PROBING WOLF–RAYET WINDS: CHANDRA/HETG X-RAY SPECTRA OF WR 6

The lines are well resolved by HETG and are very non-Gaussian. They are fin-shaped, with a sharp blue edge, upward-convex, sloping down to the red. Figure 1 (bottom panel) shows detail for a narrow spectral region and demonstrates the near-vertical blue edge and maximum blueward of the line center. The profiles are very much like those shown in Ignace (2001) or of the profiles from optically thick (in the continuum) winds with a large central cavity (e.g., Owocki & Cohen 2001, see their Figure 2).

For WR winds it is natural to expect line profiles that sample the asymptotic flow because the winds are quite dense such that optical depth unity in photoabsorption of X-ray emission is expected to be at relatively large radii. The analytic solutions of Ignace (2001) were developed for just this case.

We have adopted the analytic form of Ignace (2001) for the line profile, f(w_z), valid in the limit of large optical depth:

$$\begin{eqnarray}&&f({w}_{{\rm{z}}})={f}_{0}{\left[\displaystyle \frac{\sqrt{1-{w}_{{\rm{z}}}{}^{2}}}{\mathrm{arccos}({-w}_{{\rm{z}}})}\right]}^{1+q}\end{eqnarray} \tag{ 1 }$$

where f₀ is a normalization constant and w_z is the dimensionless scaled velocity along the line of sight z, w_z = (c/v_∞)(λ/λ₀ – 1), for a line having rest wavelength λ₀. In this formula the emissivity per volume is assumed to vary as the square of density. However, an additional modification to the emissivity is allowed in the form of r^−q, with q > −1 as outlined in Ignace (2001, see Equation (8) and the associated discussion therein). This q parameter serves to modify the shape of the line profile from a pure density-squared result. Physically, one can think of this accompaniment to the line emissivity as representing perhaps a number of factors, including a volume filling factor to accommodate clumping, or a radius-dependent X-ray temperature distribution to accommodate variations in shock strength. In this sense different q values are to be expected from fits to different lines in contrast to seeking a single value of q that applies to all lines.

As an illustration, a family of model line profiles is shown in Figure 3 for a range of q values. Note that the photoabsorption optical depth is assumed to be large, meaning that X-rays from near the stellar photosphere are strongly absorbed and that the X-ray line profile is formed generally in the vicinity of optical depth unity in photoabsorption, although this depends in detail on the value of q. As seen in Figure 3, the case of q = 0 gives the canonical "fin"-shaped line profile. Positive values of q serve to exacerbate the relative sharpness of the fin; negative values of q reduce to the extreme that q =  − 1 recovers a "flat-top" line profile that is normally associated with the case of zero photoabsorption.

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In using the adopted form of Equation (1) to model line profiles, we have made several assumptions. First, that the X-ray line emission is taken to be well-described by collisional ionization equilibrium in which every collisional excitation is from the ground state and results in a radiative transition with negligible optical depth in the lines. This serves as the basis of the density-squared emissivity. Second, the continuum opacity of the WR 6 wind is very large. In soft X-rays, the large radial optical depth prevents us from seeing down to the acceleration zone, so constant expansion is a reasonable assumption for the visible plasma. In this limit, if we assume that all X-ray emission lines have the same profile, then it means they all sample the same terminal velocity with the same temperature (or same temperature distribution).

To relax the latter assumption, that all lines have a common thermal origin with a similar hot gas filling factor, we allow the exponent, q, to be non-zero. In this way, we can fit individual profiles to explore trends in expansion velocity or shape. For example, the continuum opacity is lower at shorter wavelengths; if it is significantly smaller such that we can see deeper, where conditions may be different, we might expect the shortest wavelength lines to have a different shape from the longer wavelength lines even though all the lines form in the asymptotic terminal speed flow.

We have implemented the model line profile as a parametric fit function, but also as a global intrinsic line profile in the APEC model evaluation (that is, our APEC model, in addition to the usual parameters of temperatures, normalizations, abundances, and Doppler shift, has wind-profile parameters). To determine the profile parameters (since the global plasma model is not necessarily the best model for all features), we independently fit narrow spectral regions containing strong or important lines by adopting the four-temperature model as a starting point and then fit the normalization, relevant elemental abundances (to allow optimization of the line-to-continuum ratios), and—of primary interest—wind parameters q and v_∞. We adopted a line of sight Doppler velocity of 46.2 km s⁻¹, which is the exposure-time weighted mean of the systemic (Firmani et al. 1980) plus line of sight velocities for the three observations that ranged from 34 to 66 km s⁻¹. The differences between the observations are negligible considering the resolution and the line width, though very important to set a priori because the terminal velocity and Doppler shift are degenerate parameters. We take the Doppler velocity as a given and do not fit the line center.

One must be careful to distinguish the line center from a line centroid. A common diagnostic of stellar winds is often referred to as a "blueshifted profile." This is incorrect when referring to the volume-integrated profile: the centroid is blueward of the line center because the wind opacity causes the emergent profile (centered at zero velocity) to be skewed through absorption of locally redshifted wind emission. Here we specifically refer to the theoretical line profiles' centers when we indicate the line position.

In Figure 4, we show observed and model profiles for relatively clean portions of the spectrum to demonstrate the "fin"-shape and relative position of the line center. The models were APEC plasmas fit within the narrow regions as described above.

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For the He-like lines, we also used density as a free parameter to allow the important forbidden (f) to intercombination (i) line flux ratio (R = f/i) to be free; use of density is simply a convenient proxy for consideration of UV photoexcitation from the forbidden-to-intercombination levels (Blumenthal et al. 1972). The density dependence was computed with APEC, then parameterized for use as a line emissivity modifier.⁹ As an alternative, we also fit the He-like lines parametrically using a linear combination of a continuum and line components. This is less physically constrained than the plasma-model approach since, for instance, there is no a priori relation between the forbidden and intercombination line. Uncertainties in this approach tend to be large because the lower limit on the intercombination line can be very small, and the forbidden-to-intercombination ratio arbitrarily large; hence we favor the APEC-based results. The fitted values are given in Table 4.

We show as an example the fit to the Si xiii lines in Figure 5 as well as the decomposition into the component profiles. The lines are well resolved. One discrepancy for Si xiii is a relatively large feature in the residuals, which might mean that the i-component is narrower than the others (all three components shared the same profile parameters in the fit, as shown in Figure 7 and Table 5).

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In Figure 6 we show a broader region of the spectrum along with the same spectral region as observed with RGS (bottom panel pair). This clearly demonstrates the character of the profiles' vertical blue edge and the great advantage of the HETG's higher resolution for determining the profile shape. With RGS, we could determine that the lines are broad, but a near-Gaussian profile was sufficient to fit them.

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From fitting the narrow spectral regions with the APEC-based model including the model line profile of Equation (1), we have determined an error-weighted-mean expansion velocity of 1950 ± 20 km s⁻¹, somewhat larger than the average value of 1700 km s⁻¹ as determined by Hamann et al. (2006) from analysis of the full spectrum, but smaller than the maximum value of 2100–2500 km s⁻¹ as observed among the UV lines in the several hundred archived IUE spectra. Our result is dominated by the best-determined value for Si xiii. A straight mean and standard deviation gives 1880 ± 140 km s⁻¹. The lines are all consistent with a shape parameter of q ≃ −0.2 (Ignace 2001), which is close to zero, the nominal value for density-squared emissivity and uniform expansion (see Equation (1) and Figure 3). We show the determinations for each feature measured in Figure 7, and the values are listed in Table 5.

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To examine the time history of the X-ray emission, we binned count-rate light curves from both the dispersed and zeroth-order events. For dispersed events, we used the program, aglc ¹⁰ which handles the dispersed photon coordinates and CCD exposure frames over multiple CCD chips. We used first-order photons from both HEG and MEG gratings over the range 1.7–17.0 Å. For zeroth-order curves, which involve only one CCD chip, we used the CIAO program, dmextract. Count rates from the dispersed spectrum were slightly higher than from zeroth order. Figure 8 shows the combined zeroth and first order rates for each of the three observations. Table 2 lists the mean count rates per observation and the overall means for dispersed and zeroth orders. Hardness ratios were also computed, but since these showed no trend, we have not included them in the figure.

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Optical photometry was obtained with the Chandra Aspect Camera Assembly (ACA) simultaneously with the X-ray data. This camera has an approximately flat broad-band response between 4000 and 8000 Å. Details of this system as used for studying stellar variability can be found in the "Chandra Variable Guide Star Catalog"¹¹ (VGuide; Nichols et al. 2010). Empirical uncertainties were estimated from the variance in flat portions of VGuide light curves for several stars over a range of magnitudes. The optical light curve, obtained during the Chandra observations, is shown in Figure 8.

The line profiles of WR 6 are indicative of a constant spherical expansion. All the lines in the HETGS range have similar shapes and widths. This implies that the radiation in all lines likely suffers from equally strong wind absorption, and that for each line we see only radiation originating from a flow with similar velocity ranges. In the relatively thin-wind OB stars, there is a strong correlation between the line width and the wavelength. Since the continuum opacity is proportional to wavelength, shorter wavelength lines are formed deeper in the wind where the expansion velocity is smaller. In stars like ζ Oph or δ Ori, there is a trend of a factor of two or more in line widths over the HETGS bandpass (Cassinelli et al. 2001; Nichols et al. 2015). Furthermore, the line shape is strongly affected by material over a broad range of velocities, and in some cases, there is evidence of temperature stratification (Hervé et al. 2013). In Figure 7 we see little or no trend in the line width with wavelength and perhaps a weak trend in the shape. Hence, the evidence is strong that even down to Si and S (5–7 Å, or to 2.5 keV), we are only seeing X-ray emission from large radii. Recall that for no photoabsorption, q = −1 and a flat-topped profile would result. The weak trend in q with wavelength in Figure 7 is consistent with seeing more emitting volume at shorter wavelengths, where the continuum opacity is lower. However, it will take higher sensitivity to determine if this trend is real. It will be very interesting when high-resolution profiles can be obtained in Fe xxv (such as with Astro-H) where we expect to be able to see to below ∼10 R_* to determine whether q is indeed smaller and also to see if the line is narrower since at those radii we expect the wind velocity to be below about 75% of the terminal velocity.

The strong UV radiation emerging from the star affects the observed f/i ratios of He-like ions, which otherwise depend solely on the temperature of the hot plasma. By using the stellar UV field as an input, the observed f/i ratios can be used to trace the formation region of these lines (Gabriel & Jordan 1969; Porquet et al. 2001; Waldron & Cassinelli 2007). A detailed treatment allows one to construct an equation that predicts the f/i line ratio ${\mathcal{R}}$ as a function of the radiative excitation rate ϕ_ν and the electron density n_e (cf. Blumenthal et al. 1972, Equation (1c)). In the case of hot stars, the contribution of n_e is almost always negligible compared to that of ϕ_ν (see, e.g., Shenar et al. 2015). The simplest approach for estimating the formation region would be to assume that the X-ray emitting gas is sharply located at a certain radial layer, which we refer to as the formation radius. It is more likely, however, that the X-rays originate over an extended region. In this case, one can derive the minimal radius where the X-ray emission of the concerned lines is originating, referred to as the onset radius. This involves the integration of the X-ray radiation emanating from a continuous range of radii, a method described by Leutenegger et al. (2006), and here extended to include the effect of K-shell absorption in the cold wind.

To determine the UV excitation rate ϕ_ν and the cold wind opacity κ_ν, we calculated a model for WR 6 using the non-LTE Potsdam Wolf–Rayet (PoWR) code (Hamann & Gräfener 2004) with the parameters listed in Table 4 as input (also shown in Figure 9). The PoWR code solves the non-LTE radiative transfer in a spherically expanding atmosphere simultaneously with the statistical equilibrium equations while accounting for energy conservation. Complex model atoms with hundreds of levels and thousands of transitions are taken into account, along with millions of iron and iron-group lines which are handled using superlevels (Gräfener et al. 2002). The PoWR models account for stellar wind clumping in the standard volume filling factor micro-clumping approach (e.g., Hamann & Koesterke 1998a) or with an approximate correction for wind clumps of arbitrary optical depth (macro-clumping, Oskinova et al. 2007). The X-ray emission and its effects on the ionization structure of the wind are included in the PoWR atmosphere models according to the recipe of Baum et al. (1992). The absorption of the X-ray radiation by the relatively cool (non-X-ray emitting) stellar wind is taken into account as well as its effect on the ionization stratification by the Auger process. The contributions of diffuse emission from the stellar wind and of limb darkening are accounted for and the mean intensity is accurately calculated in the reference frame of the wind. For the He-like lines, the constants R₀ and ϕ_c per ion, which are calculated at a temperature at which the X-ray emission of the ion in question peaks, are adopted from Leutenegger et al. (2006).

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The right panel of Figure 9 graphically summarizes our results for the He-like ions S xv, Si xiii, Mg xi, and Ne ix. The red bars (upper of the pair) depict the derived 90% confidence lower limit formation radius for each He-like ion, assuming a localized formation region. The blue bars (lower of the pair) similarly depict the onset radii, assuming an extended formation region. (These correspond to the lower limits of the R ratios as shown in the left-hand panel of Figure 9; the best fit values yield large, unconstrained upper radii, except for N vi.) At radii within the gray area, the wind is optically thick to X-rays, i.e., τ_λ > 1. Emission is not expected to be seen at radii much below this surface if opacity remains high. At first glance, it seems that the formation regions are very distant from the photosphere, ranging between ≈10 and ≈1000 R_*. However, there also seems to exist a clear correlation between the τ_λ = 1 surface and the formation radii (or onset radii), especially for the S xv and Si xiii ions. The results imply that we see the X-rays emerging from the minimum visible radii, whereas X-rays formed below the τ_λ = 1 surface are absorbed. Therefore, although the obtained formation radii are very large, the results may actually imply that the formation regions of X-rays originating in these ions is much deeper—otherwise, there is no reason to expect a clear correlation between the τ_λ = 1 and the formation radii. These results are also consistent with a formation radius of ≥600 stellar radii from the N vi lines seen with XMM-Newton-RGS (Oskinova et al. 2012).

The same PoWR wind model as used to evaluate He-like line ratios (see Section 4.1) was used to model emission line profiles using the detailed information about the opacity for X-rays in the cool wind of WR 6. The model provides the wind ionization structure and opacity as a function of radius, and hence the wind radial optical depth in the X-ray band. In this model, the ionization structure (and consequently the mass-absorption coefficient) changes drastically with radius. In particular, helium recombines from double to single ionization at about 45 R_*.

It is well established that the winds of WR stars are clumped (e.g., Lépine & Moffat 1999). Therefore, to compute the X-ray emission line profiles, we used a 2.5 D stochastic wind model (see the full description in Oskinova et al. 2004, 2006). For simplicity, we assumed an idealized case of spherical clumps as well as a constant filling factor (i.e., the case of q  =  0 of Equation (1)). The wind opacity and velocity law are provided by PoWR models. These models are determined by the UV/optical spectra and are completely independent of the X-ray spectra. With no additional free parameters, we obtained a line profile fully consistent with our asymptotic solution of Equation (1), which justifies the assumptions made in the analytic profile fits and further supports the fact that X-rays are generated at large radii outside the acceleration zone.

If we were to assume that X-rays were only from wind shocks in the wind acceleration zone—as in O stars—but which in WR 6 occurs at radii where τ ≫ 1, then we would be seeing a very small fraction of the total intrinsic X-ray flux produced—wind models indicate that the optical depth of the wind for X-rays is τ ≥ 10. The emergent X-rays have about 10⁻⁵ of the wind kinetic power ($\frac{1}{2}\dot{M}\;{v}_{\infty }^{2}$). If the X-rays were all produced in the acceleration zone (below ∼30 R_*), then we would need all or more of the mechanical energy to be converted into X-rays to obtain what we see emerging from optical depths >10.

The quantitative models show that plasma responsible for the emergent X-ray line emission is distributed over the large range of radii between ∼30 and 500 R_*. The He-like lines also show rather directly that emission is not coming solely from deep in the wind.

At first glance, it might seem surprising that these winds produce X-rays at much larger radii than seen in winds of single OB stars, as the latter generally form their X-rays not too distantly from the wind acceleration zone where the instability is active (Krtička et al. 2009).

A much denser wind has a higher kinetic energy flux from which to generate X-rays in shocks, and also has locally higher emission measures at all radii. Such a wind also has an overall higher radiative cooling rate as a result of a higher density, so X-ray generation should generally compete more effectively against the adiabatic cooling of expansion. Thus it would be possible for the X-rays from these winds to suffer a kind of "embarrassment of riches," were it not for wind absorption.

Thus we may simply be seeing the effects of how higher density winds shift their emission to regions where the densities are somewhat comparable to observable X-ray generation in the winds of OB stars. It is not obvious that a completely new mechanism is required, although the hardness of the X-rays from WR 6 remains a puzzle, given that the wind velocity is characteristic of OB stars as well. All this suggests that if we are to look for a unified X-ray generation mechanism in OB and W–R stars, it will need to be an extended emission process that only exhibits its harder and larger-radius components if the densities are high enough for radiative cooling to compete successfully against expansion cooling at such radii.

It has only recently become known (mainly due to the absence of adequate data) that the intrinsic X-ray emission arising in the winds of single hot stars is subject to slow variability of low amplitude of typically a few percent. This can be seen in the O-type stars ζ Oph, ζ Pup, ξ Per, ζ Ori, and λ Cep (Oskinova et al. 2001; Nazé et al. 2013; Massa et al. 2014; Pollock & Guainazzi 2014; Rauw et al. 2015). The 2010 XMM-Newton campaign on WR 6 (Ignace et al. 2013) revealed similar behavior of somewhat larger amplitude over days and weeks, adding to the historical record in which the first set of short X-ray observations that were made with the Einstein Observatory between 1979 and 1981 varied in count rate by about a factor of three (Pollock 1987). The long Chandra observation of WR 6 is ideal for investigating X-ray variability. While the overall count rate changed by about 13% over the observing period, none of the X-ray fluctuations seen appear to be obviously related to the 3.7650 day period of rather variable character seen at longer wavelengths.

During the 2013 Chandra campaign, judged by the overall count rates in the dispersed and zeroth-order data, the mean intensity of WR 6 increased by 9% between May and August and by a further 4% over the three-day gap between the two final Chandra observations. These were similar in scope to the variations seen in the XMM-Newton campaign 3 years earlier. With the high count rates detected with the XMM-Newton EPIC instruments, which exceed those of the Chandra instruments by factors of more than 30, it was possible to study in detail shorter-term variability within an observation to show the smooth changes that occurred over several hours. We have performed a similar analysis with the Chandra data.

The X-ray light curves are shown in Figure 8 and display the same type of slow evolution detected with higher precision with XMM-Newton. At its Chandra maximum at the beginning of the final Chandra observation, WR 6 was at the same brightness within the errors as the maximum observed at the beginning of the XMM-Newton campaign in 2010. We did not detect any chromatic component to the variability of the high-resolution spectra; we formed harness ratio light curves using the first order dispersed photons between the 1.7–8.0 Å "hard" and 8.0–17.0 Å "soft" bands, with null results for variability within the uncertainties. We also searched for spectral and line variability in somewhat coarser bins than the light curves (28 ks) with null results within the statistics.

Hence, we can only conclude that the overall flux is changing slowly, but cannot say whether it is due to changes in X-ray temperature or volume, or if it is due to variable absorption.

The optical light curve is also shown in Figure 8 and presents some of the most densely sampled optical photometry ever obtained of this or any Wolf–Rayet star. WR 6 was rapidly variable in the optical during the X-ray observations including a rapid decline at the beginning of the second observation and coherent structures lasting for many hours up to as long as a day. The X-ray variability was much slower and of higher amplitude and bears no apparent relation to the optical light curve.

Our spectral model adopted abundances from Asplund et al. (2009) with CNO modified according to the WN-type and WR 6 optical and UV models computed with PoWR (Hamann et al. 2006). Abundances of a few species with strong lines were left free in the fit to compensate for systematic effects due to using only four discrete temperature components and a simplified absorption model (see Appendix A.1 for details). With this model, we found that we had very large residuals for the H- and He-like lines of sodium (Na xi, 10.021, 10.027 Å; Na x, 10.990 (resonance line), 11.066, 11.074 (intercombination lines), and 11.186 (forbidden line)). Re-fitting the relative abundances and model normalization in this spectral region resulted in an overabundance of Na relative to the abundances of Asplund et al. (2009) by a factor of 6.9 (5.4–8.7, 90% confidence region). We cannot explain this phenomenon through blends of Fe lines since the many blends of Fe xviii are formed at about the same temperatures as other lines in the region, Ne ix being the coolest having maximum emissivity near 4 MK and Mg xii the hottest at 10 MK. We searched for features not in the atomic database by looking at spectra of sharp-lined coronal sources. While there are features observed near 10 Å with no identification in AtomDB, they are weak and not at the right wavelength to mimic Na xi. It would also be an unlikely coincidence to have anomalies precisely at both the H- and He-like Na wavelengths. Hence, we conclude that the lines are due to Na and that the abundance is enhanced. Figure 10 shows our best fit to the region along with spectra without Na and without both Na and Fe.

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Identification of Na in stellar X-ray spectra is rare, but not unprecedented. Sanz-Forcada et al. (2003) measured a flux for Na xi in Chandra/HETG spectra of AB Dor, a young rapidly rotating, coronally active K-star, but did not identify the line. Garci´a-Alvarez et al. (2005) identified Na xi in the same AB Dor spectrum and also in a Chandra/LETGS spectrum of V471 Tau, a rapidly rotating K2 dwarf and white dwarf binary. Huenemoerder et al. (2013) measured Na xi in the RS CVn stars σ Gem and HR 1099, two late-type coronally active binaries with among the highest fluences collected with the CXO/HETGS. Coronally active stars have an advantage in detecting these weak features in that the lines are generally unresolved; the stars are rapidly rotating, but velocities are still below the instrumental resolution and hence have relatively high contrast. Abundances in these cases were near solar to within a factor of two.

We do not know of any instances, however, of Na detection in other hot star wind spectra. Here the broadening of the lines makes such a detection difficult, especially without a deep exposure or enhanced abundances.

We interpret the enhancement of Na as due to nuclear processing—the CNO cycle can produce Na through the Ne–Na cycle (Cavanna et al. 2014). The amount depends upon the core temperature and somewhat poorly known nuclear rates (Izzard et al. 2007), but enhancement factors of 6–10 have been predicted by models (Woosley et al. 1995; Chieffi et al. 1998). The abundances of Ne, Na, Mg, and Al are all related and strongly dependent upon the details of nuclear processing, ultimately determined by the initial mass of the evolving star. The soft X-ray spectrum may be the best place to determine these abundances in WR stars since the emission mechanisms are relatively simple—no radiative transfer calculations are required in an optically thin plasma. Features of Ne and Mg are strong in the WR 6 spectrum, and Na and Al lines are present. These certainly warrant more careful, detailed analysis to determine their relative abundances since they may provide unique constraints on evolutionary states.

Oskinova et al. (2012) detected Fe K flourescence in XMM-Newton spectra. In our spectra for dispersed or zeroth order, we see no obvious Fe K emission next to the strong Fe xxv emission lines (Figure 2). The fit to the zeroth-order spectrum, however, is slightly improved if we introduce an additional component at 1.94 Å. The fluorescent flux we obtained (3.5 × 10⁻⁷ photons cm⁻² s⁻¹, with a 1σ confidence region of 1.7–5.4 × 10⁻⁷ photons cm⁻² s⁻¹), is consistent with that measured by Oskinova et al. (2012) in XMM-Newton spectra, so the HETGS spectrum is not inconsistent with the prior observations.

The presence of Fe K fluorescence requires hard photons, roughly 7–20 keV, incident on cold Fe (see Drake et al. 2008, for example). Hence, we not only have temperatures high enough to produce line emission far out in the wind, there may also be a significant source of fairly hard continuum emission. Our plasma model gives a 7.0–20 keV flux of 6.5 × 10⁻⁶ erg cm⁻² s⁻¹, implying a yield factor of about 0.05.

Fe K fluorescence is interesting because it can provide constraints on geometry since the amount of fluorescence depends on the hard spectrum and on the relative locations of the cold Fe and hard photons. As such, it has the potential to provide another diagnostic of the distribution of hot and cold matter within the wind. The current data, however, are not sufficient to pursue this in detail.

Figure 12 shows the result of a simultaneous fit of the WR 6 spectra over all instruments. The model was a four-temperature AtomDB (Smith et al. 2001; Foster et al. 2012) plasma with free temperatures and normalizations and a few free abundances (Ne, Mg, Si, S, and Fe). The model also included a wind-absorption component (using wind abundances); absorption from ionized C, N, and O (C V, N IV, O IV, O V; though the oxygen and carbon abundances are very small); and foreground interstellar absorption. The AtomDB model was from a custom run of APEC to provide a model without hydrogen since this is a WN star and otherwise using abundances (scaled to mass fractions for a low-H atmosphere) of Asplund et al. (2009) with modifications to CNO for a WN star. The same reduced H and CNO abundances were used for the local (neutral and ionized wind) absorption models.

The model parameters are given in Tables 6–8. The foreground absorption value adopted was that used by Oskinova et al. (2012), but which they did not quote. It is less than half that used by Skinner et al. (2002a), but this is reasonable since they only used a single absorption component for both foreground and intrinsic components, whereas we include an intrinsic wind-absorption component. The absorption components are shown in Figure 11.

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The fit function is effectively defined as

$$\begin{eqnarray*}&&{\mathtt{Aped}}\_{\mathtt{4}}\ast {\mathtt{windabs}}\ast {\mathtt{vphabs}}\_{\mathtt{noh}}\ast {\mathtt{phabs}}\end{eqnarray*}$$

where the components implemented in ISIS¹² are as follows:

• Aped_4 is a four-component APEC model using our customized low-H database,
• windabs is a wrapper on the XSPEC edge model to provide local wind absorption by ionized CNO ions (though only N iv is significant),
• vphabs_noh is a wrapper on the XSPEC to adjust the model to remove hydrogen for the wind neutral absorption function, and
• phabs is the unmodified XSPEC interstellar absorption function.

In our APEC model, we also used some modifiers to implement photoexcitation of He-like lines¹³ and to apply the line profile model to all lines.

Abundances for Na and Al were done by fitting localized regions, as described in Section 4.5 for Na.

A photon flux spectrum is an approximation to the intrinsic flux and is obtained by dividing the counts spectrum by the model counts for a constant flux spectrum. It incorporates contributions to each wavelength bin from neighboring bins as dictated by the response matrix. Hence, the calibration is better for near-diagonal matrices, such as those for grating spectrometers. Flux calibration can be useful for visualization of a model-independent source intrinsic flux. It does not entail any deconvolution, so the instrumental blur is still included in the photon flux spectrum. If lines are resolved, however, the photon flux will approximate the unconvolved model. We do not use photon flux spectra for quantitative analysis, but use forward-folding methods to properly account for spectral features in the response.

See the ISIS manual for a detailed definition, http://space.mit.edu/cxc/isis/manual.html, in particular Equations (7.4)–(7.8).