A possible imprint of quasi-periodic oscillations in the X-ray spectra of black hole binaries

0.21 MB·

by  P. Varniere

Astronomy&Astrophysicsmanuscriptno.spectralQPO˙AandA˙V3 (cid:13)c ESO2016
January13,2016
A possible imprint of quasi-periodic oscillations
in the X-ray spectra of black hole binaries
P.Varniere1,R.Mignon-Risse1,andJ.Rodriguez2
1 APC, AstroParticule et Cosmologie, Universite´ Paris Diderot, CNRS/IN2P3, CEA/Irfu,
Observatoire de Paris, Sorbonne Paris Cite´, 10, rue Alice Domon et Le´onie Duquet, 75205
ParisCedex13,[email protected]
6
1 2 LaboratoireAIM,CEA/IRFU-CNRS/INSU-Universite´ ParisDiderot,CEADSM/IRFU/SAp,
0
F-91191Gif-sur-Yvette,France.
2

n Received¡date¿/Accepted¡date¿
a
J
ABSTRACT
2
1
Context. While nobody would deny the presence of Quasi-Periodic Oscillations in the power

]
E densityspectrumofBlackholebinariesnortheirimportanceintheunderstandingofthemecha-
H nismspoweringtheX-rayemissions,thepossibleimpactonthetime-averageddiskenergyspec-
. trumfromthephenomenonresponsiblefortheQuasi-PeriodicOscillationsislargelyignoredin
h
p modelsofsourcesemission.
-
o Aims.Hereweinvestigatethepotentialimpactofsuchstructureontheresultantenergyspectrum.
r
t Methods.UsingdatafromthewelldocumentedoutburstsofXTEJ1550-564welookedatpos-
s
a siblehintsthatthepresenceofQuasi-PeriodicOscillationsactuallyimpactstheenergyspectrum
[
emitted by the source. In particular we look at the evolution of the relation between the inner

1
discradiusandtheinnerdisctemperatureobtainedfromfitstothespectraldata.Wethentestthis
v
6 furtherbydevelopingasimplemodelinordertosimulatespectraofadiskwithastructuremim-
1
ickinganincreasinginstrengthQuasi-PeriodicOscillationandcomparethesimulatedresultsto
8
2 thoseobtainedfromrealdata.
0
Results.Wedetectasimilardepartureintheinnerradius-innertemperaturecurvecomingfrom
.
1 thestandardfitofoursimulatedobservationsasisseeninXTEJ1550-564data.Weinterpretour
0
6 resultsasevidencethatthestructureattheoriginoftheQuasi-PeriodicOscillationimpactthe
1 energyspectrum.
:
v Conclusions. Furthermore, in states with a significant disk emission the inaccuracy of the de-
i
X terminationofthediskparametersincreaseswiththestrengthoftheQuasi-PeriodicOscillation,
r an increase which then renders the value given by the fit unreliable for strong Quasi-Periodic
a
Oscillation.
Keywords.X-rays:binaries,stars:individual(XTEJ1550-564),accretiondisks
1. introduction
WhenlookingatthePowerDensitySpectrum(PDS)ofmicroquasarsthemoststrikingfeaturesare
the presence of narrow peaks, called Quasi-Periodic Oscillations (QPO). These Low-Frequency
(< 30Hz, LF) and High-Frequency (> 40Hz, HF) QPOs contain a significant part of the source
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Varniere,Mignon-Risse&Rodriguez:spectralQPOs
rapid variability. Some LFQPOs can have an amplitude of up to 30%. Several distinct models
exist to describe them, and many imply a warm/hot structure orbiting the disk causing the X-
ray modulation. Such structures include axisymmetric (see e.g. Bursa et al., 2004; Schnittman et
al.,2006b;Vincentetal.,2014),orprecessingtori(Schnittmanetal.,2006c;Ingrametal.,2009),
hotspots(Karasetal.,1992;Schnittman&Bertschinger,2004;Tagger&Varniere,2006;Pechacek
etal.,2013)orspirals(Tagger&Pellat,1999;Varniereetal.,2002).
Nevertheless,whenanalyzingthesourcesenergyspectrathediskismostlyconsideredasrela-
tivelyhomogeneousandwithasmooth,monotonictemperatureprofile.Ifsuchafeaturelessdisk
maybeagoodrepresentationfortheso-calledthermalstatesduringwhichtheenergyspectrare-
semble “pure” blackbody and the PDS associated show little or no variability, with no or weak
QPO, this model is not appropriate to describe states with prominent QPOs. Here we aim to ex-
ploreifthestructureattheoriginofQPOsindeedhasameasurableimpactontheenergyspectrum
anditsfits.
The shape and the existence of more than one component in the X-ray spectra makes it hard
to look at a direct impact from the structure at the origin of the QPO. Nevertheless, we can look
at a possible impact of the presence of QPOs on the spectral fit parameters and the correlations
between them. Many correlations between spectral parameters and QPO parameters have been
presented(Munoetal,1999;Remillardetal.,2002;Rodriguezetal,2002;Vignarcaetal,2003)
butnotmanystudieshavebeendonetoinvestigateanychangeinthecorrelationbetweenspectral
parametersdependingontheQPOpresence.
In section 2 we use data from two outbursts of XTE J1550-564 observed by RXTE, which
have the advantage of being long and well observed, to see if some trends are indeed visible in
the correlation between spectral parameters depending on the presence of QPOs. In order to test
furtherthisidea,wepresentinsection3asimplifiedmodelofadiskhavinganincreasinglystrong
QPOthatwethenusetocomputethesource’senergyspectrum.Insection4weusethismodelin
conjecture with the module fakeit from XSPEC to test the impact on the energy spectrum of a
hotstructureinthedisk.ThisallowsustodirectlymeasuretheimpactoftheQPOasthedifference
betweenthemodelparametersandtheresultingfitsbutalsotocomparethosesimulatedfitsresults
againstrealcorrelations.
2. LinkbetweenthediskparametersandQPOs
IthasbeenassertedearlyonthatthepropertiesoftheLFQPOs,inparticulartheirfrequencies,are
related to parameters of the disk (Muno et al, 1999; Rodriguez et al, 2002; Vignarca et al, 2003;
Varniere et al., 2002) obtained through spectral fitting. As there is much less data for HFQPOs,
nosimilarstudyhasbeendoneyetbutHFQPOsseemtobelinkedwiththepresenceofLFQPOs
of type A or B (Remillard et al., 2002). Here we are using data from XTE J1550-564 during the
outbursts of 98-99 and 2000, both known to harbor HFQPOs, to see if there is any difference in
the behavior of the different spectral parameters depending if there is or not a QPO of any types
observed.
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Varniere,Mignon-Risse&Rodriguez:spectralQPOs
2.1. ObservationsandDataReduction
XTEJ1554−564hasundergone5differentoutburstsduringthelifetimeofRXTE.Thelastthreeoc-
curredin2001,2002,and2003areconsideredas“failed”sincethesourcedidnotshowanyspectral
transitiontosoftflavored(i.e.disk)states.Wethereforeconsiderhereonlythefirsttwooutbursts
that also are the two brightest. They respectively occurred from 1998, Sept 6, until roughly the
beginning of May 1999 for the discovery one and from 2000, April 10 to 2000, July 16 for the
second and fainter outburst. Both outbursts have been extensively described in the literature (e.g
Sobczaketal,2000;Remillardetal.,2002;Milleretal.,2001;Rodriguezetal,2003,2004).Inthe
followingstudyweconsideronlytheobservationsshowingthepresenceofLFQPOand/orHFQPO
as reported in these articles. The QPO parameters are taken from Remillard et al. (2002); Miller
et al. (2001); Rodriguez et al (2004). Since the spectral calibration of the Proportional Counter
Array (PCA) has significantly evolved since the publication of these articles, we re-reduced and
re-analyzedthespectraldatainordertopresentthemostaccuratespectralparametersbutwekept
theparameters.Inordertocomparewiththepreviousresults(e.gRemillardetal.,2002)wekept
thedistance(D = 6kpc)andinclination(70◦)thatwereusedintheseearlierpapers.Thedistance
andinclinationweuseareonlyascalingfactorappliedtotheradius(seefullexpressionifeq1).
Aslongasweusethesamefortheobservationsandthesimulatedobservationswecancompare
theresults.
ThePCAdatawerereducedwiththeHEASOFTv6.16suite.Goodtimeintervalsweredefined
as intervals with a satellite elevation angle above the Earth greater than 10◦, an offset between
the pointing and the source direction less than 0.02◦, and recommended limitations on propor-
tionalcounterunits(PCU)potentialbreakdowns.Spectrawerethenextractedfromthetoplayerof
PCU2.Backgroundspectrawereobtainedwiththebrightbackgroundmodelandgeneratedwith
pcabackest, while response files were generated through pcarsp. 0.8% systematic errors were
addedtoallspectralchannelsbeforefitting.
ThePCAspectrawerefittedwithXSPECv12.6.2,between3and30keV.Aswewereinterested
in basic parameters we only considered simple spectral models. All spectra are well represented
with an absorbed (phabs) disk (diskbb) plus power law (powerlaw) model. The value of the
highspectralboundaryofourfitsdidnotallowustosignificantlyconstrainthepotentialpresence
andpropertiesofareflectionbump.WeneverthelessnotethataGaussianat6.5keVrepresenting
fluorescentemissionofiron,usuallytakenasasignatureforreflection,was,inafewcases,added
tothemodeltoobtainagoodfit. TheabsorptionwasfixedtoN =0.8×1022cm−2(Milleretal.,
H
2003).
The spectral fit gives access to the slope of the power-law (i.e. the photon index Γ), its nor-
malization,thetemperatureoftheinneredgeofthediskandthedisknormalization.Thelatteris
relatedtotheinnerapparentdiskradiusR followingNorm=((R /km)/(D/(10kpc)))2cosiwith
in in
Dthedistancetothesourceanditheviewingangleofthedisk.Itisknownthattheapparentradius
relatestotherealinnerradiusthrougha”hardeningfactor” f (Shimura&Takahara,1995).Here
wechoosetokeepthatR andnotaddacorrectionfactorasweareinterestedintherawoutputof
in
thefitthatwethenintendtocomparewithoursimulatedobservations.
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Varniere,Mignon-Risse&Rodriguez:spectralQPOs
2.2. Departurefromr -T correlation
in in
In Fig. 1 we represent the evolution of the disk parameters r vs. T obtained from the spectral
in in
fitstothedata.Twobehavioremergefromthisplot,atlargeradiusthemajorityofpointsnarrowly
Tin (keV) vs Rin (km)(HFQPO in red)
1.2 LFQPOType (black C, blue B, red A)
Fit of Tin (keV) vs Rin (km)
1.0
V) 0.8
e
k
n (
Ti 0.6
0.4
20 50 100
Rin (km)
Fig.1. Correlation between the inner edge position and inner edge temperature as directly given
by the spectral fits for the outburst of 98-99 and 2000 of XTE J1550-564. Red dots represent
observations with HFQPOs detected while there is none in the black dots. The crosses represent
thetypeofLFQPO,blackforthecommontypeC,bluefortypeBandredfortypeA.Timingdata
fromRemillardetal.(2002);Rodriguezetal(2002).
followapower-law,whilethereisanobviousdepartureastheinneredgeofthediskgetssmaller
than50km.InterestinglythisdepartureoccurswhenHFQPOsorsimilarlytypeA/BLFQPOsare
observed1.Itisalsointerestingtonotethatthisdepartureisalwaysinthesamedirection,namely,
atsimilarinnerradius,wegetahotterdiskinthecaseofadetectedHFQPO/typeA/BLFQPOthan
in the standard case with a type C (hard state). This may be compatible with the HFQPOs being
somekindofhotstructureinthedisk.
Atthispoint,onehastowonderif,asallthosedatapointscomefromthespectralfittingwitha
smoothmonotonicdisk,itispossiblethatthedeparturefromthecorrelationcouldberootedfrom
thepresenceofaQPO/warmstructurewhichcausesthefittofailandgivesinaccuratevalues.In
ordertotestthisassumption,thatinthepresenceofalocalizedhotstructureinthediskspectral
fitusingasmoothtemperatureprofilewillgiveinaccuratevalue,wewillperformfitsofadisk
withsuchstructurebutinacontrolled,hencesimulated,mannerandcomparetheresultsofthefit
withtherealvalues.
3. Simplemodelforthetemperatureprofile
QPO models often connect the signal modulations to the presence of structures embedded in the
disk.Ourmainconcernhereisnottheoriginofthestructure,buttheconsequencesontheemission
andifiteverneedstobetakenintoaccountwhendoingaspectralfit.Thismeansthat,ratherthan
takingfullmagnetohydrodynamic(MHD)simulationsofthedifferentmodelsproposedtoexplain
QPOs we are interested in, we decided to create a simple, analytical, model in order to test in a
cleanerandeasierway,itsimpact.Indeed,inafullfluidsimulationchangingoneparameterinthe
initialconditioncanhaverepercussionsonseveralobservableparametersandthereforeitisharder
1 Asasidenotewearelookingtoseeifthefewpointsthatdepartfromthecorrelationwithoutapublished
HFQPOfrequencyhaveornotsomehighfrequencystructurefineenoughtobeaHFQPO.
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Varniere,Mignon-Risse&Rodriguez:spectralQPOs
tostudythedifferenteffectsseparately.
Here we are using a similar perturbative approach as in Varniere & Blackman (2005) and
take a regular diskbb disk model with T (r) ∝ r−3/4 on which we add a component mim-
0
icking the structure at the origin of the QPOs that depends on radius and azimuthal angle as
T (r,ϕ) = h(r) . s(r −r ,ϕ). For simplicity we choose to decompose T as a height function h
1 s 1
that depends only on r and a shape function s which is finite only near the disk structure we are
studyingwhichisinturndefinedbyr =r (t,ϕ).Alsoforsimplicitywetaketheshapefunctionto
s s
begaussianandtheheightfunctiontoberelatedtotheequilibriumtemperatureT (r).
0
Usingthisstructurewecantakeintoaccountavarietyofshapesmimickingavarietyofmodels,
forexample:
-atoruswithr (t,ϕ)=cte×sin(νt)andνtheoscillatingfrequencyofthetorus,
s
-ahotspotwithr (t,ϕ)=cteforthehotspotazimuthalsizeandzerootherwise.
s
Inthegeneralcasethisconstant,whichdefinesthepositionofthestructureinthedisk,iscalledr ,
c
thecorotationradiusofthestructure.Inthecaseofnon-axisymmetricalstructuressuchasablob
Ω(r ),thefrequencyatwhichthestructureisrotatingisalsothefrequencyatwhichthefluxwill
c
bemodulated,hencetheQPOfrequency.
Thisprovidesasimplebutusefulframeworktomodeladiskwithaddedperturbativestructures.
Withinthisframeworktheperturbedtemperaturereads
T(r,ϕ) = T0(r)×1+γexp−21(cid:32)r−δrrs(ϕ)(cid:33)22 (1)
c
where r (t) is the position of the temperature maximum in the disk (the center of the torus or
c
hotspot). δ parametrizes the radial extent of the structure while γ is the maximum amplitude of
the perturbation. In the general case r is allowed to be a function of time to take into account a
c
changeinfrequencyofthemodulation,buthereweareconsideringonlythecasewheretheQPO
frequencyisstableduringone‘simulatedobservation’hencekeepingr aconstant.Indeed,inthe
c
blobmodelthefrequencyofthemodulationisΩ(r ).Inthatcase,thewidthofthepeakinthePDS
c
representstheradialextentofthestructure,hereparametrizedbyδ.
These last two parameters, (γ,δ) are the ones we will be using to mimic a growing flux
modulation. Indeed, using similar models we are able to reproduce several timing observables
suchas,forexample,thermsamplitudeofQPOsasshowninVarniere&Blackman(2005)fora
pseudo-newtonian potential and Varniere & Vincent (2016) in general relativy, hence validating
thissimplemodelasarepresentationofadiskgivingrisetoafluxmodulation,henceaQPO.All
the simulations presented in Table 1 represent an evolving flux modulation from zero to about
∼20%hencewellinsidetheobservedlimits.
Using these parametrized temperature profiles we then can compute the emitted thermal flux
fromtheentirediskconsideringitmadeofmultipleblackbodycomponentsinasimilarmanneras
5
Varniere,Mignon-Risse&Rodriguez:spectralQPOs
doneinthewidelyusedXSPECmodeldiskbbforamonotonicprofile:
r2 2E3 (cid:90) 2π(cid:90) ∞ r
f(E)= in cosi (cid:63) dr dφ (2)
D2 c2h3 E (cid:63)
0 1 ekbT(r(cid:63),φ) −1
where r is the radius in units of r the inner disk radius, k is Boltzmann’s constant, h is
(cid:63) in b
Planck’s constant and c the speed of light. The only difference with the diskbb model is that our
T(r,φ)isanon-monotonicfunctionofr andalsoofφ,hencewehavetokeepbothintegrals.We
thencreatedanXSPECmodelofdiskwiththisstructure(whichwenameddiskblobforthecase
ofanelongatedhotspot)whichwillbemadeavailableonceoptimized.
This allows two things: first we can fit observations with our non-monotonic disk profile and
second,usingtheprocedurefakeitinXSPECwecancreatesyntheticspectraofapower-lawplus
thedisktakingintoaccountthepresenceofawarm/hotstructure.Usingthesimulatedspectrawe
canthentestifthepresenceofastructurecausingaQPOinthePDSwouldalsohaveadetectable
impactontheenergyspectrum.UsingfakeitinXSPECgivesusseverallimitationsaswecannot
usetimedependenttemperatureprofiles,hencewecannottakeintoaccountthedopplerboosting
onthestructure.Bothofthoselimitationscanbeaddressed.Indeed,thesimulatedspectraaremade
asobservationsof3000seconds,henceareaveragedoverseveralthousandsofQPOperiods.For
each‘observation’wetookaconstantQPOfrequency(namelyr isconstant)sothetemperature
c
profile for the case of an elongated blob is conserved by rotation at the QPO frequency, which
allowsustousethetime-averagespectrum2. ConcerningtheimpactoftheDopplerboosting,this
effectisgreatlydiminishedinthecaseofaface-ondisksothecalculationdoneherewillbevalid
foraface-ondiskandrepresentalowerlimitformoreedge-ondisksastheDopplereffectboosts
theemissionofthehotspot,henceincreasingitsimpact.Hereweareinterestedtoseeifthislower
limitisalreadydetectable.
4. Impactontheenergyspectrumfitting
In order to see if the presence of a QPO has any impact on the energy spectrum we computed
severals synthetic spectra. We used the parameters of XTE J1550-564 which is extensively
observed and against which we could then test our results. For each simulation we will use the
procedurefakeitonanabsorbed(phabs)disk(diskblob)pluspowerlaw(powerlaw)model.
diskblobwillallowustomimicadiskwithaslowlyincreasinghotstructureaimingtoreproduce
the time evolution effect of a growing QPO. The latter is introduced in the model through two
parameters(inthatcaseγandδonly).WethenfittedthesyntheticspectrawithXSPECfollowing
thestandardprocedurewithdiskbbandpowerlaw.
UsingthemodelpresentedinEq.1γrepresentstheamplitude/strengthoftheinstabilitycausing
thestructurewhileδparametrizeditsradialextent,whichcan,inturn,relatetotheFWHMofthe
QPO we are modeling. The value of γ and δ in Table 1 are coherent with the QPO features one
wouldexpectduringanoutburst(asseeninthegeneralcaseinVarniere&Blackman,2005,then
2 We also compared an extended blob with a fully axi-symmetrical (ring) structure with the same tem-
peratureprofileandfoundtheresultstobegloballyconsistent.Indeedtheaverageprofileofabloboffinite
azimuthalsizewouldbesmallerthantheaxi-symmetric(azimuthof2π)versionofthesameblob.Thiscom-
fortedusthatahotterstructurepresentinthediskwillindeedhaveaneffectontheoverallenergy-spectrum.
6
Varniere,Mignon-Risse&Rodriguez:spectralQPOs
for a particular outburst in Varniere & Vincent 2016b). Here we took an ‘origin point’ from the
curveonFig.1.at(r ,T ) = (45,0.7)whereT isthenormalizationofT inEq.1.Wechosethis
in in in 0
pointasitisjustbeforewestartseeingadepartureinthecorrelation.Thismeansthat,inallour
simulations,ourdiskhasaninneredgeatr =45kmandanassociatedinneredgetemperatureof
in
0.7keV.Thisallowustoseethediscrepancybetweenthe‘real’valueandthevaluegivenbythefit,
measuredby∆ =(Xreal−Xfit)/Xreal).Thisdiscrepancyisameasureoftheaccuracyofthefitand
X
itsreliability.InallthesetsinTable1(r ,T )=(45,0.7)andonlythecouple(γ,δ)ismodified.
in in
γ δ Tfit Rfit
in in
0 0.05 0.71 41.4
0.1 0.05 0.73 40.1
0.1 0.1 0.69 48.2
0.2 0.1 0.70 44.2
0.3 0.1 0.74 40.9
0.4 0.1 0.79 36.8
0.4 0.15 0.80 37.9
0.45 0.1 0.81 35.5
0.45 0.15 0.82 36.1
0.45 0.18 0.86 34.1
0.5 0.15 0.84 35.4
0.5 0.18 0.87 33.9
0.5 0.2 0.89 33.8
0.7 0.1 0.92 28.6
0.7 0.15 0.98 27.9
0.7 0.18 0.99 28.6
0.7 0.2 1.02 27.5
0.9 0.18 1.14 24.0
0.9 0.2 1.16 24.8
1 0.18 1.22 22.8
Table1.Hotstructureparametersandtheresultsfromthefit,asareminderforallofthosethereal
inner edge of the disk is at 45km and the temperature is 0.7keV. All those have an amplitude of
modulationsbetweenzeroand20%,seeVarniere&Vincent(2016)fordetailsontheamplitudes
calculation.
Followingtheevolutionofthefitparameters,weseethatassoonastheQPOhasanon-zeroam-
plitudethereisadiscrepancybetweenthefittedvalueofthediskparametersgivenbythespectral
fitandtherealvalueusedtocreatethespectrum.
This discrepancy grows with the QPO amplitude (represented by the parameter γ in our
model):alreadywithafeaturehavingparameters(γ,δ)=(0.4,0.15),whichtranslateina5%flux
modulation we get ∆ = 14% and ∆ = 12%. It is interesting to note that the fitted value for
Tin Rin
r are almost always smaller than the actual value of the disk we input while the T are almost
in in
alwaysoverestimated.Indeedinourcaseofa‘real’inneredgeat45kmwegetsomefitresultsup
toabout23kmforourlargestfeatureswhichisequivalenttoanrmsof20%.Whilethediscrepancy
is always higher for the temperature, the impact on the determination of the inner radius of the
7
Varniere,Mignon-Risse&Rodriguez:spectralQPOs
diskisactuallymoreimportant.Indeed,theminimalpositionoftheinneredgeofthediskisoften
usedtoputsomelimitonthespinoftheblackhole.Inthatcaseanunderdeterminationbyalmost
factoroftwobetweenthe‘real’valueandthefittedonewouldleadtoamuchhigherinferredspin.
In the case here, where the inner edge of the disk is at 45km, which is approximatively 3r for a
g
10M ,thefitgivesbackaalueof23kmrepresentingabout1.6r ,whichwouldinturnindicatean
(cid:12) g
almost maximal spin. As this happens when we have strong QPO, it is better to continue using
onlythevalueoftheradiusfromstateswithoutQPOstoputconstraintsonthecentralobjectspin.
Furthermore, when we plot the results of the fit from the synthetic spectra together with data
pointsfromXTEJ1550-564wesee,inFig.2.,thatthegreystarrepresentingoursimulatedspectra
occupy the same space as the HFQPO/type B LFQPO data points from XTE J1550-564 hence
strengtheningthelinkbetweenQPO,hotspot,andfit-difficulties.
Tin (keV) vs Rin (km)(HFQPO in red)
1.2 LFQPOType (black C, blue B, red A)
blob model
Fit of Tin (keV) vs Rin (km)
1.0
)
V 0.8
e
k
(

n
Ti
0.6
0.4
20 50 100
Rin (km)
Fig.2. Correlation between the inner edge position and inner edge temperature as given by the
spectralfitsfortheoutburstof98-99and2000ofXTEJ1550-564.Reddotsrepresentobservations
with HFQPOs detected while there is none in the black dots. The crosses represent the type of
LFQPO,blackforthecommontypeC,bluefortypeBandredfortypeA.Thegreystarsarethe
resultofthesyntheticspectrafit.TimingdatafromRemillardetal.(2002);Rodriguezetal(2002).
We see that, even with the RXTE resolution and range, neglecting the QPO in the spectral
analysiscanleadtolargediscrepancies.Asasidenote,suchdeparturefromcorrelationcouldbe
usedtodetect,purelyfromspectralanalysis,thepossiblepresenceofHFQPOsbutwouldnotallow
topredictitsparametersaswecannotdisentangletheimpactofδandγonthespectrum.
5. Conclusion
Using a simple model to mimic the emission from a disk with a non-monotonic temperature, as
hasbeentheorizedtobethecaseinthepresenceofQPOs,wehavecreatedsyntheticspectraofa
system exhibiting an increasingly strong QPOs. This allowed us to study in a clean environment
8
Varniere,Mignon-Risse&Rodriguez:spectralQPOs
theimpactofathestructureattheoriginoftheQPOontheenergyspectrumanddetermineifwe
canneglecttheminthespectralfit.
First, our simulated observations are coherent with the departure from correlation seen in the
T -r diagramofXTEJ1550-564inpresenceofHFQPOandLFQPOsBorA.Inthecaseofvery
in in
smallamplitudeQPOsthereisanegligibleimpactontheenergyspectrumanditcanbeignoredin
thespectralfit.
Nevertheless,inpresenceofamediumstrength/impactQPO(morethan5%rmsamplitude)we
cannotneglectthepresenceofthehotstructureasitleadstosignificantdiscrepancybetweenthe
fittedvalueandthephysicalparameters.Especiallythoseerrorstendtoalmostexclusivelygivea
smaller inner radius and higher inner temperature. Therefore there is a need to improve the disk
fitting by taking into account the structures at the origin of the QPOs if we want to constrain the
diskparametersintheirpresence.
Acknowledgements. Theauthorthankstheanonymousrefereethathelpedclarifythepapertothisfinalform.Weacknowl-
edgethefinancialsupportoftheUnivEarthSLabexprogramatSorbonneParisCite(ANR-10-LABX-0023andANR-11-
IDEX-0005-02).
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