Clumped stellar winds in supergiant high-mass X-ray binaries: X-ray variability and photoionization

0.87 MB·English

by  L. M. Oskinova

Mon.Not.R.Astron.Soc.000,1–12(2005) Printed11January2012 (MNLATEXstylefilev2.2)
Clumped stellar winds in supergiant high-mass X-ray binaries:
X-ray variability and photoionization
1 ⋆ 1 2
2 L. M. Oskinova , , A. Feldmeier , P. Kretschmar
1 1InstituteforPhysicsandAstronomy,UniversityofPotsdam,14476Potsdam,Germany
0 2EuropeanSpaceAstronomyCentre(ESA/ESAC),ScienceOperationsDepartment,VillanuevadelaCaada(Madrid),Spain
2

n
a Accepted.Received;inoriginalform21.02.201122:32
J

9
ABSTRACT

] Theclumpingofmassivestarwindsisanestablishedparadigmconfirmedbymultiplelinesof
R
evidenceandsupportedbystellarwindtheory.Thepurposeofthispaperistobridgethegap
S
betweendetailedmodelsofinhomogeneousstellarwindsinsinglestarsandthephenomeno-
.
h logicaldescriptionofdonorwindsinsupergianthigh-massX-raybinaries(HMXBs).Weuse
p resultsfromtime-dependenthydrodynamicalmodelsoftheinstabilityintheline-drivenwind
- ofamassivesupergiantstartoderivethetime-dependentaccretionrateontoacompactobject
o
intheBondi-Hoyle-Lyttletonapproximation.Thestrongdensityandvelocityfluctuationsin
r
t thewindresultinstrongvariabilityofthesyntheticX-raylightcurves.Themodelpredictsa
s
a largescale X-rayvariability,upto eightordersofmagnitude,onrelativelyshorttimescales.
[ The apparentlack of evidenceforsuch strong variabilityin the observedHMXBs indicates

thatthedetailsofaccretionprocessacttoreducethevariabilityduetothestellarwindvelocity
1
anddensityjumps.
v
WestudytheabsorptionofX-raysintheclumpedstellarwindbymeansofa2-Dstochas-
5
ticwindmodel.Themonochromaticabsorptionincoolstellarwindindependenceonorbital
1
9 phaseiscomputedforrealisticstellarwindopacity.WefindthatabsorptionofX-rayschanges
1 stronglyatdifferentorbitalphases.Thedegreeofthevariabilityduetotheabsorptioninthe
. winddependsontheshapeofthewindclumpsandisstrongerincaseofoblateclumps.
1
Weaddressthephotoionizationintheclumpedwind,andshowthatthedegreeofioniza-
0
tionisaffectedbythewindclumping.Acorrectionfactorforthephotoionizationparameter
2
1 isderived.ItisshownthatthephotoionizationparameterisreducedbyafactorX compared
: tothesmoothwindmodelswiththesamemass-lossrate,whereX isthewindinhomogeneity
v
parameter.Weconcludethatwindclumpingmustalsobetakenintoaccountwhencomparing
i
X theobservedandmodelspectraofthephotoionizedstellarwind.
r Keywords: accretion,X-rays:binaries,instabilities,stars:neutron,X-rays:stars
a
1 INTRODUCTION rarefiedflowbystrongshocks.Feldmeieretal.(1997a,b)usedhy-
drodynamicsimulationstomodeltheevolutionofwindinstabilities
MassiveluminousOB-typestarspossessstrongstellarwinds.The
and predicted the X-ray emission from single stars matching the
windsarefast,withtypicalvelocitiesupto2500kms−1,anddense,
observedX-rayfluxes.Thesenon-stationaryhydrodynamic simu-
withmass-lossratesM˙>∼10−7M⊙yr−1.Thedrivingmechanism lationsareusedinthispaper.Runacres&Owocki (2002)studied
for the mass-loss from OB stars has been identified with radia-
theevolution of wind structures and demonstrated that the winds
tionpressureonspectrallines(Castoretal.1975,CAK).Earlyon
can remain inhomogeneous out to distances of 1000R*, while
Lucy&Solomon(1970)suggestedthatthestationarysolutionfor
Dessart&Owocki(2005)presentedfirstattemptsof2-Dradiative
a line-driven wind is unstable leading to shocks in stellar winds.
hydrodynamicmodelsofstellarwinds.
Lucy&White(1980)proposedthatthewindsbreakupintoapop-
ulation of dense blobs. Owockietal. (1988) performed numeri- Thesetheoreticalpredictionsofstellarwindclumpingarecon-
calsimulationsofthenonlinearevolutionofwindinstabilitiesand firmedbyobservations.FromanalysisofwindlinesintheUVspec-
showed that even small-amplitude perturbations in the radial ve- traLucy(1982)postulatedtheexistenceofnon-monotonic veloc-
locitynear thewindbase result inahighly structured wind, with ityfieldsinthewinds.Hillier(1991)inducedtheexistenceofwind
relativelyslow,denseshellsseparatedfromregionsofhigh-speed, clumpingfromtheshapeofelectron-scatteringwingsinemission
lines of Wolf-Rayet (WR) stars. Stochastic variable structures in
the HeII λ4686A˚ emission line in an O-supergiant were found
⋆ E-mail:[email protected] byEversbergetal.(1998),andexplainedasexcessemissionfrom
2 Oskinova,Feldmeier& Kretschmar
thewindclumps.Markovaetal.(2005)investigatedtheline-profile
Table 1. Stellar model parameters (see the full set of parameters in
variability of Hα for a large sample of O-type supergiants. They Feldmeieretal.(1997a))
concludedthattheobservedvariabilitycanbeexplainedbyawind
model consisting of coherent or broken shells. Le´pine&Moffat
Spectraltype O9.7Ib
(1999,2008)presenteddirectspectroscopicevidenceofclumping
inOandWRstarwinds.Prinja&Massa(2010)establishedspec- Mass M∗ 34M⊙
troscopicsignaturesofthewide-spreadexistenceofwindclumping Radius R∗ 24R⊙
inBsupergiants. Terminalspeed v∞ 1850km/s
The inhomogeneity affects stellar wind diagnostics. Masslossrate M˙ 3×10−6M⊙yr−1
Stewart&Fabian (1981) used Einstein spectra of O-stars to
study the transfer of X-rays through a uniform stellar wind. By
matching the model and the observed X-ray spectrum of the ontothecompactcompanionpowersthehighX-rayluminosityof
O-typesupergiantζPuptheyfoundthatthemass-lossratederived 1033–1039ergs−1. HMXBs can be divided in subclasses de-
fromX-rayspectraislowerbyfactorofafewthanthemass-loss ∼pendingonthespectraltypeofthedonorstar–supergiant(SG)or
ratesobtainedfromfittingtheHαlineaswellasfromobservations Be-star,andthetypeofvariability–persistentortransient.
at radio and IR wavelengths. As most plausible explanation for Inthispaper weconsider SGHMXBs.Thebasicphysicsof
this discrepancy they suggested the neglect of the clumping in neutron-star accretion in stellar winds was described in the sem-
O-starwinds.Waldron&Cassinelli(2001)proposedthataclumpy inal paper by Davidson&Ostriker (1973), who suggest that the
wind structure may help to explain the observed X-ray emission Bondi-Hoyle-Lyttleton accretion powers the X-ray luminosity in
line profiles in the spectra of O-supergiants. A theory of X-ray HMXBs.Kallman&McCray(1982)presentedtheoreticalmodels
transfer in clumped wins that accounts for clumps of any shapes forthetemperatureandionizationstructureofsphericallysymmet-
andopticaldepthswasfirstdeveloped byFeldmeieretal.(2003); ric,constantdensity,gaseousnebulaesurroundingcompactX-ray
Oskinovaetal. (2004). Indeed, accounting for wind clumping sources. Two-dimensional hydrodynamic simulations of the gas
allowstoconsistentlymodeltheUV/opticalandtheX-rayspectra flow in the orbital plane of a massive X-ray binary system were
ofO-stars(Oskinovaetal.2006). presented by Blondinetal. (1990). The simulations revealed the
Presently, clumping in first approximation (“microclump- presenceofdensefilamentsofcompressedgasformedinthenon-
ing”) is taken into account in all up-to-date stellar wind codes. steadyaccretionbow shockandwakeofthecompact object.The
This approximation assumes that clumps are optically thin and underlying assumption in all these models is an initially smooth
that the interclump medium is void. Microclumping leads to donor stellarwind withthe CAKdensity distribution. Inarecent
smaller empirical mass-loss rates when using diagnostics that review,Edgar(2004)demonstratedthatdespitethesimplifications
depend on processes scaling with density squared (ρ2), such made,Bondi-Hoyle-Lyttletonpredictionsfortheaccretionrateare
as Hα and other emission lines, or radio free-free emission quiteaccurate. Negueruela(2010) reviewedrecent workson stel-
(Hillier1991;Hamann&Koesterke1998).Bouretetal.(2005)and larwindaccretion,andsuggestedthattherealsourcesdifferfrom
Fullertonetal. (2006) demonstrated that mass-loss rates must be theidealizedsituationofBondi-Hoyle-Lyttletonaccretioninthree
reduced by orders of magnitude in order to reproduce the UV- mainways:thewindsofmassivestarsarehighlystructured;accre-
resonant lines(which depend on density linearly) simultaneously tiontoacompact objectisanunstableprocess; andthemagnetic
withtheρ2baseddiagnostics1.Thesedrasticreductionsofempir- fieldoftheneutronstarmayaffecttheflowofmaterial.Inthispaper
icallydeducedmass-lossrateswouldhavestrongconsequencesfor weinvestigatetheimmediateconsequencesofstellarwindclump-
thestellarevolutionandstellarfeedbackmodels. ing for the accretion rate, wind ionization, and the absorption of
AwaytosolvethisproblemwassuggestedbyOskinovaetal. X-raysintheunperturbedportionofthewind.
(2007).It wasfound thatwaiving themicroclumping approxima- Theobservational evidenceofclumpedaccretionflowinSG
tion i.e. allowing for clumps of arbitrary optical depth (“macro- HMXBsisgrowing.Sakoetal.(2003)reviewedspectroscopicre-
clumping”) inthespectralmodelseliminatestheneedtostrongly sultsobtainedbyX-rayobservatoriesforseveralwind-fedHMXBs.
reduce stellar mass-loss rates. It was shown that the strength of Theyconcludedthattheobservedspectracanbeexplainedonlyas
optically thick diagnostic lines, such as thePV resonance linein originatinginaclumpedstellarwindwherecooldenseclumpsare
OB star spectra, is reduced by macroclumping effects, while the embeddedinrarefiedphotoionizedgas.vanderMeeretal.(2005)
strengthofopticallythinlines,suchasHα,isnotaffected.There- studiedtheX-raylightcurveandspectraoftheHMXB4U1700-
fore, accounting for macroclumping in analyzing stellar spectra 37.TheyshowedthatthefeedingoftheNSbyastronglyclumped
yieldsempiricallyderivedmass-lossratesthatareonlyafactor2– stellarwindisconsistentwiththeobservedstochasticvariability.
3 lower than the “classical” CAK mass-loss rates. These conclu- in’tZand(2005)proposed thattheflaringbehavior ofsuper-
sions are confirmed by 2D model studies (Sundqvistetal. 2010) giantfastX-raytransients(SFXT)canbeexplainedbytheaccre-
andfull3Dradiative-transfermodels(Sˇurlanetal.,submitted). tionofwindblobs.Thissuggestionwascorroboratedbythestud-
TheCAKmass-lossratesofmassivestarsareingoodagree- iesofhardX-rayflaresandquiescent emissionof SFXTsystems
ment with observed X-ray fluxes from high-mass X-ray binaries by Walter&ZuritaHeras (2007), who estimated wind clump pa-
(HMXBs).HMXBsaretheproductsofbinarystarevolution(e.g. rametersandfoundthemtobeinagreementwiththemacroclump-
Shklovsky 1967; Ibenetal. 1995). These systems consist of an ing paradigm of stellar winds. Negueruelaetal. (2008) presented
early-type massive star and a compact companion, neutron star a common framework for wind accreting sources, in the context
(NS)orblackhole(BH),onacloseorbit.Accretionofstellarwind ofclumpywindmodels.Theypostulatedthatthedifferentflaring
behavior canbe animmediate consequence of diverse orbital ge-
ometries.
1 Waldron&Cassinelli(2010)pointedoutthattheextremeUVradiation Kreykenbohmetal.(2008)studiedthetemporalvariabilityof
maybeimportantforthemass-lossdiagnosticsbasedonresonantlines. VelaX-1. They interpreted flares and off states as being due to a
Clumpedstellarwindsin HMXBs 3
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2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Distance (R )
Figure1. Asnapshotofthedensity (upperpanel) and thevelocity (lower panel) structure ofthestellar windinaO9.5supergiant staraspredicted by
time-dependenthydrodynamicsimulations(Feldmeieretal.1997a,b).Theupperpanelshowsthatthedensityfluctuationsinthewindhavemanyordersof
magnitude,whilethelowerpanelshowsthestrongwindvelocityjumps.
stronglystructuredwindoftheopticalcompanion.Theysuggested sityandvelocity.TheBondi-Hoyle-Lyttletonaccretionformalism
thatwhentheNSinVelaX-1encountersacavitywithstronglyre- isappliedinSect.3tosimulatetheresultingtime-dependentX-ray
duceddensity,theX-rayfluxdrops,thustriggeringtheonsetofthe luminosity.Thephotoionizationintheclumpedwindisconsidered
propellbibdefinitions.texer effect, which inhibits further accretion inSect.4. InSect.5weapply our 2Dmodel ofaclumped stellar
(off states). From the analysis of the flaring behavior of VelaX- windtopredictthechangesinabsorptionduringtheorbitalmotion
1 Fu¨rstetal. (2010) concluded that a mixture of a clumpy wind, oftheNS.Thediscussion ispresented inSect.6andconclusions
shocks, and turbulence can explain the flare brightness distribu- aredrawninSect.7.
tion.Sidolietal.(2010)suggestedthattheX-rayvariabilityofthe
HMXBIGRJ08408–4503maybeexplainedbystellarwindclump-
ing.Bozzoetal.(2011)observedabrightX-rayflareintheHMXB
2 HYDRODYNAMICALSIMULATIONS
IGRJ18410-0535. Theyconcludedthattheflarewasproducedby
theaccretionofmassiveclumpontothecompactobjecthostedin Weemploy the resultsof hydrodynamical simulations of theline
thissystem. driven stellarwind presented in Feldmeieretal. (1997a,b). These
Duccietal. (2009) developed a phenomenological stellar hydrodynamic simulations derive thedynamic and thermal struc-
windmodelforOBsupergiantstoinvestigatetheeffectsofaccre- tureofstellarwindsfromthebasicunderlyingphysicalprinciple,
tion from a clumpy wind on the luminosity and variability prop- namely the acceleration of stellar wind by the line scattering of
ertiesofhigh-massX-raybinaries.Theyconcludedthatthemodel stellarUVphotons(CAK).
can reproduce the observed light curves well. They also pointed The simulations were performed using the smooth source
outthattheoverallmasslossfromthesupergiantshouldbeabout functionmethod(Owocki&Puls1996).Theline-driveninstability
afactorof3–10smallerthanthevaluesinferredfromultraviolet (LDI)ishandledbyacarefulintegrationoftheline-opticaldepth
linestudiesthatassumeahomogeneous wind.This,aswellasall witharesolutionofthreeobserver-framefrequencypointsperline
otherworksonthephenomenologyofclumpedwindsinHMXBs, Doppler width and by accounting for non-local couplings in the
accountonlyforthepresenceofdensewindclumpsandignorethe non-monotonic velocitylawofthewind.Theangleintegrationin
non-monotonicwindvelocity. the radiative flux is limited to one single ray which hits the star
Inthispaper weemploy time-dependent hydrodynamic sim- at 0.7R∗. This accounts with sufficient accuracy for the finite-
≈
ulationsofnon-stationarystellarwindsandusethepredictednon- disk correction factor. The pure hydrodynamics part of the code
monotonicdensityandvelocityfieldstocomputetheaccretionrate. is a standard van Leer solver. The seed perturbations for unsta-
We deliberately concentrate on the general consequences of stel- ble growth, in the shape of turbulent variation of the velocity at
larwindclumpingfortheHMXBs.Multi-Dhydrodynamicmodels alevelofroughly onethirdofthesound speed, areintroducedat
andtheprocessesintheimmediatevicinityofthecompactobject the base of the wind. These perturbations have a coherence time
arebeyondthescopeofthispaper.Weconsiderheresystemsofin- in the friction term of 1.4hr, which is not too far off the acous-
termediateandsmallX-rayluminosity,suchthatthedonorstellar ticcutoffperiodofthestaratwhichacousticperturbationsofthe
windatlargeisnotperturbedbythepresenceofthecompactobject photosphere should accumulate. Further details can be found in
anditsX-rayemission. Feldmeier(1995);Feldmeieretal.(1997a,b).
Thepaperisorganizedasfollows.InSect.2wedescribethe The hydrodynamic simulations were performed using stel-
hydrodynamicmodelsusedtoobtainthetime-dependentwindden- lar parameters of a typical late O-type supergiant star ζOrionis
4 Oskinova,Feldmeier& Kretschmar
(O9.7Ib)(seeTable1).Asnapshotofawindstructureatsomegiven 3000
momentoftimeisshowninFig.1.Thevarietyofdynamicalstruc-
]
s
turesintheinstability-induced,line-drivenwindturbulenceseems m/
tobesimilarlyintricatetothatfoundinotherturbulentflowsinas- k
[2000
trophysicalMHDsettings.Thereareindicationsofthepresenceof y
aquasi-continuous hierarchyofdensityandvelocitystructuresin cit
o
thewind.Denseshellsareformedclosetothestar,inafirststageof el
V
unstablegrowth.Thesedenseshellshaverathersmallradialextent, d 1000
and contain a large fraction of the wind mass. In the framework n
Wi
ofthesehydrodynamicmodels,thecolloquialterm“windclumps”
referstothesedenseshells.Thespacebetweentheshellsisfilled
bytenuousandhotgas(Feldmeieretal.1997a,b). 5 10 15 20 25 30 35 40
Furtheroutinthewind,inasecondstageofunstablegrowth,
Time (hours)
asomewhatdifferenttypeofdensestructuresareformed:thesmall
“clouds” that are “ablated” from the outer rim of the remaining Figure 2. The model (see text) wind velocity as function of time at the
mass reservoir at CAK densities, and are accelerated by the stel- radiusa=2.5R∗.Theamplitudeofvelocityvariationsmayexceedorder
larradiationfieldthroughtheemptiedregions,eventuallycolliding ofmagnitudeinonlyfewhours.
withthenext-outershell.TheX-rayemissionfromsingleearlytype
starwindsisexplainedbythesecloud-shellcollisions.
TheX-rayluminosityofanaccretingneutronstaristhen
Whiletheaveragevelocityfieldfollowstheso-calledβ-law:
v(r)=v∞(1 1/r)β, (1) LdX(a,t)=ηSaccrc2, (7)
−
where v∞ is the wind terminal speed, there are strong velocity wherecisthespeedoflight,andηisaconstantdependingonthe
jumps with negative gradients across the shells. In Figure2 we exactphysicsofaccretionandtypicallytakentobeη 0.1.
∼
showthewindvelocityatsomespecificradiusinthewindasfunc-
tionoftime.Thefigureillustrates,thatrelativelyclosetothestar
(weselectedaradius2.5R∗ fromthestellarsurface)thewindve- 3.2 Syntheticaccretionlightcurves
locitychanges byuptoanorder ofmagnitude onatimescaleof
The time dependent hydrodynamic simulations described in sec-
hours.
tion2provideabsolutevaluesforthewinddensityandvelocityas
functions of radius and time for a star withparameters as shown
inTable1.Weusethesedensityandvelocitytocomputesynthetic
3 ACCRETIONOFANON-STATIONARYSTELLAR X-raylightcurvesaccordingtoEqs.(4)–(7).
WIND AdoptingamassofthecompactobjectmX =1.4M⊙andan
efficiencyparameterη =0.1,wegeneratedsimulatedlightcurves
3.1 BasicsofBondi-Hoyleaccretion
for different values of theorbital separation a.Theresultingpre-
The following is based on the treatment of Davidson&Ostriker dictedvariationsinX-rayluminosityLd areshowninFig.3.
X
(1973). They considered a neutron star of mass mX, traveling at Thesyntheticlightcurvesarehighlyvariable,withX-raylu-
relative speed vrel through a gas density ρ. If vrel is supersonic, minositychangingbyuptoeightordersofmagnitude!Thisstrong
thegasflowsinamannerdescribedbyBondi&Hoyle(1944).The variabilityisaconsequenceofthehighlyvariabledensityandve-
massaccretionrateisgivenby locity in the stellar wind. Specifically we would like to empha-
S =πζr2 v ρ(a,t) (2) sizethattheshocksandcorresponding jumpsinthevelocitywith
accr accr rel δv 1000kms−1 are responsible for the predicted strong vari-
where abili∼ty, since the accretion rate scales with v−3. Thus models
∝
r = 2GmX (3) whichaccount onlyforthedensityfluctuationsinthewinds(e.g.
accr v2 Walter&ZuritaHeras2007;Duccietal.2009)mayunderestimate
rel
theresultingvariability.
andthefactorζisintendedtocorrectforradiationpressureandthe
Itisinterestingtonote,thatthecharacterof thelightcurves
finitecooling timeof gas. Inmoderately luminous X-raysources
cannot be characterized as steady quiescent emission and some
ζ<1 (Davidson&Ostriker 1973). For our calculations we adopt
∼ strong flaresontop it.Reflecting thenature of non-stationary in-
ζ =1.
homogeneous stellar winds the accretion light curves are truly
In non-stationary stellar winds, thewind density ρ(a,t) and
stochastic.
the wind velocity v (a,t) depend on time (see Section2). Com-
w The X-ray observations of real celestial HMXBs are sensi-
biningequations(2)and(3)theaccretionrateis
tive to the X-ray flux only about some threshold. In an arbitrary
S =4πζ(GmX)2ρ(a,t). (4) waywechoosethisthresholdcorrespondingtotheX-rayluminos-
accr v3 ity1034ergs−1.Figure4showsthefractionoftimetheluminosity
rel
Therelativevelocity of model source is above this threshold. It demonstrates that the
fractionoftimethesourceisX-raybrightdecreasessharplywith
v2 =v2(a)+v2(a,t), (5)
rel X w increasing orbitalseparation.InHMXBswithlargerorbitalsepara-
wherev isthestellarwindvelocityattheneutronstarorbitalsep- tion,theperiodsofhighestaccretionaresignificantlylessfrequent.
w
arationa,andtheorbitalvelocityoftheneutronstarisgivenby WecalculatetheaverageX-rayluminosityresultingfromdi-
vX2 ≈ GMa ∗. (6) arebciltiatyccσreLt/ioL¯ndX,L.¯OdXu,rthmeosdtaenlsdasrhdodwevthiaattiothneσreLi,sanndotahpepraerleanttivdeevpaerni--
Clumpedstellarwindsin HMXBs 5
38
s]36 L¯d = 2×1034erg s-1
g/ X
er34
) [
dLX32
g(
Lo30 a=10R
*
28
38
s]36 L¯d = 7×1035erg s-1
g/ X
er34
) [
dLX32
g(
Lo30 a=4R
*
28
s]38 L¯d = 3×1036erg s-1
g/36 X
er
) [34
dLX
g(32
Lo30 a=2.5R*
s]38 L¯d = 7×1036erg s-1
g/36 X
er
) [34
dLX
g(32
Lo30 a=2R*
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Time (hours)
Figure3.SyntheticX-raylightcurvesforBondi-Hoyleaccretionofanon-stationarystellarwindontoaneutronstarwithmX = 1.4M⊙.Thesupergiant
donorparametersaregiveninTable1.Fromtoptobottompanel,theorbitalseparationaisdecreasing,asindicatedinthelowerleftcornerofeachpanel.The
averageX-rayluminosityisindicatedintheupperleftcorner.TherelativevariabilityσL/L¯dX=4.8,4.9,4.9,4.6fromtoptobottompanel.
0.6 4 THEPHOTOIONIZATIONPARAMETERINTHE
CLUMPEDWINDOFHMXBS
s
/ The total X-ray emission in HMXB results from direct accretion
g
r which we considered in the previous section as well as from the
e
4 photoionized fraction of stellar wind. Due to the highly variable
3
10 0.4 accretion rate, the ionizing source is highly variable (see Fig.3).
> Moreover,theambientstellarwindishighlyinhomogeneous (see
x
L Fig.1).Inthissectionweinvestigatehowtheionizationparameter

e is changed in a clumped wind compared to a smooth medium –
m
i thelatteriscommonlyadoptedinthecomputationsofspectrafrom
t
f photoionizedplasma.
o
n 0.2 Tostudytheseeffectsweadoptastatisticalapproach,assum-
o ingalargenumberofclumps.Theuseofastatisticalapproachis
i
t
c convenient for at least two reasons. First, the non-stationary hy-
a
r drodynamic simulations we presented in the previous section are
F
1D, and while they are well suited to compute the luminosity of
theaccretingpointsource,weneedadditionalinformationtostudy
0.0 spatiallyextendedphotoionizedregions.Second,therearesophis-
2 4 6 8 10
ticated photoionization codes, such as xstar (Kallman&Bautista
Orbital separation a [R ] 2001)thataccountrealisticallyforatomicphysicsofphotoionized
*
gases.Usingastatisticaltreatmentoftheclumpedstellarwind,we
Figure4.Thefractionoftimethesyntheticaccretionlightcurveisabove attempttofindcorrectionfactorsthatwouldallowtoadjustthein-
thelevel1034ergs−1independenceontheorbitalseparationa. put parameters for a photoionization code in order to reflect the
windinhomogeneity.
The fundamentals of interaction of X-ray sources with
denceoftherelativevariabilityonorbitalseparationwithinthepa- ambient stellar winds are developed in Tarteretal. (1969),
rameterspacewehavechosen.Thisreflectsthestochasticnatureof Tarter&Salpeter(1969).Hatchett&McCray(1977)considereda
stellarwindevenrelativelyfarfromthestellarcore. modelofaconstantX-raysourceimmersedinastellarwindfrom
6 Oskinova,Feldmeier& Kretschmar
itscompanionstar.Thestellarwindmodelwasaspredictedbythe i.e.itisreducedbyfactor comparedtothesmoothwindcase.
X
thenrecentCAKtheory.Theseworksconsideranebulagasofcon- Theparticledensityaveragedoversomeunitevolumeatdis-
stantdensityN (orsmoothdensitygradient)illuminatedbyacon- tancer, N isdefinedbythecontinuityequation:
h i
stantsourceof X-rayradiation. TheratioN /N isdeterminedin
e M˙
eachcasefromchargeneutrality.AdoptingTarteretal.(1969)no- N = , (14)
tations,neglectingabsorptiononemaytakeforthemeanprimary h i 4πµmHv(r)r2
photonintensityatfrequencyνatadistancerfromthesource whereµisthemeanmolecularweight,m istheatomicmassunit,
H
andv(r)isastationaryvelocitylaw.
L
J(ν)dν = 4πr2f(ν,kTX), (8) The simplest structure of a clumped wind is a two phase
mediumwhereallmatterisclumpedwithdenseclumpsoccupying
where function f(ν,kTX) describes the spectral shape of the X- only a small volume compared to the interclump medium filling
rayradiation.Theequationofionizationequilibriumforahomo- thelargevolume.Theinterclumpmediumcanbeassumedvoidor
geneousmediumis filledwithtenuousgas.Inthiscaseavolumefillingfactorf canbe
V
definedasthefractionoftotalvolumeV thatisfilledbyclumps:
tot
N(Z,z+1)Neα(Te)=N(Z,z)Z J(ν)σ(ν)dν+NeC(Te), fV ≡ Vcl/Vtot.IftheinterclumpmediumisvoidX = fV−1.The
(9) clumpdensity insuch twophase mediumisNc = N . Ifthe
Xh i
where C is the collisional ionization rate and σ is the photo- interclumpmediumisnotvoid,itsparticlenumberdensitycanbe
ionizationcross-sectionforthechangingionicchargez (z+1) approximatedas:
→
ofionwithnuclearchargeZ;αisthetotalcoefficientforrecombi-
N (1 f ) N . (15)
nationfor(z+1) z. ic ≈ −X V h i
→
AsfollowsfromEq.(8)and Eq.(9) for anopticallythingas
in local ionization and thermal balance, irradiated by a constant 4.1 Ontheclumpopticaldepth
pointsourceofX-raysofgivenspectralshape,onlyasinglepho-
Equation(8)neglectstheabsorptionofionizingradiation.Thiscon-
toionizationparametermustbespecifiedinordertodeterminethe
dition may not be valid when clumps are optically thick for the
ionization state and temperature of any local region of the gas:
ionizingradiation.Inthissectionweinvestigatetherestrictionson
ξ L /Na2, where N is the local atomic number density of
≡ X theclumpparametersimposedbythiscondition.Todosowees-
thegasattheorbitoftheX-raysource,andaisthedistancefrom
timatethegeometricalsizeaclumpwhichhasopticaldepthunity.
thecenteroftheprimarytotheX-raysource.
Assumeforsimplicitythattheinterclumpmediumisvoid,sothat
In the medium where the density is inhomogeneous, Eq.(9)
f = −1,theopticaldepthofanisotropicclump(i.e.,withthe
shallberewrittenas V X
samedimensionsd in3D)fortheincidentradiationatwavelength
c
λis
hN(Z,z+1)Neiα(Te)=hN(Z,z)iZ J(ν)σ(ν)dν+hNeiC(Te), τc(λ)=ρwκλfV−1dcR∗, (16)
(10)
wheretheaveragingoversomelocalvolumeisrepresentedbythe where R∗[cm] is the stellar radius, dc is in the units of R∗ and
κ [cm2g−1]isthemassabsorptioncoefficient.Thedensityofthe
angular brackets. Considering Eq.(10)itisclear, that,ingeneral, λ
coolwind(ρ )canbedefinedfromthecontinuityequation.
the ionization parameter ξ is not the same as in smooth density w
Theclumpdimensiond canbederivedfromEq.(16).Adopt-
case.Itisalsoclear,thatinthemediumwithdensityfluctuations, c
ingτ (λ)=1:
the number of recombinations which is proportional to the den- c
sity squared is enhanced compared to the number of ionizations f 1 β
dτ=1= V 1 r2. (17)
whichisproportionaltothedensity.Therefore,intheclumpedstel- c τ∗(λ) ·(cid:18) − r(cid:19)
larwind,thephotoionizationparametermustbereducedcompared
tothesmoothwind.Moreover,thesizeofthephotoionizedregion whereτ∗isaparameterandaβ-lawforthevelocityisassumed.If
atsomeradiusr,theclumpsizeislargerthandτ=1 ,suchaclump
willbereducedinaclumpedwindcomparedtothesmoothwind clump
isnolongeropticallythinforX-rayradiationatλ.Theparameter
ofthesamemass-lossrate.
To describe the density fluctuations we follow Allen (1973) τ∗(λ)canbeconvenientlyexpressedas
anddefinethewindinhomogeneityparameter τ∗(λ) 722 M˙−6 κλ, (18)
N2 ≈ v∞ ∗ ·
h i. (11) R
X ≡ hNi2 whereM˙−6isthemass-lossrateinunits10−6M⊙yr−1,v∞isthe
Thentherootmeansquare(rms)localdensityisNrms =hNi√X. t2e0r1m1i)n.alvelocityin[kms−1],andR∗ = R∗/R⊙ (Oskinovaetal.
The rms density describes in a statistical sense the magnitude of
The K-shell opacity of stellar wind is a strong function of
densityvariations.
wavelength,andcanbetakenasκ κ λγ,withγ intherange
Assumingthattherearenodramaticchangesintheionization λ ≈ 0
2–3, and κ a constant that depends on abundances (Baumetal.
stateoversomelocalvolume,wecanwrite 0
1992;Ignace&Oskinova1999).ItfollowsfromEqs.(17)and(18)
N(Z,z+1)N N(Z,z+1) N , (12) that the same clump can be optically thin at shorter wavelengths
e e
h i≈Xh ih i andopticallythickatlongerwavelengths.
In this case, the photoionization parameter for a clumped stellar Realisticvaluesofthemass-absorptioncoefficienthavetobe
windis computedusingnon-LTEmodelstellaratmospherecodes,suchas,
ξ LX , (13) e.g., PoWR (Hamann&Gra¨fener 2004). The values of κλ for a
≡ N a2 sampleofO-starsaregivenine.g.Oskinovaetal.(2006).
Xh i
Clumpedstellarwindsin HMXBs 7
The SG HMXB are hard X-ray sources. The maximum (2007) showed that correctly accounting for the wind porosity in
of spectral energy distribution in VelaX-1 is at 4A˚ (e.g. the analysis of UV resonant lines eliminates the need for very
≈
Doroshenkoetal.2011).UsingparametersofζOriandassuming small volume filling factors and that realistic values are rather
fV = 0.1,ata = 2R∗,dτcl=um1p(ζOri) ≈ 20κ−λ1.I.e. atthedis- fV ∼ 0.1. Sundqvistetal. (2011) also used the hydrodynamic
tance2R∗ fromthestellarcore,onlygeometricallylargeclumps modelsofFeldmeieretal.(1997a,b)andfoundthatinthesemod-
wiziitnhgdriaadmiaettieornlsahrgoertrwthaardns∼of01.05AR˚.∗areopticallythickfortheion- setlusdtiheestoyfpitchaelXcl-uramypsinpgecftarcatofrrosmarpehfoV−to1io∼niz1e0d.gInast,htihsecaiosen,iziantitohne
Suchaclumpsizeappearsratherlarge,thereforeitisprobably parameter ξ should be reduced by afactor <10 inclumped wind
∼
reasonabletoassumethatthewindclumpsareopticallythinforthe modelscomparedtotheunclumpedones.
ionizingradiationresultingfromtheaccretionontoaNS2
4.3 Clumpsofarbitraryopticaldepth
4.2 Opticallythinclumps
While it is likely that the wind clumps are optically thin for the
Asshown above, thewindclumpsaremost probably thinforthe hardionizingradiation,(seeSection4.1),forcompletenessinthis
hardX-rayemissionresultingfromtheaccretiononacompactob- sectionweconsider acaseof opticallythickclumps. Accounting
ject.Inthiscase,the“microclumping”approximationcanbeused. fortheclumpsofarbitraryopticaldepthinstellaratmospheremod-
IfthemeanprimaryphotonintensityisdescribedbyEq.(8),then elsissometimes referredto as“macroclumping”. If the optically
inatwophasemediumwhere = f−1,thephotoionizationpa- thickstructures, τ >1, are present inthe wind, themean primary
X V c∼
rametercanbewrittenas photonintensityofionizingradiationJν mustbecorrectedforthe
L absorptionintheclumps
ξ=f X . (19)
V· N a2 L
The meaning of Eq.(19) is thaththei ionization parameter in a Jν = 4πXr2 ·f(kT)·e−τ¯(r), (20)
clumpedwindisreducedbyafactorfV whentheaveragedensity where f(kT) is a function of atomic parameters and tempera-
at distance a is given by Eq.(14). Following Hatchett&McCray ture that describes the spectrum of the incident ionizing radia-
(1977) the nondimensional variable q ξ N a2(LXfV)−1 de- tion, and τ¯ is the effective optical depth of the clumped medium
≡ h i
scribes the shape of the surfaces for which ξ =constant. In (Feldmeieretal.2003).
clumped stellar wind, the parameter q will be larger than in a At a distance R from the source of ionizing radiation the
X
smooth wind. Considering the case of constant wind velocity, it effectiveopticaldepthis
would mean that the radius of spherical photoionized region is
RX
smaller in clumped wind compared to the smooth wind. This is τ¯= n σ (1 e−τc)dr , (21)
C C x
easy to understand recalling that the number of recombination is Z0 −
enhanced in clumped wind compared to smooth wind, while the where n (r) v−1(r)r−2 is the average number of clumps
C
numberofionizationsremainsthesame. within a unit v∝olume, and σ is the clump geometrical cross-
C
Overthelastdecadetherehavebeennumerousstudiestoes-
section(Oskinovaetal.2008,2011).Notethatthestellarwindpa-
tablishthedegreeofwindclumpinginOBsupergiants.Pulsetal. rametersM˙ andκ appearintheexpressionforτ¯onlyindirectly
λ
(2006)analyzedasampleof19GalacticO-typesupergiants/giants, via τ given by Eq.(16). Besides stellar wind parameters, the ef-
c
coveringspectraltypesO3toO9.5usingmultiwavelengthobserva-
fectiveoptical depth alsodepends onthegeometrical distribution
tionsinradio,IR,andoptical.Theyusedtheconventionalassump-
oftheclumpsvian andσ .Theclumpcross-sectionisdifferent
C C
tion of the interclump medium being void. It was found that the for the different clump geometries, e.g. for the spherical clumps
upper limit on thevolume fillingfactor intheinnermost region ( σ d2,whilefortheoblateclumpsthecross-sectiondependson
r . 2R⋆)ofstarswithHα inemissionisabout0.25.Itislikely thCec∝lumCporientation.Inthelimitofτ 1,theeffectiveoptical
C
that the winds of donor stars in HMXBs have similar properties. depthisfullydeterminedbythegeometri≫caldistributionofclumps
Inthiscase,theionizationparametershouldbereducedbyamini-
(Feldmeieretal.2003;Oskinovaetal.2004).
mumfactoroffourtoaccountforwindclumping.
Nowwewouldliketoaddressthequestionofionizationbal-
Fullertonetal. (2006) analyzed 40 Galactic O-type stars by anceinthewindwherethelargestportionofthematterisinform
fitting stellar wind profiles to observations of the PV resonance ofopticallythickclumps.TheX-rayemissionfromsuchmedium
doubletintheUV.Thefoundthattoreconcilemass-lossratesem-
will have two components: X-rays due to scattering of radiation
piricallyinferredfromtheanalysisofUVandradio/optical spec- within the clumps, and the X-rays from the photoionized inter-
tra, the volume filling factors must be fV<∼0.01. Similar conclu- clumpmedium. Thescatteringof photons insuch amedium was
sionswerereachedbyBouretetal.(2005)whofoundfV 0.04 consideredbySuleimanovetal.(2003).Here,weconsidertheion-
≈
in an O-type supergiant and fV 0.02 in an O-type dwarf. If izationoftheinterclumpmediumandneglectthediffuseradiation.
≈
these clumping factors were realistic, the ionization parameter ξ Using Eq.(15) for the particle number density in the interclump
would have to be reduced by factors of 25...100. Oskinovaetal.
medium, the ionization parameter for the tenuous interclump gas
becomes
2 Note,thattheintrinsicX-rayradiationinsingleSGOBstarsisthermal ξ = LX e−τ¯ . (22)
andsoft,withthemaximumofthedifferentialemissionmeasuredistribu- ic N a2 · 1 fV
tionat≈60A˚ orevensofter(e.g.Raassenetal.2008).Evengeometrically h i −X
verysmallclumpswithdiameter10−3...−5R∗areopticallythickatthese Whenthebulkofstellarwindmassisintheformofafewdense
wavelengths.Therefore,generally,intheinnerwindregionsofsingleSG opticallythickclumps,theinterclumpmediumcanbeverytenuous
OBstarstheopticallythinclumpapproximationfortheintrinsicX-rayra- f−1.Inthiscasetheeffectiveopticaldepthcanbeverysmall
X → V
diationisfalse. (i.e.thewindisveryporous).AsfollowsfromEq.(22),inthiscase
8 Oskinova,Feldmeier& Kretschmar
p
p ϑX Iν0 Iν0 e−τc
X
rX r c
ϑ
c
z z
X
Figure5.Sketchofthecoordinatesystemforthefragmentedwindmodel.
X-rayradiationwithintensityI0isemittedatthelocationwithcoordinates
ν
(pi,zi).Thecoolwindconsists ofclumpsthatarerandomlydistributed.
Forclarity,onlyoneclump(shadedarea)isshowninthesketch.TheX-ray
radiationpropagatingtowardstheobserveratz→∞hastocrossaclump.
Theopticaldepthacrosstheclumpfortherayinzdirectionisτc,reducing
thelineintensityIν0byafactorexp(−τc).
theionizationparameterinthetenuousinterclumpgascanbevery
high,muchhigherthanwouldbeexpectedforthesmoothwindof
thesamemass-lossrate.
Figure6.Onerandomtrialofour2-Dmodelwheretheclumpsareran-
Weconcludethatclumpingstronglyaffectstheionizationbal- domlydistributedinradius(uniformlybetween1.2and316R∗).Onav-
ance. A higher degree of ionization in the less dense interclump erage there are 400 clumps along each radial direction (see text for de-
gaswithinthephotoionizedregioncanbeexpected.Thesizeofthe tails).Onlytheinnerpartofthewindbetween1R∗and5R∗isshown.The
photoionizedregionwillbemuchlargerincaseofopticallythick smoothwindisin-between1R∗and1.2R∗.Thefilledcirclerepresentsthe
clumpscomparedtoasmoothwind. stellar core; the outercircles areat2R∗ and4R∗ toscale. Thisrandom
modelwasusedtocalculateopticaldepthsshowninFig.,8andFig.,7.
5 ABSORPTIONOFX-RAYRADIATIONINA exp( τ(p,z,ϕ)): I+(p,z,ϕ) = I0(p,z,ϕ)exp( τ(p,z,ϕ)).
− −
CLUMPEDSTELLARWIND Theopticaldepthτ(p,z,ϕ)isgivenbythesummationofoptical
depthsofallclumpsonthelineofsign.Thegeometryofthemodel
TheX-rayphotonsemittedeitherinclosevicinitytotheNS,orfar-
isshowninFig.5. Duetothelackofsynchronizationbetweendif-
theroutinthephotoionizedportionofthestellarwind,sufferthe
ferent radial directions, the fragments probably have rather small
K-shell continuum absorption in the cool component of the stel-
lateral extent. Despite the expansion due to the internal pressure,
lar wind asthey propagate towards the observer. Asdiscussed in
thecoolfragmentsaremaintainedtodistancesofhundredsofthe
Sect.4.1 the wind clumps are, most likely, optically thin for the
stellarradius, beforethey gradually dissolve intoahomogeneous
radiation at the short wavelengths (shortward of 8A˚). On the
≈ outflow.Our2-Dstochasticwindmodelisdesignedtodescribein
otherhand,thewindclumpsorlargerscalewindstructurescanbe
ageneric way the structures and physical conditions of the inho-
opticallythickforthesofterX-rays.Theseopticallythickinhomo-
mogeneousstellarwind:
geneities can be traced observationally as changes in the absorb-
ingcolumndensityonthetimescalecomparabletotheorbitalpe- 1.theflowissphericallysymmetricinastatisticalsenseandprop-
riod.Suchvariabilityofabsorbingcolumnisindeeddetected(e.g. agatesaccordingtoaβvelocitylaw.Themass-fluxandtotalradial
Fu¨rstetal.2011).Ifthestellarwindofdonorstarweresmooth,the opticaldepthineachradialdirectionispreserved.
absorbingcolumnwouldsmoothlyincreasefromthemomentwhen 2.allclumpscoverthesamesolidangleasseenfromthecenterof
theNSisattheperiastrontowhenitisintheapastron. thestar,andpreservethisangleduringtheirpropagation.
In this section we investigate the K-shell continuous X-ray
3.weconsidertwodifferentshapesofclumps,thesphericallysym-
absorption in stellar wind. Our goal is to model the absorption
metric clumps (“balls”) and radially compressed clumps (“pan-
of monochromatic X-ray flux emerging from the NS in depen-
cakes”).
dence on orbital phase. We employ a 2D model of a stochas-
4.tosimulatestochasticX-rayemissionwemodel X-raysasdis-
tic stellar wind by Oskinovaetal. (2004), where the model de-
creterandomflashesofX-raylightalongtheNSorbit.Thereisno
tails are fully described. Here we only briefly introduce its ba-
self-absorptionbyemittingmaterialandnore-emissionofX-rays
sic features. The model assumes the structure and physical con-
whichbecameabsorbedbycoolfragments.
ditionsinthewindaccordingtothehydrodynamicsimulationsby
Feldmeieretal.(1997a,b).Theemissionisdecoupledfromabsorp- 5.weconsideranedgeonsystem,i.e. theobserverislocatedinthe
tion, which allows for the formal solution of the radiative trans- orbitalplaneoftheNS
fer equation. In order to take advantage of the rotational sym- Weneglectthedensityfluctuationswhicharelikelytoresultin
metry of our model around the z axis, cylindrical coordinates theNSwake.Thehydrodynamicsimulationsofwindstructurethat
(p,z,ϕ)areused.AlongeachlineofsighttowardsanX-rayemit- predicttheexistenceofawakewereperformedforsmoothwinds
tingregionlocatedatspherical coordinates(ri,ϑi),theemergent (Blondinetal.1990).Itisnotnotobvioushowaccountingforwind
monochromaticX-rayintensityI+(p,z,ϕ)isreducedbyafactor clumping can affect the results of hydrodynamic simulations and
Clumpedstellarwindsin HMXBs 9
0.8 0.25
0.7 Spherical clumps
0.20 Spherical clumps
0.6
oA o9A
=80.5 =10.15
λ λ
at 0.4 at
) )
τλ τλ0.10
p(-0.3 p(-
x x
e0.2 e0.05
0.1
0.00
0.0
0.8 0.25
0.7 Radially compressed clumps
0.20 Radially compressed clumps
0.6 oA
oA 9
=80.5 =10.15
λ λ
τ) at exp(-λ000...234 τ) at exp(-λ00..0150
0.1
0.00
0.0
0 50 100 150 200 250 300 350
0 50 100 150 200 250 300 350
Degree along the orbit
Degree along the orbit
Figure 8. The same as in Fig.7 but for the radiation emitted at 19A˚
Figure7.Thevariationofthefactorexp(−τλ)independenceonorbital (0.65keV).
phasefortheX-rayradiationat8A˚ (1.55keV)emittedbyasourcelocated
at ≈ 2R∗. The horizontal axis shows the orbital location of the X-ray
source,ϑi.At0◦ thesourceisinconjunction, whileat180◦ itistotally
eclipsed.Theredcurveshowsthechangesofexp(−τλ)inasmoothwind. gradually decreases outwards. To find the optical depths towards
TheparametersofthewindaregiveninTable1.Avelocitylawwithexpo- theobserveratdifferentorbitallocation,wesumupthecontribu-
nentβ = 0.8isassumed.Thestochasticwindmodeliscalculated using tionsfromalltheclumpsalongthelineofsign.
therandomtrialshowninFig.6.Upperpanel:thewindmodelwherethe Themass-fluxineachdirectionispreservedinourmodel.To
clumps areassumedtobespherically symmetric(“balls”). Lower panel:
calculatetheopticaldepthofeachclump(intotalthereare144000
thewindmodelwheretheclumpsareassumedtobeflattenedintheradial
clumps in the wind model, part of which is shown in Fig.6) we
direction(“pancakes”).
assumethataclumpmassequalstothemassofthesmoothwind
confinedbetweentorandomsubsequentradiiinthewindr andr
a b
theshapeand densityinthewake. Moreover, thepresenceof the (seeOskinovaetal.(2004)fordetails).Forastarwiththeparam-
wake should introduce some regular pattern in the absorption of etersshowninTable1andsolarabundances, themass-absorption
X-rays along the orbital motion of the NS, while our goal is to coefficientκ is 40cm2g−1atλ = 8A˚ and 170cm2g−1at
λ
investigatethebasiceffectsofstochasticwindsontheabsorption λ=19A˚ (Oskin≈ovaetal.2006). ≈
ofX-rays. Littleisknownaboutthegeometricalshapeoftheclumps.The
Wealsoneglectthechangesintheionizationstructureofthe comparisonwiththeobservedX-rayemissionlineprofilesinspec-
wind due to the X-ray photoionization close to the NS. As dis- traofsingleO-starsindicatethattheclumpscanbeflattenedinra-
cussed in Section4, the clumping is likely to reduce the size of dialdirection(Oskinovaetal.2006).Theshapeofclumpsplaysan
photoionization zone. Theoptical depth of theclumps withinthe importantroleinthetransferofX-rayradiationthroughthewind:
photoionized portion of the wind may be different from the rest incaseofflattenedclumpsthewindopacitybecomesanisotropic,
of the wind, however thiseffect may be small on average due to whileitremainsisotropic(thesameasforthesmoothwindopacity
thedifferenceinthesizeofthegeneralwind,anditsphotoionized albeitsmaller)incaseofball-likeclumps(Oskinovaetal.2006).
portion. Figures7and8showthetransmissionfactorexp( τ )forra-
λ
Figure6showsasnapshotoftheinnerwindstructure,between diationat8A˚ and19A˚ (1.55keVand0.65keV,respecti−vely)calcu-
1R∗ and 5R∗ (in the simulations clumping is maintained up to latedassumingdifferentclumpgeometriesandasmoothwind.The
316R∗).Weassumethelateralextendofclumpstobe1◦.Tostudy windismoretransparentfortheradiationatshorterwavelengths.
howthewindopticaldepthchangesduringtheorbitalmotionofthe Incaseofflattenedclumpsthechangesinopticaldeptharelarger,
NS,weassumedthedonor stellarparametersaslistedinTable1. becausetheclumpopticaldepthdependsontheclumpsorientation.
Theclumpnumberdensityobeysthecontinuityequation,therefore Thechangesinthewindabsorbingcolumnatdifferentorbital
theclumpdensityishigherintheinnermostpartofthewindand phases should result in changes in the X-ray spectra. Indeed, the
10 Oskinova,Feldmeier&Kretschmar
0.8 drodynamicsimulationspredictwindstructureconsistingofstrong
0.7 Radially compressed clumps velocity and density jumps. Since the Bondi-Hoyle-Lyttleton ac-
o8A τ at 8Ao, at 19Ao cretion rate depends on both velocity and density fluctuations, it
λ=0.6 strongly varies with time. Combining the Bondi-Hoyle model of
nd accretionwithhydrodynamicwindsimulationswecomputedsyn-
a0.5
oA thetic X-ray light curves for the different orbital separations (see
190.4 Fig.3).
=
λ Averaged over time model X-ray luminosity is in general
at 0.3 agreementwithobservations.ThemoderatereductionofM˙ byfac-
) λ tor2...3comparedtotheunclumpedwindmodelsexplainswellthe
τ 0.2
(- opticalandtheUVspectraofsinglestars,aswellasaverageX-ray
p
ex0.1 luminosityresultingfromwindaccretioninHMXBs.
TheapplicationoftheBondi-Hoyle-Lyttletonapproximation
0.0 fortheaccretionratepredictsverystrongX-rayvariability:theX-
0.8 rayluminositychangesbymanyordersofmagnitudeonthetime
0.7 Smooth wind scaleofhoursasadirectconsequenceofthestrongdensityandve-
o8A τ at 8Ao, at 19Ao locityjumpsintheaccretionflow.Theeffectofthenon-stationary
λ=0.6 windvelocityontheaccretionratewasoverlookedpreviously.Ne-
nd glectingthiseffectmayleadtoerroneousestimatesofclumpmass
a0.5
oA andsizefromthetotalfluxanddurationoftheX-rayflare.Weem-
190.4 phasizethatthestrongvelocityjumpsinthestellarwindsleadto
λ= strongvariabilityofaccretionX-rayluminosity.
at 0.3 Thedetailedcomparisonofmodellight-curvesandtheobser-
) λ vationswillbeafocusof our forthcoming study. However, itap-
τ 0.2
(- pearssafetoconclude,thatthesyntheticlight-curvesdonotagree
p
ex0.1 well with the observations over-predicting the amplitude of vari-
ability.Givenoursimpleapproximationfortheaccretionthisisnot
0.0 surprising.Thedetailedhydrodynamicstudiesthatwindaccretion
0 50 100 150 200 250 300 350
isahighlycomplexprocess.E.g. whenthereisadensityandve-
Degree along the orbit
locitygradientintheflow,atransferofangularmomentumcanbe-
come possible. The hydrodynamics of Bondi-Hoyle-Lyttleton ac-
Figure9.ThesameasinFig.8.Upperpanel:comparingtheexp(−τλ)
factorat19A˚ (red)and8A˚ (blue)atdifferent orbitalphasesforamodel cretioninamediumwithcontinuousdensityandvelocitygradients
wind that consists of flattened clumps. Lower panel: the same as upper wasconsideredbyRuffert(1997,1999)andFoglizzoetal.(2005).
panelbutforasmoothwindmodel. Toour knowledge, uptonow therewereno studiesofaccretions
fromamediumwithstrongvelocityanddensityjumps.Wespec-
ulatethatthedetailedphysicsoftheaccretionflowsregulatesthe
strong variations of absorbing column density at different orbital temporalbehaviorofaccretionandispivotalindampingthestrong
phasesareoftendeducedfromtheobservedspectra(e.gFu¨rstetal. variationsduetothestructurednatureofstellarwinds.
2010;Bozzoetal.2011). Anotherprocessthatcanreducethevariabilityisthedestruc-
TheK-shellabsorptioninstellarwindisstronglywavelength tionof clumps inthevicinityof theNS.Asaninteresting exam-
dependent,changingbyatwoordersofmagnitudeacrossthe0.1- pleofclumpdestruction,Pittard(2007)performedahydrodynam-
12keVX-rayband.Thisisreflectedinsmallervariationsintheop- icalsimulationofwind-windcollisioninmassivenon-degenerate
ticaldepthspredictedforthe8A˚ radiation(wherethewindopacity binary star. The simulations revealed that the clumps are rapidly
issmaller,Fig.7)comparedtothelargeopticaldepthvariationsat destroyedafterpassingthroughtheconfiningshocksofthewind-
19A˚ (wherethewindopacityislarger,Fig.8).Theattenuationof wind collision region (assuming adiabatic flow inthe wind colli-
X-ray radiation in a clumped wind has a weaker dependence on sionregion).Despitelargedensityandtemperaturefluctuationsin
thewavelengththaninasmoothwind(Oskinovaetal.2004).This thepostshockgas,theoveralleffectoftheinteractionistosmooth
predictionholdsalsofortheHMXB.InFig.9wecomparethedu- theexistingstructureinthewinds.Onemayspeculatethatincon-
rationoftheX-rayeclipseattwodifferentwavelengthsforclumped ceptually similar fashion, the wind clumps and the wind velocity
andsmoothwindmodels.Inasmoothwind,theeclipseatlonger gradientsare“smoothed out”inthestrongshockoftheaccretion
wavelength starts earlier, and lasts longer, while at shorter wave- wakeinHMXBs.
lengththeeclipseismorenarrow.Ontheotherhand,inaclumped Fu¨rstetal. (2010) found that the accreted clump masses de-
windmodel, thedifference between eclipsedurations islesspro- rivedfromtheINTEGRALdataonVelaX-1areontheorderof5
nounced. Even in the phases close to the eclipse, optical depths 1019 1021g.Bozzoetal.(2011)estimateamassandaradiusof×a
mayoccasionallybeaslowasinthephasesfarfromtheeclipse. clump−responsibleforaflareinaSFXTas 1022gand 1012cm
∼ ∼
correspondingly. These are important independent estimates of a
clumpmassthatcanbecomparedwithwhatweknowaboutclumps
insinglestars.Le´pine&Moffat(1999)foundstochasticlineprofile
6 DISCUSSION
variationsintheformofnarrow( 100kms−1)emissionsub-peaks
≈
It emerged from our analysis that the stellar wind clumping has ontopofemissionlinesinWolf-Rayetstarwinds.Theyexplained
drasticconsequencesforthephenomenologyofSGHMXBs.The their data by 103<N <104 ”blobs” being present at any time in
∼ C∼
effectofwindstructureontheaccretionrateisprofound.Thehy- thelineemissionregion.InOskinovaetal.(2006)wereproduced