Chandra grating spectroscopy of embedded wind shock X-ray emission from O stars shows low plasma temperatures and significant wind absorption
David H. Cohen, Vanessa Vaughn Parts, Graham M. Doskoch, Jiaming Wang, Véronique Petit, Maurice A. Leutenegger, Marc Gagné
MMon. Not. R. Astron. Soc. , 000–000 (0000) Printed Wednesday 3 rd February, 2021 (MN L A TEX style file v2.2)
Chandra grating spectroscopy of embedded wind shock X-rayemission from O stars shows low plasma temperatures andsignificant wind absorption
David H. Cohen, (cid:63) Vanessa Vaughn Parts, Graham M. Doskoch, Jiaming Wang, V´eronique Petit, Maurice A. Leutenegger, Marc Gagn´e Swarthmore College, Department of Physics and Astronomy, Swarthmore, Pennsylvania 19081, USA University of Delaware, Department of Physics and Astronomy, Newark, Delaware 19716, USA NASA/Goddard Space Flight Center, Code 662, Greenbelt, Maryland 20771, USA West Chester University, Department of Earth and Space Sciences, West Chester, Pennsylvania 19383, USA
Wednesday 3 rd February, 2021
ABSTRACT
We present a uniform analysis of six examples of embedded wind shock (EWS) O star X-raysources observed at high resolution with the
Chandra grating spectrometers. By modelingboth the hot plasma emission and the continuum absorption of the soft X-rays by the cool,partially ionized bulk of the wind we derive the temperature distribution of the shock-heatedplasma and the wind mass-loss rate of each star. We find a similar temperature distributionfor each star’s hot wind plasma, consistent with a power-law differential emission measure, d log EMd log T , with a slope a little steeper than -2, up to temperatures of only about K. Thewind mass-loss rates, which are derived from the broadband X-ray absorption signatures inthe spectra, are consistent with those found from other diagnostics. The most notable con-clusion of this study is that wind absorption is a very important effect, especially at longerwavelengths. More than 90 per cent of the X-rays between 18 and 25 ˚A produced by shocksin the wind of ζ Pup are absorbed, for example. It appears that the empirical trend of X-rayhardness with spectral subtype among O stars is primarily an absorption effect.
Key words: radiative transfer – stars: early-type – stars: massive – stars: mass-loss – stars:winds, outflows – X-rays: stars
The dense and highly supersonic radiation-driven winds of O starsgenerate thermal soft X-ray emission from the cooling of shock-heated plasma. These embedded wind shocks (EWS) are thoughtto be produced by the line deshadowing instability (LDI) intrinsicto radiation-driven flows in which momentum transfer is mediatedby spectral lines (Owocki, Castor & Rybicki 1988; Feldmeier, Puls& Pauldrach 1997; Sundqvist, Owocki & Puls 2018). Although thispicture is widely accepted, it is far from completely tested and char-acterized. There are numerous physically plausible model ingredi-ents that can affect the amount of shock-heated wind plasma and itstemperature distribution. In this paper we present a comprehensiveand uniform analysis of the
Chandra grating spectra of six O starswith EWS X-ray emission in order to characterize the wind plasma (cid:63)
E-mail: [email protected] temperature distribution in ways that will be useful for constrainingshock heating and cooling models.From the observational perspective, a trend of X-ray hard-ness correlated with spectral subtype has been noted in the en-semble of
Chandra grating spectra of O and early B stars, inter-preted as an underlying correlation between X-ray plasma temper-ature and stellar effective temperature or wind strength (Walborn,Nichols & Waldron 2009). Leutenegger et al. 2010 suggested thatwind absorption could account for all or most of the trend andpresented a new, simple but realistic model of X-ray transport inthe EWS scenario. This built on earlier work exploring the broad-band wind absorption of X-rays in OB stars (Waldron 1984; Hillieret al. 1993; Cohen et al. 1996; Owocki & Cohen 1999; Waldron &Cassinelli 2007). Previous analyses of
Chandra grating spectra ofhot stars have found a plasma temperature distribution (Wojdowski& Schulz 2005) or a shock distribution (Zhekov & Palla 2007; Co-hen et al. 2014a) skewed heavily toward lower temperatures, buthave not identified a clear trend with stellar or wind properties. © 0000 RAS a r X i v : . [ a s t r o - ph . H E ] J a n D.Cohen et al.
We aim here to present a uniform analysis of O stars with highquality
Chandra grating spectra whose emission is thought to bedominated by the EWS mechanism, and not by magnetically chan-neled wind shocks (MCWS) or colliding wind shocks (CWS) ina binary system. This analysis enables direct comparison of emis-sion temperature distributions of different stars and includes bothrealistic radiation transport through the wind – accounting for windionization and the spatial distribution of the emitting and absorbingplasma – and non-solar CNO abundances when applicable.Wind absorption and the shocked plasma emission tempera-ture distribution are quite degenerate when it comes to controllingthe overall appearance of broadband X-ray spectra of O stars, withboth higher temperatures and more absorption leading to harderspectra. The earliest O star in the Galaxy, HD 93129A (O2If) hasthe hardest X-ray spectrum in the Walborn, Nichols & Waldron(2009) sample, but detailed, simultaneous broadband modeling ofits medium-resolution zeroth order
Chandra spectrum and its X-ray emission line profiles show that the plasma temperature is notin fact high but rather that there is a significant amount of spec-tral hardening due to wind absorption (Cohen et al. 2011). Indeed,80 per cent of the X-rays emitted in the
Chandra bandpass are ab-sorbed before they can escape the wind of HD 93129A. So windabsorption should be important in interpreting other O stars’ ob-served X-ray spectral energy distributions as well, and it may havea systematic effect on altering derived plasma temperature distri-butions when compared to those derived without accounting forwind absorption. By accurately accounting for absorption, the de-rived emission-measure distributions as a function of temperaturecan be more readily compared to numerical models of embeddedwind shocks.We use the windtabs stellar wind X-ray absorption model(Leutenegger et al. 2010), which treats the radiation transport of adistributed emitter embedded in an absorbing medium and includesa user-specified opacity model for the wind. Both of these featuresrepresent a significant improvement over treating wind absorptionas exponential attenuation by a neutral medium as ISM absorptionmodels do. The windtabs model is implemented in
XSPEC (Dor-man & Arnaud 2001) and runs quickly and so can be used as eas-ily as the standard ISM absorption models. We couple this windabsorption model to a multi-temperature, line-broadened, variableabundance, bvapec thermal spectral emission model (Foster et al.2012). For both conceptual simplicity and to facilitate comparisonsamong stars we approximate the continuous temperature distribu-tion – the differential emission measure (DEM) – as a sum of sixfixed temperatures, the choice of which is based both on the emis-sivity functions of the lines measured with the
Chandra gratingsand on empirical testing with different temperature values. Fittingthis wind emission and absorption model enables us to measure theDEM and also to measure the wind mass-loss rate as well as nitro-gen and oxygen abundances.We describe the sample and data in §2. In §3 we elaborate onthe modeling summarized here in the Introduction. We present ourresults in §4, discuss the implications in §5, and summarize ourmain conclusions in §6.
There are grating spectra of about two dozen O and early B starsin the
Chandra archive. This includes quite a few O+O and O+WRcolliding wind binary sources as well as several objects whose X-ray emission is dominated by magnetically channeled wind shock X-rays. In their comprehensive study of line profiles in
Chandra grating spectra of non-magnetic, non-binary O star X-ray sourcesCohen et al. (2014b) analyzed twelve O stars (also including theB0 supergiant (cid:15)
Ori) that were not known definitively to be eitherCWS or MCWS X-ray sources. X-ray line profile shapes are sensi-tive to absorption but not to emission temperature and this analysisshowed that several of those stars have X-ray spectra that are in-deed contaminated by CWS X-ray emission. We therefore defineour sample as the subset of the Cohen et al. (2014b) sample thatwere determined to be dominated by EWS X-rays. We list theseobjects and the properties we adopt for them in Table 1. Note thatwe order the sample by their winds’ (theoretical) mass-loss rates.The sample does not include HD 93129A, which is also primarilyan EWS X-ray source, because its
Chandra grating spectrum is soabsorbed that only a handful of lines are measurable (Cohen et al.2011) and the six-temperature DEM cannot be well constrained.The
Chandra
High Energy Transmission Grating Spectrom-eter (HETGS) consists of two grating arrays – the medium en-ergy grating (MEG) and the high energy grating (HEG). The HEGhas superior spectral resolution but poorer throughput at the wave-lengths where the sample stars radiate most of their X-rays and sothe MEG spectra are generally more useful in our analysis. We re-trieved the published HETGS data available in the
Chandra archivein late 2017 for all the sample stars and reprocessed all the data us-ing standard CIAO (v. 4.9) scripts. We co-added the negative andpositive first-order MEG spectra, and likewise for the HEG spectra.We then adaptively grouped the resultant co-added spectra, requir-ing at least 40 counts per bin to effectively smooth the continuum.Finally, we grouped the forbidden and intercombination lines to-gether into one large bin for each helium-like complex as the apec
X-ray emission model does not include the effects of photoexci-tation from the metastable upper level of the forbidden line to theupper level of the intercombination line by the photospheric UVradiation. The model does compute the sum of the two line fluxescorrectly. We present an observing log in Table 2 and display theco-added, grouped MEG and HEG spectra, along with the best-fitmodels that we describe in §4, in Figs. 1 and 2.
We model the emission portion of our program stars’ spec-tra with a sum of six bvapec thermal spectral emission com-ponents of fixed temperatures at evenly spaced ( . dex) loga-rithmic intervals from roughly K to × K ( kT = . , . , . , . , . , . keV). This summed model ap-proximates the spectrum from the expected continuous tempera-ture distribution, with the fixed temperatures separated by roughlythe characteristic width of any particular line’s emissivity and thussampling the temperature distribution as finely as is reasonable.We selected the particular temperatures to sample the peaks of theemissivity functions of all important spectral lines, as shown in Fig.3. In the formalism and implementation of apec and similar models,the emissivity has units of photons emitted cm s − and is multi-plied by the emission measure (cm − ) to give the luminosity as afunction of wavelength. The emissivities of individual lines, likethose shown in Fig. 3, are computed from a collisional-radiativenon-LTE ionization and excitation model that gives the relevantlevel populations as a function of temperature.The apec model (Foster et al. 2012) is used for opticallythin plasma in collisional ionization equilibrium, with line emis-sion resulting from collisional excitation followed by radiative de- © 0000 RAS, MNRAS , 000–000 handra O star wind emission and absorption Figure 1.
The co-added and grouped MEG spectra (red, with error bars) for ζ Pup, 9 Sgr, ζ Ori, (cid:15)
Ori, ξ Per, and ζ Oph (top to bottom, ordered by theoreticalwind mass-loss rate). The shaded (blue) histograms are the best-fit models presented in §4. Noticeable emission lines are labeled according to their parent ionsin the top panel. The labels apply to all the spectra.© 0000 RAS, MNRAS , 000–000
D.Cohen et al.
Figure 2.
Same as for Fig. 1, but showing the HEG data. © 0000 RAS, MNRAS , 000–000 handra O star wind emission and absorption Table 1.
Stellar and wind propertiesStar HD T eff R ∗ log L bol v ∞ ˙M theory N ISM (pc) (kK) ( R (cid:12) ) ( L (cid:12) ) (km s − ) ( M (cid:12) yr − ) ( cm − ) ζ Pup 66811 O4 If 332 a b b . b . × − c d d d . × − ζ Ori 37742 O9.7 Ib 226 a d d . d . × − (cid:15) Ori 37128 B0 Ia 363 e e e e . × − ξ Per 24912 O7.5 III 408 c f f . f . × − ζ Oph 149757 O9.5 V c f f . f . × − a van Leeuwen (2007); b Howarth & van Leeuwen (2019); c Gaia Collaboration et al. (2020); d Martins, Schaerer & Hillier (2005); e Searle et al.(2008); f Repolust, Puls & Herrero (2004); all terminal velocities from Haser (1995), and all ISM column densities from Fruscione et al. (1994). For ζ Ophand ξ Per, we made adjustments to the radii from Repolust, Puls & Herrero (2004) based on the Gaia distances. Theoretical mass-loss rates are from therecipe in Vink, de Koter & Lamers (2000). Note that we have adopted parameters for ζ Pup that are based on the
Hipparcos distance, which leads to a smallerradius and luminosity and slightly smaller theoretical mass-loss rate than we have adopted previously (e.g. Cohen et al. 2010, 2014a).
Table 2.
Chandra observing logStar Observation ID Exposure Time Date(ks) ζ Pup 640 67.74 28 Mar 20009 Sgr 5398 101.23 11 May 20056285 44.6 09 Jun 2005 total 145.83 ζ Ori 13460 142.9 29 Nov 201113461 53.0 10 Dec 201114373 46.42 09 Dec 201114374 15.34 06 Dec 201114375 36.06 13 Dec 2011 total 293.72 (cid:15)
Ori 3753 91.65 12 Dec 2003 ξ Per 4512 158.8 22 Mar 2004 ζ Oph 2571 35.41 04 Sep 20024367 48.34 05 Sep 2002 total 83.75 excitation, and continuum emission resulting from bremsstrahlungand recombination. The bvapec variant additionally accounts forDoppler broadening via convolution with a Gaussian, as well asvariable abundances for up to a dozen elements. We report abun-dances on a linear scale with respect to the Solar standard of As-plund et al. (2009).We use vwindtab , a version of windtabs (Leutenegger et al.2010) allowing variable abundances, to model the absorption fromthe colder portion of the wind that composes the vast majority ofits mass. This absorption arises from inner-shell photoionization offew-times-ionized metals and is dominated in much of the
Chan-dra bandpass by the opacity of nitrogen and oxygen. We allowthe abundances of these two elements to be free parameters of the vwindtab model and tie them to the corresponding abundance pa-rameters in the bvapec emission model. We use the tbabs model(Wilms, Allen & McCray 2000) to account for interstellar absorp-tion, using fixed hydrogen column density values taken from theliterature for each star, as listed in Table 1.Because we fix the temperatures of all six emission compo-nents, the only free parameters of the emission model are the sixnormalizations, the N and O abundances, a single line width value,and a Doppler shift value. This last value is an uninteresting param-eter in the context of the present work, encompassing both wave-length calibration errors and space motion of the stars. It also isaffected by the line profile asymmetry caused by wind attenuation
Figure 3.
Emissivities of the lines seen in the sample stars’
Chandra spec-tra, taken from
ATOMDB (Foster et al. 2012) and implemented in bvapec ,and color-coded according to species. Solar abundances are assumed hereand each curve is scaled by its abundance – multiplying any curve by theproduct of the electron density and hydrogen density gives the luminosityof the line. The six fixed temperatures we use in all of the model-fittingshown in this paper are indicated by the vertical dashed lines. Looking ata given vertical line and noting which spectral lines’ emissivity curves itintersects gives a sense of which lines seen in the spectra are controlled bywhich emission model temperature component. (Owocki & Cohen 2001). Because the N and O abundance values inthe vwindtab model are tied to those in the bvapec emission model,the wind absorption model introduces only one new free parameter,the wind’s fiducial mass column density Σ ∗ = ˙M4 πR ∗ v ∞ (g cm − ).By measuring this quantity, we can infer the wind mass-loss rate.We note that we fix the shock onset radius and acceleration pa-rameter of the wind velocity law at R o =1.5 R ∗ and β = 1 in the vwindtab model.For fitting photon-counting Poissonian data the maximumlikelihood estimator is the C statistic (Cash 1979), and so we min-imize that quantity to find the best-fit model for each dataset weanalyze. Testing showed very similar results when using χ withChurazov weighting. Because our DEM and mass-loss rate mea-surements depend more on spectral lines than continua, we adap-tively grouped our spectra, as described in the previous section.Despite the spectral grouping, our model fitting is dominated bysystematic rather than statistical errors – not just due to errors in theatomic and spectral models, which should be no more than about © 0000 RAS, MNRAS , 000–000 D.Cohen et al.
Figure 4.
Emission measure distributions of the six program stars are dis-played as dots representing each bvapec normalization, with line segmentsconnecting them. For ζ Pup and (cid:15)
Ori the emission measure in the hottestcomponent is negligible. For Sgr the hottest component has a significantcontribution from CWS X-rays. For all stars we averaged and combined thetwo lowest temperature components into a single bin.
25 per cent, cumulatively, for the prominent lines we model (Fos-ter et al. 2012; Hitomi Collaboration et al. 2018), but also due tothe approximation of asymmetric line profile shapes as Gaussians– and so we generally do not achieve formally good statistical fits.However, for some of the lower signal-to-noise datasets, the un-weighted reduced χ values are close to unity, indicating formallygood fits to those statistical-noise-dominated spectra. We report onparameter confidence limit estimation on that subset of our samplein the next section.To supplement the formal statistical model fitting, we assessthe fit quality for the strongest spectral emission lines by comparingthe integrated line flux of the model to that of the data. To do this wefit and subtract the continuum of the model and the data, separately,and numerically integrate the flux across the line. We then computeand display the model-to-data line flux ratios. This technique – withresults discussed in §4.3 – provides a good means of exploratorydata analysis and also a visual representation of a model’s successin reproducing the emission line fluxes in each spectrum. We find similar shaped DEMs for all six program stars – shown inFig. 4 – with the emission measure a relatively smooth and stronglydecreasing function of temperature such that the vast majority ofthe X-ray-emitting plasma has a temperature of no more than eightor nine million Kelvin. The stars’ DEMs between two and 11 mil-lion K are relatively well fit by a power law, for which we find anaverage index of n = − . . The overall levels of the DEMs varyfrom star to star, with total emission measures of hot plasma rang-ing from cm − for the star with the weakest wind ( ζ Oph) toabout cm − for the stars with the strongest winds ( ζ Pup and9 Sgr).All the best-fit model parameters, corresponding to the spec-tral models shown in Figs. 1 and 2 and including the normalizationscorresponding to the emission measures plotted in Fig. 4, are listedin Table 3. These parameters include the characteristic wind masscolumn density Σ ∗ (g cm − ), which is the primary adjustable pa-rameter of the wind absorption component of the spectral model. We use these fitted Σ ∗ values, along with the parameters listed inTable 1, to calculate wind mass-loss rates for each star, which welist in Table 4.For all of the sample stars, wind absorption is a significant ef-fect and for some, it dominates the appearances of the spectra. Fig.5 compares the intrinsic (“emitted”) and emergent X-ray spectrumof ζ Pup, computed simply by zeroing out the Σ ∗ parameter in thebest-fit model. More than 95 percent of the photons emitted by theoxygen and nitrogen lines between 18 and 25 ˚A are absorbed bythe wind.For each star except Sgr we find log( L X /L bol ) (the stan-dard definition – emergent L X , not corrected for wind absorption)to be close to the canonical value of -7, with an average of -7.1for the other five stars. For Sgr, we find a value of -6.3, which,although high, is consistent with the value of -6.35 found using
XMM-Newton data by Rauw et al. (2002). We calculate the X-rayfluxes by integrating the best-fit models over the 0.5 to 10 keVrange, correcting for ISM attenuation, and using the distances givenin Table 1 to convert from flux to L X .To compute the X-ray luminosity generated by the shockedwind plasma, which may be more directly useful for evaluatingsimulations than the emergent X-ray luminosity is, we can correctfor the wind attenuation by setting Σ ∗ of the best-fit model to zero.The quantity calculated this way, log( L X /L bol ) emit , is reportedin the last column of Table 4. The uncorrected quantity is the onetypically quoted in the literature, but the corrected quantity pro-vides information about the efficiency of the X-ray production ofthe wind.In the subsections below we elaborate on the emission mea-sures, secondary model parameters including abundances, and onthe model-fitting technique itself. Although the DEMs shown in Fig. 4 are relatively well behaved anddisplay important common properties – moderately smooth distri-butions, consistent with steep decreasing power laws having similarslopes and very little contribution from hot plasma with tempera-tures much above K – there are several results that bear furtherdiscussion.As noted in §3, we use a six-temperature emission model, butfor a number of stars, we find negligible emission in the lowest-temperature component. This can be explained by the strong de-generacy between components 1 and 2 in the effective
Chandra bandpass of 5-25 ˚A. Fig. 3 shows that only one N VI line con-tributes significantly to the lowest-temperature component (compo-nent 1). This line is blended with a stronger N VII line near 25 ˚A,so these
Chandra grating data provide very few independent con-straints on component 1 relative to component 2. For the sake ofuniformity in the logarithmic temperature spacing, we include bothlow-temperature components in our fitting and list the results in Ta-ble 3, despite their relative degeneracy, but average their emissionmeasure levels when we display the results in Fig. 4.We find a negligible normalization for the highest-temperaturecomponent in two of stars and a norm at least an order of mag-nitude less than norm in two more. The emission measure in thehighest temperature component is, for five of the six sample stars(the exception being 9 Sgr), much less than one per cent of the to-tal X-ray emission measure. For Sgr we find a somewhat largernormalization for the highest-temperature bvapec component. Mul-tiple spectral lines became weaker or disappeared when we exper-imented with removing this component from the spectral model © 0000 RAS, MNRAS , 000–000 handra O star wind emission and absorption Table 3.
Best-fit model parametersParameter ζ Pup 9 Sgr ζ Ori (cid:15)
Ori ξ Per ζ Ophnorm +47 − +20 − . +21 − . norm +21 −
166 122 +19 − +13 − norm +4 −
70 30 ± +5 − norm . +2 . − .
15 6.7 ± . +1 − norm . +0 . − . . ± . . +0 . − . norm . +0 . − . . ± . . +0 . − . N abundance 17.8 . +1 . − . . +1 . − . . +0 . − . O abundance 0.81 . +0 . − . . ± .
08 0 . ± . ∗
26 10 +2 − . . . +1 . − . . +1 . − . N H ± -97 -120 -120 +20 − -29 ± line width 790 +100 −
680 600 +30 − +10 − N data
593 190 772 247 227 229 χ kT = . , .187, .318, .540, .919, 1.56 keV) are given in units of · πd cm − , where d is thedistance to the star. N and O abundances are relative to Solar (Asplund et al. 2009). The wind column mass, Σ ∗ , is in units of − g cm − , while theinterstellar column densities are in units of H-atoms cm − and are fixed at the values listed in Table 1. The redshifts and line widths (Gaussian σ ) arefree parameters of the model and are given in km s − . The final three rows list the number of bins in the co-added and grouped MEG and HEG spectra,combined, along with the values of two fits statistics, noting that the C statistic is what is minimized in the fitting; the χ value is provided for illustrativepurposes, to give a sense of the extent to which the fits are formally good, and likely dominated by statistical errors, versus formally bad, and likelydominated by systematics. Table 4.
Mass-loss rates and X-ray luminositiesStar Spectral Theory: Vink et al. 2001 Cohen et al. 2014 This Work log( L X L bol ) log( L X L bol ) emit Type ( M (cid:12) yr − ) ( M (cid:12) yr − ) ( M (cid:12) yr − ) ζ Pup O4 I . × − . × − . × − − . − . . × − . × − . × − − . − . ζ Ori O9.7 I . × − . × − . × − − . − . (cid:15) Ori B0 I . × − . × − . × − − . − . ξ Per O7.5 III . × − . × − . × − − . − . ζ Oph O9 V . × − . × − . × − − . − . Because we use a smaller value for the radius of ζ Pup than was used in Cohen et al. (2014a), the mass-loss rates in the first row are not directly comparable –using the older value for the stellar radius, we find ˙M = 1 . × − M (cid:12) yr − from the wind column density derived in this paper. That value is inagreement with the line-profile-based determination from Cohen et al. (2014a) at the 20 per cent level. The X-ray luminosities in the last column arecorrected both for ISM and wind absorption whereas the values in the second-from-last column are corrected solely for ISM absorption. In both cases theX-ray luminosities are integrated over photon energies from . to keV. and refit the data, indicating that there is some line emission fromplasma with temperatures above K. However, the presence ofthis high-temperature plasma in Sgr can be at least mostly ac-counted for by the contribution from colliding wind shock emis-sion. The star has a binary companion with an eccentric, P = 9 . yr orbit (Rauw et al. 2016). These authors conclude that the CWScontribution is modest but more manifest in the harder X-rays thanin the rest of the spectrum, implying that the hottest component ofthe DEM we derive could be due to the CWS emission. The com-panion, only slightly less luminous than the primary, likely con-tributes about a third of the X-ray emission from its own embeddedwind shocks (Rauw et al. 2016). Even with the contribution fromthe companion, however, the overall amount of EWS emission andthe X-ray to bolometric luminosity ratio is higher for 9 Sgr than forthe other stars in the sample. ζ Pup also has a DEM that is modestly different from our otherprogram stars, with a peak near 4 × K rather than at lower tem-peratures. However, the fluxes of the three strongest lines that con-tribute to the two lowest temperature components (O
VII , O
VIII , and N
VII ) are not as well fit as most other lines, perhaps indicat-ing that the systematic errors on the low-temperature portion of theDEM are bigger than they are elsewhere. Despite this, the DEM wederive for ζ Pup is not very different from that of the other programstars.
The N and O abundances listed in Table 3 are constrained by the NVII Ly α line, the O VIII Ly α and β lines, and the O VII He-likeline complex just shortward of 22 ˚A, as well as the wind opacitycontributed by N and O. While the N/O abundance ratio is super-solar for all six stars, we find only mildly non-solar abundancesfor ζ Oph, (cid:15)
Ori, and ζ Ori, each of which is known from opticaland UV studies to have solar or close-to-solar abundances (Cazorlaet al. 2017; Puebla et al. 2016; Blaz`ere et al. 2015). We found sub-stantially super-solar N and sub-solar O in ξ Per, ζ Pup, and Sgr,of which ξ Per and ζ Pup are both already known to have enhancedN/O abundance ratios (Martins et al. 2017; Kahn et al. 2001), while © 0000 RAS, MNRAS , 000–000
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Figure 5.
Best-fit model spectrum for ζ Pup (black line) compared to the intrinsic emitted spectrum, corrected for wind attenuation (pink line). The strongwavelength-dependence of the wind absorption can easily be seen, as can the very significant degree of wind absorption of the softer X-rays. Both models arecorrected for ISM absorption. Sgr is expected to have only a slightly elevated N abundance(Rauw et al. 2016). This consistency with optical- and UV-derivedabundances suggests that X-ray spectral fitting can provide approx-imate N and O abundance determinations via the relatively simpleprocedure we present in this paper.We find that the neon line fluxes are consistently among thehardest to fit, so we tried fitting models with the Ne abundance afree parameter. For most stars, we found no significant improve-ment to the fit, but for ζ Oph and (cid:15)
Ori, allowing the Ne abundanceto be free yielded significant improvements to the three measurableNe lines and line complexes in the spectrum without worsening thefits to other lines. The best-fit values of 1.78 times solar for ζ Ophand 1.69 times solar for (cid:15)
Ori indicate that these stars may havemildly enhanced Ne abundance. We note that B stars in the Solarneighbourhood have higher than Solar (Asplund et al. 2009) neonabundances (Alexeeva et al. 2020). It is also possible that the errorsin the atomic model in apec are larger for Ne than for other ele-ments or that errors in neon line emissivities’ temperature depen-dence interact with the errors in iron line emissivities. The two setsof lines form at similar temperatures but there is more contributionfrom iron and so it tends to dominate the fits. Excluding either theiron or the neon lines from the fitting does not significantly affectthe derived DEMs.The global line width values listed in Table 3 correlate wellwith the terminal velocity of each star’s wind given in Table 1. ζ Oph has an exceptionally small line width relative to its windterminal velocity as a result of its weak wind, a phenomenon thatis seen in early B stars (Cohen et al. 2008; Cazorla & Naz´e 2017)and late-O main sequence stars (Skinner et al. 2008; Huenemoerderet al. 2012) and is attributed to the large post-shock cooling lengthsin low-density winds. The redshift values listed in Tab. 3 are non-zero due largely to the wind absorption effect that causes asymmet-ric line profiles (Cohen et al. 2014b). These values correlate wellwith the stars’ mass-loss rates and fitted Σ ∗ values, as expected. We conclude this section with a summary of some of the fit qualityand technique-related results. First of all, the fitting in
XSPEC wasfast, with only slightly longer run times than more standard two-temperature apec plus ISM absorption models. The fits were notformally good – they were dominated in each case to one extent oranother by systematic errors. However, the line fluxes in all caseswere well reproduced by the best-fit models. In Fig. 6 it can beseen that nearly all lines for all six program stars had their fluxesfit to better than ± per cent. The figure shows that the excep- tions are a small number of weak, low signal-to-noise lines and insome cases the neon lines (which led us to explore non-solar neonabundances as described above), and some of the iron lines, pri-marily in the spectrum of ζ Pup. Many of the discrepancies in theiron L-shell lines are consistent with known uncertainties in atomicmodels (Brown et al. 2006; Chen et al. 2006). Furthermore, dielec-tronic satellite lines from Na-like Fe XVI are not included in apec ,but are known to be important for plasma with temperatures of afew × K (Beiersdorfer, Hell & Lepson 2018); these lines ap-pear mostly between the 15.01 and 15.26 ˚A lines.To get a sense of the confidence limits on our derived modelparameters – at least those due to statistical errors – we performedstandard error analysis on the three lowest signal-to-noise spectra,for which the best-fit models give a reduced χ value close to unitywhen using standard weighting of the χ statistic in XSPEC . Wecomputed the 68 per cent parameter confidence limits using the ∆ C = 1 criterion (Nousek & Shue 1989) while all the other modelparameters were allowed to be free. Fig. 7 shows quite tight confi-dence limits leading to a relatively narrow band of allowed DEMsfor each star. For these same three stars, we also found relativelytight confidence limits on Σ ∗ , of better than ± per cent of thebest-fit value in each case. Presumably the statistical errors on theDEMs and wind column masses of the other three program starsare similar, although we do not repeat this exercise for those starsbecause their higher signal-to-noise spectra are dominated by sys-tematic errors. Our study has two main results: wind absorption of soft X-rays is astrong effect, accurate modeling of which is crucial for interpretingsoft X-ray spectra of massive stars; and the intrinsic emission fromour program stars appears to follow a universal differential emis-sion measure distribution. This distribution is well approximatedby a power law with a slope of about − . that cuts off around atemperature of K and with an intrinsic flux that scales with themass-loss rate of the wind. This implies that the fundamental shockphysics associated with the LDI is similar for O stars with windsthat span more than two orders of magnitude in mass-loss rate. Theprimary caveat being that the sample of stars is quite small.The DEM results are consistent with an earlier study of X-rayline emission in the same datasets that assessed the shock heatingrate (Cohen et al. 2014a) and found a power-law heating rate witha slope of about − and marginal detection of a cut-off above T ≈ K. The universal DEM we present here is not as steep because © 0000 RAS, MNRAS , 000–000 handra O star wind emission and absorption Figure 6.
Line flux ratios (model/data) for ζ Pup, 9 Sgr, ζ Ori, (cid:15)
Ori, ξ Per, and ζ Oph (upper left to lower right). The plotted model/data ratios are acount-rate-weighted average of the MEG and HEG data (except for longer wavelength lines for which there is negligible HEG data and we include only theMEG data in the fit). The colors of the circles are proportional to the temperature of peak emissivity of the line (see color bars at the right of each panel whichshow the temperature in K), and the area of each circle is proportional to the number of counts in the line. We indicate a range of ± percent with thehorizontal gray dotted lines about a flux ratio of unity, which would represent a perfect fit of the line flux. the integrated radiative cooling of plasma between 1 and 10 millionK is a modestly decreasing function of temperature (see e.g. Fosteret al. (2012)). The temperature distribution – the DEM - is set byheating-cooling equilibrium and if both are power-law functions oftemperature, the power-law DEM has an index that is the differencebetween the indices of the heating and cooling functions.Unfortunately, at present it is difficult to make quantitativecomparisons between theoretical predictions of EWS propertiesand the DEMs we measure. Simulations that treat the radiationtransport in enough detail to include the LDI are too expensive todo in more than one dimension and also include an energy equation (Dessart & Owocki 2005; Sundqvist, Owocki & Puls 2018). There-fore there are no multi-dimensional simulations of LDI-inducedembedded wind shocks that make detailed predictions of the shock-heated plasma DEM or the emergent X-ray spectrum. Further, thereare important parameters of the simulations that seem to control theoverall X-ray luminosity and the shock onset radius in the wind.These include the description of photospheric perturbations thatpropagate into the wind and seed instabilities (Feldmeier, Puls &Pauldrach 1997) and the inclusion of limb darkening (Sundqvist &Owocki 2013) and rotation (Sundqvist, Owocki & Puls 2018). Itis conceivable that these physical ingredients could also affect the © 0000 RAS, MNRAS , 000–000 D.Cohen et al.
Figure 7.
The 68 percent confidence limits on the DEM are shown as gray bands surrounding the best-fit DEMs (blue points and lines) for the three programstars that have statistically good fits according to the unweighted χ values of the best-fit models. Note that unlike in Fig. 4, we do not add together the twolowest-temperature bins but rather show them separately. shock strength distribution and hence the X-ray DEM of a wind.While it is possible that stronger shocks and hotter plasma couldoccur in such simulations, the LDI does seem to have difficultyproducing very strong shocks, and so the DEMs we find in this pa-per are semi-quantitatively consistent with the shock strength dis-tributions seen in simulations (Feldmeier, Puls & Pauldrach 1997;Runacres & Owocki 2002; Dessart & Owocki 2005; Sundqvist,Owocki & Puls 2018). Future computational advances will be re-quired to make direct comparisons between the results we presenthere and numerical simulations of embedded wind shocks.The mass-loss rates we derive from the wind column-densityparameter, Σ ∗ , are a factor of several lower than the traditional the-oretical values (Vink, de Koter & Lamers 2000) and consistent withmulti-wavelength diagnostics that account for modest wind clump-ing (Puls et al. 2006). Our broadband X-ray absorption mass-lossrates are also consistent with the X-ray line-profile-based results(Cohen et al. 2014b), with the exception of the weak-wind star ζ Oph which shows some soft-X-ray attenuation in this study in-dicating a low mass-loss rate but not as low as indicated by X-rayline profile analysis (Cohen et al. 2014b). The effects of wind at-tenuation on the longer-wavelength portions of the sample stars’
Chandra spectra are generally quite significant, even for ζ Oph, asa comparison between the last two columns of Table 4 shows. Tosome extent it seems that the observed L x ∝ L bol trend may in-deed be due to wind absorption as suggested by Owocki & Cohen(1999), given that stars with higher mass-loss rates tend to havehigher log( L X /L bol ) emit but roughly the same log( L X /L bol ) asstars with lower mass-loss rates.Fig. 5 emphasizes not just the magnitude of the X-ray ab-sorption effect but its strong wavelength dependence. The univer-sal shape of the DEMs shown in Fig. 4 suggests that the X-rayspectral hardness trend discovered by Walborn, Nichols & Waldron(2009) is largely or entirely a wind absorption effect. Followingthose authors, we investigate the extent of any residual absorption-independent plasma temperature trend in the six EWS stars in oursample by fitting isothermal bapec models to just the H-like andHe-like neon K α lines to derive a single emission temperature. Thisshould show relatively little bias from absorption effects, since thewavelengths are similar. We repeat the exercise for Mg and Si andshow the results in Fig. 8. Our Ne results agree almost exactly withthose from Walborn, Nichols & Waldron (2009). The X-ray ioniza-tion temperatures we find are essentially the same from star to starfor each element. We tried modeling these temperatures as a linearfunction of photospheric effective temperature and obtained only aweak positive correlation of Ne and Mg with T eff while finding aslightly negative correlation for Si. Notably the two stars with the Figure 8.
The line-ratio based temperatures for Si
XIV / XIII , Mg
XII / XI , andNe X / IX (blue, green, red) are quite constant from star to star. Note that theeffective temperature scale does not map exactly onto the theoretical mass-loss rate ordering of the sample that we use throughout the paper becausethe Orion belt stars are supergiants and have higher mass-loss rates than ξ Per and ζ Oph. strongest winds and highest X-ray luminosities – Sgr and ζ Pup– have X-ray ionization temperatures that are consistent with thoseof the other stars. This further indicates that there is little or no in-trinsic X-ray emission temperature trend with stellar spectral typeor effective temperature or wind mass-loss rate – although a sampleof six stars is admittedly quite small.Perhaps it is not surprising that the temperature distributionof EWS plasma does not scale with the stellar effective temper-ature. Wind properties scale primarily with the luminosity of thestar and shock properties seem much more likely to be affected bythe nature of the perturbations at the base of the wind than by smalldifferences in the stellar effective temperature (Feldmeier, Puls &Pauldrach 1997). By their nature, the reverse shocks formed by theLDI have a strength governed by how anomalously fast the pre-shock wind flow is accelerated above the local ambient velocity.The X-ray spectral analysis technique we present here is sim-ple to use and though in some ways is likely to be less accurate thanthe results of customized multi-wavelength non-LTE modeling ofan individual star’s wind (e.g. Herv´e, Rauw & Naz´e 2013), it con-tains more of the first-order physics than do generic emission andabsorption spectral models. The line flux model-to-data ratio diag- © 0000 RAS, MNRAS , 000–000 handra O star wind emission and absorption nostic (Fig. 6) is useful both for exploratory analysis and to avoidover-interpretation of data. The particular six temperatures we use,with their good sampling of line emissivity functions and spacingof 0.7 dex in temperature produce relatively smooth DEMs, whichare physically plausible given that shock-heated plasma radiates atall temperatures below the initial shock temperature over the timeit takes to cool back down to the ambient wind temperature.In the future, when X-ray spectral missions observe numerousO stars, the model-fitting procedure we have presented here canbe used to easily and consistently extract physically meaningfulparameters from high-quality data sets and likely estimate mass-loss-rates and temperature distributions even from lower-qualitydatasets. It also holds out the promise of providing a complemen-tary means for determining nitrogen and oxygen abundances in Ostars, especially as applied to XMM-Newton
RGS spectra, which,for low ISM column density sources, includes a measurement ofboth important ionization stages of nitrogen, while the
Chandra
HETGS includes only one.
The technique we present here – approximating the continuousDEM with six specific fixed temperatures and using a variableabundance, Gaussian-broadened thermal spectral emission modelin combination with the vwindtab
X-ray transport model for thewind attenuation – is a fast and relatively easy way to derive phys-ically meaningful wind model parameters within a standard fittingpackage like
XSPEC . Applying this technique to six O stars (in-cluding one B0 supergiant) yields several interesting quantitativeresults, centering on the strong effect of soft X-ray wind absorp-tion. (i) We show that for all six stars, more than one-third of theX-rays generated in the
Chandra
HETGS bandpass are absorbedby the wind, and much more than that for the more luminous starswith the higher mass-loss rates. Modeling this strongly wavelength-dependent attenuation is critical for extracting parameters of theshock-heated X-ray emitting component of the wind plasma.(ii) The emission parameters yield differential emission mea-sures for the program stars that are smooth and strongly decreasingfunctions of temperature, having almost no plasma with tempera-tures above K. The emission measure levels are consistent witha scaling proportional to the stars’ mass-loss rates ( Sgr lies some-what above this relationship), as is expected for radiative shocks.The shapes of all the star’s DEMs are quite similar, suggesting auniversal nature to embedded wind shock physics in O stars acrossmore than an order of magnitude in wind mass-loss rate.(iii) In addition to measuring the DEMs, we measure the windmass-loss rates from the attenuation signatures in the spectra andfind values consistent with other recent determinations, includingX-ray line profile based measurements, providing yet more confir-mation that O star wind mass-loss rates are lower than theoreticalpredictions.(iv) We also measure nitrogen and oxygen abundances, findingelevated N/O ratios in several of the stars. And we measure a char-acteristic wind velocity for each star via their X-ray line widths.The technique we have presented here will be useful when fu-ture high-resolution X-ray spectral missions produce large numbersof even intermediate-quality spectra of O stars, as it will enable thestraightforward measurements of DEMs, mass-loss rates, elementalabundances, and wind speeds.
ACKNOWLEDGMENTS
The scientific results in this article are based on data retrieved fromthe
Chandra data archive. Support for this work was provided bythe National Aeronautics and Space Administration through grantAR2-13001A and TM3-14001B to Swarthmore College. VVP, GD,and JW were also supported by the Physics and Astronomy De-partment and the Provost’s Office of Swarthmore College via theVandervelde-Cheung and Eugene M. Lang Summer Research Fel-lowships. MAL acknowledges support from NASA’s AstrophysicsProgram. We also thank the anonymous referee for their helpfulsuggestions.
DATA AVAILABILITY
The X-ray spectral data underlying this article are available inthe Chandra Data Archive at https://cxc.cfa.harvard.edu/cda/ , and are uniquely identified with the observation iden-tifiers (Obs IDs) listed in Table 2.
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