We present a new method for using measured X-ray emission line fluxes from O stars to determine the shock-heating rate due to instabilities in their radiation-driven winds. The high densities of these winds means that their embedded shocks quickly co
ol by local radiative emission, while cooling by expansion should be negligible. Ignoring for simplicity any non-radiative mixing or conductive cooling, the method presented here exploits the idea that the cooling post-shock plasma systematically passes through the temperature characteristic of distinct emission lines in the X-ray spectrum. In this way, the observed flux distribution among these X-ray lines can be used to construct the cumulative probability distribution of shock strengths that a typical wind parcel encounters as it advects through the wind. We apply this new method (Gayley 2014) to Chandra grating spectra from five O stars with X-ray emission indicative of embedded wind shocks in effectively single massive stars. Correcting for wind absorption of the X-ray line emission is a crucial component of our analysis, and we use wind optical depth values derived from X-ray line-profile fitting (Cohen et al. 2014) in order to make that correction. The shock-heating rate results we derive for all the stars are quite similar: the average wind mass element passes through roughly one shock that heats it to at least $10^6$ K as it advects through the wind, and the cumulative distribution of shock strengths is a strongly decreasing function of temperature, consistent with a negative power-law of index $n approx 3$, implying a marginal distribution of shock strengths that scales as $T^{-4}$, and with hints of an even steeper decline or cut-off above $10^7$ K.
We quantitatively investigate the extent of wind absorption signatures in the X-ray grating spectra of all non-magnetic, effectively single O stars in the Chandra archive via line profile fitting. Under the usual assumption of a spherically symmetric
wind with embedded shocks, we confirm previous claims that some objects show little or no wind absorption. However, many other objects do show asymmetric and blue shifted line profiles, indicative of wind absorption. For these stars, we are able to derive wind mass-loss rates from the ensemble of line profiles, and find values lower by an average factor of 3 than those predicted by current theoretical models, and consistent with H-alpha if clumping factors of f_cl ~ 20 are assumed. The same profile fitting indicates an onset radius of X-rays typically at r ~ 1.5 R_star, and terminal velocities for the X-ray emitting wind component that are consistent with that of the bulk wind. We explore the likelihood that the stars in the sample that do not show significant wind absorption signatures in their line profiles have at least some X-ray emission that arises from colliding wind shocks with a close binary companion. The one clear exception is zeta Oph, a weak-wind star that appears to simply have a very low mass-loss rate. We also reanalyse the results from the canonical O supergiant zeta Pup, using a solar-metallicity wind opacity model and find Mdot = 1.8 times 10^{-6} M_sun/yr, consistent with recent multi-wavelength determinations.
We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra grating spectra of the early O supergiant Zeta Pup with models that include the effects of porosity in the stellar wind. We explore the effects of porosity due to both sphe
rical and flattened clumps. We find that porosity models with flattened clumps oriented parallel to the photosphere provide poor fits to observed line shapes. However, porosity models with isotropic clumps can provide acceptable fits to observed line shapes, but only if the porosity effect is moderate. We quantify the degeneracy between porosity effects from isotropic clumps and the mass-loss rate inferred from the X-ray line shapes, and we show that only modest increases in the mass-loss rate (<~ 40%) are allowed if moderate porosity effects (h_infinity <~ R_*) are assumed to be important. Large porosity lengths, and thus strong porosity effects, are ruled out regardless of assumptions about clump shape. Thus, X-ray mass-loss rate estimates are relatively insensitive to both optically thin and optically thick clumping. This supports the use of X-ray spectroscopy as a mass-loss rate calibration for bright, nearby O stars.
X-ray satellites since Einstein have empirically established that the X-ray luminosity from single O-stars scales linearly with bolometric luminosity, Lx ~ 10^{-7} Lbol. But straightforward forms of the most favored model, in which X-rays arise from
instability-generated shocks embedded in the stellar wind, predict a steeper scaling, either with mass loss rate Lx ~ Mdot ~ Lbol^{1.7} if the shocks are radiative, or with Lx ~ Mdot^{2} ~ Lbol^{3.4} if they are adiabatic. This paper presents a generalized formalism that bridges these radiative vs. adiabatic limits in terms of the ratio of the shock cooling length to the local radius. Noting that the thin-shell instability of radiative shocks should lead to extensive mixing of hot and cool material, we propose that the associated softening and weakening of the X-ray emission can be parametrized as scaling with the cooling length ratio raised to a power m$, the mixing exponent. For physically reasonable values m ~= 0.4, this leads to an X-ray luminosity Lx ~ Mdot^{0.6} ~ Lbol that matches the empirical scaling. To fit observed X-ray line profiles, we find such radiative-shock-mixing models require the number of shocks to drop sharply above the initial shock onset radius. This in turn implies that the X-ray luminosity should saturate and even decrease for optically thick winds with very high mass-loss rates. In the opposite limit of adiabatic shocks in low-density winds (e.g., from B-stars), the X-ray luminosity should drop steeply with Mdot^2. Future numerical simulation studies will be needed to test the general thin-shell mixing ansatz for X-ray emission.
We present analysis of both the resolved X-ray emission line profiles and the broadband X-ray spectrum of the O2 If* star HD 93129A, measured with the Chandra HETGS. This star is among the earliest and most massive stars in the Galaxy, and provides a
test of the embedded wind shock scenario in a very dense and powerful wind. A major new result is that continuum absorption by the dense wind is the primary cause of the hardness of the observed X-ray spectrum, while intrinsically hard emission from colliding wind shocks contributes less than 10% of the X-ray flux. We find results consistent with the predictions of numerical simulations of the line-driving instability, including line broadening indicating an onset radius of X-ray emission of several tenths Rstar. Helium-like forbidden-to-intercombination line ratios are consistent with this onset radius, and inconsistent with being formed in a wind-collision interface with the stars closest visual companion at a distance of ~100 AU. The broadband X-ray spectrum is fit with a dominant emission temperature of just kT = 0.6 keV along with significant wind absorption. The broadband wind absorption and the line profiles provide two independent measurements of the wind mass-loss rate: Mdot = 5.2_{-1.5}^{+1.8} times 10^{-6} Msun/yr and Mdot = 6.8_{-2.2}^{+2.8} times 10^{-6} Msun/yr, respectively. This is the first consistent modeling of the X-ray line profile shapes and broadband X-ray spectral energy distribution in a massive star, and represents a reduction of a factor of 3 to 4 compared to the standard H-alpha mass-loss rate that assumes a smooth wind.
We fit every emission line in the high-resolution Chandra grating spectrum of zeta Pup with an empirical line profile model that accounts for the effects of Doppler broadening and attenuation by the bulk wind. For each of sixteen lines or line comple
xes that can be reliably measured, we determine a best-fitting fiducial optical depth, tau_* = kappa*Mdot/4{pi}R_{ast}v_{infty}, and place confidence limits on this parameter. These sixteen lines include seven that have not previously been reported on in the literature. The extended wavelength range of these lines allows us to infer, for the first time, a clear increase in tau_* with line wavelength, as expected from the wavelength increase of bound-free absorption opacity. The small overall values of tau_*, reflected in the rather modest asymmetry in the line profiles, can moreover all be fit simultaneously by simply assuming a moderate mass-loss rate of 3.5 pm 0.3 times 10^{-6} Msun/yr, without any need to invoke porosity effects in the wind. The quoted uncertainty is statistical, but the largest source of uncertainty in the derived mass-loss rate is due to the uncertainty in the elemental abundances of zeta Pup, which affects the continuum opacity of the wind, and which we estimate to be a factor of two. Even so, the mass-loss rate we find is significantly below the most recent smooth-wind H-alpha mass-loss rate determinations for zeta Pup, but is in line with newer determinations that account for small-scale wind clumping. If zeta Pup is representative of other massive stars, these results will have important implications for stellar and galactic evolution.
In order to test the O star wind-shock scenario for X-ray production in less luminous stars with weaker winds, we made a pointed 74 ks observation of the nearby early B giant, beta Cru (B0.5 III), with the Chandra HETGS. We find that the X-ray spectr
um is quite soft, with a dominant thermal component near 3 million K, and that the emission lines are resolved but quite narrow, with half-widths of 150 km/s. The forbidden-to-intercombination line ratios of Ne IX and Mg XI indicate that the hot plasma is distributed in the wind, rather than confined near the photosphere. It is difficult to understand the X-ray data in the context of the standard wind-shock paradigm for OB stars, primarily because of the narrow lines, but also because of the high X-ray production efficiency. A scenario in which the bulk of the outer wind is shock heated is broadly consistent with the data, but not very well motivated theoretically. It is possible that magnetic channeling could explain the X-ray properties, although no field has been detected on beta Cru. We detected periodic variability in the hard (hnu > 1 keV) X-rays, modulated on the known optical period of 4.58 hours, which is the period of the primary beta Cep pulsation mode for this star. We also have detected, for the first time, an apparent companion to beta Cru at a projected separation of 4 arcsec. This companion was likely never seen in optical images because of the presumed very high contrast between it and beta Cru in the optical. However, the brightness contrast in the X-ray is only 3:1, which is consistent with the companion being an X-ray active low-mass pre-main-sequence star. The companions X-ray spectrum is relatively hard and variable, as would be expected from a post T Tauri star.
Young O stars are strong, hard, and variable X-ray sources, properties which strongly affect their circumstellar and galactic environments. After ~1 Myr, these stars settle down to become steady sources of soft X-rays. I use high-resolution X-ray spe
ctroscopy and MHD modeling to show that young O stars like theta-1 Ori C are well explained by the magnetically channeled wind shock scenario. After their magnetic fields dissipate, older O stars produce X-rays via shock heating in their unstable stellar winds. Here too I use X-ray spectroscopy and numerical modeling to confirm this scenario. In addition to elucidating the nature and cause of the O star X-ray emission, modeling of the high-resolution X-ray spectra of O supergiants provides strong evidence that mass-loss rates of these O stars have been overestimated.
By quantitatively fitting simple emission line profile models that include both atomic opacity and porosity to the Chandra X-ray spectrum of $zeta$ Pup, we are able to explore the trade-offs between reduced mass-loss rates and wind porosity. We find
that reducing the mass-loss rate of $zeta$ Pup by roughly a factor of four, to 1.5 times 10^{-6} M_sun/yr, enables simple non-porous wind models to provide good fits to the data. If, on the other hand, we take the literature mass-loss rate of 6 times 10^{-6} M_sun/yr, then to produce X-ray line profiles that fit the data, extreme porosity lengths -- of $h_{infty} approx 3$ Rstar -- are required. Moreover, these porous models do not provide better fits to the data than the non-porous, low optical depth models. Additionally, such huge porosity lengths do not seem realistic in light of 2-D numerical simulations of the wind instability.
