Emma's paper on X-ray profiles, section 5 draft text \section{Discussion} While the empirical line profile model provides good fits to nearly all the lines in all the sample stars, one of the primary results of this study is the overall weakness -- or even absence -- of wind absorption signatures in the Chandra grating spectra of O stars. This has been noted before by various authors examining individual objects, generally via fitting Gaussian profile models (e.g. Miller et al. 2002), but here we have systematically quantified this result using a more physically meaningful line profile model. There are three classes of explanations for the weak wind absorption signatures we measure: (1) the line profile model is missing some crucial physics that masks the actual effects of wind absorption; (2) processes other than embedded wind shocks are contributing to the X-ray line emission and thereby diluting the characteristic shifted and skewed profiles that are the signature of wind absorption; and (3) the actual mass-loss rates of these stars are lower than expected. Examining the trends in \taustar\/ and \Ro\/ shown in Figs.\ 3 and 4, we can identify several stars with extremely low wind optical depths and shock onset radii that deviate from the expectations of the embedded wind shock scenario. These include HD 93250, HD 150136, iota Ori, zeta Oph, and delta Ori. \footnote{Note that we are excluding HD 206267, 15 Mon, and tau CMa from further discussion, due to their very poor data quality, each with only one very weak line that is not potentially subject to resonance scattering.} As we show below, it is likely that nearly all of these stars, and also Cyg OB2 8A, have a significant contribution from colliding wind shocks in their observed X-ray line profiles. The other stars in the sample: 9 Sgr, xi Per, zeta Ori, and epsilon Ori have line profiles that are consistent with the expectations of the embedded wind shock scenario, with $\Ro \approx 1.5$ \Rstar\/ and \taustar\/ values that, while low, are consistent with the expected wavelength trend of the atomic opacity of their winds. The mass-loss rates we derive for these four stars from their ensembles of \taustar\/ values are listed in Tab. 2 and are generally a factor of a few lower than the theoretical values computed by Vink et al. (2000). We summarize the X-ray-derived mass-loss rates for all the stars in the sample (even those for which the derived values cannot be trusted) in Fig. 6, and compare these mass-loss rates to the theoretical values. We also include zeta Pup and HD 93129A in this figure, as the X-ray line profiles of those two O supergiants were analyzed in earlier papers using the same techniques we employ here. We will discuss the results shown in this figure further, below, but first let us consider each star in our sample, with an eye toward differentiating among the three scenarios outlined above. - Individual stars (comments are enclosed in square brackets) \subsection{HD 93250} The Chandra grating spectrum of this early O main sequence star is quite hard and bremsstrahlung dominated, indicating that the spectral hardness is due to high plasma temperatures rather than being a by-product of wind and ISM absorption. The early O supergiant HD 93129A similarly has a hard X-ray spectrum, but in that star, the hardness is due almost entirely to high levels of wind and interstellar absorption (Cohen et al. 2011). HD 93250 was identified as being anomalous in X-rays in the recent Chandra Carina Complex Project (Townsley et al. 2011), with an X-ray luminosity even higher than that of HD 93129A, and a high X-ray temperature derived from low-spectral-resolution Chandra ACIS data (Gagn\'{e} et al. 2011). Those authors suggested that the X-rays in HD 93250 are dominated by colliding wind shocks from interactions with an assumed binary companion having an orbital period greater than 30 days. Soon after the publication of that paper, Sana et al. (2011) announced an interferometric detection of a binary companion at a separation of 1.5 mas, corresponding to 3.5 AU. Thus it seems that the hard and strong X-ray spectrum and the symmetric and unshifted X-ray emission lines can be readily explained in the context of CWS X-ray emission. [ ~ strongest X-ray source in Carina (aside from eta Car) ~ 20% X-ray variability ~ non-thermal radio source (Leitherer et al. 1995) ~ Fe XXV emission at 6.7 keV -- some quite hot (>40 MK) plasma ~ (Sana) period could be as short as a year and still be consistent with non-detection of RV variations ] \subsection{9 Sgr} This star is known to be a spectroscopic binary with a massive companion in an 8 or 9 year orbit (Rauw et al. 2005). The X-ray properties of 9 Sgr were described by Rauw et al. (2002) based on XMM-Newton observations. These authors noted blue-shifted line profiles, based on Gaussian fits, and also a somewhat higher than normal Lx/Lbol ratio and a moderate amount of hot (~20 MK) plasma based on fits to the EPIC spectrum, although only about 1\% of the X-ray emission measure is due to this hot component. A simple CWS model computed by Rauw et al. (2002) shows that the observed X-ray emission levels cannot be explained by colliding wind shocks, and the authors conclude that the X-ray emission is dominated by embedded wind shocks. Presumably the separation of the components and/or their relative wind momenta are not optimal for producing CWS X-ray emission. It is reasonable to assume that while there may be a small amount of contamination from CWS X-rays, the line profiles we measure in the Chandra grating spectrum are dominated by the EWS mechanism, and therefore the mass-loss rate we derive from the profile fitting is indeed a good approximation to the true mass-loss rate. We note, also, that according to the radial velocity curve shown in Rauw et al. (2005) the Chandra grating spectrum we analyze in this paper was taken during a phase of the orbit when the primary's radial velocity was close to zero. \subsection{HD 150136} A well-known spectroscopic binary, with a period of only 2.662 days (Niemela & Gamen 2005), the HD 150136 system has previously been studied in the X-ray using the same data we reanalyze here (Skinner et al. 2005). Those authors find a very high X-ray luminosity but a soft spectrum with broad X-ray emission lines. They also detect some short period X-ray variability that they tentatively attribute to an occultation effect. Although colliding wind binaries with strong X-ray emission are generally thought to produce hard X-ray emission, it has recently been shown that many massive O+O binaries have relatively soft emission and modest X-ray luminosities, especially if their orbital periods are short (Gagne et al. 2011; Gagne et al. 2012 -- note this is the Quebec proceedings, which Marc hasn't yet posted to astro-ph). We discuss physics behind this in more detail below. [Should this - the previous two sentences - even be discussed here at all?] And in any case, this star's X-ray emission stands out from the other giants and supergiants in the X-ray spectral morphology study of Walborn, Nichols, & Waldron (2009) by virtue of its high H-like/He-like silicon line ratio, indicating the presence of some hotter plasma. We conclude that although a few of the X-ray emission lines measured in this star's spectrum have non-zero \taustar\/ values, overall the lines are too heavily contaminated by X-rays from colliding wind shocks to be used as a reliable mass-loss rate indicator. \subsection{Cyg OB2 8A} With phase-locked X-ray variability, a high Lx/Lbol, and significant plasma with temperatures above 20 MK (de Becker et al. 2006), Cyg OB2 8A has X-ray properties expected from colliding wind shocks. It is a spectroscopic binary with a 21 day period in an eccentric orbit, and a semi-major axis of 0.3 AU. The small number of short-wavelength lines we are able to fit are not terribly inconsistent with the expectations of embedded wind shocks, although the inferred mass-loss rate is roughly an order of magnitude lower than the theoretically expected value. However, because they are only present at short wavelengths, where the wind opacity is low, they do not provide very much leverage on the mass-loss rate, and are generally consistent with $\taustar = 0$. We included this star in our sample because of prior analysis of the same Chandra grating data in the context of embedded wind shocks (Waldron et al. 2004), but given the thorough analysis by de Becker et al. (2006), we must conclude that the X-rays are dominated by colliding wind shocks, and the profile fits we present here do not provide information about embedded wind shocks or the wind mass-loss rate. \subsection{xi Per} A runaway star without a close binary companion and constant radial velocities (Sota et al. 2008), xi Per should not have any binary colliding wind shock emission contaminating the X-ray emission lines we analyze. It does, however, show significant UV and Halpha variability, at least some of which is rotationally-modulated (de Jong et al. 2001). Thus the assumptions of spherical symmetry and a wind that is smooth on large scales is violated to some extent. Still, the X-ray line profiles should provide a relatively reliable mass-loss rate. The \taustar\/ values we find are significantly larger than zero and are consistent with the expected wavelength trend. The mass-loss rate we derive is roughly a factor of five below the theoretic value from Vink et al. (2000). \subsection{iota Ori} Of all the stars in the sample, iota Ori shows the least amount of line asymmetry and blue shift, with all seven lines and line complexes we analyze having \taustar\/ values consistent with zero. Taken at face value, the derived mass-loss rate is three orders of magnitude below the theoretical value. The derived \Ro\/ values are also unusual, being consistently higher than 1.5 \Rstar. The star is in a multiple system, with the closest component a spectroscopic binary in a highly eccentric, 29 day period (Bagnuolo et al. 2001). Although there are no definitive signatures of CWS X-ray emission (such as orbital modulation of the X-rays), it is very likely that the quite broad but symmetric emission lines we have measured are from colliding, rather than embedded, wind shocks. \subsection{zeta Oph} This star also has a nearly complete lack of wind absorption signatures in its line profiles, as shown in Fig. 3. And its lines are narrower than expected in the EWS scenario, as shown by the low \Ro\/ values in Fig. 4. Unlike the other stars in the sample that have X-ray profiles that are difficult to understand in the context of embedded wind shocks, zeta Ori does not have a binary companion likely to produce colliding wind shock X-rays. It is, however, a very rapid rotator ($v\sin{i} = 351$ km s$^{-1}$ (Conti \& Ebbets 1977)), goes through H-alpha emission episodes that qualify it as an Oe star (Barker \& Brown 1974), and has an equatorially concentrated wind (Massa 1995). The wind's deviation from spherical symmetry could explain the relatively symmetric and narrow X-ray emission lines, most likely through alterations to the line-of-sight velocity distribution of the emitting plasma in the wind. Detailed modeling, which is beyond the scope of this paper, would be required to place constraints on the degree of wind absorption in the X-ray lines. \subsection{$\delta$ Ori} With a quite small amount of wind attenuation evident in its line profiles and narrower than expected lines, the results from delta Ori are also suspect, although there are some emission lines with non-zero taustar values in its Chandra spectrum. This star is a member of a multiple system that includes an eclipsing, spectroscopic binary companion with an orbital period of 5.7 days. The companion is an early B star, and an earlier analysis of these same Chandra data indicated that colliding wind shocks were not likely to be strong enough to account for the X-ray luminosity of roughly $10^{32}$ ergs s^{-1}$ (Miller et al. 2002). Given the uncertainty in the companion's wind properties as well as general uncertainties in the CWS model's X-ray emission predictions, it seems quite likely that a significant fraction, if not all, of the observed X-ray line emission arises in the wind-wind interaction zone between the late O star and its early B companion. \subsection{$\zeta$ Ori} Significant wind absorption signatures are seen in the X-ray profiles of $\zeta$ Ori, which has the highest signal-to-noise Chandra spectrum of any of the stars in our sample. The expected wavelength trend is seen in the taustar results, and the fitted Ro values are consistent with 1.5 \Rstar, expected in the embedded wind shock scenario. While it is possible that there could be some contamination from CWS X-ray emission, the binary companion of $\zeta$ Ori is two magnitudes fainter than the primary and is at a separation of about 10 AU, making strong CWS emission an unlikely scenario (Hummel et al. 2000; Rivinius et al. 2011). \subsection{$\epsilon$ Ori} The only B star in our sample, $\epsilon$ Ori is a B0Ia MK standard, and given its evolved state and high luminosity, its wind is as strong as many of the O stars in our sample. Nearly all of the X-ray emission lines show wind signatures with taustar values that deviate significantly from zero. It is also the only star in our sample for which eliminating the lines most likely subject to resonance scattering has a material effect on our derived mass-loss rate, increasing it from $2.1 \times 10^{-7}$ \Msunyr\/ to $6.4 \times 10^{-7}$ \Msunyr. Eliminating those lines also significantly improves the fit to the taustar values. And the low wind terminal velocity of $\epsilon$ Ori makes resonance scattering Sobolev optical depths larger, all things being equal. So, we report the higher mass-loss rate in Tab. 2 and show the fit from which that value is derived in Fig. 3. There is no reason to believe that CWS X-ray emission exists in this star's Chandra spectrum. Its only known companion is at 3 \arcmin\/ (Halbedel et al. 1985) and is not seen in the Chandra data, while interferometric observations show no binary companion down to small separations (Richichi et al. 2002). Taking the X-ray profile information we have analyzed here, along with knowledge of the multiplicity and other properties of the sample stars, it seems that at least half of the viable stars in the current sample have some significant contamination of their X-ray profiles from colliding wind shock X-ray emission due to the interaction of their winds with those from binary companions. CWS X-ray emission is generally considered to be harder and stronger than that from embedded wind shocks, but that seems to be the case primarily in systems where both components have very strong winds with relatively closely matched wind momenta. Furthermore, systems with short periods often lack hard X-rays emission and the expected X-ray over-luminosity (Gagne et al. 2012), and thus might not be immediately obvious as CWS-dominated systems based on a snapshot of their X-ray spectral energy distributions. Furthermore, while idealized CWS models predict distinctive X-ray emission line profile shapes (Henley et al. 2003), such shapes are not observed in real systems (e.g.\ Henley et al. 2005), perhaps because of shock instabilities and the associated mixing and large random velocity components of the X-ray emitting plasma (Pittard \& Parkin 2010). Therefore, when a mixture of CWS and EWS X-rays are present, the observed, hybrid line profiles should be relatively symmetric and broad, mimicking pure EWS profiles with little or no absorption. The three earliest O stars in our sample where we suspect CWS X-ray contamination do in fact have X-ray properties that are quite different than normal O stars dominated by EWS X-ray emission. HD 93250, HD 150136, and Cyg OB2 8A are overluminous in the X-ray and/or have unusually hard X-ray emission. All three have O star binary companions with separations likely to lead to enhanced CWS X-ray emission. The later O stars where we suspect binary CWS contamination, $\iota$ Ori and $\delta$ Ori have overall X-ray emission levels and temperatures that are not far out of line with those expected from EWS sources. But they do have close, massive binary companions and X-ray line properties that are inconsistent with a purely EWS origin. It is possible that they are only partially contaminated by CWS emission (perhaps this is the case, too, for HD 150136, where some of the X-ray emission lines do show non-zero taustar values). While the five stars mentioned in the previous paragraph all seem to fall into case (2) enumerated in the opening paragraph of this section -- contamination of the observed X-rays by a process other than the EWS mechanism -- the other object with results difficult to interpret in the EWS framework based on the results of our line profile model fits likely falls into case (1), a breakdown of the assumptions in our simple X-ray line profile model. That object is $\zeta$ Oph, for which there is strong evidence for a non-spherical wind. Because the line profile model we employ assumes spherical symmetry and the resulting geometry and kinematics governs the manifestation of wind attenuation in the line profiles, we cannot interpret the derived taustar values in terms of wind attenuation for this star. The remaining stars in the sample: 9 Sgr, xi Per, zeta Ori, and epsilon Ori have X-ray profiles that are consistent with the expectations of the EWS scenario, with significant wind attenuation evident from the fitted taustar values, which also show the expected wavelength trend of longer-wavelength lines having larger optical depths due to the greater wind opacities at those wavelengths. These stars have fitted Ro values of $\Ro \approx 1.5$ \Rstar, confirming the predictions of LDI simulations of embedded wind shocks (Feldmeier et al. 1997; Runacres and Owocki 2002). We note also that there is no strong evidence for a wavelength trend in the derived Ro values for these stars. For each star, the shock onset radius is consistent with a single value, although there are hints of a positive correlation between Ro and wavelength for $\epsilon$ Ori. Additionally, for each of these four stars, we fit some of the stronger lines with models for which we allowed the wind terminal velocity to be a free parameter. In each case, we find values consistent withe terminal velocities of their bulk, UV absorbing winds. This confirms the predictions of LDI simulations which show that the shocked wind plasma is typically moving at roughly the same speed as the ambient, unshocked wind. [Should we add comments on whether some mild degree of contamination or lack of spherical symmetry could also be affecting the "good" stars in the sample?] [What about comments on systematics related to beta=1 assumption and perhaps also to wind opacity assumptions? And comments on resonance scattering and porosity?] The mass-loss rates we derive from fitting the ensemble of taustar values for each star are listed in Table 2, where we also compare them to theoretical mass-loss rates from Vink et al. (2000). We summarize these results and comparisons in Fig. 6, which graphically compares the theoretical and X-ray profile mass-loss rates. We also include $\zeta$ Pup and HD 93129A in this figure, as we derived mass-loss rates from X-ray profiles for those stars in earlier papers using the same methodology we employ here. We also include the other six sample stars in that figure to show the extent to which they are outliers. While Cyg OB2 8A's X-rays are surely dominated by CWS emission, because the only lines we can analyze are at short wavelengths where the wind opacity is low, the X-ray based mass-loss rate for that star is not extremely low. The stars delta Ori and HD 150136 have X-ray based mass-loss rate determinations only an order of magnitude lower than theoretical predictions, indicating that there could be some contribution to the observed emission lines from EWS X-rays. The X-ray mass-loss rates of HD 93250, iota Ori, and zeta Oph are very low, however, indicating significant wind contamination or non-spherical wind geometry in those objects. Of the four stars in this study with reliable X-ray mass-loss rates and the two from previous studies, we find mass-loss rates that range from being slightly less than theoretical predictions ($\epsilon$ Ori, $\zeta$ Pup, HD 93129A) to about six times less (9 Sgr, $\ksi$ Per, and $\zeta$ Ori). [Should we comment further on the X-ray derived mass-loss rates (e.g. could O star mass-loss rates really be six times lower than Vink?)] [What about comparisons with other diagnostics (and thus insights about clumping and clumping factors)? And comments on the H-alpha profile properties themselves (maybe emphasizing how none of the sample stars really have H-alpha in emission nor is the emission component constant)?] [How about comments/conclusions on the utility of X-ray mass-loss rates diagnostics (there aren't many more stars where this technique can be applied with current instrumentation, but we can provide motivation for future high-resolution X-ray missions, and maybe also make connections to broadband X-ray mass-loss rate diagnostics (i.e. windtabs))?] [Seems like there's interesting results related to the rejected, or suspect, stars (e.g. broad, symmetric lines for some CWS systems; hybrid CWS/EWS spectra) -- should we discuss that more? We've already noted twice that delta Ori and HD 150136 may be hybrid cases.]