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Global modelling of X-ray spectra produced in O-type star winds A. Herve´ and 2 G. Rauw 1 and 0 2 Y. Naze´1 n GAPHE,De´partementAGO,Universite´ deLie`ge,Alleédu6Aouˆt17,Baˆt. B5c,4000Lie`ge,Belgium a [email protected] J and 4 2 A. Foster ] R SmithsonianAstrophysicalObservatory,60GardenStreet,CambridgeMA02138,USA S [email protected] . h p - o r t ABSTRACT s a High-resolution X-ray spectra of O-type stars revealed less wind absorption than expected from [ smoothwindswithconventionalmass-lossrates. Varioussolutionshavebeenproposed,includingporous 2 winds,opticallythickclumpsoranoverallreductionofthemass-lossrates. Thelatterhasastrongimpact v ontheevolutionofthestar. OurfinalgoalistoanalysehighresolutionX-rayspectraofO-typestarswith 6 amultitemperatureplasmamodelinordertodeterminecrucialstellar andwindparameterssuchasthe 1 massloss rate, theCNO abundancesandthe X-raytemperatureplasmadistributioninthe wind. Inthis 7 4 contextwe are developinga modelling tool to calculate synthetic X-ray spectra. We present, here, the . main ingredientsand physics necessary for a such work. Our code uses the most recent version of the 1 0 AtomDBemissivitiestocomputetheintrinsicemissivityofthehotplasmaaswellastheCMFGENmodel 2 atmospherecode to evaluate the opacity of the coolwind. Following the comparisonbetween two for- 1 malismsofstellarwindfragmentation,weintroduce,forthefirsttimeinX-rays,theeffectsofatenuous : v inter-clumpmedium.WethenexplorethequantitativeimpactofdifferentmodelparametersontheX-ray i spectra such as the position in the wind of the X-ray emitting plasma. For the first time, we also show X thatthetwoformalismsofstellarwindfragmentationyielddifferentresults,althoughthedifferencesfor r a individuallinesaresmallandcanprobablynotbetestedwiththecurrentgenerationofX-raytelescopes. Asanillustrationofourmethod,wecomparevarioussyntheticlineprofilestotheobservedOVIIIλ18.97 ÅlineinthespectrumofζPuppis. We illustratehowdifferentcombinationsofparameterscanactually lead to the same morphologyof a single line, underliningthe need to analyse the whole spectrum in a consistentwaywhenattemptingtoconstraintheparametersofthewind. Subjectheadings: stars:early-type–stars:mass-loss–X-rays:stars 1. Introduction teractions with their environment. In fact, mass-loss plays a fundamental role in the evolution of massive Thestudyofstellarwindsiscrucialforourunder- stars(e.g.Hirschi 2008)aswellasinthemechanical standingoftheevolutionofmassivestarsandtheirin- andchemicalfeedbackofthesestarsintotheinterstel- larmedium(e.g.Dopita 2008). Overthelastdecade, 1ResearchAssociateFRS-FNRS(Belgium) ourviewonthemass-lossofmassivestarshaschanged 1 astheimportanceofwindfragmentationbecameclear. (e.g. Milleretal. 2002; Kramer,Cohen&Owocki Direct observational evidence for the existence of 2003; Oskinova,Feldmeier&Hamann 2006; see clumps in the winds of O-type stars was obtained also Gu¨del&Naze´ 2009 for a review), although from the low-level, rapid variability of the He II Cohenetal. (2010) argue in favour of an overall re- λ4686 emission line in the spectrum of ζPuppis duction of the mass-loss rate of the wind without the (Eversbergetal. 1998). Indirectevidencestems from needtoincludeporosityeffects. the analysis of the spectra of O-type stars. Indeed, In a fragmentedwind with optically thick clumps, withobservationsfromtheFUSE satellite,itbecame X-raylinesaresensitivetoporosity,whichdependson clear thatthe modellingof linesofionssuch as O V, clump continuum optical depth, and thus clump size N IV and P V with model atmosphere codes such as as well as the clumping factor. That is why high- CMFGEN, is impossible if clumping is not included resolution X-ray spectra are important tools to study (e.g.Bouretetal.2005). the structure of the wind and help us determinemass The existence of such small-scale wind structures loss rates which must be consistent with the other has important consequences on many diagnostics of wavelength domain analyses. Previous works in the mass-loss rates. Indeed, strong clumping often im- X-ray domain (e.g. Oskinova,Feldmeier&Hamann pliesasubstantialreduction,byfactorsbetweenafew 2006), were performed on a line-by-line basis; the andaboutten, ofthe overallmass-lossrate compared spectrawereneveranalysedasawholeatonce.Using to a homogeneous stellar wind. In this context, our multi-temperature plasma models in future work, the ignorance of the properties of these wind structures global fit of observations will give information con- translates into uncomfortably large uncertainties on cerningthedifferentshocktemperaturesaswellasthe the actual mass-loss rates. For instance, whilst the size and the position of the different X-ray emitting spacebetweenclumpsisgenerallysupposedtobeto- shells. tally empty, some recent studies (Zsargo´ etal. 2008; With this in mind, we have designed a new code Sundqvist,Puls&Feldmeier 2010) showed that it is for the purpose of simulating the full high-resolution necessary to include the effects of a tenuous inter- X-rayspectrumof a single massive star. Our method clumpmediumtocorrectlypredictthestrengthofvar- properlyaccountsfortheeffectoflineblendingonthe iouslinesintheobservedUVspectraofO-typestars. lineprofiles,andallowstestingtheconsistencyofcur- By doing so, these authors even found that the ob- rent models for the X-ray emission of massive stars served profiles might again be compatible with the over the full range of the X-ray domain. Therefore, conventionalmass-lossrates. ourcodeismeantasafurthersteptowardsextracting Mass-loss rate diagnostics in different wavelength the maximum amount of information from the high- domains are strongly sensitive to different aspects of resolution X-ray spectra. In this paper, we introduce the wind fragmentation. For instance, H and radio the differentfree parametersandinvestigatetheir im- α emission are collisional processes which scale with pactonsingletemperaturesyntheticX-rayspectra.We densitysquaredandarethussensitivetotheclumping further discuss the main assumptions and physics in factorregardlessofthesizeoftheclumps.Inclumped our code and compare different formulations of the winds with a void inter-clump medium, the velocity wind fragmentation. In particular, we investigate for lawisintermittentandsomevelocitiesarenotpresent the first time the impact of a tenuous, but non-void, along a given sight line. This porosity in the veloc- inter-clump medium on the synthetic X-ray spectra. ityfieldiscalled’vorosity’(Owocki2011). Thelatter Finally,wepresentthefirstapplicationofourcodeto stronglymodifiestheSobolevlengthanditsimpactis fit the region around the O VIII λ 18.97Å line in the mainlyvisibleontheUVresonancelines. XMM spectrum of ζPuppis and illustrate the degen- eraciesonthestellarwindparametersthatexistwhen The present paper deals with the impact of wind asinglelineisfitted.Infuturework,wewillapplythis structureonthemorphologyofX-rayspectraofmas- codetothefullX-raybandspectraofζPuppis. sive stars. High-resolution Chandra and XMM − Newton X-ray spectra of presumably single O-type 2. Assumptionsandmainconceptsofthecode stars revealed less absorption of the X-rays by the cool wind than expected for a homogeneous wind Beforeusinga multitemperatureplasmamodelto with conventionalmass-loss rates. This property can analysetheX-rayspectraofO-typestarsindetail,we be explained in the case of fragmented stellar winds 2 need to calculate single temperature synthetic spec- sivities and profiles of the strongest observed lines. tra with the most recent stellar wind theories (emis- When fitting actual observations, one further needs sion and absorption)andwith as few as possible free to account for the presence of plasma at differ- parameters. We decide to follow the wind embed- ent temperatures, located at different places in the dedshocksscenario. Consequently,weneedtoknow wind. Therefore the normalization of the model wheretheshocksariseinthewindandwhatisthetem- will result from the combination of several model perature of the resulting post-shock hot plasma. Us- spectra weighted according to their relative emis- ingup-to-dateemissivities,wecanthendeterminethe sion measure. This will be dealt with in our forth- X-ray emission of a hotplasma as a functionof tem- coming paper on model fits of ζPuppis spectrum. perature,abundancesandquantityofmatterpresentin In addition, in the X-ray emitting plasma, some ions the shocks. Next, we determine how the cool wind are present in a helium-like form. The treatment materialabsorbstheX-rayphotonsandhowthewind of the transition between the 23S and 23P levels 1 j structure(i.e homogeneousorporous)impactsonthe must be done separately. Indeed, the presence of a emergentX-rayflux. Inthefollowingsubsections,we strong UV radiation modifies the populations of the describethetoolsandassumptionsconsideredtobuild metastable upper level of the forbidden line via a ourcodeandtocalculatesyntheticspectra. pumping to the upper level of the inter-combination line(Blumenthaletal.1972;Porquetetal.2001). We 2.1. Theplasmaemissionspectrum willdiscussthisfundamentaleffectinourmorecom- plete analysis of ζPuppis presented in a forthcoming PreviousworksonX-raylineprofilefittinghaveal- paper(Herveétal.,inpreparation). ways normalized the line profiles, i.e the overall line Weconsiderthehotplasmatobeembeddedinthe fluxwasneverphysicallymodelled. Weattemptadif- coolwindandtomoveoutwardsalongwiththelatter. ferentapproachhere,byusingthetrueX-rayemissiv- We decompose the emitting volume into small cells ity of an optically thin plasma. For this purpose, we useAtomDB2 whichmodelstheemissionfromacol- wherewecalculatetheX-rayemissionofeachcelland itsshiftinwavelengthintheobserver’sframeofrefer- lisionally ionized, opticallythin isothermalplasma in enceduetotheoverallwindmotion. thermalequilibrium. Many processes are includedin the model: collisional excitation, ionization, and di- 2.2. Windopticaldepth andmass-absorptionco- electronic recombinationdrive the ionization balance efficient andemissionspectrafromtheplasma.Continuumpro- cesses such as two-photondecay and bremsstrahlung The X-ray emitting plasma is assumed to be op- are also included. Photon-driven processes such as tically thin to X-rays. An X-ray photon emitted by photo-excitationandphoto-ionizationarenotincluded thehotplasma,eitherescapesfromthewindorisab- in the model. The assumption of an optically thin sorbed by the cool wind material. Thus the radiative plasma requires a low density ( 1013cm−3), there- transfer is reduced to the calculation of τ, the opti- ≤ forethreebodyeffectsarenotincluded. Thestandard caldepthalongtheline-of-sightdueto the coolwind AtomDB modeldata has beenrecalculated on a finer material. FollowingtheapproachofOwocki&Cohen 0.025keV/stepelectrontemperaturegridforthisanal- (2001), the absorption by the stellar wind is essen- ysisandweuseanenergyresolutionof0.2eV. tiallycharacterizedbytheτ parameterandthemass- Inadditionto the strongestlinesthatdominatethe absorptioncoefficientκ, wh∗icharelinkedbytherela- spectrum, the high-resolution theoretical spectra re- tionτ κM˙ . Theseabsorptioncoefficientsarede- veal the presence of numerous weak lines and also pende∗nt≡on4πvth∞Re∗wavelengthandtheabundancesofthe discontinuitiesin the continuum(Fig. 1). Their con- different elements. To evaluate the mass-absorption tributiontotheemergentfluxisnon-nullanditisnec- coefficients, we use the radiative transfer code CM- essary to take them into account for the computation FGEN (Hillier & Miller 1998) which computes the ofemergentspectraastheycertainlymodifytheemis- ionization structure of the cool wind as a function of temperature,abundancesofmanyelementsandmass- 2 This was previously known as the APEC model (Smithetal. loss rate. In the ionization calculations, CMFGEN 2001). Theinterestedreaderisinvitedtovisitthesection’physics’ accountsfor differentphysicalprocessessuch as col- on the AtomDB website for a precise description of the calcu- lisional excitation, photo-ionisation by photospheric lation of the continuum and lines in a hot plasma at the url http://www.atomdb.org/ lightandX-rays,andradiativeanddielectronicrecom- 3 bination.Fromtheknownionizationstructure,wecan models. then compute κ. In the X-ray domain, the opacity is At the microscopiclevel, the absorptionof X-rays dominatedbythephoto-ionizationofthemetals. This byastellarwindismainlyduetothebound-freetran- absorptionisbyfarthedominantsourceofopacityand sitions from the K and L energy levels. To start, wecansafelyneglectotherphysicalprocessessuchas we assume that the clumps are spherical and very freeelectronscattering. small. We consider clumps over a wide range of Thewavelengthdependenceofκ(Fig.2)andthere- optical depth, from optically thin to optically thick. foreτ ,isquitesensitivetothemodelelementalabun- In a situation where the individual clumps are opti- ∗ daces and to the ionization fraction of singly ionized cally thick, the effective opacity is essentially deter- helium. Inthisrespect,westressthatthelargevalues mined by the geometrical properties of the clumps ofthemassabsorptioncoefficient,usedinthepresent (Feldmeier,Oskinova,&Hamann 2003) and can be paper, reflect the fact that the sum of the CNO abun- writtenκ = l2 = κ whereκisthemass-absorption eff mc τc dancesinthebest-fitmodeloftheUVandopticalspec- coefficient,listhegeometricalscaleoftheclump,m c trumofζPuppisissupersolar(Bouretetal.,inprepa- its mass and τ its optical depth. This latter can be c ration). writtenas(Owocki&Cohen2006): Thedetailedbehaviourofκasafunctionofradius l κM˙ 1 l andwavelength(especiallyatlongerwavelengths)also τ =κ ρ = (1) c h if 4πr2 v f dependsupontheionizationstructureofthewindand more specifically on the details of the recombination where ρ isthemeandensityofthestellarwind, f ofHe2+ intoHe+ (Leuteneggeretal.2010). However, thevolumhefiillingfactor,M˙ isthemass-lossrateofthe forsimplicity,weassumeherethatκisindependentof starandvthevelocityofthewindattheradiusrwhich the position in the wind3 andwe evaluate its value at isdeterminedbyaβ-law(i.ev(r) = v (1 R )β with r = 10R . In our detailed analysisof the RGS spec- β=1throughoutthiswork). ∞ − r∗ ∗ trumofζPuppis(Herveétal.,inpreparation),wewill Under this assumption, it appears that the effective dropthisassumptionandratherintroducearadialde- reduction depends on the ratio between the clump pendenceofκ. scaleandfillingfactor,alsocalledtheporositylength Finally, the values of the mass-absorption coeffi- (Owocki&Cohen 2006). The concept of effective cient or the wind optical depth as a function of the opacitycanbeextendedtotheopticallythinlimitus- wavelength are used in Eq.3 and 4 (see Sect.2.3 be- ingasimplebridginglaw(Owocki&Cohen2006): low)todeterminetheabsorptionofX-raysbythestel- larwind. κeff = 1 (2) κ 1+τ c 2.3. X-rayabsorptionbyafragmentedwind Using this result in a steady state (i.e. non variable) Previous studies of stellar winds revealed that wind, one obtains the wind optical depth in conven- they are not homogeneous but fragmented. The ab- tional(p,z)coordinates(Owocki&Cohen2006): sorption of X-rays by a clumpy wind has been ad- dferreesnsetdfobrymsaelivsemraslfaourthtohresswahmoeapdhoepnteodmselnigohnt.lyTdhife- τ(p,z)=τ∗Zz∞ r′(r′−RR∗∗)d+z′τ∗h(r′) (3) porosity length prescription is based on the con- wherer = p2+z2,τ κM˙ istheopticaldepth cept of the mean free path of photons between two paramet′er ofpthe wi′nd, v∗ ≡is4πtvh∞eR∗terminal velocity of successive interactions with clumps, and the opac- thewind,R istheradius∞ofthestarandh(r) l the ity of the latter (Owocki&Cohen 2006). In the porositylen∗gth.Inthefollowingweadopth(r)≡=hf r. fragmentation frequency prescription, the opacity of × Thefragmentationofstellarwindshellsisaconse- the wind in the X-ray band is estimated by the fre- quence of hydrodynamical instabilities. Rather than quency of clumps passing through a reference radius being spherically symmetric, the resulting clumps (Oskinova,Feldmeier&Hamann 2006). In this sec- couldactuallyhaveaflattened,elongatedshape.Using tion, we briefly summarize the main aspects of these thenumbern offragmentspassingthroughsomeref- 0 3Thisassumptionallowsustotakeκoutoftheopticaldepthintegral erenceradiusperunittime,alsocalledthefragmenta- (Eq.3)andthustoachieveananalyticalevaluationofthisintegral. tionfrequency,andtheopacityofeachfragmentatthis 4 reference radius, Oskinova,Feldmeier&Hamann isotropic clumps (µ = 1), both models should be es- (2006) showed that the wind opacity can be written sentiallyequivalent. inthegeneralcaseas: In a first step, we reproduce the profile of various lines(Table1)foreachprescriptionandcomparethem τ(p,z)=n0Z zmax(1−e−τj)|µ(r′)|vd(rz′) (4) witheachotherandwiththeresultsforahomogeneous z ′ windmodel. Weconsideradistributionofspherically symmetricclumpsandwethussetµ = 1inEq.4and whereτ istheopticaldepthofaflattenedfragment j j alongthe line-of-sightandµ(r′) = √zz2′+p2 represents 5o.usOsuturdgieens.erFailrrset,suthlteslaagrgreeertwheellpworiothsittyhoosfethoefpwrienvdi-, ′ its orientation. The optical depth along the line-of- thelargerthemeanfreepathofaphotoninthestellar sight: wind and the lower the absorption(Owocki&Cohen τ = τrjad = κM˙ 1 1 1 (5) 2006).Second,thelargerthefragmentationfrequency, j µ 4π r2n µ thelowertheopacityinthefragmentationprescription, 0 | | | | seeOskinova,Feldmeier&Hamann (2006). withκthemass-absorptioncoefficientandτrad theav- j Wehavesimulatedfourspecificlineswithn =1.7 erageradialopticaldepthofafragmentlocatedatdis- 0 10 4s 1adoptedfromOskinova,Feldmeier&Hamann tancer(Oskinova,Feldmeier&Hamann2004).Inthe − − (2006). This parameter is found by the authors to case of an isotropic opacity (i.e. small-scale spheri- callysymmetricclumps),µistakenequaltounity(i.e. best fit the O VIII λ 18.97 Å line in the HETG and RGSspectraofζPuppis. Thenwederivetheporosity theline-of-sightcrosseseachclumpalongaradialdi- length, h, needed to reproduce the line profiles com- rection). putedwith thisfragmentationfrequency(Fig. 4). For In Section 3.1, we compare the profiles obtained differentvaluesofτ ,hencedifferentvaluesofwave- with τ given by Eq.4 to those computed with Eq.3, ∗ length(see Table1),thetwo lineprofilesare, ineach firstinthecaseofanisotropicopacitywhereµistaken case, very close. Note however that we obtain dif- equal to one, then in a case of an anisotropic opac- ferent values for the porosity length when matching ity where the clumps are assumed to be flattened (i.e differentlinescomputedwiththesamefragmentation µ,1). frequency:wehavetodecreasetheporosityparameter when τ increases. In other words, when we com- 2.3.1. Differencesandcommonfeaturesofthediffer- ⋆ pare simulated global spectra using a single porosity entprescriptions parameter to those obtained for a specific value of As we will show below, the porosity length pre- the fragmentation frequency, we find that the spectra scriptionandthefragmentationfrequencyprescription are exactly the same in the wavelength bandnear the are essentially equivalent to first order, although in line used to find the parameter h that best matches their originalwork, Owocki&Cohen(2006) concen- the value of n0 (in our case the O VIII λ 18.9 Å tratedonsphericalclumps,whilstOskinova,Feldmeier&Hamalninne), but differ over the other wavelength domains (2006)accountedforflattenedstructuresbyintroduc- (Fig.5).Morespecifically,theporositymodelpredicts ing the line-of-sightorientation via the µ parameter4. a slightly lower flux in the short wavelength domain Actually, the geometryassumedby Owocki&Cohen andahigherfluxinthelongwavelengthband. (2006) is even more idealized than a pure spherical There are some underlying assumptions in both geometry since it assumes that the line-of-sight al- models,andwithcurrentdataitseemsdifficulttotell ways crosses the clump along the radial direction. which prescription provides the better description of Strictly speaking, this is valid only if the clumps are reality. Theporosityprescriptionhastheadvantageto very small. The main differences between the two provide an analytical form of the opacity that speeds approaches hence concern the geometry of the wind up the computation. Therefore, in the following, we fragments and the way the optical depth of a clump concentrate mainly on the porosity prescription. The is included in the model, i.e. Eq.2 for the porosity overall results and conclusions obtained in the study prescription, and the (1 e−τj) term in Eq.4 for the for the different parameters, in the next section, are − fragmentationfrequency.Forsmallopticaldepthsand the same for the fragmentationmodel in an isotropic (µ=1)case. 4NotethatthisparametercouldalsoeasilybeinsertedintoEq.2. 5 3. The impact ofmodel parametersonthe emer- theprofilesarelessasymmetricalandthefullwidthat gentspectrum halfmaximumincreases. Theconsequencesaremore intensespectra(byafactor1.2intheshortwavelengths Foreachsimulationinthissection,weuseatermi- and3.0inthelongerwavelengthsdomain)andanin- nal velocity v of 2250kms 1. We further assume a − creasedoverlapoflines inthe anisotropicmodel(see ∞ kT of0.217keV,solarabundancesforthechem- plasma Fig.8). ical composition of the plasma, a stellar radius R of 18.6R and a mass-loss rate of 4.2 10−6M yr−1∗. 3.2. Outerradiusoftheemittingregion ⊙ ⊙ Thesestellarandwindparameterscorrespondtothose Another parameter of our model is the size of the usedbyOskinovaetal(2006)intheirworktofitlines X-rayemittingplasma(R ). Astheemissivityispro- of ζPuppis, exceptfor the plasma temperaturewhich out portionalto ρ2, the outerparts of the wind contribute correspondstotheclosestvalueinAtomDBtothere- less to the total intrinsic (i.e. before wind absorption sultofHillieretal.(1993). is accounted for) X-ray emission, but cannot be ne- Intheremainderofthissection,wesimulateaseries glectedforthewind-absorbedemissionascanbeseen ofspectraforsuchasingleOstarinordertoillustrate forspecific lineprofilesinFig.9. Theeffectisbyfar thesensitivityofthesyntheticspectraonthedifferent strongest in the long wavelength domain where κ is modelparameters. λ largest. The intensity of the lines in Fig.9 varies by afactorbetween1.1and 80(fromshortertolonger 3.1. Porosity ∼ wavelengths)whentheouterradiusoftheemittingvol- Thefirstexploredparameteristheporositylength. ume is multiplied by a factor 2.0. Moreover,extend- The impact of this parameter for broad band spectra ingtheemittingregiontolargerdistancesimpliesthat wasneverpresented,intheliterature. Fig.6illustrates thevelocityoftheX-rayemittingplasma(assumedto our results. We have chosen to explore a wide range movealongwiththecoolwind)becomeslargerifthe of values of the parameter h. As expected, we find outerradiusisstilllocatedinsidethewindacceleration a strong impact on the emergent flux. At the short- zone.Thisinturnincreasesthefullwidthathalfmax- estwavelengths,whereκislowest,theporositylength imumofthelinesaswellasthelinewidthatthecon- haslittleimpactonthespectrum. However,thesitua- tinuumlevel. Theeffectisbestseenintheredwingof tionisradicallydifferentatlongerwavelengths,where thelinewhichismoststronglydepressedbythewind thewindopacityκbecomeshuge(Fig.3,Tab.1). Here, absorption. With a larger emitting volume, a larger theimpactoftheporositylengthismuchmoreimpor- fraction of the redshifted photonsfrom the rear outer tant. We find differencesof several orders of magni- partsofthewindescapethewindsincetheycrosslay- tude between the spectrum for a homogeneous wind ersoflowerdensity. Theimpactoftheincreaseofthe and the simulations with the largest porosity. For a sizeoftheemittingregionontheoverallspectrumcan highly porouswind, the variationsof h have less im- beseeninFig.10. pactasthewindisalreadysofragmentedthatthepho- tonshavefewremaininginteractionswiththeclumps. 3.3. Inneremissionboundary Asasecondstep,weconsidertheeffectoftheshape Thelocationoftheinnerboundaryoftheemission of fragmented shells. For this purpose, the factor µ regionisoneoftheopenquestionsintheunderstand- inEq.4and5,whichrepresentstheorientationofthe ingoftheX-rayemissionofmassivestars. However, fragmented shells with respect to the line-of-sight, is a variationof this parametercan have importantcon- re-introduced into our simulations. Compared to the sequences. Aswepointedoutintheprevioussection, isotropic case, the opacity of the wind decreases(see the density of matter increases as one movesinwards Fig.7). The radiation from the back side of the star in the stellar wind, and therefore the contribution to islessattenuatedthaninthecaseofisotropicclumps. the intrinsic X-ray emission increases as well. Still, Indeed, the fact that fragments are flattened and that as far as the observable emission is concerned, part photons coming from the rear side of the wind cross of this increase in emission measure is compensated these shells mainly perpendicularly implies that they by the increase of the amount of absorbing material have to cross less matter, and are thus less absorbed, that the photons have to cross before they escape. If than in the isotropic case. As a result, the total flux we adopt an inner radius of 2.5R instead of 1.5R , andintensityarehigherintheanisotropiccase. Also, ∗ ∗ 6 withanouterradiusof10.R ,fortheemittingplasma, the optical depth for an homogeneous wind with the ∗ wenotethatthelineintensityintheshortwavelength remaining matter. Finally we take the sum of the range, where τ is low, decreasesroughlyby a factor two contributions and determine the absorption for a two. Inthelong∗wavelengthdomain,whereτ ishigh, mixedwind model. Asa homogeneouswindabsorbs ∗ the reduction of the stellar wind absorption is more more photons, the intensity of the line profiles of the importantthan that of the emission. In consequence, mixedmodelshouldactuallybelowerthanforafully the inner part of an X-ray emission shell is fully ab- clumpedmodel(seeFig.13)andtheimpactisstronger sorbedbythecoolmaterial. Theresultisthatthelines at longer wavelengths, and hence at larger opacities at longer wavelength are rather insensitive to the lo- κ. These considerations are confirmed by our sim- cation of the inner boundary of the emission region ulations of the overall X-ray spectrum (see Fig.14). (Fig.11). Thesamequalitativeconsiderationsholdfor Asasecondstep,weattempttofitthespectrumofthe theoverallspectrumwhichisshowninFig.12. mixedmodelwith97%ofmatterclumpedtoamodel We note that the FIR triplet of helium-like ions spectrumforafullyclumpedwind. Fig.15illustrates provides in principle a powerful diagnostic of the the results: the individual line profiles of the mixed inner emission boundary (Leuteneggeretal. 2006). model are almost perfectly fitted by a fully clumped However,inthecasewheretheobservedX-rayemis- modelwith a slightly lower porosity parameter. This sionstemsfromamulti-temperatureplasmawitheach has important consequences in practice: whilst the componentpossiblyhavingitsownvalueoftheinner X-ray line profiles might allow us to infer the pres- boundary,itmustbestressedthattheresultanttriplets ence of clumps and to constrain their geometry, it are the sum (weighted by the emission measures) of seemsalmostimpossibletodistinguishbetweenafully the triplets in the various components. This situa- clumpedwindandamixedmodelwithoutconstraints tion renders the interpretation of the FIR diagnostics from observationsat other wavelengths(e.g. UV, op- morecomplexthanexpectedfromasingletemperature tical).We thus conclude that X-ray line profiles alone plasma. cannotrevealthepresenceofaninter-clumpmedium. 3.4. Thecontributionoftheinter-clumpmedium 4. FirstapplicationtotheO VIIIλ18.97Ålineof ζPuppis In their work, Zsargo´ etal. (2008) have shown the needtointroduceahomogeneousinter-clumpmedium Intheprevioussections,wehavediscussedtheim- to better fit the profile of the O VI λλ1032,1038 pactofdifferentparametersandofdifferentfragmen- doublet with the model atmosphere code CMFGEN. tation prescriptions on the line profiles and on the These authors conclude that the inclusion of a small emergent X-ray spectra. In this section, we use our percentage ( 5%) of homogeneous material in be- codetofitthe O VIII Lymanα doubletλ18.97Å and ∼ tween the clumps is needed to achieve a good fit theneighbouringN VIIλ19.36Å,λ19.82Ålinesof of the line. Similar conclusions were reached by the massive star ζPuppis and determine some stellar Sundqvist,Puls&Feldmeier (2010). windparameters. Wedecidedtoworkonanextended What is the consequence of such a tenuous, but region around the strong O VIII line since Fig.1 re- homogeneous,inter-clumpmediumon the X-rayline vealsthepresenceofweaklinesthataffectthe wings profiles? Toanswerthisquestion,weincorporatethis of the O VIII line and produce a pseudo-continuum situation in our model. In practice, we work with that contributesof order 5%of the flux of the O VIII a constant mass-loss rate and we consider that the line. For this purpose, we have extracted, reduced size of the clumps is small. We distribute an im- and combined 18 RGS spectra of ζPuppis from the portant percentage of matter (90%, 95% or 97%) in XMM Newtonarchive(Naze´,Flores&Rauw 2012; − clumpsandwecomputetheopticaldepthduetoato- the different aspects of the data reduction are treated tally clumped wind. As a first assumption, we con- in detail in that paper). We also apply the absorp- siderthattheionizationisthesameinthecoolclump tionbytheinterstellarmedium(N =8.9 1019cm 2, H − × as in the inter-clump medium5. Next, we compute Diplas&Savage 1994)tothesyntheticspectra.Then, weconvolvethespectrawithaLorentzianprofilewith 5Constrainingtheionizationoftheinter-clumpmediumrequireshy- ahalf-widthathalf-maximumof0.07Åtoaccountfor drodynamicalsimulationsthatarebeyondthescopeofthepresent paper(seealsoSundqvist,Puls&Feldmeier 2010andZsargoétal. 2008). 7 the instrumental resolution of the RGS spectrograph hence the width of the synthetic line emission would onboardXMM Newton. Finally,wecomparethere- betoolargeincomparisontotheobservations(Fig.18, − sultstotheobservation. on the right). Second, a good fit to the O VIII line AsshowninFig.16and17,weobtainadegeneracy and its close neighboursis only found if one uses an ofthestellar windparameters. Indeed,fortheO VIII overabundanceof N and a depletionof O (Tab.2 and line profile, we demonstratethatwe can use a homo- Fig.16). Third, a quick look at a wider wavelength geneousoraporouswindmodeltofitthedataequally band(Fig.19)showsthata singletemperatureplasma well (see Fig.16 and Table 2) though with different cannot reproducethe whole spectrum of ζPuppis. A values for the hot gas filling factors. Note that these multi-temperatureplasmamodelis requiredfora full valuesareinagreementwiththeresultsofHillieretal. analysisoftheX-rayspectrum.Thustheobservedline (1993). We onlyneedtoadaptthemass-lossrateand profilesandintensitiesareacombinationofthecontri- the abundanceof oxygento obtain similar results. In butionofthedifferenttemperatureplasmaspresentin a denser wind (i.e. with a larger mass loss rate), the thewind. increase of absorption dominates the increase of X- Finally, it should be noted that part of the degen- rayphotonproductionatlongerwavelengthswherethe eracyof the resultsis due to the limited resolutionof opacityis largest. In consequencewe have two ways present-day high-resolution X-ray spectrographs. In toincreasethenumberofX-rayphotonswhichescape Sect.3, we show the impact on a line profile of a from a denser wind. The first solution is to increase changeinporositylengthorinnerradiusforexample, the number of X-rays resulting from shocks. To first butthe convolutionby the responsematrix of current order, we could imagine that the number of shocks, instrumentswashesoutpartofthedifferenceinduced and hence the hot gas filling factor, would be larger bythedifferentparameters. in a denser wind (Tab.2, models A and C). Alterna- tively, we can increase the number of photon which 5. Conclusions escape. Consequently, we have to increase the free meanpathofphotonsinthestellarwind. Thiscanbe In this paper, we have studied the impact of the achieved with a more porouswind (Tab.2, models A two differentprescriptionsof stellar wind fragmenta- andD).Normally,thelineprofilesofthetwoprevious tionontheemergentbroad-bandX-rayspectrum. For solutions should be different. Unfortunately, the in- spherical clumps with an isotropic opacity, the dif- strumentresolutionis notsufficientto distinguishthe ferences between the two prescriptions are the most subtledifferences. obviouswhencomparingthe overallX-ray spectrum. Indeed, in this case, we find that a given simulation Furthermore, we can also fit this line equally well with a single value of the fragmentation frequency with a model where the inter-clump medium is not cannot be represented by a spectrum calculated with void(Fig.18,ontheleft). a singlevalueofthe porosityparameter. However,in It is thus obvious that a single line does not per- practice, with the quality of current high-resolution mit to discriminate between models. These prelimi- X-ray spectra of O-type stars, it seems almost im- naryresultsthereforeemphasizethenecessitytowork possible to distinguish the two models in a real case on the full X-ray spectrum. The analysis of the full whenworkingonaline-by-linebasis. Thisisbecause RGS spectrumisbeyondthe scopeof the presentpa- the differences are often small and are washed out per,butwillbepresentedinafuturework(Herveétal., by the coarse resolution of present-day instruments. in preparation). As we demonstratedin Sect. 3, each Moreover, the differences are most easily seen when parameterhasadifferentimpactoverdifferentpartsof comparingtheshapeofthefullspectrumwhichissel- thespectrumandwearethereforeconfidentthatsome dom done. In addition, one must keep in mind that degeneracies on e.g. porosity or mass-loss rate, will the shape of spectrum is also affected by the amount thenbelifted. of interstellar absorption and the fact that the X-ray Nevertheless, already on this small region of the emission from a real stellar wind most likely spans spectrum, three results are found. First, the possibil- a range of plasma temperatures rather than a single ity of an anisotropy (i.e., µ , 1, in the fragmenta- temperatureasassumedhere(seee.g.Zhekov&Palla tion prescription) of the wind absorption appears un- 2007; Naze´ 2009). In both prescriptions we find likely. Indeed, the flux from the back side of the that the X-ray emission is more intense in a frag- star would be too large (Fig.7, on the top right) and 8 mented stellar wind than in a homogeneous wind. The introduction of an anisotropic opacity in the fragmentation frequency prescription yields spectra that are more intense than in the isotropic case and Table 1: Lines considered in this study and the wind of course than in an homogeneous wind. Sophis- opticaldepthextractedfromFig.3andcorresponding ticated, 3-dimensional hydrodynamical calculations toourstellarandwindparameters mighteventuallybe neededto clarifythe issue of the geometryoftheclumps. Line Wavelength(Å) τ As pointed out previously, both models rely on ∗ SiXIV 6.18 1.8 a series of assumptions and, currently, we do not OVIII 18.97 21.9 have enough knowledge on the stellar wind frag- CVI 33.73 46.2 mentation to privilege one model over the other. SiVIII 61.02 187 Our investigation of the impact of the various model parametersontheemergingspectrumshowedthatboth 1 We are aware that the Si VIII λ 61.02 line will thepositionandthesizeoftheX-rayemittingplasma be impossible to observe in practice because it are very important. An increase in the size leads to isexpectedto be intrinsicallyfaintandmostof a more luminous spectrum, although we have shown allbecauseofthe hugeabsorptionbythe inter- that the amplitude of the intensity increase depends stellarmediumatthesewavelengths. However, uponwavelength. here we use this line to illustrate the behaviour For a given mass-loss rate, the differences be- oflinesathighτ values. tween fully clumped and homogeneous wind mod- ∗ els are quite large. However, in light of the simulations presented here, it will be very difficult to estimate correctly the value of the porosity if we include the effect of an inter-clump medium. In fact, the incorporation of a few percent of the wind material in the inter-clump medium yields the same emergent spectrum as obtained for a purely clumpedmodelwith a slightly less fragmentedwind. Finally, we present preliminary fits of the region near the O VIII λ 18.97Å emission line of ζPuppis withourcode. Ourfirstresultsrevealthatanisotropic clumps are unlikely, and that non-solar abundances (overabundance of N, depletion of O) are needed to reproducetheX-rayspectrum. However,thereisalso adegeneracyofstellarwindparameters. Eventhough aporouswindisclosestto theobservationaldata,we can not totally exclude an homogeneous wind. The mass-lossrate,theporosityparameterandthehotgas fillingfactorarestronglytied. However,simultaneous fitsofthetotalspectrumwilllikelyallowtoreducethe degeneracyontheporosityandotherparameters.But, itappearsthatasingletemperatureX-rayplasmaisin- Fig.1.—Theoreticalemissionofaplasmawithatem- sufficientto fit the globalspectrum of ζPuppis. This perature of kT=0.273 keV and with a O = 0.3 and resultimpliesthenecessitytouseseveraltemperatures O∗ and we will have to include the contribution of each N =4.bynumber. ⊙ N∗ temperatureplasmatothelineintensityandprofileof ⊙ OVIIIλ18.97Å(andalltheotherlines)butalsotothe continuum. 9 Fig. 2.—Evolutionofthemass-absorptioncoefficient Fig. 4.— Illustration of the impact of porosity (h = as a function of the wavelength. In black, the mass 0.07, 0.07, 0.055and 0.043R , dashed red line, from absorptioncoefficientwith our preliminaryresults on ∗ lefttorightandtopto bottom)onthe profilesoffour the abundances determined in the X-ray spectrum of specificlines(seeTable1). Theprofilesarecompared ζPuppis reveals a less opaque wind than with the withthosecomputedinthefragmentationprescription abundancesdeterminedinthemostrecentUV/optical forn =1.710 4s 1(blacksolidline)andforahomo- 0 − − analysis (in red, J-C Bouret, private communication, geneouswindmodel(dot-dashedgreenline). Bouretetal.,inpreparation). Fig. 5.— Comparison between a synthetic spectrum computed with the porosity prescription adopt- Fig. 3.— τ computed with solar abundances, M˙ = ing h = 0.07R (dashed red line), a spectrum com- 4.210−6M ∗yr−1,v =2250kms−1andR =18.6R . puted with the∗fragmentation frequency theory with ⊙ ∞ ∗ ⊙ ThesevaluesareusedinSection3. n =1.710 4s 1(blacksolidline)andahomogeneous 0 − − wind(dot-dashedgreenline). 10