An Extensive Collection of Stellar Wind X-ray Source Region Emission Line Parameters,Temperatures, Velocities, and Their Radial Distributions as Obtained from Chandra Observations of 17 OB Stars
aa r X i v : . [ a s t r o - ph ] M a r Published in 2007, ApJ, 668, 456; ERRATUM (see Appendix)scheduled for 2008, ApJ, 680
An Extensive Collection of Stellar Wind X-ray Source RegionEmission Line Parameters, Temperatures, Velocities, and TheirRadial Distributions as Obtained from Chandra Observations of17 OB Stars
W. L. Waldron and J. P. Cassinelli Eureka Scientific Inc., 2452 Delmer St., Oakland CA, 94602; [email protected] Dept. of Astronomy, University of Wisconsin-Madison, Madison, WI 53711;[email protected]
ABSTRACT
Chandra high energy resolution observations have now been obtained fromnumerous non-peculiar O and early B stars. The observed X-ray emission lineproperties differ from pre-launch predictions, and the interpretations are stillproblematic. We present a straightforward analysis of a broad collection of OBstellar line profile data to search for morphological trends. X-ray line emissionparameters and the spatial distributions of derived quantities are examined withrespect to luminosity class. The X-ray source locations and their correspondingtemperatures are extracted by using the He-like f /i line ratios and the H-liketo He-like line ratios respectively. Our luminosity class study reveals line widthsincreasing with luminosity. Although the majority of the OB emission lines arefound to be symmetric, with little central line displacement, there is evidence forsmall, but finite, blue-ward line-shifts that also increase with luminosity. Thespatial X-ray temperature distributions indicate that the highest temperaturesoccur near the star and steadily decrease outward. This trend is most pronouncedin the OB supergiants. For the lower density wind stars, both high and low X-raysource temperatures exist near the star. However, we find no evidence of any hightemperature X-ray emission in the outer wind regions for any OB star. Since thetemperature distributions are counter to basic shock model predictions, we callthis the “near-star high-ion problem” for OB stars. By invoking the traditionalOB stellar mass loss rates, we find a good correlation between the f ir -inferredradii and their associated X-ray continuum optical depth unity radii. We concludeby presenting some possible explanations to the X-ray source problems that havebeen revealed by this study. 2 –
Subject headings: stars: early-type – stars: X-rays – stars: winds, outflows –stars: shocks – stars: magnetic fields – X-rays: stars
1. Introduction
The
Chandra
Satellite has provided astronomers the ability to study the high energyresolution X-ray emission line spectra of numerous stars other than the Sun. With regardsto early-type stars (hereafter OB stars), these line profiles allow us to study the complexstellar wind distribution of the X-ray source regions. The X-ray line profile shapes provideinformation on the Doppler velocities associated with the line formation regions, and allowus to comment on the shocks embedded in these stellar winds. In addition, emission line fluxratios allow us to explore the radial distributions of the source regions and their associatedX-ray temperatures.The main goal of this paper is to present the X-ray data from a large collection of“normal“ OB stars and use the data to search for trends in the X-ray emission line parametersas a function of spectral type and luminosity class. Morphological trends in the X-rayemission line characteristics can help define important properties of X-ray emission thatwill be used to constrain the subsequent X-ray source modeling efforts. Although this typeof study involves fewer assumptions than used in the modeling of each specific star, wesuggest that it provides a broader, more comprehensive view of the X-ray source regioncharacteristics.In our analysis we will also be interested in comparing how X-ray parameters that canbe expressed in terms of velocities (i.e., line widths, line shifts, and X-ray temperatures)relate to the stellar wind terminal velocities and radial velocity structures. There are avariety of ways to discuss the data within the framework of several different shock pictures:1) an ambient stellar wind impinging on dense blobs (Lucy & White 1980); 2) a distributionof “saw-tooth“ forward shocks (Lucy 1982); 3) a wind running into a driven wave whichproduces forward and reverse shocks (MacFarlane & Cassinelli 1989), and; 4) a detailedhydrodynamic numerical simulation of the line-driven instability which incorporates thecomplex time-dependence of the line driving force which also produces forward and reverseshocks (Owocki, Castor, & Rybicki 1988; Feldmeier 1995). The primary difference betweenthese models is that the line-driven instability, or more appropriately the “de-shadowinginstability“, accelerates the pre-shock wind plasma to velocities that are larger than theambient wind velocities resulting in a highly rarefied wind structure prior to the shock jump,and the post-shock velocity (i.e., the velocity of the X-ray emitting plasma) is predictedto be comparable to the ambient wind velocity. In the other shock models, the post-shock 3 –velocity is some fraction ( <
1, with a typical value of ∼ .
5) of the ambient wind velocity.Correspondingly, the post-shock density (i.e., the density of the X-ray emitting plasma) ofthe de-shadowing model is then also comparable to the ambient wind density, whereas, forthe other shock models, the post-shock density is a factor of four times larger than theambient wind density as determined by the Rankine-Hugoniot equations when the pre-shockMach number is very large. Since our goal is to provide a global view of the OB stellar X-rayemission line properties and their dependencies on stellar parameters, we choose to use whatwe will refer to as a “basic shock model“ description in our discussion of the relationshipsbetween the X-ray and wind velocity parameters. The premise of this model is in-line withthe blob, saw-tooth, and driven wave shock models where the pre-shock velocity at any givenradius is equal to the local ambient wind velocity as defined by the standard β -law velocitystructure.In § § Chandra
High Energy Transmission Grating Spectrom-eter (HETGS) data along with the available archived
Chandra data, a total of 17 OB starsare studied in this analysis. The observed velocity information (half-width-half-maximumand line-shifts of the line emission peak) displayed as histogram distributions, illustratingtheir dependence on luminosity class, are presented in §
4. In § § ”near-star high-ion problem” found in earlier isolated stellar studies.The results and conclusions are summarized in §
2. Summary of OB Stellar X-ray Emission
Spectral lines and their profiles have been providing crucial information about OB stellarX-ray astronomy since the beginning of the field. Broad UV spectral lines of superionizationstages such as O vi were discovered in Copernicus observations (Lamers & Morton 1976).These broad profiles and the persistence of the superionization stages over a well delimitedrange in spectral types led to the realization that these ions were produced by the AugerEffect in which two electrons are removed from the dominant stages of ionization followingK-shell absorption of X-rays (Cassinelli & Olson 1979). These authors suggested that the X-rays responsible for the superionization could come from a hot corona at the base of the cool 4 –wind. Soon thereafter the
Einstein
Observatory discovered X-rays from OB stars (Harndenet al. 1979; Seward et al. 1979). However, the observations did not show the expected largeattenuation of soft X-rays by the overlying cool wind. This led to the realization that theX-ray emission must arise from shock structures embedded within the stellar wind (Lucy &White 1980). The origin of these shocks is associated with the instability of line driven windsto velocity distribution disturbances (Lucy & Solomon 1970). In the Lucy & White case, theshocks are bow-shocks around radiative-driven clumps, whereas in the model of Lucy (1982),the X-rays are formed in a periodic shock structure. Spectral lines at X-ray wavelengths weredetected by the
Einstein
Sold State Spectrometer (SSS) (Cassinelli & Swank 1983). Theyfound evidence of high energy ion line emission (Si xiii & S xv ) from the late O-supergiant, ζ Ori. Since these lines are formed at such high temperatures, they suggested that theseions are located in magnetically confined regions at the base of the wind. In addition,since the overall X-ray fluxes from OB stars are less variable than would be expected fromspherical shells of shocked wind material, Cassinelli & Swank also suggested that the shockswere fragmentary in form, such that there would be a statistically steady supply of X-rayemission from these wind distributed “shock fragments“. Some of these early ideas regardingX-ray source regions have persisted to the present time.The
ROSAT
Satellite had a greater sensitivity than the
Einstein
Satellite, although notthe energy resolution of the SSS instrument. In a survey of the Bright Star Catalogue OBstars, Bergh¨ofer et al. (1996 & 1997) confirmed that all O-stars are X-rays sources, withX-ray luminosities following the “hot-star law“ L X /L Bol = 10 − until about B1. For thelater B stars, Cohen et al. (1996) found a rapid decrease in X-ray luminosity with spectraltype which could be explained primarily by the slower speeds of the B star winds and thereduced mass loss rates.With Chandra , high spectral resolution of X-ray line emission from OB stars has nowbecome observable with the HETGS Medium Energy Grating (MEG) and High EnergyGrating (HEG) detectors. The impact of this diagnostic capability became very clear in thefirst detailed study of HETGS data from an O-star ( ζ Ori) by Waldron & Cassinelli (2001).Their analysis found three fundamental unexpected results associated with: 1) X-ray lineprofile shape characteristics; 2) the correlation between the wind X-ray source locations andtheir respective X-ray continuum optical depth unity radii, and; 3) the presence of deeplyembedded high energy ionization stages.One of the biggest surprises from
Chandra and
XMM-Newton high energy resolutionobservations of OB stars is the absence of blue-shifted, asymmetric X-ray emission lines.These resolved spectral lines had been predicted by MacFarlane et al. (1991) to be broadand skewed towards the blue, owing to the fact that the long-ward (“red-ward“) radiation 5 –from the back side of the star is more strongly attenuated than the short-ward (“blue-ward“)radiation from the near side. In the Waldron & Cassinelli (2001) analysis of ζ Ori broadline profiles were seen, but these lines lacked the predicted skewness and blue-shifts. In thecase of the O4f star ζ Pup the lines are somewhat similar to the predicted blue-shifts (Kahnet al. 2001; Cassinelli et al. 2001). However, nearly all other OB stars show minimal blue-shifted lines (within the resolving power of the instruments), and the lines are essentiallysymmetric (Waldron & Cassinelli 2002; Miller et al. 2002; Cohen et al. 2003; Mewe et al.2003; Schulz et al. 2003; Waldron et al. 2004; Gagne et al. 2005). Hence, explaining thelack of substantial blue-shifted lines that are presumably formed in an outflowing wind hasbecome one of the most perplexing problems to emerge from high spectral resolution X-rayobservations.Waldron & Cassinelli (2001) were the first to demonstrate that a stellar wind distributionof X-ray sources distributed above 1.5 stellar radii could explain the observed lines profileshapes seen in ζ Ori if the stellar wind mass loss rate is at least an order of magnitudesmaller than previously thought . Since then, several studies (e.g., Kramer, Cohen & Owocki2003; Leutenegger et al. 2006; Cohen et al. 2006) have found that reduced mass loss ratesare needed to explain the observed line profile shapes if the X-ray sources are originatingfrom a distribution of stellar wind shocks (e.g., the shock model developed by Feldmeier1995), and the majority of the observed X-ray emission is found to arise from a stellarwind location between 1.5 to 2 stellar radii (Leutenegger et al. 2006; Cohen et al. 2006).At first this apparent mass loss rate reduction requirement was addressed as evidence thatthese winds are highly clumped, since a clumped wind would provide channels to allow thedeeply embedded X-rays to escape more freely. Furthermore, a clumped wind would also beconsistent with the mass loss determination results from IR and radio observations, since alower mass loss rate could lead to the same emergent flux as an un-clumped wind of a highermass loss rate. A key effect of wind clumping is to enhance the escape probability of X-rayphotons, and this has also become known as the “porosity“ of a stellar wind. However, aswe will see later, for some of our stars, the reduced mass loss idea runs counter to a keyX-ray observational result, the observed X-ray sources are located at their respective X-raycontinuum optical depth unity wind radii as determined from using traditional mass lossrates (see discussions in Sec. 5.1 & 7).The perception that these stars do have reduced mass loss rates is based primarilyon FUSE observations and analyses of the P v P-Cygni line profiles from several O-stars(Fullerton, Massa, & Prinja 2006). From this study, it now appears that either the mass lossrates are a factor of 10 or more lower than previously thought, or these winds are severelyclumped over small spatial scales. Fullerton et al. argue that UV lines from the ion P v (1118, 1128 ˚A) should give line depths that are independent of clumping, consequently, their 6 –results imply lower mass loss rates for these stars. However, if there are clumps in thesewinds and these are surrounded by X-ray producing shocks, it is questionable to assumethat the ionization balance of phosphorus is not shifted to higher states by the Auger effect,or whether recombination in the high clump density decreases the ion abundance of P v .So the assumption that P v is dominant everywhere is arguable. With regards to X-rays,some authors find that clumping over small spatial scales appears to be able to explainthe observed X-ray line profile shapes (Feldmeier, Oskinova, & Hamann 2003; Oskinova,Feldmeier, & Hamann 2004). However, Owocki & Cohen (2006) argue that the requiredporosity lengths are unlikely, hence, they conclude in favor of reduced mass loss rates. Wefind it ironic that 25 years ago the possibility of reduced mass loss rates would have permittedbase coronae models to be an acceptable explanation of the X-ray emission from OB stars(Cassinelli et al. 1981; Waldron 1984). However, base coronae models were rejected becausethe needed mass loss rates disagreed with values derived from the available radio fluxes.Nevertheless, a better picture involving fragmented shocks in the winds emerged from theobservations, and it is now abundantly clear that shocks are responsible for a major fractionof the X-ray emission from OB stars. However, there remain a large number of problemsthat we address in this paper that have led to questions about the overall nature of thesewind distributed X-ray sources.The Chandra high energy resolution data has allowed us to exploit a major line emissiondiagnostic, the ratio of the forbidden to intercombination emission lines ( f /i ) arising fromHe-like ions (ranging from O vii to S xv ). This ratio had long been known as a veryuseful diagnostic tool for determining solar X-ray electron densities (Gabriel & Jordan 1969).However, it was clear that the densities derived with this interpretation turned out to be fartoo high ( > cm − ) for ζ Pup and ζ Ori. Kahn et al. (2001) and Waldron & Cassinelli(2001) quickly realized that the cause of this weakening of the f − line relative to the i − lineis not from collisional excitation, but rather radiative excitation from the presence of thestrong UV/EUV flux from the photospheres of OB stars. The effect of radiation fields onthe f /i ratio had been accounted for in the calculations of Blumenthal, Drake, & Tucker(1972). The intense photospheric radiation near OB stars causes a depopulation of the 2 S level ( f − line) and a higher population of the 2 P J levels (J = 0, 1, 2) ( i − lines) by photo-excitation. This better understanding of the excitation process meant that the f /i ratiocould be used to derive the radial distances of the predominant X-ray sources using thegeometric dilution factor of the UV/EUV radiation. Basically, the smaller the f /i ratio, thecloser the X-ray source is to the star.Waldron & Cassinelli (2001) found that the fir-inferred radii ( R fir ) derived from analysesof the observed f /i ratios indicated that the He-like ions are present over a wide rangein radial distances from the star. This means that there are X-ray sources distributed 7 –throughout the stellar wind as would be expected from a distributed of stellar wind shocks.In addition, these R fir were found to correlate with their respective X-ray continuum opticaldepth unity radii, R τ =1 , i.e., the wind location where the X-ray continuum optical depthhas a value approximately equal to unity. This observed correlation means that the highestenergy He-like ions are located deep in the wind, with a steady progression outward of thelower energy He-like ions. This spatial distribution has now been observed in other stars withdense winds, ζ Pup (Cassinelli et al. 2001), δ Ori (Miller et al. 2002), and ǫ Ori (Waldron2005). Somewhat surprisingly, this correlated behavior has also been observed in the highlyluminous O-star, Cyg OB2 No. 8a, a star which is believed to have a mass loss rate at least5 times larger than ζ Pup (Waldron et al. 2004). As discussed by Waldron et al. (2004),although the relationship between the R fir and corresponding R τ =1 is not exact, the generalconformance is rather good. Our understanding of this behavior is related to the strengthof the stellar wind opacity at a given energy. Since the opacity scales as ≈ λ , at longwavelengths the wind can be very optically thick to X-rays. Hence, we can only see the longwavelength line radiation, i.e., the lower ion stages, that is emerging from the outer layers ofthe wind. In contrast, at short wavelengths, the wind becomes more transparent to X-raysand we can detect line emission that originates from deep within the wind. At these shortwavelengths it is the higher ion stages that are producing the line emission. Since the X-rayemissivity depends on the square of the electron density, even if the line emission for a givenion is arising from all depths in a wind, we would predominantly only see the emission fromthe highest density regions, which tend to be those as close to the star as possible. Becauseof attenuation by X-ray continuum opacity we expect to be able to detect radiation that isproduced predominantly near optical depth unity. At this corresponding radial depth andfarther out, the radiation can escape freely, but radiation from sources deeper in the wind isattenuated by the overlying material. The fact that there is agreement between R fir derivedfrom emission line ratios, and R τ =1 derived from a consideration of the ambient wind opticaldepth, is certainly a relation that is to be expected. We ourselves had not predicted it, butfound that it provided an explanation of the wide range of radii that are inferred from theobserved f /i ratios. However, even this favorable relation has come into question since thereis a call for the mass loss rates to be reduced by a large factor. We intend to see whetherthe R fir and R τ =1 are correlated in this sample of many more stars than had been in ourearlier studies of one or a few stars.This spatial distribution of He-like ions leads to what is perhaps the most significantproblem in OB stellar X-ray astronomy. Very high He-like ionization stages such as Ar xvii (3.95 ˚A) seen in Cyg OB2 No. 8a (Waldron et al. 2004) and S xv (5.04 ˚A) seen in ζ Pup(Cassinelli et al. 2001) occur at wavelengths where the continuum opacity is very low,hence, any line emission from these ions can be detected from very deep within the wind. 8 –The observed f /i ratios from these ions have confirmed that these high ion stages are infact forming very close to the stellar surface ( < . T X ) for OB supergiantssteadily decreases outward from 20 MK near the surface to, 10 MK at 1.5 R ∗ , 5 MK at 3 R ∗ , and 2.5 MK at around 8 R ∗ . Such a decreasing temperature distribution poses a problemin current X-ray studies because the temperatures required for the high ionization stages arehigher than should be producible by shocks at such small radial heights in the wind!
For shocksthere is a maximal temperature which is determined by the jump in velocity across the shockfront. One would expect that this velocity jump should be no more than the local wind speed,which is small near the base of the wind. Some authors (Leutenegger et al. 2006; Cohen etal. 2006) have presented arguments that this is not a problem because shocks can in factform at the radii in question. However, that is not the full extent of the problem, not onlyare shocks needed, but the shocks must have the velocity jump sufficient to produce the hottemperatures and high ions that are observed to be originating near the star. Shock modelpredictions (e.g., Feldmeier, Puls, & Pauldrach 1997a; Runacres & Owocki 2002) show thatshocks can form at and above 1.5 R ∗ , and the derived X-ray shock temperatures ( T X ) at theselow radial locations are found to be highly dependent on the line-driven instability triggeringmechanism. For wind structures that are either self-excited or includes explicit photosphericperturbations, the predicted shock T X at these low radial locations are < MK; well belowthe temperature required to produce the observed high ionization stages . However, as shownby Feldmeier et al. (1997a), photospheric turbulence can generate a shock T X of ∼
10 MKat ≥ . R ∗ , but the contribution from this shock with regards to the overall observed X-rayemission appears to be quite small. Furthermore, although these models indicate that weakshocks can form below 1.5 R ∗ , these shocks cannot generate X-ray temperatures.Since the expected maximum shock temperatures are found to be significantly smallerthan the temperatures required for these high ion stages, we call this the “near-star high-ion problem“ (hereafter abbreviated as N SHIP ). Possible explanations of the
N SHIP have been proposed, but a consensus has not yet been reached. For the specific case of τ Sco(B0V), Howk et al. (2000) suggested that clumps form from the density enhancements in theembedded wind shocks and these clumps become decoupled from the ambient wind velocitylaw. The clumps follow trajectories that have them fall back toward the star which could leadto high relative velocities between the clumps and the wind even at relatively small radialdistances from the star. Each clump would also have a range of temperatures distributed overthe frontal bow-shock extending from low T X in the wings of the bow-shock to a maximum T X at the frontal apex of the bow-shock. Howk et al. suggested that the conditions allowingfor an in-fall of clump material might only be present in main sequence stars such as τ Sco, 9 –because wind clump drag forces would prevent the in-fall in more luminous stars with denserand faster winds. However, in light of the observational demand for clumpy winds, thismodel warrants a closer look. Very high T X are seen in some OB stars such as θ Ori C(which has a field strength of several kilogauss; see Gagne et al. 2005) which are believedto have magnetically controlled outflows analogous to Bp stars (ud-Doula & Owocki 2002).Even with more moderate fields there could also be solar-like phenomena occurring in thesestars which may help explain the
N SHIP . Studies have found that moderate magneticfield structures could rise buoyantly through the radiative envelope of OB stars (MacGregor& Cassinelli 2003; Mullan & MacDonald 2005), and, in fact, the first complex magnetictopological map of the early B main sequence star, τ Sco, has been revealed (Donati et al.2006). Hence, as had been proposed by Cassinelli & Swank (1983), one could envision thatthese high ion stages may reside in magnetically confined loops close to the stellar surface.Alternatively there could be“coronal bullets“ or “plasmoids“ of fast moving material thatmight be ejected from the surface of the star owing perhaps to magnetic reconnection in thesub-photospheric region as proposed for the sun by Cargill & Pneuman (1984). Although ourstudy will primarily focus on the OB stars that do not show the extreme kilogauss magneticfields with the hope of understanding the X-ray emission problems of ordinary OB stars, weinclude θ Ori C in our study so that comparisons can be made between ”normal” stars anda highly magnetic one.
3. Determining X-ray Emission Line Characteristics
Existing detailed studies of individual OB stars have provided many interesting resultsabout the stellar X-ray sources. However, a study of many stars, using identical analysistechniques is called for and is needed to search for general trends in the OB stellar X-raysource properties. In particular, we explore the line characteristics as a function of stellarluminosity class since stellar luminosity is considered to be the dominant contributor in thedriving of these OB stellar winds. In this section, we present the OB stars used in our study,their relevant stellar parameters, and the X-ray emission lines used in our analysis. We alsodiscuss our line fitting approach and the emission line parameters that can be extracted.
We have compiled the available archived HETGS data for 17 OB stars. Our analysisincludes both the MEG and HEG spectral data. Although for most of our stars the HEGspectral lines have much lower signal-to-noise (
S/N ) than their respective MEG lines, we 10 –use both data sets to check the consistency in derived parameters and possibly add supportto the conclusions. Our program stars are listed in Table 1, along with the relevant adoptedstellar parameters, and the
Chandra observation identification numbers (Obs ID). For a fewstars, their observations were carried out over two or more separate time segments. TheMEG and HEG spectra and relevant spectral response files (ARFs & RMFs) were extractedusing the standard CIAO software (version 3.2.2). For stars with multiple observations, theseobservations were co-added. Our study will focus only on the H-like and He-like lines andtwo Fe XVII lines. For the H-like and Fe XVII lines we consider only those lines with signal-to-noise ratio of
S/N >
5. For the He-like f ir (forbidden, intercombination, resonance)lines, we require that the total flux from the three lines must have
S/N >
5. In a few cases,primarily for the high energy lines, if a reasonable flux has been established (i.e., ≥ N W O listed in Table 1 is the scale factor associated with the stellar wind column density (seeTable 1 notes for a definition). Table 2 lists the emission lines used, their rest wavelengths,and the temperature ( T L ) associated with the peak emission for each line. Also includedin the table are the wavelength dependent X-ray continuum absorption cross sections forthe stellar wind ( σ W ), the ISM ( σ ISM ), and several atomic parameters that are needed tocalculate the He-like f /i ratio. The σ ISM cross sections represent the “cold“ gas limit, i.e.,ISM absorption cross sections. However, it has long been known that for all O and early Bstars, the value of σ W is always less than σ ISM for energies < < σ W is ≈ σ ISM .For example, from Table 2 we see that the difference between σ ISM and σ W first becomesless than 20% at wavelengths short-ward of 12 ˚A( > σ W listed in Table2 are representative of a typical O-star at a T eff = 35000 K . In general, σ W at energies < . T eff , and conversely for stars with lower T eff . For each star, the product N W O × σ W gives the commonly used scaling parameter, τ ∗ .This optical depth parameter has often been used in various emission line profile modelingefforts (e.g., Owocki & Cohen 2001). To obtain the radial and wavelength dependent X-raycontinuum optical depth, we consider a standard “ β -law“ velocity structure with β = 0 . τ ( r, λ ) = 5 σ W ( λ ) N W O (1 − w ( r ) . ),where w(r) is the radial wind velocity normalized by the terminal velocity (the procedurefor determining R τ =1 is discussed in the Appendix of Waldron et al. 2004). 11 – We examine four basic X-ray emission line parameters: the total “observed“ line flux, the “observed“ line emission measure ( EM X ), the line width or more specifically the half-width-at-half-maximum ( HW HM ), and for the line shift, we introduce a new terminology whichwe will refer to as the “peak line shift velocity“ ( V P ) as discussed below. Line widths and lineshifts are expressed either in physical units (km s − ) or as normalized to the terminal velocityof the wind, v ∞ . In search studies for global trends, the important velocity parameters arethose relative to the ambient wind, and not the actual physically velocities. We have toemphasize that the line fluxes and their associated EM X are the observed values since, inprinciple, the actual line fluxes and EM X of the X-ray emitting sources may be influencedby the presence of wind absorption.a) The total observed line flux is the total energy integrated line flux determined fromour statistical best-fit modeling, and provides the line fluxes needed in our study of line ratiodiagnostics. The extraction of a line flux for a given wavelength region must be handled withcare if one wishes to compare various observed line flux ratios with theoretical predictions. Inparticular, we find that it is extremely important to account for all of the lines that could becontributing to a given wavelength sector of the line, such as other strong lines and satellitelines. The importance of including other lines was clearly demonstrated by Ness et al. (2003)in their analysis of the He-like Ne ix f ir lines from Capella. Also, appropriate adjustmentsfor contaminating lines must be made in the model line flux ratios before comparisons withobserved ratios can be made as discussed in Section 5.b) In general astrophysical studies, if distance and the temperature (which provides aline emissivity) are known, the total line flux ( F X ) can be used to extract an ”observed” lineemission measure using EM X ( cm − ) = 4 πd F X ǫ ( T L ) (1)where d is the stellar distance, and ǫ ( T L ) is the maximum line emissivity (e.g., see Kahnet al. 2001) evaluated at T L . However, in the case of OB stars, the interpretation of thetotal observed line flux can be somewhat ambiguous, especially for OB stars with massivewinds, because there can be unobservable sources located deep within the wind. To accountfor the total amount of hot material in a wind, one would need to find the attenuationof the line flux by the overlying wind. In addition, this definition of EM X assumes thatall the emission for a given line is at the same temperature throughout the wind, and asdiscussed in Section 6, we now know that there is a radial dependent X-ray temperaturestructure. However, these two effects would require a significant amount of modeling of the 12 –wind structure, and the introduction of significant uncertainties. In this paper we want tofocus on a uniform discussion of observational properties. Therefore, we choose to deal onlywith the “observable“ EM X . Of course one who is interested in the total X-ray productivityof the wind needs to understand that our derived EM X are to be strictly treated as lowerlimits.c) The breadth of a line is expressed as a HW HM . This provides information regardingthe dispersion in the velocity of the line emitting plasma. For the general case in which thereis a spatial distribution of X-ray sources, the derived
HW HM represent integrals over bothdepth and impact parameters within each small range in the line-of-sight (LOS) velocity.However, even in the absence of details regarding the line formation process, we find usefulinformation can be derived from the line widths. For example, if a line is only producedvery close to the star, one would expect it to be narrow, with a width perhaps comparableto the expected thermal or turbulent speed at the base of the wind. In fact, this is oftenseen in the X-ray observations of cool stars such as Capella. In an OB star, a narrow linecould also result from certain asymmetric wind structures such as X-ray material confinedto volume sectors which are seen inclined relative to the observer’s LOS. Even if the totaloutflow velocity in these sectors may be large, the line width could be highly dependenton the inclination angle. For example, an observer’s LOS perpendicular to the flow wouldessentially see a near zero line width. We find that almost all OB stellar X-ray emissionlines have moderate to large
HW HM , although a few stars do have very narrow lines (e.g., τ Sco; Cohen et al. 2003).d) We have introduced the phrase, “peak-line shift velocity“ ( V P ) to represent the re-quired Gaussian line profile model velocity-shift needed to obtain a best-fit to the givenobserved line profile. We use this terminology to emphasize that, in general, V P does notcorrespond to a Doppler shift of any specific part of the wind or atmosphere. The observedshift is affected both by the spatial distribution of the X-ray sources in the wind, and bythe degree to which the wind absorption attenuates the radiation from each X-ray sourceregion. The observed peak-line shift is weighted by the dominant source locations, fromwhich the emitted X-ray line radiation can escape through the overlying wind. Consider thesimplest case of a single spherically symmetric shell of X-ray emitting material moving atsome velocity V . For an optically thin wind, the observed line profile would be symmetricand flat topped extending from about − V to + V (neglecting stellar occultation effects),with negligible line shift, V P ≈
0, and a
HW HM ≤ V . However, for the case of an opticallythick wind, the red-ward side of the line is more heavily attenuated, and thus the peak in theemission, V P , would occur at a blue-ward shift. This velocity could be slightly smaller than V , and the line shape would be sloped down long-ward from this V P , producing a triangularshaped line as had been predicted by MacFarlane et al. (1991). For this thick wind case, the 13 – HW HM can be significantly less than V . For even more complicated scenarios, such as astellar wind with many discrete X-ray source regions, the observed line shift V P represents an“average“ over all the source regions that are both capable of contributing to the observedline emission which are located at an X-ray continuum optical depth of about unity or less. To obtain a totally unbiased collection of emission line parameters we want to use amodel-independent extraction method. Two methods have been considered: 1) Gaussianfits to the line profiles, and; 2) the “moment“ method discussed by Cohen et al. (2006).In the latter, one calculates the first three moments of a line profile using only the actualobserved count spectrum (no ARF and RMF corrections) which in turn provide informationon the line shift, line width, and asymmetry of the line profile. Although this would appearto be a good unbiased way to describe a line, there are limitations as discussed by Cohenet al. (2006): 1) with regards to obtaining the
HW HM from the 2 nd moment, the momentanalysis does not allow one to separate the effects of instrumental broadening from physicalbroadening, and; 2) the moment method cannot extract reliable information from blendedlines (e.g., the He-like f ir lines). Furthermore, the moment method cannot be used toextract the total line flux. Since our goal is to provide a collection of physical line emissionparameters and line fluxes for single and blended lines in a self-consistent manner, we choseto use the Gaussian line fitting procedure described by Waldron et al. (2004). However, wedo find that the 1 st moment method, which is used to extract V P , provides almost identicalresults as compared to those obtained using the Gaussian method.For the Gaussian line fitting procedure, we assume that all lines within a given wave-length region have Gaussian line profiles superimposed on a bremsstrahlung continuum. Weuse χ statistics to determine the best fit parameters (line flux, HW HM , V P , & EM X ). Wealso considered the C-Stat (Cash 1979) approach to line fitting but did not find any advan-tage over the χ approach used in this analysis, basically because the C-Stat method wasdeveloped for handling weak lines and in this paper we are considering only the strongestlines. The error bars for each parameter are determined from the 90% confidence regions.For all line fits we assume a continuum temperature of 10 MK. The actual value assumedis not critical to our results since we are only interested in fitting the shape of the line andthe strength of the line emission relative to the continuum. All line flux emissivities andline rest wavelengths are taken from the Astrophysical Plasma Emission Database (APED;Smith & Brickhouse 2000; Smith et al. 2001). It is worth stressing again that even thoughwe have only chosen to analyze the strongest observed lines, many of the line regions contain 14 –overlaps with other fairly strong lines. We find it important to include all extraneous linesthat may be contributing in a given wavelength region in order to get an accurate fit to theline profile of interest. In the case of the three He-like f ir lines, all three lines are likelyto be formed under the same physical conditions, and our model fitting procedure assumesthat the HW HM and V P are the same for all three lines, and only the line strengths aredifferent. The model count spectrum is determined for the default wavelength binning of theMEG (0.005 ˚A) and HEG (0.0025 ˚A), using the appropriate ± st order ARFs and RMFs.To obtain the best fit model parameters and associated errors, both the model and MEGand HEG ± st order spectra are re-binned to bin sizes of 0.02 ˚A and 0.01 ˚A, which arerespectively the approximate resolution limit of the MEG (0.023 ˚A) and HEG (0.012 ˚A).The main advantage of this approach is that it provides tighter constraints on the modelparameters. The determination of line ratios (discussed in §
6) are based on the resultantbest-fit model line fluxes.
4. Distributions Versus Luminosity for the
HW HM , V P , and EM X We provide histograms of the
HW HM and V P in physical units (km s − ) for the case ofcomparing all OB stars, and HW HM and V P normalized to their respective star’s terminalvelocity ( v ∞ ) in our study of luminosity class dependence. It is these normalized distributionsthat are of interest for developing an understanding of the behavior of the X-ray emission lineparameters versus OB spectral types and luminosity classes, but is not necessarily relevantwhen looking at the overall OB distributions for all classes. The EM X histograms representthe physical observed emission measure ( cm − ).First we show the line parameter distributions for all 17 OB stars, then we examine howboth the MEG and HEG derived parameter distributions depend on the stellar luminosityclass. We consider three luminosity class groupings: 1) main sequence, MS (luminosity classV); 2) giants (luminosity classes IV & III), and; 3) supergiants (luminosity classes II & I). Forall histograms, the bins represent the percentage of lines within a given range of HW HM , V P , or EM X . The HW HM and V P bin sizes are 200 km s − for the actual velocity values,and 0.1 for the normalized case. For the V P histograms, the bin spacing is set up to centeron V P = 0.The observed EM X are derived from the total line flux by using the approach discussedby Kahn et al. (2001), using the APED emissivities and eq. 1. The major assumption usedin extracting EM X is that we have assumed each line is at its maximum emissivity level(i.e., maximum temperature T L ). In our study of X-ray temperatures (see Sec. 5.2) we findthat this is not a bad assumption since all extracted temperatures are very close to their 15 –maximum values. We present the EM X histogram distributions in units of the log EM X inincrements of 0.5. HW HM , V P , and EM X Distributions for All OB Stars
The
HW HM , V P , and EM X MEG and HEG histograms for all OB stars are shown inFigure 1. Several key features are noted: 1) the MEG and HEG V P distributions are nearlysymmetric (both show slight asymmetry blue-ward) around V P = 0 with ∼
80% of all lineslying between ±
250 km s − ; 2) the MEG and HEG EM X distributions indicate that morethan half of all lines lie within a relatively small range of ∼ . EM X ; 3) theMEG and HEG HW HM distributions show a large range from 0 to 1800 km s − , and; 4)the MEG HW HM shows a double peaked distribution with peaks at 350 km s − and 850km s − which is not seen in the HEG distribution which only shows a peak at 350 km s − .The explanation is related to the sensitivity of the instruments in that the MEG 850 km s − peak is due primarily to lines from low ion stages which are inaccessible or very weak inHEG spectra.The V P distributions illustrate one of the most surprising results arising from HETGSdata analyses, the majority of all OB lines show essentially no line shifts . We emphasizethat almost all V P are typically within the wavelength resolution limits of the MEG (0.024˚A) and HEG (0.012 ˚A). For example, the MEG velocity resolutions at wavelengths of 25, 20,15, 10, and 5 ˚A are respectively 276, 345, 460, 690, and 1380 km s − . Correspondingly, theHEG limits can be obtained by taking half of the MEG determined values (long-ward of 20˚A is out of the HEG wavelength range).These OB stellar distributions illustrate a basic dilemma in early attempts to understandthe X-ray emission from OB stars. As in pre-launch expectations (e.g., MacFarlane et al.1991), the expected line broadness is observed, but there is clearly a lack of substantial blue-shifted line profiles. From this sample, it is now clear that this non-shifted line behaviorholds for essentially all OB stars. Hence there must be some common property relatedto X-ray production that needs to be determined. In the following subsections we explorethe HW HM , V P , and EM X distributions versus luminosity class to search for a betterunderstanding of the non-shifted behavior seen in the distributions of Figure 1. 16 – HW HM
Dependence on Luminosity Class
The MEG and HEG histograms showing the
HW HM dependence on the three lumi-nosity class groups are shown in Figure 2 (normalized to v ∞ ). With regards to all luminosityclasses, a key finding is that all HW HM are < v ∞ . We see that the histogram distribu-tions are similar for supergiant and giants with peaks between 0.35 to 0.45, and both showasymmetries towards lower values (except in their HEG distributions). The most notabledifference is the HW HM / v ∞ histogram for the MS stars where there is no sharp peak. In-stead, a rather a large range of 0.1 to 0.5 × v ∞ is evident. A partial explanation of this canbe seen from an inspection of the observed v ∞ and N W O listed in Table 1. We see that thesupergiant stars all have similar v ∞ and N W O , but the MS stars have a rather large rangein v ∞ . For the MS stars the broad peak may be due to the fact that their N W O are weak,and thus the wind absorption effects do not play a major role in determining the line profileshapes. The giants also show a larger range in both v ∞ and N W O .The actual velocities from the
HW HM values are consistent with X-rays arising fromshocks located in the accelerating parts of the wind and/or in the case of rotationally dis-torted flows, from sectors of the wind with low velocities along the line of sight. Surprisingly,both the supergiants and giants show significant line emission at
HW HM /v ∞ < .
3. Atleast for the supergiants, we would have expected to see very little emission at these valuessince, due to their dense winds, one simply cannot see to the base of the wind owing to thestrong wind attenuation. A possible explanation is that if one cannot see to the back sideof the star owing to wind attenuation, this would also tend to make the
HW HM smaller,but this would also require a large blue-shift in V P , which is not observed. For the MS stars,although they also have a large range in v ∞ , their HW HM / v ∞ histogram is not affected.It may be that the low mass loss rates of the MS stars relative to the giant and supergaintstars leads to lower wind column densities, hence, the observer can see deeper into the MSwinds. Thus we are primarily detecting X-rays from regions of low velocities instead of re-gions with speeds near v ∞ . Whereas for the supergaint and giant stars, depending on theline wavelength and the X-ray opacity, we can observe to a broader range of depths and havea HW HM that depends on v ∞ . Furthermore, since none of the groups show significantnumber of lines with HW HM /v ∞ > .
5, the majority of the observed X-ray emission mustarise relatively close to the star ( < The MEG and HEG histograms showing the peak line-shift, V P , dependence on thethree luminosity class groups are shown in Figure 3 (normalized to v ∞ ). Most notable,with respect to the maximum of the V P distribution, is that each luminosity group hasa maximum that is nearly identical to the sample as a whole. That is, each class hasa maximum in its distribution occurring at very small velocities, which are less than theMEG and HEG spectral resolutions. Next, in regards to the skewness or asymmetry of thedistributions, there is an increasing blue-ward asymmetry of V P with luminosity group. Thisindicates that a small fraction of the lines do indeed exhibit finite blue-shifts. The blue-wardasymmetry extends only to about -0.15 v ∞ for MS stars and -0.20 v ∞ for the giants. Forthe supergiants the V P asymmetry distribution is well pronounced up to approximately -0.35 v ∞ . Nevertheless, this is still far less than had been expected from early line calculationmodeling by MacFarlane et al. (1991), and from the empirical shock model calculations ofOwocki & Cohen (2001).The observed peak-shifts can be deduced from the uniform wind modeling expectationsin several ways: • If the wind mass loss rate is less than the value inferred from radio observations (assuggested by Fullerton et al. 2006), this reduction in wind density would allow moreX-ray radiation to emerge from the back side of the star (i.e., the red-shifted emission).This approach was first demonstrated by Waldron & Cassinelli (2001) in their analysisof ζ Ori, and used by Kramer et al. (2003) to model the X-ray line profiles and peak-shifts from ζ Pup. The Cohen et al. (2006) re-analysis of ζ Ori has also confirmedthat this approach can provide a fit to these lines. However, as mentioned before, thereare some questions about the new ˙ M estimates associated with the actual ionizationfractions of phosphorus. At the present time we choose to adopt the traditional massloss rates until the major change in mass loss properties has been verified and widelyaccepted. • If the X-rays can escape more easily from the sides of a shocked region, then the X-rayplasma produced along a LOS perpendicular to the observer (i.e., from the wind on bothsides of the star) would dominate the emergent X-ray emission. This is the solutionoffered by Ignace & Gayley (2002), who used Sobolev escape probability theory toderive the line profile shapes. However, it is questionable that the Sobolev theory theyused is valid for non-monotonic cases with discontinuities in the velocity, and jumpsin the velocity gradient. Furthermore, the X-ray formation region is almost surely notbeing accelerated at the same rate that the stellar UV radiation is accelerating the 18 –wind that is colliding with the shocks. Perhaps the treatment could be improved usingthe Rybicki & Hummer (1978) approach for non-monotonic velocities. Nevertheless,the results of Ignace & Gayley do illustrate that by having the line radiation escapeout from the sides of a shock provides a plausible explanation of the symmetric lineproblem. • If the winds are clumpy, photon mean free paths can be increased and one can see moreeasily to the back side of the star. This increased porosity effect has been investigatedby Feldmeier, Shlosman, & Hamann (2002). It also addresses the reason why the radiofluxes could be larger than inferred from a laminar wind case. Although, it appearsthat one should expect to see more flat topped X-ray emission lines than are actuallyobserved from this initial picture, Oskinova, Feldmeier, & Hamann (2006) have madeimprovements which appear to explain the minimal blue-shifts, provided that thesewinds are highly clumped. • If the outflowing stellar winds are geometrically confined, then the observed line profileswill be dependent on the observer’s orientation relative to the geometric structure ofthe wind. This approach was studied by Mullan & Waldron (2006) by considering atwo-component wind structure (i.e., a polar and an equatorial wind), where the polarwind is slower and less dense than the equatorial wind owing to the fact that thepolar wind is hindered by surface magnetic structures. Their results indicated that theobserved line-shifts will be dependent on the LOS where a pole-on view would yieldminimal blue-shifts. The main advantage of this model is that a fairly large sector ofthe outflowing wind does not have to be clumped.There are surely other more complicated scenarios that could explain the properties ofthe observed line shifts, but these suggestions cover the recently studied ideas. Althoughseveral of these can explain the observed lack of substantial blue-ward peak shifts, a con-sensus has not been reached. Furthermore, this issue of un-shifted lines became even moreproblematic with the HETGS X-ray emission line analysis for Cyg OB2 No. 8a (Waldron etal. 2004). This star is believed to have an ˙ M that is at least 5 times larger than any otherpreviously studied OB star, which implied that large blue-ward peak shifts should be seen.However, the observations show that the X-ray lines from Cyg OB2 No. 8a are similar toother OB stars in that only minimal peak shifts were observed. A particularly perplexingquestion is why do substantial blue-ward peak shifts show up only in ζ Pup? This star hasfor many years been the prototypical early O-star in regards to its wind properties, andobservations of it played a major role in the development of line driven wind theory. 19 – EM X Dependence on Luminosity Class
The MEG and HEG histograms showing the EM X dependence on the three luminosityclass groups are shown in Figure 4. There are several interesting results shown in thesedistributions. First we should recall that EM X is a measure of the X-ray density squaredtimes a volume element, and EM X scales as ( ˙ M /v ∞ ) /R ∗ . With this in mind, the resultsshown in Figure 4 suggest the following, using the data listed in Table 1. 1) Since thesupergiants have very similar ˙ M , v ∞ , and R ∗ then they should have almost identical EM X and indeed that is exactly what we see (the exceptions are Cyg OB2 Nos. 8A & 9). 2) Thegiants have the largest ranges in ˙ M and v ∞ hence, what we see in their EM X distributionis clearly consistent with this spread in wind parameters. 3) The MS stars show a doublepeaked distribution. The explanation is clear by inspection of their wind parameters, whichshows two extreme groupings of ˙ M and v ∞ (i.e., early MS stars have larger ˙ M as comparedto late MS stars). In principle, these EM X values which were determined solely by fittingthe observed line profiles, independent of any wind parameters, should provide a means forestablishing X-ray source densities if we know the radial location, temperature, and geometricextent of the region (e.g., cooling length). This is beyond the scope of this paper but weplan to explore this possibility in a later paper.
5. Line Ratio Diagnostics
In astrophysical studies line emission ratios are commonly used as diagnostic tools. Inour study of high spectral resolution X-ray astronomy, we focus on two line emission ratiosthat will be used to establish X-ray source spatial locations and temperatures. Spatialinformation is obtained from the ratio of the He-like ion forbidden to intercombination( f /i ) emission lines. This ratio provides a diagnostic for estimating either the distanceof the dominant X-ray emission zone from the central EUV/UV radiation source (radiationdominated case) or the electron density of the X-ray emission region (collisional dominatedcase). Although we commonly refer to the i − line as if it were a single line, it actually consistsof two lines that are unresolvable in both the MEG and HEG. All theoretical f /i line ratiocalculations include the total emission from both lines. To determine X-ray temperatures,we use the temperature sensitive line ratios from H-like ions to He-like ions (here abbreviatedas the H/He ratio). The
H/He line ratio increases dramatically with temperature as shownin Figure 5. As discussed by Waldron et al. (2004), the temperatures derived from
H/He ratios provide a measure of the “average“ temperature of the He-like ions and the morehighly ionized H-like ions.Another temperature sensitive line ratio is the He-like G-ratio defined as ( i + f ) /r . 20 –This ratio (introduced by Gabriel & Jordan 1969) has been used extensively as a temperaturediagnostic in solar X-ray studies, and has been used in early studies of O-stars (e.g., Schulzet al. 2000; Waldron & Cassinelli 2001). The G-ratio dependence on temperature is oppositeto that of the H/He ratio, the G-ratio decreases with increasing temperature and the slopeversus temperature is much weaker than is the case for the
H/He ratio. An advantageof the G-ratio is that it provides a temperature of only one ion, the He-like ion, but, asshown by Waldron et al. (2004), significant differences in the derived G-ratio temperaturesas compared to the
H/He derived temperatures and their associated T L were found. Thesediscrepancies may be related to “line-blending“ effects and/or resonance line scattering inthe r -line as discussed by Porquet et al. (2001). Complications in interpreting G-ratioderived temperatures have also been discussed in studies of late-type stars (e.g., Ness etal. 2003). Recently, Leutenegger et al. (2007) state that they have found evidence forresonance line scattering among the low energy He-like ions in their analysis of the ζ Pup
XM M − N ewton
RGS spectra. Although we provide a tabulation of the observed MEGand HEG G-ratios (see Table 7), we believe that until we have a clear understanding of theG-ratio idiosyncrasies, it is premature at this time to tabulate derived G-ratio temperaturesas it may lead to confusion and misinterpretations.Line ratio diagnostics require good energy resolution of the observed lines. Even withthe high energy resolution capabilities of the HETGS, we still must allow for possible con-tamination from the blended dielectronic satellite lines and any other lines that are withinthe instrumental resolution limits (these lines are easily identified in the APED data tables).These line-blending effects are most pronounced when dealing with ratios that use at leastone or more of the He-like f ir lines. For
H/He line ratios, the effects of line-blending areminimal, with the largest effect occurring for neon. The line-blending effects on the f /i lineratio are also expected, but will not be explored in this paper. The main reason is thatthe f /i ratio is dependent on three parameters (UV/EUV flux, spatial location, and X-raytemperature), whereas the
H/He ratios are essentially only dependent on one parameter,the X-ray temperature. This allows us to easily tabulate the expected line ratios, includingline-blending, that we use when comparing with observed
H/He ratios. Although the
H/He ratios may also be somewhat dependent on wind absorption and resonance line scatteringeffects (see Appendix), all
H/He ratio derived temperatures ( T HHe ) presented in this paperonly include line-blending effects. 21 – f /i
Ratios
The most widely used line ratio diagnostic to have emerged from
Chandra studies of OBstellar X-ray emission is the He-like f /i line ratio. This ratio has proven to be a valuableobservable because, for the first time, we have a direct means of finding the predominantX-ray source stellar wind locations. As we have seen, X-rays can arise from a wide rangeof wind radii. However, as is the case in line formation in stellar atmospheres, there isa depth for which the contribution function is maximal. Since the X-ray line emissionvaries as the square of the density, deeper layers tend to contribute more strongly to theobservable line strengths. It is information about the predominant zone in radial distancethat we can obtain information from using the f /i ratio. Ever since the beginning of OBstellar X-ray astronomy, determining the location of this X-ray emitting plasma has beenconsidered to be the most crucial quantity required for understanding the X-ray emissionprocess in OB stars. The
Einstein and
ROSAT satellites provided only low resolution data,hence, the only information regarding the source location was estimated from the changein X-ray attenuation across the major continuum jumps, such as the Oxygen K-shell edge.Historically, this was sufficient to show that the X-rays from OB supergiants could not allbe coming from a thin coronal zone at the base of the winds (Cassinelli et al. 1981).The He-like f /i line ratios have been used in solar coronal studies as a diagnostic of theelectron density of the X-ray emitting medium as first demonstrated by Gabriel & Jordan(1969). As the electron density is increases, a larger fraction of the ion is excited from the2 S level (the ground state of the triplet sequence) to the 2 P J levels which results in adiminution of the strength of the 2 S → S transition ( f − line) and an increase in thestrength of the 2 P J → S transition ( i − line). As discussed previously, the total i − lineemission actually consists of two transition from the 2 P J levels (J = 1 & 2). Although theJ = 0 level does not contribute to the i − line emission since it is strictly forbidden, it is acontributing transition in the rate equations which establish the relative populations of theselevels (e.g., Gabriel & Jordan 1969; Blumenthal et al. 1972).In all O stars and early B stars the enhancement of the i − line relative to the f − line iscaused by photo-excitation from the 2 S level by the strong UV/EUV photospheric emis-sion. The radiation required depends on the ion, and ranges from 1638 ˚A (O vii ) to 674˚A (S xv ) (see Table 2). The photospheric lines required to excite O vii Ne ix and Mg xi all have wavelengths long-ward of the Lyman limit (directly observable regions), whereasthe lines required to excite Si xiii and S xv have their wavelengths in the EUV, short-wardof the Lyman limit (unobservable). Hence, theoretical f /i ratios for Si xiii and S xv aredependent on model atmosphere fluxes. If one of these excitation line wavelengths happensto coincide with a photospheric absorption line that for some reason is deeper than predicted 22 –by the photospheric models, the distance inferred from the f /i ratio would be even closer.Conversely if the overall EUV continuum is larger than expected from model atmospheres theformation region is located farther out. An example of these effects is shown by Leuteneggeret al. (2006).In the early Chandra studies by Waldron & Cassinelli (2001), Cassinelli et al. (2001),and Miller et al. (2002), we felt assured that the we were not too far off in our radial distanceestimate by the fact that the radii derived from f /i ( R fir ) and from the X-ray continuumoptical depth unity radii ( R τ =1 ) turned out to be nearly the same. However, it is importantto point out that this correspondence is not exactly one-to-one, as discussed by Waldron etal.(2004). Furthermore, the recent arguments by Fullerton et al. (2006), and others, thatthe mass loss rates of OB stars are incorrect, are a source of concern and confusion as towhy the R fir and R τ =1 are in reasonably good agreement. We will return to this later.Following the approach used by Blumenthal et al. (1972), the radial dependence of the f /i ratio (commonly labeled as R ) can be determined by R ( r ) = R O n e ( r ) /N C + W ( r ) φ/φ C (2)where φ is the photo-excitation rate from 2 S → P J ; φ = c πhν U ν (3)and R O represents the low density and φ = 0 limit, n e ( r ) is the X-ray electron density of theX-ray emitting plasma, N C is the critical density, φ C is the critical photo-excitation rate,and U ν is defined as the surface photospheric radiation flux density which allows us to factorout the radial dependent geometric dilution factor, W ( r ) = 0 . − (1 − ( R ∗ /r ) ) / ). Thevalues of N C , φ C , and wavelengths of the 2 S → S J transitions are given in Table 2.Although φ C is only dependent on atomic parameters, N C is inversely proportional to thecollision rate. Hence, N C is also weakly dependent on the temperature, and the values listedin Table 2 are evaluated at each ion’s expected maximum line emission X-ray temperature( T L ).The format of eq. 2 allows us to see the distinction between collisional domination andradiation domination which is determined by the relative strengths of φ/φ C and n e ( r ) /N C .For OB stars, the radiation term is dominant throughout the wind except when one isinterested in conditions very close to the photosphere. Assuming that the radiation termis dominant, we can neglect the density term and obtain a relationship between radius, thestellar photospheric radiation (i.e., the stellar effective temperature, T eff ), and the observed 23 – f /i ratio ( R ), which is given by W ( r ) = φ C φ ( R O R ( r ) −
1) (4)The main advantage of this equation is that for any OB star with an observed f /i ratio wecan estimate a radial distance corresponding to the source of He-like ion emission, providedthat we know the corresponding radiative fluxes at the three λ f − i (see Table 2) which canbe determined using stellar atmospheric model spectra (e.g., Kurucz 1993; Hubeny & Lanz1995). Leutenegger et al. (2006) found that there are model atmosphere dependent differ-ences in the f /i ratio. We find that these differences appear to be relatively minor and wechose to use the Kurucz (1993) model atmospheres in our calculations.The f /i ratio defined in eq. 2 is referred to here as the “ localized “ f /i ratio. Tounderstand the difference between this localized f /i ratio approach and the more complicatedscenario, consider a single small isolated test packet of X-ray emitting plasma, at someconstant X-ray temperature ( T X ), which can be placed at any wind radial location. Asthis isolated test packet moves outward through the wind towards larger radii, the f /i ratioincreases because there is now less depletion of the f − line and less enhancement of the i − line. This change is due to the radial decreasing strength of the radiation field (i.e., thedecreasing dilution factor). In general, the f /i ratio is also weakly dependent on T X throughthe critical density term since this term is inversely proportional to the collision rate, andobviously, the strengths of the f ir lines are dependent on the fractional abundance of theHe-like ion as determined by the temperature of the X-ray emitting plasma.Now consider a more general f /i case, the “ distributed “ f /i where there is a radialdistribution of X-ray sources throughout the wind. Here, as compared to the localized case,the total line fluxes of both the f − and i − lines are determined by an integration process (seeLeutenegger et al. 2006), or equivalently, a summation of a very large (or infinite) number ofisolated test packets distributed throughout the wind. However, since the strength of eachline emissivity scales as the packet’s density-squared, the contributions to f − line deep in thewind are depleted by radiative excitation, and only the i − line accumulation benefits fromthe density-squared effect since the i − line is much stronger than the f − line at low radialdistances. On the other hand, the flux in the f − line only accumulates at larger radii wherethe density is lower. The resultant f /i ratio is then obtained from the ratio of the summed i − line and f − line fluxes. The key parameter in this distributed f /i emission case is theradial location of the densest X-ray source that is capable of contributing to the observed i − line and f − line fluxes, i.e., the densest X-ray source that is not heavily attenuated by theoverlying stellar wind.The main difference between these approaches is that the distributed f /i will increase 24 –faster with radius than the localized f /i case as shown by Leutenegger et al. (2006). Thedensity-squared dependence of the line emissivity is the primary reason for this shift, al-though there is also some change owing to the r term in the volume integral. An even morecomplex f /i scenario can be envisioned with the inclusion of a radial temperature distribu-tion and stellar wind absorption. This approach is beyond the scope of our current paper,and we plan to address this issue in a subsequent paper.In this paper (as assumed in all our previous papers on this subject) all quoted values ofthe f /i ratio are based on the localized approach, assuming that the He-like ion T X is alwaysequal to its respective T L (i.e., the temperature where the given ion’s X-ray line emissivity isat a maximum which is known for every ion). We know that a given set of He-like f ir linesmust be forming somewhere in the wind where T X = T L and what the localized approachprovides is the most likely location where this occurs. Furthermore, detailed shock modelingsuch as that of Feldmeier (1995), indicate that the localized approximation for treating f /i may indeed be appropriate since the dominant X-ray regions are spatially well separated,and the largest contribution to the two lines will arise from the highest density shockedplasmas that are capable of producing X-ray emission. Regardless, the main advantage ofthis approach is that it provides results that are only dependent of the adopted atomicphysics and the UV/EUV model atmosphere. This allows us to study our collection ofstars in a nearly identical way so as to reveal any significant differences associated withbasic stellar parameters. However, if the He-like emission is indeed distributed continuouslythroughout the wind as discussed by Leutenegger et al. (2006), the resultant R fir for a givenset of He-like f ir lines represents the lower radial boundary of the distributed X-ray emissionintegration. Hence, for a wind distribution of X-ray sources there can be no emission belowthis lower radial boundary. In general, these lower radial boundaries are expected to belower than our tabulated localized R fir values.The observed f /i ratios and their associated derived R fir are given in Tables 3 (MEGresults) and 4 (HEG results). The results for O vii are not given in the HEG table since thision is outside the energy band of the HEG. In addition, although the He-like Ar xvii f ir lineswere detected in Cyg OB2 No. 8a (Waldron et al. 2004), these results are not presented heresince none of the other stars have sufficient Ar xvii S/N to carry out a meaningful analysis.The most notable observation is that for the supergiants, where there is a clear progressionin the R fir being large for low energy ions and small for high energy ions. This behavioris what we have referred to as the N SHIP . There is also another interesting observationfor the supergiants from examination of the Mg xi and Si xiii R fir . We see that essentiallyall of the R fir for Mg xi are located between 3 and 6 R ∗ , whereas, the R fir for Si xiii arelocated in a narrower range of 1.8 to 2.3 R ∗ . For both the giants and MS stars, there is asimilar dependence, but not as noticeable as for the supergiants. 25 –An important observational feature that has emerged from analyses of He-like f ir linesis the correlation between R fir and their associated X-ray continuum optical depth unityradii ( R τ =1 ) as first noticed by Waldron & Cassinelli (2001). A discussion on the calculationof R τ =1 is given by Waldron et al. (2004). Figure 6 shows a scatter plot of the dependence of R fir on R τ =1 for our luminosity groups (we refer to these plot types as scatter plots becausethe data are shown with error bars in both the ordinate and abscissa directions). Thecorrespondence between the two radii is evident in the supergiants which was first shown byWaldron & Cassinelli (2002) using a small collection of OB stars. There is a key distinctionpresent in all luminosity groups in that there are very few data points that lie fully below thedashed line which represents the exact one-to-one correspondence, i.e., R fir = R τ =1 . This isconsistent with the idea that we do not see any observed line emission arising from below theoptical depth unity radii which is exactly what one would expect from basic radiation transferarguments, i.e., radiation can only escape from those radial locations where the associatedoptical depths are ≤
1. For the supergiants, the most likely explanation of this correlationis that a very large number of X-ray sources are distributed throughout these winds atessentially all radii, and the observed emission line characteristics (line strength and windlocations, R fir ) are primarily determined by the dominant X-ray sources. These dominantsources are those with the largest emission measures (the density-squared dependence of theemissivity) which are no longer hindered by significant wind absorption effects, and theirmaxima emissions arise from their associated X-ray continuum optical depth unity radii( R τ =1 ). For the giants and MS stars, the X-ray emission is seen to be occurring at windradii that are larger than their associated R τ =1 . Clearly, radiation can always escape fromany region that has a small optical depth, but the fact that there is evidence for radiationemerging from radii > R τ =1 may be an indication that the number of wind distributed X-raysources in these stars are greatly reduced as compared to the supergiant winds. For example,consider a very simple case where there is “one“ spherical expanding shock wave, then thelocation of the X-ray emission will always be associated with the radial location of the shockwave, independent of the location of R τ =1 . By considering say, 1 to 5 expanding shock wavesat different X-ray temperatures, this may be able to explain the observed scatter shown inFigure 6 for the giants and MS stars. Although this is a highly unlikely scenario primarilybecause such a structure would predict strong X-ray variability and we are not aware thatthis is the case. A more likely explanation is that the ˙ M of the giants and MS stars mayactually be larger than is traditionally assumed, so that the R τ =1 values may be larger.As evident in Figure 6 there are four supergiant data points that do indicate emissionoccurring below R τ =1 . One of these is the δ Ori A Ne ix emission, and the other threeare associated with the He-like ions of Cyg OB2 No. 8a. A possible explanation of thisdiscrepancy for Cyg OB2 No. 8a may be related to the uncertainty in the mass loss rate as 26 –discussed by Waldron et al. (2004). In the original analysis of δ Ori A by Miller et al. (2002),the derived Ne ix f /i indicated a radial upper limit of ∼ R ∗ , significantly larger than ourupper limit shown in Table 3. This discrepancy illustrates the importance of including line-blending effects in the extraction of individual line fluxes. The Ne ix wavelength region ishighly contaminated by many lines. Although we believe that our quoted Ne ix results arecorrect, we still do not have an answer as to why the Ne ix R fir is ∼ R ∗ . A possible answermay be related to wind-wind interactions since δ Ori A is a well known binary system. Itmay be that the majority of the observed Ne ix emission is actually occurring very close tothe stellar surface of δ Ori A binary companion, a B0.5 III star (Miller et al. 2002).A controversy has recently arisen with regards to the Si xiii f /i ratio for the late Osupergiant, ζ Ori, as discussed by Leutenegger et al. (2006) and Cohen et al. (2006). In theoriginal analysis of ζ Ori, Waldron & Cassinelli (2001) used the HEG f /i rather than theMEG f /i in their analysis primarily due to possible problems in the interpretation of MEG f /i ratio. It is well known that the MEG ancillary response file (ARF) has a significant Si K-shell edge (produced by the instrument silicon chip) within the MEG resolution limits of theSi xiii f − line which is less prominent in the HEG ARF. Our tabulated ζ Ori MEG Si xiii f /i (see Tables 3 and 4) is consistent with the one derived by Leutenegger et al., but bothof these are larger than the value determined by Oskinova et al. (2006). However, our HEGSi xiii f /i is consistent with the MEG Si xiii f /i given by Oskinova et al. (2006). Since mostof the MEG and HEG determined Si xiii f /i ratios are consistent in all the other OB stars,it is unclear as to whether this ζ Ori discrepancy in the Si xiii f /i is related to a specificproblem with the ζ Ori MEG ARF (different software versions), a problem associated withthe extracted ζ Ori count spectrum, or maybe some other unknown problem. For example,there are noticeable differences in the Si xiii f ir lines when comparing the MEG+1 andMEG-1 dispersed spectra which could be evidence of contamination by an unknown X-raysource in either the MEG+1 or MEG-1 dispersed spectrum in the energy vicinity of theSi xiii f ir lines. Until this disagreement between the MEG and HEG Si xiii f /i for ζ Oriis resolved, we choose to adopt the HEG f /i for ζ Ori as being the most appropriate value(as originally proposed by Waldron & Cassinelli 2001).
H/He
Line Ratio
Deriving the temperature distribution versus radius of the X-rays sources in OB stars isa major goal of this study. Establishing the X-ray temperatures ( T X ) in OB stellar winds is acrucial aspect in understanding the mechanisms responsible for the observed X-ray emission.Prior to the availability of HETGS data, our knowledge of T X was limited to one or two 27 –temperatures as determined from fitting broad band X-ray spectral data. From HETGSdata we now know that the OB stellar X-ray emission is produced by a large range of T X ( ∼ T X should be construedas representing the dominant T X at each associated radius. By knowing T X we can alsodetermine the pre-shock velocity relative to the shock front ( U rel ), defined as U rel = V − V S where V is the pre-shock gas velocity, V S is the velocity of the shock front, and V and V S aremeasured in the rest frame of the star. From the Rankine-Hugoniot relation, the dependencebetween T X (or post-shock temperature) and U rel is given by T X ( M K ) = 14 (cid:18) U rel (cid:19) (5)The quantity U rel is the fundamental parameter required to determine the physicalcharacteristics of a shock. In general, U rel can be used to determine the shock strength,post-shock temperature, and relative post-shock speed ( = 1 / U rel ). For a basic shockmodel description, since the pre-shock gas velocity in the rest frame ( V ) is defined as equalto the ambient wind velocity (hereafter denoted as V O ), U rel can also be used to determinethe speed of the shock front and a constraint on the shock front radial location provided weknow the radial dependence of T X . It is implied that all of these quantities ( T X , U rel , V , V S , and V O ) are dependent on radius.The relevance of the H/He emission line ratio as a diagnostic of the X-ray sourcetemperatures in OB stellar winds has been explored by Schulz et al. (2000), Miller et al.(2002), and Waldron et al. (2004). The advantages of using
H/He ratios are: 1) the H-like and He-like lines are very strong in HETGS data; 2) the line ratios display a strongdependence on the X-ray temperature as shown in Figure 5, and; 3) line-blending effects onthe
H/He ratio are minimal, with the exception being the Neon
H/He ratio. We point outthat our results shown in Figure 5 are slightly different from those shown by Miller et al.(2002) in that their He-like line emission used in their
H/He ratio included all the f ir lines,while we choose to only consider the He-like r − line to represent the He-like line emission(see discussion by Waldron et al. 2004).The one possible disadvantage in the usage of the H/He ratio with regard to studies ofOB stars is that the H-like and He-line ions could possibly form in different regions of thestellar wind which implies that they may suffer from different amounts of wind absorption 28 –and/or resonance line scattering. For example, Porquet et al. (2001) suggest that theobserved G-ratio may be larger than expected since the He-like r − line can be stronglyaffected by resonance line scattering escape probability effects in contrast to the i − and f − lines. Hence, the presence of resonance line scattering would lead to an underestimateof the actual X-ray temperature. In the Appendix we explore the possible effects of X-ray continuum absorption and resonance line scattering on the observed H/He ratios. Ourresults suggest that the temperatures derived from
H/He ratios are good indicators of thetrue X-ray temperatures. Although the expected temperature dependent behavior of thisratio shown in Figure 5 is based on the MEG energy resolution limits to determine therange of line-blending, we find that the HEG energy resolution produces only very minordifferences.We extract
H/He temperatures, T HHe , for all available OB H-He line pairs using theexpected temperature dependent
H/He ratios shown in Figure 5 to determine the range intemperature associated with the range in the observed ratios. Prior to the extraction of T HHe , all lines in these observed ratios are corrected for ISM absorption, but no attemptis made to estimate wind absorption and resonance line scattering. The observed
H/He ratios and their inferred T HHe are listed in Tables 5(MEG results) and 6 (HEG results). Forcompleteness, the observed MEG and HEG G-ratios are listed in Table 7.The T HHe data listed in Tables 5 and 6 illustrate several important results: 1) these X-ray sources show a large range in X-ray temperature, from ∼ T HHe are found to be within the temperature range as specified by their respective H and He T L ,i.e., the T L range shown in Tables 5 and 6 where T L represents the temperature associatedwith the maximum line emission of a particular ion (seeTable 2); 3) the consistency between T HHe and T L for all ions can be interpreted as a verification that the OB observed X-rayemission lines arise from a thermal plasma since T L represents the collisional ionizationequilibrium temperature associated with a given line’s maximum line emission; 4) for agiven ion and a given luminosity class, the values of the derived T HHe are very similar, and;5) comparisons of the mean T HHe for each luminosity group show no significant differences,except possibility the supergiant Mg xi mean T HHe which is somewhat larger than the otherluminosity groups, but this difference is traced to the higher T HHe of the Cyg OB2 stars.Note that the mean T HHe for the MS stars does not include the results for θ Ori C, a wellknown peculiar magnetic star. The most obvious difference between the θ Ori C T HHe foreach
H/He line pair is that they are larger than those of the other stars in our sample (seeTables 5 & 6). In addition, the θ Ori C temperatures are only slightly larger than those of τ Sco which has also been confirmed to have magnetic structures (Donati et al. 2006).If the
H/He line pairs were sensitive to wind attenuation owing to continuum opacity, 29 –we would have expected a wider dispersion in T HHe since our program stars contain a widediversity in stellar wind properties. However, there are a few stars in each luminosity groupwhere there is some noticeable difference among individual star T HHe with respect to themean of the group. This may signify certain effects such as, an overall higher tempera-ture structure, wind absorption, and resonance line scattering. In general, since the
H/He temperature diagnostic appears to predict temperatures that appear to be independent ofwind structure (i.e., individual stars), we suggest that this ratio should be considered tobe the best available diagnostic for establishing the X-ray source region temperatures. Theoverall consistency in these temperatures is a very interesting result, in that, regardless ofluminosity group, as well as individual stars, the expected temperature for any given H-liketo He-like line pair is always the same which implies a global commonality among the X-raytemperature distributions for all OB stars.
6. The Stellar Wind Distributions of
HW HM , V P , T X , and U rel In the previous sections, we have determined the line emission parameters (
HW HM , V P ,and EM X ), spatial locations of the He-like ions ( R fir ), and X-ray temperatures ( T HHe ). Wenow combine this information to find the stellar wind spatial distribution of the line emissionparameters and temperatures. We will not explore the radial dependence of EM X primarilybecause these are the observed emission measures and not the intrinsic emission measures,plus there is some uncertainty owing to the makeup of EM X such as shock density andtemperature, and geometric factors, such as surface area and thickness. In our discussionsof the radial dependence of HW HM , V P , and U rel it is beneficial to use “velocity versusvelocity“ type plots where the abscissa for any given radius, R , is defined as V O ( R ) /v ∞ .The transformation between R and V O is obtained through the standard “ β -law“ velocity, V O ( R ) /v ∞ = (1 − R O /R ) β , assuming a β = 0 . HW HM and V P of the He-like ions versusthe normalized ambient wind velocities [ V O ( R fir )], where all quantities are evaluated at their R fir for all OB luminosity classes. From the basic shock model description one would expectthe HW HM and V P at any given radius (R) to be less than the V O ( R ) associated with theline formation region since there is a significant decrease in the flow velocity across a shock.For lines forming at large radii, the HW HM are < V O ( R fir ) as shown in the upper panel ofFigure 7. However, for lines near the star, although the HW HM are < v ∞ these HW HM are > V O at these low radial positions, which presents a problem in that the lines formed nearthe star are too broad. This is also a problem for the de-shadowing shock model (Feldmeieret al. 1997a) which predicts that the post-shock velocities are comparable to the ambient 30 –wind velocities. Our results indicate that the spread in HW HM ranges from 0 to 0.6 v ∞ atall radii. In the lower panel of Figure 7, we see that the V P values are barely shifted and thespread is only ± . v ∞ . Therefore, we find that observed distributions of both the HW HM and V P are nearly independent of the wind location of the X-ray emitting plasma. This isan odd result that has only become apparent from our multi-star study, i.e., there was noindication of such behavior emerging from analyses of individual stars.Figure 8 shows a scatter plot of the dependence of T HHe on R fir for the three luminositygroups. Our results confirm the initial results reported by Waldron (2005), the T HHe of thesupergiants show a well defined radial distribution that decreases outward from the stellarsurface as evident in both the MEG and HEG data. The supergiant data show a strongcorrelation in which the highest temperatures (20 MK) only occur very close to the star, andthe lowest temperatures (2 MK) occur only in the outer wind regions. Although this behavioris not as obvious in the giants and MS stars, it is clear that the highest temperatures are onlylocated near the surface, but low temperature can occur anywhere within the wind. It isalso interesting that the observed radial distribution of T HHe indicates that for all luminosityclasses there is a radial dependent maximum X-ray temperature which decreases with radius.To our knowledge, this behavior has not been predicted by any shock model. The mostlikely reason as to why the supergiants show such a tight correlation between temperatureand radius is that the supergiants have larger wind densities and column densities, hence,we cannot see the low temperature regions that are present at small wind radii. This followsfrom the optical depth unity argument. For the giants and MS stars shown in Figure 8,one sees a large range in temperature at small and intermediate radii with no cutoff as seenin the supergiant case. This is probably also the case for the supergiants as well, but wecannot see the lower temperatures at small and intermediate radii due to larger stellar windabsorption. Furthermore, since all three luminosity groups show high energy ions existingvery close to the stellar surfaces, the
N SHIP is a common feature identified with all OBstars.We now choose to examine the radial dependent distribution of the He-like ion values of U rel (the relative pre-shock velocity discussed in Sec. 5.2) with regards to the radial depen-dent ambient wind velocity, V O , where U rel and V O are evaluated at their R fir . The valuesof U rel are obtained directly from eq. 5 using the radial dependent X-ray temperature struc-tures [ T HHe ( R fir )] shown in Figure 8. Our discussion will incorporate a useful parameter, η ,which in general should also be dependent on radius, and is defined as η ( r ) = U rel ( r ) V ( r ) = 1 − V S ( r ) V ( r ) (6) 31 –This ratio measures the ratio of the pre-shock velocity relative to the shock front to thefixed frame pre-shock velocity. For outflows ( V > V S ≥ η has a maximum value of1 when V S = 0 which implies that the shock front is stationary in the rest frame of the star,and U rel = V , the maximum value of U rel . For the case of in-falling gas clumps, i.e., V S < η can be >
1, and the actual value of η is determined by the magnitude of the clump in-fallvelocity.In the following discussion we will address the results as relevant to the basic shock modeldescription for an outflowing gas, then, by definition, V = V O (the ambient wind velocity).The scatter plot of U rel versus V O evaluated at the associated MEG determined R fir is shownin Figure 9 for all the OB luminosity classes. The data display several interesting features: 1)there does not appear to be any obvious correlation between U rel and V O ; 2) the majority ofthe data indicate a range in U rel /v ∞ from ≈ . V O ( R fir ) /v ∞ > .
6) occur where η < .
5, indicating weak relative pre-shock velocities which implies that the shock front velocity ( V S ) is becoming comparable tothe pre-shock velocity ( V ), since V S = V (1 − η ), as η →
0, then, V S → V ; 4) at intermediateambient wind speeds ( ∼ . v ∞ , a radius of ∼ . R ∗ ), η ≤ V S → V O < . v ∞ ,or a radius < . R ∗ , with a large range in U rel from 0.2 to 0.8 v ∞ , and these are the linesdiscussed earlier regarding the near-star-high-ion problem ( N SHIP ).The data appear to support the idea that the majority of the He-like ion lines areconsistent with a basic shock model interpretation provided that these winds have shock frontvelocities that are initially stationary at various points in the wind where η = 1 and then theyaccelerate outwards where eventually the shock front velocities become comparable to thepre-shock velocities and these weak shocks are no longer capable of producing detectable X-ray emission. This interpretation is consistent with our derived X-ray temperature structuresshown in Figure 8. It is also likely that similar conclusions may be attainable from othershock models with appropriate parameter adjustments.However, the He-like ion lines at low radial locations ( V O ( R fir ) < . v ∞ ) cannot beexplained by this basic shock model description. We explore two possible alternatives, anduse the observed data point with U rel = 0 . V O = 0 . η = 5 and an in-fall velocity of V S = − . v ∞ . It is unclearas to whether such large in-fall velocities can occur at small radii. Now we examine whetherthe rapid acceleration in the de-shadowing instability model is applicable. As discussedearlier, for outflowing gas, the maximum of η is 1 which means that V = U rel = 0 . v ∞ ,and this acceleration must occur at a radius ≤ . R ∗ . From inspection of several numerical 32 –simulations (Owocki et al. 1988, MacFarlane & Cassinelli, 1989, Feldmeier 1995, Feldmeieret al. 1997a, Runacres & Owocki 2002) we do not see any evidence for large pre-shockvelocities of 0 . v ∞ at such low stellar radii.
7. Summary
The main goal of this paper has been to present a large collection of observationalresults and examine these in a uniform way so as to draw out general facts regarding OBstellar X-ray emission characteristics. We have analyzed the
Chandra
HETGS MEG andHEG data from 17 OB stars. Although the HEG spectra are typically much weaker thantheir associated MEG spectra, we have chosen to use both data sets to illustrate the rathergood agreement between their observed and derived attributes. As a slight departure fromour original goal of analyzing only “normal OB stars“ we have also included θ Ori C in oursample, primarily to allow one to compare the X-ray properties of a know peculiar O-starwith those of other OB stars.We use a well recognized Gaussian line-fitting method to extract the pertinent X-rayemission line parameters which ensures that our results are easily reproducible. This model-independent line fitting procedure has allowed us to determine the observed line emissionparameters (
HW HM , V P , EM X , and line flux) and line emission ratios ( f /i and H/He ) inorder to obtain an easily verifiable description of these X-ray emission properties. We haveprimarily focused on searching for luminosity class regularities in the data, and the radialdistributions of several X-ray derived parameters.
HW HM /v ∞ Histograms:
The
HW HM /v ∞ plots show peaks that are well below thewind terminal velocity for all luminosity classes. We have argued that the differences from oneluminosity class to another in regards to the asymmetries in these distributions are due to thedifferences in wind column densities. The fact that a large percentage of HW HM /v ∞ < . V P /v ∞ Histograms:
The V P /v ∞ plots show that the majority of the lines are symmetric,with very little line-shifts. There is some tendency for stars of all luminosity classes to showa small but finite blue-ward asymmetry in their line shift distributions. Such an asymmetrywould occur if the X-rays are primarily arising from the near side of the star. Several ideashave been discussed, ranging from in-falling clumps, the orientation of elongated clumpswith respect to observer’s LOS (line-of-sight), a two-component wind geometry consistingof a polar wind and an equatorial wind which have different wind densities and velocity 33 –structures, to a major decrease in mass loss rates as compared to traditional values. Theactual explanation is not yet clear. Emission Measure Histograms:
The supergiant EM X values show a well defined peak atlog EM X = 54.75 which is due to the fact that these stars all have similar ˙ M , v ∞ , and R ∗ .However, this is not the case for the giants and MS stars, and the resultant distributions aremore spread out. In addition, the MS stars show a double peaked distribution in EM X whichis due to the fact that there is a broader range in wind properties along the MS spectralclass. X-ray Source Locations:
Using the He-like f /i line ratios we have derived the stellar windlocation, R fir , of the O, Ne, Mg, Si, and S He-like ion emission. The results clearly emphasizethe N SHIP (near-star-high-ion problem) as evident from the S xv derived R fir . We stressthat these R fir are based on the localized interpretation and a distributed interpretationwould result in a distribution that starts at an even smaller R fir . Our result confirms whathas been shown for individual stars, all OB stars display the same basic distributions withthe He-like O and Ne ions located in the outer wind regions, the He-like Mg and Si ionsat intermediate locations, and the He-like S ions located near the stellar surface. For allsupergiants, the MEG He-like Mg and Si f /i ratios predict a narrow radial region of 3.7 to5.6 R ∗ , and 1.5 to 3.0 R ∗ respectively, whereas the He-like Ne and O f /i ratios predict radiallocations from 6.2 to 13.5 R ∗ . The MEG He-like S f /i predict locations that are essentiallyon the surface. In general, there is good agreement between the MEG and HEG derived R fir , with one exception, the Si xiii results for ζ Ori (see discussion in Sec. 5.1).
X-ray Temperatures:
We think our most interesting results are in regards to the T X radial distributions. We have derived X-ray temperatures ( T HHe ) using the
H/He line ratiotemperature diagnostic. First, we emphasize the T HHe should be considered as an averagetemperature of the H-like and He-like ions (i.e., basically an average of the associated ionpeak T L given in Table 2). Overall our results are consistent with this interpretation, e.g.,by comparing the T L range with the mean values listed in Tables 5 and 6. In general, fora given H/He line pair, the resultant T HHe are found to be essential the same regardlessof the luminosity class. These results can provide valuable information regarding the shockformation processes that are actually operating in OB stellar winds. However, there aresome notable differences. The silicon mean T HHe for all luminosity classes are at the lowerend of the T L range with a larger spread in T HHe as compared to the other H-He line pairs.The spread in T HHe suggests that the mechanism producing these higher temperatures maybe dependent on the individual stellar characteristics and probably related to resonance linescattering as discussed in the Appendix. The three stars that have their silicon T HHe closerto the upper T L limit are the two Cygnus OB2 stars and the known peculiar star, θ Ori C. 34 –As to whether these Cygnus OB2 stars are similar to θ Ori C remains to be determined.Ideally, one would like to have a more complete collection of sulfur T HHe to explore the highertemperature behavior, but the data do not allow reasonable signal-to-noise extractions.
The Correlation Between R fir and R τ =1 : Since the initial detailed studies of O super-giants (e.g., Waldron & Cassinelli 2001; Cassinelli et al. 2001), the basic idea that the R fir are correlated with R τ =1 has continually surfaced as a reasonable observational result. Totest this correlation we have examined the luminosity class dependence. Our results showthat this correlation is clearly evident in the supergiants. But, the data from the giants andMS stars indicate that the X-ray emission arises primarily from radial locations above their R τ =1 surfaces. We suggest two possible explanations, either the giants and MS stars havelarger mass loss rates, or their number of distributed wind shocks are significantly reduced ascompared to those in supergiant winds (see discussion in Sec. 5.1). However, what is clearlyemerging from our results is that for all luminosity classes, there are very few observed X-raysources where R fir is less than R τ =1 . This supports our basic interpretation of this correla-tion. One can only see those X-rays that are capable of escaping the wind, and since the lineemission is proportional to n e , one is likely seeing the peak of the contribution function asdeep in the wind as possible. If the mass loss rates of these stars are indeed much smallerthan previously thought, one would have expected to see an uncorrelated scatter plot, i.e.,we should also be seeing a scattering of X-ray emission from regions where R fir < R τ =1 . Wedo not see any plausible explanation as to why such a correlation should hold in a highlyporous or clumped wind since the X-ray continuum absorption is determined by the “cool“stellar wind opacity (as determined by bound-free transitions) which is linearly dependenton the density in the X-ray energy range. Hence, a reduced wind density or clumped windstructure would predict R τ =1 values much lower than those adopted in our study. In addi-tion, this correlation implies that we can now predict a particular He-like f /i ratio by simplycalculating the expected R τ =1 . We therefore choose to present this as a challenge to the ideathat the ˙ M values are so much lower, and perhaps also a problem for a clumped wind. Radial Distribution of
HW HM and V P : Since we know the radial locations of theHe-like f ir emitting ions we can explore the radial dependence of the He-like X-ray lineproperties. Almost all line
HW HM are found to be less than the radial ambient windvelocity as expected from all shock model descriptions, but there is no apparent correlationbetween
HW HM and the ambient wind velocity. However, several deeply embedded sourceshave
HW HM that are significantly greater than the radial ambient wind velocity whichimplies a new interesting problem, the lines from deep in the flow are too broad!
There isno obvious radial dependence of V P where the majority of observed V P /v ∞ remain between ± . V P is an important problem that must be addressed before we can fully understand the source 35 –of the X-ray emission from OB stars. Radial Distribution of X-ray Temperatures:
Although in principle we can only addressthe radial locations of temperatures associated with the He-like f ir emission lines, we haveargued that the
H/He line ratios derived T HHe provide reasonable estimates of the averagetemperature associated with the H-like and He-like ions. Waldron (2005) was the first toshow a correlation between the T HHe and R fir for OB supergiants. We have now shownthat this correlation is consistent with both the MEG and HEG results. Our analysis hasverified that the temperature steadily decreases outward through the wind with the highesttemperatures occurring near the stellar surface. For the other luminosity classes, althoughthe tight correlation breaks down, we still find that the highest temperatures only occurnear the stellar surface. Hence, there is no evidence of any high temperature in the outerwind regions which is perhaps surprising since shock velocity jumps could in principle beat their largest at these large radial locations. Our results support two interesting results.1) There appears to be a well defined radial dependent maximum X-ray temperature. Thisradial dependent maximum temperature can be extremely useful in determining basic shockcharacteristics such as, the efficiency of the conversion of shock energy into X-ray emission.2) The magnitude of the derived X-ray temperatures and associated radial distributions aredependent on wind density. In the dense winds of the supergiants we see little evidence oflow T X at low radial locations, whereas, in the lower density winds of the giants and MSstars, a large range in T X exists at lower radii. The implications are clear, X-ray emissionis probably existent throughout these winds at all temperatures provided they are belowthe radial dependent maximum temperature. However, as the wind density gets larger, onecannot detect the low T X at low radii due to wind absorption effects. This is exactly whatone would expect based on our optical depth unity radii arguments. Furthermore, for all OBluminosity classes we find that the radial dependence of the pre-shock velocities relative tothe shock front ( U rel ) evaluated at T HHe , indicate that the majority of all lines at large radialdistances are consistent with the basic shock model interpretation. These results also supportoutward accelerating shock front velocities which are consistent with the decreasing X-raytemperature structure. However, a fundamental problem exists at low radial locations ( < . R ∗ ) where there are several lines, characterized by the high ion stages, with temperaturesthat appear to be too hot, and line profiles that have HW HM that are too broad. As towhether any wind shock mechanism can explain these too hot, and too broad X-ray emissionlines, needs to be investigated.Some of the problems discussed here have recently been addressed in repeated analyses ofthe X-ray emission from a few select O-stars such as ζ Pup and ζ Ori using a semi-empiricalshock model description (e.g., Oskinova et al. 2006; Leutenegger et al. 2006; Cohen etal. 2006). Cohen et al. (2006) argues that all emission lines from ζ Ori can be explained 36 –by a shock model description if the X-rays are distributed above 1.5 R ∗ , provided that thewind density is greatly reduced or highly clumped. Cohen et al. further argue that thereis no problem with understanding the X-ray emission from OB stars. However, we see twopotential problems with these conclusions: 1) their modeling efforts assume that everywhere T X = T L regardless of the ion being considered, and as we have shown in Section 5.2, thisis not a good assumption, and more importantly; 2) the X-ray emission from below 2 R ∗ is a notoriously difficult problem due to the line drag effect (Lucy 1984) or strong sourcefunction gradients (Owocki & Puls 1999) that affect the line-driven instability. Hence, weargue that until we have a better understanding of the shock properties below 2 R ∗ , suchconclusions are premature.We have provided a summary of our results and emphasized the critical problems asso-ciated with current interpretations. Our results have verified that essentially all OB X-rayemission lines are un-shifted. We have introduce a new problem associated with the X-raytemperatures and spatial locations which we have labeled as the “near-star high-ion problem“ ( N SHIP ) and we believe this problem is far more critical than the un-shifted line prob-lem. Resolution of this problem will lead to a better understanding of the X-ray productionmechanisms at work in OB stars. It seems that the wind shock model may be responsiblefor the observed X-ray emission in the outer wind regions (although we still must figure outwhy these lines are un-shifted), but we must consider alternatives for the remaining X-rayemission. The un-shifted line problem has been addressed by either lowering the mass lossrates or proposing a clumpy wind. Either approach produces the same desired effect, anoverall reduction in the stellar wind X-ray absorption. This reduction in X-ray absorptionallows for more X-rays to emerge from the far side of the star (the red-ward emission) whichmakes it possible to explain symmetrical line profiles. Although this provides an explanationfor the observed line symmetry, we are then left with a dilemma as to why such a strongcorrelation exist between R fir and R τ =1 (as determined from the traditional mass loss rates)where the premise of this correlation is based on fundamental radiation transfer arguments.With regards to the observed X-ray emission not explainable by standard wind shocks,a continuing possibility is that these deeply embedded X-ray sources are associated withmagnetic fields on or near the stellar surface. It is becoming increasing clear that these starsare theoretically allowed to have surface magnetic structures (e.g., MacGregor & Cassinelli2003; Mullan & MacDonald 2005). In any case, if there is an alternative source of X-rays operating in these stars, it will be an exciting new feature associated with OB stellarastronomy.We would like to thank the anonymous referee for his detailed critique of our manuscriptand several informative suggestions. WLW acknowledges support by award GO2-3027A 37 –issued by the Chandra
X-ray Observatory Center. JPC has been supported in part by awardTM3-4001 issued by the
Chandra
X-ray Observatory Center.
Chandra is operated by theSmithsonian Astrophysical Observatory under NASA contract NAS8-03060.
A. Wind Absorption and Resonance Line Scattering Effects
To examine the possible effects of continuum absorption and escape probability effects,consider the following simple illustration. If H represents the observed H/He ratio and H O represents the intrinsic temperature dependent H/He ratio, then, H = H O ap He ap H exp ( τ He − τ H ) (A1)where τ He and τ H are respectively the X-ray continuum wind absorption optical depths forthe He-like and H-like lines, and p He and p H represent the associated resonance line scattering τ using the approximate escape probability formalism developed by Osterbrock (1974) (a isa constant equal to 0.58). First we examine the effects of continuum absorption only (i.e., p He = p H = 0). Since the OB stellar wind opacities scale roughly as λ , all H-He line pairsobservable in HETGS data are expected to have τ He ≥ τ H if both lines are formed at thesame radial position. Hence, for the case of negligible resonance line scattering, H wouldbe expected to be larger than H O which means that a temperature derived from H willbe greater than the actual value. There is one exception to this scaling. For the oxygenH-He lines, the reverse is expected, i.e., τ H ≥ τ He which would imply that the H derivedtemperature is actually lower than the real value (from Table 2 notice that the σ W of O viii is significantly larger than σ W of O vii ). Now we consider the presence of finite resonanceline scattering. If we again assume that both H-like and He-like lines are formed at the samedensity and temperature, then p He = 2 p H based on atomic physics considerations. Hence,an additional increase in H would also occur for the case of finite resonance line scattering.For example, consider an extreme case where τ He - τ H = 1 and p H = 1 ( p He = 2), then H = 3.7 H O . Now suppose we know that are observing a Si plasma at a temperature of 10MK ( H O = 0 . H = 1.5 (Fig.5). The resultantobserved H-He ratio would predict a temperature ∼
15 MK respectively. However, a morelikely scenario would be τ He - τ H = 0 since it seems that all observed line emissions seem toalways arise from near their respective X-ray continuum optical depth unity radii as shown inFigure 6. For this case, the H would be equal to 1.4 H O and the predicted H-He temperaturewould be ∼
11 MK, much closer to the actual temperature. Hence, we argue that these
H/He derived temperatures provide very good estimates of the actual X-ray temperatures. 38 –
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This preprint was prepared with the AAS L A TEX macros v5.2.
42 –Table 1. Adopted Stellar Parameters and HETGS Data Identification Numbers
Star Spectral HETGS d T eff R ∗ ˙ M v ∞ N WO Type Obs ID kpc K R ⊙ − M ⊙ yr − km s − cm − Supergiants (I, II) ζ Pup O4 If 640 0.43 42400 16.5 2.40 2200 1.98Cyg OB2 No. 9 O5 f 2572 1.82 44700 34.0 12.70 2200 5.10Cyg OB2 No. 8a O5.5 I(f) 2572 1.82 38500 27.9 13.50 2650 5.48 δ Ori A O9.5 II 639 0.50 32900 17.0 1.07 2300 0.82 ζ Ori A O9.7 Ib 610, 1524 0.50 30900 31.0 2.50 2100 1.15 ǫ Ori B0 Ia 3753 0.46 28000 33.7 4.07 1500 2.42
Giants (IV, III)
HD150136 O5 III(f) 2569 1.35 43000 16.0 3.98 3700 2.02 ξ Per O7.5 III(n)(f) 4512 0.40 36000 11.0 0.32 2600 0.33 ι Ori O9 III 599, 2420 0.50 34000 17.8 1.10 2000 0.92 β Cru B0.5 III 2575 0.15 27500 13.0 0.05 1600 0.07
Main Sequence θ Ori C O7 Vp 3, 4 0.55 38000 9.0 0.20 1650 0.40 ζ Oph O9.5 Ve 2571, 4367 0.15 34000 8.0 0.13 1500 0.30 σ Ori O9.5 V 3738 0.50 33000 9.0 0.08 1250 0.21 τ Sco B0 V 638, 2305 0.17 32000 6.2 0.03 2400 0.06Note. — The majority of stellar parameters are taken from Howarth & Prinja (1989) and Lamers & Leitherer (1993), alongwith input from Koch & Hrivnak (1981), Leitherer (1988), Howarth et al. (1993), Cassinelli et al. (1994), and Waldron et al.(2004). Distances are taken from Savage et al. (1977), Shull & Van Steenberg (1985), and Bergh¨ofer et al. (1996).Note. — N WO is the scale factor of the stellar wind column density defined as N WO = ˙ M/ πµ H m H v ∞ R ∗ where µ H and m H are respectively the mean molecular weight and mass of H atom.
43 –Table 2. Lines Used in Analysis, Wind and ISM Cross Sections, and Relevant f /i
Parameters
Ion λ ◦ T L σ W σ ISM λ f − i N C φ C ˚ A MK 10 − cm J = 0, 1, 2 cm − photons s − S xvi · · · · · · · · · S xv (r) 5.039 15.85 0.240 0.247 · · · · · · · · · S xv (i) 5.063, 5,066 12.59 0.242 0.249 · · · · · · · · · S xv (f) 5.102 15.85 0.247 0.255 673.9, 738.2, 756.0 1 . x . x Si xiv · · · · · · · · · Si xiii (r) 6.648 10.00 0.424 0.529 · · · · · · · · · Si xiii (i) 6.685, 6.882 10.00 0.429 0.536 · · · · · · · · · Si xiii (f) 6.740 10.00 0.438 0.496 815.2, 865.2, 878.4 4 . x . x Mg xii · · · · · · · · · Mg xi (r) 9.169 6.31 0.897 1.148 · · · · · · · · · Mg xi (i) 9.228, 9.231 6.31 0.912 1.169 · · · · · · · · · Mg xi (f) 9.314 6.31 0.933 1.196 997.7, 1034.3, 1043.3 6 . x . x Ne x · · · · · · · · · Ne ix (r) 13.447 3.98 2.138 3.021 · · · · · · · · · Ne ix (i) 13.550, 13.553 3.98 2.125 3.082 · · · · · · · · · Ne ix (f) 13.669 3.98 2.186 3.174 1247.8, 1273.2, 1277.7 6 . x . x Fe xvii · · · · · · · · · Fe xvii · · · · · · · · · O viii · · · · · · · · · O vii (r) 21.602 2.00 1.735 8.417 · · · · · · · · · O vii (i) 21.801, 21.804 2.00 1.736 8.631 · · · · · · · · · O vii (f) 22.098 2.00 1.796 8.959 1623.9, 1634.0, 1638.5 3 . x . x N vii · · · · · · · · · Note. — λ ◦ and T L are taken from the APED line list. The λ f − i are the EUV/UV wavelengths neededfor the radiative excitation from the 2 S → P J levels (J = 0, 1, 2). N C and φ C are the critical densityand critical photo-excitation rate. If φ = 0 then N C represents the density required to reduce the f /i ratioby one-half, whereas, if the density is << N C then φ C represents the radiative excitation rate required toreduce the f /i ratio by one-half. Table 3. Observed MEG f /i
Line Ratios and f ir -inferred Radii
Star O VII Ne IX Mg XI Si XIII S XV f/i R fir f/i R fir f/i R fir f/i R fir f/i R fir
Supergiants (I, II) ζ Pup 0 . ± .
02 7 . ± .
29 0 . ± .
05 10 . ± .
81 0 . ± .
03 3 . ± .
20 1 . ± .
11 2 . ± .
21 0 . ± . ≤ . · · · · · · · · · · · · · · · · · · . ± .
15 1 . ± . · · · · · · Cyg OB2 No. 8a · · · · · · . ± .
24 11 . ± .
25 0 . ± .
22 5 . ± .
99 1 . ± .
13 1 . ± .
18 0 . ± . ≤ . δ Ori A 0 . ± .
03 13 . ± . ≤ . ≤ .
01 0 . ± .
19 4 . ± .
69 1 . ± .
42 1 . ± . · · · · · · ζ Ori A 0 . ± .
02 13 . ± .
18 0 . ± .
05 6 . ± .
56 1 . ± .
14 4 . ± .
49 2 . ± . ≥ .
62 0 . ± . ≤ . ǫ Ori 0 . ± .
03 10 . ± .
44 0 . ± .
08 7 . ± .
72 1 . ± .
24 4 . ± .
73 1 . ± .
52 2 . ± . · · · · · · Giants (IV, III)
HD150136 · · · · · · . ± .
04 5 . ± .
02 0 . ± .
06 4 . ± .
37 1 . ± .
17 2 . ± .
37 2 . ± . ≥ . ξ Per < . < . ± .
03 4 . ± .
74 0 . ± .
05 2 . ± .
28 2 . ± . ≥ . · · · · · · ι Ori 0 . ± .
02 8 . ± .
14 0 . ± .
19 11 . ± .
13 0 . ± .
17 4 . ± .
67 1 . ± .
49 2 . ± . · · · · · · β Cru ≤ . ≤ · · · · · · . ± .
17 1 . ± .
55 1 . ± . ≥ . · · · · · · Main Sequence . ± .
12 31 . ± .
03 0 . ± .
02 2 . ± .
06 0 . ± .
17 5 . ± .
92 1 . ± .
37 3 . ± . · · · · · · HD206267 ≤ . ≤ .
51 0 . ± .
19 12 . ± .
94 0 . ± .
12 3 . ± .
76 0 . ± . ≤ . · · · · · ·
15 Mon 0 . ± .
05 13 . ± . ≤ . ≤ .
15 0 . ± .
24 2 . ± .
59 1 . ± . ≥ . · · · · · · θ Ori C · · · · · · . ± .
08 7 . ± .
31 0 . ± .
03 1 . ± .
21 1 . ± .
16 3 . ± .
49 1 . ± .
30 1 . ± . ζ Oph 0 .
00 1 . ≤ . ≤ .
12 0 . ± .
06 2 . ± .
28 1 . ± .
29 1 . ± .
38 0 . ± . ≤ . σ Ori 0 .
00 1 .
00 0 . ± .
05 4 . ± . ≤ . ≤ .
04 0 . ± . ≤ . · · · · · · τ Sco 0 .
00 1 . ≤ . ≤ .
32 0 . ± .
05 2 . ± .
20 2 . ± . ≥ .
35 1 . ± . ≥ . Table 4. Observed HEG f /i
Line Ratios and f ir -inferred Radii
Star Ne IX Mg XI Si XIII S XV f/i R fir f/i R fir f/i R fir f/i R fir
Supergiants (I, II) ζ Pup 0 . ± .
05 6 . ± .
16 0 . ± .
06 3 . ± .
39 0 . ± .
16 2 . ± .
28 1 . ± . ≤ . · · · · · · ≤ . ≤ . ≤ . ≤ . · · · · · · Cyg OB2 No. 8a ≤ . ≤ .
33 0 . ± .
34 6 . ± .
58 1 . ± .
20 2 . ± .
33 0 . ± . ≤ . δ Ori A · · · · · · . ± .
47 4 . ± .
77 2 . ± . ≥ . · · · · · · ζ Ori A 0 . ± .
10 6 . ± .
20 0 . ± .
18 3 . ± .
60 1 . ± . ≤ . ≤ . ≤ . ǫ Ori 0 . ± .
12 5 . ± .
21 2 . ± .
64 11 . ± .
94 3 . ± . ≥ . · · · · · · Giants (IV, III)
HD150136 0 . ± .
13 7 . ± .
82 0 . ± .
08 3 . ± .
51 1 . ± .
27 2 . ± . · · · · · · ξ Per · · · · · · . ± .
10 2 . ± .
50 0 . ± . ≤ . · · · · · · ι Ori 0 . ± .
43 9 . ± .
38 0 . ± .
20 4 . ± . ≤ . ≤ . · · · · · · β Cru · · · · · · · · · · · · · · · · · · · · · · · ·
Main Sequence ≤ . ≤ .
85 0 . ± .
22 4 . ± . · · · · · · · · · · · · HD206267 · · · · · · · · · · · · · · · · · · · · · · · ·
15 Mon ≤ . ≤ .
20 0 . ± .
42 5 . ± . · · · · · · · · · · · · θ Ori C ≤ . ≤ .
20 0 . ± .
10 3 . ± .
52 1 . ± .
14 1 . ± .
21 0 . ± . ≤ . ζ Oph 0 . ± .
11 5 . ± .
87 0 . ± .
10 2 . ± .
49 1 . ± .
49 1 . ± . · · · · · · σ Ori 0 . ± .
15 4 . ± . · · · · · · · · · · · · · · · · · · τ Sco 0 . ± .
03 2 . ± .
98 0 . ± .
10 2 . ± .
41 1 . ± .
34 1 . ± . · · · · · · Table 5. Observed MEG
H/He
Line Ratios and Derived T HHe
Star Oxygen Neon Magnesium Silicon Sulfur
H/He T
HHe
H/He T
HHe
H/He T
HHe
H/He T
HHe
H/He T
HHe T L range · · · · · · · · · · · · · · · Supergiants (I, II) ζ Pup 1 . ± .
20 2 . ± .
10 0 . ± .
05 3 . ± .
06 0 . ± .
03 6 . ± .
12 0 . ± .
02 7 . ± . · · · · · · Cyg OB2 No. 9 · · · · · · · · · · · · . ± .
92 12 . ± .
53 1 . ± .
30 13 . ± . · · · · · · Cyg OB2 No. 8a · · · · · · · · · · · · . ± .
15 8 . ± .
38 1 . ± .
09 13 . ± .
42 1 . ± .
38 23 . ± . δ Ori A 1 . ± .
13 2 . ± .
07 0 . ± .
09 3 . ± .
11 0 . ± .
05 5 . ± .
24 0 . ± .
14 10 . ± . · · · · · · ζ Ori A 1 . ± .
07 2 . ± .
04 0 . ± .
04 3 . ± .
07 0 . ± .
04 5 . ± .
18 0 . ± .
05 8 . ± . · · · · · · ǫ Ori 1 . ± .
10 2 . ± .
06 0 . ± .
05 3 . ± .
09 0 . ± .
03 5 . ± .
19 0 . ± .
02 5 . ± . · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . · · · . ± . Giants (IV, III)
HD150136 · · · · · · . ± .
18 4 . ± .
15 0 . ± .
04 6 . ± .
14 0 . ± .
06 10 . ± .
36 0 . ± .
25 17 . ± . ξ Per 2 . ± .
43 3 . ± .
17 0 . ± .
09 3 . ± .
11 0 . ± .
03 4 . ± .
17 0 . ± .
04 6 . ± . · · · · · · ι Ori 1 . ± .
13 2 . ± .
08 0 . ± .
03 2 . ± .
08 0 . ± .
08 5 . ± .
35 0 . ± .
20 11 . ± . · · · · · · β Cru 1 . ± .
18 2 . ± .
11 0 . ± .
09 3 . ± . · · · · · · · · · · · · · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . · · · . ± . Main Sequence . ± .
55 3 . ± .
22 0 . ± .
05 3 . ± .
10 0 . ± .
05 5 . ± .
24 0 . ± .
05 7 . ± . · · · · · · HD206267 · · · · · · . ± .
27 4 . ± .
26 0 . ± .
08 5 . ± .
43 0 . ± .
08 7 . ± . · · · · · ·
15 Mon 0 . ± .
11 2 . ± .
08 0 . ± .
04 2 . ± .
14 0 . ± .
05 4 . ± . · · · · · · · · · · · · θ Ori C · · · · · · . ± .
25 5 . ± .
21 2 . ± .
18 10 . ± .
35 1 . ± .
09 15 . ± .
31 1 . ± .
16 22 . ± . ζ Oph 1 . ± .
28 2 . ± .
14 1 . ± .
14 4 . ± .
13 0 . ± .
08 6 . ± .
28 0 . ± .
08 9 . ± . · · · · · · σ Ori 1 . ± .
32 2 . ± .
16 0 . ± .
12 3 . ± .
17 0 . ± .
03 2 . ± . · · · · · · · · · · · · τ Sco 3 . ± .
49 3 . ± .
17 1 . ± .
12 4 . ± .
10 0 . ± .
07 7 . ± .
19 0 . ± .
06 10 . ± .
35 0 . ± .
26 18 . ± . T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . · · · . ± . H/He ratios are ISM corrected and T HHe are the derived X-ray temperatures in MK. The results for θ Ori C are not included in the mean T HHe . Table 6. Observed HEG
H/He
Line Ratios and Derived T HHe
Star Neon Magnesium Silicon Sulfur
H/He T
HHe
H/He T
HHe
H/He T
HHe
H/He T
HHe T L range · · · · · · · · · · · · Supergiants (I, II) ζ Pup 0 . ± .
09 3 . ± .
12 0 . ± .
04 5 . ± .
18 0 . ± .
03 6 . ± . · · · · · · Cyg OB2 No. 9 · · · · · · · · · · · · · · · · · · · · · · · ·
Cyg OB2 No. 8a · · · · · · . ± .
24 8 . ± .
60 1 . ± .
16 13 . ± .
69 0 . ± .
27 18 . ± . δ Ori A 0 . ± .
06 2 . ± .
19 1 . ± .
33 7 . ± .
87 0 . ± .
10 8 . ± . · · · · · · ζ Ori A 0 . ± .
06 3 . ± .
12 0 . ± .
06 5 . ± .
29 0 . ± .
10 8 . ± . · · · · · · ǫ Ori 0 . ± .
09 3 . ± .
16 0 . ± .
07 5 . ± .
37 0 . ± .
05 6 . ± . · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . Giants (IV, III)
HD150136 0 . ± .
16 3 . ± .
27 0 . ± .
08 6 . ± .
28 0 . ± .
09 10 . ± . · · · · · · ξ Per 0 . ± .
09 3 . ± .
19 0 . ± .
07 5 . ± .
39 0 . ± .
10 8 . ± . · · · · · · ι Ori 0 . ± .
23 3 . ± . · · · · · · · · · · · · · · · · · · β Cru · · · · · · · · · · · · · · · · · · · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · · · · Main Sequence . ± .
27 4 . ± .
31 0 . ± .
08 5 . ± .
42 0 . ± .
13 9 . ± . · · · · · · HD206267 · · · · · · · · · · · · · · · · · · · · · · · ·
15 Mon 0 . ± .
11 2 . ± . · · · · · · · · · · · · · · · · · · θ Ori C · · · · · · . ± .
38 12 . ± .
64 1 . ± .
13 15 . ± .
46 1 . ± .
15 19 . ± . ζ Oph 1 . ± .
22 4 . ± .
25 0 . ± .
15 7 . ± .
47 0 . ± .
10 8 . ± . · · · · · · τ Sco 1 . ± .
26 4 . ± .
21 0 . ± .
12 7 . ± .
32 0 . ± .
10 11 . ± .
55 0 . ± .
09 10 . ± . T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . H/He ratios are ISM corrected and T HHe are the derived X-ray temperatures in MK. The results for θ Ori C are not includedin the mean T HHe . Table 7. Observed MEG and HEG G-Ratios
Star Oxygen Neon Magnesium Silicon SulfurMEG HEG MEG HEG MEG HEG MEG HEG MEG HEG
Supergiants (I, II) ζ Pup 1 . ± . · · · . ± .
04 0 . ± .
09 0 . ± .
05 0 . ± .
08 0 . ± .
06 1 . ± .
14 2 . ± .
67 1 . ± . · · · · · · · · · · · · . ± . · · · . ± . · · · · · · · · · Cyg OB2 No. 8a · · · · · · · · · · · · . ± .
06 0 . ± .
15 0 . ± .
08 1 . ± .
18 1 . ± .
46 1 . ± . δ Ori A 0 . ± . · · · . ± .
08 0 . ± .
16 0 . ± .
09 0 . ± .
30 0 . ± .
18 0 . ± .
19 2 . ± .
51 0 . ± . ζ Ori A 0 . ± . · · · . ± .
05 0 . ± .
09 1 . ± .
09 0 . ± .
12 1 . ± .
17 0 . ± .
22 1 . ± . ≤ . ǫ Ori 0 . ± . · · · . ± .
08 0 . ± .
12 0 . ± .
09 0 . ± .
19 1 . ± .
18 0 . ± . · · · · · · Giants (IV, III)
HD150136 · · · · · · . ± .
11 1 . ± .
32 0 . ± .
05 0 . ± .
13 0 . ± .
07 0 . ± .
14 1 . ± .
36 0 . ± . ξ Per 0 . ± . · · · . ± .
08 0 . ± .
21 0 . ± .
09 1 . ± .
23 0 . ± .
13 1 . ± .
34 1 . ± . · · · ι Ori 0 . ± . · · · . ± .
03 0 . ± .
13 0 . ± .
14 3 . ± .
05 1 . ± .
42 1 . ± . · · · · · · β Cru 1 . ± . · · · . ± . · · · . ± . · · · . ± . · · · · · · · · · Main Sequence . ± . · · · . ± .
06 0 . ± .
23 0 . ± .
05 0 . ± .
19 0 . ± .
09 0 . ± . · · · · · · HD206267 0 . ± . · · · . ± . · · · . ± . · · · . ± . · · · · · · · · ·
15 Mon 0 . ± . · · · . ± .
18 0 . ± .
22 0 . ± .
23 2 . ± .
59 0 . ± .
33 0 . ± . · · · · · · θ Ori C 1 . ± . · · · . ± .
08 0 . ± .
34 0 . ± .
07 0 . ± .
15 0 . ± .
04 0 . ± .
08 0 . ± .
10 0 . ± . ζ Oph 0 . ± . · · · . ± .
08 0 . ± .
16 0 . ± .
09 1 . ± .
22 0 . ± .
13 0 . ± .
20 1 . ± . · · · σ Ori 1 . ± . · · · . ± .
18 0 . ± .
22 0 . ± .
23 1 . ± .
53 1 . ± .
59 0 . ± . · · · · · · τ Sco 1 . ± . · · · . ± .
08 0 . ± .
15 0 . ± .
07 0 . ± .
10 1 . ± .
09 1 . ± .
15 1 . ± .
47 0 . ± .
49 –Fig. 1.— The MEG and HEG
HW HM , V P , and EM X histograms for all OB stars illustratingthe percentage of lines within a given parameter bin range. 50 –Fig. 2.— The MEG and HEG HW HM /v ∞ histograms illustrating the luminosity classdependence of the percentage of lines within a given bin range. 51 –Fig. 3.— The MEG and HEG V P /v ∞ histograms illustrating the luminosity class dependenceof the percentage of lines within a given bin range. 52 –Fig. 4.— The MEG and HEG log EM X histograms illustrating the luminosity class depen-dence of the percentage of lines within a given bin range. The EM X have units of cm − . 53 –Fig. 5.— The H/He line ratio dependence on T X for O, Ne, Mg, Si, and S as determinedfrom the APED data. For the He-like lines we only use r -line (see text). For each H-like andHe-like line region all lines within the instrumental wavelength resolution are included indetermining the corresponding total emission at a given temperature. Since the H-like Ne x line ( ∼ xvii ( ∼ xvii and Ne x line emission to the Ne ix r -line emission). For T X > ix r -line is enhanced by other Fe lines producing the drop in the Ne ix H/He ratio. 54 –Fig. 6.— MEG and HEG scatter plots showing the relation between R fir and R τ =1 for allluminosity classes. The error bars for R τ =1 are determined for a X-ray continuum opticaldepth of 1 ± . R τ =1 is the average of these limits. 55 –Fig. 7.— Scatter plots showing the dependence of the MEG derived He-like ion HW HM (top panel) and V P (bottom panel) on the ambient wind velocity, V O , for all OB luminosityclasses. All quantities are determined for each at their R fir value and normalized to theirstar’s v ∞ . The dashed-lines represent special cases when HW HM = V O and V P = − V O (negative means the expected maximum blue-shift velocity). The HW HM range from 0 to0.6 v ∞ with no clear indication of any dependence on V O . The HW HM < v ∞ pose aproblem since they are > the local ambient velocities at these low radial positions. All V P are concentrated about zero velocity with no indication of any large blue-shifted lines. 56 –Fig. 8.— MEG and HEG scatter plots showing the dependence of T X (MK) (determinedfrom H/He line ratios) on the He-like f ir -inferred radii, R fir (determined from He-like f /i line ratios), for all OB luminosity classes. 57 –Fig. 9.— Scatter plot of U rel (pre-shock velocity relative to the shock front) versus V O (theambient wind velocity) for all OB luminosity classes. The values of U rel are determined fromthe MEG derived values of T HHe using eq. 5. Both U rel and V O for each star are evaluatedat their R fir value and normalized to their star’s v ∞ . The dashed-lines represent two specialcases where U rel = V O and U rel = 0 . V O . A detailed discussion is given in Section 6. 58 – A. ERRATUM: “An Extensive Collection of Stellar Wind X-ray SourceRegion Emission Line Parameters, Temperatures, Velocities, and TheirRadial Distributions as Obtained from Chandra Observations of 17 OBStars” (ApJ, 608, 456 [2007] )
The major objective of the paper was to provide a detailed tabulation of the observedHETGS X-ray emission line flux ratios. We presented the MEG and HEG He-like f /i lineratios, the H-like to He-like (
H/He ) line ratios, and the He-like G-ratios. The stellar windspatial locations of the X-ray sources were derived from the f /i ratios and their associatedX-ray temperatures were obtained from the
H/He ratios ( T HHe ). This information was usedto verify the correlations between R fir and R τ =1 (Figure 6) and T HHe and R fir (Figure 8).However, we have realized that some of our tabulated uncertainties for these line ratios wereunderestimated, primarily for those lines with low S/N data. Hence, the primary purposeof this erratum is to provide a tabulation of the corrected line ratios and their uncertainties.The details of our line fitting procedure are discussed in Section 3.3. All uncertaintieswere determined using standard χ statistics (e.g., Bevington 1969). First, we would liketo clarify a statement in Section 3.3 (second paragraph), which states that all parameteruncertainties were determined from 90% confidence regions, but in actuality all uncertaintieswere established using 68% confidence regions. With regards to the main point of thiserratum, we found that our algorithm for determining the χ covariance matrix which isused to determine the uncertainties of the fitting parameters had an indexing error in thecoding logic which produced errors in some of the off-diagonal terms. From our detailedexamination of the code, we found that certain cases were especially vulnerable to thiscoding error, in particular, those cases where the χ normalization ranges were large (i.e.,low S/N data). This code correction has also produced changes in some of the line ratiosand their derived quantities (e.g., R fir and T HHe ).The algorithm has been corrected and the affected Tables (Tables 3, 4, 5, 6, and 7) havebeen updated and re-produced in this erratum. We also corrected a few entries that wereoriginally tabulated incorrectly, and some data were removed as they did not satisfy our
S/N criterion, i.e., the HEG S xv f /i data for ζ Ori, the MEG S xv f /i data for ζ Oph, and theHEG Mg xi and Si xiii f /i data for Cyg OB2 No. 9. As discussed in Section 3.1, we statedthat if a reasonable flux had been established, these results would be used only for estimatingline ratios that provide interesting limits. However, the meaning of a “reasonable“ flux limitwas unclear; the criterion used is that the observed total net counts from all three He-like f ir lines must have a S/N ≥
3. We also need to clarify the significance of blank entries in ourTables. The blanks just indicate that the given line ratio has either an unphysical result thatproduces an anomalously large uncertainty, or did not satisfy our He-like
S/N ≥ i -line flux thatis too small. This occurs primarily in low S/N high energy He-like f ir lines where the effectsof line overlap can lead to a poor determination of the i -line.In addition, we would like to clarify why the relative uncertainties in R fir are typicallysmaller than the corresponding f /i relative uncertainties. As shown in eq. (2) of the paper,for φ/φ C > n e << N C (valid throughout the wind except when extremely close tothe star), the f /i ratio is inversely proportional to the dilution factor, W(r), which changesrapidly for small changes in radius. Hence, dramatic changes in the f /i ratio can occur foronly small changes in radius, which explains the differences seen in the relative uncertainties.Plus, another key point that was not mentioned in the original paper is that there is a lowerlimit on the f /i ratio for the case where n e << N C determined by setting W = 0.5. Thisimplies that any observed f /i ratio below this limit indicates that density effects may beimportant. We are currently investigating this possibility.The format of the data presented in these new tables have been changed slightly: 1)all best-fit line ratios ( f /i and H/He ) and their uncertainties are tabulated, regardless ofthe size of the uncertainty; 2) as before, all derived R fir and T HHe represent an averageof their respective ranges predicted by the f /i and
H/He line ratios, and their associateduncertainties are equal to half the difference in these ranges; 3) for those cases where the f /i uncertainty is > the best-fit f /i ratio, the derived R fir average is determined using a lowerlimit of R fir = R ∗ , and an upper limit on R fir determined by the f /i + uncertainty; 5) forthose cases where the minimum f /i ( f /i - uncertainty) ratio predicts a finite R fir , but theupper limit in the f /i range is at or greater than its asymptotic value (i.e., the low-densityand zero UV flux limit), the upper limit on R fir is undetermined (i.e., R fir → ∞ ), and these R fir values are tabulated as lower limits, and; 5) for those cases where the H/He uncertaintyis > the H/He ratio, upper limits on T HHe are presented.The two key figures of the paper (Figures 6 and 8) have also been re-produced. Inthese figures only data with finite limits on R fir and T HHe are plotted, i.e., data withjust lower limits on R fir and upper limits on T HHe are not shown. For clarity, we alsochose not to display any R fir data where the uncertainty is > R ∗ . The impact of thesechanges in the other figures that depend on the new derived R fir and uncertainties (Figure7 and 9) are found to show minimal differences from the original results. However, wedid find an erroneous high temperature data point in Figure 9 at V O ( R fir ) /v ∞ ≈ U rel ( T HHe ) /v ∞ ≈ .
82 and it should be ignored. This same data point at low R fir was alsoin the original Figure 8 for the giants in both the MEG and HEG plots, and it has beenremoved from the re-produced Figure 8. The source of this data point was traced to thestar γ Vel, originally considered in our analysis, but was dropped from our study due to its 60 –highly unusual X-ray spectra which were deemed inappropriate for this study of “normal”OB stars. We have confirmed that no other data points from γ Vel were present in any ofthe original plots.We would also like to add a comment concerning the importance of obtaining high
S/N
HEG data as illustrated by comparing the S xv MEG and HEG determined f /i ratiosfor θ Ori C. This is a clear example of how line overlap, either caused by the physical linewidth or the energy resolution capabilities of the instrument, can lead to larger uncertainties.Although for this case both the MEG and HEG do have comparable
S/N data, the MEG datahad significant line overlap produced by the best-fit line width and lower energy resolutionof the MEG, whereas, in the HEG data the S xv f ir were resolved leading to a significantreduction in the uncertainty.In general, comparisons of these new derived quantities with the original tabulated datashow that the largest differences are seen in the uncertainties, primarily the uncertaintyresults for O vii and S xv and any other low S/N lines. In addition, there are minorchanges evident in some of the f /i ratios, the
H/He ratios, and the G-ratios. In addition,the newly tabulated data and the reproduced Figures 6 and 8 indicate that the fundamentalresults discussed in the paper have not changed, and these corrections have not altered anyof the conclusions discussed in the paper.We wish to thank Maurice Leutenegger for his communication concerning the specificdetails of our line fitting approach. This inquiry motivated us to re-examine all aspects ofour line fitting algorithms whereupon we found the above mentioned coding mistake in theline flux uncertainties.Bevington, P. R. 1969, “Data Reduction and Error Analysis for the Physical Sciences”,McGraw-Hill, Inc.
Table 3. Observed MEG f /i
Line Ratios and f ir -inferred Radii
Star O VII Ne IX Mg XI Si XIII S XV f/i R fir f/i R fir f/i R fir f/i R fir f/i R fir
Supergiants (I, II) ζ Pup 0 . ± .
11 11 . ± .
21 0 . ± .
13 10 . ± .
15 0 . ± .
05 3 . ± .
30 1 . ± .
17 2 . ± .
33 0 . ± .
62 1 . ± . · · · · · · · · · · · · · · · · · · . ± .
20 1 . ± . · · · · · · Cyg OB2 No. 8a · · · · · · . ± .
29 15 . ± .
32 0 . ± .
65 5 . ± .
20 1 . ± .
22 1 . ± .
31 0 . ± .
34 1 . ± . δ Ori A 0 . ± .
08 12 . ± .
45 0 . ± .
02 1 . ± .
43 0 . ± .
27 4 . ± .
98 1 . ± .
54 1 . ± . · · · · · · ζ Ori A 0 . ± .
03 13 . ± .
60 0 . ± .
10 6 . ± .
16 1 . ± .
18 4 . ± .
64 3 . ± . ≥ .
80 0 . ± .
21 1 . ± . ǫ Ori 0 . ± .
05 10 . ± .
56 0 . ± .
11 7 . ± .
99 1 . ± .
35 4 . ± .
09 1 . ± . ≥ . · · · · · · Giants (IV, III)
HD150136 0 . ± .
10 9 . ± .
80 0 . ± .
10 5 . ± .
96 0 . ± .
16 4 . ± .
90 1 . ± .
40 2 . ± .
91 1 . ± . ≥ . ξ Per 0 . ± .
09 7 . ± .
62 0 . ± .
08 3 . ± .
19 0 . ± .
10 2 . ± .
52 2 . ± . ≥ . · · · · · · ι Ori 0 . ± .
08 7 . ± .
64 0 . ± .
06 12 . ± .
29 0 . ± .
23 4 . ± .
90 1 . ± . ≥ . · · · · · · β Cru 0 . ± .
04 4 . ± .
03 0 . ± .
06 1 . ± .
67 0 . ± .
26 1 . ± .
79 1 . ± . ≥ . · · · · · · Main Sequence . ± .
44 25 . ± .
75 0 . ± .
11 4 . ± .
06 0 . ± .
96 19 . ± .
14 1 . ± . ≥ . · · · · · · HD206267 0 . ± .
56 22 . ± .
12 0 . ± .
45 12 . ± .
08 0 . ± .
21 3 . ± .
38 0 . ± .
32 1 . ± . · · · · · ·
15 Mon 0 . ± .
26 16 . ± .
00 0 . ± .
11 3 . ± .
35 0 . ± .
62 3 . ± .
56 1 . ± . ≥ . · · · · · · θ Ori C 0 . ± .
12 8 . ± .
96 0 . ± .
21 5 . ± .
22 0 . ± .
09 1 . ± .
72 1 . ± .
27 3 . ± .
84 1 . ± .
66 2 . ± . ζ Oph 0 . ± .
16 9 . ± .
25 0 . ± .
05 2 . ± .
12 0 . ± .
08 2 . ± .
38 1 . ± .
34 1 . ± . · · · · · · σ Ori 0 . ± .
03 3 . ± .
92 0 . ± .
06 4 . ± .
19 0 . ± .
10 1 . ± .
29 0 . ± . < . · · · · · · τ Sco 0 . ± .
01 2 . ± .
37 0 . ± .
03 1 . ± .
61 0 . ± .
07 2 . ± .
27 2 . ± . ≥ .
76 1 . ± . ≥ . Table 4. Observed HEG f /i
Line Ratios and f ir -inferred Radii
Star Ne IX Mg XI Si XIII S XV f/i R fir f/i R fir f/i R fir f/i R fir
Supergiants (I, II) ζ Pup 0 . ± .
10 5 . ± .
55 0 . ± .
09 3 . ± .
53 0 . ± .
20 2 . ± .
35 0 . ± .
65 1 . ± . · · · · · · · · · · · · · · · · · · · · · · · · Cyg OB2 No. 8a · · · · · · . ± .
61 5 . ± .
97 1 . ± .
33 2 . ± .
53 0 . ± .
37 1 . ± . δ Ori A 0 . ± .
22 3 . ± .
52 0 . ± .
93 4 . ± .
64 2 . ± . ≥ . · · · · · · ζ Ori A 0 . ± .
17 6 . ± .
12 0 . ± .
24 3 . ± .
82 1 . ± . ≥ . · · · · · · ǫ Ori 0 . ± .
25 5 . ± .
80 2 . ± .
84 15 . ± . · · · · · · · · · · · · Giants (IV, III)
HD150136 0 . ± .
60 9 . ± .
77 0 . ± .
12 3 . ± .
77 1 . ± .
58 2 . ± . · · · · · · ξ Per 0 . ± .
09 2 . ± .
58 0 . ± .
16 2 . ± .
78 0 . ± .
26 1 . ± . · · · · · · ι Ori 0 . ± .
94 22 . ± .
84 0 . ± .
33 4 . ± .
30 2 . ± . ≥ . · · · · · · β Cru 0 . ± .
53 4 . ± .
70 0 . ± .
54 2 . ± . · · · · · · · · · · · · Main Sequence . ± .
50 7 . ± .
40 0 . ± .
41 4 . ± . · · · · · · · · · · · · HD206267 · · · · · · . ± .
00 7 . ± .
52 1 . ± . ≥ . · · · · · ·
15 Mon 0 . ± .
39 5 . ± .
83 0 . ± .
94 6 . ± . · · · · · · · · · · · · θ Ori C 0 . ± .
14 3 . ± .
31 0 . ± .
20 3 . ± .
01 1 . ± .
19 1 . ± .
28 0 . ± .
25 1 . ± . ζ Oph 0 . ± .
33 5 . ± .
75 0 . ± .
14 2 . ± .
68 1 . ± .
57 1 . ± . · · · · · · σ Ori 0 . ± .
43 5 . ± .
80 0 . ± .
12 5 . ± . · · · · · · · · · · · · τ Sco 0 . ± .
09 2 . ± .
59 0 . ± .
13 2 . ± .
56 1 . ± .
37 1 . ± . · · · · · · Table 5. Observed MEG
H/He
Line Ratios and Derived T HHe
Star Oxygen Neon Magnesium Silicon Sulfur
H/He T
HHe
H/He T
HHe
H/He T
HHe
H/He T
HHe
H/He T
HHe T L range · · · · · · · · · · · · · · · Supergiants (I, II) ζ Pup 1 . ± .
27 2 . ± .
13 0 . ± .
10 3 . ± .
12 0 . ± .
05 5 . ± .
20 0 . ± .
03 7 . ± .
42 0 . ± . < · · · · · · · · · · · · . ± .
53 7 . ± .
61 1 . ± .
33 12 . ± . · · · · · · Cyg OB2 No. 8a · · · · · · · · · · · · . ± .
22 7 . ± .
63 0 . ± .
12 12 . ± .
57 2 . ± .
44 26 . ± . δ Ori A 1 . ± .
13 2 . ± .
07 0 . ± .
13 3 . ± .
17 0 . ± .
07 5 . ± .
31 0 . ± .
18 10 . ± . · · · · · · ζ Ori A 0 . ± .
06 2 . ± .
05 0 . ± .
06 3 . ± .
09 0 . ± .
05 5 . ± .
23 0 . ± .
07 7 . ± .
70 1 . ± . < ǫ Ori 1 . ± .
09 2 . ± .
07 0 . ± .
07 3 . ± .
10 0 . ± .
04 4 . ± .
25 0 . ± . < . . ± . < T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . · · · . ± . Giants (IV, III)
HD150136 1 . ± .
06 2 . ± .
51 1 . ± .
24 4 . ± .
22 0 . ± .
08 6 . ± .
34 0 . ± .
09 10 . ± .
52 1 . ± . < ξ Per 1 . ± .
36 2 . ± .
18 0 . ± .
11 3 . ± .
16 0 . ± .
05 4 . ± .
34 0 . ± .
09 7 . ± . · · · · · · ι Ori 1 . ± .
16 2 . ± .
08 0 . ± .
13 2 . ± .
29 0 . ± .
10 5 . ± .
48 0 . ± .
32 10 . ± . · · · · · · β Cru 1 . ± .
18 2 . ± .
11 0 . ± .
10 3 . ± .
20 0 . ± . < . · · · · · · · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . · · · · · · Main Sequence . ± .
33 2 . ± .
24 0 . ± .
09 3 . ± .
18 0 . ± .
13 5 . ± .
65 0 . ± .
07 7 . ± . · · · · · · HD206267 0 . ± .
23 1 . ± .
23 0 . ± .
09 2 . ± .
22 0 . ± .
08 4 . ± .
57 0 . ± . < . · · · · · ·
15 Mon 0 . ± .
15 2 . ± .
11 0 . ± .
07 2 . ± .
21 0 . ± . < . . ± . < · · · · · · θ Ori C 3 . ± .
84 3 . ± .
73 2 . ± .
36 5 . ± .
26 2 . ± .
22 10 . ± .
43 1 . ± .
11 15 . ± .
43 1 . ± .
26 22 . ± . ζ Oph 1 . ± .
25 2 . ± .
14 1 . ± .
14 4 . ± .
13 0 . ± .
09 6 . ± .
32 0 . ± .
09 9 . ± .
71 0 . ± . < σ Ori 1 . ± .
32 2 . ± .
16 0 . ± .
12 3 . ± .
17 0 . ± . < . . ± . < · · · · · · τ Sco 3 . ± .
44 3 . ± .
15 1 . ± .
14 4 . ± .
13 0 . ± .
09 7 . ± .
26 0 . ± .
07 10 . ± .
37 0 . ± .
38 18 . ± . T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . · · · . ± . H/He ratios are ISM corrected and T HHe are the derived X-ray temperatures in MK. The results for θ Ori C are not included in the mean T HHe . Table 6. Observed HEG
H/He
Line Ratios and Derived T HHe
Star Neon Magnesium Silicon Sulfur
H/He T
HHe
H/He T
HHe
H/He T
HHe
H/He T
HHe T L range · · · · · · · · · · · · Supergiants (I, II) ζ Pup 1 . ± .
16 4 . ± .
15 0 . ± .
05 5 . ± .
22 0 . ± .
04 6 . ± .
59 0 . ± . < · · · · · · · · · · · · · · · · · · · · · · · · Cyg OB2 No. 8a · · · · · · . ± .
25 7 . ± .
73 0 . ± .
19 12 . ± .
90 0 . ± .
41 17 . ± . δ Ori A 0 . ± .
32 3 . ± .
50 0 . ± .
45 7 . ± .
22 0 . ± .
17 8 . ± .
62 0 . ± . < ζ Ori A 0 . ± .
10 3 . ± .
14 0 . ± .
08 5 . ± .
35 0 . ± .
16 8 . ± . · · · · · · ǫ Ori 0 . ± .
11 3 . ± .
16 0 . ± .
11 5 . ± .
56 0 . ± . < . · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · . ± . Giants (IV, III)
HD150136 0 . ± .
36 3 . ± .
56 0 . ± .
10 6 . ± .
41 0 . ± .
17 10 . ± .
99 0 . ± . < ξ Per 0 . ± .
12 3 . ± .
26 0 . ± .
09 4 . ± .
61 0 . ± . < · · · · · · ι Ori 0 . ± .
30 3 . ± .
40 0 . ± .
53 6 . ± .
91 0 . ± . < · · · · · · β Cru 0 . ± .
12 2 . ± .
38 0 . ± . < . · · · · · · · · · · · · mean T HHe · · · . ± . · · · . ± . · · · . ± . · · · · · · Main Sequence . ± .
34 3 . ± .
45 0 . ± .
27 5 . ± .
33 0 . ± . < · · · · · · HD206267 0 . ± . < . ± . < . . ± . < · · · · · ·
15 Mon 0 . ± . < . . ± . < · · · · · · · · · · · · θ Ori C 2 . ± .
25 5 . ± .
06 2 . ± .
49 11 . ± .
93 1 . ± .
15 15 . ± .
58 1 . ± .
19 19 . ± . ζ Oph 1 . ± .
22 3 . ± .
26 0 . ± .
17 6 . ± .
51 0 . ± .
16 8 . ± . · · · · · · σ Ori 0 . ± .
13 2 . ± .
28 0 . ± . < · · · · · · · · · · · · τ Sco 1 . ± .
31 4 . ± .
28 0 . ± .
14 7 . ± .
40 0 . ± .
11 11 . ± .
58 0 . ± . < T HHe · · · . ± . · · · . ± . · · · . ± . · · · · · · Note. —
H/He ratios are ISM corrected and T HHe are the derived X-ray temperatures in MK. The results for θ Ori C are not includedin the mean T HHe . Table 7. Observed MEG and HEG G-Ratios
Star Oxygen Neon Magnesium Silicon SulfurMEG HEG MEG HEG MEG HEG MEG HEG MEG HEG
Supergiants (I, II) ζ Pup 1 . ± . · · · . ± .
04 0 . ± .
07 0 . ± .
04 0 . ± .
06 0 . ± .
06 1 . ± .
12 0 . ± .
49 1 . ± . · · · · · · · · · · · · . ± . · · · . ± . · · · · · · · · · Cyg OB2 No. 8a · · · · · · · · · · · · . ± .
07 0 . ± .
15 0 . ± .
08 1 . ± .
21 3 . ± .
70 1 . ± . δ Ori A 0 . ± . · · · . ± .
07 0 . ± .
19 0 . ± .
06 0 . ± .
31 0 . ± .
14 0 . ± .
14 2 . ± .
19 0 . ± . ζ Ori A 0 . ± . · · · . ± .
04 0 . ± .
06 0 . ± .
08 0 . ± .
10 1 . ± .
16 1 . ± .
26 2 . ± . · · · ǫ Ori 1 . ± . · · · . ± .
06 0 . ± .
10 0 . ± .
07 0 . ± .
14 1 . ± .
16 0 . ± .
09 1 . ± . · · · Giants (IV, III)
HD150136 1 . ± . · · · . ± .
15 0 . ± .
48 0 . ± .
10 0 . ± .
14 0 . ± .
08 0 . ± .
18 1 . ± .
72 0 . ± . ξ Per 0 . ± . · · · . ± .
08 0 . ± .
18 0 . ± .
12 1 . ± .
21 0 . ± .
14 1 . ± .
99 0 . ± . · · · ι Ori 0 . ± . · · · . ± .
06 0 . ± .
09 0 . ± .
13 3 . ± .
20 1 . ± .
61 1 . ± . · · · · · · β Cru 1 . ± . · · · . ± .
12 0 . ± .
16 1 . ± .
34 3 . ± .
56 1 . ± . · · · · · · · · · Main Sequence . ± . · · · . ± .
08 0 . ± .
27 0 . ± .
09 0 . ± .
16 0 . ± .
12 0 . ± . · · · · · · HD206267 0 . ± . · · · . ± . · · · . ± .
12 2 . ± .
14 0 . ± .
19 3 . ± . · · · · · ·
15 Mon 0 . ± . · · · . ± .
17 0 . ± .
36 0 . ± .
16 3 . ± .
54 0 . ± .
26 0 . ± . · · · · · · θ Ori C 1 . ± . · · · . ± .
07 0 . ± .
37 0 . ± .
06 0 . ± .
15 0 . ± .
04 0 . ± .
07 0 . ± .
10 0 . ± . ζ Oph 0 . ± . · · · . ± .
06 0 . ± .
09 0 . ± .
07 0 . ± .
16 0 . ± .
11 0 . ± .
14 0 . ± . · · · σ Ori 1 . ± . · · · . ± .
14 0 . ± .
14 0 . ± .
18 1 . ± .
44 1 . ± .
56 0 . ± . · · · · · · τ Sco 1 . ± . · · · . ± .
06 0 . ± .
13 0 . ± .
05 0 . ± .
06 0 . ± .
06 1 . ± .
12 1 . ± .
56 0 . ± .