Constraints on porosity and mass loss in O-star winds from modeling of X-ray emission line profile shapes

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 spherical 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.Comment: 20 pages, 20 figures. Accepted by Ap

X-ray, UV and optical analysis of supergiants: ϵ\epsilon Ori

We present a multi-wavelength (X-ray to optical) analysis, based on non-local thermodynamic equilibrium photospheric+wind models, of the B0 Ia-supergiant: $\epsilon$~Ori. The aim is to test the consistency of physical parameters, such as the mass-loss rate and CNO abundances, derived from different spectral bands. The derived mass-loss rate is $\dot{M}/\sqrt{f_\infty}\sim$1.6$\times$10$^{-6}$ M$_\odot$ yr$^{-1}$ where $f_\infty$ is the volume filling factor. However, the S IV $\lambda\lambda$1062,1073 profiles are too strong in the models; to fit the observed profiles it is necessary to use $f_\infty<$0.01. This value is a factor of 5 to 10 lower than inferred from other diagnostics, and implies $\dot{M} \lesssim1 \times 10^{-7}$ M$_\odot$ yr$^{-1}$. The discrepancy could be related to porosity-vorosity effects or a problem with the ionization of sulfur in the wind. To fit the UV profiles of N V and O VI it was necessary to include emission from an interclump medium with a density contrast ($\rho_{cl}/\rho_{ICM}$) of $\sim$100. X-ray emission in H-He like and Fe L lines was modeled using four plasma components located within the wind. We derive plasma temperatures from $1 \times 10^{6}$ to $7\times 10^{6}$ K, with lower temperatures starting in the outer regions (R$_0\sim$3-6 R$_*$), and a hot component starting closer to the star (R$_0\lesssim$2.9 R$_*$). From X-ray line profiles we infer $\dot{M} <\, 4.9\times10^{-7}$ M$_\odot$ yr$^{-1}$. The X-ray spectrum ($\geq$0.1 kev) yields an X-ray luminosity $L_{\rm X}\sim 2.0\times10^{-7} L_{\rm bol}$, consistent with the superion line profiles. X-ray abundances are in agreement with those derived from the UV and optical analysis: $\epsilon$ Ori is slightly enhanced in nitrogen and depleted in carbon and oxygen, evidence for CNO processed material.Comment: 33 pages, 25 figures. Accepted for publication in MNRA

Atomic Physics of Shocked Plasma in Winds of Massive Stars

High resolution diffraction grating spectra of X-ray emission from massive stars obtained with Chandra and XMM-Newton have revolutionized our understanding of their powerful, radiation-driven winds. Emission line shapes and line ratios provide diagnostics on a number of key wind parameters. Modeling of resolved emission line velocity profiles allows us to derive independent constraints on stellar mass-loss rates, leading to downward revisions of a factor of a few from previous measurements. Line ratios in He-like ions strongly constrain the spatial distribution of Xray emitting plasma, confirming the expectations of radiation hydrodynamic simulations that X-ray emission begins moderately close to the stellar surface and extends throughout the wind. Some outstanding questions remain, including the possibility of large optical depths in resonance lines, which is hinted at by differences in line shapes of resonance and intercombination lines from the same ion. Resonance scattering leads to nontrivial radiative transfer effects, and modeling it allows us to place constraints on shock size, density, and velocity structur

X-ray spectral diagnostics of activity in massive stars

X-rays give direct evidence of instabilities, time-variable structure, and shock heating in the winds of O stars. The observed broad X-ray emission lines provide information about the kinematics of shock-heated wind plasma, enabling us to test wind-shock models. And their shapes provide information about wind absorption, and thus about the wind mass-loss rates. Mass-loss rates determined from X-ray line profiles are not sensitive to density-squared clumping effects, and indicate mass-loss rate reductions of factors of 3 to 6 over traditional diagnostics that suffer from density-squared effects. Broad-band X-ray spectral energy distributions also provide mass-loss rate information via soft X-ray absorption signatures. In some cases, the degree of wind absorption is so high that the hardening of the X-ray SED can be quite significant. We discuss these results as applied to the early O stars zeta Pup (O4 If), 9 Sgr (O4 V((f))), and HD 93129A (O2 If*).Comment: To appear in the proceedings of IAU 272: Active OB Star

Evidence for the importance of resonance scattering in X-ray emission line profiles of the O star ζ\zeta Puppis

We fit the Doppler profiles of the He-like triplet complexes of \ion{O}{7} and \ion{N}{6} in the X-ray spectrum of the O star $\zeta$ Puppis, using XMM-Newton RGS data collected over $\sim 400$ ks of exposure. We find that they cannot be well fit if the resonance and intercombination lines are constrained to have the same profile shape. However, a significantly better fit is achieved with a model incorporating the effects of resonance scattering, which causes the resonance line to become more symmetric than the intercombination line for a given characteristic continuum optical depth $\tau_*$. We discuss the plausibility of this hypothesis, as well as its significance for our understanding of Doppler profiles of X-ray emission lines in O stars.Comment: 29 pages, 8 figures, revised version accepted by Ap

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates

Modeling broadband X-ray absorption of massive star winds

We present a method for computing the net transmission of X-rays emitted by shock-heated plasma distributed throughout a partially optically thick stellar wind from a massive star. We find the transmission by an exact integration of the formal solution, assuming that the emitting plasma and absorbing plasma are mixed at a constant mass ratio above some minimum radius, below which there is assumed to be no emission. This model is more realistic than either the slab absorption associated with a corona at the base of the wind or the exospheric approximation that assumes that all observed X-rays are emitted without attenuation from above the radius of optical depth unity. Our model is implemented in XSPEC as a pre-calculated table that can be coupled to a user-defined table of the wavelength dependent wind opacity. We provide a default wind opacity model that is more representative of real wind opacities than the commonly used neutral interstellar medium (ISM) tabulation. Preliminary modeling of \textit{Chandra} grating data indicates that the X-ray hardness trend of OB stars with spectral subtype can largely be understood as a wind absorption effect.Comment: 9 pages, 9 figures. Includes minor corrections made in proof

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and Its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates

Wind signatures in the X-ray emission line profiles of the late O supergiant ζ\zeta Orionis

X-ray line profile analysis has proved to be the most direct diagnostic of the kinematics and spatial distribution of the very hot plasma around O stars. In this paper we apply several analysis techniques to the emission lines in the Chandra HETGS spectrum of the late-O supergiant zeta Ori (O9.7 Ib), including the fitting of a simple line-profile model. We show that there is distinct evidence for blue shifts and profile asymmetry, as well as broadening in the X-ray emission lines of zeta Ori. These are the observational hallmarks of a wind-shock X-ray source, and the results for zeta Ori are very similar to those for the earlier O star, zeta Pup, which we have previously shown to be well-fit by the same wind-shock line-profile model. The more subtle effects on the line-profile morphologies in zeta Ori, as compared to zeta Pup, are consistent with the somewhat lower density wind in this later O supergiant. In both stars, the wind optical depths required to explain the mildly asymmetric X-ray line profiles imply reductions in the effective opacity of nearly an order of magnitude, which may be explained by some combination of mass-loss rate reduction and large-scale clumping, with its associated porosity-based effects on radiation transfer. In the context of the recent reanalysis of the helium-like line intensity ratios in both zeta Ori and zeta Pup, and also in light of recent work questioning the published mass-loss rates in OB stars, these new results indicate that the X-ray emission from zeta Ori can be understood within the framework of the standard wind-shock scenario for hot stars.Comment: MNRAS, accepted; 16 pages, 5 figure