelates
InFigure1weshowtheLense-Thirringprecessionfrequency wellwiththerms,formingacurvedtrack.Intheplotwemarkwith
ν evaluated at r for every mass and spin couple within the blackdotstheQPOsreportedinMottaetal.(2012,2014a,b,2015)
LT ISCO
ranges3M < M < 20M and0<a<1(i.e.weconsideredonly andwithredstarsthetype-CQPOsfoundinthiswork.
⊙ ⊙
progradeorbits).NotethatforclarityweonlyshowLense-Thirring
frequenciesspacedby9Hz.Forcomparison,wealsoshowinFig.
4.2 EvidenceofQPOsinthesoftstate
2theperiastronprecessionfrequenciesatr withthesamespin
ISCO
andmassranges. Ithasbeenshownthatfortwosourcesinoursample,GROJ1655-
40 and XTE J1550-564 (see Saitoetal. 2007 for GRO J1655-40
Inordertoplacelimitsonthespinvalue,weselectedthehigh- andKubota&Done2004forXTEJ1550-564), theaccretiondisc
est frequency type-C QPO for each source (considering both the inner radius remains constant for most of the HSS, providing a
QPOswefoundinthisworkandtheQPOsreportedinMottaetal. strong evidence for the accretion disc having reached the ISCO
2012, 2014a,b, 2015) and then solved eq. (1) for the spin a after (seealsoSteineretal.2011,Mottaetal.2014a,Plantetal.2014).
substitutingtheexpressionofrISCO.Weusedeitheraknownvalue ItisworthnoticingthattheQPOsintheHSSofthesetwosources
forM(whenavailableintheliterature),orweassumedthemassto stand out in terms of very low rms and high Q factor (see Table
lieintherangegivenabove. 1).Giventhebehavior of thesourcesof our sample(andof tran-
sientBHX-raybinariesingeneral)intheHIDs,itisreasonableto
assumethattheinnerdiscradiusdoesindeedreachtheISCOany
4 RESULTS timeasourceisobservedintheHSS,whichisbasicallythesame
assumptionusedforthespinmeasurementsbasedonspectroscopy
4.1 QPOClassification
(seee.g.McClintocketal.2014andreferencestherein).Sincethe
Plottingthetotalintegratedfractionalrmsversusthecentroidfre- type-C QPOsdetectedintheULShavefrequencies verycloseto
quency of a QPO is a useful method for distinguishing different thoseobservedintheHSS(seee.g.Mottaetal.2012),weextended
MNRAS000,1–10(2016)
Type-C QPOs insoftstate 5
100 4U1543-47 100 4U1630-47 100 GROJ1655-40 100 GX339-4
Mottaetal.(2015)
Type-C(thiswork)
10−1 10−1 10−1 10−1
10−2 10−2 10−2 10−2
100 101 102 10−1 100 101 102 10−1 100 101 102 10−1 100 101 102
10−1 XTEJ1817-330 100 XTEJ1550-564 100 H1743-322 100 XTEJ1859+226
ms
r
al
n
o
dfracti 10−1 10−1 10−1
e
grat
e
int10−2100 101 102 10−210−1 100 101 102 10−210−1 100 101 10−2100 101
100 XTEJ1650-500 100 XTEJ1748-288 100 XTEJ1752-223 100 MAXI1543-564
10−1
10−1 10−2 10−1 10−1
100 101 101 102 100 101 100 101
centroidfrequency(Hz)
Figure3.IntegratedfractionalrmsversusQPOcentroidfrequency.EachpointcorrespondstoasingleRXTEobservation.Eachpanelreferstoasinglesource
ofoursample.
thisassumptionalsototheULS.Howeverwedecidednottoplace obtained applying the RPMto our sample in Table 1. In the first
upper limitsusing type-C QPOs in the ULS since they might be column are listed the source names and the second contains the
underestimated.WedescribebelowinSection4.3theuncertainty Obs-IDofthehighestdetectedtype-CQPO.Thethird,fourthand
inthespinestimateproducedbyusingthisassumption. fifthcolumnscontainthehighesttype-CQPOfrequencyandqual-
If the highest type-C QPO is detected in the HSS, we can ityfactorandthetotalfractionalrmsrespectively.Thesixthcolumn
thereforeassumethatitwasproducedattheISCOandthusplace indicateswhetherthehighest type-CQPOwasdetectedinthisor
a lower and an upper limit on the spin assuming a lower and an inpreviousworks(Mottaetal.2012,2014a,b,2015;Homanetal.
upper limit for themass. For those sources for which wedid not 2005).Thelasttwocolumnscontainthestateinwhichthehighest
detect a type-C QPO in the soft state, we can still use the high- type-CQPOwasdetectedandthespinlimitsobtainedrespectively.
estfrequencytype-CQPOfromMottaetal.(2012,2014a,b,2015)
Wewouldliketostressthatweperformedasystematicsearch
toplaceaconservativelowerlimitassumingalowerlimitforthe
fortype-CQPOsintheHSSandULS.Forthosesourcesforwhich
masssincetheseQPOsprobablycorrespondedtoradiilargerthan
wedidnotdetectanytype-CQPOinthesestatesweusedthetype-
theISCO.Inthesecasesanupperlimitonthespinwouldbemean- CQPOsreportedinMottaetal.(2015).Forcompletenesswewere
ingless(andinfactnotcorrect)givenourassumptions. madeawareofthefactthattherearetwoQPOsatevenhigherfre-
Fig.4containstheHIDsofthe5sourcesthatshowedtype-C quencies missing in Mottaetal. (2015) for XTE J1859+226 and
QPOsinthe HSS.Thered dots represent theobservations of the XTE J1650-500. Thus our lower limitsfor these two sources are
newly detected QPOs. By looking at these diagrams and the rms slightlyunderestimated.WedecidednottoaddtheseQPOsinour
valuesintableA1itisclearthatthetype-CQPOsinGX339-4,4U worksincewedonotwanttobiastheanalysisperformed.
1543-47andXTEJ1817-330 weredetectedinsoftstates.Instead
Formostofthesourcesofoursamplethereisnoindependent
thetype-CQPOsinGROJ1655-40and4U1630-47havebeende-
massmeasurement, thusweassumed themasstolieintherange
tectedintheULS.Wecanreasonablyassumethatalsointhisstate
3−20M .Inafewcases,however,wehavebetterconstraintson
theaccretiondiscinnerradiusreachestheISCOsincethefrequen- ⊙
the black hole mass and thus on the spin value. The lower limit
cies of type-C QPOs in the ULS are similar to those detected in
for the black hole mass in GX 339-4 is 6M (Hynesetal. 2003;
theHSS.Inthe4U1543-47HIDwemarkedwithreddotsthetwo ⊙
Muñoz-Dariasetal.2008).Thuswecanplaceastricterlowerlimit
differenttype-CQPOswedetectedthatslightlyoverlapwitheach
onthespinvalue:a =0.16.SinceweareassumingBHmasses
other. ThustheseHIDscontain allthe6new QPOsfound inthis lower
up to20M , theupper limitfor thespin of GX 339-4 isa =
work. ⊙ upper
0.38.
ForbothGROJ1655-40(5.31±0.07M Mottaetal.2014a)
⊙
and XTE J1550-564 (9.1±0.6M Oroszetal. 2011) we have a
4.3 Constrainingthespin ⊙
goodindependentmassmeasurement.Usingthesedynamicallyes-
WeplacedlowerlimitsontheBHspinforeachsourceofoursam- timated mass values, we can narrow significantly the spin range
pleasdescribedinSection3.Forthesourceswiththehighesttype- ofvaluesforthetwosources(seeTable1).Thespinvaluesfound
CQPOdetectedinthesoftstatewedidalsoplaceanupperlimit by Mottaetal. (2014a,b) (a = 0.290±0.003 for GRO J1655-40
(assuminganupper limitonthemass).Wesummarizetheresults anda=0.34±0.01forXTEJ1550-564)are,asexpected,ingood
MNRAS000,1–10(2016)
6 Franchini,MottaandLodato
104 GX339-4 0.8
• 0.7
s) 103
cts/ 0.6
E( 102 0.5
T
A
R 101 a 0.4
T /
N a
U ∆ 0.3
O 100
C 0.2
10−1
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.1
HARDNESSRATIO 0.0
104 4U1630-47 1.0 1.2 1.4 1.6 1.8 2.0
rout/rin
•
s/s)103
(ct Figure5.Relative changeinthespinestimate assumingthattheQPOis
E
AT102 producedbyanextendedrigidlyprecessingstructure(Ingrametal.2009)
R ratherthanatestparticleatISCO,asafunctionoftheradialextentofthe
T
UN101 precessingstructurerout/rin,whereroutistheouterradiusandrin =rISCO
O istheinnerradiusofthestructure.
C
100
0.0 0.2 0.4 0.6 0.8 1.0 1.2
HARDNESSRATIO agreementwiththerangeweinferredusingtheRPMwiththehigh-
esttype-CQPOattheISCO.
104 4U1543-47 Asmentionedabove,theremightstillbethepossibilitythat,
•••
eveninthesoftstate,thediscdoesnotextenddowntotheISCO,
s/s) 103 butsomewhatclosetoit.Inthiscase,onecanstillrelatetheQPO
E(ct 102 frequency to the spin of the black hole, because we expect that
AT the hot inner flow would have a finite and small radial extent
R 101 so that it would precess as a rigid body (Ingram&Done 2011;
T
N
U Franchinietal.2016).Thus,wecanassumethatthehotinnerflow
O 100
C extendsfromtheISCOtoanouter radiusR ,andthencompute
out
10−1 thespinvaluethatwouldreproduceagivenQPOfrequencyusing,
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
forexampleeq.(1)inIngram&Done(2011).Inthisway,wecan
HARDNESSRATIO
thusestimatetheassociatedchangetothespinvalueobtainedfrom
104 XTEJ1817-330 theRPMmodel,asafunctionofRout.Forinstance,usingthehigh-
esttype-CQPOdetectedinGROJ1655-40(i.e.27.51Hz)together
s/s)103 • withthemassestimateforthissource,wecanevaluatetheuncer-
ct taintywithrespecttothevalueobtainedusingtheRPM.Theresults
(
E
AT102 inthiscaseareshowninFigure5.The x-axisistheratiobetween
R theouterradiusoftheinner accretionflowandtheISCOandthe
T
UN101 y-axisistherelativechangeinthespinvalue.Asimilarresultholds
O
C alsofordifferentQPOfrequencies.
100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
HARDNESSRATIO
5 DISCUSSION
105 GROJ1655-40
We analyzed RXTE observations of 12 black hole transients that
s)104 • showed a transition to the soft state. We considered observations
cts/ in the HSS and ULS of these sources. We then assumed that the
E(103 highestfrequencytype-CQPOhasbeenproducedattheISCOand
T
RA102 weappliedtheRPMinordertoplacelimitsonthespinvalue.This
NT isdone either using aknown value of theblack hole mass or as-
U
O101 sumingthemassinareasonablerangeofvalues,decidedapriori
C
(3−20M inourcase).
100 ⊙
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 This method is based on the assumption that the inner disc
HARDNESSRATIO truncation radius is constant and coincident with ISCO when a
BHB is observed in the HSS or ULS. Demonstrating the coinci-
dence of the inner disc truncation radius with ISCO is problem-
Figure4.HIDofthe5sourceswithtype-CQPOsintheHSS(GX339-4,
atic and involves spectroscopic measurements that are generally
4U1630-47,4U1543-47,XTEJ1817-330,GROJ1655-40).Thereddots
representtheobservations thatcontainthetype-CQPOswefoundinthis affected by largeuncertainties. Therefore, our assumption consti-
work.NotethattheQPOsinGX339-4,4U1543-47andXTEJ1817-330 tutesarelevantcaveat.However,bothobservationsandsimulations
weredetectedinsoftstates,whiletheonesinGROJ1655-40and4U1630- providestrongevidenceaboutthestabilityoftheinnerdiscradius
47weredetectedintheULS.IntheHIDof4U1543-47wemarkedthetwo overtimeindisc-dominatedstatesofBHBs(e.g.McClintocketal.
differenttype-CQPOswefoundwithreddots.
MNRAS000,1–10(2016)
Type-C QPOs insoftstate 7
Table1.Spinlimitsinferredfromthehighestfrequencytype-CQPOatISCOaccordingtotheRPM.Bothlimitsareevaluatedassumingablackholemass
intherange3−20M⊙.InthecaseofGX339-4thelowerlimitcorrespondsto6M⊙.ForXTEJ1550-564andGROJ1655-40thelimitscorrespondtothe
measuredmasses9.1±0.6M⊙ and5.31±0.07M⊙ respectively(MuñozDariasetal.2010;Mottaetal.2014b,a).Thefirstcolumncontainsthenameofthe
source,thesecondistheObs-IDofthehighesttype-CQPOdetected.Thethird,fourthandfifthcolumnscontainthepropertiesoftheQPO,i.e.frequencyand
theQfactor,andthetotalfractionalrms.Thesixthcolumnindicateswhetherthehighesttype-CQPOhasbeendetectedinthisworkorthepreviousones.The
seventhcolumnindicatesthestateinwhichtheQPOwasdetectedandthelastcolumncontainsthespinlimits.
Target Obs-ID νmax(Hz) Q rms New? state spinlimits
GX339-4 92085-01-02-03 10.59±0.18 3.46±0.50 5.05±0.03 yes HSS 0.16-0.38
4U1630-47 80117-01-07-01 14.80±0.28 2.17±0.27 9.5±0.4 no ULS >0.12
4U1543-47 70133-01-01-00 15.37±0.18 2.57±0.27 4.2±0.03 yes HSS 0.13-0.47
XTEJ1859+226 40124-01-14-00 8.56±0.06 2.76±0.18 12.4±0.4 no HIMS >0.07
XTEJ1650-500 60113-01-13-02 6.84±0.05 8.05±1.23 20.8±0.3 no HIMS >0.06
XTEJ1817-330 91110-02-32-00 9.6±0.5 2.93±0.82 5.7±0.1 yes HSS 0.08-0.36
XTEJ1748-288 30171-02-01-00 31.55±0.13 6.00±0.42 10.2±0.5 no HIMS >0.23
XTEJ1752-223 95360-01-11-00 6.46±0.13 3.6±1.1 23.4±1.2 no HIMS >0.06
XTEJ1550-564 40401-01-48-00 18.10±0.06 19±4 6.2±0.1 no HSS 0.31-0.34
MAXIJ1543-564 96371-02-02-01 5.72±0.04 10.2±1.4 27.3±1.2 no HIMS >0.05
H1743-322 80135-02-03-00 14.6±0.2 12.6±6.3 4.4±0.2 no ULS >0.12
GROJ1655-40 91702-01-17-01 27.51±0.13 44±21 2.7±0.1 no HSS 0.29-0.31
2014).Tanaka&Lewin(1995)showedthattheinnerradiusisre- frequencyforagivensourceresultsinanunderestimationofboth
markablystablealsoifthethermalfluxofthesourcesteadilyde- upper and lower limit of the spin. In other words, when estimat-
creasesontimescalesofmonthsbyoneortwoordersofmagnitude. ing the spin range from a type-C QPO that is not the highest in
Similar evidence for a constant inner disc radius in the soft state frequency, wewould befollowingthe wrongtrackinFig.1,that
hasbeendemonstratedformanysources(Doneetal.2007andref- wouldbefoundtotheleftofthetrackcorrespondingtotheactual
erences therein,Plantetal. 2014,Plantetal. 2015).According to highestfrequencytype-CQPO.ThiseffectislargerforQPOsthat
Tanaka&Lewin(1995),theconstancyoftheinnerradiussuggests arenotdetectedintheHSS,thereforeproducedataradiusthatis
that it is related to the ISCO. More recently Steineretal. (2010) almostcertainlylargerthanISCO.
foundanotherevidenceofanonvaryingdiscinnerradiusovertime We note that the different tracks in Fig. 1 tend to lay closer
forthesourceLMCX-3,unaffectedbythehighvariabilityofthis to each other for high frequencies (i.e. above 80 Hz). Thus, the
source.Nevertheless,sincewecannotbecertainofthecoincidence erroronthespinestimatemightbedominatedbythatonthemass
oftheinnerdiscradiuswithISCOforallthesourcesofoursample, iftheQPOfrequencyisveryhigh.Ingeneral,thetwouncertainty
excludedGROJ1655-40andXTEJ1550-564(forwhichthecoin- thatcontributetotheerroronthespinvaluearethatontheblack
cidencehasbeendemonstratedexplicitly),weadvicethereaderto hole mass and the identification of the highest type-C QPO. For
considertheinferredlimitswithcaution. instance,iftheactualhighesttype-CQPOwasproducedat,say,30
The rigid precession of the inner accretion flow as an ex- Hzinsteadofbeingdetectedat21Hz,theerrorthatwecommiton
planation of type-C QPOs has been supported by several stud- thespinestimateisoftheorderofafewpercent.
ies(Ingrametal.2009;Ingram&Motta2014;Ingrametal.2016).
The rigid precession model tends asymptotically to the RPM for
radii approaching the ISCO, therefore, given the stability of the 5.1 Comparisonwithothermethods
discinner radiusinthesoftstate,theRPMrepresentsagoodap-
Forsomesources of our sample thespinhasbeen alsomeasured
proximationoftherigidprecessionfortruncationradii(hencehot
throughX-rayspectroscopybyfittingthethermaldiscemissionor
flowouterradii)veryclosetotheISCO(Ingrametal.2009).
by modelling the disc reflection spectrum. Fig. 6 shows the spin
The approach we used in this work differs from that of measurements found in the literature obtained from X-ray spec-
Ingram&Motta (2014), which always requires that at least two troscopy versus the spin values we inferred from timing analysis
QPOs are detected simultaneously (the type-C QPO and one in this work. The black line marks the position where the mea-
HFQPO)inordertoplaceanupperorlowerlimitonspinandmass, surementsshouldfalliftherewasperfectagreementbetweenspec-
dependingonthecaseconsidered.Hereweassumedthatthehigh- troscopybasedmeasurementsandtimingbasedmeasurements.In
estfrequencytype-CQPOisproducedattheISCO.ThustheRPM twooutoffivesources(XTEJ1550-564and4U1543-47)thespin
systemofequationsisreducedtojustoneequation(i.e.eq.(1))that measurements obtained with spectroscopy and timing do agree.
giveseitheralowerlimit(ifthehighest type-C QPOwasnotde- In particular, Morningstar&Miller (2014) obtained a spin value
tectedintheHSS)orarangeofspinvalues.Therangesarebroadif a = 0.43+0.22, in agreement with our values, for 4U 1543-47 us-
−0.31
thereisnoindependent(e.g.dynamical)massmeasurementavail- ing both the spectral continuum fitting method and the iron line
able,orsignificantlynarrowerifthemassisknown.Thereasonis fittingmethodsimultaneously.Steineretal.(2011)useddatafrom
thattheuncertaintyonthespiniscompletelydominatedbytheer- theBHBXTEJ1550-564tomodelthecontinuumandtofittheiron
ror on themass (much larger thanthe error on theQPO centroid lineobtainingtwodifferentspinmeasurements,thatcombinedre-
frequency). sultedinaspinofa=0.49+0.13whichismarginallyconsistentwith
−0.20
Inprinciplewecanneverbecompletelysurethatthetype-C thespinrangethatwereport(seeTable1).
QPOweassumedtobethehighestisactuallythehighestproduced For4U1630-47Kingetal.(2014)measuredthespinbyfitting
bythesourceinthesoftstate.Thereisalwaysthepossibilitythat thecontinuum spectrum of thesource, obtaining a = 0.985+0.005,
−0.014
anevenhigherfrequencytype-CQPOhasbeenproducedandnot which is in principle compatible with our lower limit (i.e. 0.12).
detected. Using a type-C QPO that is not at the highest possible For XTE J1752-223 and GX 339-4, spectroscopy returned high
MNRAS000,1–10(2016)
8 Franchini,MottaandLodato
spinvaluesusingbothcontinuum fittingandthereflectionmodel
1.0
(Reisetal. 2011; Milleretal. 2002; Reisetal. 2008). Reisetal.
(2011)foundanintermediateblackholespina = 0.52±0.11for
XTEJ1752-223whileforGX339-4analmostextremespinvalue 0.8
a=0.935±0.010hasbeeninferred.WhileforXTEJ1752-223we
wereabletoplaceonlyalowerlimitonthespinthusourfindings
arestillconsistentwiththeresultsobtainedusingspectroscopy,the 0.6
spectroscopic estimate of the spin in GX 339-4 is not consistent ec
p
withtherangeobtainedusingtheRPM. as
0.4
Mottaetal. (2014a) measured with unprecedented precision
4U1543
the mass and spin of the BH in GRO J1655-40 applying the
XTEJ1550
RPM using the three QPOs that have been simultaneously ob- 0.2
GX339-4
served(Mottaetal.2012;Strohmayer2001).Theyinferredamass
GROJ1655
M = 5.31±0.07M and aspin value a = 0.290±0.003 that is,
⊙
0.0
asexpected,ingoodagreementwiththerangeobtainedinthispa-
0.0 0.2 0.4 0.6 0.8 1.0
per.Throughspectroscopicstudies,different,muchhigher,values a
RPM
ofthespinhavebeeninferred.Bymodellingthethermalspectral
continuumShafeeetal.(2006)foundaspinrangea=0.65−0.75.
Reisetal.(2010)placedalowerlimita=0.9byfittingthestrong
reflectionfeaturesinthespectrumandMilleretal.(2009)obtained Figure6.Thehorizontallinesrepresentthedifferentrangesofspinvalues
ahighlyspinningblackholewitha = 0.94−0.98usingthesame obtainedinthisworkforeachsource.Theblack,red,greenandcyanlines
referto4U1543,XTEJ1550,GX339-4andGROJ1655respectively.On
method. Both the spectroscopic methods rely on the assumption
they-axisthedotsrepresentthevaluesobtainedusingspectroscopicmeth-
that the inner edge of the disc corresponds to the ISCO, which
odswiththecorrespondent errorbars.Theblacklinerepresents thecase
might not be a correct assumption in all spectral states of active
aspec=aRPM.
black holes (see, e.g. Doneetal. (2007)). Furthermore, in order
tousethespectralcontinuumfittingmethod,onemustalsoknow
the black hole mass, the inclination of the (inner) accretion disc thenappliedtheRPM.Thischoiceisjustifiedbythefactthatinthe
withrespecttothelineofsightandthedistancetothesource.All HSSthediscisexpectedtoextenddownorveryclosetotheISCO.
thesefactorsintroducelargeuncertaintiesandpossiblysignificant Asaconsequence,theinneraccretionflowisextremelynarrowin
biasesinthespinmeasurement. Forinstance,asalreadynotedby thisstateandweassumedthatitsLense-Thirringfrequencycanbe
Mottaetal. (2014b) in the case of GRO J1655-40, the disagree- welldescribedbythatofatestparticleattheISCO.Accordingto
mentbetweenspinmeasurementsinferredthroughdifferentmeth- the RPM, we associated the highest frequency type-C QPO with
odsmightbeduetothehighinclinationoftheinneraccretiondisc the Lense-Thirring precession frequency of a test particle at the
with respect to the outer disc (i.e. the orbital inclination) and to ISCO.Wetheninferredlowerspinlimitsforallthesourcesofour
the line of sight. When such misalignment is not taken into ac- sampleandupperlimitsfortheonesthatshowedtype-CQPOsin
count,thefinalspinmeasurementcanbelargelybiased.TheRPM theHSSorULS,assumingareasonablerangeofblackholemasses
methoddoesnotdependonanyofthesevariables,andinthecase orusingtheactualmassvalueforthosesourcewhereadynamical
where3QPOsaresimultaneouslydetected,itallowstoobtainself massmeasurementisavailable.WesuccessfullyappliedtheRPM
consistentlymassandspinoftheBH.Theprecisionontheinferred toall the sources inour sample that showed type-C QPOsin the
parametersisonlydrivenbytheprecisionintheQPOfrequencies HSSorULS.
measurement. Our results are in good agreement withthose inferred using
Morespectroscopy-basedandtiming-basedmeasurementsof other spectroscopy-based methods (continuum fittingmethodand
thespinarenecessarytoconfirmthevalidityoftheRPMmethod theK-αlinemodelling)onlyintwocases.Nextgenerationsatel-
and to test its consistency with other methods. New generation lites,characterizedbyahigher signal-to-noiseratiomighthelpin
satellites(suchaseXTPZhangetal.(2016))willprovidemoreand solvingtheissueofspinmeasurements.
betterdatatotestthisandothermethodsforspinmeasurements.
Finally, as already noted by Mottaetal. (2014a), we would
liketostressthattheRPMisasimplifiedmodelaimedatdescribing
7 ACKNOWLEDGMENTS
rather complex physical conditions, such as those encountered in
theinnermostdiscregionsaroundanaccretingcompactobject.The Wearegratefultothereferee,Dr.JeroenHoman,thatprovideduse-
RPM does not include yet a production mechanism for the QPO fulcommentsandsuggestionsthathelpedinsignificantlyimprove
signals(butseePsaltis&Norman2000 orSchnittmanetal.2006 ourwork. AFacknowledges thetransitiongrant oftheUniversità
for possible mechanisms), which remains an open question to be degliStudidiMilanoandtheUniversityofOxfordforhospitality.
investigatedinthefuture. SEMacknowledgestheUniversityofOxfordandtheVioletteand
SamuelGlasstoneResearchFellowshipprogram.
6 SUMMARYANDCONCLUSIONS
APPENDIXA: POWERDENSITYSPECTRAAND
Inthisworkweplacedlimitsonthevalueoftheblackholespinfor
PROPERTIESOFQPOS
severalbinariesthroughthesoleuseofX-raytiming.Inparticular
welookedfortype-CQPOsinthesoftstateforanumberofsources FigureA1showsaselectionofPDScontainingatype-CQPOde-
selectedbasedonthepresenceoftype-CQPOsintheirPDS,and tected in the HSS and in the ULS. Fromtop to bottom, the PDS
MNRAS000,1–10(2016)
Type-C QPOs insoftstate 9
ObsID ν(Hz) Q rms
GX339-4 10−2 GX339-4
92085-01-02-03 10.59 3.46 0.05
4U1630-47
70417-01-09-00 12.3 2.15 0.033 y
4U1543-47 sit
n
70133-01-01-00 15.37 2.57 0.042 e
d
70133-01-05-00 15.0 3.75 0.046 al
XTEJ1817-330 ctr
e
91110-02-32-00 9.6 2.93 0.057 p
s
GROJ1655-40 er
10255-01-05-00 10.7 2.7 0.011 w
o
P
TableA1.PropertiesoftheQPOsfoundinthisworkdividedbysource.For
eachQPOthefirstcolumncontainstheObsID,thesecondisthecentroid
frequency,thethirdisthequalityfactorQandthelastoneistheintegrated
fractionalrms. 10−1 100 101 102 103
Frequency(Hz)
comefromGX339-4,4U1543-47andGROJ1655-40respectively.
ThefirsttwoQPOsarecharacterizedbyastrongandnarrowpeak 4U1543-47
at frequencies of theorder of 10 Hz. Thethird isa small though
significant(3.96σ,singletrial)peakat27.5Hz.
WereportinTableA1thepropertiesofthenewQPOsdetected y
inthiswork:theObsID,thecentroidfrequency,thequalityfactor sit
n
e
andtheintegratedfractionalrms.Notethatthetotalfractionalrms d
measuredfortheobservationwhereagivenQPOisdetectedisal- al
ways65%,whichshowsthatalltheseQPOsweredetectedinsoft ctr
e
states. As noted elsewhere, this impliesthat the inner disc radius sp
iscloseorcoincidenttotheISCOandtheRPMcanbeappliedto er
w
obtainaconstrainonthespinofthecentralblackhole. o
P
10−3
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MNRAS000,1–10(2016)